Elastic–plastic FE analysis of a notched shaft under multiaxial nonproportional synchronous cyclic loading

An elastic–plastic finite element analysis is presented for a notched shaft subjected to multiaxial nonproportional synchronous cyclic tension/torsion loading. The elastic–plastic material property is described by the von Mises yield criterion and the kinematic hardening rule of Prager/Ziegler. The finite element program system ABAQUS is used to solve the boundary value problem. Special emphasis is given to explore the effects of the stress amplitude, the mean-stress, and the mutual interactions on the local stress–strain responses at the notch root.     

Elastic-plastic behaviour of dual-phase, high-strength steel under strain-path changes

The elastic-plastic behaviour of dual-phase, high-strength steel sheets under two-stage strain-path changes has been investigated. Three different loading sequences, namely monotonic, 45° tensile path changes and orthogonal tensile path changes complied by sequences of simple uniaxial tensile tests, were analysed at room temperature. From the experiments, it was found that there is a considerable reduction of the initial flow stress over the strain-path changes. The transient softening phenomenon is observed to be a function of orientation, and the period of the transient behaviour following the strain-path change is lengthened with the amount of pre-strain. A constitutive model is adopted that includes combined isotropic and kinematic hardening and is capable of describing the marked transient softening behaviour after the pre-straining. The experimental stress–strain behaviour subsequent to the strain path change is predicted with reasonable accuracy, while the model fails to accurately describe the transient, deformation-induced anisotropy in the plastic flow.     

Elastic–plastic and elastic anti-plane shear of two parallel cracks

Two infinite interacting parallel cracks in an elastic–plastic and in an elastic body under anti-plane strain (mode III) loading conditions are considered. The body is subjected to vanishing remote loading and the cracks are traction free. Closed-form solution is found for the elastic–plastic problem in terms of elementary functions, where the shape of the plastic boundary is obtained. The complete stress distribution is obtained in an inverse form i.e. physical coordinates are functions of stresses.     

Finite element modeling of plastic anisotropy induced by texture and strain-path change

Consideration of plastic anisotropy is essential in accurate simulations of metal forming processes. In this study, finite element (FE) simulations have been performed to predict the plastic anisotropy of sheet metals using a texture- and microstructure-based constitutive model. The effect of crystallographic texture is incorporated through the use of an anisotropic plastic potential in strain-rate space, which gives the shape of the yield locus. The effect of dislocation is captured by use of a hardening model with four internal variables, which characterize the position and the size of the yield locus. Two applications are presented to evaluate the accuracy and the efficiency of the model: a cup drawing test and a two-stage pseudo-orthogonal sequential test (biaxial stretching in hydraulic bulging followed by uniaxial tension), using an interstitial-free steel sheet. The experimental results of earing behavior in the cup drawing test, maximum pressure and strain distribution in bulging, and transient hardening in the sequential test are compared against the FE predictions. It is shown that the current model is capable of predicting the plastic anisotropy induced by both the texture and the strain-path change. The relative significance of texture and strain-path change in the predictions is discussed.     

Perfect Plasticity Theory: State of the Art and Development Trends

The state of the art and development trends of model conceptions in perfect plasticity theory are overviewed. The paper does not consider limit equilibrium theorems, theory of optimum design and adaptability, flow problems in metal forming, dynamic behavior of rigid–plastic and elastic–plastic bodies, etc     

Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD

The forming limit diagram (FLD) is used in sheet metal forming analysis to determine how close the sheet metal is to tearing when it is formed into a product shape in a stamping process. The strain-path dependent nature of the FLD causes the method to become ineffective in the analysis of complex forming process, especially restrikes, flanging operations, hydroforming, and even first draw dies with deep pockets or embossments. Experimental evidence for a path-independent stress-based FLD has been reported in the literature, suggesting that the path dependency of the strain-based approach arises from the path dependent constitutive laws governing the relationship between the stress and strain tensors. This paper reviews several theoretical models of sheet metal forming instability, including bifurcation analyses of diffuse and through-thickness neck formation, the M-K model and microscopic void damage models. The equations governing the deformation at the instant of the bifurcation is shown to be independent of path in all of these models, providing a solid theoretical bases for the stress-based approach. The stress-based FLD can now be used equally well for all forming processes, without concern for path effects.     

Rate-dependent quasi-flow corner theory for elastic/visco-plastic materials

A rate-dependent quasi-flow plastic constitutive model with punch-speed sensitivity is proposed for the large-deformation sheet metal forming process, which is based on the quasi-flow corner theory and U–L formulation for the virtual work-rate equation. Three kinds of constitutive theories with strain rate dependence, classical flow theory, deformation theory with rate form obeying non-orthogonality rule, and the present quasi-flow corner theory, are introduced into the U–L finite element formulation to simulate the deformation localization processes of plane strain tension in order to investigate effects of strain rate sensitivity on the localizing deformation characters. Furthermore, three kinds of typical forming processes sheet metals, one being an uniaxial stretching and another being a square cup drawing with circular blank, and third being a deep drawing of an oil pan, actual industrial forming part, are also numerically simulated by the present model and compared with experimental results. Good agreement between numerical simulation and experimental ones exhibits the validity of the quasi-flow corner theory.     

Numerical analysis and elastic–plastic deformation behavior of anisotropically damaged solids

The present paper is concerned with the numerical modelling of the large elastic–plastic deformation behavior and localization prediction of ductile metals which are sensitive to hydrostatic stress and anisotropically damaged. The model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics. The formulation relies on a multiplicative decomposition of the metric transformation tensor into elastic and damaged-plastic parts. Furthermore, undamaged configurations are introduced which are related to the damaged configurations via associated metric transformations which allow for the interpretation as damage tensors. Strain rates are shown to be additively decomposed into elastic, plastic and damage strain rate tensors. Moreover, based on the standard dissipative material approach the constitutive framework is completed by different stress tensors, a yield criterion and a separate damage condition as well as corresponding potential functions. The evolution laws for plastic and damage strain rates are discussed in some detail. Estimates of the stress and strain histories are obtained via an explicit integration procedure which employs an inelastic (damage-plastic) predictor followed by an elastic corrector step. Numerical simulations of the elastic–plastic deformation behavior of damaged solids demonstrate the efficiency of the formulation. A variety of large strain elastic–plastic-damage problems including severe localization is presented, and the influence of different model parameters on the deformation and localization prediction of ductile metals is discussed.     

Prediction of strength using flat cylindrical indentation method

Strength of structural components is predicted. Two cases have been studied to explore the possibility of determining the damage level of the materials by the flat cylindrical indentation method with the help of the finite element method (FEM). The first uses the Gurson model for analyzing the elastic–plastic damage. The second uses the Katchanov–Robotnov law to predict the creep damage. The analytical results show that the damage levels can be determined by the flat cylindrical indentation experimental method.     

A simple isotropic-distortional hardening model and its application in elastic–plastic analysis of localized necking in orthotropic sheet metals

In the present work an elastic–plastic constitutive model including mixed isotropic-distortional hardening is presented. The approach is very simple and requires only experimental data that are part of the standard characterization of sheet metals. It is shown that the distortional hardening contribution can be of considerable importance for localized necking prediction in orthotropic sheet metals.     

Investigation of advanced strain-path dependent material models for sheet metal forming simulations

Sheet metal forming processes often involve complex loading sequences. To improve the prediction of some undesirable phenomena, such as springback, physical behavior models should be considered. This paper investigates springback behavior predicted by advanced elastoplastic hardening models which combine isotropic and kinematic hardening and take strain-path changes into account. A dislocation-based microstructural hardening model formulated from physical observations and the more classical cyclic model of Chaboche have been considered in this work. Numerical implementation was carried out in the ABAQUS software using a return mapping algorithm with a combined backward Euler and semi-analytical integration scheme of the constitutive equations. The capability of each model to reproduce transient hardening phenomena at abrupt strain-path changes has been shown via simulations of sequential rheological tests. A springback analysis of strip drawing tests was performed in order to emphasize the impact of several influential parameters, namely: process, numerical and behavior parameters. The effect of the two hardening models with respect to the process parameters has been specifically highlighted.     

Elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with progressive debonding damage

This paper deals with elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with debonding damage of particle-matrix interface. Numerical analyses are carried out on a crack-tip field in elastic-matrix and elastic–plastic-matrix composites reinforced with elastic particles, using a finite element method developed based on an incremental damage theory of particulate-reinforced composites. A particle volume fraction and interfacial strength between particles and matrix of the composites are parametrically changed. In the elastic-matrix composites, a unique elastic singular field is created on the complete damage zone in the vicinity of a crack-tip in addition to the conventional elastic singular field on the no damage zone. The macroscopic stress level around a crack-tip is reduced by the debonding damage while the microscopic stress level of the matrix remains unchanged. In the elastic–plastic-matrix composites, the damage zone develops in addition to the plastic zone due to matrix plasticity, and both the macroscopic and microscopic stress revels around a crack-tip are reduced by the debonding damage. It is concluded from the numerical results that the toughening due to damage could be expected in the elastic–plastic-matrix composites, while it is questionable in the elastic-matrix composites.     

A physico-mechanical approach to modeling of metal forming processes—part I: theoretical framework

A combined physico-mechanical approach to research and modeling of forming processes for metals with predictable properties is developed. The constitutive equations describing large plastic deformations under complex loading are based on both plastic flow theory and continuum damage mechanics. The model which is developed in order to study strongly plastically deformed materials represents their mechanical behavior by taking micro-structural damage induced by strain micro-defects into account. The symmetric second-rank order tensor of damage is applied for the estimation of the material damage connected with volume, shape, and orientation of micro-defects. The definition offered for this tensor is physically motivated since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume and shape of micro-defects, respectively. Such a representation of damage kinetics allows us to use two integral measures for the calculation of damage in deformed materials. The first measure determines plastic dilatation related to an increase in void volume. A critical amount of plastic dilatation enables a quantitative assessment of the risk of fracture of the deformed metal. By means of an experimental analysis we can determine the function of plastic dilatation which depends on the strain accumulated by material particles under various stress and temperature-rate conditions of forming. The second measure accounts for the deviatoric strain of voids which is connected with a change in their shape. The critical deformation of ellipsoidal voids corresponds to their intense coalescence and to formation of large cavernous defects. These two damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques. Experimental results of various previous investigations are used during modeling of the damage process.      

J-integral and crack driving force in elastic–plastic materials

This paper discusses the crack driving force in elastic–plastic materials, with particular emphasis on incremental plasticity. Using the configurational forces approach we identify a “plasticity influence term” that describes crack tip shielding or anti-shielding due to plastic deformation in the body. Standard constitutive models for finite strain as well as small strain incremental plasticity are used to obtain explicit expressions for the plasticity influence term in a two-dimensional setting. The total dissipation in the body is related to the near-tip and far-field J-integrals and the plasticity influence term. In the special case of deformation plasticity the plasticity influence term vanishes identically whereas for rigid plasticity and elastic-ideal plasticity the crack driving force vanishes. For steady state crack growth in incremental elastic–plastic materials, the plasticity influence term is equal to the negative of the plastic work per unit crack extension and the total dissipation in the body due to crack propagation and plastic deformation is determined by the far-field J-integral. For non-steady state crack growth, the plasticity influence term can be evaluated by post-processing after a conventional finite element stress analysis. Theory and computations are applied to a stationary crack in a C(T)-specimen to examine the effects of contained, uncontained and general yielding. A novel method is proposed for evaluating J-integrals under incremental plasticity conditions through the configurational body force. The incremental plasticity near-tip and far-field J-integrals are compared to conventional deformational plasticity and experimental J-integrals.     

The shear fracture of dual-phase steel

Unexpected fractures at high-curvature die radii in sheet forming operations limit the adoption of advanced high strength steels (AHSS) that otherwise offer remarkable combinations of high strength and tensile ductility. Identified as “shear fractures” or “shear failures,” these often show little sign of through-thickness localization and are not predicted by standard industrial simulations and forming limit diagrams. To understand the origins of shear failure and improve its prediction, a new displacement-controlled draw-bending test was developed, carried out, and simulated using a coupled thermo-mechanical finite element model. The model incorporates 3D solid elements and a novel constitutive law taking into account the effects of strain, strain rate, and temperature on flow stress. The simulation results were compared with companion draw-bend tests for three grades of dual-phase (DP) steel over a range of process conditions. Shear failures were accurately predicted without resorting to damage mechanics, but less satisfactorily for DP 980 steel. Deformation-induced heating has a dominant effect on the occurrence of shear failure in these alloys because of the large energy dissipated and the sensitivity of strain hardening to temperature increases of the order of 75 °C. Isothermal simulations greatly overestimated the formability and the critical bending ratio for shear failures, thus accounting for the dominant effect leading to the inability of current industrial methods to predict forming performance accurately. Use of shell elements (similar to industrial practice) contributes to the prediction error, and fracture (as opposed to strain localization) contributes for higher-strength alloys, particularly for transverse direction tests. The results illustrate the pitfall of using low-rate, isothermal, small-curvature forming limit measurements and simulations to predict the failure of high-rate, quasi-adiabatic, large-curvature industrial forming operations of AHSS.     

On an elastic-plastic transition zone in cellular metals

Summary A theory of plasticity is proposed for cellular metals to describe their elastic-plastic transition zone at small strain. Under certain conditions, only a plane strain test is necessary to determine the yield surface. The method to derive the elastic–plastic behaviour [14, 15] was originally proposed for classical metals. A simple cubic model of a cellular metal is used to demonstrate the method by the finite element method. Recommendations for the numerical simulation are given. The influence of the relative density and the hardening behaviour of the cell wall material is investigated.     

用损伤理论方法预测铝合金薄板成型极限

应用各向异性损伤理论研究2024-T3铝合金薄板的成形极限,通过构造有限元单胞模型预测薄板结构的极限应变.单胞模型由两相材料组成:铝合金基体和金属强化物.基体采用全耦合弹塑性-损伤本构方程描述,而金属强化物则视为弹脆性材料.采用所提出的缩颈准则,得到了双轴拉伸状态下铝合金薄板的极限应变,和实验结果比较两者吻合较好.研究结果揭示有限元单胞模型可以提供铝合金的细观损伤机理信息,当忽略材料的损伤影响,采用金属薄板成型理论的研究结果将过高估计薄板的极限应变.     

A class of plastic constitutive equations with vertex effect—IV. Applications to prediction of forming limit strains of metal sheets under nonproportional loadings

The new plastic (elastoplastic) constitutive equation with vertex effect which was proposed and developed in the previous papers is applied to prediction of the forming limit strains of metal sheets which are subjected to various nonproportional loading without unloading and to proportional loading after another proportional loading with or without unloading. It is demonstrated that the constitutive equation is very effective, that appropriately curved strain-paths give much larger limiting strains than the corresponding straight paths do, that abrupt change in stress- or strain-path very often induces a catastrophic breakage at the instant of the path-change, and that very useful secondary FLDs (forming limit diagrams) can be drawn.