A nonclassical constitutive model for crystal plasticity and its application

I.IntroductionTheresearchoncrystalplasticitycanbedatedbackto1930'sill.AherHill[=],HillandRicely]builtupaperfectsystemofthegeometryandkineticsofCrystalplasticity,itsapplicatiollbecolllesmoreandmoreattractive,especiallyintheallalysisofpolycrystallinelllaterialssubjectedtoInultiaxiallynonproportionalcyclicloading.Ithasalreadybeenrealizedthattileillll,ol'talltforthepracticalapplicationis:tofindal.ealisticalldeasilyapplicableof'ystallineconstitutiverelationandaneffectivenumericalapproach.Tilecon…     

A constitutive model accounting for strain ageing effects on work-hardening. Application to a C–Mn steel

One of the most successful models for describing the Portevin–Le Chatelier effect in engineering applications is the Kubin–Estrin–McCormick model (KEMC). In the present work, the influence of dynamic strain ageing on dynamic recovery due to dislocation annihilation is introduced in order to improve the KEMC model. This modification accounts for additional strain hardening rate due to limited dislocation annihilation by the diffusion of solute atoms and dislocation pinning at low strain rate and/or high temperature. The parameters associated with this novel formulation are identified based on tensile tests for a C–Mn steel at seven temperatures ranging from 20 °C to 350 °C. The validity of the model and the improvement compared to existing models are tested using 2D and 3D finite element simulations of the Portevin–Le Chatelier effect in tension.     

A viscoplastic model combined smedamage and smeared crack for softening of concrete

A viscoplastic model accounting for developing damage in concrete is proposed by assuming the rate of damage to be dependent on viscous strain and stress rates. The damage is measured by a scalar parameter affecting both the yield stress and the material viscosity. For a post-critical range of deformation, the localized mode occurs for which additional constitutive equations are specified. The model is applied to simulate uniaxial strain rate controlled and creep response for the concrete.     

Yield criterion and elasto-plastic damage constitutive model for frozen sandy soil

A series of triaxial compression tests was carried out on a frozen sandy soil under confining pressures of 0–18 MPa at −6 °C. The experimental results indicate that, the strength of frozen sandy soil increases versus the increase in the confining pressures when σ₃ ? 3 MPa, but decreases when σ₃ > 3 MPa. This phenomenon is called the strengthening and weakening effects of confining pressures. A yield function, considering both effects, is proposed using the experimental method according to Drucker’s postulate, and the mathematical expression of the hardening parameter, which can describe the softening and hardening phenomenon, is provided. An elasto-plastic constitutive model for frozen sandy soil is developed. Based on the continuum damage theory, the cross anisotropic damage variables are deduced and their change regularities are investigated. Then the elasto-plastic damage constitutive model is proposed by introducing damage variables into elasto-plastic constitutive model. The validity of the model is verified by comparing its modeling results with experimental results obtained from triaxial tests. It is found that, this model can predict the deformation regularity of frozen soil exactly. It can simulate the stress–strain process under high confining pressures when pressure melting phenomena appear especially well.     

Cosserat连续体模型中本构参数对应变局部化模拟结果影响的数值分析

基于所发展的压力相关弹塑性Cosserat连续体模型及相应的数值方法,以一维剪切层及二维平板压缩问题为例,数值分析了Cosserat连续体模型中的本构参数Cosserat剪模、软化模量及内部长度参数对应变局部化数值模拟结果的影响.结果表明在一定取值范围内,Cosserat剪模对数值模拟结果几乎没有影响,并给出了具体数值计算时的取值范围;软化模量绝对值越大,后破坏段的荷载-位移曲线越陡,计算得到的剪切带宽度越窄;内部长度参数越大,后破坏段的荷载-位移曲线越平缓,计算得到的剪切带越宽.     

Effect of microstructure on the hardening and softening behavIors of polycrystalline shape memory alloys Part I: Micromechanics constitutive modeling

The effects of microstructure and its evolution on the macroscopic superelastic stress-strain response of polycrystalline Shape Memory Alloy (SMA) are studied by a microstructure-based constitutive model developed in this paper. The model is established on the following basis: (1) the transformation conditions of the unconstrained single crystal SMA microdomain (to be distinguished from the bulk single crystal), which serve as the local criterion for the derivation of overall transformation yield conditions of the polycrystal; (2) the micro- to macro-transition scheme by which the connection between the polycrystal aggregates and the single crystal microdomain is established and the macroscopic transformation conditions of the polycrystal SMA are derived; (3) the quantitative incorporation of three microstructure factors (i.e., nucleation, growth and orientation distribution of martensite) into the modeling. These microstructural factors are intrinsic of specific polycrystal SMA systems and the role of each factor in the macroscopic constitutive response is quantitatively modeled. It is demonstrated that the interplay of these factors will result in different macroscopic transformation kinematics and kinetics which are responsible for the observed macroscopic stress-strain hardening or softening response, the latter will lead to the localization and propagation of transformation bands in TiNi SMA. The project supported by the Research Grant Committee (RGC) of Hong Kong SAR, the National Natural Science Foundation of China and the Provincial Natural Foundation of Jiangxi Province of China     

A modified Stillinger–Weber potential-based hyperelastic constitutive model for nonlinear elasticity

The Stillinger–Weber (SW) potential, which is a combination of the two- and three-body interaction, states that the bond energy is not only related to the distance between atoms, but also related to the bond angles subtended by this given bond and other bonds. The bond energy mechanism presented by the SW potential is different from that by the classical potentials, such as the Lennard–Jones, Tersoff and Embedded Atom potentials. Different micro energy mechanism reveals different micro fracture mechanism. The original SW potential takes the ‘ideal’ tetrahedral angle as the reference value of each bond angle in the current configuration, which makes it only applicable to the silicon materials. However, the micro fracture mechanism revealed by the SW potential should not be confined to the silicon materials. To extend the SW potential to a wider range of materials, the value of the bond angle in the reference configuration, not the ‘ideal’ tetrahedral angle, is taken as the reference value of this bond angle in the current configuration. Based on this modified SW potential, a constitutive model is developed. By this way, the micro fracture mechanism invoked by the SW potential is incorporated into the constitutive relation. Through this proposed constitutive model, it is found that the Hookean matrix derived from the SW potential matches that of a linear elastic continuum, which suggests that there exists a corresponding relationship between the micro physical parameters of SW potential and the macro material constants. The corresponding micro–macro parameter relationship is derived in this paper. To examine the application of this method to other materials, it is used to simulate the mixed fracture growth in concrete under static and dynamic load. The simulation results suggest that the present method can capture the characters of fracture growth in the quasi-brittle materials. It suggests that the constitutive model based on the modified SW potential can be applied to materials other than silicon. Because the interatomic potential-incorporated constitutive model makes the fracture criterion as the intrinsic property of a constitutive relation, it presents many advantages in fracture simulation. This paper enriches the constitutive relation with the micro fracture mechanism presented in SW potential, providing a new micro constitutive model for materials. Besides this, it also provides a feasible approach to calibrating the parameters of the SW potential for a certain material.     

A constitutive model for the formation of martensite in austenitic steels under large strain plasticity

A constitutive model for diffusionless phase transitions in elastoplastic materials undergoing large deformations is developed. The model takes basic thermodynamic relations as its starting point and the phase transition is treated through an internal variable (the phase fractions) approach. The usual yield potential is used together with a transformation potential to describe the evolution of the new phase. A numerical implementation of the model is presented, along with the derivation of a consistent algorithmic tangent modulus. Simulations based on the presented model are shown to agree well with experimental findings. The proposed model provides a robust tool suitable for large-scale simulations of phase transformations in austenitic steels undergoing extensive deformations, as is demonstrated in simulations of the necking of a bar under tensile loading and also in simulations of a cup deep-drawing process.     

Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

A mechanism-based constitutive model is presented for the inelastic deformation and fracture of ceramics. The model comprises four essential features: (i) micro-crack extension rates based on stress-intensity calculations and a crack growth law, (ii) the effect of the crack density on the stiffness, inclusive of crack closure, (iii) plasticity at high confining pressures, and (iv) initial flaws that scale with the grain size. Predictions of stress/strain responses for a range of stress states demonstrate that the model captures the transition from deformation by micro-cracking at low triaxiality to plastic slip at high triaxialities. Moreover, natural outcomes of the model include dilation (or bulking) upon micro-cracking, as well as the increase in the shear strength of the damaged ceramic with increasing triaxiality. Cavity expansion calculations are used to extract some key physics relevant to penetration. Three domains have been identified: (i) quasi-static, where the ceramic fails due to the outward propagation of a compression damage front, (ii) intermediate velocity, where an outward propagating compression damage front is accompanied by an inward propagating tensile (or spallation) front caused by the reflection of the elastic wave from the outer surface and (iii) high velocity, wherein plastic deformation initiates at the inner surface of the shell followed by spalling within a tensile damage front when the elastic wave reflects from the outer surface. Consistent with experimental observations, the cavity pressure is sensitive to the grain size under quasi-static conditions but relatively insensitive under dynamic loadings.     

A unified plasticity model for cyclic behaviour of clay and sand

This paper presents the development and an experimental evaluation of a simple unified bounding surface plasticity theory for modelling the stress–strain behaviour of sand and clay under both drained and undrained cyclic loading conditions. The model concerned is called CASM-c, which is based on the unified critical state model CASM developed by Yu [Yu, H.S., 1995. A unified critical state model for clay and sand. Civil Engineering Research Report No. 112.08.1995. University of Newcastle, NSW 2308, Australia; Yu, H.S., 1998. CASM: a unified state parameter model for clay and sand. International Journal of Numerical and Analytical Methods in Geomechanics 22, 621–653]. CASM is a relatively simple model as it only requires seven model constants, five of which are the same as those used in the modified Cam-clay model. All these constants have clear physical meanings and may be easily determined from the results of triaxial tests. A key advantage of CASM over many other existing critical state models lies on its simplicity and unified nature as it can model the behaviour of both clay and sand.The extension of the model CASM presented in this paper consists of adopting the bounding surface plasticity theory and treating the reloading and unloading processes differently when calculating the hardening modulus. As a result, a smooth transition of stiffness and gradual accumulation of permanent strain and/or pore pressure in unload–reload cycles as well as the hysteretic behaviour can be reproduced. The results of model simulations show an encouraging agreement with experimental data from triaxial tests subjected to both one-way and two-way cyclic loading conditions.