Ⅱ型Ⅲ型动态裂纹尖端断裂过程区近似评估方法

动态裂纹尖端断裂过程区轮廓的确定问题仍然是一个没有得到完全解决的问题。基于弹性动力学的理论和复应力函数方法,提出一种伪应力函数方法,用于近似评估动态裂纹尖端应力场。通过与已知应力场计算结果对比,验证了伪应力函数的正确性。利用此近似方法通过Von Mises强度准则和Tresca强度准则,分别确定了不同强度准则条件下、不同裂纹扩展速度下断裂过程区的轮廓。计算结果表明:II型和III型动态裂纹尖端断裂过程区关于裂纹面对称分布,随着裂纹扩展速度增大而增大。当裂纹传播速度接近瑞利波速时,断裂过程区变化加剧。利用Tresca强度准则计算得到的动态裂纹尖端断裂过程区面积比利用Von Mises强度准则计算得到的断裂过程区的面积大。     

发展基于CB壳单元的扩展有限元模拟三维任意扩展裂纹

该文提出了一种新的基于连续体壳单元的扩展有限元格式,以用于对曲面上任意形状裂纹的扩展问题进行模拟。扩充形函数的构造和应力强度因子的计算都是基于三维实体单元进行,因此可以模拟复杂的三维断裂情况,壳体厚度的变化也可以得到考虑。三维应力强度因子的计算公式被引入到这种方法中。为模拟裂纹扩展,三维最大能量释放率准则被用作裂纹扩展准则。计算结果显示了曲面上的裂纹扩展路径可以与网格无关,并且由于在裂纹尖端的单元设置了具有奇异性的形函数,裂尖应力场被精确捕捉,从而证明了这种方法的优越性。     

GM屈服准则求解Ⅰ型裂尖塑性区

用几何中线(GM)屈服准则求解了Ⅰ型裂尖塑性区的形状与尺寸,对比了基于Mises和Tresca准则的求解结果。表明在平面应变条件下,GM准则求解的塑性区面积在Tresca和Mises结果之间,Tresca塑性区面积最大,Mises面积最小,GM塑性区与Mises塑性区非常接近,三者的塑性区均成哑铃状。在平面应力下,GM和Mises塑性区二者仍最接近并为豆芽状,Tresca的塑性区最大。无论平面应力还是平面应变,GM准则计算结果与Mises结果均有最佳接近度。     

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。     

用圆孔内单边裂纹平台巴西圆盘和实验-数值-解析法确定砂岩的动态起裂和扩展韧度

在I型(张开型)动态断裂实验中,利用大直径(?100 mm)分离式霍普金森压杆径向冲击圆孔内单边裂纹平台巴西圆盘试样。考虑了材料惯性效应和裂纹扩展速度对动态应力强度因子的影响,用实验-数值-解析法确定了高加载率和高裂纹扩展速度情况下,砂岩的动态起裂韧度和动态扩展韧度。由动态实验获取试样的动荷载历程,采用裂纹扩展计(Crack Propagation Gauge,CPG)测定试样断裂时刻和裂纹扩展速度,获得裂纹扩展速度对应的普适函数值。然后将动荷载历程带入到有限元软件中进行动态数值模拟,求出静止裂纹的动态应力强度因子历程,再用普适函数值对其进行近似修正。最后根据试样的起裂时刻和穿过CPG中点的时刻,由相应的动态应力强度因子历程分别确定砂岩的动态起裂和动态扩展韧度,它们分别随动态加载率和裂纹扩展速度的提高而增加。     

金属泡沫材料平面应变裂纹缓慢扩展的奇异摄动分析

利用奇异摄动分析法研究了金属泡沫材料中平面应变Ⅰ-型裂纹的纹缓慢扩展问题，对裂纹尖端附近的应力场和速度场进行了分析，并得到了扩展裂纹尖端速度场和角应力函数的的最低阶摄动解。     

预制裂纹角度对橡胶拉伸断裂影响的有限元分析

初始裂纹的形态影响着裂纹尖端的应力场和扩展方向,进而决定着橡胶材料的使用寿命。目前人们关于预制裂纹试样拉伸断裂的研究主要集中在直裂纹,很少涉及预制裂纹角度的改变对橡胶拉伸断裂的影响。文中应用ANSYS有限元分析软件计算拉伸状态下含不同裂纹角度橡胶试样裂纹尖端的等效应力值和撕裂能的大小,判断裂纹是否扩展及扩展方向,并对橡胶试样进行拉伸验证试验测试。结果表明,在拉伸断裂过程中,裂纹尖端的应力值和撕裂能随着初始预制裂纹角度的增大而增大,裂纹尖端形状均由初始的尖点变成圆弧状;含不同裂纹角度橡胶试样的拉伸断裂形貌与裂纹预测扩展方向基本一致,验证了有限元分析的正确性。     

裂纹深度及尖端曲率对尖角裂纹周围应力场的影响

对于尖角裂纹,裂纹深度和裂纹尖端曲率对于裂纹附近应力场的影响有可能要大于裂纹张开角度的影响。根据弹性断裂理论和复变函数理论建立了一个计算模型,利用保角映射方法解决了尖角裂纹的边界条件问题,得到了具有不同深度和尖端曲率的裂纹周围应力分布,并对此应力分布规律进行了分析。     

定向断裂控制爆破爆生裂纹扩展机理的实验研究

采用新型数字激光动态焦散线实验系统,对缺陷介质双孔定向断裂控制爆破裂纹扩展的动态行为进行了研究。结果表明,预制斜裂纹阻断了爆生主裂纹的扩展,最终两条主裂纹分别与翼裂纹形成相互勾连的形状。爆生主裂纹尖端以张拉应力场为主,其断裂为近似I型断裂。当爆生主裂纹运动到预制裂纹附近时,主裂纹端部应力场与预制裂纹尖端奇异应力场相互叠加,在预制裂纹尖端形成较强的拉剪应力场,且受已有主裂纹面的影响,预制裂纹扩展表现为弯向主裂纹面的弯曲断裂。研究结果可为含节理岩体定向断裂控制爆破提供理论依据。     

定向断裂双孔爆破含缺陷介质裂纹扩展的动焦散试验

利用爆炸加载数字激光动态焦散线试验系统,进行双孔爆破爆炸应力波作用下缺陷介质裂纹扩展试验。研究了含水平预制裂纹和竖直预制裂纹的介质裂纹扩展路径、速度、加速度和裂尖动态应力强度因子变化规律。试验结果表明:在爆炸应力波作用下,预制裂纹尖端起裂,并扩展。炸药爆炸后,主裂纹的扩展速度迅速达到峰值,之后开始振荡减小,其加速度呈现波浪起伏式的振荡变化。次裂纹起裂后速度增大至峰值,然后开始减小。主裂纹尖端的动态应力强度因子K_Ⅰ从峰值振荡减小,又振荡增加至第二个峰值,之后振荡减小。次裂纹尖端的动态应力强度因子K_Ⅰ达到最大时,次裂纹起裂,之后K_Ⅰ振荡减小。裂纹扩展的过程中K_Ⅱ基本都小于K_Ⅰ。     

Extended structural criterion for numerical simulation of crack propagation and coalescence under compressive loads

An extension of the Neuber-Novozhilov structural fracture propagation criterion is presented for mode I (tensile) and mode II (shear) propagation under compressive loads. In addition to allowing numerical simulation of crack growth, the criterion can be used to model change of propagation mode, crack branching, and coalescence. The criterion can be applied effectively when the SIF is calculated accurately (at least three significant digits). A numerical method is suggested for this purpose that consists of complementing the complex variable hypersingular boundary element method (CVH-BEM) with special procedures for automatically tracing crack propagation and coalescence. The CVH-BEM code with the structural criterion has been used to investigate crack propagation in compression for both small and non-small fracture process zone (FPZ). The results of numerical experiments are in agreement with the analytical conclusions available for the case of small FPZ that indicates the possibility of three distinct patterns of crack propagation under external compressive loads. These are: (i) smooth curvilinear tensile (wing) cracks, (ii) stair-step propagation pattern with changing modes, and (iii) in plane shear propagation. The numerical study also indicates that when the critical size of the FPZ is large enough, the non-singular terms in the expansion of the stress functions strongly influence the crack trajectories. Specifically, this occurs when the size of the FPZ approaches a quarter of the half-length of the initial crack. Calculations for a closed initial crack in a half-space under compression illustrate the general features of crack propagation. Although the dominant direction of crack growth is that of the applied compressive stress, the pattern of propagation strongly depends on the particular geometry, critical size of the FPZ, and the ratio of shear-to-tensile microscopic strength.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.     

An analytical method for mixed-mode propagation of pressurized fractures in remotely compressed rocks

An analytical method for mixed-mode (mode I and mode II) propagation of pressurized fractures in remotely compressed rocks is presented in this paper. Stress intensity factors for such fractured rocks subjected to two-dimensional stress system are formulated approximately. A sequential crack tip propagation algorithm is developed in conjunction with the maximum tensile stress criterion for crack extension. For updating stress intensity factors during crack tip propagation, a dynamic fictitious fracture plane is used. Based on the displacement correlation technique, which is usually used in boundary element/finite element analyses, for computing stress intensity factors in terms of nodal displacements, further simplification in the estimation of crack opening and sliding displacements is suggested. The proposed method is verified comparing results (stress intensity factors, propagation paths and crack opening and sliding displacements) with that obtained from a boundary element based program and available in literatures. Results are found in good agreements for all the verification examples, while the proposed method requires a trivial computing time.     

Numerical simulations of a dynamically propagating crack with a nonlinear cohesive zone

Numerical solutions of a dynamic crack propagation problem are presented. Specifically, a mode III semi-infinite crack is assumed to be moving in an unbounded homogeneous linear elastic continuum while the crack tip consists of a nonlinear cohesive (or failure) zone. The numerical results are obtained via a novel semi-analytical technique based on complex variables and integral transforms. The relation between the properties of the failure zone and the resulting crack growth regime are investigated for several rate independent as well as rate dependent cohesive zone models. Based on obtained results, an hypothesis is formulated to explain the origin of the crack tip velocity periodic fluctuations that have been detected in recent dynamic crack propagation experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

VECTOR CTD CRITERION APPLIED TO MIXED MODE FATIGUE CRACK GROWTH

Abstract— This work is aimed at developing a general parameter based on the deformation intensity at a mixed mode crack tip to predict crack growth behaviour, especially in the near threshold region. Being a mechanisms-related parameter, the vector crack tip displacement (CTD) is defined as a vector summation of CTOD and CTSD_c which act, respectively in the directions of mode I and mode II fatigue crack growth. The basic assumption is that both direction and rate of mixed mode fatigue crack growth are governed by the vector ΔCTD, which represents the resultant of the "driving force"at the crack tip. The analytical predictions obtained by using the vector ΔCTD are in good agreement with the reported experimental results of mixed mode I and II fatigue cracks.     

Influence of isotropic strain hardening on plane strain dynamic growth in elastic-plastic materials

In this paper, dynamic crack growth in an elastic-plastic material is analysed under mode I, plane strain, small-scale yielding conditions using a finite element procedure. The material is assumed to obey J₂ incremental theory of plasticity with isotropic strain hardening which is of the power-law type under uniaxial tension. The influence of material inertia and strain hardening on the stress and deformation fields near the crack tip is investigated. The results demonstrate that strain hardening tends to oppose the role of inertia in decreasing plastic strains and stresses near the crack tip. The length scale near the crack tip over which inertia effects are dominant also diminishes with increase in strain hardening. A ductile crack growth criterion based on the attainment of a critical crack tip opening displacement is used to obtain the dependence of the theoretical dynamic fracture toughness on crack speed. It is found that the resistance offered by the elastic-plastic material to high speed crack propagation may be considerably reduced when it possesses some strain hardening.     

功能梯度材料II型动态裂纹尖端的焦散线分析

根据功能梯度材料II型裂纹在定常扩展速度情况下裂纹尖端离面位移场的平面应力级数解,对材料性能沿裂纹扩展方向的两种不同变化规律进行了分析,分别假设:(1)剪切模量线性变化,密度保持常数;(2)剪切模量和密度指数规律变化。在分析中泊松比保持不变。推导两种变化规律材料II型动态裂纹尖端的焦散线方程,对两种材料的焦散线进行数值模拟,并求解应力强度因子与焦散线特征尺寸之间的函数关系,以此为基础分析不同梯度变化规律对材料断裂性能的影响     

裂纹稳态扩展下正交异性材料的动应力强度因子K_(Ⅲ)解答

研究了无限大正交异性材料中半无限长Ⅲ型裂纹的动态扩展问题。裂纹尖端附近的应力和位移被表达为解析复函数的形式,而复函数可以表达为幂级数的形式,幂级数的系数由研究问题的边界条件来确定。这样就给出了裂纹尖端附近的应力分量和位移分量的简单近似表达式,由推导出的动应力分量和动位移分量可以退化为其在各向同性材料静态断裂问题中的情况。最后,裂纹扩展特性由裂纹几何参数和裂纹扩展速度来反映出来,相同的几何参数情况下,裂纹扩展愈快,裂纹尖端附近的最大应力分量和最大位移分量愈大。