An endochronic theory accounting for deformation induced anisotropy of metals under biaxial load

Using the experimental results of yield surfaces obtained by Wu and Yeh [1991] (Int. J. Plasticity, 7, 803) for 304 stainless steel, this work provides a verification of the endochronic theory of plasticity accounting for deformation induced anisotropy. The experiments were performed under proportional loading conditions. The main difference between this paper and other papers that attempt to describe the distortion of a yield surface is that, in addition to distortion, motion of yield surface (kinematic hardening) has also been addressed by this paper. The result has shown that the theory predicts the experimental data with substantial accuracy. However, since in this theory the plastic strain increment, although normal to the initial yield surface, is in the radial direction emanating from the center of the subsequent yield surface, validity of the present model must be further studied for the case involving nonproportional loading conditions.     

An endochronic theory accounted for deformation induced anisotropy

An anisotropic quadratic form of plastic strain increment is used to define the intrinsic time in the endochronic theory of plasticity. Based on this new definition, a yield function can be derived. This new version of endochronic theory can describe the expansion, translation, rotation, and distortion of the yield surface. While the initial yielding is in the form of the Mises yield criterion, the distortion of subsequent yield surfaces is expressed by the compression or stretching of the Mises yield surface. The effect of sharp front and blunt rear of the yield surface is considered to be of secondary importance and neglected in the interest of keeping the equations simple. This idealization will not much affect the prediction power of the model, because the plastic strain increment is in the radial direction emanating from the center of the current yield surface and is not normal to the current yield surface. In this theory, the plastic deformation is thus not sensitive to the exact shape of the yield surface. It has been shown that the proposed theory is capable of describing the experimental results of three different metals considered. The test series investigated include several different paths of prestress.     

An endochronic constitutive model for rate-dependent and nonproportional cyclic plasticity

The total stress response of material is decomposed into a sum of an equilibrium stress response and a non-equilibrium overstress response. Correspondingly, the rate-independent intrinsic time and the rate-dependent intrinsic time are defined respectively. Additional hardening functions for describing the isotropic and anisotropic nonproportional effects are assumed to be related to the accumulation of plastic strain component along the normal of equilibrium stress trajectory, in which the effects of geometry of the loading path are included. An endochronic constitutive model for rate-dependent, nonproportional cyclic plasticity is formulated and applied to simulate the stress responses of stainless steel XCrNi18.9 for some typical loading programs at different loading rates. A comparison between predicted results and experimental ones by Haupt and Lion shows that the former are in agrreement with the latter.     

Analysis of simple shear endochronic equations for finite plastic deformation

IntroductionThestress_strainbehaviorofmaterialswithfiniteplasticdeformationisaninterestingissue ,onwhichsignificantprogresshasbeenmadethroughboththephenomenologicalandphysicalapproaches.Thephenomenologicalapproachisbasedoncontinuummechanicsofplasticity .Ithasitsadvantageinsolvingcomplicatedproblemsbecauseofitssimplicity .Mostofphenomenologicaltheoriesareinvolvedintheconceptofcorotationalrates.Thematerialderivativeofstresswasnotobjectiveunderfinitedeformation .TheJaumannratewasusuallyusedbefo…     

Modeling of deformation induced anisotropy in free-end torsion

The main purpose of this work is to develop a phenomenological model, which accounts for the evolution of the elastic and plastic properties of fcc polycrystals due to a crystallographic texture development and predicts the axial effects in torsion experiments. The anisotropic portion of the effective elasticity tensor is modeled by a growth law. The flow rule depends on the anisotropic part of the elasticity tensor. The normalized anisotropic part of the effective elasticity tensor is equal to the 4th-order coefficient of a tensorial Fourier expansion of the crystal orientation distribution function. Hence, the evolution of elastic and viscoplastic properties is modeled by an evolution equation for the 4th-order moment tensor of the orientation distribution function of an aggregate of cubic crystals. It is shown that the model is able to predict the plastic anisotropy that leads to the monotonic and cyclic Swift effect. The predictions are compared to those of the Taylor–Lin polycrystal model and to experimental data. In contrast to other phenomenological models proposed in the literature, the present model predicts the axial effects even if the initial state of the material is isotropic.     

混凝土率型内时损伤本构模型

混凝土是一种典型的率敏感材料,为了更好地描述混凝土结构在动力、冲击荷载作用下的强度和变形特征,本文结合内时理论和损伤理论建立了一种考虑混凝土率效应的内时损伤本构模型。该模型的特点:将混凝土材料的受力软化效应分解为密实状态的塑性效应和由微裂缝扩展引起的刚度退化效应。前者由内时理论来描述,这使该模型摆脱了一般弹塑性模型中屈服面的概念,从而更符合混凝土的变形特性,并且简化了非线性计算过程;后者由损伤理论来描述,根据混凝土的动力试验结果建立了增量型的损伤演变方程,从而使该模型能够较好地反映混凝土的动力特性。最后,应用本文建议的模型对一钢筋混凝土简支梁进行了非线性分析,结果表明:当结构承受快速荷载作用时,应变率对结构的受力性能影响较大,在进行结构分析时必须予以考虑。     

Effect of yield surface evolution on bending induced cross sectional deformation of thin-walled sections

Bend–stretch forming is commonly used to shape extruded tubular aluminum parts for automotive and other applications. The tubes are pre-stretched, pressurized and bent over rigid curved dies. Tension prevents buckling of the compressed side and helps reduce springback. An unwanted byproduct of the process is distortion of the cross section. Small amounts of pressure applied during forming can reduce this distortion. The problem was studied through a combination of experiment and analysis. In numerical models of the process the inelastic behavior of the aluminum alloy was modeled through isotropically hardening plasticity. With the limitations imposed by this model, use of a J₂-type yield surface resulted in uniform underprediction of cross sectional deformation. The predictions matched the measurements when a non-quadratic yield function appropriately “calibrated,” was used instead. The change in yield function shape alters the instantaneous normals to the yield surface which, in turn, affect the calculated strain increments. This paper demonstrates how suitably calibrated nonlinear kinematic hardening models can have the same corrective effect. The calibration involves selection of a suitable kinematic hardening rule. Changes in the hardening direction alter the instantaneous normals and therefore alter the plastic strain increments resulting in approximately the same net effect as the switch from the von Mises to the non-quadratic yield function.     

Model of plastic anisotropy evolution with texture-dependent yield surface

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.     

An endochronic plasticity formulation for filled rubber

The nature of elastomeric material demands the consideration of finite deformations, nonlinear elasticity including damage as well as rate-dependent and rate-independent dissipative properties. While many models accounting for these effects have been refined over time to do better justice to the real behavior of rubber-like materials, the realistic simulation of the elastoplastic characteristics for filled rubber remains challenging.The classical elastic-ideal-plastic formulation exhibits a distinct yield-surface, whereas the elastoplastic material behavior of filled rubber components shows a yield-surface free plasticity. In order to describe this elastoplastic deformation of a material point adequately, a physically based endochronic plasticity model was developed and implemented into a Finite Element code. The formulation of the ground state elastic characteristics is based on Arruda and Boyce (1993) eight-chain model. The evolution of the constitutive equations for the nonlinear endochronic elastoplastic response are derived in analogy to the Bergström–Boyce finite viscoelasticity model discussed by Dal and Kaliske (2009).     

Open-cell cellular solids: A constitutive equation for hyperelasticity with deformation induced anisotropy

A constitutive theory is developed for an open-cell flexible cellular solid consisting of a network of struts each connecting two vertex points. A hypothesis is proposed that vertex points move affinely in the large-deformation regime, when the struts buckle, and that the force carried by a strut is a function of the longitudinal and rotational change of its vertex-to-vertex vector. The forces consist of one longitudinal force, parallel with the vertex-to-vertex vector of the strut and one transverse force. The overall stress response is initially dominated by the longitudinal force whilst the addition of the transverse force becomes significant at large deformations. The model contains three parameters: longitudinal stiffness, bending stiffness and critical stretch of a strut. These three parameters are calibrated against a simple compression test. The model is then validated against independent experiments in a simple tension, simple shear and a combined shear-compression test on an isotropic flexible polyether urethane foam. Excellent agreement is obtained between the experiments and the model.     

An interface damage model accounting for in-plane effects

The present work deals with the formulation of a kinematic enriched model for cohesive interface. In fact, the interface kinematics is defined by the relative displacement occurring between the two surfaces of the interface and, even, by the strain arising in the plane of the interface. A damage model which accounts for the mode I and mode II and for the axial deformation of the interface is proposed starting from the Drucker–Prager failure criterion. A numerical procedure is developed implementing the proposed interface model into a new finite element. The nonlinear evolutive problem is solved adopting a predictor–corrector technique within the backward time integration scheme. Simple numerical simulations are presented in order to assess the features of the model. Moreover, numerical applications are carried out in order to demonstrate the ability of the proposed model in reproducing the mechanical behavior of the cohesive elements strengthened with external FRP reinforcements. Comparisons between available experimental data and numerical results obtained using the proposed model show the effectiveness of the presented formulation.     

An historical perspective of yield surface investigations for metals

This survey reviews work dealing either directly or indirectly with initial and subsequent yield surfaces. Emphasis is placed primarily on experimental investigations. Features of the work surveyed which are discussed include motivation, discrepancies, attempts to overcome discrepancies, and the nature of further work needed.     

Extremal properties of endochronic plasticity,part II: Extremal path of the constitutive equation with a yield surface and application

Extremal paths for endochronic constitutive equations without using a yield surface and the corresponding principle of minimum potential work were obtained in Part I of this article. In this paper, the extremal properties of endochronic constitutive equation with a yield surface and the corresponding method for deformation bound analysis are proposed. An example is presented that demonstrates that the application of endochronic constitutive models to simplified analysis is not significantly different from classical models due to the derived extremal properties. The adopted constitutive model involves both nonlinear isotropic and kinematic hardening, which may provide more accurate results in simplified and bounding analysis.     

Deformation induced anisotropy and memorized back stress in constitutive model

Plastic-deformation induced anisotropy and memorization of back stress due to pre-loading affect the current loading. These phenomena are examined with tension and/or torsion tests, using SUS 304. Considering both anisotropy, and movement and memorization of back stress, equi-plastic surfaces are predicted. This explains the dependence of current loading on pre-loading well. Simulated strain paths during radial loading after shear straining show good agreement with experiments.