直裂纹的混合模式加载与表面应变梯度弹性
Mixed-mode loading of a straight crack with surface strain-gradient elasticity
AI总结：
本文通过表面应变梯度弹性理论消除裂纹尖端奇异性，研究直裂纹在混合模式加载下的应力应变场行为。
摘要：
本文利用线性化表面-基体理论建模脆性断裂，在其中裂纹面具有源自表面应变梯度弹性能量的表面应力。该模型将表面拉伸、曲率和表面拉伸梯度纳入表面能中，从而捕捉到此前表面弹性理论中缺失的小长度尺度效应。该理论结合物理动机的尖端条件，应用于无限各向同性板中有限直裂纹的混合模式-I/II加载。利用复分析技术，证明了所得应力和应变场在裂纹尖端处对于几乎所有可行参数值均保持有界。结合之前模式-III加载的结果，分析表明，线性化表面-基体模型结合表面应变梯度弹性可消除所有远场加载主模式中的裂纹尖端奇异性。
英文摘要：
This work models brittle fracture using a linearized surface-substrate theory in which the crack faces possess surface stresses derived from a surface strain-gradient elastic energy. The model incorporates surface stretching, curvature, and surface gradients of stretching into the surface energy, thereby capturing small-length-scale effects absent from earlier surface elasticity formulations. The theory, supplemented with physically motivated tip conditions, is applied to the mixed mode-I/mode-II loading of a finite straight crack in an infinite isotropic plate. Using complex-analytic techniques, it is shown that the resulting stress and strain fields remain bounded up to the crack tips for nearly all admissible parameter values. Combined with previous results for mode-III loading, the analysis demonstrates that linearized surface-substrate models incorporating surface strain-gradient elasticity eliminate crack-tip singularities across all principal modes of far-field loading.
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