韧性断裂裂纹尖端的物理特征和力学行为

本文综述了金属材料发生韧性断裂的裂尖钝化,孔洞成核和长大,孔洞-孔洞或孔洞-裂尖汇合导致裂纹扩展的物理特征,和描述这些特征的本构理论及物理模型。      

微孔洞型的分形断裂理论初探

初步研究并提出微孔洞型的分形断裂理论，建立了主裂纹与微孔洞汇合的分形模型，并以此为基础确定了分维Ｄ与连接区厚度Δ和孔洞平均半径ｒ之间的关系，推导了微孔洞与主裂纹连接的能量准则，讨论了分维与断裂韧性之间的关系。     

金属试件变形断裂过程的计算模拟分析——组合功密度模型的应用

本文作者已建立了一个既适用于裂纹体亦适用于无裂纹体的统一损伤断裂模型——组合功密度模型。在本文中,作者应用该模型并结合大应变弹塑性有限元方法对40Cr制的圆棒光滑拉伸试件、圆棒切口拉伸试件和三点弯曲裂纹试件的变形和断裂过程进行了计算模拟。模拟结果很好地再现了两种圆棒拉伸试件的实验过程;而对于三点弯曲试件,模拟得到的载荷——加载位移关系曲线、裂纹扩展量——加载位移关系曲线、J_R阻力曲线和断裂韧性J_(IC)值等均与实测结果相当吻合。证实了该模型既能用于模拟预测无裂纹体中的裂纹萌生和扩展,也能模拟预测裂纹体中的裂纹起裂和稳定扩展过程。     

裂纹面摩擦接触引起的断裂韧性增长的研究

采用弹黏塑性的材料本构关系, 建立了压、剪混合型裂纹常速准静 态扩展的力学模型, 求得了裂纹面摩擦接触条件下裂纹尖端场的数值解, 并基于数 值结果讨论了扩展裂纹的摩擦效应. 计算和分析表明, 裂纹面的摩擦效应主要表现 在两个方面. 第一方面是摩擦会导致裂纹尖端区材料的断裂韧性增高, 并且裂纹面间的摩擦作用越强, 增韧效果越显著. 摩擦增韧的机制可以解释为裂纹 面间的摩擦作用导致裂纹尖端塑性区尺寸变大, 使裂纹尖端场的塑性变形能增加, 从而使得裂纹尖端区材料增韧. 摩擦生热并不是导致材料断裂韧性增长的根本机制. 第二方面是摩擦会导致``断裂延缓'. 利用裂纹面的摩擦来提高构件的承载能力和延长构件的服役寿命具有较大的工程实用价值.     

修正的Bodner-Partom本构模型

对于含有微损伤的多孔介质,由于微裂纹和微孔洞的存在,从宏观角度看,非弹性体应变会随着外载荷的变化而发生改变,即非弹性体应变不应为零。本文修正了计及损伤效应的Bodner-Partom本构模型。并以修正的本构模型对LY-12硬铝材料受到电子束辐照时产生的热击波及材料的创伤破坏效应进行了理论计算,将计算值同实验结果比较表明,两者基本上是一致的。     

构元组集损伤断裂模型及其与内聚区模型的比较

结构的响应实质上是材料的响应,宏观结构损伤至断裂的发展过程也是材料性质不断演化的结果.构元组集模型从材料的微观物理变形机制出发,基于对泛函势理论和Cauchy-Born准则,抽象出两种构元:弹簧束构元和体积构元.在微观层次上,结构损伤和断裂的实质都是原子间键合力减弱和丧失的结果,而弹簧束构元是同一方向上的原子键的抽象,因此损伤可以通过弹簧束构元的响应曲线来反映.组集两种构元的响应,建立了材料的弹性损伤本构关系,从而能一致描述材料从弹性到损伤、破坏的发展过程.将构元组集模型的本构关系嵌入ABAQUS的用户材料单元子程序UMAT,实现对结构响应的数值模拟.论文模拟了包含中心预制裂纹三点弯曲梁的裂纹扩展过程,并与内聚区模型比较,给出了内聚区模型所假设的应力-位移关系曲线,并从材料损伤演化的角度对材料裂纹扩展过程做出了物理解释.     

构元组集模型对结构弹性损伤至断裂过程的描述及与内聚区模型的比较

结构的响应实质上是材料的响应,宏观结构损伤至断裂的发展过程也是材料性质不断演化的结果。构元组集模型从材料的微观物理变形机制出发,基于对泛函势理论和Cauchy-Born准则,抽象出两种构元——弹簧束构元和体积构元。在微观层次上,结构损伤和断裂的实质都是原子间键合力减弱和丧失的结果,而弹簧束构元是同一方向上的原子键的抽象,因此损伤可以通过弹簧束构元的响应曲线来反映。组集两种构元的响应,建立了材料的弹性损伤本构关系,从而能一致描述材料从弹性到损伤、破坏的发展过程。将构元组集模型的本构关系嵌入ABAQUS的用户材料单元子程序UMAT,实现对结构响应的数值模拟。本文模拟了包含中心预制裂纹三点弯曲梁的裂纹扩展过程,并与内聚区模型比较,给出了内聚区模型所假设的应力——位移关系曲线,并从材料损伤演化的角度对材料裂纹扩展过程做出了物理解释。     

基于近场动力学理论的准脆性材料的本构力函数的构建

近场动力学理论(PD)是基于非局部思想的连续介质力学新理论,用于研究材料破坏问题。根据准脆性材料破坏的线性和非线性的力学行为,在初始微观弹脆性材料(PMB)的本构力函数中引入了键的损伤模型,将键的断裂过程分成了线性的弹性变形阶段和非线性的损伤变形阶段,以此构建了准脆性材料的本构力函数的基本形式。以典型的准脆性材料为例构建了其本构力函数,通过在压缩载荷下对含预制不同角度单裂纹缺陷的类岩材料的裂纹扩展进行PD数值模拟仿真,裂纹起裂位置和扩展方向与试样试验结果在一定程度上保持了一致,证明了该基于近场动力学理论的典型准脆性材料的本构力函数可用于该类材料的破坏分析。     

增韧环氧树脂的动态裂纹扩展研究

本文主要进行了环氧及增韧环氧树脂的断裂韧性及裂纹快速扩展的试验研究。试验过程中采用了ＧＬＣ－１型高速裂纹扩展测试仪来测试裂纹的扩展速度,得到在裂纹扩展过程中裂纹扩展速度曲线。本文结合不同的计算公式及有限元分析方法,讨论了各个确定断裂韧性公式的准确程度,发现传统的静态断裂韧性的分析方法所得到的结果偏大,有一定的危险性,建议使用试验与数值计算相结合的方法;同时还发现增韧不仅可以提高材料的静态和动态断裂性能,而且在裂纹扩展过程中可以起到减缓裂纹扩展的作用     

基于裂纹扩展脆性岩石动力压缩力学特性研究

动态压缩荷载作用下，脆性岩石内部动态细观裂纹扩展特性，对岩石宏观动态力学特性有着重要的影响。然而，对岩石内部动态细观裂纹扩展与宏观动态力学特性的关系研究较少。基于准静态裂纹扩展作用下的应力-应变本构模型、准静态与动态裂纹扩展断裂韧度关系、裂纹速率与应变率关系模型及应变率与动态断裂韧度关系，提出了一种基于细观力学的动态应力-应变本构模型。其中裂纹速率与应变率关系，是根据裂纹长度与应变关系的时间导数推出；应变率与动态断裂韧度关系，是根据推出的裂纹速率及应变率关系，与裂纹速率及断裂韧度关系相结合而得到。研究了应变率对应力-应变本构关系及动态压缩强度影响。并通过试验结果验证了模型的合理性。讨论了岩石初始损伤、围压、模型中参数m、ε₀和R对应力-应变关系、动态压缩强度和动态弹性模量的影响。研究结果可为动态压缩荷载作用下深部地下工程脆性围岩稳定性分析提供了一定的理论支持。     

Two mechanisms of ductile fracture: void by void growth versus multiple void interaction

Two distinct mechanisms of crack initiation and advance by void growth have been identified in the literature on the mechanics of ductile fracture. One is the interaction a single void with the crack tip characterizing initiation and the subsequent void by void advance of the tip. This mechanism is represented by the early model of Rice and Johnson and the subsequent more detailed numerical computations of McMeeking and coworkers on a single void interacting with a crack tip. The second mechanism involves the simultaneous interaction of multiple voids on the plane ahead of the crack tip both during initiation and in subsequent crack growth. This mechanism is revealed by models with an embedded fracture process zone, such as those developed by Tvergaard and Hutchinson. While both mechanisms are based on void nucleation, growth and coalescence, the inferences from them with regard to crack growth initiation and growth are quantitatively different. The present paper provides a formulation and numerical analysis of a two-dimensional plane strain model with multiple discrete voids located ahead of a pre-existing crack tip. At initial void volume fractions that are sufficiently low, initiation and growth is approximately represented by the void by void mechanism. At somewhat higher initial void volume fractions, a transition in behavior occurs whereby many voids ahead of the tip grow at comparable rates and their interaction determines initiation toughness and crack growth resistance. The study demonstrates that improvements to be expected in fracture toughness by reducing the population of second phase particles responsible for nucleating voids cannot be understood in terms of trends of one mechanism alone. The transition from one mechanism to the other must be taken into account.     

Mechanical modelling of ductile fracture

Mechanical models of material failure by void growth to coalescence are described to give a brief overview of methods applied in the analysis of ductile fracture. Approximate constitutive relations for porous ductile materials are discussed, modelling both the nucleation and growth of voids. The application of the material models is illustrated by numerical analyses for a tensile test specimen and for dynamic, ductile crack growth. Unstable void growth is a relevant mechanism in ductile materials subject to a high level of triaxial tension. The analysis of such cavitation instabilities in elastic-perfectly plastic materials is discussed for axisymmetric stress states, and the relevance to metal/ceramic components is emphasized.General Lecture presented at the 10th Italian National Congress of Theoretical and Applied Mechanics; AIMETA, Pisa, October 1990.     

Dynamic toughness in elastic nonlinear viscous solids

This work addresses the interrelationship among dissipative mechanisms—material separation in the fracture process zone (FPZ), nonelastic deformation in the surrounding background material and kinetic energy—and how they affect the macroscopic dynamic fracture toughness as well as the limiting crack speed in strain rate sensitive materials. To this end, a micromechanics-based model for void growth in a nonlinear viscous solid is incorporated into a microporous strip of cell elements that forms the FPZ. The latter is surrounded by background material described by conventional constitutive relations. In the first part of the paper, the background material is assumed to be purely elastic. Here, the computed dynamic fracture toughness is a convex function of crack velocity. In the second part, the background material as well as the FPZ are described by similar rate-sensitivity parameters. Voids grow in the strain rate strengthened FPZ as the crack velocity increases. Consequently, the work of separation increases. By contrast, the inelastic dissipation in the background material appears to be a concave function of crack velocity. At the lower crack velocity regime, where dissipation in the background material is dominant, toughness decreases as crack velocity increases. At high crack velocities, inelastic deformation enhanced by the inertial force can cause a sharp increase in toughness. Here, the computed toughness increases rapidly with crack velocity. There exist regimes where the toughness is a non-monotonic function of the crack velocity. Two length scales—the width of the FPZ and the ratio of the shear wave speed to the reference strain rate—can be shown to strongly affect the dynamic fracture toughness. Our computational simulations can predict experimental data for fracture toughness vs. crack velocity reported in several studies for amorphous polymeric materials.     

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.     

混凝土拉伸软化曲线折线近似的逆解方法

研究基于Hillerborg的虚拟裂纹模型，利用有限元分析方法，求得折线近似的拉伸软化曲线的逆解方法。对弹性模量，初始开裂应力的决定方法进行了研究。以双直线模型的计算结果为算例进行了逆推分析，算例符合得很好。也较好地从实验得到的荷载位移曲线再现了拉伸软化曲线。这对于研究混凝土的断裂能，尺寸效应等问题很具意义。     

A void–crack nucleation model for ductile metals

A phenomenological void–crack nucleation model for ductile metals with secondphases is described which is motivated from fracture mechanics and microscale physicalobservations. The void–crack nucleation model is a function of the fracture toughness of theaggregate material, length scale parameter (taken to be the average size of the second phaseparticles in the examples shown in this writing) , the volume fraction of the second phase, strainlevel, and stress state. These parameters are varied to explore their effects upon the nucleationand damage rates. Examples of correlating the void–crack nucleation model to tension data in theliterature illustrate the utility of the model for several ductile metals. Furthermore, compression,tension, and torsion experiments on a cast Al–Si–Mg alloy were conducted to determinevoid–crack nucleation rates under different loading conditions. The nucleation model was thencorrelated to the cast Al–Si–Mg data as well.     

Modeling of crack growth in ductile solids: a three-dimensional analysis

A population of several spherical voids is included in a three-dimensional, small scale yielding model. Two distinct void growth mechanisms, put forth by [Int. J. Solids Struct. 39 (2002) 3581] for the case of a two-dimensional model containing cylindrical voids, are well contained in the model developed in this study for spherical voids. A material failure criterion, based on the occurrence of void coalescence in the unit cell model, is established. The critical ligament reduction ratio, which varies with stress triaxiality and initial porosity, is used to determine ligament failure between the crack tip and the nearest void. A comparison of crack initiation toughness of the model containing cylindrical voids with the model containing spherical voids reveals that the material having a sizeable fraction of spherical voids is tougher than the material having cylindrical voids. The proposed material failure determination method is then used to establish the fracture resistance curve (J–R curve) of the material. For a ductile material containing a small volume fraction of microscopic voids initially, the void by void growth mechanism prevails, which results in a J–R curve having steep slope. On the other hand, for a ductile material containing a large volume fraction of initial voids, the multiple voids interaction mechanism prevails, which results in a flat J–R curve. Next, the effect of T-stress on fracture resistance is examined. Finally, nucleation and growth of secondary microvoids and their effects on void coalescence are briefly discussed.     

Rate effects on toughness in elastic nonlinear viscous solids

A micromechanics-based constitutive relation for void growth in a nonlinear viscous solid is proposed to study rate effects on fracture toughness. This relation is incorporated into a microporous strip of cell elements embedded in a computational model for crack growth. The microporous strip is surrounded by an elastic nonlinear viscous solid referred to as the background material. Under steady-state crack growth, two dissipative processes contribute to the macroscopic fracture toughness—the work of separation in the strip of cell elements and energy dissipation by inelastic deformation in the background material. As the crack velocity increases, voids grow in the strain-rate strengthened microporous strip, thereby elevating the work of separation. In contrast, the energy dissipation in the background material decreases as the crack velocity increases. In the regime where the work of separation dominates energy dissipation, toughness increases with crack velocity. In the regime where energy dissipation is dominant, toughness decreases with crack velocity. Computational simulations show that the two regimes can exist in certain range of crack velocities for a given material. The existence of these regimes is greatly influenced by the rate dependence of the void growth mechanism (and the initial void size) as well as that of the bulk material. This competition between the two dissipative processes produces a U-shaped toughness-crack velocity curve. Our computational simulations predict trends that agree with fracture toughness vs. crack velocity data reported in several experimental studies for glassy polymers and rubber-modified epoxies.     

Mode mixity and nonlinear viscous effects on toughness of interfaces

This paper examines steady-state crack growth at interfaces between polymeric materials and hard substrates under quasi-static conditions. The polymeric material is taken to be an elastic nonlinear viscous solid while the substrate is treated as a rigid material. Void growth and coalescence in the rate-dependent fracture process zone is modeled by a nonlinear viscous porous strip of cell elements. In the first part of this paper, the polymeric background material surrounding the process zone is assumed to be purely elastic. Under fixed mode mixity, the computed interface toughness is found to be a monotonically increasing function of crack velocity; toughness also increases rapidly with higher rate sensitivity. This behavior can be explained in terms of voids growing in a strain-rate strengthened process zone. In the second part of the paper, the background material is also treated as an elastic nonlinear viscous solid. The competition between work of separation in the process zone and energy dissipation in the background material leads to a U-shaped toughness–crack velocity curve. Effects of mode mixity, initial porosity, rate sensitivity, as well as the initial yield strain on toughness are studied. The simulations produce trends that agree with interface toughness vs. crack velocity data reported in experimental studies for rubber toughened epoxy-paste adhesive and urethane acrylate adhesive.     

Modeling hydrogen attack effect on creep fracture toughness

The effect of high temperature hydrogen attack on creep crack growth rates in steels is studied by modeling the interaction between creep deformation and gaseous pressures generated by hydrogen and methane. The equilibrium methane pressure as a function of hydrogen pressure, temperature and carbide types for carbon steels and Cr–Mo steels is calculated. This gaseous driving force is incorporated into a micromechanics model for void growth along grain boundaries of a creeping solid. Growth and coalescence of voids along grain boundaries is modeled by a microporous strip of cell elements, referred to as the fracture process zone. The cell elements are governed by a nonlinear viscous constitutive relation for a voided material. Two rate sensitivities as well as two types of grain boundaries are considered in this computational study. Simulations of creep crack growth accelerated by gaseous pressures are performed under conditions of small-scale and extensive creep. The computed crack growth rates at elevated temperatures are able to reproduce the trends of experimental results.