Dynamic fracture parameters and constraint effects in functionally graded syntactic epoxy foams

Functionally graded syntactic foam sheets are developed by dispersing microballoons in epoxy for studying dynamic fracture behavior under low velocity impact loading. The volume fraction of microballoons is graded linearly over the width of the sheets. The mode-I crack initiation and growth behaviors are studied using reflection coherent gradient sensing technique and high-speed photography in samples with crack on the compliant and stiff sides and oriented along the compositional gradient. Crack growth along the gradient in each case shows sudden acceleration followed by steady state growth and deceleration during the window of observation. In both cases, the crack accelerations are similar while crack decelerations show differences. The dynamic stress intensity factor history prior to crack initiation in each case shows a rapid increase at different rates with the crack on the compliant side of the graded sheet experiencing higher rate of loading relative to the one with the crack on the stiffer side. Post-crack initiation stress intensity factor histories suggest increasing fracture toughness with crack growth in the graded sample with the crack on the compliant side while a decreasing trend is seen when the crack is on the stiffer side.Optical measurements are supplemented by finite element simulations for studying crack tip constraint effects on fracture behavior of graded foam sheets. Computed plane strain constraints in graded configurations are essentially identical to the homogeneous counterpart and the computed stress intensity factors obtained from plane stress elasto-dynamic analyses of the graded foams correlate well with the experimental measurements prior to crack initiation. The computed T-stress histories however, show an earlier loss of negative crack tip constraint in case of the graded foam sample with a crack on the compliant side. This correlates well with the higher crack tip loading rate and earlier crack initiation suggesting a possible role of in-plane constraint on fracture of graded foam. The coincidence of the time rate of change of in-plane constraint parameter becoming stationary close to experimentally observed crack initiation times are noted.     

Dynamic crack kinking from a PMMA/Homalite interface

The behavior of a pre-existing, dynamically loaded, interfacial crack kinking away from the interface separating two materials was experimentally investigated under dynamic loading conditions. Dynamic fracture experiments were performed on pre-cracked bimaterial panels of PMMA bonded with Homalite-100 impact loaded using a high-speed gas gun. By varying the location of impact, a large range of mixed mode loading at the crack tip was produced. Information about the stress state surrounding the crack tip was obtained through use of the lateral shearing interferometer of coherent gradient sensing in conjunction with high-speed photography. The high-speed interferogram corresponding, to the time of crack initiation was analyzed in each case to find the preinitiation mode mixity at the crack tip. Measurement of both the local initiation mode mixity and the crack kink angle allows for possible extension of existing quasi-static interface crack kinking criteria, such as maximum opening stress or maximum energy release rate, to the case of dynamic loading. It was found that for bimaterial systems with small material property mismatch, such as the PMMA/Homalite system, the maximum opening stress criterion accurately predicts the relation between crack tip mode mixity and resulting kink angle for small initial crack kinking speeds.     

An Experimental Study of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

Quasi-static mixed mode crack initiation and growth in functionally graded materials (FGMs) was studied through fracture experiments on polymer-based FGMs manufactured by selective ultraviolet irradiation poly(ethylene carbon monoxide)—a photo-sensitive copolymer that becomes more brittle and stiffer under ultraviolet irradiation. The objective of the study was to determine whether crack kinking criteria for homogeneous materials, e.g., maximum hoop stress criterion, also hold for FGMs. Single edge notched tension specimens with different spatial variations of Young's modulus, failure stress and failure strain, were tested. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material, and to extract the fracture parameters of stress intensity factor K _I and K _II , and the T-stress. It was found that the nonsingular T-stress term in the asymptotic expansion for stresses plays a very important role in accurately measuring fracture parameters. It was also found that the maximum tangential stress criterion can be applied to the case of FGMs to predict crack kinking provided that the effect of the T-stress is accounted for and the process zone size is small compared to the intrinsic material gradient length scale. However, for accurate crack path prediction at a length scale comparable to the material gradient, detailed material property information is required. In general, the crack will propagate towards a region that exhibits less fracture toughness, but, unlike the case of homogeneous materials, along a path where K _II is not necessarily equal to zero.     

复合型韧性断裂实验和控制参数

通过对不同韧性材料在各种平面复合载荷形式下裂纹启裂阶段裂端变形、启裂位置和扩展方向的系统的宏微观实验验证及计算分析,考察了韧性断裂参数空穴扩张比的分布特征和裂纹启裂及扩展方向的关系．得到：对于不同韧性的材料,在裂端的钝化变形区域,空穴扩张比的极大值区对应干裂纹的启裂位置,裂纹启裂时钝化裂端前缘空穴扩张比的临界值不敏感于复合比的变化．而对于裂纹启裂后的扩展方向,则需根据具体材料在相应的特定区域中比较空穴扩张比参数极大值的分布特征,需经进一步的分析,从而确定裂纹的扩展方向．实验及计算结果表明,尽管复合型断裂时裂纹启裂及扩展的机理极其复杂,用于韧性材料复合型断裂的空穴扩张比参数仍能很好地预测裂端的启裂及扩展方向,可作为复合型韧性断裂过程的控制参数．     

Atomistic/continuum simulation of interfacial fracture Part II: Atomistic/dislocation/continuum simulation

Coupled atomistic/dislocation/continuum simulation of interfacial fracture is performed in this paper. The model consists of a nanoscopic core made by atomistic assembly and a surrounding elastic continuum with discrete dislocations. Atomistic dislocations nucleate from the crack tip and move to the continuum layer where they glide according to the dislocation dynamics curve. An atoms/continuum averlapping belt is devised to facilitate the transition between the two scales. The continuum constraint on the atomic assembly is imposed through the mechanics atmosphere along the overlapping belt. Transmissions of mechanics parameters such as displacements, stresses, masses and momenta across the belt are realized. The present model allows us to explore interfacial fracture processes under different mode mixity. The effect of atomistic zigzag interface on the fracture process is revealed: it hinders dislocation emission from the crack tip, especially under high mode mixity. The project supported by the National Natural Science Foundation of China     

Atomistic/continuum simulation of interfacial fracture part I: Atomistic simulation

The phenomenon of interfacial fracture, as manifested by atomistic cleavage, debonding and dislocation emission provides a challenge for combined atomistic-continuum analysis. As a precursor for fully coupled atomistic-continuum simulation^[1] of interfacial fracture, we focus here on the atomistic behavior within a nanoscopic core surrounding the crack tip. The inter-atomic potential under Embedded Atom Method is recapitulated to form an essential framework of atomistic simulation. The calculations are performed for a side-cracked disc configuration under a remoteK field loading. It is revealed that a critical loading rate defines the brittle-to-ductile transition of homogeneous materials. We further observe that the near tip mode mixity dictates the nanoscopic profile near an interfacial crack tip. A zigzag interface structure is simulated which plays a significant role in the dislocation emission from an interfacial crack tip, as will be explored in the second part of this investigation. The project supported by the National Natural Science Foundation of China     

LC4—M材料复合型韧断主要影响因素的分析

通过分析LC4－M铝合金材料在不同复合比载荷下的断裂试验结果,参照常规断裂现象,修正了一般断裂试验中认定裂纹启裂方向的方法,结合不同复合比下裂尖附近应力三维、主应力方向的计算分析,得到：在裂端的钝化变形区域、应力三维度的极大值处,对应于裂纹的启裂位置,即使在高韧性材料中发生剪切断裂的情况下也是如此;裂纹的启裂方向在拉伸断裂时与启裂点最大拉应力方向有关,在剪切断裂时启裂点最大剪应力方向有关,引起两种形式断裂的主要因数和破坏机理有很大不同。     

An inclined surface crack subject to biaxial loading

The elastic–plastic stress fields and mode mixity parameters for semi-elliptical surface cracks on biaxial loaded plates have been investigated using detailed three-dimensional finite element calculations. Different degrees of mode mixity are given by combinations of the far-field stress level, biaxial stress ratio and inclined crack angle. These analyses were performed for different surface flaw geometries to study the combined load biaxiality and mode mixity effects on the crack-front stress fields and the size and shape of the plastic zones. It is clear from considering the local stress distributions along the crack front that the elastic crack tip singularities have been derived for several particular cases of mixed mode biaxial loading. By theoretical analysis, the new formulae have been introduced for both the elastic and plastic mode-mixity parameters, accounting for ratios between the I/II, II/III and III/I modes. Particular attention was paid to the strong variations of the mode-mixity parameters along the semi-elliptical surface crack front. The mixed-mode behavior of the crack growth direction angle along the semi-elliptical crack front for different combinations of biaxial loading and inclination crack angles was also determined. It was done using methods based on the maximum tangential stress and the strain energy density criteria.     

功能梯度材料的黏弹性断裂问题

功能梯度材料(FGM)是一种不同于传统复合材料的新型工程复合材料 [1], 国内外关于FGM的断裂力学方面的研究发展非常迅速. 关于FGM静态裂纹问题,学者们研究了不同类型裂纹尖端场的应力强度因子 [2-5], 探讨了有限长裂纹在不用载荷作用下的传播等问题. 而关于动态裂纹问题,也已经取得很大成就 [6-9]. FGM一个很重要的应用是高温结构材料,在强大的热环境中,很多材料都呈现出黏弹性. 因此,研究FGM的黏弹性断裂力学非常具有实际价值.对此,众多研究 [10-14]提出不同的分析模型,并在不同受载条件,通过理论计算,分析了黏弹性裂纹尖端场的力学 行为.本文考查了功能梯度材料板条中界面裂纹垂直于梯度方向时的黏弹性断裂问题,首先利用有限元法求解线弹性功能梯度材料板条的裂纹尖端场,然后根据黏弹性的对应性原理,求解出黏弹性功能梯度材料板条裂纹问题的应力场强度因子.      

A UNIVERSAL CRACK EXTENSION CRITERION BASED ON THE EQUIVALENT STRESS GRADIENT:I.THEORY AND NUMERICAL VERIFICATION

In this contribution,the microscopic fracture mechanism and extension criterion for mixed type crack in ductile material under plane mixed mode loading are investigated in details.A universal extension...     

Interfacial mixed-mode fracture of adhesive bonds undergoing large deformation

Interfacial fracture of adhesive bonds undergoing large-scale yielding is studied using a combined experimental/finite-element approach. The full range of in-plane mode mixity is produced over bond thickness ranging from 30 to 500 μm using the scarf and the ENF joint geometries. Novel techniques for introducing pre-cracks and surface decoration, together with in situ observations, facilitate accurate determination of the bond-average and the local shear strains at the crack tip during the onset as well as the rest of the crack propagation event. The crack generally grew along one of the two interfaces of the bond, although the failure was always fully cohesive. The local shear strain at the crack tip is independent of the bond thickness, and, under quasi-static conditions, it remains constant throughout the growth, which make it a viable fracture parameter. This quantity strongly depends on the mode mixity, the sign of the phase angle (i.e., shearing direction) and the crack speed, however.A finite-element analysis is used to obtain the crack tip deformation field for an interface crack in adhesively bonded scarf and ENF joints. Large-strain and quasi-static conditions are assumed. A distinct material model in the fracture process zone that allows for volume change in the post-yield regime is incorporated into the analysis. The local deformation is characterized by a pair of bond-normal and tangential displacements corresponding to the nodal points adjacent to the crack tip. The critical values of these quantities are obtained when the FEM bond-average shear strain at the crack tip becomes equal to its experimental counterpart. The so defined critical local displacements, after an appropriate normalization, seem to conform to a single-valued, linear type interrelationship over the entire range of mode mixity. The fact that this relationship is independent of the bond thickness, and furthermore it encompasses both cases of positive and negative phase angles, makes it a viable candidate for characterizing mixed-mode interfacial fracture under large-deformation conditions.     

Failure instability of a debonded interface in the presence of a main crack

The problem of fracture initiating from an edge crack in a nonhomogeneous beam made of two dissimilar linear elastic materials that are partially bonded along a common interface is studied by the strain energy density theory. The beam is subjected to three-point bending and the unbonded part of the interface is symmetrically located with regard to the applied loading. The applied load acts on the stiffer material, while the edge crack lies in the softer material. Fracture initiation from the tip of the edge crack and global instability of the composite beam are studied by considering both the local and global stationary values of the strain energy density function, dW/dV. A length parameter l defined by the relative distance between the maximum of the local and global minima of dW/dV is determined for evaluating the stability of failure initiation by fracture. Predictions on critical loads for fracture initiation from the tip of the edge crack, crack trajectories and fracture instability are made. In the analysis the load, the length of the edge crack and the length and position of the interfacial crack remained unchanged. The influence of the ratio of the moduli of elasticity of the two materials, the position of the edge crack and the width of the stiffer material on the local and global instability of the beam was examined. A general trend is that the critical load for crack initiation and fracture instability is enhanced as the width and the modulus of elasticity of the stiffer material increase. Thus, the stiffer material acts as a barrier in load transfer.     

基于神经网络的界面裂纹尖端场分析

通过构造反向传播神经网络,对裂纹尖端的应力场进行模拟,进而实现对裂纹尖端应力场甬数的逼近。得到的网络具有较高的联想、记忆能力和相当的稳定性,并且可以快速、准确地得到带裂纹构件的裂纹尖端应力场,从而确定裂纹尖端的塑性区和分析裂纹的扩展。数值计算给出了LY12-CZ材料裂纹扩展方向的计算结果,与实验结果吻合较好,还给出了两相材料含界面裂纹在复合型载荷作用下的塑性区形状的变化情况,并对两相材料含界面裂纹在复合型载荷作用下裂纹的扩展方向进行了预测。     

界面裂纹的路径选择与数值模拟

利用界面断裂能和荷载混合度的概念研究界面裂纹的扩展路径，利用有限元数值方法模拟界面裂纹的扩展过程，再现界面断裂的各种几何构型．研究表明，界面的断裂能和混合度完全控制了裂纹在界面附近的扩展过程．数值预测的裂纹路径与理论结果一致     

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK _I , the crack tip biaxiality parameter is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK _I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK _I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.     

Intersonic crack propagation in homogeneous media under shear-dominated loading: theoretical analysis

The mechanics of cohesive failure under mixed-mode loading is investigated for the case of a steadily propagating subsonic and intersonic dynamic crack subjected to a follower tensile and shear distributed load. The cohesive failure model chosen in this study is rate independent but accounts for the coupling between normal and tangential damage. Special emphasis is placed here on mixed-mode cases with predominantly shear loading. The analysis shows that the size of the mixed-mode cohesive zone is smaller than that obtained in the pure shear case. The relative extent of the shear and tensile cohesive damage zones depends on the crack speed and the mode mixity. In the intersonic regime, the failure process takes place exclusively in shear, even under remote mixed-mode loading conditions.     

Parameters controlling fracture resistance in functionally graded materials under mode I loading

In this investigation the fracture behavior of functionally graded materials (FGMs) was studied by means of experiments carried out on model polymer-based FGMs. Model graded materials were manufactured by selective ultraviolet irradiation of ECO [poly(ethylene carbon monoxide)], a photo-sensitive ductile copolymer that becomes more brittle and stiffer under exposure to ultraviolet light. The mechanical response of the graded material was characterized using uniaxial tensile tests. Single edge notched tension graded ECO specimens possessing different spatial variations of Young’s modulus, failure stress and failure strain were tested under remote opening loading. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material. The measured displacement field was then used to extract fracture parameters such as stress intensity factor and T-stress, and thus construct resistance curves for crack growth in the FGMs. For this loading configuration it was found that the nonsingular T-stress term in the asymptotic expansion for stresses needs to be accounted for in order to accurately measure the fracture resistance in FGMs. In addition, the influence of local failure properties (i.e., failure stress and failure strain) on crack growth resistance was investigated in detail. It was found that depending on the combined effects of the spatial variation of these two failure parameters, regardless of the spatial variation of the Young’s modulus, the FGM fracture resistance can either increase, decrease or remain constant with continued crack growth.     

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.