Some new extensions to multi-mechanism models for plastic and viscoplastic material behavior under small strains

Multi-mechanism models (MM models) have become an important tool for modeling complex material behavior. In particular, two-mechanism models are used. They are applied to model ratcheting in metal plasticity as well as steel behavior during phase transformations. We consider a small-deformation setting. The characteristic trait of multi-mechanism models is the additive decomposition of the inelastic (e.g., plastic or viscoplastic) strain into several parts. These parts are sometimes called mechanisms. In comparison with rheological models, the mechanisms can interact with each other. This leads to new properties and allows to describe important observable effects. Up to now, each mechanism has one kinematic internal variable. As a new feature, we develop multi-mechanism models (in series) with several kinematic variables for each mechanism as well as with several isotropic variables for each flow criterion. We describe this complex situation by three structural matrices which express the mutual relations between mechanisms, flow criteria, kinematic, and isotropic variables. The well-known Chaboche model with a unique inelastic strain and several kinematic variables represents a special case of these general multi-mechanism models. In this work, we also present a matrix-based approach for these new complex MM models. The presented models can form the basis for developing numerical algorithms for simulation and parameter identification.     

Analysis of axial strain in one-dimensional loading by different models

Different phenomenological equations based on plasticity, primary creep （as a viscoplastic mechanism）, secondary creep （as another viscoplastic mechanism） and different combinations of these equations are presented and used to describe the material inelastic deformation in uniaxial test. Agreement of the models with experimental results and with the theoretical concepts and physical realities is the criterion of choosing the most appropriate formulation for uniaxial test. A model is thus proposed in which plastic deformation, primary creep and secondary creep contribute to the inelastic deformation. However, it is believed that the hardening parameter is composed of plastic and primary creep parts. Accordingly, the axial plastic strain in a uniaxial test may no longer be considered as the hardening parameter. Therefore, a proportionality concept is proposed to calculate the plastic contribution of deformation.     

Generalisation de la theorie du potentiel plastique multiple en viscoplasticite†

J. Mandel has extended the classical theory of the plastic potential to materials in which the plastic strain results from several simultaneous slips that are governed by the shear stress for each slip-mechanism (multiple plastic potential). J.R. Rice has shown that if the slip rate on a particular mechanism is also governed by the same law, then the viscoplastic strain-rate tensor can be derived from a viscoplastic potential. These two workers gave only some phenomenological relations.     

Strain-rate effects in rheological models of inelastic response

Stress–strain response under constant and variable strain-rate is studied for selected models of inelastic behavior. The derived closed-form solutions for uniaxial loading enable simple evaluation of the strain-rate effects on the material response. The effect of an abrupt change of strain-rate is also examined. Non-Newtonian viscosity which decreases with an increasing strain-rate is incorporated in the analysis. Parabolic and hyperbolic hardening are used to describe the plastic response in monotonic loading. A three-dimensional generalization of an elastic–viscoplastic model is employed to study the stress relaxation in simple shear. A combined isotropic–kinematic hardening and the concept of overstress are used in the analysis. The unloading nonlinearity of the stress–strain curve is then discussed.     

SnPb钎料合金的粘塑性Anand本构方程

采用统一型粘塑性本构 Anand方程描述了电子封装焊点 Sn Pb钎料合金的非弹性变形行为 ,基于 Sn Pb 合金的弹塑性蠕变本构方程和实验数据 ,确定了6 2 Sn36 Pb2 Ag、6 0 Sn40 Pb、96 .5 Sn3.5 Ag和 97.5 Pb2 .5 Sn四种钎料合金 Anand方程的材料参数 ,验证了粘塑性 Anand本构方程对 Sn Pb合金在恒应变速率和稳态塑性流动条件下应力应变行为的预测能力。结果表明 ,Anand方程能有效描述 Sn Pb钎料的粘塑性本构行为 ,并可应用于电子封装 Sn Pb焊点的可靠性模拟和失效分析     

材料的弹粘塑性本构关系和应力波的演化

试验表明，大多数工程材料在冲击载荷作用之下的变形一般都同时包含有可恢复的瞬态性弹性变形和不可恢复的粘滞性塑性变形，即其本构关系可以用弹粘塑性模型来描述。本文从内变量理论出发，探讨了时率相关材料的弹粘塑性本构关系的一般特性，建立了增量型的弹粘塑性本构关系的一般理论框架和普适的表达式，并且对两种最常用的本构模型——Bodner-Partom模型和Johnson-Cook模型给出了在一维应变条件下的具体形式。通过计算和讨论一维应变粘塑性靶板中冲击波的衰减机制和应力波的演化规律，特别是考察各种粘塑性本构模型中的材料参数对冲击波的衰减和应力波的演化的影响，得出了一些可以直接应用或具有一定借鉴价值的结果，为研究应力波的其他衰减机制以及在人防工程中智能防护层设计时新材料的选取奠定了基础。     

Buckling of short viscoplastic cylindrical shells subjected to radial impulse

The dynamic buckling of thin viscoplastic cylindrical shells is considered in the formulation developed by Abrahamson and Goodier [1]. The constitutive equations employed describe the rate sensitive plastic material and a biaxial state of stress is considered. The influence of the viscosity parameter on the buckling process is discussed in detail and in the limiting case the solution for a perfectly plastic material is obtained. From the analysis of the final deflections as a function of the applied impulse the “stability effect” of the viscous properties of the material on the buckling process is determined.     

Singular solutions in viscoplasticity under plane strain conditions

The paper deals with asymptotic behavior of viscoplastic solutions in the vicinity of maximum friction surfaces under plane strain conditions. The definition of maximum friction surfaces is that the friction stress is equal to the shear yield stress at sliding. The constitutive equations of the viscoplastic model adopted include a saturation stress. It is shown that it is possible to choose parameters of the viscoplastic model such that the regime of sliding is possible at maximum friction surfaces. In this case solutions are singular in the vicinity of such surfaces. Because of this feature of solutions, the viscoplastic model chosen possesses a smooth transition of qualitative behavior between rigid perfectly plastic and viscoplastic solutions, and this may prove to be advantageous for some applications.     

A viscoplastic constitutive model for nickel-base superalloy,part 2: modeling under anisothermal conditions

In Part 2 of this study, extensive deformation tests were carried out on the nickel-base polycrystalline superalloy IN738LC under isothermal and anisothermal conditions between 450 and 950 °C. Under the isothermal conditions, the material showed almost no rate/time-dependency below 700 °C, while it showed distinct rate/time-dependency above 800 °C. Regarding the cyclic deformation, slight cyclic hardening behavior was observed when the temperature was below 700 °C and the imposed strain rate was fast, whereas in the case of the temperature above 800 °C or under slower strain rate conditions, the cyclic hardening behavior was scarcely observed. Unique inelastic behavior was observed under in-phase and out-of-phase anisothermal conditions: with an increase in the number of cycles, the stress at higher temperatures became smaller and the stress at lower temperatures became larger in absolute value although the stress range was approximately constant during the cyclic loading. In other words, the mean stress continues to evolve cycle-by-cycle in the direction of the stress at lower temperatures. Based on the experimental results, it was assumed that evolution of the variable Y that had been incorporated into a kinematic hardening rule in Part 1 of this study is active under higher temperatures and is negligible under lower temperatures. The material constants used in the constitutive equations were determined with the isothermal data, and were expressed as functions of temperature empirically. The extended viscoplastic constitutive equations were applied to the anisothermal cyclic loading as well as the monotonic tension, stress relaxation, creep and cyclic loading under the isothermal conditions. It was demonstrated that the present viscoplastic constitutive model was successful in describing the inelastic behavior of the material adequately, including the anomalous inelastic behavior observed under the anisothermal conditions, owing to the consideration of the variable Y.     

Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms

This work presents a model to represent ductile failure (i.e. failure controlled by nucleation, growth and coalescence) of materials whose irreversible deformation is controlled by several plastic or viscoplastic deformation mechanisms. In addition work hardening may result from both isotropic and kinematic hardening. Damage is represented by a single variable representing void volume fraction. The model uses an additive decomposition of the plastic strain rate tensor. The model is developed based on the definition of damage dependant effective scalar stresses. The model is first developed within the generalized standard material framework and expressions for Helmholtz free energy, yield potential and dissipation potential are proposed. In absence of void nucleation, the evolution of the void volume fraction is governed by mass conservation and damage does not need to be represented by state variables. The model is extended to account for void nucleation. It is implemented in a finite element software to perform structural computations. The model is applied to three case studies: (i) failure by void growth and coalescence by internal necking (pipeline steel) where plastic flow is either governed by the Gurson–Tvergaard–Needleman model or the Thomason model, (ii) creep failure (Grade 91 creep resistant steel) where viscoplastic flow is controlled by dislocation creep or diffusional creep and (iii) ductile rupture after pre-compression (aluminum alloy) where kinematic hardening plays an important role.     

一种新的岩石非线性黏弹塑性蠕变模型研究

为了克服传统元件组合模型不能描述岩石蠕变过程中非线性特征的缺陷,首先根据加速蠕变阶段的应变和应变率随蠕变时间急剧增大的特点,建立黏塑性应变与蠕变时间的指数函数关系并提出非线性黏塑性体．将该非线性黏塑性体与广义Burgers蠕变模型串联,建立可以描述岩石全蠕变过程的非线性黏弹塑性蠕变模型,根据叠加原理得到一维应力状态下的轴向蠕变方程．然后基于塑性力学理论指出岩石三维蠕变本构方程建立过程中的不足之处,并给出非线性黏弹塑性蠕变模型合理的三维蠕变方程．最后采用不同应力水平下砂岩轴向蠕变试验对模型合理性进行验证,结果表明：拟合曲线与试验曲线吻合度较高,所建蠕变模型能够很好地描述砂岩在不同应力水平下的蠕变变形规律,尤其对加速蠕变阶段的非线性特征描述效果很好,验证了模型的合理性．     

Dislocation-based micropolar single crystal plasticity: Comparison of multi- and single criterion theories

Two new formulations of micropolar single crystal plasticity are presented within a geometrically linear setting. The construction of yield criteria and flow rules for generalized continuum theories with higher-order stresses can be done in one of two ways: (i) a single criterion can be introduced in terms of a combined equivalent stress and inelastic rate or (ii) or individual criteria can be specified for each conjugate stress/inelastic kinematic rate pair, a so-called multi-criterion theory. Both single and multi-criterion theories are developed and discussed within the context of dislocation-based constitutive models. Parallels and distinctions are made between the proposed theories and some of the alternative generalized crystal plasticity models that can be found in the literature. Parametric numerical simulations of a constrained thin film subjected to simple shear are conducted via finite element analysis using a simplified 2-D version of the fully 3-D theory to highlight the influence of specific model components on the resulting deformation under both loading and unloading conditions. The deformation behavior is quantified in terms of the average stress-strain response and the local shear strain and geometrically necessary dislocation density distributions. It is demonstrated that micropolar single crystal plasticity can qualitatively capture the same range of behaviors as slip gradient-based models, while offering a simpler numerical implementation and without introducing plastic slip rates as generalized traction-conjugate velocities subject to an additional microforce balance.     

Effects of matrix inelasticity on the overall hysteretic behavior of TiNi-SMA fiber composites

The effects of the inelastic deformation of the matrix on the overall hysteretic behavior of a unidirectional titanium–nickel shape-memory alloy (TiNi-SMA) fiber composite and on the local pseudoelastic response of the embedded SMA fibers are studied under the isothermal loading and unloading condition. The multiaxial phase transformation of the SMA fibers is predicted using the phenomenological constitutive equations which can describe the two-step deformation due to the rhombohedral and martensitic transformations, and the inelastic behavior of the matrix material using the standard nonlinear viscoplastic model. The average behavior of the SMA composite is evaluated with the micromechanical method of cells. It is observed that the inelastic deformation of the matrix due to prior tension results in a compressive stress in the matrix after unloading of the SMA composite and this residual stress impedes the complete recovery of the pseudoelastic strain of the SMA fibers. This explains that a closed hysteresis behavior of the SMA composite is no longer observed in contrast with the case that an elastic behavior of matrix is assumed. The predicted local stress–strain behavior indicates that the cyclic response of matrix is crucial to the design of the hysteretic performance of the SMA composite under the repeated loading conditions.     

Roles of plastic spin in shear banding

In this paper, the effects of plastic spin on shear banding and simple shear are examined systematically. Three types of plastic constitutive model with plastic spin are considered: (i) a non-coaxial model in which the direction of the plastic strain rate depends on that of the stress rate; (ii) a strain-softening model based on the J₂ flow theory; and (iii) the pressure-sensitive porous plasticity model. All the constitutive models are formulated in viscoplastic forms and in conjunction with non-local concepts that have been recently focused and discussed. First, behavior in simple shear is examined by numerical analysee with the aforementioned constitutive models. Moreover, some experimental evidences for stress response to simple shear are shown; that is, several large torsion tests of metal tubes and bars are carried out. Next, finite element simulations of shear banding in plane strain tension are performed. A critical effect of plastic spin on shear banding is observed for the noncoaxial model, while an almost negligible effect is observed for the porous model. The identical effects of plastic spin are observed, whether nonlocality exists or not. Finally, we discuss the relationship between the behavior in simple shear and the shear band formation. It is emphasized that this is a critical issue in predicting shear banding in macroscopic grounds.     

Role of strain-rate sensitivity in the crystal plasticity of hexagonal structures

In the first part of this paper the stress and strain-rate response of hexagonal crystal structures are examined when slip is viscoplastic according to a power law. The stress and strain-rate equi-potential surfaces are constructed and discussed as a function of the strain-rate sensitivity index m. The second part of this paper deals with the case of linear viscous slip; i.e., for the case when m is equal to one. A simple analytic solution is presented to obtain the deviatoric stress state for a given strain-rate. It is shown that the plastic spin is not zero for m = 1 in hexagonal crystal structures, contrary to the cubic case where the plastic spin vanishes. In addition, the rate of texture evolution in simple shear of a magnesium polycrystal is examined as a function of m.     

Experimental stress analysis for process of nonsteady inelastic deformation by photoviscoplasticity

The proposed photoviscoplasticity is a method for determining the stress distribution in nonsteady inelastic deformation during creep. The governing fundamental relations are derived by considering the effect of time as involved in the viscoplastic strain rate and the stress rate, and by considering the distinctive deformation properties of celluloid as model material. The validity of the fundamental relations are evaluated according to calibration test by using celluloid. The proposed method is applied for two practical applications of the compression of blocks by elastic punches and the compression of strip having a circular hole or semicircular notches. The time-dependent variation of stress states can be analyzed with the same accuracy as in the photoelasticity.     

Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking

Cleavage fracture in ferritic steels is often initiated in brittle carbides randomly distributed in the material. The carbides break as a result of a fibre loading mechanism in which the stress levels in the carbides are raised, as the surrounding ferrite undergoes plastic deformation. The conditions in the vicinity of the nucleated micro-crack will then determine whether the crack will penetrate or be arrested by the ferrite. The ferrite is able to arrest nucleated cracks through the presence of mobile dislocations, which blunt and shield the microcrack and thus lowers the stresses at the crack tip. Hence, the macroscopic toughness of the material directly depends on the ability of the ferrite to arrest nucleated micro-cracks and in turn on the plastic rate sensitivity of the ferrite. The initiation of cleavage fracture is here modelled explicitly in the form of a micro-crack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder or in a few cases an elastic sphere and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, where the tractions are governed by a modified exponential cohesive law. It is shown that the critical stress, required to propagate a microcrack from a broken carbide, increases with decreasing plastic rate sensitivity of the ferrite. The results also show that a low stress triaxiality and a high aspect ratio of the carbide promote the initiation of cleavage fracture from a broken carbide.     

Modeling mixed hardening of alkali halides with a modified version of an internal state variables model

In the ductile regime of inelastic flow, alkali halides behave similarly to various metals. Their behavior is fully plastic, shows strong rate and history dependencies, and exhibits anisotropic hardening. In this paper, the authors present the most recent version of SUVIC, a viscoplastic model with internal state variables (ISV). After recalling the main features of alkali halides inelastic response, the modified equations of the model are presented. They are then used to represent the behavior of polycrystalline sodium chloride submitted to conventional triaxial compression (CTC) and reduced triaxial extension (RTE) tests, using results that highlight mixed (kinematic and isotropic) hardening of the material, hence showing a type of Bauschinger effect. A discussion follows.     

钛镍形状记忆合金冲击变形后形状记忆效应的研究

采用SHPB技术和可控速率循环加温条件下变形恢复量测定装置研究了冲击及静载变形后的TiNi形状记忆合金的单程及双程形状记忆特性。发现马氏体状态下的TiNi合金的力学特性显示出明显的应变率强化效应 ,并且高应变率压缩应力应变曲线呈现流动平台。应变率对形状记忆效应的影响具有双重性 ,当外加应力或残余应变较小 ,可逆非弹性变形机制起主导作用时 ,提高应变率可以增加其单程形状记忆效应 ;而随外加应力或残余应变增大 ,当基于位错机制的不可逆非弹性变形机制起主导作用时 ,应变率提高却抑制了其单程形状记忆效应。应变率对TiNi合金双程形状记忆效应的影响视塑性变形的大小而异 ,高应变率动载后的双程形状记忆效应在较小塑性应变时 ,比静载后的要强 ;但在较大塑性应变时两者差别不大。