TNM-Ti Al合金室温高周疲劳性能研究

采用升降法与成组法对TNM-TiAl合金试样进行了应力比R=-1的室温拉压疲劳和R=0.1的室温拉伸疲劳试验，得到TNM-TiAl合金的P-S-N曲线，并对断口进行了分析。结果表明:TNM-TiAl合金对应力十分敏感，R=-1和R=0.1时的曲线整体呈较为平直的斜线，R=-1时的疲劳极限为414.7 MPa,R=0.1时的疲劳极限为285.6 MPa。R=0.1的S-N曲线远低于R=-1的S-N曲线;R=-1时，应力幅与疲劳寿命的关系满足Basquin方程。疲劳试件宏观断口较为粗糙，静态拉伸宏观断口平整，两者差异较大。拉伸断口整体分为裂纹萌生区与扩展区，其中起裂源均位于试样表面或板状试件的边角棱线处，起裂源区域包括γ相的解理断裂面、片层团的沿层解理面以及β₀相平整的穿晶断裂平面等特征。疲劳断口整体分为裂纹萌生区、扩展区与瞬断区，其中裂纹萌生区分为表面沿层起裂和γ相起裂。TNM-TiAl合金的疲劳断裂为脆性断裂，主要体现在扩展区上大量的片层团穿层断裂、扭折撕裂、γ相解理断裂和β₀相穿晶断裂。同寿命量级下，R=-1的断口与R=0.1的断口断裂类型...     

求解双材料界面裂纹应力强度因子的扩展有限元法

基于双材料界面裂纹尖端的基本解,构造扩展有限元法(eXtended Finite Element Methods, XFEM)裂尖单元结点的改进函数。有限元网格剖分不遵从材料界面,考虑3种类型的结点改进函数:弱不连续改进函数、Heaviside改进函数和裂尖改进函数,建立XFEM的位移模式,给出计算双材料界面裂纹应力强度因子(Stress Intensity Factors, SIFs)的相互作用积分方法。数值结果表明:XFEM无需遵从材料界面剖分网格,该文的方法能够准确评价双材料界面裂纹尖端的SIFs。     

垂直界面裂纹应力强度因子的加料有限元分析

为求解裂尖位于界面上的垂直双材料界面裂纹应力强度因子,发展了一种加料有限元方法。该方法应用Williams本征函数展开和线性变换方法求解裂尖渐进位移场,将该位移场加入常规单元位移模式中,得到加料垂直界面裂纹单元和过渡单元的位移模式,给出加料有限元方程。建立了典型垂直界面裂纹平面问题的加料有限元模型,求解加料有限元方程直接得到应力强度因子,与文献结果对比表明该方法具有较高的精度,可方便地推广应用于垂直界面裂纹的计算分析。     

半刚性基层沥青路面反射裂缝扩展过程分析的Williams单元

该文对半刚性基层沥青路面结构采用弹性层状体系平面应变分析模型,利用改进的Williams级数,结合广义参数有限元法和常规等参元,建立了反射裂缝裂尖应力强度因子分析的广义参数Williams单元,并推导了Williams单元的刚度方程,据此研究了正对称荷载和偏载分别作用时,反射裂缝扩展过程中应力强度因子的变化规律;重点分析了偏载作用下路面结构层参数与应力强度因子之间的关系。Williams单元中含有与应力强度因子相关的参数,可以直接获得裂尖应力强度因子。算例分析表明:Williams单元与传统方法的计算结果吻合较好,且格式简单,计算精度高,适用于沥青路面反射裂缝扩展过程分析。     

基体裂纹-异型夹杂相互作用焦散线实验研究

该文通过透射式静态焦散线方法利用三点弯曲梁断裂实验对异型夹杂与基体裂纹的相互作用进行研究。首先得到不同夹杂情况下I型裂纹尖端的焦散斑图,引入焦散斑纵横轴长之比β反映焦散斑在夹杂作用下的畸变特性;其次,提取相应的焦散斑特征尺寸,并得到I型裂纹的应力强度因子K_I;最后,基于不同夹杂情况下裂尖焦散斑、裂尖应力强度因子与裂尖和夹杂之间距离的关系,揭示不同夹杂对裂纹尖端应力场奇异性影响规律。实验研究结果为含异型夹杂结构的强度设计和断裂性能评估提供实验依据。     

由小尺寸试件确定混凝土的断裂韧度与拉伸强度

该文利用骨料最大粒径d_max=10 mm,试件高度W依次为60 mm、80 mm、100 mm、140 mm、160 mm,厚度B=40 mm的小尺寸三点弯曲梁试件,来确定无尺寸效应的混凝土断裂韧度K_IC与拉伸强度f_t。区别于现有尺寸效应模型关注于"绝对尺寸W",该文提出"相对尺寸W/d_max"的概念,分析了骨料颗粒对有限尺寸试件断裂破坏的影响机理,进而将骨料最大粒径d_max与离散度参数β引入修正的边界效应模型的解析表达式中,发展建立了离散颗粒断裂模型,进而给出了由实验室条件下小尺寸试件（W=60 mm~160 mm和B=40 mm）的峰值荷载P_max同时确定混凝土材料参数-K_IC和f_t的实用方法。进而分析了不同试件组合和不同峰值荷载时裂缝扩展量取值对材料参数确定的影响规律,建立了混凝土材料破坏的完整曲线,给出了满足线弹性断裂力学条件的混凝土试件理论最小尺寸,并基于确定的材料参数对各试件的峰值荷载进行了成功预测。。     

线粘弹性断裂分析的增量加料有限元法

提出了一种用于解决线粘弹性断裂问题的增量加料有限元法。为了反映裂纹尖端的应力奇异性,在裂尖附近的应力奇异区采用若干四边形加料单元和过渡单元,非奇异区采用常规四边形单元,三种单元分区混合使用形成求解域网格划分。加料单元通过引入裂尖渐近位移场,构造出可以较好反映裂尖奇异性的单元位移模式,过渡单元在加料单元基础上引入调整函数构造单元位移模式,用于连接加料单元和常规单元,以消除加料单元和常规单元间位移不协调。基于Boltzmann叠加原理,推导了粘弹性材料的增量型本构关系,进而获得了增量加料有限元列式,并基于节点位移外推法计算粘弹性介质中裂纹应变能释放率。数值算例验证了该文方法的正确性和有效性。     

奇异薄层单元及其在双材料界面断裂分析中的应用

构造了一种平面应力奇异薄层单元并证明了其具有-1/2阶奇异性。用此单元研究了双材料界面层的刚度对界面裂纹尖端场的影响。研究发现:对于I 型界面断裂, 减小界面法向刚度对K_Ⅰ、K_Ⅱ的影响远大于减小界面切向刚度, 且法向和切向刚度的减小对K_Ⅱ的影响均大于对K_Ⅰ的影响, 降低法向刚度会显著改变裂尖正应力和剪应力的分布, 而降低切向刚度只明显改变剪应力的分布, 对正应力的分布影响不大;对于界面II 型断裂, 则减小切向刚度对K_Ⅰ、K_Ⅱ的影响远大于减小法向刚度, 且切向、法向刚度的减小对K_Ⅰ影响均大于对K_Ⅱ影响, 降低切向刚度会显著改变裂尖正应力和剪应力的分布, 而降低法向刚度只明显改变裂尖正应力的分布, 对剪应力的分布影响不大。随着界面刚度增大, 应力强度因子和裂尖应力分布均趋近无厚度理想界面情况。     

SiGw/Al复合材料的偏轴拉伸断裂行为

应用扫描电镜对挤压SiCw/6061Al复合材料的拉伸断裂过程进行了动态观察,并详细讨论了偏轴角θ对复合材料强度和断裂行为的影响。结果表明,微裂纹起源于晶须周围基体中,其萌生与扩展受晶须偏轴角的控制。复合材料由正向断裂向剪切断裂转变的特征角θ₀约为45-50°。      

考虑骨料体积含量影响的混凝土准脆性断裂预测模型及应用

基于对准脆性断裂边界影响模型参数的分析,该文将平均骨料粒径d_ave引入模型中,得到了考虑骨料体积含量及尺寸影响的混凝土准脆性断裂预测模型。模型中的有效裂缝与特征裂纹的比值,明确表征了三分点加载单边切口梁(SENB)试件的尺寸及初始缝长度变化时服从的断裂失效准则;模型中d_ave及分散系数β_ave将影响最大荷载P_max作用下临界微裂纹扩展区的平均虚拟裂纹长度Δa_fic。通过SENB试件在P_max时的受力分析,得到了临界正应力σ_n、有效裂缝长度a_e、拉伸强度f_t及断裂韧度K_IC之间的关系式。通过Amparano的试验结果,当a_fic为0.8~1.4倍d_ave时,采用混凝土准脆性断裂模型能较好预测混凝土拉伸强度及断裂韧度。通过对Δa_fic=1.2d_ave时模型得到的预测曲线与试验结果的对比,证明了模型计算结果的可靠性。考虑骨料体积含量影响的混凝土准脆性断裂模型能基于RILEM规范中三分点加载SENB试验预测混凝土断裂韧度与拉伸强度。     

Direct evaluation of stress intensity factors for curved cracks using Irwin's integral and XFEM with high‐order enrichment functions

This paper presents a comprehensive study on the use of Irwin's crack closure integral for direct evaluation of mixed‐mode stress intensity factors (SIFs) in curved crack problems, within the extended finite element method. The approach employs high‐order enrichment functions derived from the standard Williams asymptotic solution, and SIFs are computed in closed form without any special post‐processing requirements. Linear triangular elements are used to discretize the domain, and the crack curvature within an element is represented explicitly. An improved quadrature scheme using high‐order isoparametric mapping together with a generalized Duffy transformation is proposed to integrate singular fields in tip elements with curved cracks. Furthermore, because the Williams asymptotic solution is derived for straight cracks, an appropriate definition of the angle in the enrichment functions is presented and discussed. This contribution is an important extension of our previous work on straight cracks and illustrates the applicability of the SIF extraction method to curved cracks. The performance of the method is studied on several circular and parabolic arc crack benchmark examples. With two layers of elements enriched in the vicinity of the crack tip, striking accuracy, even on relatively coarse meshes, is obtained, and the method converges to the reference SIFs for the circular arc crack problem with mesh refinement. Furthermore, while the popular interaction integral (a variant of the J‐integral method) requires special auxiliary fields for curved cracks and also needs cracks to be sufficiently apart from each other in multicracks systems, the proposed approach shows none of those limitations. Copyright © 2017 John Wiley & Sons, Ltd.     

Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension (a/W=0.5) and three-point bend (a/W=0.1 and 0.5) specimens under plane stress condition. The crack growth is controlled by the experimental J-integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack- tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress. This revised version was published online in August 2006 with corrections to the Cover Date.     

Cracks emanating from a square hole in rectangular plate in tension

A numerical analysis of cracks emanating from a square hole in a rectangular plate in tension is performed using a hybrid displacement discontinuity method (a boundary element method). Detailed solutions of the stress intensity factors (SIFs) of the plane elastic crack problem are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. By comparing the calculated SIFs of the plane elastic crack problem with those of the centre crack in a rectangular plate in tension, in addition, an amplifying effect of the square hole on the SIFs is found. The numerical results reported here also prove that the boundary element method is simple, yet accurate, for calculating the SIFs of complex crack problems in finite plate.     

An over‐deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis

An over‐deterministic method has been employed for calculating the stress intensity factors (SIFs) as well as the coefficients of the higher‐order terms in the Williams series expansions in cracked bodies, using the conventional finite element analysis. For a large number of nodes around the crack tip, an over‐determined set of simultaneous linear equations is obtained, and using the fundamental concepts of the least‐squares method, the coefficients of the Williams expansion can be calculated for pure mode I, pure mode II and mixed mode I/II conditions. A convergence study has been conducted to examine the effects of the number of nodes used, the number of terms in Williams expansion and the distance of the selected nodes from the crack tip, on the accuracy of the results. It is shown that the simple method presented in this paper, yields accurate results even for coarse finite element meshes or in the absence of singular elements. The accuracy of SIFs and the coefficients of higher‐order terms are validated by using the available results in the literature.     

承受双向等拉应力的平面应变I型裂纹线弹性断裂的I1准则与K准则一致性分析

采用线弹性有限元方法计算了承受双向等拉应力的平面应变I型裂纹的应力场,分析了裂纹尖端各应力分量间的关系,拟合了各非零应力分量关于裂纹半长度a和裂纹尖端最小网格尺寸l₁的函数,分析了应力第一不变量I₁与应力场强度因子K_I的相关性。结果表明,裂纹尖端各非零应力分量间存在稳定的比例关系;各非零应力分量值和加载应力的比值与裂纹半长度a的1/2次幂呈正比例关系、与裂纹尖端最小网格尺寸l₁的1/2次幂呈反比例关系;相同最小网格尺寸条件下,裂纹尖端的应力第一不变量与应力场强度因子的比值l₁/K_I为与加载应力和裂纹长度无关的常数,证明了承受双向等拉应力的平面应变I型裂纹线弹性断裂的I₁准则与K准则具有一致性。     

Higher order tip enrichment of eXtended Finite Element Method in thermoelasticity

An eXtended Finite Element Method (XFEM) is presented that can accurately predict the stress intensity factors (SIFs) for thermoelastic cracks. The method uses higher order terms of the thermoelastic asymptotic crack tip fields to enrich the approximation space of the temperature and displacement fields in the vicinity of crack tips—away from the crack tip the step function is used. It is shown that improved accuracy is obtained by using the higher order crack tip enrichments and that the benefit of including such terms is greater for thermoelastic problems than for either purely elastic or steady state heat transfer problems. The computation of SIFs directly from the XFEM degrees of freedom and using the interaction integral is studied. Directly computed SIFs are shown to be significantly less accurate than those computed using the interaction integral. Furthermore, the numerical examples suggest that the directly computed SIFs do not converge to the exact SIFs values, but converge roughly to values near the exact result. Numerical simulations of straight cracks show that with the higher order enrichment scheme, the energy norm converges monotonically with increasing number of asymptotic enrichment terms and with decreasing element size. For curved crack there is no further increase in accuracy when more than four asymptotic enrichment terms are used and the numerical simulations indicate that the SIFs obtained directly from the XFEM degrees of freedom are inaccurate, while those obtained using the interaction integral remain accurate for small integration domains. It is recommended in general that at least four higher order terms of the asymptotic solution be used to enrich the temperature and displacement fields near the crack tips and that the J- or interaction integral should always be used to compute the SIFs.     

Direct evaluation of accurate coefficients of the linear elastic crack tip asymptotic field

An improvement to the extended finite element method (XFEM) and generalised finite element method (GFEM) is introduced. It enriches the finite element approximation of the crack tip node as well as its surrounding nodes with not only the first term but also the higher order terms of the linear elastic crack tip asymptotic field using a partition of unity method (PUM). Numerical results show that together with a reduced quadrature rule to the enriched elements, this approach predicts accurate stress intensity factors (SIFs) directly (i.e. without extra post‐processing) after constraining the enriched nodes properly. However, it does not predict accurately the coefficients of the higher order terms. For that a hybrid crack element (HCE) is introduced which is powerful and convenient not only for directly determining the SIF but also the coefficients of higher order terms in the plane linear elastic crack tip asymptotic field. Finally, the general expressions for the coefficients of the second to fifth terms of the linear elastic crack tip asymptotic field of three‐point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are extended to very deep cracks with the use of the HCE.     

A unified and integrated numerical‐analytical approach for evaluation of Jk‐integrals of an interfacial crack in orthotropic and isotropic bimaterials

A new unified and integrated method for the numerical‐analytical calculation of J_k‐integrals of an in‐plane traction free interfacial crack in homogeneous orthotropic and isotropic bimaterials is presented. The numerical algorithm, based on the boundary element crack shape sensitivities, is generic and flexible. It applies to both straight and curved interfacial cracks in anisotropic and/or isotropic bimaterials. The shape functions of semidiscontinuous quadratic quarter point crack tip elements are correctly scaled to adapt the singular oscillatory near tip field of tractions. The length of crack is designated as the design variable to compute the strain energy release rate precisely. Although an analytical equation relating J₁ and stress intensity factors (SIFs) exists, a similar relation for J₂ in debonded anisotropic solids for decoupling SIFs is not available. An analytical expression was recently derived by this author for J₂ in aligned orthotropic/orthotropic bimaterials with a straight interface crack. Using this new relation and the present computed J_k values, the SIFs can be decoupled without the need for an auxiliary equation. Here, the aforementioned analytical relation is reconstructed for cubic symmetry/isotropic bimaterials and used with the present numerical algorithm. An example with known analytical SIFs is presented. The numerical and analytical magnitudes of J_k for an interface crack in orthotropic/orthotropic and cubic symmetry/isotropic bimaterials show an excellent agreement.     

Perturbation method for the solution of a Zener–Stroh crack with a slightly curved configuration

This paper investigates the Zener–Stroh crack with curved configuration in plane elasticity. A singular integral equation is suggested to solve the problem. Formulae for evaluating the SIFs and T-stress at the crack tip are suggested. If the curve configuration is a product of a small parameter and a quadratic function, a perturbation method based on the singular integral equation is suggested. In the method, the singular integral equation can be expanded into a series with respect to the small parameter. Therefore, many singular integral equations can be separated from the same power order for the small parameter. These singular integral equations can be solved successively. The solution of the successive singular integral equations will provide results for stress intensity factors and T-stress at the crack tip. It is found that the behaviors for the solution of SIFs and T-stress in the Zener–Stroh crack and the Griffith crack are quite different. This can be seen from the presented comparison results.