I型裂纹虚拟裂纹闭合法的误差分析及修正

An Error-correction Analysis of the Virtual Crack Closure Technique for Mode I Crack

对虚拟裂纹闭合法的误差来源进行了分析.依据Griffith的椭圆裂纹近似理论,针对虚拟裂纹闭合法的位移相等假设,提出了一种修正方法.用有限元程序计算了二维I型裂纹的扩展问题,并与理论近似解做了比较.计算结果表明,修正以后可以得到更好的精度,在裂纹长度较短时,修正效果更好.

The commonly used crack parameter calculation method in the finite element analysis include displacement method, stress method, J integral method and the virtual crack closure technique, etc. The precision of stress method and displacement method depends on the singularity assumption of the crack tip element, which is often difficult in the practical application. The calculation of J integral is inconvenient for programming and users, due to the need for a specification of the integral path. The virtual crack closure technique （VCCT） only requires the crack front nodal forces and opening displacements for the calculation of energy release rate, and is easy to implement in a numerical calculation program. Therefore, it has become one of the main approaches for the analysis of crack problems in recent years. A further improvement in precision without increasing the amount of calculation is of great significance to promote the use of the method. In this paper, the error sources of VCCT have been analyzed. The analysis results show that the er- ror is derived from two aspects=one is the stress and displacement calculation error; the other is the error of the virtual crack tip opening displacement and the actual crack tip opening displacement assumed approx- imately equal. According to the ellipse approximation of mode I crack, a correction method is proposed in view of the second error source. Two numerical examples have been designed to validate the method,including a pulled center crack specimen and a three-point bending specimen. The calculation error of the correction method is compared with that of the original method. The result indicates that the correction method can achieve better precision especially for short crack; and the required amount for extra calculation is very small. The results of this study can be used to improve the calculation precision of crack problems.