考虑表面弹性效应时正三角形孔边裂纹反平面剪切问题的断裂力学分析

基于表面弹性理论和保角映射技术,研究了远场作用反平面剪切载荷作用下考虑表面弹性效应时正三角形孔边裂纹问题的断裂性能.给出了孔边应力场的精确解,获得了裂纹尖端应力强度因子的解析解答.数值算例中讨论了裂尖应力强度因子随三角形孔尺寸、裂纹长度和表面性能的变化规律.结果表明:当三角形孔的尺寸在纳米量级时,无量纲应力强度因子具有显著的尺寸效应;随着三角形孔尺寸的增大,论文结果趋近于经典断裂理论解答;无量纲应力强度因子随孔边裂纹长度的增加,先增大而后减小;当孔边裂纹长度较小时,表面效应影响较弱;应力强度因子的尺寸效应受表面性能影响显著.     

冲击载荷下含空孔三点弯曲梁的动态断裂行为

为得到圆孔缺陷对运动裂纹扩展过程的影响规律,采用动态焦散线实验方法进行模型实验,研究了冲击载荷下含空孔三点弯曲梁的动态断裂行为。研究结果表明:空孔对裂纹扩展有极大的阻碍作用,在一定范围内,空孔直径越大,阻碍作用越明显。裂纹扩展到空孔附近时,扩展速度会下降。裂纹在空孔上部再次起裂后,最大扩展速度远远大于裂纹与空孔贯通前的最大扩展速度。裂纹扩展至空孔附近时,裂纹尖端动态应力强度因子KdⅠ和KdⅡ均会下降。裂纹在空孔上部再次起裂后,裂尖的应力强度因子KdⅠ和KdⅡ均大于裂纹与空孔贯通前裂尖的KdⅠ和KdⅡ。在整个扩展过程中,裂纹尖端的动态应力强度因子KdⅡ远小于KdⅠ,说明KdⅠ在裂纹扩展过程中起主要作用。     

双轴载荷作用下源于椭圆孔的分支裂纹的一种边界元分析

利用一种边界元方法来研究双轴载荷作用下无限大板中源于椭圆孔的分支裂纹．该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者提出的裂尖位移不连续单元构成．在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界,文中算例说明本数值方法对计算平面弹性裂纹的应力强度因子是非常有效的。该文对双轴载荷作用下无限大板中源于椭圆孔的分支裂纹的数值结果进一步证实本数值方法对计算复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示双轴载荷及裂纹体几何对应力强度因子的影响。     

基于有限元方法的航空发动机叶片应力强度因子计算

为研究叶片裂纹尖端的应力奇异性,以某型航空发动机压气机叶片为例,利用有限元方法研究了叶片裂纹尖端应力强度因子的计算方法,并研究了旋转叶片振动状态下裂尖应力强度因子随裂纹长度的变化规律。建立计算模型时,在裂纹尖端划分了三维奇异单元,在裂尖外围划分了过渡单元。计算结果表明：研究旋转叶片振动状态下的裂尖应力奇异性,仅利用I型应力强度因子就具有足够的精度;对于同一裂纹,绝大多数情况下叶盆面应力强度因子大于叶背面应力强度因子,故研究叶片应力强度因子时只需研究叶盆应力强度因子即可;随着裂纹扩展,叶盆面I型应力强度因子不断增大。本文的研究方法及结论为进一步研究叶片的裂纹扩展规律及损伤容限奠定了基础。     

双压电体界面上的电偶极子和裂纹5

求得了压电体双材料界面上的孤立二维电偶极子的解析解，结果表明某点电偶极子激发的应力－电位移场与该点到电偶极子的距离的平方成反比。研究了压电体双材料界面上的电偶极子对裂纹的作用，得到了问题的闭合解。在电偶极子的作用下，界面裂纹裂尖近区应力－电位移仍具有r^-1/2 iεα的振荡奇异性，文中求得裂尖应力强度因子，当电偶极子距裂尖距离ρ很近时，裂尖应力强度因子与ρ^-3/2-iεα成比例。     

应用半权函数法计算界面裂纹的应力强度因子

应用半权函数法求解双材料界面裂纹的应力强度因子，得到以半权函数对参考位移与应力加权积分的形式表示的应力强度因子。针对特征值为复数λ的双材料界面裂纹裂尖应力和位移场，设置与之对应特征值为-λ的位移函数，即半权函数。半权函数的应力函数满足平衡方程，应力应变关系，界面的连续条件以及在裂纹面上面力为0；半权函数与裂纹体的几何尺寸无关，对边界条件没有要求。由功的互等定理得到应力强度因子KⅠ和KⅡ的积分形式表达式。本文计算了多种情况下界面裂纹应力强度因子的算例，与文献结果符合得很好。由于裂尖应力的振荡奇异性已经在积分中避免，只需考虑绕裂尖远场的任意路径上位移和应力，即使采用该路径上较粗糙的参考解也可以得到较精确的结果。     

三点弯曲试样动态应力强度因子计算研究

利用Hopkinson压杆对三点弯曲试样进行冲击加载,采集了垂直裂纹面距裂尖2mm和与裂纹面成60°距裂尖5mm处的应变信号。根据裂尖附近测试的应变信号计算试样的动态应力强度因子,并与有限元计算结果进行比较,结果表明由于裂尖有一段疲劳裂纹区,通过裂尖附近应变信号来计算动态应力强度因子时,如果裂尖位置确定不准及粘贴应变片位置不够准确对计算结果将带来很大影响。因此利用应变片法计算动态应力强度因子时,为了获得更准确的计算结果,在实验后应对试件裂纹面进行分析测量,重新确定裂尖位置,必要时需对应变片至裂尖距离进行修正后再计算动态应力强度因子值。     

高加载率下Ⅱ型裂纹试样的动态应力强度因子及断裂行为

采用Ｈｏｐｋｉｎｓｏｎ单压杆技术对单边平行双裂缝试样进行高速剪切加载，用实测的试样加载面上的载荷ｐ（ｔ）结合有限元计算确定其动态应力强度因子。同时还发展了一种用实测的裂尖动态应变，通过在准静态下标定的裂尖应变与应力强度因子间的关系来确定动态应力强度因子的近似方法。实验结果表明，对于稳定裂纹在无边界反射应力波干扰的情况下，两种方法获得的动态应力强度因子吻合得相当好。对４０Ｃｒ钢和Ｔｉ６Ａｌ４Ｖ钛合金两种材料的动态Ⅱ型断裂实验结果显示出两种完全不同的剪切破坏模式和机理。     

各向异性双材料界面裂纹扩展裂尖场

应用界面断裂力学理论和Stroh方法,研究了广义平面变形下动态裂纹沿着各向异性双材料界面扩展时的裂尖奇异应力及动态应力强度因子.双材料界面的动态裂尖区域特性主要由两个实矩阵W和D确定,且裂尖奇异应力和动态应力强度因子可以由包含这两个矩阵的柯西奇异积分方程确定,同时给出了动态应力强度因子和能量释放率的显示表达式.算例得出当裂纹以小速度扩展时,裂尖振荡因子ε与静态时几乎相同,当界面裂纹扩展速度接近瑞利波速时,ε趋于无穷大;同时得出应力强度因子及能量释放率随裂纹扩展速度的变化关系.     

基于数字散斑相关方法测定Ⅰ型裂纹应力强度因子

提出了一种通过数字散斑相关方法测定金属材料Ⅰ型裂纹尖端位置和应力强度因子的实验方法.实验采用疲劳试验机对含Ⅰ型缺口的Cr12MoV钢试件预制裂纹,通过数字散斑相关方法测试试件在三点弯曲加载条件下裂纹的扩展过程及裂尖区域的位移场.将位移场数据代入裂尖位移场方程组,采用牛顿-拉普森方法求解含未知参量的裂尖非线性位移场方程组,计算裂尖位置和应力强度因子.实验结果表明,采用该方法可以准确地测定金属材料Ⅰ型裂纹应力强度因子、裂尖位置及裂纹扩展长度,解决了以往研究中因不能准确测定裂纹尖端位置,而无法准确计算Ⅰ型裂纹裂尖断裂参数的难题,揭示了金属材料裂纹扩展过程中应力强度因子演化特征.     

In-plane/out-of-plane concentrated forces and moments on composite laminates with elliptical elastic inclusions

The problems of composite laminates containing elliptical elastic inclusions subjected to concentrated forces and moments are considered in this paper. By employing Stroh-like formalism for the coupled stretching–bending analysis, analytical closed form solutions are obtained explicitly. The generality of the solutions provided in this paper can be shown as follows: (1) The laminates include any kinds of laminate lay-ups, symmetric or unsymmetric, which allow the stretching and bending deformations couple each other. (2) The concentrated forces and moments can be applied in in-plane and/or out-of-plane directions, located inside and/or outside the inclusions. (3) The elliptical elastic inclusions can be any kinds of elastic materials including the limiting cases such as holes, rigid inclusions, cracks, line inclusions, etc. Since no such general solution has been found in the literature, the solutions are checked and verified by the special cases that no inclusions are embedded in the laminates, and that the inclusions are replaced by holes. Moreover, with various hardness ratios of inclusion and matrix some numerical examples showing the stress resultants along the interface are presented. Like the Green’s functions for the infinite laminates and those containing holes/cracks, the present solutions associated with the in-plane concentrated forces and out-of-plane concentrated moments have exactly the same mathematical form as those of the corresponding two-dimensional problems, in which the only difference is the contents of the symbols. While for the other loading cases, new types of solutions are obtained explicitly.     

Electroelastic state of an infinite multiply connected piezoelectric plate with known electric potentials applied to its boundaries

Generalized complex potentials, their expressions for a domain with elliptic holes, and the discrete least-squares method are used to analyze the generalized plane electroelastic state of a piezoelectric plate having holes and cracks with electric potentials applied to their boundaries. There are no mechanical loads. A numerical analysis is conducted. The effect of the applied voltage on the electroelastic state of the plate is examined     

Electromagnetoelastic problem for an infinite plate with known electrical potentials at hole boundaries

The plane electromagnetoelastic problem for an infinite plate with cracks and holes for known electrical potentials at the boundaries of the cracks and holes is solved using generalized complex potentials and conformal mapping, series, and least squares methods. The electromagnetoelastic state and variation of the stress intensity coefficient versus the geometric and physicomechanical properties of the material was studied for plates with two circular holes, a crack and a circular hole, or two cracks.     

Electromagnetoelastic problem for a plate with holes and cracks

The methods of complex potentials, conformal mappings, and least squares are used to solve a plane problem of electromagnetoelasticity for a plate with holes and cracks. Numerical solutions are found for a ring and a disk with a crack under internal concentrated forces or electric charges as well as electric potentials applied to the boundaries     

The evolution of caustics from holes to cracks

The method of caustics was used for the study of the evolution of stress concentration around a circular hole, which progressively changes in shape and becomes an elliptic hole, tending to an internal crack. The influence of the amount of ellipticity of the holes and their orientation relative to the axis of the applied external loads at infinity on the form of caustics created around the discontinuity was studied, as the elliptic holes tended to become internal cracks. A series of experiments with tension specimens containing small elliptic holes of any ellipticity and orientation was performed. Comparison of experimentally obtained caustics with theory yielded a good agreement of both results. Finally, the use of small elliptic holes drilled all over a biaxial stress field for the determination of the individual principal stresses and the principal directions at the area of the holes was outlined.     

双周期平行四边形排列裂纹反平面问题的有限元分析

提出了双周期平行四边形排列裂纹反平面问题的有限元方法,通过对单位胞元引入周期边界条件,在裂纹尖端采用奇异单元,解决了有限元分析这类问题的效率和精度问题.利用Ansys软件计算,在各种有解析解对照的情形下,应力强度因子的相对误差都在0.2%以内.与现有通常限于对称阵列的双周期裂纹的研究相比,本文发展的方法适用于一般的非对称平行四边形裂纹阵列.算例揭示了行向裂纹间的相互干涉放大应力强度因子,而叠向裂纹间的作用相互屏蔽.对于平行四边形阵列的情形,这两种相反的干涉效应使应力强度因子与裂纹错动参数间呈现非单调依赖关系.     

定向断裂控制爆破的空孔效应实验分析

采用新型数字激光动态焦散线实验系统, 对爆炸荷载作用下空孔周围的动应力场分布及空孔对爆生主裂纹扩展行为的影响进行了研究。研究结果表明, 在空孔周围强应力场的影响下, 2条相向扩展的爆生主裂纹逐渐向空孔处偏转, 并在空孔处贯通; 空孔附近的主应力方向与炮孔连心线夹角基本稳定在约12°, 增大空孔尺寸对空孔附近的主应力方向影响不明显; 爆炸应力波与空孔相互作用, 产生反射拉伸波, 改变了主裂纹尖端的应力场, 降低了主裂纹的扩展速度, 且空孔直径越大, 主裂纹的扩展速度越低; 当爆生主裂纹扩展到空孔附近时, 主裂纹尖端动态应力强度因子再次出现上升的趋势。     

基于数字图像处理的含缺陷混凝土破裂过程研究

混凝土破坏规律受其缺陷的影响,为了从细观尺度研究含缺陷混凝土破坏规律,基于数字图像处理技术表征混凝土骨料形状、大小及空间分布,运用RFPA2D-DIP软件构建混凝土真实细观模型并进行单轴压缩试验,研究了含不同缺陷混凝土的破坏规律。试验结果表明:相比完整试件,含缺陷试件强度更低,破坏过程应力跌落次数更多,其初始裂纹在预制裂隙及孔洞两端萌生,缺陷与新裂纹的贯通最终导致试件破坏;混凝土中同时存在孔洞和裂隙时,孔洞与裂隙相互影响并形成应力集中的岩桥区域,当孔洞直径不变时,随着裂隙长度增加,试件峰值强度下降,在同一裂隙长度下,随着孔洞直径增大,混凝土峰值强度降低。     

Tests on the ductility of asymmetric part-through center cracks in plates

Welds, shoulders or other asymmetries may eliminate one of the shear bands of symmetrically cracked parts, giving less ductility than the corresponding symmetric specimens and increasing the stiffness requirements for stability. Experiments on part-through center cracks in plates of 1018 cold finished steel show that the growth displacement in the asymmetric case is about half that of the symmetric one. Unconstrained plane strain singly grooved asymmetric tests of the same material show less ductility by a factor of two to three. Expressions for theJ integral and the tearing modulus in both the asymmetric and symmetric cases are found and used to describe the growth resistance. To further understand the deformation, a macromechanical model represented by sliding off and fracture, based on an idealization of the underlying physical mechanisms, is applied to the test data.     

Stress wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 79–84, February 2006.