Formulation of a damage internal state variable model for amorphous glassy polymers

The following article proposes a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.     

Modeling stress state dependent damage evolution in a cast Al–Si–Mg aluminum alloy

Internal state variable rate equations are cast in a continuum framework to model void nucleation, growth, and coalescence in a cast Al–Si–Mg aluminum alloy. The kinematics and constitutive relations for damage resulting from void nucleation, growth, and coalescence are discussed. Because damage evolution is intimately coupled with the stress state, internal state variable hardening rate equations are developed to distinguish between compression, tension, and torsion straining conditions. The scalar isotropic hardening equation and second rank tensorial kinematic hardening equation from the Bammann–Chiesa–Johnson (BCJ) Plasticity model are modified to account for hardening rate differences under tension, compression, and torsion. A method for determining the material constants for the plasticity and damage equations is presented. Parameter determination for the proposed phenomenological nucleation rate equation, motivated from fracture mechanics and microscale physical observations, involves counting nucleation sites as a function of strain from optical micrographs. Although different void growth models can be included, the McClintock void growth model is used in this study. A coalescence model is also introduced. The damage framework is then evaluated with respect to experimental tensile data of notched Al–Si–Mg cast aluminum alloy specimens. Finite element results employing the damage framework are shown to illustrate its usefulness.     

伴随微孔洞生长的裂纹弹塑性定常扩展

裂纹在韧性材料中扩展时,将们随着微孔洞的萌生和生长,孔洞的萌生和深化将直接影响着材料的总体断裂韧性和强度,以往的研究主要集中在将裂纹的扩展刻划为微孔洞的萌生、生长和汇合这样一个过程。从传统的断裂过程区模型出发研究微孔洞的萌生和生长对材料总体断裂韧性的影响,通过采用Ｇｕｒｓｏｎ模型,建立塑性增量本构关系,然后针对定常扩展情况直接进行分析,孔洞对材料断裂韧性的影响由本构关系刻划,而在孔洞汇合模型中,上     

平面碰撞与强激光加载下金属铝的层裂行为

在轻气炮和神光Ⅱ强激光装置上开展了金属铝的层裂实验。针对激光打靶层裂实验中样品自由面速度剖面后期振荡容易丢失问题,改进靶设计,获得很好效果。利用轻气炮加载和强激光加载层裂实验应变率的显著差异,并通过数值模拟,讨论了在建立具有预测能力的理论建模中需要关注的损伤成核、演化与汇合问题中的材料特性与应变率相关特性因素。结果表明,对于我们以前建立的动态损伤与断裂模型,微孔洞成核的平均半径、阈值压力、成核速率相关参数以及微孔洞长大的阈值压力等具有材料特性属性,但微孔洞的表面能以及决定材料发生完全层裂的临界损伤度等具有明显的应变率效应。另外,分析还发现,虽然层裂强度具有明显的应变率效应,但是在样品层裂当地,样品由持续拉伸向收缩转变的临界行为,取决于一个很小的临界损伤,这个临界值很可能是材料常数,与应变率无关。     

金属基复合材料和强度与损伤分析

用观察计算力学的方法分析了金属基复合材料（ＭＭＣ）多重损伤与强度的关系,采用唯象的内聚力模型模拟纤维／基体界面的脱粘和采用Ｇ－Ｔ模型描述韧性基体的损伤。并用上述模型分析了长纤维增强ＭＭＣ在横向荷载作用下损伤演化的规律,讨论了不同界面性质与材料强度及损伤、破坏模式之间的关系。     

Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms

This work presents a model to represent ductile failure (i.e. failure controlled by nucleation, growth and coalescence) of materials whose irreversible deformation is controlled by several plastic or viscoplastic deformation mechanisms. In addition work hardening may result from both isotropic and kinematic hardening. Damage is represented by a single variable representing void volume fraction. The model uses an additive decomposition of the plastic strain rate tensor. The model is developed based on the definition of damage dependant effective scalar stresses. The model is first developed within the generalized standard material framework and expressions for Helmholtz free energy, yield potential and dissipation potential are proposed. In absence of void nucleation, the evolution of the void volume fraction is governed by mass conservation and damage does not need to be represented by state variables. The model is extended to account for void nucleation. It is implemented in a finite element software to perform structural computations. The model is applied to three case studies: (i) failure by void growth and coalescence by internal necking (pipeline steel) where plastic flow is either governed by the Gurson–Tvergaard–Needleman model or the Thomason model, (ii) creep failure (Grade 91 creep resistant steel) where viscoplastic flow is controlled by dislocation creep or diffusional creep and (iii) ductile rupture after pre-compression (aluminum alloy) where kinematic hardening plays an important role.     

点蚀演化及腐蚀疲劳裂纹成核的能量原理

作为一种不可逆的热力学过程,腐蚀疲劳的点蚀演化受到体系应变能、表面能和电化学能的共同影响.基于能量学原理,对腐蚀疲劳点蚀演化过程中的能量问题进行探索性研究.引入双变量半椭球模型描述点蚀的演化过程,推导了点蚀形状参数在演化过程中的变化方程.基于应力强度因子准则建立点蚀向疲劳裂纹转化的临界条件,同时分析应力幅值对腐蚀疲劳裂纹成核寿命的影响.     

脆性岩石蠕变裂纹成核宏细观力学机理研究

脆性岩石内部细观裂纹扩展、贯通及成核影响下的脆性蠕变行为,对深部地下工程围岩微震及岩爆事件评价有着重要意义.然而,目前能够解释裂纹成核损伤突变影响下,脆性岩石完整蠕变宏细观力学机理模型的研究很少.本文基于脆性岩石亚临界裂纹扩展模型、裂纹?应变?声发射事件相关的损伤模型及裂纹成核损伤时间演化路径函数,提出了一种脆性岩石裂...     

A constitutive model for elastoplastic solids containing primary and secondary voids

In many ductile metallic alloys, the damage process controlled by the growth and coalescence of primary voids nucleated on particles with a size varying typically between 1 and 100 μm, is affected by the growth of much smaller secondary voids nucleated on inclusions with a size varying typically between 0.1 and 3 μm. The goal of this work is first to quantify the potential effect of the growth of these secondary voids on the coalescence of primary voids using finite element (FE) unit cell calculations and second to formulate a new constitutive model incorporating this effect. The nucleation and growth of secondary voids do essentially not affect the growth of the primary voids but mainly accelerate the void coalescence process. The drop of the ductility caused by the presence of secondary voids increases if the nucleation strain decreases and/or if their volume fraction increases and/or if the primary voids are flat. A strong coupling is indeed observed between the shape of the primary voids and the growth of the second population enhancing the anisotropy of the ductility induced by void shape effects. The new micromechanics-based coalescence condition for internal necking introduces the softening induced by secondary voids growing in the ligament between two primary voids. The FE cell calculations were used to guide and assess the development of this model. The use of the coalescence condition relies on a closed-form model for estimating the evolution of the secondary voids in the vicinity of a primary cavity. This coalescence criterion is connected to an extended Gurson model for the first population including the effect of the void aspect ratio. With respect to classical models for single void population, this new constitutive model improves the predictive potential of damage constitutive models devoted to ductile metal while requiring only two new parameters, i.e. the initial porosity of second population and a void nucleation stress, without any additional adjustment.     

Damage evolution of ductile material under impact loading

Nucleation, growth and coalescence of micro-voids result in the fracture of materials. Most mathematical models neglect nucleation and introduce initial damage, assuming it as a material constant. However, the original damage, which is formed during material working, is a material constant. The initial damage is a model parameter and depends on the load. Apparently, the predictability of such a model is poor.This paper made comparison and analysis of the four classical void growth models and showed their similarities. At the beginning of damage evolution, all the models follow a linear relationship in the form , where c is the size of micro voids and k is a parameter which relates the material and loading condition. With the concept of statistical micro-damage and the assumption of uniform void radius for new voids, a damage evolution equation was deduced based on the above void growth model. With this equation the effects of nucleation and growth at the beginning of the damage stage on the whole process of damage evolution can be calculated. The transition time from the nucleation dominant phase to the growth dominant phase can be determined. When the transition time is applied to the damage failure model of ductile material proposed by Johnson, the initial damage (f₀), a model parameter in the original model, can also be determined. The results of the derived damage evolution equation agree well with the previous research results.     

航空铝合金力学与电化学耦合点蚀损伤模型研究

点蚀是航空铝合金材料在服役环境下常见的损伤形式,点蚀损伤会导致材料性能的下降,严重地威胁着结构的承载能力.作为承力构件,航空铝合金不仅承受环境腐蚀的作用,还承受应力作用.论文根据点蚀基本原理,引入细观损伤变量孔隙率,考虑力学化学效应,建立了点蚀损伤弹性模量计算模型.使用2219铝合金,进行加速腐蚀试验和单向拉伸试验,利用显微扫描技术研究了点蚀坑深度随时间和载荷的变化,并对腐蚀后试验件的损伤宏观形貌进行观察分析.根据拉伸实验结果,对模型的正确性进行验证.模型计算与实验结果的对比证明了论文方法的可行性与正确性.     

Dynamic damage constitutive relation of mesoscopic heterogenous brittle rock under rotation of principal stress axes

A micro-mechanics-based model is developed to investigate microcrack damage mechanism of four stages of brittle rock under rotation of the principal stress axes. They consist of linear elastic, non-linear hardening, rapid stress drop and strain softening. The frictional sliding crack model is applied to analyze microcracks nucleation, propagation and coalescence. The strain energy density factor approach is applied to determine the critical condition of microcrack nucleation, propagation and coalescence. The inelastic strain increments are formulated within the framework of thermodynamics with internal variables. Rotation of principal stress axes affect the dynamic damage constitutive relationship and the failure strength of brittle rock.     

Numerical, experimental, nondestructive, and image analyses of damage progression in cast A356 aluminum notch tensile bars

Void nucleation, growth, and coalescence in A356 aluminum notch specimens was determined from a combination of experiments, finite element analysis, nondestructive analysis, and image analysis. Notch Bridgman tension experiments were performed on specimens to failure and then other specimens were tested to 90%, 95%, and 98% of the failure load. The specimens were evaluated with nondestructive X-ray tomography and optical image analysis. Finite element simulations of the notch tests were performed with an elastic–plastic internal state variable material model that incorporated the pertinent microstructures (silicon particle volume fraction and size distribution and porosity volume fraction and size distribution). Parametric finite element simulations were performed to give insight into various initial conditions and responses of the notch tensile bars. The various methods all corroborated the same damage progression.     

Evaluation of the probability distribution of pitting corrosion fatigue life in aircraft materials

Corrosion and fatigue properties of aircraft materials are known to have a considerable scatter due to the random nature of materials, loading, and environmental conditions. A probabilistic approach for predicting the pitting corrosion fatigue life has been investigated which captures the effect of the interaction of the cyclic load and corrosive environment and all stages of the corrosion fatigue process (i.e. the pit nucleation and growth, pit-crack transition, short- and long-crack propagation). The probabilistic model investigated considers the uncertainties in the initial pit size, corrosion pitting current, and material properties due to the scatter found in the experimental data. Monte Carlo simulations were performed to define the failure probability distribution. Predicted cumulative distribution functions of fatigue life agreed reasonably well with the existing experimental data. The project supported by SRF for ROCS, State Education Ministry of China, and the Society for the Promotion of Science (JSPS) of Japan (JSPS-P02042)     

海工混凝土环境损伤力学研究进展

海工混凝土结构的安全性与耐久性是值得力学学科关注的重要问题。钢筋混凝土是由素混凝土基体和加强钢筋组成的复合材料。在海水中的氯离子腐蚀下钢筋会发生锈蚀,而在海洋环境的各种化学因素和物理因素作用下会导致素混凝土基体中的微裂纹成核与长大。腐蚀损伤会导致氯离子扩散系数增加,钢筋锈蚀加速,最终导致混凝土结构的安全性与耐久性降低。海工混凝土的损伤由化学因素和物理因素所诱发,化学因素包括碳化和侵蚀性离子（氯离子、硫酸根离子和镁离子）的攻击,而物理因素包括温度、湿度、波浪冲蚀和紫外辐射等。本文介绍了海工混凝土环境损伤力学的研究进展,首先讨论了环境损伤的诱发机理,然后介绍了环境损伤力学的理论模型,包括钢筋坑蚀的概率模型、硫酸盐腐蚀下混凝土损伤演化的模型和断裂韧性演化模型、波浪冲蚀模型等。腐蚀损伤对氯离子扩散的耦合作用也进行了评述,强调了如果不考虑腐蚀损伤的影响,关于氯离子在混凝土中扩散的分析结果有可能是错误的。最后,提出了几个未来需要解决的重要问题。

     

Damage accumulation for growth of anti-plane crack in work-hardening material

Elastic–plastic solutions of an anti-plane crack in an infinite body are used in conjunction with a continuum damage model to describe the conditions necessary for the onset of crack instability, fatigue crack propagation due to cyclic loading, and rates of crack growth due to time dependent events. A power law relates the stress to the strain of the material. The damage, which invokes nucleation, growth and coalescence of microvoids due to elevated strain, is confined to the plastic zone surrounding the crack tip. For applied loading below the yield stress, the small-scale and large-scale yielding solutions are used to determine the influence of strain hardening on crack instability and failure. Crack growth due to cyclic loading and time-dependent deformations are studied using the small-scale yielding solution of the deformation theory of plasticity.     

The size dependence of micro-toughness in ductile fracture

Micro-toughness in ductile fracture is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. A micromechanics model for the estimation of the size dependence of micro-toughness in ductile fracture is presented. Size effects are incorporated in the model using the conventional mechanism-based strain gradient plasticity (CMSG) theory. A finite element model of an axisymmetric representative unit cell with an initial spherical void is used to validate model predictions. Two characteristic length scales emerge from the model. The initial void radius sets the scale for the initial spherical void growth. For the subsequent void coalescence, the scale is set by the width of the intervoid ligament. Energy dissipation in ductile fracture is found to be dominated by the mechanisms of coalescence, and the micro-toughness in ductile fracture is found to be size dependent for dimple sizes approximately one order of magnitude larger than the material length scale.     

Peridynamic modeling of pitting corrosion damage

In this paper we introduce a peridynamic model for the evolution of damage from pitting corrosion capable of capturing subsurface damage. We model the anodic reaction in corrosion processes (in which electroplating is negligible) as an effective peridynamic diffusion process in the electrolyte/solid system coupled with a phase-change mechanism that allows for autonomous evolution of the moving interface. In order to simulate creation of subsurface damage, we introduce a corrosion damage model based on a stochastic relationship that connects the concentration in the metal to the damage of peridynamic mechanical-bonds that are superposed onto diffusion-bonds. We study convergence of this formulation for diffusion-dominated stage. The model leads to formation of a subsurface damage layer, seen in experiments. We validate results against experiments on pit growth rate and polarization data for pitting corrosion. We extend the 1D model to the 2D and 3D, and introduce a new damage-dependent corrosion model to account for broken mechanical bonds that enhance the corrosion rate. This coupled model can predict the pit shape and damage profile in materials with microstructural heterogeneities, such as defects, interfaces, inclusions, and grain boundaries.     

FCC晶体中不均匀变形对空洞长大的影响

通过编制率相关有限元用户子程序,采用一个单胞模型研究了FCC晶体中孔洞在单晶及晶界的长大行为,分析了由于晶体取向及变形失配对孔洞长大和聚合的影响。研究结果表明：孔洞的形状和长大方向与晶体取向密切相关;晶界上孔洞的长大速度大于单晶中孔洞的长大速度;晶粒间的变形失配加速了晶界上孔洞的长大趋势,因而使材料易发生沿晶断裂,随着晶粒间取向因子差异的增加,孔洞越易沿着晶界长大。