An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

Experimental study of the plastic yielding of rolled sheet metals with the cruciform plate specimen

In the current paper, an experimental technique for the evaluation of the in-plane yield loci of sheet metals with the cruciform plate specimen is presented. The measurement system is shown to conform to the optimized design concept proposed by other researchers. Finite element analysis demonstrates a reasonably wide area of uniform stress distribution in the center of the cruciform specimen, which allows the measurement of in-plane strain field by using a stacked strain rosette. Based on the designed apparatus, the yield loci of the 1100-F aluminum sheets corresponding to the as-received condition, and 25% and 50% thickness reductions by further rolling, were constructed, respectively, by applying biaxial loadings along the two principal axes of the cruciform specimen. A set of uniaxial tension tests were also performed to determine the plastic properties of the aluminum sheet along different directions with respect to the rolling direction. Finally, Hill's 1990 yield criterion is examined based on the experimental data from both biaxial and uniaxial tension tests.     

Mechanical and optical characterization of cellulose acetate

To obtain the basic relations for photo-viscoelastoplastic stress analysis using cellulose acetate, the effect of strain rate as well as room temperature on mechanical and optical properties was precisely investigated by the uniaxial tension test. As a result, the nonlinear stress-strain, the non-linear-stress-fringe order and the nonlinear-fringe-order strain relations were uniquely reoresented in their nondimensional forms regardless of strain rate and room temperature. Young's modulus, yield stress and the yield fringe order were linearly related both to room temperature and to logarithm of strain rate. The effect of strain rate on these relations has caused great difficulties in experimental stress analysis with respect to photoplasticity. However, it was found in this work that the value of the strain rate at any points in the model can be determined by the fringe-order rate measured. Therefore, it is possible to estimate not only the distribution of strain rate but that of stress or strain in the photo-viscoelastoplastic model with cellulose acetate.     

A plane stress anisotropic plastic flow theory for orthotropic sheet metals

A phenomenological theory is presented for describing the anisotropic plastic flow of orthotropic polycrystalline aluminum sheet metals under plane stress. The theory uses a stress exponent, a rate-dependent effective flow strength function, and five anisotropic material functions to specify a flow potential, an associated flow rule of plastic strain rates, a flow rule of plastic spin, and an evolution law of isotropic hardening of a sheet metal. Each of the five anisotropic material functions may be represented by a truncated Fourier series based on the orthotropic symmetry of the sheet metal and their Fourier coefficients can be determined using experimental data obtained from uniaxial tension and equal biaxial tension tests. Depending on the number of uniaxial tension tests conducted, three models with various degrees of planar anisotropy are constructed based on the proposed plasticity theory for power-law strain hardening sheet metals. These models are applied successfully to describe the anisotropic plastic flow behavior of 10 commercial aluminum alloy sheet metals reported in the literature.     

Photovisco-elastoplastic behavior of polycarbonate material under creep and tension tests

Polymers are widely used as photomechanical models of a prototype material (often a metal). Photoplasticity is one of the methods used in order to show the behavior of plastic materials stressed beyond the linear elastic limit. To illustrate this process we have analyzed the photovisco-elastoplastic behavior of polycarbonate as a photoplastic material. In this paper a technique for local and simultaneous measurement of birefringence and principal strains is presented. The mechanical and optical properties, at room temperature, have been evaluated by means of uniaxial tension tests. A series of creep tests has been carried out in order to study the photovisco-elastoplastic behavior of polycarbonate. In two different experiments we analyzed nonlinear birefringence and the amplitude of the corresponding strains. We could thus evaluate the distribution of strains and the distribution of uniaxial stress for each birefringence state and vice versa.     

Analysis of Stretching of Elastoplastic Samples and Necking with Edge Effects

Large deformations of elastoplastic cylindrical rods and shells of different thicknesses under tension are studied. The effect of sample geometry and the dependence of stresses on deformations under uniaxial tension on edge effects and necking are estimated. The applicability of the Considere criterion for determining the instance of stability loss of plastic tensile strain is analyzed. The computational experiments confirm that the role of similarity in the processes of nonuniform tensile strain of samples can be played by the ratio of the tangent of the slope of the true strain diagram to the stress intensity.     

Determining Stress–Strain in Rubber with In-Plane Biaxial Tensile Tester

The nominal stress–strain relationships of industrial rubber materials under multiaxial deformation are essential for precisely determining the constitutive laws of those materials. This paper proposes a new method for precisely estimating the nominal stress–stretch relationships of carbon-black-filled styrene butadiene rubbers (SBRs) under uniaxial tension, pure shear, and equibiaxial tension by using an in-plane biaxial tensile tester. The proposed method employs sheet-shaped rubber samples with notches for the pure-shear and equibiaxial tension tests to mitigate the influence of non-uniform deformation around the clamps. Finite element analysis and biaxial tensile tests were performed to verify the effectiveness of the proposed method. Performance evaluations based on both numerical calculations and experiments revealed that the proposed method enabled the precise calculation of the nominal stress–stretch relationship for uniform deformation from a tensile load and deformation of the reference area defined at the center of the samples.     

Photomechanical behavior of cellulose acetate under viscoelastoplastic deformation

To confirm the possibilities of cellulose acetate as a material for a model analysis during viscoelastoplastic deformation, the time-dependent photomechanical properties of the material were examined by means of creep tests under constant stress and recovery tests after removal of stress. Consequently, though the strain and the fringe order of cellulose acetate during creep and recovery are greatly influenced by stress and room temperature, both of them can be described simply by a power function of time, and the coefficient of each of these formulas can be represented by a function of the ratio of active stress to yield stress only. The effect of temperature is included in the formulation of the yield stress. In addition, the strain and the fringe order can be represented by the viscous-viscoelastic model proposed by Findleyet al.,^1,2 in which both of them are divided into four components: elastic, plastic, time-dependent irrecoverable viscous and time-dependent recoverable viscoelastic. The relation between viscoelastic strain and viscoelastic fringe order, and the relation between viscous strain and viscous fringe order were verified to be equivalent to that between plastic strain and plastic fringe order, all of which do not depend on stress, temperature or time. Therefore, the strain distribution of cellulose acetate under viscoelastoplastic deformation can be determined directly from the value of the fringe order measured.     

Stochastic damage model for concrete based on energy equivalent strain

Starting with the framework of conventional elastoplastic damage mechanics, a class of stochastic damage constitutive model is derived based on the concept of energy equivalent strain. The stochastic damage model derived from the parallel element model is adopted to develop the uniaxial damage evolution function. Based on the expressions of damage energy release rates (DERRs) conjugated to the damage variables thermodynamically, the concept and its tensor formulations of energy equivalent strain is proposed to bridge the gap between the uniaxial and the multiaxial constitutive models. Furthermore, a simplified coupling model is proposed to consider the evolution of plastic strain. And the analytical expressions of the constitutive model in 2-D are established from the abstract tensor expression. Several numerical simulations are presented against the biaxial loading test results of concrete, demonstrating that the proposed models can reflect the salient features for concrete under uniaxial and biaxial loading conditions.     

The effect of low-frequency biaxial loads on stress-concentration factors in plates

It is generally recognized that stress-concentration factors under stress-wave loading are lower than those under static loads. In this work, the effect of low-range frequency of biaxial sinusoidally varying alternating stresses on the stress-concentration factors for circular and elliptical holes in Plexiglas plates is investigated. The experiments have been performed on a specially designed and built “biaxial cyclic-stress machine” and the results are presented in the form of curves. In the case of biaxial alternating stresses, the stress-concentration factor is defined as the ratio of amplitude of the maximum alternating stress around the geometrical discontinuity to the larger of the amplitudes of the two principal alternating stresses which would occur at the same point, if the geometrical discontinuity was not present. Both values are considered over a stress cycle. The results indicate a slight decrease in the values of stress-concentration factors with increase in frequency.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

Large-deformation properties of wheat dough in uni- and biaxial extension. Part I. Flour dough

Rheological and fracture properties of optimally mixed flour doughs from three wheat cultivars which perform differently in cereal products were studied in uniaxial and biaxial extension. Doughs were also tested in small angle sinusoidal oscillation. In accordance with previously published results the linear region was found to be very small. The rheological properties at small deformations hardly depended on the cultivar. A higher water content of the dough resulted in a lower value for the storage modulus and a slightly higher value for tan . For both uniaxial and biaxial extension a more than proportional increase in stress was found with increasing strain, a phenomenon called strain hardening. In uniaxial extension (i) stresses at a certain strain were higher and (ii) the stress was less dependent on the strain rate than in biaxial extension. This indicates that in elongational flow orientational effects are of large importance for the mechanical properties of flour dough. This conclusion is consistent with published data on birefringence of stretched gluten. Fracture stress and strain increased with increasing deformation rate. The observed time-dependency of fracture properties can best be explained by inefficient transport of energy to the crack tip. Presumably, this is caused by energy dissipation due to inhomogeneous deformation because of friction between structural elements, e.g. between dispersed particles and the network. Differences in the rheological properties at large deformations between the cultivars were observed with respect to (i) stress, (ii) strain hardening, (iii) strain rate dependency of the stress, (iv) fracture properties and (v) the stress difference between uniaxial and biaxial extension.     

Fatigue crack opening stress based on the strip-yield model

The modified strip-yield model based on the Dugdale model and two-dimensional approximate weight function method were utilized to evaluate the effect of in-plane constraint, transverse stress, on the fatigue crack closure. The plastic zone sizes and the crack opening stresses considering transverse stress were calculated for four specimens: single edge-notched tension (SENT) specimen, single edge-notched bend (SENB) specimen, center-cracked tension (CCT) specimen, double edge-notched tension (DENT) specimen under uniaxial loading. And the crack opening behavior of the center-cracked specimen under biaxial loading was also evaluated. Normalized crack opening stresses σ_op/σ_max for four specimens were successfully described by the normalized plastic zone parameter Δω^′_rev/ω^′ considering transverse stress, where Δω^′_rev and ω^′ are the size of the reversed plastic zone at the moment of first crack tip closure and the size of the forward plastic zone for maximum stress, respectively. The normalized plastic zone parameter with transverse stress also was satisfactorily correlated with the behavior of crack closure for CCT specimen under biaxial loading.     

A plasticity and anisotropic damage model for plain concrete

A plastic-damage constitutive model for plain concrete is developed in this work. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. Moreover, in order to account for different effects under tensile and compressive loadings, two damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. Stiffness recovery caused by crack opening/closing is also incorporated. The strain equivalence hypothesis is used in deriving the constitutive equations such that the strains in the effective (undamaged) and damaged configurations are set equal. This leads to a decoupled algorithm for the effective stress computation and the damage evolution. It is also shown that the proposed constitutive relations comply with the laws of thermodynamics. A detailed numerical algorithm is coded using the user subroutine UMAT and then implemented in the advanced finite element program ABAQUS. The numerical simulations are shown for uniaxial and biaxial tension and compression. The results show very good correlation with the experimental data.     

基于中间构形的大变形弹塑性模型

在大变形弹塑性本构理论中,一个基本的问题是弹性变形和塑性变形的分解.通常采用两种分解方式,一是将变形率(或应变率)加法分解为弹性和塑性两部分,其中,弹性变形率与Kirchhoff应力的客观率通过弹性张量联系起来构成所谓的次弹性模型,而塑性变形率与Kirchhoff应力使用流动法则建立联系;另一种是基于中间构形将变形梯度进行乘法分解,它假定通过虚拟的卸载过程得到一个无应力的中间构形,建立所谓超弹性-塑性模型.研究了基于变形梯度乘法分解并且基于中间构形的大变形弹塑性模型所具有的若干性质,包括:在不同的构形上,塑性旋率的存在性、背应力的对称性、塑性变形率与屈服面的正交性以及它们之间的关系.首先,使用张量函数表示理论,建立了各向同性函数的若干特殊性质,并导出了张量的张量值函数在中间构形到当前构形之间进行前推后拉的简单关系式.然后,基于这些特殊性质和关系式,从热力学定律出发,建立模型在不同构形上的数学表达,包括客观率表示的率形式和连续切向刚度等,从而获得模型所具有的若干性质.最后,将模型与4种其他模型进行了比较分析.      

低碳钢单轴拉伸实验颈缩段的应力分析

为了深入研究塑性材料在单轴拉伸过程中的颈缩应力分布,结合Aramis三维应变测量系统对Q235钢和Q345钢进行了单轴拉伸实验。基于已有文献的颈缩外形理论,结合实验数据提出了颈缩阶段几何尺寸的变化规律公式,并与传统经验公式进行了对比。采用本文给出的颈缩阶段几何尺寸的变化规律公式计算,Q235钢误差率为27.73%,Q345钢误差率为20.49%;采用传统经验公式计算,Q235钢误差率为64.33%,Q345钢误差率为70.78%。结果表明,本文提出的变化规律公式精确度远高于传统公式精确度。基于此,在考虑材料系数的基础上推导出了包含材料系数的半解析半经验应力分布方程。     

Degradation of elastic modulus in elastoplastic coupling with finite strains

An elastic potential W is postulated for the case of the finite-strain theory of elastoplastic coupling with damage effects. The potential is defined in terms of the invariants of two internal variables p and q. The internal variables are used to express the degradation of the elastic stiffness tensor due to the accumulation of plastic strains. The material damage is independently introduced to both Lame's coefficients H and G. The physical significance of this softening of the elastic stiffness is demonstrated experimentally in uniaxial loading, reverse loading of metals at finite strains.

For elastoplastic coupling, the Il'Iushin postulate does not yield normality of the plastic strain increment. An associative flow rule is postulated in this work for the combined components of the plastic strain increment and the elastic coupling strain increment.

The formulation is implemented in the Langrangian coordinate system. Through the use of the Oldroyd or Truesdell stress rate, the equivalent consistent spatial coordinate formulation is presented.     

Unit cell debonding analyses for arbitrary orientation of plastic anisotropy

Debonding of rigid inclusions embedded in the elastic–plastic aluminum alloy Al 2090-T3 is analyzed numerically using a unit cell model taking full account of finite strains. The cell is subjected to overall biaxial plane strain tension and periodical boundary conditions are applied to represent arbitrary orientations of plastic anisotropy. Plastic anisotropy is considered using two phenomenological anisotropic yield criteria, namely Hill [Proceedings of the Royal Society of London A 193 (1948) 281] and Barlat et al. [International Journal of Plasticity 7 (1991) 693]. For this material plastic anisotropy delays debonding compared to plastic isotropy except for the case of Hill’s yield function when the tensile directions coincided with the principal axes of anisotropy. For some inclinations of the principal axes of anisotropy relative to the tensile directions, the stress strain responses are identical but the deformation modes are mirror images of each other.     

A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions

A combined necking and shear localization analysis is adopted to model the failures of two aluminum sheets, AA5754 and AA6111, under biaxial stretching conditions. The approach is based on the assumption that the reduction of thickness or the necking mode is modeled by a plane stress formulation and the final failure mode of shear localization is modeled by a generalized plane strain formulation. The sheet material is modeled by an elastic-viscoplastic constitutive relation that accounts for the potential surface curvature, material plastic anisotropy, material rate sensitivity, and the softening due to the nucleation, growth, and coalescence of microvoids. Specifically, the necking/shear failure of the aluminum sheets is modeled under uniaxial tension, plane strain tension and equal biaxial tension. The results based on the mechanics model presented in this paper are in agreement with those based on the forming limit diagrams (FLDs) and tensile tests. When the necking mode is suppressed, the failure strains are also determined under plane strain conditions. These failure strains can be used as guidances for estimation of the surface failure strains on the stretching sides of the aluminum sheets under plane strain bending conditions. The estimated surface failure strains are higher than the failure strains of the forming limit diagrams under plane strain stretching conditions. The results are consistent with experimental observations where the surface failure strains of the aluminum sheets increase significantly on the stretching sides of the sheets under bending conditions. The results also indicate that when a considerable amount of necking is observed for a sheet metal under stretching conditions, the surface failure strains on the stretching sides of the sheet metal under bending conditions can be significantly higher.