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.      

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

Integrated numerical–experimental analysis of interfacial fatigue fracture in SnAgCu solder joints

In ball grid array (BGA) packages, solder balls are exposed to cyclic thermo-mechanical strains arising from the thermal mismatch between package components. Thermo-mechanical fatigue crack propagation in solder balls is almost always observed at the chip side of the bump/pad junction. The objective of the experimental part of this study is to characterize the bump/pad interface under fatigue loading. Fatigue specimens are prepared by reflowing Sn3.8Ag0.5Cu lead-free solder alloy on Ni/Au substrates. Obtained results show that fatigue damage evolution strongly depends on the microstructure. Applied strain and solder volume both have an influence on the fatigue damage mechanism. In the numerical part of the study, fatigue experiments are modeled using the finite element technique. A cohesive zone approach is used to predict the fatigue damage evolution in soldered connections. Crack propagation is simulated by an irreversible linear traction–separation cohesive zone law accompanied by a non-linear damage parameter. Cohesive zone elements are placed where failure is experimentally observed. Damage evolution parameters for normal and tangential interaction are scrutinized through dedicated fatigue tests in pure tensile and shear directions. The proposed cohesive zone model is quantitatively capable of describing fatigue failure in soldered joints, which can be further extended to a numerical life-time prediction tool in microelectronic packages.     

A cohesive zone model for fatigue crack growth allowing for crack retardation

A damage-based cohesive model is developed for simulating crack growth due to fatigue loading. The cohesive model follows a linear damage-dependent traction–separation relation coupled with a damage evolution equation. The rate of damage evolution is characterized by three material parameters corresponding to common features of fatigue behavior captured by the model, namely, damage accumulation, crack retardation and stress threshold. Good agreement is obtained between finite element solutions using the model and fatigue test results for an aluminum alloy under different load ratios and for the overload effect on ductile 316 L steel.     

新型各向异性核工业石墨断裂力学行为的实验研究和数值分析

本文分别采用激光和白光DSCM(数字散斑相关测量)方法对一种新型各向异性核工业石墨的裂纹尖端位移、应变场进行了实验研究，两种方法都取得了较好的结果。考虑核工业石墨制备过程形成的各向异性特点，本文构建了三维各向异性有限元模型，采用奇异单元，计算模拟石墨裂纹尖端的变形和应力场，通过对实验结果和有限元计算结果的比较可以发现两者具有相近的趋势。     

考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法

混凝土结构在服役期间受外界载荷的影响容易产生裂缝, 导致结构刚度降低、构件承载性能衰退, 而采用准确的计算方法预测混凝土裂缝的发展是治理裂缝的基本前提, 也是保障结构安全的重要手段. 连续损伤力学方法(continuou damage method, CDM)能够描述微裂缝的扩展过程, 但不能表示离散的开裂面, 且存在网格诱导偏差及虚假应力传递的弊端, 扩展有限单元法(mechanics-extended finite element method, XFEM)能够描述宏观裂纹的扩展过程, 但不能反映微裂缝的动态扩展, 两者计算出的裂纹分布与实际差异均较大. 现有的CDM-XFEM方法已经能够模拟混凝土微裂缝及宏观裂缝发展的整个过程, 但忽略了宏观裂缝出现时混凝土产生的塑性应变, CDM与XFEM的能量转化过程欠缺平衡性. 因此, 本文重点考虑能量转化时的塑性耗散, 选取指数型函数为粘结裂缝的牵引-分离模式, 基于能量及应力等效的条件重新构建了CDM与XFEM之间的能量转化方程. 采用广义逆最小二乘法求解能量转化系数, 确定能量转化时的临界位移, 并给出了裂缝面水平集的更新算法及整体计算方法的程序流程. 以双切口混凝土受剪拉开裂试验为例, 采用多种裂缝计算方法与试验进行了对比. 结果表明, 采用考虑混凝土塑性耗散的CDM-XFEM方法算出的裂缝分布及拉力-张开位移曲线与试验结果差异最小, 说明采用考虑混凝土塑性耗散的CDM-XFEM计算方法能够更好地计算混凝土裂缝.      

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

基于能量耗散分析的混凝土随机疲劳损伤模型

基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型。该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程。在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡。由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述。此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达。通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等。     

混凝土疲劳分析方法综述

从探究物理机制的视角对混凝土疲劳研究进行了逻辑上的梳理,表明既有研究可分为3 类主要模型:基于疲劳试验分析的现象学模型、基于断裂力学的疲劳裂纹扩展模型和基于损伤力学的疲劳损伤演化模型. 通过解析具有典型性的研究,论述了不同类型研究的特点. 进而,从还原论的角度出发,阐明了速率过程理论可以作为解释混凝土材料疲劳损伤演化的物理基础. 注意到疲劳试验结果所表现出的显著随机性,阐述了应以物理随机系统思想研究混凝土疲劳问题的观点.     

含缺口试件疲劳全寿命预测一种建议的方法

传统的研究含缺口构件的疲劳的方法是将疲劳启裂和疲劳裂纹扩展两个过程完全独立起来,用不同的方法来模拟,相互间并没有定量的关系。本文是基于最新发展的多轴疲劳损伤理论,建立了一种适用于各种载荷条件下的疲劳启裂和裂纹扩展的普适方法。根据从弹塑性分析中得到的应力应变,确定疲劳损伤模型,建立能够预测疲劳启裂、裂纹扩展速率和扩展方向的新方法。整个模拟可以分为两步:弹-塑性应力分析得到材料的应力应变分布;再运用一个通用的疲劳准则预测疲劳裂纹启裂和裂纹扩展。通过对1070号钢含缺口试件的疲劳全寿命预测,得到了与实验非常吻合的模拟结果。     

A cohesive plastic and damage zone model for dynamic crack growth in rate-dependent materials

Mode I steady-state dynamic crack growth in rate-dependent viscoplastic solids containing damage, under small scale yielding conditions, is analyzed based on a modified cohesive zone model. A multi-scale approach is used to describe the entire non-linear zone consisting of a plastic region and a damage region, each of which has its own constitutive law. Traction in the damage region is characterized by a softening power-law, in terms of the ultimate strength, a softening index and a rate sensitivity factor. In the plastic region, the cohesive law is assumed to be both strain hardening and rate dependent. The critical crack opening displacement at the physical crack-tip controls crack growth. The governing integral equations are derived and solved by a collocation method combined with associated boundary conditions. Numerical results are presented for the traction and opening profiles along the cohesive zone, the fracture energy and lengths of the damage and non-linear zones at different crack speeds and for different material parameters. The importance of factors, such as material softening, plastic deformation, crack speed and viscosity, is identified by parametric studies. In addition, the competition of plastic flow and material damage, and its effect on crack growth, are discussed.     

Development of a multiaxial fatigue theory by considering constraint effects on small mixed-mode cracks

The effects of the transverse strain (the normal strain in the crack-line direction) on the near-tip fields of small shallow surface cracks (Case A cracks) in power-law hardening materials are investigated by finite element analyses. The small Case A cracks are under plane stress, general yielding, and mixed mode I and II conditions. Constant effective stress contours representing the intense straining zones near the tip, deformed crack-tip profiles and near-tip mode mixity factors are presented for different transverse strains in the crack-line direction. Based on the concept of characterization of fatigue crack growth by the cyclic J-integral, the effects of the transverse strain on J are investigated. The results suggest that the fatigue life prediction based on multiaxial fatigue theories and the critical plane approach should include the constraint effects due to the transverse strain. Consequently, the concept of constant fatigue life contour on the Γ-plane in multiaxial fatigue theories is generalized to the constant fatigue life surface in the Γ-space where the shear strain and the two normal strains are the three axes. Finally, a damage parameter as a function of the shear strain and the two normal strains is proposed for evaluation of fatigue damage under multiaxial loading conditions.     

扫描电镜下的数字散斑相关方法及其应用

对数字散斑相关方法(digital speckle correlation method,DSCM)在扫描电镜(scanningelectron microscope,SEM)下的应用进行了研究。将DSCM与带电液伺服试验系统的SEM结合起来,对二者结合的过程进行了分析,实现了SEM下细微观变形场的测量,扩展了DSCM和SEM的应用范围。为了定量地把握SEM在扫描图像时放大倍数的不稳定性、非线性和内部噪声对DSCM的影响,还对SEM下的DSCM精度和误差进行了实验分析。统计结果表明,SEM下应用DSCM进行变形场的测量,其位移测量误差最大可达2像素,其精度可以满足一般变形场测量的需要。作为应用实例,对混凝土试件在SEM下的断裂行为进行了研究,得到了混凝土试件表面随着载荷的变化而变化的表面细观变形场。     

Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces

The cohesive surface methodology is used in a numerical study of fracture of concrete. The traction vs. separation response is governed by an isotropic damage law in which damage evolves according to a prescribed one-dimensional linear or exponential softening law. Cohesive surfaces are immersed in the continuum to allow for a maximum freedom of crack path selection. The single edge notched four point shear beam and the double edge notched tensile bar are used to study: (i) the influence of the tangential cohesive response on the development of the fracture path and (ii) the mesh alignment sensitivity. It is shown that in the present formulation, the tangential cohesive response has a minor influence on both crack path and global characteristics. Mesh alignment does have a significant influence on the outcome of the numerical analysis.     

沥青混合料疲劳过程的损伤力学分析

采用损伤力学方法研究沥青混合料的疲劳失效问题。针对悬壁梁弯曲疲劳试件,推导出疲劳过程中应力场、损伤场和疲劳裂纹形成寿命的工程封闭公式。根据沥青混合料特点,提出一种模拟疲劳裂纹扩展的特征单元失效模式,从而将疲劳裂纹形成与扩展两个阶段统一用损伤力学理论进行描述和分析。本文对沥青混合料试件的疲劳裂纹形成寿命与扩展寿命分段进行了预测,还对疲劳过程中刚度衰减及位移幅值的演化过程进行了数值模拟计算。理论预期与实验结果吻合良好。     

An isolated cohesive crack in tension

The shape of the back-calculated stress-separation curves obtained from the in-situ fracture of first-year sea ice in the Arctic and Antarctic is convex, and radically different from those for concrete. In these tests, the process zone size changes with crack growth, but the nature of this change differs with the test conditions, load-control or displacement control. These results prompted a closer examination of the cohesive crack model using the simplest cracked configuration, a finite cohesive crack in an infinite elastic medium loaded in tension by a uniform stress at infinity. Different types of strain softening are examined: rectangular softening, linear softening, prescribed cohesive stresses, and prescribed cohesive crack-opening displacements. For each of these cases, crack nucleation is examined; close attention is paid to test control conditions, be they load-control or fixed-grip. The test control conditions alter the fracture, crack nucleation, crack growth, and process zone size behavior significantly. Accurate approximate solutions to linear softening are presented and examined.     

混凝土断裂过程区的虚拟裂纹粘聚力奇异性

混凝土断裂过程区视为具有粘聚阻力作用的虚拟裂纹，其非线性断裂和尺寸效应特性是与该虚拟裂纹粘聚力分布规律密切相关的。通过得到的粘聚应力分布函数解析结果，对该粘聚力分布特征的分析得知，在基于断裂过程区之外用线弹性场的力学模型上，该粘聚力随距离虚拟裂纹尖点的靠近，仍具有平方根奇异性。从而本文提出一个能够反映裂纹发展状态的粘聚应力奇异性强度参数，它是无粘聚力的线弹性裂纹应力强度因子和表征裂纹张开位移分布多项式参数的函数；因此，该参数可以作为混凝土非线性断裂的一个参量。文中就已有断裂试验测试结果进行了算例分析和相应的讨论。     

裂纹体分析的权函数理论与应用: 回顾和展望

断裂力学是工程材料和结构的疲劳与断裂分析、损伤容限设计和结构完整性评定的理论基础. 应力强度因子作为线弹性裂纹尖端奇异场的单一表征参量和裂纹扩展驱动力, 在裂纹体的断裂力学分析中发挥着关键作用. 权函数法为复杂受载裂纹体的应力强度因子求解计算提供了强有力的解析工具, 不但具有远高于各类数值解法的计算效率, 而且精度可靠, 使用方便. 本文结合笔者团队在权函数法方面的长期研究工作, 对该方法自20世纪70年代初提出至今半个世纪以来, 国际断裂界在二维和三维权函数理论与应用方面的主要研究进展作了回顾和评述, 并对其未来发展提出了展望. 主要内容涵盖: 当前国际断裂界广泛应用的3种二维裂纹解析权函数法简介和以格林函数为基准的验证评价; 三维裂纹问题的片条合成权函数法和点载荷权函数法; 权函数法在复杂受载裂纹体的应力强度因子和裂纹张开位移等关键力学参量计算、内聚力/桥连等裂纹模型分析、共线多裂纹权函数理论及其在剩余强度预测等方面的应用, 以及复杂裂纹几何的工程化权函数分析和权函数法的反向应用问题.      

准脆性材料中强不连续问题的数值方法若干应用及其研究进展

综述了模拟准脆性材料开裂过程的数值计算方法的研究进展和工程应用,比较了表征强不连续问题的显式非连续模型和隐式非连续模型的优缺点.结合混凝土粘结裂纹, 重点讨论了嵌入非连续模型,扩展有限元方法和富集有限元技术等非连续方法的构造特征和本质区别.从各种富集方法的理论完备性考察,以假定发展应变为基础的嵌入非连续方法虽然可以解决混凝土开裂过程中的应力锁死,满足内部边界的静力平衡条件以及反映开裂后的位移不连续问题,但嵌入非连续所采用的富集函数在开裂单元中并不能满足协调条件,使非连续两侧的应变不独立. 其局限性是由于富集自由度在单元的水平上引入,而以单位分解为基础的扩展有限元和富集有限元的富集函数以节点自由度的方式引入,除具有嵌入非连续的优点, 还可以有效消除嵌入非连续引起裂纹两侧应变的相互影响.文中同时指出了网格重构技术,弥散裂纹模型的局限性以及扩展有限元和富集有限元技术在构造方式上的细微差别.对于节点自由度方式引入的富集函数, 其操作困难性在文中也作了说明.      

Dislocation shielding of a cohesive crack

Dislocation interaction with a cohesive crack is of increasing importance to computational modelling of crack nucleation/growth and related toughening mechanisms in confined structures and under cyclic fatigue conditions. Here, dislocation shielding of a Dugdale cohesive crack described by a rectangular traction-separation law is studied. The shielding is completely characterized by three non-dimensional parameters representing the effective fracture toughness, the cohesive strength, and the distance between the dislocations and the crack tip. A closed form analytical solution shows that, while the classical singular crack model predicts that a dislocation can shield or anti-shield a crack depending on the sign of its Burgers vector, at low cohesive strengths a dislocation always shields the cohesive crack irrespective of the Burgers vector. A numerical study shows the transition in shielding from the classical solution of Lin and Thomson (1986) in the high strength limit to the solution in the low strength limit. An asymptotic analysis yields an approximate analytical model for the shielding over the full range of cohesive strengths. A discrete dislocation (DD) simulation of a large (>10³) number of edge dislocations interacting with a cohesive crack described by a trapezoidal traction-separation law confirms the transition in shielding, showing that the cohesive crack does behave like a singular crack at very high cohesive strengths (∼7 GPa), but that significant deviations in shielding between singular and cohesive crack predictions arise at cohesive strengths around 1GPa, consistent with the analytic models. Both analytical and numerical studies indicate that an appropriate crack tip model is essential for accurately quantifying dislocation shielding for cohesive strengths in the GPa range.