Abstract The applicability of Irwin’s estimate to metals containing particles becomes dubious when the plastic zone (PZ) size is comparable to the particle spacing. Therefore, a multiscale model is used to investigate the crack tip plasticity in a cyclically loaded elastic-perfectly plastic matrix containing a realistic distribution of spherical particles. Homogenization and dimensional analysis demonstrate that the PZ shape differs from what is expected based on von Mises plasticity. The scaling of the PZ size with the square of the stress intensity factor is confirmed, but the proportionality coefficient is strongly affected by the particle volume fraction. Consequently, a new compact formula for the PZ size is proposed, which holds for material properties ranging from metal matrix composites to cast irons and is robust to minor particle deviations from the spherical shape.

中文翻译：

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估算含弹性颗粒金属中循环塑性区大小的简化公式

摘要 当塑性区 (PZ) 尺寸与颗粒间距相当时，欧文估计对含有颗粒的金属的适用性变得可疑。因此，使用多尺度模型来研究循环加载的完美弹塑性基体中的裂纹尖端塑性，该基体包含真实分布的球形颗粒。均质化和尺寸分析表明 PZ 形状与基于 von Mises 塑性的预期不同。确认了 PZ 尺寸与应力强度因子平方的缩放比例，但比例系数受颗粒体积分数的影响很大。因此，提出了一个新的 PZ 大小的紧凑公式，