断裂过程区应力应变场的数学分析

本文将条状分离区看作是位错连续分布区域,利用复变函数理论及切比雪夫多项式级数展开提出了一种统一的数学分析的方法,用以对均匀材料裂纹前方分离过程区的非线性效应进行有效的,精确的解析分析。避免以前各种模型一般都需要借助于有限元法或其他离散方法才能得到数值解答的难点。本文利用这一新方法,对断裂过程区是内聚力模型,条状屈服区模型的裂纹问题,受约束金属薄膜的裂纹问题,进行了分析计算,并与已有的结果进行了比较,得到了满意的结果。

MATHEMATICAL ANALYSES OF STRESS AND STRAIN FIELDS IN FRACTURE PROCESS ZONE

Assuming the dislocation distribution along the adhesive zone, a new mathematical analysis method was established by means of complex-variable function and series expansion of Chebyshev polynomial in this paper. The non-linear phenomena of the adhesive zone ahead of the crack tip were analyzed accurately by this method. The difficult problem that the previously existing models must use the finite element method or other discrete method to get the numerical results was successfully solved. The various crack problems of cohesive zone model, noarrow-strip yield zone model and the constrained metal foil were analyzed. Compared with some existing results, the new mathematical analysis method has shown to be accurate and efficient.