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About this book

This book presents the proceedings of the 3rd edition of the International Conference on Theoretical, Applied and Experimental Mechanics.

The papers focus on all aspects of theoretical, applied and experimental mechanics, including biomechanics, composite materials, computational mechanics, constitutive modeling of materials, dynamics, elasticity, experimental mechanics, fracture mechanics, mechanical properties of materials, micromechanics, nanomechanics, plasticity, stress analysis, structures, wave propagation.

Table of Contents


Materials: Properties, Manufacturing, Modelling


High-Speed Mode-I Delamination

The analytical theory of mode-I delamination propagation in double cantilever beams (DCBs) under high loading rates is developed by accounting for structural vibration and wave dispersion, and by using Euler-Bernoulli beam theory. The developed analytical theory is validated against experimental data and against finite element method (FEM) simulations, showing excellent agreement. It is shown that the developed analytical theory can accurately calculate energy release rate (ERR) for both stationary and propagating delamination, and that structural vibration can have a significant effect on ERR. It is further shown how the theory can be used to post-process experimental results from high-speed delamination tests to determine fracture toughness. Among other examples, the work is therefore expected to be useful to engineers and academic researchers to determine the initiation, arrest and propagation fracture toughness of laminated materials against delamination. The developed theory also provides useful benchmark solutions for the development of numerical codes.

Tianyu Chen, Christopher M. Harvey, Simon Wang, Vadim V. Silberschmidt

Characterization of Dynamic Fractures for Compressed PMMA Material

Polymethyl methacrylate (PMMA) is a quasi-brittle material and dynamic behaviors usually present thermoplastic characteristic. But in some cases, PMMA breaks with the complete brittle characteristic. The complex behaviors need to be studied for a further understanding. A series of PMMA specimens are designed to study the behaviors on a Spilt Hopkinson Pressure Bar (SHPB) device. The complex behaviors are found to be dominated by the impulsive energy and there exists a critical energy for the specimens to create the complete brittle fracture.

C. Huang

Tensile Behavior of a Titanium Alloy Additively Manufactured via Selective Electron Beam Melting

Additive manufacturing or 3D-printing of titanium alloys with a high strength-to-weight ratio holds significant interest in the aerospace and biomedical industries. The purpose of this investigation was to determine microstructure and tensile deformation behavior of a 3D-printed Ti-6Al-4V alloy via selective electron beam melting (SEBM). Plentiful multi-oriented α-lamellae were present in the prior columnar β grains, which were oriented in the building direction because of the presence of temperature gradients during 3D-printing. The processing parameters selected in this study ensured superior strength and high ductility by controlling the thickness of α-lamellae, with both surpassing the values specified in the ASTM standard. The horizontally orientated 3D-printed alloy demonstrated a certain extent of strain rate sensitivity which decreased with increasing strain, suggesting that dislocation slip was a predominant deformation mode, since the fine and abundant multi-oriented α-lamellae could impede the formation of extension twinning. Fracture surface was observed to be characterized by typical dimples and some entrapped gas pores.

Yinling Zhang, Shoujiang Qu, Aihan Feng, Daolun Chen

The Rule of Mixtures on the Elastic Buckling Response of Rectangular GLARE FML Plates Under Shear Stresses

Fiber Metal Laminates (FMLs) are hybrid composite materials consisting of alternating metal layers bonded to fiber-reinforced prepreg layers. ARALL, CARALL and GLARE belong to this new family of materials. GLARE is the most successful FML up to now and is currently being used for the construction of primary aerospace structures. In this study, the elastic buckling response of rectangular GLARE FMLs subjected to shearing stresses is investigated using the finite element method and eigenvalue buckling analysis. Simply supported, clamped and mixed boundary conditions are considered. Using validated FEM models, the buckling coefficient-aspect ratio diagrams of seven GLARE grades are obtained along with the diagrams of three UD glass-epoxy composites and monolithic 2024-T3 aluminum. The rule of mixtures is evaluated and found to be a simple method to estimate approximately the elastic buckling stress of the GLARE plates. An approximate formula is derived for the estimation of the critical buckling coefficient of the GLARE plates using the buckling coefficients of their constituents.

Costas D. Kalfountzos, George S. E. Bikakis, Efstathios E. Theotokoglou

Evaluating Bonding Characteristics of Joggled Lap CFRP Using Acoustic Emission Techniques

In this study, the carbon fiber reinforced plastics (CFRP) specimens bonded adhesively in joggled lap configuration are tested for their bonding characteristics. The acoustic emission (AE) technique is used as a characterizing tool and peak amplitude is taken as the primary acoustic descriptor. The peak amplitude distributed in the time domain of the test is clustered by using an unsupervised pattern recognition algorithm (k-means++ algorithm) to differentiate the different damage modes. Furthermore, the waveforms of the acoustic signals recorded were studied using wavelet packet transform (WPT). The frequency band associated with each damage mode is identified using the wavelet packet transform. It is identified that the dominant damage mode responsible for failure is the interfacial debonding and interlaminar crack growth through the thickness of the adhesive layer. Overall, the acoustic emission technique proved to be a powerful tool in evaluating the bonding characteristics of the tested CFRP joggled lap specimens.

Claudia Barile, Caterina Casavola, Giovanni Pappalettera, Carmine Pappalettere, Paramsamy Kannan Vimalathithan

Experimental Study of Low Concentration Diffusible Hydrogen Effect on Mechanical Behaviour of Carbon Steel

The presented work is dedicated to the evaluation of the mechanical behaviour of the ferrite-pearlite carbon steel under a low concentration of diffusible hydrogen in the bulk of the metal. Received standard stress-strain diagrams under different hydrogen concentration $$ C_{H} $$CH in the specimens have shown on the existence of some specific value of the hydrogen concentration $$ C_{H}^{ * } $$CH∗ at which the mechanism of hydrogen influence changes, namely: below this value the enhanced plasticity (decreasing of the yield stress) takes places and above – the hydrogen embrittlement occurs. This phenomenon was explained based on the special tests of tensile specimens, which were preliminary charged by hydrogen to concentration $$ C_{H}^{ * } $$CH∗ and then discharged to the concentration $$ C_{H} \approx 0 $$CH≈0. It has been found that increasing the number of cycles of charging-discharging leads to decreasing the value of yield stress. Thus, even a short-term presence of the hydrogen in the material leads to irreversible changes in the structure of the material, namely: the appearance of defects at the microlevel. This facilitates the deforming ability of steel and reduces the value of the plasticity limit.

I. M. Dmytrakh, R. L. Leshchak, A. M. Syrotyuk

Effects of Temperature on Tensile and Fracture Behavior of Dissimilar Metal Welded Joint for Nuclear Safe-End

The effects of temperature on tensile and the fracture behavior of dissimilar metal welded joint for nuclear safe-end were studied. The results show that the strength, elongation and fracture toughness of DMWJ significantly decrease with increasing temperature. At room temperature, more deformation twins can make the deflection of the crack propagation direction, so the crack propagation path is extended, and the alloy can absorb more energy during the fracture process, so as to the toughness of the joint is enhanced. While at the evaluated temperature, the second phase particles are more likely to be a crack initiation, which makes the crack propagation easier. In addition, the dislocation density is reduced, resulting in the decreased strength.

Lei Wang, Yang Liu, Xiu Song, Jiahua Liu

A Multi-attribute Information Based Method of Material Strength Distribution Fitting

Information fusion technique has been widely applied to a variety of subjects such as fault diagnosis and image identification. Bayes estimation is a special type of information fusion technique applied to parameter estimation for probability distribution of random variable. The present paper presents a new type of information fusion technique for material strength distribution estimation in the situation of small size sample. To precisely describe material strength, three-parameter Weibull distribution is used. To find out a reasonable location parameter in the situation that only a few experimental observations are available, the knowledge and information from different aspects are utilized. First, an empirical shape parameter is chosen with reference to the strength distribution of similar material. Then, a location parameter is assigned to make the estimated material strength variation at a realistic level, by judging the rationality of the location parameter through the strength probability distribution thus estimated. At last, big data technique is applied to further verify the rationality of the estimated material strength distribution by testing the relation between location parameter and the minimum observation in a sample of particular size for a special three-parameter Weibull distribution.

Liyang Xie, Bo Qin, Ningxiang Wu

Performance of a Carburizing Bearing Steel After Surface Nanosized

Nanobainite and dispersed carbides were gained on surface layer of a modified carburizing 23Cr2Ni2Si1Mo bainitic bearing steel based on carburization, tempering at high temperature, and succedent low-temperature isothermal quenching. As compared with the conventional carburizing 20Cr2Ni4 martensitic bearing steel, the novel carburizing 23Cr2Ni2Si1Mo nanobainitic bearing steel showed a much higher wear-resisting performance and rolling contact fatigue performance. The excellent properties suggest that the novel carburizing 23Cr2Ni2Si1Mo nanostructured bainitic steel is very promising to manufacture heavy-duty bearing, especially for bearings that bear impact load and need high wear-resisting performance and high rolling contact fatigue performance during their service life.

Yanhui Wang, Fucheng Zhang, Zhinan Yang, Hezong Li, Qian Yang

Residual Strength and Toughness of Nano and Micro Scale Fiber Reinforced Cementitious Composites

This study reports a significant synergistic effect of using combined networks of nanoscale fibers (CNTs) and micro scale fibers (PPs) on the key mechanical properties of OPC mortars that define a uniquely tough and energy-absorbing material. The flexural strength at the first crack, δ, were firstly investigated by conducting three point close loop bending tests on prismatic specimens of mortars reinforced with 0.1 wt% CNTs and/or 0.73 wt% PPs. To further assess the mechanical performance of the proposed nanocomposites after the formation of the first-crack, the residual strength and the energy absorption capability of the nanocomposite mortars are also investigated at three post-crack stages, 3δ, 5.5δ and 10.5δ, according to the ASTM C1018. The experimental results showed that a combination of nano and micro scale fiber reinforcement yields a composite with a significantly enhanced load-carrying capacity at the elastic stage, as defined by the approximately 100% higher first crack strength. The multi scale fiber reinforcement has also an exceptional impact on improving the tensile strain-capacity of resultant composite after the formation of the first crack. The observed 90% increased residual strength and post-crack toughness of CNT-PP reinforced mortars indicate an improved ductility over the mortars reinforced with microscale PP fibers alone.

Panagiotis A. Danoglidis, Maria S. Konsta-Gdoutos, Emmanuel E. Gdoutos

Experimental and Numerical Strategy for the Determination of Mechanical Properties Related to Human Cortical Bone Fracture

The paper presents an experimental test of macrocrack propagation in bones associated with a numerical strategy to determine from this test some mechanical properties by inverse identification. A 3 point bending test is performed on a notched segment of long human bone, and the load vs notch opening displacement is measured. The compliance method is applied in the context of a realistic FE simulation of the test. A first application of this methodology is described and shows its feasibility and capabilities. The ultimate objective of this research project is to develop a probabilistic modelling of the macrocracking processes in human long bone tissues based on an experimental database of mechanical parameters fed up by this methodology.

J.-L. Tailhan, Y. Godio-Raboutet, C. Boulay

Effect of External Field Treatment on the Microstructure and Deformation Behavior of Nickel-Base Superalloy

The electrostatic field and electropulsing were applied to the nickel-base superalloy and the effect and mechanism of the external field on the microstructure were investigated in the present study. The results showed that the electrostatic field has significant effect on the vacancy movement and atomic diffusion. As a consequence, a lot of twins can be obtained in the alloy by electrostatic field treatment and both the precipitation and growth of the strengthening phase changed. The plastic deformation resistance of the nickel-based superalloy can be effectively reduced by the adding of pulse current as well as the improvement of the plastic deformation ability. At the same time, the activation energy of the recrystallization can also be reduced by the adding of the pulse current, and the promotion of the nucleation and growth of the recrystallization of the alloy.

Yang Liu, Lei Wang, Xiu Song, Yao Wang

Dynamic Speckle Contrast Imaging for Surface Defect Detection

We propose to explore the dynamic speckle contrast imaging (DSCI) modality for non-contact surface defect detection. In this approach, the object under investigation is subjected to a continuous and monotonic loading. A number of speckle images are recorded during the continuous deformation of object surface. Speckle contrast analysis algorithm is applied to the stack of images which utilizes the fact that the variations on the object surface is reflected in significant changes in the speckle intensity variations. A simulation study was performed with the speckle images and with specklegrams recorded in the speckle interferometry and Shearographic setup. The results motivate the applicability of the DSCI technique in surface defect detection.

Rishikesh Kulkarni, Shanta Patil, Pramod Rastogi

Experimental Investigation of the Elastic Modulus of Timber by Using Density and Fiber Orientation

Wood is a material found in nature with distinct applications in construction engineering. For the sake of greenhouse gas emissions, wood has been widely used. Two essential factors, i.e. fiber orientation and density, of the timber were adopted in the prediction model proposed in this paper to obtain the modulus of elasticity (MOE) of the timber. Besides, a bending test was used to verify the accuracy of the prediction model. Good agreement was found between the results obtained from the prediction model and static bending test along the longitudinal direction. Therefore, the proposed model presented in this paper has an excellent feasibility of predicting the MOE of the timber to ensure the reliability and safety of wood construction.

Wei-Chung Wang, Tzu-Yu Kuo

Effect of pH on Microstructure and Properties of Ultrasonic-Assisted Electroless Ni-P Coatings

Ni-P coatings with various pH values (4.5~5.4) were fabricated on Ti6Al4V titanium alloy by ultrasonic-assisted electroless deposition. The effect of pH on the deposition rate and phosphorus content was studied, as well as pH on the surface morphology, phase structure and microhardness of the deposited Ni-P coatings. The results showed that the increasing pH enhanced the deposition reaction, and ultrasonic cavitation and mass transfer effect improved the catalytic activity of the substrate surface and the reaction system. So the deposition rate was increased. But the higher pH decreased the stability of the bath and precipitated NiHPO3, resulting in the decrease of deposition rate. With the increase of pH, the phosphorus content decreased at first and then kept stable (17 ± 0.45wt%),while the microhardness enhanced at first and then kept stable (605 ± 2HV). The ultrasonic-assisted electroless Ni-P coatings had the typical cauliflower-like morphology and microcrystalline structure characteristics.

Jingjing Cao, Xiaoyu Wang, Yifan Zhao, Guofang Kong

Tailoring the Toughness and Electrochemical Capacitance of CNT Reinforced Mortars

To unlock the contribution of carbon nanotubes in potential applications it is necessary to take into consideration the degree of their dispersion. In this work, a simple technique has been used for characterizing the degree of CNT dispersion in mortar based on values of the capacitive reactance measured using AC impedance spectroscopy. The relationship between capacitance values and fracture toughness provides valuable information on the actual CNT distribution in the matrix.

Maria S. Konsta-Gdoutos, Panagiotis A. Danoglidis, Myrsini E. Maglogianni



The Creep Resistance of Short-Fibre Reinforced Metal Matrix Composites

The creep resistance of two discontinuously reinforced with 20 vol.% alumina short-fibres magnesium composites were examined by performing a comparison between the creep properties of these composites and their magnesium matrix alloys AZ 91 and QE 22. It was found that the magnesium AZ 91 composite exhibits an improved creep resistance arising mainly from an efficient load transfer effect and the existence of a threshold stress, respectively. By contrast, the beneficial effect of reinforcement and the improved creep resistance of the QE 22 composite is significantly influenced by the creep loading conditions.

Vaclav Sklenicka, Kveta Kucharova, Milan Svoboda, Petr Kral, Marie Kvapilova, Jiri Dvorak

Adhesive Joint Fracture Under Combined Pulsed and Vibrational Loading

The strength of the adhesion joint under the combined vibrational-pulsed loading is considered. Beam and membrane models on elastic foundation is applied to simulate behavior of adhesion zone. The incubation time criterion is used to determine the threshold parameters of a load required to adhesive zone fracture. The solution of the differential equation describing the behavior of the adhesive zone is obtained by the Fourier method. Different types of combination of pulsed loading with high-frequency external fields are considered. It demonstrates that background vibration fields of even low intensity at certain frequencies can significantly reduce these critical values. The dependence of the threshold value of the external pulse on the model parameters is shown. The possible way to control to adhesive joint strength by background vibrational fields is suggested.

Yuri Petrov, Andrey Logachev, Nickolay Granichin, Grigory Volkov

Study on the Fracture Mechanism of the P91 Steel During Small Punch Tensile Testing

This paper investigates the fracture generation processing of the P91 steel during a small punch tensile test. P91 disc specimens, 8 mm in diameter and 0.5 mm in thickness, were tested in a small punch test rig at 600 °C using a constant displacement rate of 2 µm/s. Interrupted tests were performed to investigate the crack generation and evolution of P91 in small punch tensile tests. The disc-shaped specimens were deformed into domes of different depths during the tests. Cross-sectional microstructure analysis revealed that thinning and circumferential necking started to occur at the edge of contact before the maximum load was reached, and then significant point necking occurred in the circumferential necking area after the maximum load. The crack formed during the tests aligns with the plastic flow of the specimen. Alignment of crack propagation occurred in the plastic deformation direction, before achieving the maximum small punch load.

Hezong Li, Hao Chen, H. K. Al-Abedy, Wei Sun

Damage Accumulation and Growth Models for the Creep-Fatigue Interaction

The residual life prediction based on damage accumulation models for the BT3-1 titanium alloy are present. Mechanical properties were obtained at temperature 370 °C. Life prediction was based on the Kachanov–Rabotnov damage model for creep and the Duyi-Zhenlin model for fatigue. The contribution of each type of loading to the generalized damage parameter was calculated according to the law proposed by Skelton and Grandy. Damage accumulation laws were integrated into ANSYS software. Cyclic loading with a trapezoidal form cycle was simulated. The integrated model of damage accumulation under creep-fatigue interaction allows obtaining a fatigue life of structural elements. The model is recommended to be used for cases when the scalar damage parameter is justified.

A. V. Tumanov, V. N. Shlyannikov

Crack Growth and Plastic, Fracture Process and Damage Zones Behavior Under Mixed Mode Loading

Fatigue crack paths for inclined cracks are studied through experiments and computations under different mixed-mode loading. The experimental study of fatigue crack growth in the aluminum and titanium alloys and two types of the steels is performed on compact tension shear specimens. The cyclic fracture process and damage zone concepts are introduced and used for numerical analysis of the crack tip fields. The elastic K1, K2 and plastic KP stress intensity factors are calculated by finite element method to characterize the fracture resistance along the curvilinear trajectories in compact tension shear specimens. The influence of mode-mixity and elastic-plastic material properties on the behavior of three crack tip regions as a function of cyclic loading is demonstrated.

Valery Shlyannikov, Daria Fedotova

Miscellaneous (Computational Mechanics, Dynamics, Nanomaterials, Plasticity, Wave Propagation)


Parametric Resonance of a Micro-beam with Flexible Support Under Fringing Field Excitation

A new resonance structure with flexible support under electrostatic fringing field excitation is designed. This structure can be used in sensor. In this paper, the nonlinear frequency responses of the movable beam in resonance structure are analyzed by the Method of Multiple Scales. The effects of electrode thickness, slit gap and initial displacement on the vibration of the movable beam are investigated in detail. The key results are as follows. A smaller electrode thickness and slit gap can lead to a larger change of the actuated frequency, and they can also lead to a larger vibration amplitude. The initial displacement has an influence on the frequency response, but this influence is not obvious, since the electrostatic force is small when the initial displacement is not large. This resonance structure can avoid superposition of input signal and output signal. Thus, the signal-to-noise ratio and the accuracy of the sensor can be improved.

Zhichong Wang

Measurement of Elastic Nonlinearities Using the Fundamental Edge Wave Mode

Measurement of the nonlinear elastic properties of materials represents a great interest in engineering and materials science. Changes of these properties are often related to mechanical damage and applied stresses, which are paramount for maintaining integrity and safety of structures. Current ultrasonic techniques typically utilise bulk, Lamb, or Rayleigh waves to measure material nonlinearities, however, spatial and velocity dispersion make this a very difficult task, and the use of several (empirical) correction factors is usually required. In this work we suggest using the fundamental edge wave mode – a natural analogue of the classical Rayleigh wave propagating in a finite thickness plate – for the purpose of measuring elastic nonlinearities. Edge waves naturally avoid spatial dispersion as they are guided by the apex of a plate, thus avoiding the need for correction factors. Additionally, the fundamental edge wave mode can propagate long distances without significant attenuation under certain conditions. The outcomes of this study demonstrate that the measurement of material nonlinearities is achievable using the fundamental edge wave mode. A linear trend between the nonlinearity parameter and propagation distance is experimentally observed, which is predicated by theoretical studies. Therefore, potential applications of the fundamental edge wave mode are very promising for the evaluation of mechanical damage and measurement of applied or residual stresses.

James Martin Hughes, Andrei Kotousov, Ching-Tai Ng

Unsteady Axisymmetric Electro-Magneto-Elastic Oscillations of a Continuous Cylinder Under the External Displacement Field

In the present work is considered an axisymmetric time-dependent waves of an infinite cylindrical body. The body material is taken to be isotropic and electro magneto elastic. Piezoelectric effects are not taken into account. The deformation process is described by a system of equation with respect to radial and angular components of deformation of the body points in cylindrical coordinate system. In additional, it takes into account the effect of current density, surface charges, electric and magnetic fields. All parameters and ratios are reduced to dimensionless form. To solve the problem, are used the Fourier transformation of angles and the Laplace transformation of time. Then, the resulting expressions expansion in series in terms of a small parameter. The small parameter characterizes the relationship between mechanic and electro-magnetic fields. To move into the space of the originals using the inverse Laplace transformation via residue theorem.

Vladimir Vestyak, Vasily Scherbakov

Development of Micro-mechanical Models of Fatigue Damage

Accumulation of fatigue damage in high and low cycle regimes is largely associated with nucleation and development of irreversible plastic deformations and voids. The effect of these microstructural changes on conventional (second-order) elastic constants is typically very small, which makes experimental evaluation of the progressive fatigue damage accumulation difficult and the classical damage theories inapplicable. It was demonstrated in the past that the third-order elastic constants are sensitive to fatigue damage and these material constants can be evaluated using various ultrasonic techniques. The ultimate aim of this study is to develop micro-mechanical models, which link the micro-porosity and micro-plastic deformations, to the effective third-order elastic constants of the material. These models could provide a foundation for the evaluation of early fatigue damage, i.e. the damage prior formation of a micro-defect (crack), as well as the remaining fatigue life of structures.

James Vidler, Andrei Kotousov, Ching-Tai Ng

Research on Springback of 5A02 Aluminum Alloy Considering Thickness Normal Stress in Hydroforming

Springback is an unavoidable problem in sheet metal forming. When the amount of sheet springback exceeds the allowable range, it becomes a forming defect. In the process of hydraulic bulging, the fluid medium acts on the surface of the sheet uniformly instead of the rigid mold, so that the material is simultaneously stressed, which makes the deformation law of the material different from that of the sheet in the traditional rigid bulging. In this paper, the research on the springback of 5A02 aluminum alloy is carried out by taking the active hydroforming process of a typical shallow drawn rotatory body arc surface part as the research object. The theoretical analysis method is used to take the thickness normal stress into the theoretical calculation of the springback amount, and a theoretical springback amount calculation model of the three-dimensional state of stress. Numerical simulations are carried out under different loading paths with hydraulic pressure of 1, 2, 3, 10, 20 and 30 MPa. The influence and law of springback of the parts under different loading paths and different hydraulic conditions are also obtained.

Peicheng Jiang, Lihui Lang, Sergei Alexandrov

On the Friction Test for Metal Forming Applications

The ring compression test is a conventional test for identifying the friction law for metal forming applications. This test is very widely used but has a significant disadvantage. In particular, if the friction stress is high, then a sticking region occurs over a part of the friction surface. In this case, the interpretation of experimental results is difficult because the friction law at sliding is not valid over the sticking region. If the friction stress is very high, then this region occupies the entire friction surface. In this case, the process becomes insensitive to the friction factor at sliding at all. In order to overcome this difficulty and keep the conventional procedure for identifying the friction law, it is proposed to carry out the compression test between fat and conical dies. The geometry of the conical die should be chosen such that no sticking region occurs on the friction surface.

Sergei Alexandrov, Marko Vilotic, Dragisa Vilotic

From the Linear Theory of Elasticity to Bending Equations for Beams with Variable Cross-Section

A formulation of a boundary value problem to find natural frequencies of an inhomogeneous beam in the framework of the linear theory of elasticity is represented. The main attention in the article is paid to the analysis of transverse vibrations of beams with a variable cross-section. A system of two connected ordinary differential equations with variable coefficients is obtained in the framework of the linear theory of elasticity, by using semidiscrete approximations and a projection approach. Various bilateral energy quality estimates for approximate solutions that follow from the method of integro-differential relations are proposed. In the final part of the paper the advantages of the variational technique in problems of free vibrations of inhomogeneous beams are discussed based on a numerical example.

Boris Gusev, Vasily Saurin

On Different Representations of Equations for Beam with Variable Cross-Section

The main part of the paper is devoted to the formulations of the boundary value problem to finding natural frequencies of an inhomogeneous beam in the framework of the Euler-Bernoulli hypotheses. Three different formulations of the beam equation in displacements, momentums, and bending moments are discussed. Next, the possibilities to constructing various bilateral energy quality estimates for approximate solutions that follow from the method of integro-differential relations are investigated. In the final part, based on a numerical model example, the advantages of the variational technique in problems of free vibrations of inhomogeneous beams are discussed.

Vladimir Poliakov, Vasily Saurin

Shear Residual Stresses Induced by Torsional Loading

Residual stresses can be induced by fabrication processes and service conditions that lead to non-uniform deformations. In the standard test method for residual stress analysis by x-ray diffraction (EN 15305), the validation is done by using reference specimens with known normal residual stress. However, the method also stablishes restrictions to the values of both normal and shear stresses, although the latter can be negligible with respect to the former. Consequently, it would be interesting to have a reference specimen with known shear residual stresses for independent validation. In the present work, torsion tests have been performed in a steel sample with the aim of producing shear residual stresses. Residual stresses were simulated by FEM modelling and measured by X-ray diffraction.

D. Pérez Gallego, J. Ruiz Hervías, D. A. Cendón Franco

Elastoplastic Analysis of Re-entrant Cell Formation in Auxetic Foams Under Compression and Heat Treatment

Negative Poisson’s ratio of polymeric foam can be obtained by using the thermal transformation method to convert cell shape from convex to reentrant ones. In this work, the large-deformation finite element analysis is performed to quantify the magnitudes of compression and temperature for subsequent heat treatment to reduce elastic recovery, such that the reentrant shape can be maintained when the compression is removed. The amount of compression and temperature for heat treatment that can produce NPR foam can be used as a guide for experimental investigations, instead of trial-and-error methods to determine manufacturing parameters.

Yun-Che Wang, Tsai-Wen Ko, Hsiang-Wei Lai

Analytical Modeling of the Thermo-Mechanical Behavior of a Friction-Pendulum Seismic Isolator

The contribution outlines the modeling of the thermo-mechanical behavior of a curved surface slider employed as a device for passive seismic isolation of buildings and structures. The Lagrange formalism is employed to derive the equation of motion of the slider on the spherical surface of the lower sliding pad. Besides the equations of motion, accurate modeling requires the formulation of the response of the friction interface. Previous studies have shown the dependence of the friction coefficient on the sliding velocity. Reportedly, the rise in temperature during sliding also affects the magnitude of the friction coefficient. The model is being developed in order to be further integrated into a finite element model of a base-isolated structure.

Todor Zhelyazov

Symposium on Theoretical and Experimental Approaches in Mechanics of Solids with Nonhomogeneities and Defects, by Roman Kushnir


Damage Accumulation and Limit State of Welded Pipelines with Corrosion-Erosion Metal Loss Due to Ultra-Low-Cycle Fatigue

Analytical prediction of the reliability of pipelines under ultra-low-cycle loading demands the consideration of the several interrelated damaging factors, those determine the limit state of specific structure. For that in this work it was developed the complex numerical technique for finite-element assessment of damage accumulation and limit state of welded pipelines with corrosion-erosion metal loss. The ductile mechanism of subcritical damage was considered as the main one that assumes certain material softening due to voids nucleation and accumulation up to limit state. Additionally, it was necessary to take into account the material hardening and softening in plastic strain that was described by isotropic and kinematic mixed hardening laws. This complex approach allowed revealing the major physical-mechanical mechanisms of structure failure depending on the type of external loading, size of the local metal loss and the features of welding on the limit state of typical pipeline element.

Alexey Milenin, Elena Velikoivanenko, Galina Rozynka, Nina Pivtorak

Unsteady Elastic-Diffusion Oscillations of a Simply Supported Kirchhoff Plate Under the Distributed Transverse Load Action

We study unsteady vibrations of a isotropic Kirchhoff plate considering mass transfer. In the general case, the plate is subjected to tensile and shear forces as well as bending moments and torque. Densities of diffusion fluxes are also defined. For the problem formulation, we use the coupled elastic diffusion continuum model in a rectangular Cartesian coordinate system. Further, the unsteady model of an elastodiffusive Kirchhoff plate is obtained using the d’Alembert variational principle. The solution is sought in integral form. To find the Green’s functions, we use the Laplace integral transform and Fourier series expansion.

O. A. Afanasieva, A. V. Zemskov

A Dynamic Contact Problem of Torsion that Reduces to the Singular Integral Equation with Two Fixed Singularities

An elastic cylinder of finite length, one of the ends of which is perfectly coupled to the surface of the elastic half-space is considered. A round rigid plate of the same radius is coupled to the other end of the cylinder, and is loaded the torsion moment that is harmonic depend of time. The surface of the half-space outside the contact area with the cylinder and the side surface of the cylinder are been unload. The formulated boundary problem is reduced to a singular integral equation for a function related to stresses in the contact area of the cylinder and half-space. Since the kernel of this integral equation contains fixed singularities, a numerical method for solving this equation the is main result. After solving the integral equation, approximate formulas for calculating the contact stresses .

V. Popov, O. Kyrylova

Some Dynamic Problems for Layered Composites

The problems of constructing analytical solutions of non-stationary dynamic problems for layered composites in the case when all the layers are linearly viscoelastic, but their hereditary properties are determined by only one kernel, the same for all layers, are considered. In this case, the Poisson’s ratio of the material of each layer becomes time-independent. A special case is considered when all the layers are linearly elastic. The perturbation propagation region is assumed to be limited. The integral Laplace transform in time is applied, followed by inversion. Sufficient conditions, under which all the poles of the solution in the transforms are simple, are formulated. The question of the location of these poles is considered. An example is given of constructing an analytical solution to a two-dimensional non-stationary dynamic problem for a cylindrical body consisting of elastic or viscoelastic layers under the above assumption. The results of a study of two-dimensional transient wave processes in a layered cylindrical elastic body, based on the corresponding analytical solution, are presented.

Sergey Pshenichnov

The Influence of Geometric Parameters on the Bearing Capacity of Transformable-Volume Structure

The metal transformable-volume structure (TVS) for aerospace purposes, which consist of corrugated conical sections, was investigated. The design scheme of the TVS with a minimum mass should provide stability to the action of inertial loads in operating conditions in space orbit. The influence of the main geometric parameters of TVS made of stainless steel on the bearing capacity are determined. The effect of corrugation of the conical sections on natural frequency of TVS was considered. The results of calculating estimation of stress-strain state of the TVS under specified for space orbital station inertial loads were showed.

L. M. Lobanov, V. S. Volkov, O. V. Makhnenko, S. M. Kandala, Y. V. Borovyk

The Influence of Mixed Conditions on the Stress Concentration in the Neighborhood of Interfacial Inclusions in an Inhomogeneous Transversely Isotropic Space

Two mixed non-axisymmetric problems on an absolutely rigid circular interphase inclusion in a piecewise-homogeneous trans-versal-isotropic space are considered. One face of inclusion is in conditions of smooth contact, and on the other, conditions of full adhesion to the medium are realized or there is no contact with the medium. Using exact solutions to these problems, the influence of the boundary conditions on the stress concentration in the neighborhood of the inclusion is analyzed. In particular, it has been established that under mixed conditions the stresses have a power-law singularity, the indices of which depend on the elastic constant transversally isotropic half-spaces. In the case of detachment, the power-law singularity is amplified by oscillatory multiplier.

Oleksandr Kryvyi, Yurii Morozov

On an Approach to the Thermoelastic Analysis of Nonhomogeneous Solids

A general approach to the analysis of thermoelastic response of solids exhibiting spatial or thermal variation in their material properties is addressed in this study. The approach is based on the idea of the direct integration method, which allows for the construction of analytical solutions to the relevant thermoelasticity problems in explicit functional form satisfying the thermal and force boundary conditions on the entire surface of a solid.

Roman Kushnir, Yuriy Tokovyy

The Stress State Near the Corner Point of the Interface of Piecewise Homogeneous Plane in the Presence of Interfacial Shear Cracks

In the framework of plane deformation, a piecewise homogeneous isotropic elastic body with interfacial shear cracks near the corner point of the interface is considered. The exact solution of the corresponding problem of the theory of elasticity for a wedge-shaped body is constructed by the Wiener-Hopf method. Based on the constructed solution, the behavior of stresses near the corner point is investigated.

V. M. Nazarenko, A. L. Kipnis

Coupled Non-stationary Longitudinal Vibrations of an Infinite Electromagnetoelastic Rod

We study the associated non-stationary longitudinal vibrations of an infinite electromagnetoelastic rod. It is assumed that the material of the rod is a homogeneous isotropic conductor. In this case, the initial electromagnetic field, the Lorentz force, Maxwell’s equations and the generalized Ohm’s law are taken into account. Assuming that the desired functions depend only on the longitudinal coordinate, using the corresponding relations for the shells, a closed system of equations of motion is obtained. The desired functions are assumed to be bounded, and the initial conditions to be zero. The Fourier transform in the coordinate and the Laplace transform in time, as well as the small parameter method characterizing the relationship of mechanical and electromagnetic fields, are used to solve this problem. The solution is presented in integral form with the cores in the form of Green functions for which images and originals are constructed. An example of calculation is given.

Thong D. Pham, Dmitry V. Tarlakovskii, Vladimir A. Vestyak

The Effect of Cracks Interaction in Materials Under Loading Along Cracks

The non-classical problems of the fracture of materials loaded along the cracks they contain are analyzed. Two fracture mechanisms are considered, namely, the fracture of materials with initial (residual) stresses acting in parallel to the surfaces of cracks location and the fracture of the bodies compressed along cracks. In the study of such problems, a new combined approach developed in the framework of the three-dimensional linearized mechanics of deformable bodies is used. The results of the investigation of two- and three-dimensional problems for typical configurations of parallel coaxial Mode I and Mode II cracks are presented. The effect of residual stresses on stress intensity factors is analyzed for highly elastic materials and composites. The compressive strength for bodies with interacting cracks located in parallel planes under compression is calculated using the approach mentioned. The crack length (diameter), mechanical properties of materials and the mutual position of cracks were found to influence the critical fracture parameters.

Viacheslav Bogdanov, Vladimir Nazarenko

Safe Loading of the Orthotropic Plate with Periodic System of Collinear Cracks

On the basis of a modified $$ \delta_{c} $$δc-model of crack, the safe loading of an orthotropic plate with periodic system of collinear cracks is studied. The plate material is satisfying the strength condition in general form. The relations for the determination of major parameters of the crack model (the size of process zones, stresses in these zones, and the crack-tip opening displacements) are deduced. The mechanism of fracture of the plate containing a periodic system of collinear cracks is investigated. The influence of the degree of anisotropy and geometric parameters of the problem on the formation of the process zones and limiting state of the elastic orthotropic plate is revealed. The region of safe loading of an orthotropic viscoelastic plate with cracks is determined. The influence of the rheological parameters of the material on the region of safe loading is analyzed.

Olga Bogdanova

Boundary Element Analysis of Partially Debonded Shell-Like Rigid Inclusions in Anisotropic Medium

The paper presents boundary element models of anisotropic thermoelastic medium containing partially debonded shell-like rigid inclusions, which possess high rates of heat conduction. Boundary integral equations are derived, which account for partial debonding of a shell-like inclusion at one of its faces. Special attention is paid to full debonding of a rigid shell at two faces simultaneously (bilateral debonding). Obtained equations are implemented in a fast and accurate boundary element approach.

Heorhiy Sulym, Nataliia Ilchuk, Iaroslav Pasternak

The Transmission of an Acoustic Wave Through a Composite Plate with Energy Dissipation in a Material Taken into Account Based on Three-Dimensional Equations of Elasticity Theory

The problem of a plane monoharmonic sound wave passage through a thin composite rectangular plate hinged in the opening of an absolutely stiff dividing wall has been considered on the basis of two-dimensional in spatial coordinates motion equations. These equations have been constructed by the reduction of three-dimensional equations on the basis of the discrete layered model of a multilayer plate deformation at small displacements and deformations with account of the internal damping of layers according to the Kelvin–Voight model. Behavior of acoustic media has been described by the classical wave equations based on the model of an ideal compressible fluid. The exact analytical solutions of the formulated problem have been constructed. The dependence of sound insulation properties and parameters of the stress-strain state of a composite plate reinforced with carbon fiber textile on the incident sound wave frequency was studied. It is shown that under high-frequency acoustic impact, the deformation mechanics of the structures made of fiber reinforced composite must be described by refined equations of motion as they have a high degree of accuracy and intensionality since the formation of the stress-strain state in them is almost three-dimensional with components of the same order.

V. N. Paimushin, R. K. Gazizullin

Vibration of the Plate with Integral Layer Damping: Experimental and Theoretical Studies

The paper discusses the classical methods of surface damping of bending vibrations in thin-walled structures. Furthermore, the perspective integral version of a damping coating has been proposed. Such coating consists of two layers of material with pronounced viscoelastic properties with a thin reinforcing layer of high modulus material between them. Dynamic tests of cantilevered duralumin specimens under the damped bending vibrations were carried out using the created experimental setup. The purpose of these tests is to compare the effectiveness of the known and proposed methods of surface vibration damping. The influence of aerodynamic drag forces on the vibration damping of specimens is noted. A refined finite element model of an elongated plate with an integral layer damping is constructed on the basis of the four-layer finite element. This model allows taking into account the effect of transverse compression of damping layers under high-frequency deformation. The analysis of the stress-strain state of the damping layers of a simply supported elongated plate under resonance vibrations in several lower eigenmodes has been carried out. The analysis showed a significant increase in the transverse compression stresses of the damping layers with frequency increasing.

V. N. Paimushin, V. A. Firsov, V. M. Shishkin, R. K. Gazizullin

Thermomagnetoelectroelasticity of Bimaterial Solids with High Temperature Conducting Interface and Thin Internal Inhomogeneities

This work studies the problem of a thermomagnetoelectroelastic anisotropic bimaterial with imperfect high temperature-conducting coherent interface, which components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus the Somigliana type integral formulae and corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high temperature-conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented.

Andrii Vasylyshyn, Iaroslav Pasternak, Heorhiy Sulym

Fracture of Composite Materials Under Compression Along Cracks

The axisymmetrical problems of fracture of bodies with near-surface penny-shaped cracks and two parallel penny-shaped cracks under compressive loads directed along cracks are considered. In the situation examined the start of the process of material fracture is determined by the local loss of stability of the equilibrium of the material surrounding cracks. There are two approaches that are used to investigate such problems, namely, so-called “beam approximation” based on applied theories of mechanics of thin-walled structures and the approach in the framework of the rigorous three-dimensional linearized theory of stability of deformable bodies. According to the second approach we reduce the problems to systems of integral Fredholm equations and then to system of algebraic linear equations with use the Bubnov-Galerkin method and numerically analytic technique. As an example we present the numerical calculation for a composite material. The values of critical loads corresponding to the start of fracture are obtained for small and large distance between the cracks (or between the crack and the body surface).

Mykhailo Dovzhyk, Viacheslav Bogdanov, Vladimir Nazarenko

Development of Welded Elements of the Railway Freight Car Bogie with Increased Characteristics of Fatigue Resistance and Survivability

In last years in the railroad territory of 1520 mm accidents have often occurred due to the destruction (failure) of the casting elements of three-element freight car bogie. The quality and durability of load-bearing elements, which is traditionally produced by casting technology, is insufficient. The development of new welded designs of the load-bearing elements were carried out on the basis of wide use of mathematical modeling to determine the stress-strain state of the welded elements under the action of regulated loads and to make the assessment of strength according to Ukrainian standards and current world approaches. The accelerated fatigue tests on prototypes were carried out, which showed that the service life of the welded structure of the side frame is ten times longer than the service life of the cast structure, and its survivability is longer in several times.

L. Lobanov, O. Makhnenko, A. Pustovoy, S. Solovey

Electron Beam Additive Technology Optimization Using Mathematical Modeling

Additive manufacturing technology are developing fast these days. Economical profit of manufacturing parts with complex geometry which have either hollow section or complex three-dimensional curvature, using 3D printers are higher than using standard manufacturing methods. Which means that 3D printer could be an alternative to traditional ways of manufacturing. This technology used in aerospace and medicine right now, and have a future in other industries. Currently the technology of wire electron xBeam 3D Metal Printer of parts with complex geometry from titanium alloy has been developing in Ukraine. Using of mathematical modeling for optimization of the technology parameters is very promising.

Oleh Makhnenko, Nikita Ananchenko, Stepan Kandala, Andriy Babenko

Non-stationary Contact Problems for Thin Shells and Solids

A spatial non-stationary contact problem with moving boundaries of the interaction region for a thin elastic cylindrical shell and an absolutely rigid indenter bounded by a smooth convex surface is considered. A closed mathematical formulation is given and a system of resolving equations is constructed. The system of resolving equations is based on the spatial-temporal integral equation resulting from the principle of superposition and contact conditions. The core of this equation is the transient function for the cylindrical shell. To a closed system of resolving equations, it is supplemented by a kinematic relation for determining the moving boundary of the contact area and the equation of motion of the indenter as an absolutely rigid body. An algorithm for solving the spatial non-stationary contact problem for an infinitely long cylindrical shell and absolutely rigid indenter in the case of a normal impact on the side surface of the shell is constructed and implemented. Examples of calculations are given.

Grigory Fedotenkov, Dmitry Tarlakovskii

Shear Buckling Mode and Failure of Sandwich Specimen Facing Layer Under Four-Point Bending

The geometrically and physically nonlinear problem of four-point bending of a sandwich specimen with a transversally flexible core and facing layers from fiber reinforced plastic, characterized by a nonlinear relationship between transverse shear stresses and the corresponding shear strains, is formulated. The statement of the problem is given taking into account the contact interaction of the facing layers with the support and loading rollers, a numerical method for solving it is developed based on the finite sum method (method of integrating matrices). Equations based on the refined kinematic model of S.P. Tymoshenko taking into account the transverse compression of the facing layers and the equations of elasticity theory for the core, simplified in the framework of the model of the transversally flexible layuer. The latter allow integration along the transverse coordinate when introducing as unknown transverse shear stresses in the core, constant in thickness. An investigation of the prebuckling and postbuckling behavior of the specimen was carried out, based on the method of continuing the solution with respect to the parameter, when the transverse shear strain in the loaded facing layer was chosen as the parameter. It was shown that during tests for four-point bending of specimens of the class under consideration, their failure can be due to the implementation of transverse-shear buckling modes of the facing layer in the vicinity of the loading roller.

V. N. Paimushin, M. V. Makarov, S. A. Kholmogorov, M. A. Shishov

Model of Low-Cycle Deformation of Stainless Steel Under Soft Loading

A variant of the plasticity model is proposed that allows describing the kinetics of plastic deformation of materials under different modes of low-cycle loads. In the model, the radius of the flow surface is represented as a function depending on temperature and accumulated plastic deformation, and the coordinates of the center are described by two Armstrong-Frederick-Kadashevich-type evolutionary equations, the first of which additionally introduces corrective material functions. Changes in plastic deformations in the model are determined based on the associated flow law. Receiving material functions of the model and testing it was carried out on the basis of the results of experimental study of the deformation of a cylindrical sample under soft cyclic loading with maximum control and minimum effort in the cycle. The experiments were carried out on the Amsler HA 100 servo-hydraulic fatigue testing machine. Comparative analysis of the results of numerical simulation and experiment shows that the proposed model allows us to describe the main effects of plastic deformation of the material under consideration under soft asymmetric loads (displacement of the plastic hysteresis loop and reduction of its width) quite well.

Vasilii Gorokhov, Sergei Kapustin, Yuriy Churilov, Dmitriy Kazakov, Dmitriy Zhegalov

Creep and Long-Term Strength of Structures

The issue of evaluating strength and service life is discussed as applied to structures performance of which is characterized by multi-parametric nonstationary thermal-mechanical effects. The major degradation mechanisms of structural materials are considered. In the framework of mechanics of damaged media, a mathematical model describing the processes of viscoplastic deformation and damage accumulation due to creep is developed. The results of numerical simulation of the carrying capacity of a power plant reactor vessel in the event of a hypothetical emergency are presented. A number of characteristic features accompanying the deformation and failure processes connected with the time and place of macrocrack nucleation, the stress-strain state history and damage degree are given. By comparing numerical and experimental results we can conclude that the proposed constitutive relations of MDM adequately describe degradation of the initial strength properties of the material in terms of creep and long-term strength.

Ivan Volkov, Leonid Igumnov, Svetlana Litvinchuk

Mathematical Modeling of Nonlinear Dynamic Deformation and Failure of Metal-Plastic Shells of Revolution

A technique for numerical analysis of nonlinear dynamic deformation and progressive failure of multi-layered metal-plastic shells of revolution is developed with account for their strain-rate dependent strength characteristics. The geometric dependencies are formulated on the basis of quadratic version of the nonlinear theory of elasticity. The relationship between stress and strain tensors in a composite macrolayer is based of Hooke’s law for an orthotropic body combined with the theory of effective modules. The process of progressive layer-by-layer failure is described in the framework of the degradation model of stiffness characteristics. The strain rate dependent stiffness and strength characteristics are accounted for. An energetically consistent system of equations of motion is constructed using the principle of possible displacements. A numerical method for solving the problem is based on an explicit variational-difference scheme. The proposed technique was verified on the problem of unsteady deformation of a cylindrical shell subjected to pulse pressure.

Leonid Igumnov, Nikolai Abrosimov, Nadezhda Novoseltseva, Vasilii Gorokhov

Impact of Transient Pressure on a Half-Space with Membrane Type Coating

The unsteady influence of an external load on the base, which is an elastic half-space with a membrane-type coating is investigated. The load acting on the “half-space-membrane” system is directed normally to the surface of the membrane and is a function that depends on the coordinate and time.A system of resolving equations is built. Its basic equation follows from the boundary condition, which corresponds to the equality of normal displacements on the surface of the half-space to the deflections of the membrane. The normal displacements of half-space and deflections of the membrane are connected with contact pressure and stresses by integral relations based on the principle of superposition. The basic equation is supplemented by initial conditions to a closed system of resolving equations.To solve the system of resolving equations, a numerical-analytical algorithm based on the method of quadratures is used.The results of calculations for the external load specified by various functions are presented.

Elena Mikhailova, Grigory Fedotenkov, Dmitry Tarlakovskii

Fracture Nanomechanics, Fatigue and Fracture at Small Scales (experiments and simulations) by Pasquale Gallo


Some Considerations on Stress Intensity Factor at Atomic Scale

This work reviews recent molecular statistics (MS) numerical experiments of cracked samples, and discusses the crack-tip region stress field of ideal brittle materials. Continuum-based linear elastic fracture mechanics, indeed, breaks down at extremely small scale, where the discrete nature of atoms is considered. Surprisingly, recent results have shown that the concept of stress intensity factor (SIF) is still valid. In this work, by means of MS simulations on single-edge cracked samples of ideal brittle silicon, it is shown that the stress intensity factor derived from the virial stress may be useful to describe the fracture at extremely small dimensions and to quantify the breakdown of continuum-based linear elastic fracture mechanics. However, it is still debated whether a continuum-based concept such as the “stress” should be applied to a system made of atoms.

Pasquale Gallo

Initial Intergranular Cracking of Ni-Base Superalloys Due to the Degradation of the Crystallinity of Grain Boundaries Under Creep-Fatigue Loading

The mechanism of the drastic decrease in the lifetime of Ni-base superalloy, Alloy 617 under creep-fatigue loading at elevated temperatures was clarified by using EBSD (Electron Back-Scatter Diffraction) analysis. The degradation process was monitored by using an intermittent creep-fatigue test and EBSD analysis. The change of the crystallinity of grains and grain boundaries was quantitatively analyzed by using the image quality (IQ) value obtained from the EBSD analysis. The IQ value indicated the density of defects such as vacancies, dislocations, local strain, and so on. The decrease in the IQ value corresponded to the decrease in the crystallinity of the observed area. The accumulation of fine voids was found to be accelerated under the creep-fatigue loading, and it caused the drastic decrease of not only the IQ value, but also the strength of the grain boundaries. Intergranular cracking started to occur when the crystallinity of grain boundaries decreased to the critical value due to the degradation of the crystallinity caused by the local accumulation of dislocations and voids around the grain boundaries.

Wataru Suzuki, Yifan Luo, Kenta Ishihara, Kens Suzuki, Hideo Miura

Characterization of Microstructurally Small Fatigue Crack Behavior

Aiming to understand the fracture mechanism accompanying the small fatigue crack propagation in polycrystalline metallic materials like steels the full-field strain measurement using digital image correlation (DIC) method was performed. The developed experimental approach was applied to study the small fatigue crack behavior in body-centered Fe-Cr ferritic stainless steel with the relatively large grain size of about 350 µm. The high spatial measurement accuracy of the strain field analysis was performed using the unique patterning technique with a characteristic speckle size of approximately 10 µm.

Evgenii Malitckii, Heikki Remes, Pauli Lehto, Sven Bossuyt

An Atomic-Level Unified Criterion for Brittle Fracture

This paper aims to propose a unified criterion for brittle fracture of general (blunt) notches and ideal (sharp) cracks. A new fracture parameter, i.e., atomic energy release rate (ERR), for which the atomic discrete nature is fully taken into account, is defined based on the concept of atomic fracture mechanics (AFM). The results show that the proposed atomic ERR criterion works well for a nano-sized notch even when the notched sample becomes extremely small. Compared with an ideal crack, it is found that the magnitude of the critical atomic ERR at fracture is in good agreement with that of an ideal crack. Hence, brittle fracture of both a notch and a crack can be described by using a unique fracture parameter, providing a unified description at the atomic level.

Kai Huang, Takashi Sumigawa, Takahiro Shimada, Takayuki Kitamura

Fatigue of Micro/Nano Metals

As materials with nanoscale dimensions are used in various industrial applications such as semiconductors, sensors, and micro- or nano-electromechanical-systems, the investigations on their mechanical behavior have been attracting many engineers/researchers. Especially, the knowledge on fracture mechanics/mechanism in the nanometer scale becomes important in terms of the reliability of small devices. Of course, this contributes an essential understanding of the strength of macro-components as well. The fatigue behavior is one of the key issues in terms of reliability.Extensive experimental works have been conducted on the crack initiation mechanism in the fatigue of bulk metals. These have reported that the dislocation structures induce specific slips on the surface known as persistent slip bands (PSBs), which brings about a crack on the surface. However, the size of under-structure is in micron-scale independent of specimen size. As small metals in the micron- or nanometer-scale cannot have enough space to form the understructure, the cracking mechanism must be different from the one of bulk counterparts. My team has investigated the fatigue behavior of micro- and nano-metals in this decade [1–11]. In this talk, we present the characteristic fatigue damage/failure process and mechanics of small metals. Especially, we introduce our novel experimental methodology of TEM/SEM in situ observations for the investigation.

Takayuki Kitamura, Takashi Sumigawa, Kai Huang


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