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About this book

This book provides a comprehensive reference for the studies of mechanical properties of materials over multiple length and time scales. The topics include nanomechanics, micromechanics, continuum mechanics, mechanical property measurements, and materials design. The handbook employs a consistent and systematic approach offering readers a user friendly reference ideal for frequent consultation. It is appropriate for an audience at of graduate students, faculties, researchers, and professionals in the fields of Materials Science, Mechanical Engineering, Civil Engineering, Engineering Mechanics, and Aerospace Engineering.

Table of Contents

Frontmatter

Nanomechanics

Frontmatter

1. Dislocation Nucleation Mediated Plasticity of FCC Nanowires

Nanowires have gained a significant attention as a key component applicable to various devices and advanced materials. Hence, it is essential to ensure the mechanical stability and reliability of nanowires for the realization of devices based on nanowires. In addition, nanowires provide a unique test bed for studying the fundamental mechanism associated with plastic deformations of materials. When the size of specimen reduces below a critical scale (sub-100 nm), the population of vacancies, dislocations, as well as the grain boundaries decreases significantly, which allows us to study a completely new deformation mechanism that cannot be observed in bulk scale. This chapter involves a brief review on the deformation mechanism of sub-100 nm crystalline nanowires with FCC (face-centered cubic) crystal structure, which is relatively well characterized via molecular dynamics and dislocation dynamics simulations as well as in-situ and ex-situ nanotension experiments.

Seunghwa Ryu, Jaemin Kim, Sangryun Lee

2. Indentation Behavior of Metallic Glass Via Molecular Dynamics Simulation

Metallic glasses, also known as glassy metals, exhibit unique mechanical properties in terms of their strength and ductility due to their noncrystalline microstructures. By performing molecular dynamics simulations, thin-film metallic glasses can be prepared by simulated sputter deposition processes. The deposition simulations were conducted with a tight-binding interatomic potential, and argon working gas was modeled by the pair-wise Moliere potential. The atomic structures of the glasses are verified by the radial distribution functions. After deposition simulation and suitable equilibration, the deposited amorphous films were simulated for their indentation properties by a right-angle conical indenter tip at selected temperatures. The hardness and Young’s modulus of the glasses show strong temperature dependence. The calculated pileup index of the films may be used to indicate the glass transition temperature.

Chun-Yi Wu, Yun-Che Wang

3. Surface/Interface Stress and Thin Film Stress

Thin film stress is critical for the reliability and electronic/optoelectronic properties of thin film devices. In this chapter, we systematically discussed the effects of surface and interface stresses on the film stress development during growth of polycrystalline films at the initial and final growth stage. We demonstrate that surface stress plays an important role at the initial stage of film growth (island growth stage), and conventional stress analysis technology such as wafer curveture experiments may not be applicable at this stage. At the late stage of film growth, we also show that adatom insertion into the grain boundaries is the primary mechanism of compressive stress development.

Chun-Wei Pao

4. Characterizing Mechanical Properties of Polymeric Material: A Bottom-Up Approach

Polymeric materials have received tremendous attention in both industrial and scientific communities, and can be readily found in applications across a large range of length scales, ranging from the nanoscale structures, such as the photoresist lithography in the micro-electro-mechanical systems, to the macroscale components, such as the adhesive bonding in the aerospace industry and civil infrastructures. The durability of these applications is mainly determined by the mechanical reliability of the constituent polymeric materials. In this chapter, a review of the bottom-up approach to investigate the mechanical properties of the polymeric materials is provided. A dynamic algorithm is developed to achieve the cross-linking process of the atomistic network, which possesses the mechanical properties in a good accordance with the experimental measurements. Meanwhile, the moisture effect on the mechanical properties is studied based on the atomistic model, and it is found that the mechanical properties of the solvated models show no significant deterioration. Furthermore, the predicted mechanical properties at the atomistic level are used to develop the cross-linked network at the mesoscale, which enables the investigation of the effect of the structural voids on the polymeric materials. The simulation results demonstrate the strong mechanical reliability of the synthetic polymeric materials during the long-term service life. The multiscale method summarized in this chapter provides a versatile tool to link the nano-level mechanical properties of the polymeric materials to the macro-level material behaviors.

Lik-ho Tam, Denvid Lau

5. Fracture Nanomechanics

This chapter reviews recent advances in experimental studies on fracture mechanics of small materials on nanometer scales. In particular, experimental systems and some testing methods developed by the current authors are introduced for investigating the fracture behavior of interface in nanoscale multilayered components and low-dimensional single crystalline materials, and main experimental results are presented as well. The experimental studies discussed are: (1) crack initiation from the free edge of interface and its mechanical criterion, (2) modulation of the location of crack initiation and the mode mixity for interface cracking with different types of cantilever specimens, (3) evaluation of the effect of microscopic structure on the interface cracking by an inverted-T-shaped cantilever method, (4) creep crack initiation at an interface edge in nanoscale components, (5) fatigue fracture behavior of interface and the environmental effect, (6) novel resonant vibration based high-cycle fatigue method and the fatigue properties of nano-metals, and (7) evaluation of deformation and fracture properties of nanoscale single crystalline materials. From the obtained results, authors pointed out the applicability of conventional fracture mechanics in nanoscale components. Meanwhile, the main challenges and difficulties in experimental studies on the fracture behavior of nanoscale materials are demonstrated, and several future research topics are outlined.

Yabin Yan, Takashi Sumigawa, Licheng Guo, Takayuki Kitamura

6. In Situ Transmission Electron Microscopy Investigation of Dislocation Interactions

This chapter provides a broad overview of dislocation interactions investigated via in situ transmission electron microscopy (TEM) deformation experiments. The discussion of these interactions is divided according to the interaction of interest, with the first section exploring the mechanics and energetics governing dislocation nucleation, propagation, and multiplication. The following two sections investigate dislocation interactions with isolated defects and defect fields, including interactions involving irradiation-induced defects, solute atoms, and second-phase particles. The final section discusses dislocation–grain boundary interactions with a focus on understanding how the local grain boundary structure and surrounding microstructure dictate the dislocation transfer process. Two unique advantages of TEM imaging for dislocation interactions will be highlighted throughout this chapter: the ability to capture dislocation interactions at sufficient spatial and temporal resolution to resolve complex interactions, and the ability to resolve salient features of the dislocation interactions using diffraction contrast imaging. This second advantage is used to characterize structural and geometrical factors influencing dislocation interactions, including the dislocation Burgers vector, line direction, and slip plane, crystallographic orientation, and boundary habitat planes.

Josh Kacher, Ben P. Eftink, Ian M. Robertson

7. Multiscale Modeling of Radiation Hardening

All materials used in nuclear reactors experience radiation hardening, thus altering significantly their mechanical behavior. Despite the large efforts made by the scientific community to correctly predict the radiation effects on nuclear materials, many difficulties persist in modeling radiation defects. Although radiation hardening is responsible for macroscopic consequences such as embrittlement, its fundamental mechanisms prevail at the atomic scale. The fast development of simulation techniques, especially atomistic simulations, helped in exploring many features of dislocation interactions with radiation-induced defects. For a long time, the obtained results were used to validate theoretical models and to qualitatively explain and rationalize experimental observations.More recently, with the ubiquity of simulation results and techniques at different scales, quantitative physically based predictions of the mechanical behavior became a realistic objective. Efforts were made to couple simulation results at different scales through the development of scale transition methods and the construction of constitutive equations of the local mechanical behavior. The objective of this chapter is to trace the evolution and progress of this strategy, thus enabling the construction of a chain of physical knowledge across the scales. Details of simulations techniques and methods are not presented. We emphasize on basic achievements of simulations and on the treatment of results with the aim to bridge the different scales of interest for the mechanical behavior.

Ghiath Monnet, Ludovic Vincent

8. Atomistic Simulations of Metal–Al2O3 Interfaces

Interfaces between metals and ceramics are of great importance for a wide range of industrial applications such as multifunctional devices, fuel cells, thermal barrier coatings, corrosion protection, and microelectronics. The technological interest arises from the possibility to obtain composite materials with much better characteristics than that of both constituents. In order to control the metal–ceramic interfaces it is necessary to understand them at different scale levels. The approaches used for this goal can be ranged from models at the macroscale to first principles calculations. Atomistic theoretical studies of varied metal–ceramic systems are based on ab initio calculations or molecular dynamics simulations which allow to understand the interactions at the interface at the atomic level. Using the plane wave pseudopotential method within density functional theory, the electronic and mechanical properties of Me–Al2O3 interfaces with fcc (Ni, Cu, Pd, Ag, Pt, Au) and bcc (Nb, Mo, Ta, W) metals are investigated to find correlations between the work of separation and crystal structure, strain conditions, and electronic properties of both constituents. Stress–displacement relationships of separation perpendicular to the interface are calculated in case of Al, Cu, Ag, and Nb on the Al-terminated Al2O3(0001) surface. It is shown that obtained results such as work of separation and tensile strength can be understood from the electronic structure. The influence of misfit dislocations on the fracture behavior of an Al–Al2O3 interface is demonstrated using classical molecular dynamics simulations. The comparison with experimental data provides good agreement for both the work of separation and qualitative prediction of mechanical reinforcement.

Stephen Hocker, Alexander Bakulin, Hansjörg Lipp, Siegfried Schmauder, Svetlana Kulkova

9. Multiscale Simulation of Precipitation in Copper-Alloyed Pipeline Steels and in Cu-Ni-Si Alloys

In crystalline solids, the formation of precipitates is caused by the clustering of individual solute atoms dissolved in the matrix. This can happen, if the formation of clusters is energetically favorable relative to the dissolved state of atoms randomly distributed within the matrix. The clustering is driven by the stochastic process of diffusion and depending on diffusion speed, solute concentration, and mixing energies, atom clusters will form and grow, shrink or reach an equilibrium state after a long time of diffusion. As the presence of precipitates can greatly alter the mechanical properties of materials, the simulation of this nanoscopic process starting from the alloy composition up to the final distribution of precipitate numbers and sizes is key for computational design of alloys with desired mechanical properties. For achieving this, the atomistic kinetic Monte Carlo (AKMC) simulation method is used to mimic the stochastical diffusion process. For later stages of precipitation involving bigger clusters, the continuum phase-field method (PFM) can be used to accelerate the simulation. In this chapter, we will present two successful examples for the simulation of precipitation: One coupled approach of AKMC and PFM that was used for predicting the precipitation in copper-alloyed iron and another example of AKMC in the multicomponent Cu-Ni-Si system.

Dennis Rapp, Seyedsaeid Sajadi, David Molnar, Peter Binkele, Ulrich Weber, Stephen Hocker, Alejandro Mora, Joerg Seeger, Siegfried Schmauder

10. Atomistic Simulations of Hydrogen Effects on Lattice Defects in Alpha Iron

Solute hydrogen atoms degrade the strength of materials. This phenomenon, termed as hydrogen embrittlement (HE), has been a matter of concern for various industrial applications for more than a century. In recent years, HE has to be addressed because of the need for more efficient storage and transport of hydrogen. In this chapter, we present an overview of the current state of knowledge of the interaction between hydrogen and lattice defects. In Sect. 2, the hydrogen trap energy of various trap sites in alpha iron is reviewed and summarized. In Sect. 3, first, the hydrogen concentration around the defects is outlined based on the evaluation of the occupancy at each trap site. Subsequently, the effect of hydrogen on the stability and the kinetics of the lattice defects that trap hydrogen atoms are reviewed. In Sect. 4, mesoscopic calculations of the complex interactions among hydrogen-affected lattice defects are reviewed. Finally, the current state of knowledge of hydrogen effects on lattice defects and future directions are discussed. Alpha iron is considered because it is a basic steel component, and steel is a potential material for hydrogen storage and transport systems from engineering and economic viewpoints.

Shinya Taketomi, Ryosuke Matsumoto

11. Molecular Dynamics Simulations of Nanopolycrystals

Nanopolycrystals are polycrystalline metals with an average grain size below 100 nm and exhibit extraordinary strength values. In contrast to the coarse-grained polycrystals, the confinement by grain boundaries of the plastic deformation in the grains approaches limits, where the conventional theories break down. In the grain size regime 10–20 nm, molecular dynamics simulations play a crucial role to elucidate the possible and surprising deformation mechanisms in nanocrystalline metals although the MD method uses assumptions, which ad hoc do not allow for a straightforward extrapolation to experimental conditions. This chapter presents the nanocrystalline-specific methods for MD simulations with their subtleties and summarizes the deformation mechanisms in nanopolycrystals with their signatures on the (experimental) deformation behavior. A comprehensive understanding on the interplay of the deformation mechanisms is suggested in this chapter, which is closed with a list of still-open issues in the field.

Christian Brandl

12. Modeling Dislocation in Binary Magnesium-Based Alloys Using Atomistic Method

In the wake of developing biodegradable metallic implants for orthopedic practice or lightweight structural components for the automotive industry, both fundamental and applied research on magnesium and its alloys regained a high interest in the last decade. As of today, the major issues delaying the integration of the magnesium technology in the medical and automotive industries are (i) a lack of ductility and (ii) a poor corrosion resistance. Alloying is a common strategy used to improve the ductility and the corrosion resistance. Although density functional theory is a powerful method that allows one to quantify material parameters to be used later in a theoretical model, atomistic methods in the framework of semi-empirical potentials are complementary to density functional theory. While the data obtained from semi-empirical potentials are more qualitative than quantitative, it does not prevent atomistic calculations in the framework of semi-empirical potentials to validate/disprove/enrich an existing theoretical model or even to provide insights for the development of a new theoretical model. The validity of the data derived from atomistic calculations in the framework of semi-empirical potentials depends on the accuracy and transferability of the potentials to capture the physics involved in the problem. In view of modeling the mechanical properties of a binary magnesium-based alloy using semi-empirical potentials, one has to validate the ability of the potentials to capture the physics governing the interactions between the alloying element and the micromechanisms carrying the inelastic behavior. In this chapter, we are reviewing the interaction between alloying elements and (i) stacking faults and (ii) <a> dislocations from the basal and prismatic slip systems.

Sébastien Groh, Mohammad K. Nahhas

13. Atomistic Simulation Techniques to Model Hydrogen Segregation and Hydrogen Embrittlement in Metallic Materials

Hydrogen embrittlement is an important phenomenon where the mechanical properties of a metallic material are degraded in the presence of hydrogen, sometimes leading to a change in the failure mode of the metallic material. Although mechanical failures due to hydrogen embrittlement have been observed for over a century, the atomic-level mechanisms associated with the hydrogen embrittlement process are still under debate. In this chapter, atomistic simulation efforts focused on hydrogen segregation and hydrogen embrittlement are reviewed. Atomistic simulation methods provide a nanoscale modeling technique capable of studying the role of hydrogen atoms on dislocation nucleation, crack propagation, and grain boundary decohesion. Examples are provided in this chapter of the use of a site-energy selection method to study hydrogen segregation and molecular dynamics simulations to study hydrogen-induced grain boundary decohesion in nickel. Grain boundary strength and work of separation in the presence of segregated hydrogen are computed from the molecular dynamics simulations. Subsequently, this data may be used in higher length scale models and simulations of the hydrogen embrittlement process.

Douglas E. Spearot, Rémi Dingreville, Christopher J. O’Brien

14. Modeling and Simulation of Bio-inspired Nanoarmors

The exploitation of bio-inspired solutions and of novel nanomaterials is gaining increasing attention in the field of impact protection. Indeed, especially for advanced applications, there is a growing pressure towards the reduction of the weight of protective structures without compromising their energy absorption capability. The complexity of the phenomena induced by high-energy contacts requires advanced and efficient computational models, which are also fundamental for achieving the optimum, overcoming the limits of experimental tests and physical prototyping in exploring the whole design space. At the same time, the modeling of bio-inspired toughening mechanisms requires additional capability of these methods to efficiently cover and merge different -and even disparate- size and time scales. In this chapter, we review computational methods for modeling the mechanical behavior of materials and structures under high-velocity (e.g., ballistic) impacts and crushing, with a particular focus on the nonlinear finite element method. Some recent developments in numerical simulation of impact are presented underlining merits, limits, and open problems in the modeling of bio-inspired and nanomaterial-based armors. In the end, two modeling examples, a bio-inspired ceramic-composite armor with ballistic protection capabilities and a modified honeycomb structure for energy absorption, are proposed.

Stefano Signetti, Nicola M. Pugno

15. Thermal Vibration of Carbon Nanostructures

The chapter presents the study on thermal vibration of nanostructures, such as carbon nanotube (CNT) and graphene, as well as the basic finding for the relation between the temperature and the root-of-mean-square (RMS) amplitude Root-of-Mean-Squared (RMS) amplitude of the thermal vibration of the carbon nanostructures. In this study, the molecular dynamics (MD)Molecular dynamics (MD) based on modified Langevin dynamicsLangevin dynamics, which accounts for quantum statistics by introducing a quantum heat bath, is used to simulate the thermal vibration of carbon nanostructures. The simulations show that the Root-of-Mean-Squared (RMS) amplitude RMS amplitude of the thermal vibration of the carbon nanostructures obtained from the semi-quantum MD is lower than that obtained from the classical MD, especially for very low temperature and high-order vibration modes. The RMS amplitudes of the thermal vibrations of the single-walled CNT (SWCNT)Single-walled CNT (SWCNT) and graphene obtained from the semi-quantum MD coincide well with those from the models of Timoshenko beam and Kirchhoff plate with quantum effects. These results indicate that quantum effects are important for the thermal vibration of the SWCNT and graphene in the case of high-order vibration modes, small size, and low temperature. Furthermore, the thermal vibration of a simply supported SWCNT subject to thermal stress is investigated by using the models of planar and non-planar nonlinear beams, respectively. The whirling motion with energy transfer between flexural motions is found in the SWCNT when the geometric nonlinearity is significant. The energies of different vibration modes are not equal even over a time scale of tens of nanoseconds, which is much larger than the period of fundamental natural vibration of the SWCNT at equilibrium state. The energies of different modes become equal when the time scale increases to the range of microseconds.

Lifeng Wang, Haiyan Hu, Rumeng Liu

16. Mechanics of Carbon Nanotubes and Their Composites

Carbon nanotubes (CNTs) display superior mechanical properties and have been used as reinforcements in polymer matrix composites. The first part of this chapter reviewed the finite-deformation shell theory, established directly from the atomic structure of CNT and the interatomic potential, for single-wall carbon nanotubes. This atomistic-based finite-deformation shell theory has been used to study the rigidity and instability of single-wall CNTs subject to tension, compression, internal and external pressure, and torsion. The second part of this chapter reviewed the cohesive law for interfaces between carbon nanotubes and polymers due to the van der Waals force. A micromechanics model for carbon nanotubes-reinforced composite with the incorporation of the nonlinear cohesive law has been established to investigate the mechanical behavior of nanocomposites.

Jian Wu, Chenxi Zhang, Jizhou Song, Keh-Chih Hwang

17. Flexoelectric Effect at the Nanoscale

Flexoelectric effect is a universal electromechanical coupling effect in solids. Nevertheless, it has been ignored for a long time, due to the usual small strain gradients in materials. The case is different for nanomaterials, where strain gradients can usually reach to the order of 106 m−1. Moreover, as the flexoelectric effect scales with dielectric susceptibility, it can be much more apparent in materials with higher dielectric constants, such as ferroelectrics. Due to this reason, increasing attention has been attracted on the flexoelectric effect in nanomaterials (with ferroelectrics as the representatives) during the past few years. The large flexoelectric effect in nanomaterials not only makes them promising candidates to design novel electromechanical nanodevices but also strongly modifies many material properties such as polarization switching, ferroelectric domains and domain walls, polarization-mediated electronic transport effects, etc. Focusing on flexoelectric effect at the nanoscale and with ferroelectrics as the representatives, this chapter aims to provide an overview of this rapidly growing field, including the theoretical models and experimental characterization methods of flexoelectric effect, the recent important progress of flexoelectric effect, as well as the potential applications.

Lele L. Ma, Weijin J. Chen, Yue Zheng

18. Mechanical Properties of Nanostructured Metals: Molecular Dynamics Studies

This chapter overviews our recent work on MD simulations of the mechanical properties of nanostructured metals with an emphasis on revealing the controlling deformation mechanisms, interpreting the experimental data, and guiding further research in structural optimization and processing.

Haofei Zhou, Shaoxing Qu

19. Processes in Nano-Length-Scale Copper Crystal Under Dynamic Loads: A Molecular Dynamics Study

This chapter is devoted to the research of rotary field formation in a nano-length-scale metal crystal under acting of different kinds of mechanical loads by molecular dynamics method. It was considered two sorts of loads: compressive dynamic load and stretching at a constant deformation velocity. The simulation technique of such vortex structures in solid was developed. It is shown that there exists a critical energy flux at which the system experiences an avalanche change both in the time and load dependence of energy absorption and in the type of wave processes in its structure. It was revealed that this process is a type of nanostructure self-organization in response to an external energy flux with subsequent development of a strong rotational field. The critical role of a rotary wave in the process of material fracture was defined, as the rotary wave energy exceeds 30% of the total internal energy of the structure at the strain rate greater than 200 m/s. The interpretation of vortex structure formation and spread in solids is proposed from the point of view of structure self-organization. The authors studied the structure size influence on rotary field formation, and it was revealed their appearance is not a result of nanoscale smallness of the sample. At the same time, the influence of a nanostructure’s cross size on the rotary field energy is being researched.

I. F. Golovnev, E. I. Golovneva

20. Understanding Fracture and Fatigue at the Chemical Bond Scale: Potential of Raman Spectroscopy

Coupled mechanical and Raman analysis of a material under tension or compression provides much information on the material’s (nano)structure. Raman extensometry can be applied to synthetic and natural polymer fibers (e.g., polyamides [polyamide 66], polyethyleneterephthalate, polypropylene, poly[paraphenylene benzobisoxazole], keratin/hair, and silkworm and spider silks). The technique allows differentiation between crystalline and amorphous macromolecules. Bonding is similar in the two cases, but each exhibits different Raman signatures, especially at low wavenumbers, and a broader distribution of conformations is observed for amorphous macromolecules. These conclusions are used to discuss modifications induced by the application of a tensile or compressive stress up to the point of fracture – in particular the effects of fatigue.

Philippe Colomban

21. Atomistic Modeling of Radiation Damage in Metallic Alloys

The primary damage in metallic alloys, i.e., the point defect distribution resulting from the interaction between an energetic particle and a metallic matrix has been investigated for more than 60 years using atomistic simulations. In this chapter, we present an overview of the techniques used as well as the results achieved so far to conclude on the open questions and future directions.

Charlotte S. Becquart, Andrée De Backer, Christophe Domain

22. Monte Carlo Simulations of Precipitation Under Irradiation

Atomistic kinetic Monte Carlo (AKMC) is a powerful technique to study the microstructural and microchemical evolution of alloys controlled by diffusion processes. AKMC simulations are thus ideal tools to study precipitation, under irradiation and during thermal aging. In this chapter, we briefly present the method, underlining the different hypotheses usually made in the studies which have been done so far and the increasing contribution of density functional theory (DFT) calculations. We then proceed to present several simulations of the first stages of precipitation that can be quantitatively compared with experimental studies, in order to show the complexity introduced by the irradiation. We move to the mesoscale and introduce event kinetic Monte Carlo (EKMC) and object kinetic Monte Carlo (OKMC) methods which until now have mostly dealt with point defect cluster distributions in pure metals or “gray alloys” and were thus not really appropriate to study precipitation. However, they can be coupled with AKMC to speed up the calculations and recent developments take into account solute atoms more explicitly. We expose then recent advances that relieve some of the simplifying assumptions of standard AKMC models and conclude with a few challenging issues that we feel need to be addressed to predict correctly the behavior of alloys under irradiation but have been barely introduced in the models.

Charlotte S. Becquart, Frédéric Soisson

23. Mechanics of Auxetic Materials

Poisson’s ratio is a mechanical property that represents the lateral behavior of materials under an axial load. In contrast to typical natural materials with a positive Poisson’s ratio, auxetic materials have a negative Poisson’s ratio (NPR) characterized by unilateral shrinkage or expansion against axial compressive or tensile loadings, respectively. Here, based on a comparison between conventional and auxetic materials, a review of auxetic materials that exhibit various types of deformation mechanisms and characteristics induced by a negative Poisson’s ratio is provided. First, the deformation mechanisms in auxetic materials resulting in lateral expansion under tensile loads are described. They are classified according to their deformation mechanism or the structural motif enabling the auxetic behavior including re-entrant structures, rotating unit structures, chiral structures, fibril/nodule structures, buckling-induced structures, helical yarn structures, Miura-folded structures, and crumpled structures. Then, the expected properties of auxetic materials in several aspects are discussed. The mechanical response of these materials can be drastically changed depending on the amount of applied loads, and auxetic materials are expected to have unusual, possibly enhanced geometrical and mechanical characteristics such as synclastic curvature in bending, deformation-dependent permeability, high shear stiffness, indentation resistance, and fracture toughness, and improved damping and sound absorption properties. Finally, some representative potential applications of auxetic materials are illustrated with a short discussion on the limitations and outlook of auxetic materials.

Hyeonho Cho, Dongsik Seo, Do-Nyun Kim

24. Nanoindentation and Indentation Size Effects: Continuum Model and Atomistic Simulation

Nanoindentation is one of the most widely used methods to measure the mechanical properties of materials at the nanoscale. For spherical indenters, when radius decreases, the hardness increases. The phenomenon is known as the indentation size effect (ISE). Nix and Gao developed a continuum model to explain the ISE in microindentation. However, the model overestimates the hardness at the nanoscale. The objective of this study is to develop proper methods to probe key quantities such as hardness and geometric necessary dislocation (GND) density from the quasi-static version of molecular dynamics (MD) simulations and to develop a mechanism-based model to elucidate the ISE phenomenon at the nanoscale. A reliable method is presented to extract the GND directly from dislocation length and the volume of plastic zone in the MD simulations. We conclude that the hardness determined directly from MD simulations matches well with the hardness determined from the Oliver–Pharr method. The ISE can be observed directly from the MD simulations without any free parameters. The model by Swadener et al. rooted from the Nix and Gao model underestimates the GND density at the nanoscale. However, this model can accurately predict the hardness size effects in nanoindentation if it uses the GND density directly calculated from the MD simulations.

Chi-Hua Yu, Kuan-Po Lin, Chuin-Shan Chen

25. Continuum Theory for Deformable Interfaces/Surfaces with Multi-field Coupling

Continuum mechanics is a well-demonstrated powerful tool for dealing with comprehensive physical problems of macroscopic bodies involving deformation and flow processes. It has also been successfully and extensively applied to deformable bodies at micro- and nano-scales without or with appropriate modifications. One particular and interesting phenomenon of small-sized subjects is that they usually exhibit size-dependent characteristics, which cannot be well explained within the conventional framework of continuum mechanics. A modified version that accounts for the so-called surface elasticity has been developed. The rigorous derivation of surface elasticity is due to Gurtin and Murdoch as early in 1975 by creating a two-dimensional set of elasticity. This chapter aims to introduce a relatively traditional method to derive the interface/surface elasticity, which further incorporates the coupling among multiple physical fields (e.g., elastic, electric, and magnetic). The method is illustrated here by only considering the electroelastic coupling, but there is completely no difficulty to make a further step toward the situation where more fields are involved. The method first assumes a finite thickness of the interface/surface so that an interphase layer model is actually adopted, which is governed by the traditional three-dimensional theory of piezoelectricity. Then, the state-space formalism is derived, based on which a transfer relation between the state vectors at the upper and lower surfaces of the interphase layer can be easily obtained. By series expansion and truncation, various theories of interface/surface piezoelectricity of different orders can then be established. Comparison is made with those reported in the literature, which shows good agreement and hence validates the present approach.

B. Wu, W. Q. Chen

Micromechanics

Frontmatter

26. Interaction Between Stress and Diffusion in Lithium-Ion Batteries: Analysis of Diffusion-Induced Buckling of Nanowires

This chapter summarizes the frameworks of the diffusion-induced stress both in the theory of linear elasticity and the theory of nonlinear elasticity, which provide the theoretical principles to investigate the coupling between stress and diffusion in analyzing the elastic deformation of materials induced by the migration/diffusion of solute atoms. The buckling behavior of an elastic core-shell nanowire induced by the migration/diffusion of lithium during lithiation is analyzed by using the theory of linear elasticity and diffusion equation. Closed-form solution is obtained for the calculation of the critical time for the onset of buckling of the nanowire. The effects of current density, length, and the radius ratio on the critical concentration and critical time for the occurrence of the buckling are studied. For an elastic-perfectly plastic core-shell nanowire, numerical analysis of the lithiation-induced buckling of the core-shell nanowire is performed, using the commercial finite element software ABAQUS. The effects of the radius ratio and yield stress of the outer shell on the critical average concentration and critical time for the occurrence of the buckling are investigated.

F. Q. Yang, Yan Li, B. L. Zheng, K. Zhang

27. Dynamic Compressive Mechanical Behavior of Magnesium-Based Materials: Magnesium Single Crystal, Polycrystalline Magnesium, and Magnesium Alloy

This book chapter focuses on compressive mechanical behavior of magnesium-based materials under dynamic loadings, especially high strain rate loadings. The content is organized into five sections: Section 1 provides an introduction of related literature results, Section 2 presents an overview of the split Hopkinson pressure bar technique for high strain rate tests and its fundamental data processing method, Section 3 delineates some widely used constitutive models for predicting mechanical responses of materials under high strain rate loadings, Section 4 reports the experimental results, theoretical modeling, and computational simulations of compressive dynamic mechanical behavior of magnesium-based materials under different high strain rate loadings, and Section 5 presents the conclusions. In Section 4, three types of magnesium-based materials (i.e., magnesium single crystal, polycrystalline magnesium, and AZ31 magnesium alloy) were tested at both quasistatic and dynamic loading strain rates to investigate their compressive mechanical behavior. The employed strain rates are in the range of 0.001~3600 s−1. Theoretical stress-strain relations based on the empirical Johnson-Cook model were also derived for each type of the studied materials. The theoretically predicted stress-strain curves agree well with the experimental curves for these three types of materials. Finite element modeling was also performed to investigate the dynamic compressive behavior of the three types of the studied materials. The computational stress-strain curves match the experimental data for magnesium single crystal and polycrystalline magnesium, while a simulation was conducted to predict the compressive properties of AZ31 magnesium alloy at a randomly chosen strain rate.

Qizhen Li

28. Micropillar Mechanics of Sn-Based Intermetallic Compounds

The semiconductor industry is exploring a new scheme called “More-than-Moore” to overcome the high cost and difficulty of smaller node fabrications when facing the end of Moore’s law. For this purpose, the three-dimensional integrated circuit (3D IC) architecture is favored by most major semiconductor companies. The stacking of chips in 3D IC architecture with design of microbumps and through silicon vias (TSVs) allows integration of heterogeneous function within a single chip for enhancing performance with small form factor by increasing I/O density, shortening interconnect distance. Due to this reduction in solder volume, it is anticipated that Sn-based solder in microbumps will be totally converted into intermetallics (IMCs) during the assembly or the operation of further process. Sn-based IMCs therefore dominate the properties of microbump and become potential candidates of structural materials. The mechanical behaviors of IMCs and the preferred types of IMC become questions of importance. This chapter focuses on the micromechanical behaviors of single-crystalline Cu6Sn5 and Ni3Sn4 by micropillar compression.The failure mode of single-crystalline Cu6Sn5 and Ni3Sn4 are cleavage, but they both performed strain bursts as a result of dislocation gliding with certain slip system before failure. They are not as brittle as people thought and have adequate mechanical properties. For Cu6Sn5, grains with the c-axis aligned with the load direction have better mechanical properties. The compound Ni3Sn4 can withstand more than 4% strain along the slip system, (100)[010]. Compared to Cu6Sn5, Ni3Sn4 has better mechanical performance as well as toughness and should be more favorable to be adopted as structure materials of 3D IC microbumps.

J. J. Yu, J. Y. Wu, L. J. Yu, C. R. Kao

29. Micro-mechanics in Electrochemical Systems

A framework is presented that treats the combined effects of nonlinear elastic deformation, lattice constraints, and electrochemical potentials. The electro-chemo-mechanical diffusion potential is derived, and the particular case where ionic species are subject to a crystal lattice constraint is also derived. By combining energy balance and local entropy production, the framework provides a consistent method to treat the evolution of charged species which also carry anelastic deformations in a crystal lattice. The framework is used to derive a finite element formulation that applies to general cases of interest for diffusion of active species in battery electrodes and in fuel cells. We demonstrate the application of the finite element formulation first with two cases: ambipolar diffusion and kinetic demixing. The predicted system response demonstrates how mechanical effects cannot be disregarded, even in the presence of dominant electrostatic forces acting on ion transport. A cation-rich surface layer is predicted when elastic forces, due to Vegard’s stress, participate in the migration of defects in multicomponent oxides. Simulations show how stress plays a central role in the cation segregation to interfaces, a phenomenon regarded as critical to power and durability of solid oxide fuel cells. Then, we analyze the interplay between electro-chemo-mechanics and fracture in battery electrodes. The presence of fracture in the electrode particles perturbs the stress field and results in stress concentration around the crack tips, which locally affects lithium concentration. This may prevent full lithiation and promote further fracture propagation. Finally, we simulate mechanical degradation of all-solid-state batteries via fracture within the solid electrolyte material. Such cracks would block Li diffusion and reduce the composite electrode’s effective ionic conductivity.

Giovanna Bucci, W. Craig Carter

30. Fiber Reinforced Ceramic Matrix Composites: A Probabilistic Micromechanics-Based Approach

Being damage tolerant, the CMCs exhibit nonlinear deformations as a result of cracks that form in the matrix, in the interfaces, and in the fibers. The sequence of cracking modes displays several features that depend on the arrangement of fibers, the microstructure, and the respective properties of constituents. Being ceramic materials, the constituents are highly sensitive to inherent microstructural flaws generated during processing. The flaw populations govern matrix cracking and fiber failures, so that strengths of constituents exhibit statistical distributions. A bottom-up multiscale approach based on micromechanics must account for the contribution of inherent fracture-inducing flaws, variability of constituent strengths, and associated size effects.The chapter deals with modeling of the stochastic processes of multiple fracture of the matrix and the fibers that govern damage and failure on fiber-reinforced ceramic matrix composites. The models are based on probabilistic approaches to brittle fracture, including the Weibull phenomenological model and the physics-based elemental strength model that considers the flaws as physical entities. The probabilistic models that are discussed permit determination of stresses at crack initiation from microstructural flaws and resulting crack pattern. Applications to the prediction of tensile behavior of unidirectional or woven composites are then discussed.

Jacques Lamon

31. Micromechanics of Polymeric Materials in Aggressive Environments

The advantages of polymeric materials have led to substantial interests in a variety of engineering applications, such as high-speed aircrafts, ultra-deepwater operations, and biomedical devices. Polymeric materials used in these systems must be capable of withstanding aggressive environments and still maintain their long-term load-bearing capability. With the development of novel polymer blends and composites to meet physical, chemical, thermal, and mechanical requirements, constitutive relations, deformation and toughening mechanisms, and damage and fracture characteristics of these multiphase polymeric materials have drawn significant attention. Multidisciplinary principles are required for studying the behavior of polymeric materials subjected to combined thermomechanical loading and physicochemically active environment exposure. The major challenge lies in the coupling of physical, chemical, thermal, and mechanical effects at multiple scales. It is necessary to establish generally applicable material models for implementation in robust design analysis tools. In this chapter, an overview on development of coupled multidisciplinary approach and advancement in computational micromechanics for polymeric materials in aggressive environments is provided with discussion on key methods, future directions, and open issues.

Xiaohong Chen

32. Crack Paths in Graded and Layered Structures

This chapter reviews the prediction of crack paths in materials with graded, and/or layered, composition, microstructure, and/or properties. The relevant applications span a wide variety of technologies where structural integrity is important and includes composites, layered materials, coatings, and joints. For most cases, the prediction of failure requires a priori knowledge of the crack path. In many cases, the crack path may be sufficiently defined by considering just crack kinking, that is, a small or infinitesimal increment of crack deviation from its plane. For other cases, the full crack path needs to be determined, something usually done with remeshing techniques in numerical simulation. In linear elastic systems, the residual stress that arises from the coefficient of thermal expansion mismatch between constituents generally dominates the behavior, but not if the elastic mismatch is very large or if there are big toughness mismatches. For linear elastic systems where plasticity occurs, but small-scale yielding still applies, the crack is usually drawn toward the softer material which also is generally tougher. For all cases, if the crack stress fields from all the sources are accurately defined, and materials properties known, it is possible to predict the crack path.

Ivar Reimanis

33. Micromechanics Modeling of Creep Fracture of High-Temperature Ceramics

Ultrahigh-temperature ceramics has great potential for applications as refractory materials at high temperatures. ZrB2-SiC has been considered as an excellent candidate of the ultrahigh-temperature ceramics due to its relatively low density and excellent refractory properties. However, the creep fracture of ZrB2-SiC limits its potential applications. Mitigation of the creep fracture is thus imperative. It has been concluded from several experiments that the creep resistance of ZrB2-SiC decreases with the increasing temperature, and there also exists a transition of creep mechanism for temperature above 1500 °C.The effects of grain boundary heterogeneity on the creep resistance were studied. The creep resistance of an isotropic and homogeneous ZrB2 polycrystalline material is affected by the applied strain rate and the grain boundary properties. Grain boundary heterogeneity would initiate the microcrack and thus lead to fracture. An isotropic grain interior modeled by user-defined material properties (UMAT) subroutine along with the grain boundary simulated by a rate-dependent cohesive zone modeling using user-defined element (UEL) subroutine was constructed to study the creep fracture of ZrB2-20% SiC composites. The model is accounted for nucleation, growth, and coalescence of cavities along the grain boundaries in a localized and inhomogeneous manner, link up of microcracks to form macrocracks, and grain boundary sliding. For ZrB2-20% SiC composites, a micromechanism shift form diffusional creep-control for temperatures below 1500 °C to grain boundary sliding-control for temperatures above 1500 °C was concluded from simulations. Also, the simulation results revealed the accommodation of grain rotation and grain boundary sliding by grain boundary cavitation for creep at temperatures above 1500 °C which was in agreement with experimental observations.

Chi-Hua Yu, Chang-Wei Huang, Chuin-Shan Chen, Chun-Hway Hsueh

34. Modeling of Multilayered Disc Subjected to Biaxial Flexure Tests

Although standard test methods for biaxial strength measurements of ceramics have been established and the corresponding formulas for relating the biaxial strength to the fracture load have been approved by the American Society for Testing and Materials (ASTM) and International Organization for Standardization, respectively, they are limited to the case of monolayered discs. Despite the increasing applications of multilayered ceramics, characterization of their strengths using biaxial flexure tests has been difficult because the analytical description of the relation between the strength and the fracture load for multilayers subjected to biaxial flexure tests is unavailable until recently. Using ring-on-ring tests as an example, the closed-form solutions for stresses in (i) monolayered discs based on ASTM formulas, (ii) bilayered discs based on Roark’s formulas, (iii) multilayered discs based on Hsueh et al.’s rigorous formulas, and (iv) multilayered discs based on Hsueh et al.’s simplified formulas are reviewed in this chapter. Finite element results for ring-on-ring tests performed on (i) zirconia monolayered discs, (ii) dental crown materials of porcelain/zirconia bilayered discs, and (iii) solid oxide fuel cell trilayered discs are also presented to validate the closed-form solutions. Finally, a case study of layer thickness effects in bilayered dental ceramics subjected to both thermal stresses and ring-on-ring tests is presented.

Chun-Hway Hsueh

35. Micromechanics of Dual-Phase Steels: Deformation, Damage, and Fatigue

Ferritic–martensitic dual-phase (DP) steels are increasingly being used in various automotive components because of their favorable material behavior for lightweight and crash-safe designs. DP steels deform with strong strain and stress partitioning at the microscale. Deformation pattern of ferrite and martensite phases under tensile loading condition is the most important issue which can be effective on the prediction of mechanical behavior of DP steel. Deformation pattern and strain localization play an important role in the process of damage initiation and final fracture. Failure in DP steels is a phenomenon that has been extensively investigated in the last decade through experimental tests and simulation methods. Experimental procedures have shown that failure has a ductile pattern and that shear failure of ferrite matrix is dominant in these materials. On the other hand, experimental findings have shown that failure due to fatigue loading occurred with different pattern comparing to the other loading conditions. To understand and improve DP steels, it is important to identify connections between the microstructural parameters and the mechanical behavior of these materials at macroscale. This work provides a detailed micromechanical investigation of DP steels focusing on micro-deformation, micro-damage, and micro-fatigue analysis of DP steels based on experimental and numerical approaches to highlight the current and future directions and open problems about these materials.

Behnam Anbarlooie, Javad Kadkhodapour, Hossein Hosseini Toudeshky, Siegfried Schmauder

36. Defect Accumulation in Nanoporous Wear-Resistant Coatings Under Collective Recrystallization: Simulation by Hybrid Cellular Automaton Method

A modification of a multiscale hybrid discrete-continual approach of excitable cellular automata is developed. The new version of the method is accomplished by considering the porosity and nanocrystalline structure of a material and the algorithms of calculation of local force moments and angular velocities of microscale rotations. The excitable cellular automata method was used to carry out numerical experiment (NE) for heating of continuous and nanoporous specimens with nanocrystalline TiAlC coatings. The numerical experiments have shown that nanoporosity allows to substantially reduce the rate of collective crystallization. In so doing the nanoporosity slowed down propagation of the heat front in the specimens. This fact can play both positive and negative roles at deposition of the coatings and their further use. On the one hand, by slowing the heat front propagation, one can significantly reduce the level of thermal stresses in deeper layers of the material. On the other hand, such deceleration in case of the high value of the thermal expansion coefficient can give rise to the formation of large gradients of thermal stress, which initiate nucleation and rapid growth of a main crack.

Dmitry D. Moiseenko, Pavel V. Maksimov, Sergey V. Panin, Dmitriy S. Babich, Victor E. Panin

37. Multiscale Fatigue Crack Growth Modeling for Welded Stiffened Panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics (MD) simulations as well as a Tanaka-Mura approach for the analysis of the problem. Mode I stress intensity factors (SIFs), KI, were calculated by the finite element method (FEM) using shell elements and the crack tip displacement extrapolation technique. The total SIF value, Ktot, is derived by a part due to the applied load, Kappl, and by a part due to welding residual stresses, Kres. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.

Ž. Božić, Siegfried Schmauder, M. Mlikota, M. Hummel

38. Dislocation Density-Based Modeling of Crystal Plasticity Finite Element Analysis

Dislocations play a major role in plastic deformation and fracture of metallic materials. A number of metallographic aspects such as grain boundaries, precipitates, and others contribute to the dislocations’ behavior, and therefore, we have to consider their effects too when we intend to understand the mechanical behavior of metals with microstructure. Finite element method is a powerful tool to express the shape and arrangement of metal microstructures and analyze the deformation under a prescribed boundary and loading conditions. We tried to develop models for the movement, interaction, and accumulation of dislocations during plastic slip deformation in metal microstructure and implemented them to the framework of finite element method. Models originate from physics of discrete dislocations and are brought to dislocation density-based numerical models. In this chapter, the physical pictures and expressions of dislocation density-based models are shown. Some examples of analyses are also shown.

Tetsuya Ohashi

39. Competing Grain Boundary and Interior Deformation Mechanisms with Varying Sizes

In typical coarse-grained alloys, the dominant plastic deformations are dislocation gliding or climbing, and material strengths can be tuned by dislocation interactions with grain boundaries, precipitates, solid solutions, and other defects. With the reduction of grain size, the increase of material strengths follows the classic Hall-Petch relationship up to nano-grained materials. Even at room temperatures, nano-grained materials exhibit strength softening, or called the inverse Hall-Petch effect, as grain boundary processes take over as the dominant deformation mechanisms. On the other hand, at elevated temperatures, grain boundary processes compete with grain interior deformation mechanisms over a wide range of the applied stress and grain sizes. This book chapter reviews and compares the rate equation model and the microstructure-based finite element simulations. The latter explicitly accounts for the grain boundary sliding, grain boundary diffusion and migration, as well as the grain interior dislocation creep. Therefore the explicit finite element method has clear advantages in problems where microstructural heterogeneities play a critical role, such as in the gradient microstructure in shot peening or weldment. Furthermore, combined with the Hall-Petch effect and its breakdown, the above competing processes help construct deformation mechanism maps by extending from the classic Frost-Ashby type to the ones with the dependence of grain size.

Wei Zhang, Yanfei Gao, Tai-Gang Nieh

40. Multiscale Translation-Rotation Plastic Flow in Polycrystals

The problem of plastic shear propagation in conditions of high crystal lattice curvature has been researched theoretically and experimentally on the basis of the gauge theory. It has been shown that in conditions of high crystal lattice curvature, the flows of deformation defects reveal plastic distortion, vorticity of plastic shears, and the possibility of their non-crystallographic propagation by a shear banding. Experimental research on the mechanical behavior of the commercially pure Ti samples under alternating bending demonstrated the strong influence of their structural state on the development of high crystal lattice curvature and shear banding. The high crystal lattice curvature under a cyclic loading appears in the hydrogenated surface layers, where shear banding and microporosity develop and fatigue life is greatly reduced. High crystal lattice curvature in surface layer of Ti samples produced by ultrasonic processing determines the fourfold increase of Ti fatigue life. The translation-rotation deformation against developed grain boundary sliding in high-purity A999 Al polycrystals under creep and in A999 Al foils glued on commercial A7 Al plates under alternate bending was studied. The stage of steady-state creep provides intragranular sliding in the material mainly by dislocation mechanisms. The stage of tertiary creep causes multiscale fragmentation, non-crystallographic sliding, and fracture. Under alternate bending, the Al foils are involved in rotations by dislocation mechanisms only up to a strain of ~50%, and as they become highly corrugated, shear bands propagate in them. The observed shear banding provides the generation of elastoplastic rotations in zones of high lattice curvature.

Victor E. Panin, Valerii E. Egorushkin, Tamara F. Elsukova, Natalya S. Surikova, Yurii I. Pochivalov, Alexey V. Panin

41. Micromechanics of Hierarchical Materials: Modeling and Perspectives

Hierarchical materials represent a new, promising direction of the materials development, inspired by biological materials and allowing the creation of multiscale materials design and multiple functionalities and achieving extraordinary material properties. In this article, a short overview of possible applications and perspectives on hierarchical materials is given. Several examples of the modeling of strength and damage in hierarchical materials are summarized. The main areas of research in micromechanics of hierarchical materials are identified, among them, the investigations of the effects of load redistribution between reinforcing elements at different scale levels, possibilities to control different material properties and to ensure synergy of strengthening effects at different scale levels and using the nanoreinforcement effects.

Leon Mishnaevsky

42. Modelling the Behavior of Complex Media by Jointly Using Discrete and Continuum Approaches

Usually, computer simulation of the behavior of materials and complex media is based on the continuum approach, which uses highly developed mathematical apparatus of continuous functions. The capabilities of this approach are extremely wide, and the results obtained are well known. However, for of a number of very important processes, such as severe plastic deformation, mass mixing, damages initiation and development, material fragmentation, and so on, continuum methods of solid mechanics face certain hard difficulties. As a result, a great interest for the approach based on a discrete description of materials and media has been growing up in recent years. Because both continuum and discrete approaches have their own advantages and disadvantages and a great number of engineering software has been created based on continuum mechanics, the main line of discrete approach development seems to be not a substitute but a supplement to continuum methods in solving complex specific problems based on a joint using of the continuum and discrete approaches.This chapter shows an example of joining discrete element method and grid method in an effort to model mechanical behavior of complex fluid-saturated poroelastic medium. The presented model adequately accounts for the deformation, fracture, and multiscale internal structure of a porous solid skeleton. The multiscale porous structure is taken into account implicitly by assigning the porosity and permeability values for the enclosing skeleton, which determine the rate of filtration of a fluid. Macroscopic pores and voids are taken into account explicitly by specifying the computational domain geometry. The relationship between the stress-strain state of the solid skeleton and pore fluid pressure is described in the approximations of a simply deformable discrete element and Biot’s model of poroelasticity. The capabilities of the presented approach were demonstrated in the case study of the shear loading of fluid-saturated samples of brittle material. Based on simulation results, a generalized logistic dependence of uniaxial compressive strength on loading rate, mechanical properties of the fluid, and enclosing skeleton and on sample dimensions was constructed. The logistic form of the generalized dependence of the strength of fluid-saturated elastic-brittle porous materials is due to the competition of two interrelated processes, such as pore fluid pressure increase under solid skeleton compression and fluid outflow from the enclosing skeleton to the environment. Another application of the presented approach is the study of the shear strength of a water-filled sample under constrained conditions. An elastic-plastic interface was situated between purely elastic permeable blocks that were loaded in the lateral direction with a constant velocity; periodic boundary conditions were applied in the lateral direction. In order to create an initial hydrostatic compression in a volume, a pre-loading was performed before shearing. The results of simulation show that shear strength of an elastic-plastic interface depends nonlinearly on the values of permeability and loading parameters. An analytical relation that approximates the obtained results of numerical simulation was proposed.

Sergey G. Psakhie, Alexey Yu. Smolin, Evgeny V. Shilko, Andrey V. Dimaki

43. Spectral Solvers for Crystal Plasticity and Multi-physics Simulations

The local and global behavior of materials with internal microstructure is often investigated on a (representative) volume element. Typically, periodic boundary conditions are applied on such “virtual specimens” to reflect the situation in the bulk of the material. Spectral methods based on Fast Fourier Transforms (FFT) have been established as a powerful numerical tool especially suited for this task. Starting from the pioneering work of Moulinec and Suquet, FFT-based solvers have been significantly improved with respect to performance and stability. Recent advancements of using the spectral approach to solve coupled field equations enable also the modeling of multiphysical phenomena such as fracture propagation, temperature evolution, chemical diffusion, and phase transformation in conjunction with the mechanical boundary value problem. The fundamentals of such a multi-physics framework, which is implemented in the Düsseldorf Advanced Materials Simulation Kit (DAMASK), are presented here together with implementation aspects. The capabilities of this approach are demonstrated on illustrative examples.

Pratheek Shanthraj, Martin Diehl, Philip Eisenlohr, Franz Roters, Dierk Raabe

44. Interface Delamination Analysis of Dissimilar Materials: Application to Thermal Barrier Coatings

Recent progress of gas turbine technologies requires protection of superalloy components from harsh use environments. To satisfy this requirement, surface protection coatings have been developed. The coatings allow protection of superalloy substrate from use environments, which includes temperature. Among the coatings, thermal barrier coatings (TBCs) have been developed to protect high temperature metal components. TBCs are usually composed of oxide ceramic topcoat layer, metal or intermetallic bond coat layer, and substrate. Currently, yttria stabilized zirconia (YSZ) is believed the best material for TBCs. YSZ-TBCs reduce temperature of a metal component because of its low thermal conductivity and cooling of metal substrate, and allows safety operation of superalloy components.

Yutaka Kagawa, Makoto Tanaka, Makoto Hasegawa

Macromechanics

Frontmatter

45. Smoothed Particle Hydrodynamics for Ductile Solid Continua

In this chapter, a numerical simulation model for ductile solid continua is presented. It is based on the Smoothed Particle Hydrodynamics (SPH) method, which serves to spatially discretize and, thus, solve the governing equations of continuum mechanics. Due to the meshless, Lagrangian character of the SPH spatial discretization technique, the introduced model is naturally well-suited for the simulation of continua featuring large deformations, major changes in topology, material failure including structure disintegration, and/or a large number of contacts with the environment occurring at the same time. For this reason, it has the potential to become a beneficial complement to the well-established numerical solid models, which mainly make use of mesh-based methods. To that end, however, the original SPH discretization scheme is to be variously extended and modified as discussed in detail in the course of this chapter. Besides, also its efficient implementation, i.e. the efficient numerical solution of the SPH-discretized governing equations of continuum mechanics, is addressed. The quality of the developed SPH formulation for ductile solids including its versatility and accuracy is demonstrated on the basis of two exemplary applications, namely, the industrial processes of friction stir welding and orthogonal metal cutting. It is shown as part of this contribution that, in either case, the proposed SPH model for ductile solid continua is capable of reproducing both the mechanical and the thermal macroscopic behavior of the real processed material in the simulation.

Peter Eberhard, Fabian Spreng

46. Simulation of Crack Propagation Under Mixed-Mode Loading

Engineering components frequently contain cracks, either as an unavoidable consequence of their manufacturing (for example, pores in sintering processes or machining flaws) or due to processes occurring in service (cyclic loads, corrosive attacks, wear, etc.). Since it is not possible to completely avoid the formation of cracks, engineering safety requires to ensure that cracks do not lead to failure of a structure.

Martin Bäker, Stefanie Reese, Vadim V. Silberschmidt

47. Relaxation Element Method in Mechanics of Deformable Solid

In this chapter a new method – the relaxation element method is justified. The definition of the changing of stress fields in solids under loading as a result of the change of elastic energy in a local volume, undergoing plastic deformation, is laid down at the basis of the method.The Relaxation Element Method (REM) solves effectively two problems of a deforming solid (DS): 1. The construction of the different distributions of plastic deformation in local regions of various geometrical shape. 2. Modelling of the consequent involvement of separate structural elements into plastic deformation, operating on the principle of an inverse task of mechanics of deforming solids. With this method a stress-strain state of the elastic plane with the sites of plastic deformation in the form of a circle, rectangle, and a localized shear band is analytically described. Examples of the construction of the sites of plastic deformation with gradients are given. The stress-strain state of a plane with a round inclusion is considered.Examples of the simulations by the REM of the effects of Lüders band formation and interrupted flow in polycrystals are given. The analysis of the influence of rigidity of a testing device on qualitative and quantitative characteristics of the loading diagram is presented.The effect of the gradients of plastic deformation on the stress of Lüders band initiation is analyzed. It is shown that the dependence of the stress of Lüders band initiation on grain sizes is the consequence of the independency of the gradient of plastic deformation under the changing of grain sizes.A modified model of Griffith crack surrounded by a layer of plastically deformed material is proposed. Plastic deformation is shown to eliminate the singularity at the crack tip. The maximum stresses are observed at the boundary of the plastic zone in an elastically deformed matrix. The stress concentration increases as the thickness of the plastic layer decreases.The obtained results testify to high predictable possibilities of the developed method. They are in a good agreement with known experimental data.

Ye. Ye. Deryugin, G. V. Lasko, Siegfried Schmauder

48. Damping Characteristics of Shape Memory Alloys on Their Inherent and Intrinsic Internal Friction

In this chapter, damping characteristics of the inherent and intrinsic internal friction (IFPT + IFI) peaks for Ti50Ni50, Ti50Ni50-xCux, Ti50Ni50-xFex, Ni2MnGa, Ni-Mn-Ti, and Cu-Al-Ni shape memory alloys (SMAs) are reviewed. Ti50Ni50 SMA exhibits obvious (IFPT + IFI) peaks with tan δ above 0.02 during martensitic transformations, but they only exist in a narrow and low temperature range. Ti50Ni50-xCux (x ≥ 10) SMAs show higher (IFPT + IFI) peaks than Ti50Ni50 SMA because B19 martensite in Ti50Ni50-xCux SMAs is originated by substituting Ni with Cu atoms while R-phase in Ti50Ni50 SMA is caused by the introduction of abundant defects/dislocations. Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs also exhibit higher (IFPT + IFI) peaks than Ti50Ni50 SMA because R-phase formation is due to the substitution of Ni by Fe atoms rather than induced by introduced dislocations. However, the martensitic transformation temperatures of Ti50Ni50-xFex SMAs are suppressed to lower temperatures simultaneously by the addition of Fe atoms. Ni-Mn-Ti and Ni-Mn-Ga magnetic SMAs both exhibit relatively high martensitic transformation temperatures. Unfortunately, the undesirable brittle nature of Ni-Mn-Ti and Ni-Mn-Ga SMAs critically limits their workability and high-damping applications. Cu-Al-Ni SMAs exhibit acceptable martensitic transformation temperatures and good workability; however, their (IFPT + IFI) peaks are relatively low. Among these various types of SMAs, Ti50Ni40Cu10 SMA is more suitable for high-damping applications because it possesses the advantages of high (IFPT + IFI) peaks, adequate workability, and an acceptable martensitic transformation temperature near room temperature.

Shih-Hang Chang, Shyi-Kaan Wu

49. Application of Homogenization of Material Properties

The limit flow stresses for transverse loading of metal matrix composites reinforced with continuous fibers and for uniaxial loading of spherical particle-reinforced metal matrix composites are investigated by recently developed embedded cell models in conjunction with the finite element method. A fiber of circular cross section or a spherical particle is surrounded by a metal matrix, which is again embedded in the composite material with the mechanical behavior to be determined iteratively in a self-consistent manner. Good agreement has been obtained between experiment and calculation, and the embedded cell model is thus found to represent well metal matrix composites with randomly arranged inclusions.Systematic studies of the mechanical behavior of fiber and particle-reinforced composites with plane strain and axisymmetric embedded cell models are carried out to determine the influence of fiber or particle volume fraction and matrix strain-hardening ability on composite strengthening levels. Results for random inclusion arrangements obtained with self-consistent embedded cell models are compared with strengthening levels for regular inclusion arrangements from conventional unit cell models.Based on the self-consistent embedded cell models, a self-consistent matricity model has been developed to simulate the mechanical behavior of composites with two randomly distributed phases of interpenetrating microstructures. The model is an extension of the self-consistent model for matrices with randomly distributed inclusions. In addition to the volume fraction of the phases, the matricity model allows a further parameter of the microstructure, the matricity M of each phase, to be included into the simulation of the mechanical behavior of composites with interpenetrating microstructures. Good agreement has been obtained between experiment and calculation with respect to the composites’ mechanical behavior, and the matricity model is thus found to represent well metal matrix composites with interpenetrating microstructures. The matricity model can be applied to describe the mechanical behavior of arbitrary microstructures as observed in two-phase functionally graded materials, where the volume fraction as well as the matricity of the phases varies between the extreme values of 0 and 1.

Ming Dong, Siegfried Schmauder

50. Fatigue Behavior of 9–12% Cr Ferritic-Martensitic Steel

In this chapter, the cyclic fatigue behavior of the 9–12%Cr ferritic-martensitic steel used in power plants is systematically summarized. At first, the application background and the basic information of these kinds of materials are discussed. The 9–12%Cr martensitic steel has been extensively used in the supercritical steam turbine components in the thermal power plants. The fully understanding of the effects of materials properties and softening behavior on low cycle fatigue (LCF) are important in the improvement of structural design and the reliability assessment for its safety operation. Subsequently, the LCF properties, the nucleation and growth of fatigue crack, and the evolution of microstructure are further discussed. The previous research results and the factors that affect the LCF behavior are also summarized in these sections. Lastly, a brief summary of the chapter and the new research method related to the fatigue behavior of 9–12%Cr ferritic-martensitic steel are introduced for further investigating. This chapter serves as a quick reference of entering the fatigue behavior of materials for researchers, engineers, and students in the mechanical and materials engineering field.

Zhen Zhang, Zhengfei Hu, Siegfried Schmauder

51. Coupling of Discrete and Continuum Approaches in Modeling the Behavior of Materials

For computer simulation of the mechanical behavior of materials and various media, methods of continuum mechanics are mainly used. Continuum approach uses highly developed mathematical apparatus of continuous functions, and capabilities of this approach are extremely wide and well known. However, for a number of very important processes, such as severe plastic deformation, mass mixing, damage initiation and development, material fragmentation, and so on, continuum methods of solid mechanics face certain hard difficulties. As a result, a great interest for the approach based on a discrete description of materials and media has been growing up in recent years.It is obvious that both continuum and discrete approaches have their own advantages and disadvantages. A great number of commercial software has been created for solving numerous scientific and engineering problems based on continuum mechanics. Hence, the main line of discrete approach development seems to be not a substitute but a supplement to continuum methods in solving complex specific problems based on a coupling of the continuum and discrete approaches.This chapter shows how to solve this problem on the example of the finite-difference method for numerical solution of dynamic problems on elastic-plastic deformation of continua, which is based on the continuum approach, and the movable cellular automaton method based on the discrete approach. Two particular applications of the coupled method are considered. The first example concerns simulation of target penetration by long rod at the macroscale. The second one deals with simulation of sliding friction at the scale of contact patch (mesoscale).

Alexey Yu. Smolin, Igor Yu. Smolin, Evgeny V. Shilko, Yuri P. Stefanov, Sergey G. Psakhie

52. Numerical Simulation of Material Separation Using Cohesive Zone Models

This chapter will very briefly summarize the general foundations and developments of the cohesive zone model, which have been reported in literature during the past 50 years. According to the scope of the book, only material separation due to mechanical loading modeled by a cohesive interface will be considered, even though additional environmental effects may be taken into account. The reduction of the load bearing capacity of a cracked (or damaged) region by a separating interface is a strong simplification, but it reduces the complexity of the crack models significantly such that the model gained high interest in research and also in industry. The use of cohesive zone models for the simulation of crack propagation in engineering structures has first been reported in 1976. The increase in computer power, which promoted the use of the finite element method as well, has increased the possibilities in the application of the cohesive zone model. It is now used for almost all kinds of materials and many different processes, and it has undergone many extensions and improvements with respect to materials, loading conditions, numerical techniques, and mechanical formulations. After a short historical overview starting with the very beginning of the cohesive interface model, the chapter addresses several recent developments such as identification and use of traction-separation laws, mixed-mode behavior, unloading issues, and cyclic loading.

Ingo Scheider

53. Current Applications of Finite Element Methods in Dentistry

This chapter introduces recent applications of finite element method (FEM) as one of the promising methodological options in the clinical dental sciences. A PubMed-based review indicated that the number of published FEM studies in dentistry was 2,919 in all time and 1,896 during the last decade on the 7th of July 2017. The articles have increased during the last two decades from 35 (0.3% of all scientific articles from the dental society) in 1996 to 97 (0.7%) in 2006 and 216 (0.7%) in 2016. The FEM studies on dental implant accounted for 40.0% of all FEM studies in dentistry during the last decade. Unlike manufactory products of relatively uniform configuration, 3D modeling has a considerable advantage in the analyses of the oral tissues with complex and irregular morphology. Nonlinear analysis has become an increasingly powerful methodology for the simulations of the tooth-to-tooth contacts, restorative interface degradation and debonding, and the incomplete bone-implant osseointegration. While, a relatively low increase rate of the nonlinear studies was indicated, presumably because the simulations of the oral environment may still pose some difficulties to complete model solutions. The use of CT data of patients to create the maxillary and mandibular bone models has increased with incorporated CAD-based implant models. The mathematical approach to allocate Young’s modulus to a local bone segment is still a challenging issue to establish validity of large and realistic models of oral soft and hard tissues.

Noriyuki Wakabayashi, Natsuko Murakami, Atsushi Takaichi

54. Elastic-Plastic and Quasi-Brittle Fracture

This chapter presents a simple Elastic-Plastic and Quasi-Brittle Fracture Approach that can be used by graduate students and design engineers in their structural integrity analyses to determine safe design loads or to predict critical failure loads. The simple model can also be used to extrapolate the tensile strength and fracture toughness KIC of various metals and composites from elastic-plastic fracture results of small test samples, which otherwise would require impractically large specimens for the fracture toughness measurements and well-polished specimens for the strength measurements. Elastic-plastic fracture of metals and quasi-brittle fracture of coarse-structured brittle composites such as concrete and rock can also be fairly accurately predicted by the predictive model if both strength and toughness are known. The model is derived by a simple modification of the stress intensity factor commonly used in Linear Elastic Fracture Mechanics (LEFM). Experimental results of AISI-1040 like carbon steel and Aluminum Alloy 6061 and concrete are used to verify the new approach. The new design model can be applied to different fracture situations from strength-controlled failure to LEFM KIC-controlled fracture and the elastic-plastic and quasi-brittle fracture region (or non-LEFM fracture) between the two distinct strength and toughness territories. The model also explains the limitations of LEFM imposed by the stringent requirements for the fracture toughness KIC measurements and the reason why Elastic and Plastic Fracture Mechanics (EPFM) is necessary to most structural integrity analyses.

Xiaozhi Hu, Li Liang

55. Coupling Models of New Material Synthesis in Modern Technologies

Today, additive manufacturing (AM) technologies attract large attention. One can define these technologies as step-by-step construction or synthesis of parts from identical or different materials. Stereolithography, selective laser melting, selective laser sintering, hot isostatic pressing, and combined technologies belong to AM technologies. Electron-beam (EB) technologies are also popular. Coating synthesis and surface treatment using EB, composite material synthesis, and various technologies of material joining could be also added to additive manufacturing. Since the experimental investigation of technological processes (dynamics of chemical composition, evolution of structure and properties) is very complicated, mathematical modeling can help in this field. This section presents the approach to predictive model construction. Together with chemical reactions accompanying the change of properties, the technological conditions are analyzed. General equations include the energy equation, balance equations for species, equilibrium equation, and governing equation containing terms describing numerous cross effects. Examples of particular model are presented for accepted technologies of surface treatment. The first model describes the surface modification using electron beam and particles that dissolve in a melting pool and change the composition. The second model describes the composition change during the coating deposition and includes coupling effects between transfer processes and mechanical ones. Multilayered coating forms on the metal surface during ion deposition from gas, solution, or plasma. The third model gives the modeling concept for choosing the technological conditions for homogeneous coating creation on the substrate using chemical reactions and external heating. These models relate immediately to additive manufacturing where metals are used.

Anna Knyazeva, Olga Kryukova, Svetlana Sorokova, Sergey Shanin

56. Simulation of Fracture Behavior of Weldments

In this chapter, the fracture behavior of an S355 electron beam welded joint is simulated with the Rousselier, Gurson-Tvergaard-Needleman (GTN), and cohesive zone models separately. First, each model is discussed and the method identifying the model parameters is given. Second, the simulation results on the crack propagation of compact tension (C(T)) specimens with the initial crack located at different weld regions are given. Finally, the cohesive zone model is compared with the other two models, showing its superiority.

Haoyun Tu, Siegfried Schmauder, Yan Li

Measurement and Applications

Frontmatter

57. Very High Cycle Fatigue

In this chapter, an introduction into the experimental challenges of fatigue testing beyond the classical fatigue limit will be presented. For many applications, strength assessment according to the classical durability (N ≤ 107) is no longer sufficient, since increasingly more components are subjected to cyclic loading up to the very high cycle fatigue (VHCF) regime. Recent studies have shown that the effective damage mechanism need not be inferred readily from low- and high-cycle fatigue (HCF) behavior of materials, since competing failure modes resulting from microstructural discontinuities play a prominent role in crack initiation. An identification of the failure-relevant microstructural feature poses a genuine experimental challenge, since from a macroscopic perspective purely elastic deformation is applied. Moreover, a shift from surface to interior crack initiation is observable for several materials. All of these aspects together with the need to test at elevated frequencies to reach numbers of cycles as high as N = 109 call for new experimental strategies. After a brief introduction of the motivation for VHCF testing and a short excursion into the world of VHCF-relevant damage mechanisms, an overview of high-frequency fatigue testing machines and their characteristic features is presented. Particular attention will be paid to the innovative test method of ultrasonic fatigue. A critical discourse of likely influence factors such as frequency and environment in the context of high-frequency testing is given. Finally, particular attention will be drawn to in situ damage monitoring during VHCF test conditions.

Martina Zimmermann

58. High Temperature Mechanical Testing of Metals

Performing mechanical tests at high temperatures is a nontrivial issue: Compared to room temperature testing, additional phenomena like time-dependent deformation processes and oxidation effects raise the complexity of the material’s response, while more sophisticated test setups and additional control parameters increase the number of potential sources of error. To a large extent, these complications can be overcome by carefully following all recommendations given in the respective high temperature testing standards, but more comprehensive background information helps to identify points of specific importance in particular test campaigns. In this chapter, an overview is given on general high temperature testing issues like the appropriate choice of experimental equipment and key aspects of temperature measurement. In subsequent sections, the major static and dynamic high temperature test methods are reviewed and their special features, as compared to testing at room temperature, are highlighted based on example data sets. Influences of specimen size and environmental effects are shortly outlined in a concluding section. In the whole chapter, a focus is set on testing of “classical” metallic high temperature materials, but many considerations are equally valid for testing of intermetallics, composites, and high temperature ceramics.

Birgit Skrotzki, Jürgen Olbricht, Hans-Joachim Kühn

59. Microelectromechanical Systems (MEMS)-Based Testing of Materials

Mechanical behavior of micro- and nanoscale materials has received considerable attention in recent years because of their widespread use in micro−/nanotechnology applications. These materials are also intriguing from a scientific standpoint because their small-size scale results in mechanical behavior that is significantly different from the behavior of macroscale materials. As a result, a variety of experimental methodologies have been developed to accurately determine the mechanical properties (modulus, strength, fracture toughness, etc.) of micro- and nanoscale materials and uncover the microscopic mechanisms that lead to those properties. Among these approaches, microelectromechanical systems (MEMS)-based platforms have proven to be highly suitable because of their capability to apply and resolve extremely small forces (nN) and displacements (nm). In addition, MEMS-based testing platforms, because of their small size, are ideal for in situ characterization in electron and scanning probe microscopes, which often have stringent space limitations. This chapter provides an overview of the development and advances in MEMS-based materials characterization with an emphasis on in situ techniques. Different actuation and sensing mechanisms as well as device configurations for various types of testing (tensile, fatigue, thermomechanical) are reviewed. Key results and insights obtained from the nanomechanical characterization of thin films, nanowires, and nanotubes using MEMS-based platforms are summarized. Finally, some of the challenges and opportunities for MEMS-based micro- and nanoscale materials characterization are discussed.

Jagannathan Rajagopalan

60. Nanoindentation for Testing Material Properties

Nanoindentation has seen widespread applications for characterizing the mechanical properties of materials. The technique involves the measurement of applied load and penetration depth, at very small scales, when the indenter is pressed against the test material. An indentation test requires minimal material preparation, and can be performed multiple times on a single specimen. It is particularly suited for thin films, coatings and modified surfaces, as well as materials in their bulk form. Rooted in classical contact mechanics, theories and practice of nanoindentation testing have been developed to extract a wide array of material properties. This chapter presents a comprehensive overview of the fundamentals of nanoindentation. Background information about the indentation theories is first reviewed, with emphasis on the relevant Hertzian contact analysis and Sneddon’s solutions. Common indenter types are then presented, which is followed by discussion on the two most frequently measured properties, hardness and elastic modulus. Guidelines and best practices for the determination of contact stiffness and contact area, along with corrections of thermal drift and machine compliance, are discussed. Representative indentation methodologies for characterizing residual stresses, time-dependent deformation for metals and polymers, fracture toughness for brittle materials, and adhesion of coatings on substrates are also included in the presentation. Computational modeling is shown to yield valuable information of internal deformation field which can be correlated with the indentation response. Unique indentation features and uncertainties associated with material heterogeneity, as well as remaining challenges and future directions, are also discussed.

Yu-Lin Shen

61. 3D/4D X-Ray Microtomography: Probing the Mechanical Behavior of Materials

A fundamental principle in materials science and engineering is that the microstructure controls material properties. The use of three-dimensional techniques has gained popularity in establishing structure-property relationships in a variety of material systems. In particular, X-ray microtomography is being widely used as it requires minimal sample preparation and is nondestructive in nature. Moreover, being a nondestructive technique, it is very well suited to perform 4D studies (the fourth dimension being time) where the evolution of microstructure can be captured over time. This chapter describes the fundamentals of X-ray microtomography followed by applications of the use of X-ray microtomography to understand the mechanical properties of materials under a variety of loading conditions, such as tensile loading, fatigue loading, corrosion fatigue, and stress corrosion cracking.

Sudhanshu S. Singh, Nikhilesh Chawla

62. Mechanical Testing of Single Fibers

Materials in the form of long fibers are used in a variety of structural applications. Examples include cables, ropes, woven or nonwoven fabrics, and as reinforcements in composite materials. Thus, it is important to have knowledge of their mechanical characteristics. Mechanical testing of long, slender individual fibers is a nontrivial matter. Many techniques for testing single fibers are available. We describe some of the important ones in this chapter: tensile testing by using cardboard frame technique, recoil compression test, shear modulus by means of torsional pendulum test, loop test, techniques involving laser interferometry, Raman spectroscopy, and insitu techniques involving the use of scanning electron and transmission electron microscopy.

Krishan K. Chawla

63. Stress Measurement in Thin Films Using Wafer Curvature: Principles and Applications

Wafer curvature is a useful and sensitive technique for measuring stress in thin films. This work describes the basis for wafer curvature measurements and how they can be used to understand stress evolution. Various approaches to the measurement of curvature are discussed with their strengths and drawbacks. The information that can be obtained from wafer curvature is illustrated by examples from different studies. Measurements during thin film growth (evaporation, electrodeposition, and sputter deposition) enable the relationship between residual stress and many different processing parameters (temperature, growth rate, microstructure, material types, deposition process, etc.) to be quantified. Studies of the real-time evolution have played a large part in identifying the physical mechanisms that are responsible for the resulting stress. A kinetic model is described that incorporates these mechanisms into equations that predict the stress under different conditions. Another set of examples describes the stress that leads to the formation of whiskers in Pb-free Sn coatings on Cu. Simultaneous measurement of the Sn-Cu intermetallic volume, stress, and whisker density show how these processes are correlated. The controlled application of stress via thermal expansion mismatch is used to study the mechanical properties and plasticity in Sn layers. It also allows the nucleation kinetics as a function of applied stress to be measured.

Eric Chason

64. Testing of Foams

Foams are lightweight cellular materials that are widely used in applications such as packaging, thermal insulation, sound absorption, underwater vehicle structures, and as the core in sandwich structures used in aircraft. Testing of foams to obtain reliable properties that are relevant to a given application is a significant challenge. High damping, high compressive or tensile strain, and high volume of air in the structure are among the challenges that make it difficult to apply the common test methods to these materials. For example, use of strain gauges for tensile or compression testing is usually not possible because bonding the strain gauges to the surface of a cellular material may not be possible, the small measurement range of a strain gauge may not be enough to capture the strain in the entire loading range, and microscopic material structure may dominate the measurement. This chapter discusses test techniques that include quasi-static compression, high strain rate compression, impact, dynamic mechanical analysis, vibration methods, and imaging techniques that are relevant to testing of foams. The imaging methods include ultrasonic imaging and microCT-scanning. Test techniques are described and results on representative foam materials are presented to understand the test outcomes.

Nikhil Gupta, Steven Eric Zeltmann, Dung D. Luong, Mrityunjay Doddamani

65. Crack-Dislocation Interactions Ahead of a Crack Tip

An overview of interactions of crack and dislocations emitted from the crack is provided with particular emphasis on theoretical approaches. Several existing models, such as due to Bilby, Cottrell and Swinden, Burns and Majumdar, Lin and Thomson, and Pande and Masamura, are presented. These models provide a formalism that gives the equilibrium positions of dislocations in an array ahead of crack tip, from which important parameters such as plastic zone size, dislocation-free zone, and dislocation stress intensity factor can be determined, which are useful in discussing the phenomenon of fatigue. Following these overviews, the experimental results on the dislocation-free zone and plastic zone observed ahead of the cracks in aluminum using transmission electron microscopy are presented and compared with the existing models. The experimentally measured values of these zones are shown to be in reasonably good agreement with theoretical models of crack-dislocation configuration based on a continuum distribution of dislocations ahead of the crack. However, these models fail to predict the total number of emitted dislocations, underlying the need for better analytical models. We also provide a brief overview on crack tip dislocation behavior under fatigue loading.

R. Goswami, C. S. Pande

66. In-Situ Nanomechanical Testing in Electron Microscopes

Understanding the mechanical behavior of nanostructured and nanosized materials at the nanoscale is very important in improving their structural stability and operational reliability. This chapter introduces unique in-situ nanomechanical testing techniques in electron microscopes that assist in the precise positioning and direct characterization of nanoscale samples, while avoiding their aging or contamination by the environment. The first two short sections address the importance of mechanical behavior at the nanoscale and present some examples of conventional nanomechanical testing and ex-situ deformation observations. The third section introduces the instrument for in-situ nanomechanical testing in electron microscopes, the preparation of samples for testing, and some complimentary components of the tools. The final section presents some applications of the powerful techniques to achieve precise mechanical measurements and direct deformation/failure observations at the nanoscale of various materials of various dimensions.

Shou-Yi Chang

67. Deformation Measurement for Multiscale and Multifield Problems Using the Digital Image Correlation Method

Based on the tracking of characteristic patterns in a series of images, digital image correlation (DIC) provides full-field displacements in the subpixel accuracy. The subpixel algorithm of DIC uses gradient-based method, inverse compositional Gauss-Newton, and double Fourier transform to achieve tracking results at extremely high resolutions. The noncontact nature of DIC technology provides pixel-based data for use in multi-scale measurement, which is able to analyze structure deformation at scales from meters to nanometers, and to record the duration of two images from hours to microseconds. The DIC technique developed in our laboratory makes it possible to obtain noncontact, full-field measurements with high spatial and temporal resolution. The DIC technique is used in this study to investigate numerous problems in various domains at various scales.

Chien-Ching Ma, Ching-Yuan Chang

68. High Temperature Nanomechanical Testing

Elevated temperature nanomechanical testing is becoming a very popular technique to unravel temperature effects on the deformation mechanisms of a number of material systems, especially in those cases where it is the only available technique for mechanical testing, like in thin-films and coatings. This chapter presents several success stories where nanoindentation and micropillar compression were applied at elevated temperature to study the temperature-dependent strength and strain rate-dependent behavior. Nevertheless, we recognize several areas which require further developments for elevated nanomechanical testing to become a widely used and robust technique: more automated approaches to continuously monitor and correct for thermal drift and more stable and longer-lasting new indenter materials.

Miguel A. Monclús, Jon M. Molina-Aldareguia

69. The Sliding Wear Response of High-Performance Cermets

The degradation of materials through wear is of significant concern in a wide variety of industries. As a consequence, there is a continuing drive to develop improved materials for many of these applications, and to thoroughly assess their wear response. One class of materials that is widely employed in scenarios requiring both wear and corrosion resistance is composites combining ceramics and metals, often referred to as “cermets.” Among the commonly applied cermet systems, materials based on WC with a Co-based metallic binder are widely employed. More recently, lightweight cermets based on TiC and Ti(C,N) are finding application in many industries. The present study summarizes recent investigations assessing the sliding wear response of TiC and Ti(C,N) cermets, utilizing novel metallic binder phases, including various stainless steels and ductile nickel aluminide intermetallics. It is shown that these materials present a complex response to sliding wear. Initially, two-body abrasive wear occurs, which rapidly transitions to three-body abrasive wear. The third-body material is comprised of constituents from the two contacting materials, generated through mechanisms such as binder extrusion and ceramic grain fracture and pull-out. Ultimately, the third-body material is significantly refined in size, and is deposited into the wear track via an adhesion mechanism, as a thin tribolayer. It is demonstrated that specific wear rates comparable to current commercial WC-based cermets can be achieved with these new lightweight materials.

Kevin P. Plucknett, C. Jin, C. C. Onuoha, T. L. Stewart, Z. Memarrashidi

70. Electromechanical Coupling of Botanic Cells: Theory and Applications

In this chapter, an onion actuator and tactile sensor are proposed. Actuators functionalize dynamics of mechanisms or systems via an energy conversion, such as the transformation of electricity into mechanical deformation. Most motor-driven actuators and engineered artificial muscles are very capable of either bending or contraction/elongation. However, there are currently no actuators that can accomplish these actions simultaneously. This chapter introduces the development of such a device. The simple latticed microstructure of onion epidermal cells allowed itself to simultaneously stretch and bend. By modulating the magnitude of the voltage, the actuator made of onion epidermal cells deflects in opposing directions while either contracting or elongating. This chapter also presents and demonstrates the development of flexible tactile sensor utilizing the microstructures of onion epidermal cells, which replace the intermediate dielectric layer in a typical parallel-plate capacitive sensor. The onion epidermal cells can effectively reduce the complexity of the sensor structure and thus simplify the device fabrication process. The single layer of the onion epidermal cells is robust for high tactile sensitivity, mechanical flexibility, and optical transmittance with potentially low-cost sensor manufacturing in a large area. A new type of actuator and tactile sensor can be produced from a never-used material – onion epidermal cell – in the hope of initiating a new field of fusing plant and mechatronics for the benefits of inducing large deflection measurements in both transverse and longitudinal directions in a ubiquitous and low-cost manner. And the proposed sensor array will be applied in robotic electronic skin and biomedical devices in the future.

C. C. Chen, W. P. Shih

71. Additive Manufacturing of Multidirectional Preforms and Composites: Microstructural Design, Fabrication, and Characterization

In contrast to conventional preforming methods, additive manufacturing features direct and layer-by-layer fabrication and, thus, provides new opportunities for the design and fabrication of composite materials. The rapid advancements in additive manufacturing techniques have provided us with the impetus to examine the feasibility of manufacturing multidirectional preforms and their composites based on direct, layer-wise fabrication. In this chapter, we have demonstrated the additive manufacturing of typical multidirectional preforms for composites (Sect. 2), examined the microstructural design as well as additive manufacturing of 3D orthogonal preforms and composites (Sect. 3), evaluated the microstructural features and mechanical properties of additively manufactured multidirectional preforms and composites (Sect. 4), and investigated the printing direction dependence of mechanical behavior of additively manufactured 3D preforms and their composites (Sect. 5).

Zhenzhen Quan, Tsu-Wei Chou

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