Simulation of damage evolution in ductile metals undergoing dynamic loading conditions

A set of constitutive equations for large rate-dependent elastic-plastic-damage materials at elevated temperatures is presented to be able to analyze adiabatic high strain rate deformation processes for a wide range of stress triaxialities. The model is based on the concepts of continuum damage mechanics. Since the material macroscopic thermo-mechanical response under large strain and high strain rate deformation loading is governed by different physical mechanisms, a multi-dissipative approach is proposed. It incorporates thermo-mechanical coupling effects as well as internal dissipative mechanisms through rate-dependent constitutive relations with a set of internal variables. In addition, the effect of stress triaxiality on the onset and evolution of plastic flow, damage and failure is discussed.Furthermore, the algorithm for numerical integration of the coupled constitutive rate equations is presented. It relies on operator split methodology resulting in an inelastic predictor-elastic corrector technique. The explicit finite element program LS-DYNA augmented by an user-defined material subroutine is used to approximate boundary-value problems under dynamic loading conditions. Numerical simulations of dynamic experiments with different specimens are performed and good correlation of numerical results and published experimental data is achieved. Based on numerical studies modified specimens geometries are proposed to be able to detect complex damage and failure mechanisms in Hopkinson-Bar experiments.     

Experimental study and modeling of damage of Al alloys using tensor theory

This article presents and evaluates experiments for the characterization and modeling of damage of structural aluminum and aluminum–magnesium alloys. Tensile tests were performed for specimens with artificial defects (voids) represented by different arrangements of pre-drilled micro-holes. The corresponding stress–strain curves were experimentally obtained. Plastic dilatation and deviatoric strain were determined both for the local zones with artificial defects and directly for meso-elements (i.e., material cells with artificial defects). A symmetric second-rank order tensor of damage was applied for a quantitative estimate of the material damage connected with the volume fraction and shape of micro-defects. The definition of this tensor is physically motivated, since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume fraction 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 damage related to an increase in void volume fraction (i.e., plastic dilatation). A critical amount of plastic dilatation corresponds to the moment of macro-fracture of the deformed metal. By means of 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 meso-elements, and is related to the change in their shapes. The critical deformation of ellipsoidal voids corresponds to the onset of their coalescence and to the formation of large cavernous defects. The second measure is considered as a criterion of micro-destruction due to formation of cavities in the deformed material. Based on the experimental data, some numerical modeling is realized for the investigated Al alloys to taken a change in stress triaxiality into account. It shows that a change in triaxiality toward smaller values results in an appreciable decrease of damage induced by strain. Both damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques.     

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.     

半结晶聚合物损伤演化的实验表征与数值模拟

损伤本构模型对研究材料的断裂失效行为有重要意义, 但聚合物材料损伤演化的定量表征实验研究相对匮乏. 通过4种高密度聚乙烯(high density polythylene, HDPE)缺口圆棒试样的单轴拉伸实验获得了各类试样的载荷-位移曲线和真应力-应变曲线, 采用实验和有限元模拟相结合的方法确定了HDPE材料不同应力状态下的本构关系, 并建立了缺口半径与应力三轴度之间的关系;采用两阶段实验法定量描述了4种HDPE试样单轴拉伸过程中的弹性模量变化, 并建立了基于弹性模量衰减的损伤演化方程, 结合中断实验和扫描电子显微镜分析了应力状态对HDPE材料微观结构演化的影响. 结果表明缺口半径越小, 应力三轴度越大, 损伤起始越早、演化越快; 微观表现为: 高应力三轴度促进孔洞的萌生和发展, 但抑制纤维状结构的产生;基于实验和有限元模拟获得的断裂应变、应力三轴度、损伤演化方程等信息提出了一种适用于聚合物的损伤模型参数确定方法, 最后将本文获得的本构关系和损伤模型用于HDPE平板的冲压成形模拟, 模拟结果与实验结果吻合良好.      

45钢的J-C损伤失效参量研究

为了在结构碰撞效应的有限元分析中描述材料行为,通过开展45钢在不同应力状态和温度下的准静态材料力学性能实验及拉伸SHB实验,考察了应力状态三轴度、温度和应变率对材料失效应变的影响。由实验数据得到了Johnson-Cook失效模型参量,并通过出现失效的Taylor撞击实验和数值模拟进行了一定的验证,表明模型描述与实验结果的趋势一致。     

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.     

基于应力三轴度和罗德参数的6061和7075铝合金材料断裂失效分析

分别对6061铝合金和7075铝合金材料的缺口圆棒试件和凹槽平板试件进行准静态拉伸试验,并采用ABAQUS软件对拉伸过程进行数值模拟。模拟结果与试验测试结果吻合很好,验证了有限元模型的合理性和可靠性。通过有限元模拟,分别给出了不同试件的应力三轴度和罗德参数随等效塑性应变的变化曲线以及两种材料的失效轨迹,并对它们进行了分析讨论。结果表明:形状相同、材料性质不同的试件,应力三轴度的演化规律不同;材料的失效应变受应力三轴度和罗德参数的影响,并且不同性质的材料对罗德参数的敏感性不同。     

复杂应力状态镍基单晶合金低周疲劳损伤模型

根据连续介质损伤力学理论,采用应变能释放率作为热力学广义力描述正交异性材料的疲劳损伤过程,引入取向函数考虑镍基单晶合金晶体取向对疲劳损伤的非线性影响,提出了一个各向异性疲劳损伤模型。应用多元线性回归分析方法,拟合疲劳试验数据可确定模型参数。从应变能释放率的应变空间表达式出发,导出了含有3个弹性常数的单晶合金应变三轴性因子,它既反映了材料性能的晶体取向相关性,又反映了正应力和剪应力的相互作用,并可退化为各向同性材料的应变三轴性因子。利用该模型对CMSX-2镍基单晶合金在应力控制对称循环拉-扭载荷作用下的低周疲劳寿命进行预测,预测值与试验值吻合的相当好,试验所得数据均落在2.2倍偏差的分布带内。     

On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions

One of the major drawbacks of the Gurson-type of porous plasticity models is the inability of these models to predict material failure under low stress triaxiality, shear dominated conditions. This study addresses this issue by combining the damage mechanics concept with the porous plasticity model that accounts for void nucleation, growth and coalescence. In particular, the widely adopted Gurson–Tvergaard–Needleman (GTN) model is extended by coupling two damage parameters, representing the volumetric damage (void volume fraction) and the shear damage, respectively, into the yield function and flow potential. The effectiveness of the new model is illustrated through a series of numerical tests comparing its performance with existing models. The current model not only is capable of predicting damage and fracture under low (even negative) triaxiality conditions but also suppresses spurious damage that has been shown to develop in earlier modifications of the GTN model for moderate to high triaxiality regimes. Finally the modified GTN model is applied to predict the ductile fracture behavior of a beta-treated Zircaloy-4 by coupling the proposed damage modeling framework with a recently developed J₂–J₃ plasticity model for the matrix material. Model parameters are calibrated using experimental data, and the calibrated model predicts failure initiation and propagation in various specimens experiencing a wide range of triaxiality and Lode parameter combinations.