V型缺口裂端的三维应力状态及约束分析

利用三维有限元方法，研究了有限厚度板中V型缺口根部穿透裂纹前沿的三维弹性应力场。对不同厚度、不同缺口张开角和裂纹长度对应力强度因子及裂尖附近的三维约束程度的影响进行了分析，同时还讨论了三维约束区的大小。研究结果显示：当缺口张开角小于60度时，不同缺口的应力强度因子和离面约束因子的分布基本一致，角度的影响不明显。应力强度因子是厚度的函数，板中面的应力强度因子随厚度的增加逐渐减小趋近干平面值，最大为1．08倍的平面值。当板厚超过15倍的缺口深度时，应力强度因子最大值将从中面转移至接近自由表面位置，距中面约0．4倍板厚。三维约束非常明显的区域在裂尖前沿约0.45倍厚度的范围内．二维到三维的过渡区在裂尖前沿1.5倍厚度的区域内；在中面上三维效应影响区最大，随着离中面距离的增加逐渐减小，在自由表面上降为0。     

紧凑拉剪试样中Ⅰ/Ⅱ复合型穿透裂纹的三维特性分析

进行了Ⅰ/Ⅱ复合型载荷作用下航空结构铝合金CTS试样线弹性的全场三维有限元计算,分析了复合型离面应力约束因子Tz和面内约束T应力的分布特性,研究了厚度和载荷条件对应力各分量及应力三轴性水平Rσ、应变能密度U0的影响以及这些量在实验中观察到的裂纹起裂方向上的特点。结果表明：（1）平面内约束T应力在此种试样形式下为零;（2）复合型裂纹的三维效应区与厚度成正比,为0.4-0.5B,与载荷条件基本无关,但是厚度效应随着载荷角的减小逐渐变小,到II型载荷时基本消失;（3）离面约束因子Tz随着径向和厚度尺寸的增加逐渐减小,但在周向基本不发生变化;（4）最小应变能密度U0min的方位能够表征此种材料三维复合型断裂的裂纹起裂方向。研究结果为建立三维复合型断裂准则提供了理论基础。     

含表面半椭圆裂纹板裂纹尖端应力强度因子的三维光弹分析

本文用三维光弹法得到了含表面半椭圆裂纹板拉伸载荷下应力强度因子 K_Ⅰ沿整个裂纹前缘的分布及由不同裂纹深度引起的有限厚度效应,得到的实验结果与理论结果进行了比较和分析,并对角点上的奇异性进行了定性分析.     

估算裂纹应力强度因子的新方法

根据裂纹形状与裂纹尖端应力强度因子分布之间的固有关系，在线弹性断 裂力学条件下，提出了一种按已知I型裂纹应力强度因子分布规律求裂纹形状及相应应力强 度因子的无梯度迭代法. 通过有限厚度、有限宽度板穿透裂纹和表面裂纹的数值模拟实例验 证了所提出方法的有效性和实用性，并对不同应力强度因子分布规律对裂纹形状以及相应的 应力强度因子大小的影响进行了分析和讨论. 所提出的方法有助于提高实际扩展裂纹应 力强度因子的估算精度以及更合理地预测疲劳裂纹形状演化.     

复合材料断裂力学参量的实验测定

本文采用三维云纹干涉仪同步测量含裂纹复合材料弯曲板的面内位移场及离面位移场，并对离面位移场云纹图进行计算机自动采集和处理，编制了云纹数字图像处理软件。文中推导了正交异性复合材料弯曲问题的离面位移场表达式，得到了弯曲板裂纹尖端位移w与应力场强度因子K1的关系式。通过实测位移，结合裂尖位移场推导出应力强度因子K1值。     

有限厚双边U型切口板的三维弹塑性有限元分析

针对单向拉伸载荷作用下的有限厚双边 U型切口板 ,本文对其切口根部的三维效应进行了详细的三维弹塑性大变形有限元分析 ,得到了不同于平面切口问题的新结果 :( 1 )在线弹性阶段 ,三维切口根部的应力集中因子 Kt高于二维情形 ,且 Kt在板厚 ( B)约为 8倍切口根部半径 (ρ)时达到峰值 ;进入塑性后 ,切口根部的 Kt随载荷水平的增加逐渐下降 ,并介于平面应力和平面应变情形之间 ;( 2 )切口前缘等效应变εe的最大值出现在约束最高的中面 ,且可比约束最低的自由表面处的应变值高一倍 ;( 3)薄板中 ,塑性区尺寸 xp 的最大值不是出现在约束较低的自由表面 ,而是出现在约束较高的中面 ,但随 B/ρ的增大逐渐向自由表面外推 ;( 4 )面内应力比 Tx在切口根部塑性区内的分布对板厚和载荷水平不敏感 ,可以用 Hill的滑移线解很好地近似。另外 ,对三维影响区内一些重要的三维约束参量进行了详细分析 ,总结了它们的三维分布规律。     

紧凑拉剪试样中Ⅰ/Ⅱ复合型穿透裂纹的三维特性分析

进行了Ⅰ/Ⅱ复合型载荷作用下航空结构铝合金CTS试样线弹性的全场三维有限元计算,分析了复合型离面应力约束因子Tz和面内约束T应力的分布特性,研究了厚度和载荷条件对应力各分量及应力三轴性水平Rσ、应变能密度U0的影响以及这些量在实验中观察到的裂纹起裂方向上的特点。结果表明：（1）平面内约束T应力在此种试样形式下为零;（2...     

航空结构铝合金Ⅰ/Ⅱ复合型断裂的三维弹塑性数值分析

在LC4CS铝合金三维Ⅰ/Ⅱ复合型断裂实验的基础上,对Ⅰ/Ⅱ复合型加载模型进行了细致的三维弹塑性有限元计算,系统分析了不同复合度φ和厚度B对裂纹端部应力场和起裂角的影响.结果表明,对于不同φ和B的试样,周向应力极大值和三维离面约束因子极小值出现在相同的角度;根据最大周向应力准则,在Ⅰ型载荷占主导(βeq＞65.45°)...     

功能梯度压电材料反平面裂纹问题

基于三维弹性理论和压电理论，导出了材料系数在横观各向同性平面内梯度分布的压电体的状态方程，进而对材料系数指数函数规律分布的半无限大压电体中的反平面裂纹问题进行了求解，利用Fourier变换给出了半无限大压电体中位移，应力，电势及电位移的解析表达式，并求得了裂纹尖端的应力强度因子和电位移强度因子，分析了不同的非均匀材料系数及几何尺寸对它们的影响。     

用三维光弹法确定轴表面横向半椭圆裂纹应力强度因子及其修正系数

用三维光弹法测定了轴表面横向半椭圆裂纹的应力强度因子，并分析计算了应力强度因子修正系数，结果表明，应力强度因子的分布型式对加载条件和裂纹几何不敏感；修正系数对裂纹深度呈现对称分布趋势，仅取决于裂纹几何参数。     

Experimental and numerical investigation of a cracked transversely graded plate subjected to in plane bending

The variation of stress intensity factor along the thickness in a cracked transversely graded plate subjected to in plane bending is investigated in this study. A transversely graded plate having elastic modulus varying continuously along the thickness was prepared by embedding glass beads in epoxy resin. An edge crack in this plate was subjected to in plane bending and the crack tip displacement field on the surfaces of the plate was measured using digital image correlation (DIC). Using the recently reported asymptotic displacement fields for cracked transversely graded plates (Wadgaonkar, S.C., Parameswaran, V., 2009. Structure of near tip stress field and variation of stress intensity factor for a crack in a transversely graded material, Journal of Applied Mechanics 76 (1), 011014), the stress intensity factor (SIF) on the surfaces of the plate was calculated from the experimental data. The results of this part of the study indicated that the extent of variation of the SIF across the plate thickness is nearly the same as that of the elastic modulus. An expression to calculate the variation of the SIF through the plate thickness was developed assuming simple bending of the plate. The predicted variation of SIF was verified through finite element calculations. Further, the behavior of the SIF near the intersection of the crack front and the plate surfaces, the extent of dominance of the corner singular field and the exponent of the corner singularity were also investigated in detail. Finally, the effect of gradation strength and gradation type on the SIF was also studied.     

In-plane and out-of-plane constraint effects under pressurized thermal shocks

Transferability of fracture toughness data obtained on small scale specimens to a full-scale cracked structure is one of the key issues in integrity assessment of engineering structures. In order to transfer fracture toughness under different constraints, both in-plane and out-of-plane constraint effect should be considered for the specimens and structures. In this paper both in-plane and out-of-plane constraint effects of a crack in a reference reactor pressure vessel (RPV) subjected to pressurized thermal shocks (PTSs) are analyzed by two-parameter and three-parameter methods. The comparison between elastic and elastic–plastic analysis shows that the constraint effect varies with the material property. T₁₁ (the second term of William’s extension acting parallel to the crack plane) generally displays a reversed relation to the stress intensity factor (SIF) with the transient time, which indicates that the loading (SIF) plays an important role on the in-plane constraint effect. The thickness at the crack tip contributes more than the loading to the out-of-plane constraint, such that T₃₃ (the second term of William’s extension acting along the thickness) displays a similar relation to ε₃₃ (strain along the thickness direction) and a different relation to T₁₁ during the transient. The results demonstrate that both in-plane and out-of-plane constraint effect should be analyzed separately in order to describe precisely the stress distribution ahead of the crack tip.     

CONSTRAINTS ON THE CRACK TIP PLASTIC FIELDS UNDER LARGE SCALE YIELD

Plane strain elastic-plastic finite element analyses are used to study the stress, strain fields around a straight crack in power hardening plastic material. Center crack panel (CCP), single edge crack panel (SECP) and double edge crack panel (DECP) tension specimens are analyzed with various crack lengths. Two local constraint parameters, i.e. in-plane stress ratioT _x and out-of-plane constraintT are analyzed, which are defined as tangential stress dividing normal (open) stress and out-of-plane stress dividing the sum of tangential stress and normal stress respectively. Numerical analyses indicate that the two local constraint parameters are nearly independent of the specimen geometry and the loading level in the plastic zone. Methods of estimating two constraint parameters and ways to define the boundary of the blunt zone are given. By using these parameters, the stress distributions in the plastic zone, especially in the blunt zone can be accurately predicted. Project supported by the National Foundation of Distinguished Young Scientists of China (No. 59625510).     

The concentration of stress and strain in finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of finite thickness large plate containing a hole are systematically investigated using 3D finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state except at notch root of plate surface. The maximum stress and strain do not always occur on the mid plane of plate. They occur on the mid plane only in thin plate. The maximum stress and strain concentration factors are not on mid plane and the locations of maximum stress and strain concentration factors are different in thick plate. The maximum stress and strain concentration factors of notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to each constant related to Poisson’s ratio of plate, respectively. The stress and strain concentration factors at notch root of plate surface are the same and are the monotonic descent functions of thickness. Their values decrease rapidly and tend to each constant related to Poisson’s ratio with plate thickness increasing. The difference between maximum and surface value of stress concentration factor is a monotonic ascent function of thickness. The thicker the plate is or the larger the Poisson’s ratio is, the larger the difference is. The corresponding difference of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.     

THE EVALUATION OF STRESS INTENSITY FACTORS OF PLANE CRACK FOR ORTHOTROPIC PLATE WITH EQUAL PARAMETER BY F2LFEM

In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method (F2LFEM). The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor (SIF).     

Equivalent thickness conception for corner cracks

Thickness dependence of the one-parameter-based fracture toughness has been well recognized and widely studied. However, it is still a challenge to predict the fracture of structures with curved cracks from the fracture toughness data obtained from the standard through-the-thickness cracked specimens. The complicated three-dimensional (3D) stress fields near the crack front play a vital role in the fracture strength of materials. Based on a systematical numerical study of the 3D stress fields near the crack tip of quarter elliptic corner cracks and comparison with that of ideal through-the-thickness cracks, an equivalent thickness conception for curved cracks is proposed from the viewpoint of out-of-plane constraint, and a semi-analytical solution for the equivalent thickness of corner cracks is obtained. With the evaluated equivalent thickness, the fracture toughness of corner cracked specimens is predicted efficiently by the plane-strain toughness value of the material obtained from the standard through-the-thickness specimen.     

金属材料三维断裂韧度厚度效应的有限元模拟

随着金属材料大壁厚结构件在工程中的广泛应用,对其断裂韧度的厚度效应研究具有重要的科学意义和工程价值。本研究基于有限元和实验相结合的方法,对金属材料断裂韧度的厚度效应进行预测。首先,通过一组薄壁厚金属材料标准三点弯曲试验得到试样失效时的临界载荷值,并利用内聚力模型与基于虚拟裂纹闭合技术的裂纹扩展模拟方法得到裂纹扩展时的单元临界能量释放率。随后,以此临界能量释放率作为裂纹扩展的启裂准则门槛值,通过有限元计算得到不同试样厚度下裂纹启裂时的裂尖断裂参数随着厚度的变化规律。最后,为了验证有限元模拟结果的准确性,本研究进行了另外两组不同厚度下三点弯曲试样的断裂韧度试验,并将试验结果与有限元结果进行了对比,验证了有限元所模拟的断裂韧度厚度效应的准确性。本研究旨在,通过薄壁厚三点弯曲试样的实验结果结合有限元模拟工作,即可实现金属材料断裂韧度的整个厚度效应曲线,为任意厚度下金属材料断裂韧度预测提供一种可靠的研究方法,有益于缩减试验成本,为大壁厚工程结构件的失效预测提供依据。     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.