材料的非均匀性对裂纹尖端附近应力分布的影响

INFLUENCE OF INHOMOGENEITY OF MATERIALS ON STRESS DISTRIBUTION NEAR A CRACK TIP

本文讨论材料的细观非均匀性对其断裂行为的影响,为此,采用了一个模量呈双周期分布的理想非均匀带裂纹平板来分析裂纹尖端附近的应力场,首先用渐近展开技术求出远场的近似应力分布,然后用有限元数值分析得到了裂纹尖端附近的应力分布和应力强度因子,所得结果表明,非均匀材料中由细观局部应力集中造成的最大应力与当地宏观平均应力及其各阶梯度有关,这意味着应力应变关系存在某种非局部性,计算结果还表明,无量纲应力强度因子随裂纹尖端与微结构的相对位置而变化,对宏观裂纹,其最大值是稳定的,表明通常的应力强度因子的概念是适用的。但对微裂纹,应力强度因子有增大的趋势。

This paper deals with the influence of micro-inhomogeneity of material on its fracture behaviour. A cracked inhomogeneous elastic plate in which the Young's modulus is double-periodically distributed is used to analyse the stress field near the crack tip. The stress, distribution far from the tip is obtained approximately by an asymptotic expansion technique whereas the stress distribution near the tip and the stress intensity factor are calculated by a numerical method using a finite element scheme. The results reveal that the maximum stress caused by local stress concentration is related to the stress gradients of all orders as well as to the macroaveraged stress itself, indicating a kind of nonlocality. The results also show that: the dimensionless stress intensity factor varies with the relative position of the tip to the micros-tructure. While the maximum value of this factor is constant for macro cracks it becomes greater for micro cracks.