裂纹尖端塑性区三维有限元分析

Three dimensional FE analysis of the plastic zone size near the crack tip

裂纹尖端塑性区的大小与其三维约束状态有关,而三维约束状态不仅与板厚还与外载荷、材料性质有关。因此不论是薄板还是厚板,用平面应力或者平面应变来模拟其状态都有局限性。现阶段对于三维约束状态下的裂纹还没有一个公认的可以准确计算塑性区大小的公式。文章用有限元对小范围屈服下,含I型中心穿透裂纹板裂纹尖端的三维塑性区进行了研究,分析了硬化指数、屈服强度以及泊松比对塑性区大小的影响。计算从平面应力逐渐过渡到平面应变,结果与现有理论的预测结果进行比较,进而给出了一个计算裂纹尖端塑性区大小的计算公式。

The plastic zone size of the crack tip is relative to three dimensional constraint which depends upon not only the plate thickness but also the load and the material property.That means it would have great limitation in applications when simply classifying a plate to planestress or planestrain according to its thickness.There is no acknowledged fomulae in precisely calculating the plastic zone size when three dimensional effect has to be considered.In this paper,three dimensional plastic zone size in the vicinity of a crack in a center through-cracked plate was investigated using the finite element tool,taking the influence of plate thickness and hardening exponent and yield strength and Poisson＇s ratio into account.An unique expression was given after comparing the FE results with the theoretical predictions under plane stress and plane strain conditions.