Challenges in Mechanics of Time Dependent Materials, Volume 2

Frontmatter

Chapter 1. Cracking and Durability of Composites in a Marine Environment

Abstract

New renewable marine energy sources are increasingly being pursued as alternatives since they represent an important political and economic challenge for countries. Among these new energy sources, marine tidal turbines are growing considerably. Manufacturers used thick composite material to design most of the tidal turbine blades. To ensure the lifetime of the latter, it is necessary to develop damage models that take into account sea water, and analyse its effects on composite materials.

This paper presents results from laboratory tests that were conducted to investigate the cracking of composite materials before sea water ageing. Two testing methods, image processing and acoustic emission (AE) techniques were used to evaluate the crack density within the material. Samples of the Infused and Pre-preg materials with a [0₂, 90₂]_s stacking sequence were prepared and tested in tension on an electro-mechanical testing machine. Under these stresses, the material response results in a release of energy in the form of transient elastic waves that are recorded by AE sensors. By means of the AE technique, the monitoring of material damage lies in the ability to identify the most relevant descriptors of cracking mechanisms. The latter are identified by clustering the AE data. A K-means++ algorithm was used, and two AE features—peak frequency and number of counts—represent adequately the AE events clustering. This unsupervised classification allows the AE events that were generated by intra-laminar cracks to be identified. Results show a good correlation between normalized crack density evaluated by image processing, and the one monitored by means of AE cluster analysis.

Malick Diakhate, Nicolas Tual, Nicolas Carrere, Peter Davies

Chapter 2. Analyses of Nanoscale to Microscale Strength and Crack-Tip Stresses Using Nanomechanical Raman Spectroscopy in IN-617

Abstract

In this research, Inconel 617, a solid solution Ni–Cr–CO–Mo superalloy, was studied in the temperature range of room temperature to 1073 K (800 °C) for temperature dependent strength and crack propagation behavior. Elastic modulus, hardness, creep exponent, creep strain rate and thermal activation volume of the different alloy 617 samples were studied through nanoindentation method. Indentation size effect (ISE) was studied in terms of hardness variation as a function of loading depth and temperature. Three-point bending tests for in-situ crack tip stress measurements were performed on the samples with an initial crack to measure crack tip plastic stresses under applied load. A relation between indentation depth and hardness was used to predict strain gradient length scale variation from 1.008 μm at room temperature and to 1.876 μm at 673 K then decreasing to 1.228 μm at 1073 K.

Yang Zhang, Debapriya Pinaki Mohanty, Vikas Tomar

Chapter 3. High Creep Resistance of Titanium Aluminides Sintered by SPS

Abstract

Reducing fuel consumption, noise, and greenhouse gas emission of airplanes engines requires to use lighter materials. Titanium Aluminides (TiAl) are of great interest to be employed for high temperature applications like turbine blades as they are twice lighter than superalloys currently used. A few years ago, two engines produced by GENERAL ELECTRIC and SNECMA-SAFRAN including TiAl turbine blades have been certified. However, TiAl alloys still suffer from a poor ductility at room temperature, a difficult and expensive manufacturing process, and a limited creep resistance at working temperature. We adapted the Spark Plasma Sintering, a powder metallurgy technique, to produce near-net shape turbine blades with an optimized TiAl alloy containing heavy elements to enhance the creep resistance. In this paper, we will present a study of creep properties under extreme conditions such as 700 °C/300 MPa of TiAl alloys, sintered by SPS, able to resist more than 4000 h with a minimum creep rate of 3.5 × 10⁻⁹ s⁻¹. These outstanding properties will be correlated with microstructure features, chemistry, and deformation mechanisms.

Thomas Voisin, Jean-Philippe Monchoux, Marc Thomas, Alain Couret

Chapter 4. An Investigation of the Temperature and Strain-Rate Effects on Strain-to-Failure of UHMWPE Fibers

Abstract

During a ballistic impact, Ultra High Molecular Weight Polyethylene (UHMWPE) fibers are subjected to high temperatures and high strain-rates. Their tensile strength increases with increasing strain-rate and decreases with increasing temperature. To understand the impact of both factors simultaneously, a single fiber heater has been fabricated to heat UHMWPE fibers up to the melting temperature (~148 °C) to measure the change in mechanical properties as a function of temperature and strain-rate. Custom grips have been fabricated for use with the single fiber heater and performed well across all strain rates and temperatures in this study. 251 tensile tests have been conducted on 10-mm gage length UHMWPE single fibers at temperature-strain-rate combinations spanning five strain-rates between 10⁻³and 550 s⁻¹ and 11 temperatures from 20 to 148 °C. A non-failure boundary is created by temperature-strain-rate combinations where fibers can be strained to 25 % without mechanically failing. This occurs at 75 °C for 10⁻³ s⁻¹, 100 °C for 10⁻² s⁻¹, 130 °C for 10⁻¹ s⁻¹, 148 °C for 10⁰ s⁻¹, and fail regardless of temperature at 550 s⁻¹. It is estimated that for similar mechanical response, an increase in temperature of 25–30 °C is equivalent to lowering the strain-rate by one decade for strain-rates between 10⁻³ and 10⁻¹ s⁻¹. At 550 s⁻¹ strain-rate, there was minor change in the strain-to-failure from 20 to 145 °C indicating strain-rate is the dominant factor.

Donald R. Jenket II, Amanda M. Forster, Nick G. Paulter Jr., Tusit Weerasooriya, Carey A. Gunnarsson, Mohamad Al-Sheikhly

Chapter 5. Life Prediction of CFRP Laminates Based on Accelerated Testing Methodology

Abstract

The accelerated testing methodology (ATM) developed by the authors is introduced for predicting the long-term life of CFRP laminates by using the static, creep and fatigue strengths of them measured at a short term and various temperatures. First, the time-temperature superposition principle (TTSP) held for the viscoelasticity of matrix resin is explained by using the viscoelastic model. Second, the master curves of these strengths of CFRP laminates in the wide range of failure time at a reference temperature are constructed using TTSP for the viscoelasticity of matrix resin. Third, the master curves of CFRP strengths are statistically formulated based on Christensen’s viscoelastic crack kinetic theory. Finally, the applicability of life prediction by ATM is discussed for various CFRP laminates and structures.

Yasushi Miyano, Masayuki Nakada

Chapter 6. Rate Dependent Interfacial Properties Using the JKR Experimental Technique

Abstract

Using the geometry of a rigid spherical cap on an infinite half-plane of rubber we have directly measured the contact area and the interfacial forces which arise upon loading and unloading as a function of maximum applied compressive load and loading rate. Key points are an observed hysteresis, due to viscous loss, and tensile pull-off force, due to the attractive surface interactions. We rationalize the results using the JKR model of viscous contact mechanics. Such experiments are pertinent to the problem of rate dependant damage mechanics in highly-filled particulate composites with viscous matrices.

D. M. Williamson, N. R. Hamilton, A. P. Jardine

Chapter 7. Bio-based Composites as Thermorheologically Complex Materials

Abstract

Because of their structure, natural fibers exhibit nonlinear viscoelastic behavior. Thermoset resins also behave in a similar way. With the increase in structural applications of bio-based composites, the long-term creep behavior of these materials becomes a significant issue. Time-Temperature superposition (TTS) provides a useful tool to overcome the challenge of needing a long time to perform creep tests. TTS principle assumes that the effect of temperature and time are equivalent when considering the creep behavior. In this study, frequency scans of flax/VE composites were obtained at different temperatures and storage modulus, loss modulus and tan δ were recorded. Application of horizontal and vertical shift factors to all three viscoelastic functions were studied. In addition, short-term strain creeps at different temperatures were measured and curves were shifted both with only horizontal, and with both horizontal and vertical shift factors. Resulting master curves were compared with a 24-h creep test and two creep models. Findings revealed that use of both horizontal and vertical shift factors will result in a smoother master curve for viscoelastic functions, while use of only horizontal shift factors for creep data provides an acceptable creep strain master curve. Consequently flax/VE composites can be considered as thermorheologically complex materials.

Ali Amiri, Chad Ulven

Chapter 8. Viscoelastic Properties of Longitudinal Waves in a Hollow Cylinder

Abstract

The attenuative and dispersive properties of longitudinal waves propagating in a viscoelastic materials over a wide range of frequencies were examined in this work. The first order mode vibrations of the waves propagating in a viscoelastic solid bar were measured, and the material properties were determined in the previous research. The ultrasonic wave propagation experiments by using the ultrasonic transducers having several characteristic frequencies were carried out with the hollow cylinder of a polymethyl methacrylate (PMMA) material. Then, the material properties are identified as a 5-element solid model based on the three dimensional exact theory. As a result, the attenuative and dispersive properties were able to be determined more accurately by taking into account only the first order mode vibration in the low frequency region and both the first and second order mode vibrations in the high frequency region.

T. Tamaogi, Y. Sogabe

Chapter 9. Evaluation of Viscoelastic Characteristics Under High Strain Rate by Impact Test

Abstract

In this research, the characteristics of a viscoelastic material under high strain rate are evaluated by use of a Split-Hopkinson pressure bar method. Tests are performed under several strain rates at various temperatures. A high-speed camera at the speed of one million frames per second is used to observe the strains. The validity of the experimental results is evaluated by comparing with the results obtained from digital image correlation. In addition, the time-temperature superposition principle is verified by comparing the impact and static experiments at the various temperatures.

K. Tsuchihashi, S. Yoneyama

Chapter 10. Phase Changes in Embedded HMX in Response to Periodic Mechanical Excitation

Abstract

It is well known that energy can be spatially localized when explosives are mechanically deformed; however, the heat generation mechanisms associated with this localization process are not fully understood. In this work, mesoscale hot spot formation in ultrasonically-excited energetic materials has been imaged in real-time. More specifically, periodic, mechanical excitation has been applied to Dow Corning Sylgard^® 184/octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) composite materials using contact piezoelectric transducers resulting in heating at various crystal locations. A thermally-induced phase transition from a β to δ non-centrosymmetric crystal structure for HMX results in the frequency doubling of incident laser radiation and can be used as a temperature proxy. In light of this, a high-repetition-rate 1064 nm Nd:YAG laser has been used to illuminate discrete HMX crystals, and a 532 nm filter has been applied to capture only the light emitted from δ-phase second harmonic generation (SHG). The visualization of δ-phase initiation and growth is useful for determining both heat generation mechanisms and heating rates at crystal/crystal and/or crystal/binder interfaces and contributes to the understanding and prediction of hot spots.

Z. A. Roberts, J. O. Mares, J. K. Miller, I. E. Gunduz, S. F. Son, J. F. Rhoads

Chapter 11. Effect of Crystal Density on Dynamic Deformation Behavior of PBX

Abstract

Polymer bonded explosives (PBX) are heterogeneous materials that contain solid loading varying from 80 to 95 % and bound together by 5–20 % soft binder. An experimental investigation is performed to study the effect of crystal solid loading on the failure process of PBX subjected to dynamic loading at different strain rates. Model materials, with sugar crystals and binder, are fabricated with solid loading varying from 80 to 95 %. Then dynamic compression experiments are performed on each specimens using split Hopkinson pressure bar. During loading, the deformation is captured using the high-speed camera at 1 million frames/s. Digital image correlation technique is used to obtain the local and full field deformation and strain fields at each strain rate. Based on the local deformation field and the load data, the failure process of each sample are investigated, and the effect of solid loading on the strain localization and failure mode of the PBX is discussed.

Suraj Ravindran, Addis Tessema, Addis Kidane

Chapter 12. Strain Rate Dependent Failure of Interfaces Examined via Nanoimpact Experiments

Abstract

One of the main factors contributing to the failure of composites is the failure initiated at the interfaces. Examples include interface failure at interfaces such as those between HTPB-Ammonium Perchlorate (AP) in an example energetic material. One important characteristic that could be used to develop failure theories under dynamic loading in materials with an account of interface properties is constitutive properties of interfaces under dynamic loading. In this work, interface mechanical strength of a set of HTPB-AP interfaces is characterized using dynamic indentation experiments at strain rates up to 100 s⁻¹. Stress maps were measured in the interface areas using Nano Mechanical Raman Spectroscopy (NRS) to analyze the changes in the stress distribution around interfaces. Measurements of dynamic hardness, strain rates, and plastic-residual depths were correlated to show the relation of interface mechanical strength with the bulk phase mechanical strength. A power law viscoplastic constitutive model was fitted to experimental stress-strain-strain rate data in order to obtain constitutive behavior of interfaces, particle, and matrix. Results show that interfacial properties are affected by the rate of loading and are largely dependent upon the interface structural inhomogeneity. Stress maps are obtained near the interface using In-situ Mechanical Raman Spectroscopy to analyze the changes in the stress distribution around interfaces for different loads. A bilinear cohesive zone model parameters were obtained from the consideration of local stress and the cohesive energy required for delamination.

Chandra Prakash, Devendra Verma, Matthias Exner, Emre Gunduz, Vikas Tomar

Chapter 13. A Theory of Coupled Anisothermal Chemomechanical Degradation for Finitely-Deforming Composite Materials with Higher-Gradient Interactive Forces

Abstract

The two-constituent theory of Hall and Rajagopal (2011) is recast for N constituents based on the composite Helmholtz energy and elaborated to display the higher-gradient nature of the interactive forces between constituents. These body forces are essential in the descriptions of the intracell behaviors included in the force balances of each constituent. The model may be both applied to solid composites, e.g. for interrogating the damage and failure processes developed at the constituent level, as well as to diffusion-reaction processes involving e.g. fluids and solids. Applications of interest include the evolution of asymmetric material features potentially involving finite-dimensional growth and recession (oxidation of SiC results in a 2.2x local volume increase), leading to local rotations important to the description of failure, and the description of forces between constituents especially near free edges and cut-outs.

R. B. Hall

Chapter 14. Effect of Temperature and Moisture on the Mechanical Properties of Fiber Reinforced Nylon 6 Composites

Abstract

The mechanical performance of nylon 6 composites can be adversely affected by environmental conditions. This paper examines the effects of elevated temperature and moisture on the tensile properties of nylon 6 composites reinforced with discontinuous and continuous fibers. Plasticizing effects are observed with increasing moisture content and temperature (98 degrees Celsius) but these effects are reversed at 150 degrees Celsius due to hydrolysis of the nylon matrix. The length and orientation of the reinforcing fibers are shown to influence the amount of moisture absorbed in the composites, and also influence the evolution of strength and modulus at elevated temperatures. Nylon 6 composites with continuous, aligned fibers retain their mechanical properties after exposure to increased moisture and temperature much better than composites with discontinuous, randomly aligned fibers.

Asha-Dee N. Celestine, S. Sherry Zhu

Chapter 15. Using Hydrostatic Pressure to Maximize Frequency Dependent Damping Properties of Thermoplastic Polyurethane

Abstract

One of the ways to reduce vibration transmission between source and receiver is by using polymeric damping elements. Comparing polymeric materials shows that polymeric materials with high damping factor tan δ exhibits lower stiffness compared to polymeric materials with lower damping factor. Due to their insufficient stiffness polymers with better damping are often not being used for vibration isolation. In addition, elastomeric materials with higher damping exhibit maximal damping values at high frequencies, often in frequency range far away from our hearing range. Combining both facts leads to the conclusion that there is still room to increase damping properties of polymeric material.

This paper is a continuation of previously presented work on this topic with aim to demonstrate how exposing elastomeric material to the hydrostatic pressure we can affect its frequency dependent mechanical properties. This allows full utilization of damping potential of the selected material and maximize the damping effect of the damping element. Using this unique property of viscoelastic materials enables one to designed adaptive damping elements which can be used in railroad applications as well as in other relevant cases. To demonstrate the effect of inherent hydrostatic pressure on damping behavior three thermoplastic polyurethanes were selected.

M. Bek, I. Emri

Chapter 16. Impact of Hydro-Mechanical Loadings on Rupture Process in Wood Material

Abstract

With the environmental impacts coupled with mechanical loadings, the micro-cracks can propagate and drive the collapse of wood materials or timber-based structures. In this case, the rupture in mixed mode coupling mechanical hydric and thermal loads for orthotropic materials is studied. The analytical formulation of the energy release rate is introduced by the T and A integrals generalized to mixed mode crack growth. The time dependent effects are introduced according to the generalized Kelvin Voigt model. This new formulation is based on conservation laws and real and virtual mechanical and thermal fields based on the Arbitrary, Lagrangian and Eulerian configurations. The Mixed Mode Crack Growth specimen, providing the decrease of energy release rate during crack propagation, is considered in order to compute the various mixed mode ratios. The analytical formulation is implemented in finite element software Cast3m and the crack growth is obtained by testing the Griffith criterion rewritten in time domain under orthotropic configuration. The efficiency of the proposed model is justified by showing the evolution of energy release rate and the stress intensity factors versus crack length and hydric variations within time dependent material. Also the path independency is proven for each mixed mode configuration.

Seif Eddine Hamdi, Rostand Moutou Pitti, Frédéric Dubois, Bernard Bangagoye

Chapter 17. 2D Transient Viscoplastic Model for Dislocation Generation of SiC by PVT Method

Abstract

SiC crystal grown by PVT method has attracted worldwide research attention and it has been successfully produced under various growth conditions, such as growth temperature, pressure, and growth chamber geometry. However, the dislocation multiplication in SiC crystal grown by PVT method are generated by excessed thermal stresses caused by the nonuniform temperature field in the SiC ingot. A 2 dimensional transient finite element model based on the Haasen-Sumino viscoplastic constitutive model (HAS) is developed to evaluate the dislocation densities generated in the SiC crystal grown by PVT method. The dislocation densities generated in the PVT process is the major parameter for the evaluation of final product. The result shows that the maximum dislocation density is about 1.8 × 10⁷ m⁻² when the temperature gradient equals −340/90,000 K/s, while it increases to 2.4 × 10⁷ m⁻² when the temperature gradient increases to −640/90,000 K/s.

Maohua Lin, Qingde Chen, Yunqing Kang, Chi-Tay Tsai

Chapter 18. Temperature-Dependent Small Strain Plasticity Behavior of 304L Stainless Steel

Abstract

Glass-to-metal seals are used extensively to protect and isolate electronic components. Small strains of just a few percent are typical in the metal during processing of seals, but generate substantial tensile stresses in the glass during the solidification portion of the process. These tensile stresses can lead to glass cracking either immediately or over time, which results in a loss of hermiticity of the seal. Measurement of the metal in the small strain region needs to be very accurate as small differences in the evolving state of the metal have significant influence on the stress state in the glass and glass-metal interfaces. Small strain tensile experiments were conducted over the temperatures range of 25–800 °C. Experiments were designed to quantify stress relaxation and reloading combined with mid-test thermal changes. The effect of strain rate was measured by directly varying the applied strain rate during initial loading and reloading and by monitoring the material response during stress relaxation experiments. Coupled thermal mechanical experiments were developed to capture key features of glass-to-metal seal processing details such as synchronized thermal and mechanical loading, thermal excursions at various strain levels, and thermal cycling during stress relaxation or creep loadings. Small changes in the processing cycle parameters were found to have non-insignificant effect on the metal behavior. The resulting data and findings will be presented.

Bonnie R. Antoun, Robert S. Chambers, John M. Emery, Arthur A. Brown

Chapter 19. Time and Temperature Creep Behaviour Measurement of Al and Al-Mg Alloy Thin Films Using Pressure Bulge Tests

Abstract

Metal thin films are often used as capacitance switches in Micro Electro Mechanical Systems (MEMS). But long-term reliability is always the question to be solved. If thin films have better mechanical properties, it can not only reduce the creep behavior, but also extend its lifetime.

In this study, we use solid solution strengthening to improve the mechanism of the material, adding foreign atom Mg to Al thin films in order to increase the resistance to creep behavior, the more we add Mg, the more difficult for dislocation sliding, then the mechanism of the material become better. As the result, after adding Mg into Al, it can effectively reduce the creep behavior, so Al-Mg films are much better than pure Al films using in capacitance switches.

C.-H. Lu, S.-C. Wu, A.-W. Huang, M.-T. Lin

Chapter 20. Multifunctional Wings with Flexible Batteries and Solar Cells for Robotic Birds

Abstract

Inspired by nature, Flapping Wing Aerial Vehicles (FWAVs), also known as “robotic birds” use flexible compliant wings that deform while flapping for aerodynamic force generation to achieve flight, just like real birds. However, unlike real birds, these vehicles require an artificial power source, like a battery, which limits flight time depending on how much the FWAV can carry (i.e., the payload) and the energy density of the power source. Previously, we have integrated flexible solar cells into a novel FWAV we developed called “Robo Raven” that has programmable wings capable of flapping independently. With the solar cells, energy is harvested during flight to extend the flight time of the FWAV. Recently, we have begun investigating the use of flexible batteries in the wings. By replacing wing mass with material capable of storing energy, it is possible to further increase the flight time and energy storage potential of the platform. However, we are assessing the effects of replacing the regular wing materials with battery materials on the generation of lift and thrust forces. In this paper, different wing designs were designed, built, and tested and flown with the Robo Raven platform. The aerodynamic forces generated by each wing design were measured using a test stand with a six degree of freedom load cell inside of a wind tunnel to simulate flight conditions. A mass-based multifunctional performance analysis is developed to assess the tradeoffs and benefits of using battery materials in the wings for the platform’s time-of-flight.

Alex E. Holness, Ariel Perez-Rosado, Hugh A. Bruck, Martin Peckerar, Satyandra K. Gupta

Chapter 21. Rate-Dependent Constitutive Model Development of PC/ABS Material

Abstract

Handheld consumer electronic devices such as smartphones are prone to drop impact during the field use condition. The smartphones are typically characterized for their drop impact performance to meet certain reliability test requirements before they are released into the market as commercial products. During the product development cycle, finite element analysis comes in handy to help understand the mechanics of the device and the interplay of various inner components. Of interest is the stresses generated in the chemically-strengthened glass that is used as cover glass in majority of smart phones. In order to be able to predict the stresses accurately, it is important to characterize key materials in the device for their rate-dependent non-linear elastic-plastic constitutive behavior as the drop event involves different strain rates. Polycarbonate (PC) is commonly used as back cover and sometimes the inner chassis in the smart phones. A rate-dependent constitutive model is developed through rigorous material testing in this effort for a particular type of PC/ABS blend. A finite element model of the test sample is built and used to validate the constitutive model developed.

Satish Chaparala, Josh Jacobs

Chapter 22. Comprehensive Viscoelastic Properties Characterization of EMC Using FBG Sensor

Abstract

An advanced system based on a fiber Bragg grating (FBG) sensor is proposed to characterize the comprehensive viscoelastic properties of epoxy molding compound (EMC). The FBG sensor is embedded in the center of a cylindrical EMC specimen, and the strain of the EMC is measured as a function of time under a constant loading condition. The constant loading condition is achieved by utilizing an automated gas pressure system. Two loading conditions are considered: compressive pressure for the Young’s modulus and hydrostatic pressure for the Bulk modulus. The constant loadings are repeated at different temperatures. The time dependent properties at different temperatures are shifted and overlapped to create the master curves of the Young’s modulus and bulk modulus. A piece-wise shift function is developed to fit the shift factors with extreme non-linearity. The results confirm the TRS assumption about the EMC; i.e., a single set of the shift factors can be used for both Young’s modulus and bulk modulus. The comprehensive properties are used to predict the behavior of an EMC/chip bi-material joint subjected to the thermo-mechanical loadings. The results clearly show enhanced modeling predictability.

Yong Sun, Hyun-Seop Lee, Bongtae Han

Chapter 23. Back Stress in Modeling the Response of PEEK and PC

Abstract

With the development of new methods for the characterization of equilibrium stress through cyclic loading, it is now possible to follow the evolution of back stress during the nonlinear deformation of polymers. Experiments on PEEK and PC below the glass-transition temperature indicate a back stress that may evolve with plastic deformation, and which is substantially different from that seen during the response in the rubbery range. In particular, the back stress during the response of PC shows the characteristic post-yield softening, possibly indicating that the observed post-yield softening in the response comes from the back stress. This is not seen in PEEK, which also shows no substantial post-yield softening. The equilibrium stress plays a central role in modeling both the quasi-static and dynamic response of PEEK.

Wenlong Li, George Gazonas, Eric N. Brown, Philip J. Rae, Mehrdad Negahban

Chapter 24. Dynamic Testing and Constitutive Modelling of NBR Rubbers

Abstract

The present work describes the compression behaviour of NBR rubber. Experimental tests have been conducted both in dynamic conditions. The latter ones, performed by a polymeric Split Hopkinson Bar, range from 100 to 500 1/s of strain rate. The long lasting pressure wave generated by the adopted SHB permitted to obtain a relatively high strain level in all the tests, up to 0.7–1.0 logarithmic strain. The experimental stress-strain curves were used to fit hyperelastic-perfect viscoelastic constitutive models; in particular, the Ogden and Mooney-Rivlin models were used for the hyperelasticity, while the Prony series was used for the viscoelastic part.

The analyses permitted to evaluate the dependency of the storage and loss moduli of NBR as functions of frequency and strain amplitude.

M. G. Antonelli, B. Lonzi, E. Mancini, M. Martarelli, M. Sasso

Chapter 25. A New Temperature-Dependent Storage Modulus Model of Epoxy Resin

Abstract

Temperature-dependent dynamic mechanical properties of epoxy resin were studied by dynamic mechanical analysis. A new temperature-dependent storage modulus model was developed to describe the storage modulus of epoxy resin for multi-transition regions from cryogenics to elevated temperatures. Model predictions showed good agreements with the experimental results.

Jiemin Feng, Zhansheng Guo

Chapter 26. Identification of Plastic Behaviour of Sheet Metals in High Strain Rate Tests

Abstract

In this work, dynamic tension tests have been conducted by an SHB on sheet metals in order to characterize the plastic behaviour of the materials. First of all, the sample geometry and the clamping system were optimized by FEM simulations in order to: (i) reduce impedance disturbance due to the fasteners, (ii) maximize the specimen cross-section to increase the force measurement sensitivity, (iii) reduce the elongation measurement errors due to deformation of the clamping system. Pictures of the samples were acquired during the test by means of a fast camera. On the one hand, this permitted to validate the strain measurement by the classical SHB theory formulas; on the other hand, application of DIC method permitted to obtain the actual strain distribution maps. These strain maps have been used to extract the parameters of a strain hardening constitutive model.

D. Amodio, E. Mancini, M. Rossi, M. Sasso

Chapter 27. Characterization of Fiber Composites at Lower Strain Rates

Abstract

Materials and structures are commonly subjected to dynamic loading. The behavior of materials and structures under dynamic loading, however, can be significantly different from that under static loading. This is especially true for so-called strain rate sensitive materials, such as polymeric materials and fiber reinforced polymer-matrix composite materials. Based on a previous study, this paper continues on the characterization of low strain rate effects, such as those up to 100/s, on glass-fiber-reinforced polymer-matrix composite materials. Testing techniques based on slip Hopkinson’s pressure bar have been constantly used for investigation of strain rate effects. However, because of the low strain rate range, the commonly used slip Hopkinson’s pressure bar should become over-qualified. On the other hand, the commonly used drop-weight impact testers have been found to be useful for low strain rate characterizations. The constitutive relations of the composite material at low strain rates are presented in this study based on the testing technique for lower strain rates. Besides, the effect of fiber orientation on the strain rate effects is also discussed.

Dahsin Liu, Guojing Li, Jianxiao Zheng, Wei Huang