Cyclic thermomechanical behavior of a polycrystalline pseudoelastic shape memory alloy

In this work, 3D finite element modeling is employed to examine the thermomechanical behavior of a polycrystalline Ni-Ti shape memory alloy in the pseudoelastic regime. It is shown that the tension-compression asymmetry during uniaxial cyclic loading is due to a preferred orientation of the crystallographic texture. In pure shear loading, the thermomechanical behavior exhibits symmetry in both senses of shear, due to the fiber texture of the specimen bar stock. It is also shown that the apparent strain rate-dependence is due to thermomechanical coupling with latent heat generation/absorption during phase transformation.     

An effective temperature theory for the nonequilibrium behavior of amorphous polymers

Amorphous polymers lack an organized microstructure, yet they exhibit structural evolution, where physical properties change with time, temperature, and inelastic deformation. To describe the influence of structural evolution on the mechanical behavior of amorphous polymers, we developed a thermomechanical theory that introduces the effective temperature as a thermodynamic state variable representing the nonequilibrium configurational structure. The theory couples the evolution of the effective temperature and internal state variables to describe the temperature-dependent and rate-dependent inelastic response through the glass transition. We applied the theory to model the effect of temperature, strain rate, aging time, and plastic pre-deformation on the uniaxial compression response and enthalpy change with temperature of an acrylate network. The results showed excellent agreement with experiments and demonstrate the ability of the effective temperature theory to explain the complex thermomechanical behavior of amorphous polymers.     

Plastic instability studied experimentally on a semi-crystalline polymer through thermomechanical heat source identification: the flow stress concept revisited

Micromechanical deformation phenomena such as those leading to macroscopic viscoelastic and plastic behavior must be studied from a thermodynamic viewpoint, as they induce complex and partly irreversible heat effects. Calorimetric measurements of the intrinsic volumetric thermomechanical heat sources (THS) activated in the material bulk during mechanical loads can produce valuable information with respect to that aim. They can be based on infrared imaging if submitted to inverse algorithms that allow a correct reconstruction of THS to be produced. Here, an inverse method relying on a diffusion-advection heat transfer model is applied to experimental temperature maps recorded during tensile tests. These are made on a semi-crystalline polymer that shows a strong development of plastic instabilities. Along with simultaneous kinematic observables produced with a digital image correlation system, the competition between advection and diffusion phenomena may be clearly established. 1-D profiles of the reconstructed THS and measured strain rates illustrate clearly that thermomechanical effects associated with necking onset and propagation follow the kinematic variable in a rather direct manner. Finally, we show for tensile experiments that THS estimations lead to analyze plasticity as a rheological behavior controlled by the flow stress, responsible of necking development and propagation.     

Determination of tensile flow stress beyond necking at very high strain rate

The objective of this effort was to extend the Bridgman analysis of tensile necking to obtain stress-strain data beyond the point of onset of necking from a split Hopkinson bar. For this purpose, combined analytical and experimental techniques were considered. The analytical efforts were focused on validating the use of Bridgman solutions for high rate of deformation through a finite-element analysis of a tapered tensile specimen. The experimental technique involved the development of a photographic system using a light-emitting diode and a 35-mm rotating drum camera for the observation of necking during dynamic tensile tests conducted with a split Hopkinson tension bar. The developed new technique was successfully used to measure neck profiles of 6061-T6 aluminum, HY100 and 1020 steel tensile specimens. The measured profiles were used with the Bridgman analysis and stress-strain data were obtained to over 70-percent strain.     

Thermomechanical cyclic behavior modeling of Cu-Al-Be SMA materials and structures

This paper concerns the behavior of Cu-Al-Be polycrystalline shape memory alloys under cyclic thermomechanical loadings. Sometimes, as shown by many experimental observations, a permanent inelastic strain occurs and increases with the number of cycles. A series of cyclic thermomechanical tests has been carried out and the origin of the residual strain has been identified as residual martensite. These observations have been used to develop a 3D macroscopic model for the superelasticity and stress assisted memory effect of SMAs able to describe the evolution of permanent inelastic strain during cycles. The model has been implemented in a finite elements code and used to simulate the behavior of antagonistic actuators based on SMA springs under cyclic thermomechanical loading with a residual displacement appearance.     

Formulation of a damage internal state variable model for amorphous glassy polymers

The following article proposes a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.     

Engineering models for synthetic microvascular materials with interphase mass,momentum and energy transfer

New materials are being developed that consist of a solid matrix with pores or vessels through which a functional fluid phase may pass. The fluid can provide expanded functionality such as healing and remodeling, damage disclosure, enhanced heat transfer, and controlled deformation, stiffness and damping. This paper presents a class of engineering models for synthetic microvascular materials that have fluid passages much smaller than a characteristic structural length such as panel thickness. The materials are idealized as two-phase continua with a solid phase and a fluid phase occupying every volume. The model permits the solid and fluid phases to exchange mass, momentum and energy. Balance equations and the entropy inequality for general mixtures are taken from existing continuum mixture theory. These are augmented with certain definite types of solid–fluid interactions in order to enable adequately general, but workable, engineering analysis. The thermomechanical characteristics of this restricted class of materials are delineated. By demanding that the law of increase of entropy be satisfied for all processes, much is deduced about the acceptable forms of constitutive equations and internal state variable evolution equations. The paper concludes with a study of the uniaxial tension behavior of an idealized vascular material.     

M-shaped Specimen for the High-strain Rate Tensile Testing Using a Split Hopkinson Pressure Bar Apparatus

An experimental technique is proposed to determine the tensile stress–strain curve of metals at high strain rates. An M-shaped specimen is designed which transforms a compressive loading at its boundaries into tensile loading of its gage section. The specimen can be used in a conventional split Hopkinson pressure bar apparatus, thereby circumventing experimental problems associated with the gripping of tensile specimens under dynamic loading. The M-specimen geometry provides plane strain conditions within its gage section. This feature retards necking and allows for very short gage sections. This new technique is validated both experimentally and numerically for true equivalent plastic strain rates of up to 4,250/s.     

On the formulation of coupled thermoplastic problems with phase-change

This paper deals with a numerical formulation for coupled thermoplastic problems including phase-change phenomena. The final goal is to get an accurate, efficient and robust numerical model, allowing the numerical simulation of solidification processes in the metal casting industry. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. The constitutive behavior has been defined by a thermoelastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. A brief summary of the thermomechanical frictional contact model is included. The numerical model has been implemented into the computational Finite Element code COMET developed by the authors. A numerical assessment of the isentropic and isothermal operator splits, regarding the nonlinear stability behavior, has been performed for weakly and strongly coupled thermomechanical problems. Numerical simulations of solidification processes show the performance of the computational model developed.     

Configurational mechanics of necking phenomena in engineering thermoplastics

Necking is a significant part of the yielding process in many thermoplastics. It starts as strain localization associated with microshear banding and/or cavitations and appears as a domain of oriented (drawn) material, i.e., a “neck”, separated from the domain of original (isotropic) material by a narrow transition zone, which appears as a distinct boundary of the neck region. On further increase of displacement, the neck propagates through the test specimen under constant draw stress. Strain localization such as crazing and shear bending is associated with necking on micro- and sub-microscales. As a result material toughness, i.e., resistance to cracking, as well as durability, i.e., service lifetime under various service conditions, are related to the material ability to necking and specific characteristics of necking process. Necking is manifested in significant changes in a characteristic length scale, e.g., the distance between equally spaced marks in the reference state may increases by factor of 2 in amorphous polymers and up to a factor of 10 in some semicrystalline thermoplastics. There is also a characteristic relaxation time change during the necking. Thus from continuum mechanics viewpoint, the changes of intrinsic material space-time metric are the most fundamental manifestation of necking. Therefore we model necking phenomena as space-time scales transformation and introduce a four-dimensional (4D) Riemannian metric tensor of a material space-time imbedded into 4D Newtonian (laboratory) space-time with a Euclidean metric. Kinetic equation of necking, i.e., evolution equation for material metric tensor is derived using extremal action principle. An example of traveling wave solution for neck propagation in a tensile bar is presented. Analysis of the solution and comparison with experimental observations are discussed.     

Using a split Hopkinson bar to specify the parameters of thermomechanical models of flow under high strain rate deformation

By way of numerical simulation, a method is developed to determine the parameters of the thermomechanical Bodner-Partom model of flow under high strain rate deformation using a split Hopkinson bar. The classical method is generalized in two directions. To evaluate the kinematic hardening parameters, the wave reflected from the free end of the bar is used. The thermomechanical parameters that are responsible for the stored energy of cold work are calculated from measurements of temperature changes in the specimen __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 81–92, June 2008.     

A nonlocal model with strain-based damage

A thermodynamically consistent formulation of nonlocal damage in the framework of the internal variable theories of inelastic behaviours of associative type is presented. The damage behaviour is defined in the strain space and the effective stress turns out to be additively splitted in the actual stress and in the nonlocal counterpart of the relaxation stress related to damage phenomena. An important advantage of models with strain-based loading functions and explicit damage evolution laws is that the stress corresponding to a given strain can be evaluated directly without any need for solving a nonlinear system of equations. A mixed nonlocal variational formulation in the complete set of state variables is presented and is specialized to a mixed two-field variational formulation. Hence a finite element procedure for the analysis of the elastic model with nonlocal damage is established on the basis of the proposed two-field variational formulation. Two examples concerning a one-dimensional bar in simple tension and a two-dimensional notched plate are addressed. No mesh dependence or boundary effects are apparent.     

A thermodynamical approach to contact wear as application of moving discontinuities

The propagation of a moving surface inside a body is analysed within the framework of thermomechanical couplings when the moving surface is associated with an irreversible change in mechanical properties. The moving surface is a surface of heat sources and of entropy production whose intensities are related to particular energy release rates defined in terms of Hamiltonian gradients. For example, we analyse the wear process. Wear phenomena due to contact and relative motion between two solids depend on the loading conditions and material mechanical properties. Friction between contacting bodies induces damage of materials, producing surface and subsurface cracks. Particles are detached from sound solids when some local criteria are satisfied at the boundary. As wear occurs, geometrical changes take place and contact conditions are modified, and the particle induces a specific layer with particular properties. Then the interface between the bodies is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. We propose to describe the evolution of the interface using a framework developed earlier for inducing the general form of a wear law.     

Effects of spatial grain orientation distribution and initial surface topography on sheet metal necking

The finite element method is used to numerically simulate localized necking in AA6111-T4 under stretching. The measured EBSD data (grain orientations and their spatial distributions) are directly incorporated into the finite element model and the constitutive response at an integration point is described by the single crystal plasticity theory. We assume that localized necking is associated with surface instability, the onset of unstable growth in surface roughening. It is demonstrated that such a surface instability/necking is the natural outcome of the present approach, and the artificial initial imperfection necessitated by the macroscopic M–K approach [Marciniak and Kuczynski (1967). Int. J. Mech. Sci. 9, 609–620] is not relevant in the present analysis. The effects of spatial orientation distribution, material strain rate sensitivity, texture evolution, and initial surface topography on necking are discussed. It is found that localized necking depends strongly on both the initial texture and its spatial orientation distribution. It is also demonstrated that the initial surface topography has only a small influence on necking.     

Full Field Strain Measurement in Compression and Tensile Split Hopkinson Bar Experiments

The 3D image correlation technique is used for full field measurement of strain (and strain rate) in compression and tensile split Hopkinson bar experiments using commercial image correlation software and two digital high-speed cameras that provide a synchronized stereo view of the specimen. Using an array of 128 × 80 (compression tests) and 258 × 48 (tensile tests) pixels, the cameras record about 110,000 frames per second. A random dot pattern is applied to the surface of the specimens. The image correlation algorithm uses the dot pattern to define a field of overlapping virtual gage boxes, and the 3-D coordinates of the center of each gage box are determined at each frame. The coordinates are then used for calculating the strains throughout the surface of the specimen. The strains determined with the image correlation method are compared with those determined from analyzing the elastic waves in the bars, and with strains measured with strain gages placed on the specimens. The system is used to study the response of OFE C10100 copper. In compression tests, the image correlation shows a nearly uniform deformation which agrees with the average strain that is determined from the waves in the bars and the strains measured with strain gages that are placed directly on the specimen. In tensile tests, the specimen geometry and properties affect the outcome from the experiment. The full field strain measurement provides means for examining the validity and accuracy of the tests. In tests where the deforming section of the specimen is well defined and the deformation is uniform, the strains measured with the image correlation technique agree with the average strain that is determined from the split Hopkinson bar wave records. If significant deformation is taking place outside the gage section, and when necking develops, the strains determined from the waves are not valid, but the image correlation method provides the accurate full field strain history.     

An experimental approach to low-cycle fatigue damage based on thermodynamic entropy

This paper presents an experimental approach to fatigue damage in metals based on thermodynamic theory of irreversible process. Fatigue damage is an irreversible progression of cyclic plastic strain energy that reaches its critical value at the onset of fracture. In this work, irreversible cyclic plastic energy in terms of entropy generation is utilized to experimentally determine the degradation of different specimens subjected to low cyclic bending, tension-compression, and torsional fatigue. Experimental results show that the cyclic energy dissipation in the form of thermodynamic entropy can be effectively utilized to determine the fatigue damage evolution. An experimental relation between entropy generation and damage variable is developed.     

Rate theory of nonlocal gradient damage-gradient viscoinelasticity

A general concept for the analysis of damage evolution in heterogeneous media is proposed. Since macroscopic failure is governed by physical mechanisms on two different length-scale levels, the macro- and mesolevel, we introduce a 6-dimensional kinematical model with manifold structure accounting for discontinuous fields of microcracks, microvoids and microshear bands. As point of departure a variational functional is introduced with a Lagrangian density depending on macro- and microdeformation gradients and of a damage variable representing scalar-, vector- and/or tensor-type quantities. To derive the equations of motion for viscoinelastic damage evolution on macro- and mesolevel, we introduce into the Lagrangian the macro- and microdeformation gradients, damage variable and also their gradients and time rates. The equations of motion on macro- and mesolevel are derived for non-equilibrium states. We assume that the Lagrangian can be split into two contributions, a time-independent and a time-dependent one which can be identified with the Helmholtz free energy and a dissipation potential. This split of the Lagrangian can be used to decompose the stresses and forces into reversible and irreversible ones. The latter can be considered as dissipative driving stresses and driving forces, respectively, on defects. The model presented in this paper can be considered as a framework, which enables to derive various nonlocal and gradient, respectively, damage theories by introducing simplifying assumptions. As special cases a scalar damage and a solid-void model are considered.     

单轴循环冲击下弱风化花岗岩的损伤演化

为研究爆破应力波作用下弱风化花岗岩的力学特性和损伤演化机理，利用直径50 mm的改进分离式Hopkinson压杆装置，开展以不同速度对花岗岩进行单次和等速循环冲击下的实验研究。研究结果表明:单次冲击中，用能量法确定的损伤阈值，可用于循环冲击实验中；不同应变率下弱风化岩石裂纹扩展阶段存在应力松弛平台，且随应变率升高而愈发明显，峰值应力与应变率呈正相关。等速循环冲击中，最大应力、应变与冲击速度呈正相关，与岩样累积冲击总次数呈负相关；损伤演化具有3个阶段呈倒S形，由其构建的双参数损伤演化模型拟合效果理想，且具有物理意义；利用模型中的参数α和β可计算中值点处的损伤度和相对循环次数，且与冲击速度正相关；不同损伤变量计算的损伤演化模型不同，合理定义损伤变量是必要的。     

On the mechanics of mother-of-pearl: A key feature in the material hierarchical structure

Mother-of-pearl, also known as nacre, is the iridescent material which forms the inner layer of seashells from gastropods and bivalves. It is mostly made of microscopic ceramic tablets densely packed and bonded together by a thin layer of biopolymer. The hierarchical microstructure of this biological material is the result of millions of years of evolution, and it is so well organized that its strength and toughness are far superior to the ceramic it is made of. In this work the structure of nacre is described over several length scales. The tablets were found to have wavy surfaces, which were observed and quantified using various experimental techniques. Tensile and shear tests performed on small samples revealed that nacre can withstand relatively large inelastic strains and exhibits strain hardening. In this article we argue that the inelastic mechanism responsible for this behavior is sliding of the tablets on one another accompanied by transverse expansion in the direction perpendicular to the tablet planes. Three dimensional representative volume elements, based on the identified nacre microstructure and incorporating cohesive elements with a constitutive response consistent with the interface material and nanoscale features were numerically analyzed. The simulations revealed that even in the absence of nanoscale hardening mechanism at the interfaces, the microscale waviness of the tablets could generate strain hardening, thereby spreading the inelastic deformation and suppressing damage localization leading to material instability. The formation of large regions of inelastic deformations around cracks and defects in nacre are believed to be an important contribution to its toughness. In addition, it was shown that the tablet junctions (vertical junctions between tablets) strengthen the microstructure but do not contribute to the overall material hardening. Statistical variations within the microstructure were found to be beneficial to hardening and to the overall mechanical stability of nacre. These results provide new insights into the microstructural features that make nacre tough and damage tolerant. Based on these findings, some design guidelines for composites mimicking nacre are proposed.