平面六节点等参应力奇异单元的精度研究

研究一种平面六节点应力奇异单元的计算精度问题。首先证明该单元具有1/槡r阶奇异性,然后用此单元计算同质材料中的裂纹和双材料界面裂纹的应力强度因子与裂尖应力分布,讨论裂纹尖端奇异单元的尺寸以及在奇异单元与常规单元之间布置一层过渡单元对精度的影响。研究发现,当布置在裂尖的奇异单元边长与裂纹长度的比值在0.1～0.2时,能得到足够精确的解答;而在此范围之外,随奇异单元尺寸进一步增大或减小,精度都会有所下降。对于同质材料中的裂纹以及模量比在10倍之内的双材料界面裂纹,布置过渡单元可以提高精度;而对于模量比大于20倍的界面裂纹,不设置过渡单元的计算结果却与理论解更接近。     

对偶边界元法中对数奇异积分的计算

采用三次多项式坐标变换计算边界元积分的方法，对对偶边界法中含对数奇异积分的计算进行研究。几个解析积分算例和运用对偶边界元法以二给平面裂纹问题裂尖应力强度因子的计算结果表明，多项式坐标变换法对于计算对数奇异积分是一种简单有效的方法。     

计算平面Ⅰ、Ⅱ型复合应力强度因子的半权函数法

给出计算一般平面裂纹问题应力强度因子的半权函数方法。该方法引入两个满足裂纹面零应力条件、平衡方程以及裂尖位移具有r^-1/2奇异性的虚拟位移与应力函数的解析表达式，即半权函数。从功能互等定理出发，结合从裂纹下缘到上缘绕裂尖任意路径的位移与应力的近似值，得到Ⅰ、Ⅱ复合型应力强度因子KⅠ和KⅡ积分形式的表达式。由于在积分中避开了裂尖的奇异性，因此即使采用较粗糙的模型或方法得到的近似值，也可以得到精度较高的KⅠ、KⅡ。相对于权函数法，本方法的限制条件较少，半权函数易于获得，实用性强；相对于有限元法计算量小，模型建立简便。     

基于有限元法对裂纹尖端应力强度因子的计算分析

应力在裂纹尖端会出现无限大的奇异性,但应力强度因子K则为有限值,是表征裂尖应力场强弱的物理参量。采用J积分法,位移外推法和相互作用积分法等3种不同的方法计算断裂模型裂尖的K值,并研究了受力、裂纹长度、含裂纹构件的几何参数等对裂纹尖端应力强度因子的影响。结果表明3种方法模拟出的K值结果一致性较好,与应力强度因子手册值相比都能达到较高精度。对照3种方法,分析出各种方法的优胜劣汰,对应用数值法计算应力强度因子方法的选择具有借鉴和参照作用。     

平面应力Ⅰ型准静态扩展裂纹尖端场的弹粘塑性分析

由于材料率敏感性的影响,蠕变材料中裂纹尖端场的分析更加复杂.采用弹粘塑性力学模型,并假设粘性系数为等效塑性应变率的幂函数,推导出理想弹塑性材料的一种率敏感型本构关系.通过量级匹配表明裂纹尖端场具有幂奇异性,奇异性指数由粘性系数中的幂指数唯一确定.推导出平面应力条件下准静态扩展裂纹尖端场的控制方程,并给出Ⅰ型裂纹的边界条件.采用双参数打靶法,结合各材料参数的可能取值范围,对控制方程进行了数值求解,并讨论裂尖场特性随各材料参数的变化规律.结果表明当材料服从理想塑性规律时,裂纹尖端的应力场是连续的,不存在某些无粘性解中出现的不合理间断线.裂尖场应力强度由材料的粘性所控制,泊松比对于裂尖场没有影响,并且不存在弹性卸载区.     

压电裂纹的插值型无单元伽辽金比例边界法分析

为了获得更为精确高效的压电裂纹分析方法,基于改进的插值型移动最小二乘法,提出压电材料断裂分析的插值型无单元伽辽金比例边界法,这种方法可以直接根据定义求得应力强度因子和电位移强度因子。该方法只需要在求解域的边界上采用无单元伽辽金法进行数值离散,减少了一个空间维数,并且不需要边界元法所需要的基本解。在没有离散的径向采用解析的方法求解,从而具有较高的计算精度。在改进的插值型移动最小二乘法中,不仅形函数满足Kronecker delta函数性质,而且权函数是非奇异的。此外,改进的插值型移动最小二乘法计算形函数时待定系数比传统的移动最小二乘法少一个。给出数值算例,并验证了所提方法的有效性和正确性。     

工字型梁腹板中Ⅲ型裂纹应力强度因子分析

基于能量释放率研究Ⅲ型裂纹平面应变条件下的J积分能量表达式。采用有限元软件模拟了工字梁腹板受扭转时裂纹裂尖应力奇异场,通过数值模拟得出裂纹区的应力、位移分布状态,并计算应力强度因子和J积分,从而验证表达式的可行性。     

位移法求解应力强度因子的影响因素

基于Chen-Kuang公式、1/4节点位移公式,以有限尺寸板拉伸模型和三点弯曲模型为研究对象,研究了裂尖单元径向尺寸、围绕裂尖周向单元数和力学模型对无量纲应力强度因子计算结果的影响.分别给出了用两种方法进行有限元分析时裂尖径向单元尺寸和围绕裂尖周向单元数的合理取值范围,并指出对于1/4节点位移公式,在选用裂尖单元径向尺寸时还应考虑力学模型对计算结果的影响.     

计算应力强度因子的无网格-直接位移法

目前计算裂纹尖端应力强度因子的无网格法一般均采用。积分方法,但由于该方法为间接求解,降低了求解精度与求解效率。文中采用无网格—伽辽金方法,选取带有扩展基的奇异基函数,以精确计算裂纹尖端位移场,并借鉴有限元法中计算应力强度因子的直接位移法,提出一种计算含裂结构裂纹尖端应力强度因子的新方法,即无网格—直接位移法。数值计算结果表明,该方法具有简捷、高效的特点,可以准确计算裂纹尖端应力强度因子。     

双材料界面裂纹应力强度因子计算

建立不同裂纹长度的双材料界面裂纹模型,用有限元软件计算和分析界面裂纹尖端附近的应力场和位移场.利用裂尖前沿应力和裂纹面相对位移分别计算了界面裂纹尖端的应力强度因子K,两种方法计算的K值完全吻合.通过数值分析,给出一种计算双材料界面裂纹应力强度因子K的经验公式.     

The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface

For the fracture evaluation of inclined cracks terminating at the dissimilar material interface, not only the singularities, but also the detailed stress field and its stress intensity factors are necessary. However, though there are many researches reported on the singularity analysis, the stress field and its stress intensity factors are still not clear. This paper has deduced theoretically the singular stress and displacement fields near the tip of a crack terminating at the interface between bonded dissimilar materials, for both cases of real and oscillatory singularities. From the deduced singular stress field, the stress intensity factors are defined for such a crack, and the corresponding numerical extrapolation methods are also proposed. Through the numerical examinations, it is found that the theoretical stress distributions agree well with the numerical results obtained by the finite element method. Moreover, the proposed extrapolation method shows a good linearity, thus it can be used as an efficient way to determine the characteristics of the stress and displacement fields near the tip of a crack terminating at interface.     

Numerical analysis for prediction of fatigue crack opening level

Finite element analysis (FEA) is the most popular numerical method to simulate plasticity-induced fatigue crack closure and can predict fatigue crack closure behavior. Finite element analysis under plane stress state using 4-node isoparametric elements is performed to investigate the detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The mesh of constant size elements on the crack surface can not correctly predict the opening level for fatigue crack as shown in the previous works. The crack opening behavior for the size mesh with a linear change shows almost flat stress level after a crack tip has passed by the monotonic plastic zone. The prediction of crack opening level presents a good agreement with published experimental data regardless of stress ratios, which are using the mesh of the elements that are in proportion to the reversed plastic zone size considering the opening stress intensity factors. Numerical interpolation results of finite element analysis can precisely predict the crack opening level. This method shows a good agreement with the experimental data regardless of the stress ratios and kinds of materials.     

A study on the determination of closing level for finite element analysis of fatigue crack closure

An elastic-plastic finite element analysis is performed to investigate detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The finite element analysis performed under plane stress using 4-node isoparametric elements can predict fatigue crack closure behavior. The mesh of constant element size along crack surface can not predict the opening level of fatigue crack. The crack opening level for the constant mesh size increases linearly from initial crack growth. The crack opening level for variable mesh size, is almost flat after crack tip has passed the monotonic plastic zone. The prediction of crack opening level using the variable mesh size proportioning the reversed plastic zone size with the opening stress intensity factors presents a good agreement with the experimental data regardless of stress ratios.     

Experimental and numerical determination of critical stress intensity factor of aluminum curved thin sheets under tensile stress

We determined the fracture toughness of aluminum curved thin sheets using tensile stress tests and finite element method. We applied Linear elastic fracture mechanics (LEFM) and Feddersen procedure to evaluate stress intensity factor of the samples with central wire-cut cracks and fatigue cracks with different lengths to investigate the notch radius effect. Special fixture design was utilized to establish uniform stress distribution at the crack zone. Less than 9 % difference was found between the wire-cut and the fatigue cracked samples. Since generating central fatigue crack with different lengths required so much effort, wire-cut cracked samples were used to determine critical stress intensity factor. Finite element analysis was also performed on one-quarter of the specimen using both the singular Borsum elements and the regular isoparametric elements to further investigate fracture toughness of the samples. It was observed that the singular elements presented better results than the isoparametric ones. A slight difference was also found between the results obtained from finite element method using singular elements and the experimental results.     

三维多裂纹应力强度因子的有限元分析

多处损伤和广泛分布疲劳损伤是影响军用老化飞机结构完整性的主要因素之一。三维裂纹前缘应力应变场很复杂 ,除个别理想情况外 ,绝大部分迄今为止无解析解。采用三维 2 0节点等参单元 ,运用ANSYS软件 ,对含半椭圆裂纹的半无限大体进行有限元分析 ,得到裂纹前缘各点的应力强度因子 ,通过对计算结果的分析 ,讨论裂纹长度、裂纹间距比、裂纹前缘位置对应力强度因子的影响以及多裂纹之间的相互影响 ,计算结果和手册的理论值比较表明 ,数值结果准确、方法可行     

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only-0.621％;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is-11.29％.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05％.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.     

高频谐振载荷作用下Ⅰ型疲劳裂纹尖端力学参数变化规律

为研究高频谐振式疲劳裂纹扩展试验中带有Ⅰ型预制裂纹的紧凑拉伸(CT)试件裂纹尖端力学参数的变化规律,利用动态有限元方法,采用ANSYS和MATLAB软件编写程序,计算了CT试件在高频恒幅正弦交变载荷作用下,在一个应力循环及裂纹扩展到不同长度时裂纹尖端区域的位移、应变场及裂纹尖端的应力强度因子,并分析了其变化规律。在计算裂纹尖端应力强度因子时,首先采用静态有限元方法和理论公式验证了有限元建模和计算的正确性,然后采用动态有限元方法研究了裂纹扩展过程中裂纹尖端应力强度因子的变化规律。最后进行了高频谐振式疲劳裂纹扩展试验,采用动态高精度应变仪测量了裂纹扩展到不同阶段时裂纹尖端点的应变,并对有限元计算结果进行了验证。研究结果表明：在稳态裂纹扩展阶段,高频谐振载荷作用下Ⅰ型疲劳裂纹尖端位移、应变及应力强度因子均为与载荷同一形式的交变量;随着裂纹的扩展,Ⅰ型疲劳裂纹尖端的位移、应变及应力强度因子幅不断增大;静态应力强度因子有限元计算值和理论值的误差为2.51%,裂纹尖端点应变有限元计算结果和试验结果最大误差为2.93% 。     

Modified r-method for the finite element adaptive analysis of plane elastic problems

The nodal relocation method (r-method) is used to uniformly distribute element discretization errors over an analytic model and improve the solution quality. When this r-method is performed with Zienkiewicz-Zhu’s error estimator, its converged solution can not be easily obtained without many iterative calculations. Further, this method also may deteriorate solution quality because of serious element distortion. This paper suggests a new error estimator which can evaluate the size and the distortion error of an isoparametric element separately and proposes a modified r-method based on this error estimator. Various numerical experiments show that the proposed error estimator properly evaluates the element discretization errors and the modified r-method can be easily applied to the practical analysis owing to the comparatively fast convergent characteristics.