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.     

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.     

Thin film cracking modulated by underlayer creep

In devices that integrate dissimilar materials in small dimensions, crack extension in one material often accompanies inelastic deformation in another. In this paper we analyze a channel crack advancing in an elastic film, while an underlayer creeps. The film is subject to a tensile stress. As the underlayer creeps, the stress field in the film relaxes in the crack wake, and intensifies around the crack tip. In a blanket film, the crack can attain a steady velocity, set by two rate processes: subcritical decohesion at the crack tip, and creep in the underlayer. In a thin-film microbridge over a viscous stripe, the crack cannot grow when the bridge is short, and can grow at a steady velocity when the bridge is long. We use a two-dimensional shear lag model to approximate the three-dimensional fracture process, and an extended finite element method to simulate the moving crack with an invariant, relatively coarse mesh. On the basis of the theoretical findings, we propose new experiments to measure fracture toughness and creep laws in small structures. As a byproduct, an analytical formula is found for the growth rate per temperature cycle of a channel crack in a brittle film, induced by ratcheting plastic deformation in a metal underlayer.     

On the path of a crack near a graded interface under large scale yielding

The trajectory of a crack lying parallel to a thin graded layer between two plastically dissimilar materials is studied using the exclusion region (ER) theory of fracture. The ER theory is a theoretical framework for surface separation within which a broad range of fracture phenomenologies can be represented. In the present study, the direction of crack advance is determined by maximizing the resolved normal-opening force on the near-tip region, whereas separation itself is governed by the intensity of plastic deformation near the tip. A computational study was undertaken using the ER theory. The special-purpose finite element analysis platform accommodates arbitrary––and a priori unknown––crack trajectories. The model problem considered herein involves two plastically dissimilar, but elastically identical, materials joined by a thin, graded interface layer. The initial crack lies parallel to the interface layer, and crack advance occurs under conditions of extensive plastic flow. It is found that the position of the initial crack relative to the interface layer has a strong influence on the fracture behavior. In general, the crack trajectories tend to curve toward the less-ductile material. Also, the presence of the interface layer leads to fracture toughnesses that significantly exceed those of either material individually for the configurations studied.     

A multiscale model for the ductile fracture of crystalline materials

In this paper, a multiscale model that combines both macroscopic and microscopic analyses is presented for describing the ductile fracture process of crystalline materials. In the macroscopic fracture analysis, the recently developed strain gradient plasticity theory is used to describe the fracture toughness, the shielding effects of plastic deformation on the crack growth, and the crack tip field through the use of an elastic core model. The crack tip field resulting from the macroscopic analysis using the strain gradient plasticity theory displayes the 1/2 singularity of stress within the strain gradient dominated region. In the microscopic fracture analysis, the discrete dislocation theory is used to describe the shielding effects of discrete dislocations on the crack growth. The result of the macroscopic analysis near the crack tip, i.e. a new K-field, is taken as the boundary condition for the microscopic fracture analysis. The equilibrium locations of the discrete dislocations around the crack and the shielding effects of the discrete dislocations on the crack growth at the microscale are calculated. The macroscopic fracture analysis and the microscopic fracture analysis are connected based on the elastic core model. Through a comparison of the shielding effects from plastic deformation and the discrete dislocations, the elastic core size is determined.     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

Toughness and failure of heat resistant steel before and after hydrogenation

Fracture toughness of heat-resistant steel can be increased by a preliminary thermomechanical loading called warm pre-stressing (WPS). The procedure creates a plastic deformed area around the crack tip and hence allows larger service loads to be tolerated by the cracked specimen. It is shown that a hydrogenation in the preloading stage decreases the fracture toughness of material.Investigations are also presented of the applicability of physical and mechanical approaches for the prediction of cleavage stress of materials after preliminary plastic deformation (PPD) effects and hydrogenation. Different schemes of the plastic deformation and influence of hydrogenation are considered in the preloading stage to provide different levels cleavage stress of steel 15Kh2MFA.     

Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking

Cleavage fracture in ferritic steels is often initiated in brittle carbides randomly distributed in the material. The carbides break as a result of a fibre loading mechanism in which the stress levels in the carbides are raised, as the surrounding ferrite undergoes plastic deformation. The conditions in the vicinity of the nucleated micro-crack will then determine whether the crack will penetrate or be arrested by the ferrite. The ferrite is able to arrest nucleated cracks through the presence of mobile dislocations, which blunt and shield the microcrack and thus lowers the stresses at the crack tip. Hence, the macroscopic toughness of the material directly depends on the ability of the ferrite to arrest nucleated micro-cracks and in turn on the plastic rate sensitivity of the ferrite. The initiation of cleavage fracture is here modelled explicitly in the form of a micro-crack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder or in a few cases an elastic sphere and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, where the tractions are governed by a modified exponential cohesive law. It is shown that the critical stress, required to propagate a microcrack from a broken carbide, increases with decreasing plastic rate sensitivity of the ferrite. The results also show that a low stress triaxiality and a high aspect ratio of the carbide promote the initiation of cleavage fracture from a broken carbide.     

Crack tip asymptotic character of anti-plane stress and strain rate for linear fractional constitutive relations

Linear-fractional strain rate and stress relations are used to simulate materials undergoing steady state creep. The crack tip asymptotic character of the stress and strain rate field is obtained in exact and approximate form. In the limit as the radial distance emanating from the crack tip approaches zero, the stress field corresponds to that for an ideal plastic material while the exact and approximate solutions tend to coincide. Discussed is the nonhomogeneous singular character of the strain rate field that possess different orders of singularities in a circular region around the crack tip.     

金属材料中低加载速率下的动态韧脆转变及断裂韧性测量

金属材料在冲击下的韧脆转变现象和动态断裂韧性的测量是金属材料冲击力学性能研究的重要组成部分.针对金属材料在冲击下的韧脆转变现象认识不足和韧性材料在较低加载率下动态J-R阻力曲线难以测量的现状,提出了采用高速材料试验机,设计专用试验夹具,测量15MnTi钢和11MnNiMo钢在不同加载速率下的韧脆转变过程,以及裂尖约束对...     

Preliminary study on ductile fracture of imperfect lattice materials

The ductile fracture behavior of two-dimensional imperfect lattice material under dynamic stretching is studied by finite element method using ABAQUS/Explicit code. The simulations are performed with three isotopic lattice materials: the regular hexagonal honeycomb, the Kagome lattice and the regular triangular lattice. All the three lattices are made of an elastic/visco-plastic metal material. Two typical imperfections: vacancy defect and rigid inclusion are introduced separately. The numerical results reveal novel deformation modes and crack growth patterns in the ductile fracture of lattice material. Various crack growth patterns as defined according to their profiles, “X”-type, “Butterfly”-type, “Petal”-type, are observed in different combinations of imperfection type and lattice topology. Crack propagation could induce severe material softening and deduce the plastic dissipation of the lattices. Subsequently, the effects of the strain rate, relative density, microstructure topology, and defect type on the crack growth pattern, the associated macroscopic material softening and the knock-down of total plastic dissipation are investigated.     

Influence of plasticity on interface toughness in a layered solid with residual stresses

For crack growth along an interface between two adjacent elastic–plastic materials in a layered solid, the resistance curve behaviour is analysed by approximating the behaviour in terms of a bi-material interface under small scale yielding conditions. Thus, it is assumed that the layers are thick enough so that the extent of the plastic regions around the crack tip are much smaller than the thickness of the nearest layers. The focus is on the effect of initial residual stresses in the layered material, or on T-stress components induced during loading. The fracture process is represented in terms of a cohesive zone model. It is found that the value of the T-stress component in the softer material adjacent to the interface crack plays a dominant role, such that a negative value of this T-stress gives a significant increase of the interface fracture toughness, while a positive value gives a reduction of the fracture toughness.     

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.     

韧性断裂的微观模型及其在约束断裂中的应用

详细分析了不同形状断裂试件及小范围屈服模型裂纹端部的损伤演化，提出了韧性断裂的宏观起裂相当于裂尖前方一特征位置处的损伤达到一临界值。利用此模型获得了与实验相一致的宏观断裂韧性及与约束无关的理论断裂韧性。     

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。     

Prediction of mixed-mode fracture based on an elasto–plastic energy balance criterion

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. This fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, however, the G _max criterion has been modified in order to accommodate the consideration of plastic strain energy. This modified criterion is extended to study the fatigue crack growth characteristics of mixed-mode cracks. To predict crack propagation due to fatigue loads, a new elasto–plastic energy model is presented. This new model includes the effects of material properties such as strain hardening exponent n, yield strength σ _y , and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

梁在纯弯曲力矩作用下的动态塑性断裂

本文采用刚塑性分析方法,研究了带裂纹有限长韧性材料梁在纯弯曲力矩作用下的动态塑性断裂过程,本文考虑了由于断裂引起的附加轴向力对断裂过程的影响,并在分析中考虑了应变率对断裂过程的影响。文章给出了断裂过程中断裂截面上弯曲力矩和轴向力随时间的变化规律,以及裂纹长度,裂纹扩展速度和加速度随时间的变化规律。     

含中心裂纹梯度纳晶金属的数值模拟

梯度纳晶金属由于其微观组织的梯度分布,力学属性也呈现梯度变化,这使得其表现出不同于传统均匀材料的断裂行为．利用材料力学参数的梯度分布来表征梯度纳晶金属中晶粒尺寸的梯度变化,并编写ABAQUS和MATLAB脚本程序建立分层有限元模型．通过数值模拟计算了含有初始中心裂纹的梯度纳晶金属在受远端均匀拉应力作用下的裂尖J积分,分别研究了屈服应力梯度、裂纹角度和裂纹长度对金属材料断裂韧性的影响,并与传统粗晶进行了对比．结果表明梯度纳米结构的存在导致梯度纳晶金属内部的中心裂纹两端表现出不同的断裂韧性,小晶粒一侧裂尖的抗裂韧性优于大晶粒一侧裂尖,且屈服应力梯度绝对值越大,两者差距越大．梯度纳晶金属的断裂韧性受中心裂纹角度和长度变化的影响与传统粗晶金属基本一致,同时在晶粒尺寸梯度的作用下梯度纳晶的裂尖J积分略低于粗晶,即整体上拥有更好的抗裂韧性．     

A statistical model of brittle fracture by transgranular cleavage

A model for brittle fracture by transgranular cleavage cracking is presented based on the application of weakest link statistics to the critical microstructural fracture mechanisms. The model permits prediction of the macroscopic fracture toughness, K_Ic, in single phase microstructures containing a known distribution of particles, and defines the critical distance from the crack tip at which the initial cracking event is most probable. The model is developed for unstable fracture ahead of a sharp crack considering both linear elastic and nonlinear elastic (“elastic/plastic”) crack tip stress fields. Predictions are evaluated by comparison with experimental results on the low temperature flow and fracture behavior of a low carbon mild steel with a simple ferrite/grain boundary carbide microstructure.     

混凝土黏聚开裂模型若干进展

黏聚模型是用来描述混凝土断裂行为的基本模型, 首先介绍了混凝土的黏聚开裂模型的基本概念,总结了确定黏聚区的本构方程的各种方法,即直接单轴拉伸测试、J积分方法、R曲线法、柔度法和逆推法.然后介绍了黏聚模型在I型和复合型裂纹问题、疲劳断裂问题中的应用以及黏聚模型与混凝土尺寸效应的关系.最后对黏聚开裂模型与桥联模型、带状裂缝模型进行了比较和总结, 指出了该模型存在的问题, 并对其以后的发展方向提出了建议.