Simulation of failure under cyclic plastic loading by damage models

The purpose of this work is to simulate the evolution of ductile damage and failure involved by plastic strain reversals using damage models based on either continuum damage mechanics (CDM) or porosity evolution. A low alloy steel for pressure vessels (20MnMoNi55) was chosen as reference material. The work includes both experimental and simulation phases. The experimental campaign involves different kinds of specimens and testing conditions. First, monotonic tensile tests have been performed in order to evaluate tensile and ductile damage behaviour. Then, the cyclic yielding behaviour has been characterized performing cyclic plasticity tests on cylindrical bars. Finally, cyclic loading tests in the plastic regime have been made on different round notched bars (RNBs) to study the evolution of plastic deformation and damage under multiaxial stress conditions. The predictions of the different models were compared in terms of both, the specimens macroscopic response and local damage. Special emphasis was laid on predictions of the number of cycles prior to final failure and the crack initiation loci.     

A constitutive framework of plastically deformed damaged continuum and a formulation using theendochronic concept

The concepts of continuum damage mechanics (CDM) are discussed and aconstitutive framework of CDM is proposed for infinitesimal deformation based on the internalvariables approach. The framework involves transforming the actual damaged continuum into anequivalent fictitious undamaged continuum. A distinction is made between the state of damageand the damage measure. The development makes use of the concept of damage force. Thenegative of the damage force is related to the energy required to restore the fictitious undamagedcontinuum to its undamaged state after each step of deformation and damage. A set of equationand constraint governs the deformation of the fictitious continuum, while another set of equationand constraint governs the damage behavior. The coupling between the deformation and damageprocesses is provided for by the damage restoring force concept. Within the proposedconstitutive framework, the endochronic concept has been used to derive explicit constitutiveequations. The proposed model has been shown to describe the three-dimensional state ofdeformation of a cylindrical concrete specimen subjected to uniaxial compression.     

Ductile damage evolution under triaxial state of stress: theory and experiments

In this paper, the continuum damage mechanics (CDM) model formulation proposed by [Eng. Fract. Mech. 58(1/2) (1997) 11] has been validated against ductile damage evolution experimentally measured in A533B low alloy steel under various stress triaxiality conditions. A procedure to identify the model parameters has been defined first. Then, the model has been used to simulate, via finite element analysis (FEA), tests on notched flat rectangular bars with different notch radii. The experiments and the FEA predictions are finally compared with each other. The results presented here confirm the transferability of damage parameters definition and the potential of the proposed damage model in predicting ductile failure occurrence in structures and components under multi-axial state of stress loading conditions.     

一个新的普遍形式的局部损伤断裂准则

利用损伤函数概念，建立了一个普遍形式的局部断裂准则。该准则考虑了局掊应力，应变和损伤历史对断裂的影响，根据损伤力学理选取了一个新的连续损伤函数，从而导出一个新的连续损伤断裂准则。新的临界断裂参数ＷＤＣ，具有明显的物理意义，且易通过试验测得，是一个不依赖于应力状态的材料九。文中还从细观力学理论和有关的试验资料出发，选取了相应的损伤函数，再现了前人的细观力学准则和经验准则。     

A study on the damage evaluation of weld heat affected zone

From the micro- and macroscopic points of view, the damage evolution of weld-simulated heat affected zone (HAZ) is studied. In the framework of continuum damage mechanics (CDM), the ductile and low cycle fatigue (LCF) damage evolution laws of HAZ have been examined. Two alternative laws of damage are proposed in this paper, which may meet the need for describing damage evolution of ductile rupture and LCF fracture, respectively.     

Breakage mechanics—Part I: Theory

Different measures have been suggested for quantifying the amount of fragmentation in randomly compacted crushable aggregates. A most effective and popular measure is to adopt variants of Hardin's [1985. Crushing of soil particles. J. Geotech. Eng. ASCE 111(10), 1177-1192] definition of relative breakage ‘B_r’. In this paper we further develop the concept of breakage to formulate a new continuum mechanics theory for crushable granular materials based on statistical and thermomechanical principles. Analogous to the damage internal variable ‘D’ which is used in continuum damage mechanics (CDM), here the breakage internal variable ‘B’ is adopted. This internal variable represents a particular form of the relative breakage ‘B_r’ and measures the relative distance of the current grain size distribution from the initial and ultimate distributions. Similar to ‘D’, ‘B’ varies from zero to one and describes processes of micro-fractures and the growth of surface area. However, unlike damage that is most suitable to tensioned solid-like materials, the breakage is aimed towards compressed granular matter. While damage effectively represents the opening of micro-cavities and cracks, breakage represents comminution of particles. We term the new theory continuum breakage mechanics (CBM), reflecting the analogy with CDM. A focus is given to developing fundamental concepts and postulates, and identifying the physical meaning of the various variables. In this part of the paper we limit the study to describe an ideal dissipative process that includes breakage without plasticity. Plastic strains are essential, however, in representing aspects that relate to frictional dissipation, and this is covered in Part II of this paper together with model examples.     

一个高周疲劳损伤演化修正模型

将连续损伤力学应用到疲劳问题中, 得到合理的疲劳损伤演化方程,被认为是预测疲劳寿命最有效的方法之一. 在研究Lemaitre最新疲劳损伤演化方程基础上, 根据试验数据提出了一个修正的高周疲劳损伤演化方程, 该方程可以考虑应力幅、平均应力等影响因素. 以2A12-T4铝合金为例, 得到了修正模型的材料常数. 将该修正模型以UMAT子程序形式嵌入ABAQUS主程序, 计算了两种构件14种不同受载情况下的疲劳寿命, 所得计算寿命与试验结果误差均值约15%, 说明修正的疲劳损伤演化方程可以很好地计算金属构件的高周疲劳寿命.      

A micro-mechanically based continuum damage model for fatigue life prediction of filled rubbers

This paper presents a continuum damage model based on two mechanisms: decohesion between fillers and matrix at a micro-scale followed by a crack nucleation at a macro-scale. That scenario was developed considering SEM observations and an original experimental procedure based on simple shear and tension specimens. Damage accumulation is related to fatigue life using the continuum damage mechanics (CDM). The material behavior is investigated using the statistical framework introduced by Martinez et al. (2011). A Finite Element implementation is proposed and some numerical examples are provided.     

复合材料层合板面内渐进损伤分析的CDM模型

基于连续介质损伤力学,提出了一个预测复合材料层合板面内渐进损伤分析的模型,它包括损伤表征、损伤判定和损伤演化3 部分. 模型能够区分纤维拉伸断裂、纤维压缩断裂、纤维间拉伸损伤和纤维间压缩损伤4 种损伤模式,定义了与4 个损伤模式对应的损伤状态变量,导出了材料主轴系下损伤前后材料本构之间的关系. 损伤起始采用Puck 准则判定,损伤演化由特征长度内应变能释放密度控制. 假定材料服从线性应变软化行为,建立了损伤状态变量关于断裂面上等效应变的渐进损伤演化法则. 模型涵盖了复合材料面内损伤起始、演化直至最终失效的全过程. 完成了含孔[45/0/-45/90]_2S 层合板在拉伸和压缩载荷下失效分析,结果表明该模型能合理进行层合板的强度预测和损伤失效分析.      

Strong discontinuity analysis of a class of anisotropic continuum damage constitutive models – Part I: Theoretical considerations

Several modeling techniques aiming at considering cracks as kinematics discontinuities have been proposed for the past years. Within this scope, the embedded finite element method (E-FEM) was introduced a couple of years ago. Among the features of this approach, it has been shown that a kinematic enhancement of the displacement field allows constructing a discrete model (expressed in terms of traction vector–displacement jump) from any continuous model (expressed in terms of stress–strain). This result has been rigorously established if the continuous model is formulated within the framework of either isotropic continuum damage or plasticity theories. The objectives of this study are (i) to extend this result in case where the continuous model belongs to a class of anisotropic continuum damage constitutive models and (ii) to show the main features of a specific traction/separation law derived from the aforementioned class of constitutive models through several numerical case-studies. In this paper, the light is put on the theoretical considerations which allow deriving discrete models in a consistent way.     

复合材料层合板面内渐进损伤分析的CDM模型简

基于连续介质损伤力学,提出了一个预测复合材料层合板面内渐进损伤分析的模型,它包括损伤表征、损伤判定和损伤演化3 部分. 模型能够区分纤维拉伸断裂、纤维压缩断裂、纤维间拉伸损伤和纤维间压缩损伤4 种损伤模式,定义了与4 个损伤模式对应的损伤状态变量,导出了材料主轴系下损伤前后材料本构之间的关系. 损伤起始采用Puck 准则判定,损伤演化由特征长度内应变能释放密度控制. 假定材料服从线性应变软化行为,建立了损伤状态变量关于断裂面上等效应变的渐进损伤演化法则. 模型涵盖了复合材料面内损伤起始、演化直至最终失效的全过程. 完成了含孔[45/0/-45/90]_2S 层合板在拉伸和压缩载荷下失效分析,结果表明该模型能合理进行层合板的强度预测和损伤失效分析.     

CDM modeling of ductile failure in ferritic steels: Assessment of the geometry transferability of model parameters

One of the most important features of micromechanical models, with respect to other global approaches to fracture, is that progressive damage and failure can be described only by parameters characteristic of the material and not of the geometry. In spite of the large number of papers on micromechanical modeling presented in literature, a detailed assessment the geometry transferability of model parameters has been addressed in a limited number of works. In most of the cases, the model parameters transferability is analyzed only for one geometrical configuration other than that – usually a uniaxial tensile bar – on which the parameters set has been identified. In this paper, the continuum damage mechanics approach, as proposed by [Bonora, N., 1997. A non-linear CDM model for ductile failure. Engineering Fracture Mechanics 58, 11–28] is used to model ductile damage processes in ferritic steels. The geometry transferability of the damage parameters is demonstrated both in the range of low and high stress triaxiality. The possibility to accurately predict constraint effects on material crack resistance curve is demonstrated.     

复合材料层合板低速冲击损伤分析的连续介质损伤力学模型

针对复合材料层合板低速冲击损伤问题,提出了一种各向异性材料连续介质损伤力学模型,模型涵盖损伤表征、损伤起始判定和损伤演化法则3 个方面. 通过材料断裂面坐标下的损伤状态变量矩阵完成损伤表征,并考虑断裂面角度的影响,建立了主轴坐标系下的材料损伤本构关系. 损伤起始由卜克(Puck) 失效准则预测,损伤演化由断裂面上的等效应变控制,服从基于材料应变能释放的线性软化行为. 模型区分了纤维损伤和基体损伤,并根据冲击载荷下层内产生多条基体裂纹继而扩展至界面形成层间裂纹(分层) 的试验观察,引入基体裂纹饱和密度参数表征层间分层. 以[0₃/45/-45]_S 和[45/0/-45/90]_4S 两种铺层的复合材料层合板为例,预测了不同冲击能量下复合材料层合板的低速冲击损伤响应参数,试验结果证明了连续介质损伤力学模型的有效性.模型在不同网格密度下的计算结果表明单元特征长度的引入可以在一定程度上降低损伤演化阶段对网格密度的依赖性.      

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.     

热力学相容的混凝土各向异性单边损伤模型

微裂缝演化(损伤)引起的各向异性和单边效应,对于混凝土材料和结构的变形和内力有非常重要的影响. 在描述单边效应时,已有的各向异性损伤模型均会得出与热力学基本原理相矛盾的结论即损伤卸载时能量耗散不为零. 基于不可逆热力学和内变量理论,直接以材料柔度张量的增量作为损伤内变量,建立了各向异性单边损伤模型的一般形式,给出了热力学相容的投影算子,推导了模型的率本构关系.文中详细发展了模型的Newton-Raphson数值实现算法及其算法一致性模量,建立了合理的损伤准则和演化法则并应用于混凝土材料. 数值模拟结果初步验证了建议模型的有效性. 需要说明的是,模型完全构筑于热力学基础上,无需引入应变 等效或应变能等效等经验性假定.      

Rate-dependent transition from tensile damage to discrete fracture in dynamic brittle failure

Based on the work for a combined damage/plasticity model of geologic materials and the bifurcation analysis of material failure, an analytical framework is established to study the rate-dependent transition from continuum damage to discrete fracture in dynamic brittle failure. Because of the simple formulation, a vectorized constitutive model solver can be designed for large-scale computer simulation. A continuum tangent stiffness tensor is invoked for the tensile damage evolution such that the bifurcation analysis can be performed to identify the initiation and orientation of tensile failure. It is shown that the orientation of tensile failure is rate-independent although the limit state is rate-dependent for the rate-dependent tensile damage model. Sample problems are considered to demonstrate the features of the proposed approach.     

A new constitutive analysis of hexagonal close-packed metal in equal channel angular pressing by crystal plasticity finite element method

Most of hexagonal close-packed (HCP) metals are lightweight metals. With the increasing application of light metal products, the production of light metal is increasingly attracting the attentions of researchers worldwide. To obtain a better understanding of the deformation mechanism of HCP metals (especially for Mg and its alloys), a new constitutive analysis was carried out based on previous research. In this study, combining the theories of strain gradient and continuum mechanics, the equal channel angular pressing process is analyzed and a HCP crystal plasticity constitutive model is developed especially for Mg and its alloys. The influence of elevated temperature on the deformation mechanism of the Mg alloy (slip and twin) is novelly introduced into a crystal plasticity constitutive model. The solution for the new developed constitutive model is established on the basis of the Lagrangian iterations and Newton Raphson simplification.     

A first-order strain gradient damage model for simulating quasi-brittle failure in porous elastic solids

In order to simulate quasi-brittle failure in porous elastic solids, a continuum damage model has been developed within the framework of strain gradient elasticity. An essential ingredient of the continuum damage model is the local strain energy density for pure elastic response as a function of the void volume fraction, the local strains and the strain gradients, respectively. The model adopts Griffith’s approach, widely used in linear elastic fracture mechanics, for predicting the onset and the evolution of damage due to evolving micro-cracks. The effect of those micro-cracks on the local material stiffness is taken into account by defining an effective void volume fraction. Thermodynamic considerations are used to specify the evolution of the latter. The principal features of the model are demonstrated by means of a one-dimensional example. Key aspects are discussed using analytical results and numerical simulations. Contrary to other continuum damage models with similar objectives, the model proposed here includes the effect of the internal length parameter on the onset of damage evolution. Furthermore, it is able to account for boundary layer effects.