通过标准I型断裂试验识别简化应变梯度弹性的长度尺度参数
Identification of the length scale parameter of simplified strain gradient elasticity from standard Mode I fracture tests
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中文总结 AI 辅助
本研究通过数值模拟推导回归关系，利用标准I型断裂试验数据识别简化应变梯度弹性的长度尺度参数，给出脆性材料显式公式并验证准脆性材料的尺寸效应捕捉能力。
中文摘要 AI 辅助
近期研究表明，针对脆性和准脆性材料，可基于裂纹尺寸效应的实验数据分析，识别出应变梯度弹性（SGE）的额外材料常数。本文在SGE框架内开展了精确的数值模拟，推导了用于处理纯I型加载条件下标准断裂力学试验（CCT、SENT、SENB）实验数据的回归关系。我们研究了简化SGE模型，其本构关系除经典弹性常数外，仅包含单个长度尺度参数$\boldsymbol{\u2113}$。研究表明，对于脆性材料，该参数可被明确识别为$\boldsymbol{\u2113 \u2248 0.362 (K_{Ic}/\u03c3_{ult})^2}$。该识别方法可确保经典线弹性断裂力学（LEFM）与简化SGE预测的断裂载荷在较长I型裂纹情况下保持一致。不过在简化SGE中，这些断裂载荷是通过非奇异应力场采用最大主应力准则计算得到的。针对准脆性材料，我们推导了描述强度非经典尺寸效应的回归关系。该效应通常在非线性断裂力学范畴内研究，但SGE可自然捕捉这一效应。文中还给出了基于所建立的关系，对短切纤维复合材料、多孔及致密准脆性陶瓷的实验数据进行长度尺度参数$\u2113$识别的实例。
英文摘要
Recently, it was shown that additional material constants of strain gradient elasticity (SGE) can be identified for brittle and quasi-brittle materials based on the analysis of experimental data on the crack size effect. In the present paper, we perform precise numerical simulations within SGE and derive regression relations for processing experimental data from standard fracture mechanics tests under pure Mode I loading conditions (CCT, SENT, SENB). We consider the simplified SGE, whose constitutive relations contain a single length scale parameter $\ell$ in addition to the classical elastic constants. We show that, for brittle materials, this parameter can be explicitly identified as $\ell \approx 0.362 (K_{Ic}/σ_{ult})^2$. This identification ensures that the fracture loads predicted by classical linear elastic fracture mechanics (LEFM) and by the simplified SGE coincide for relatively long Mode I cracks. However, within the simplified SGE, these fracture loads are evaluated from the nonsingular stress field using the maximum principal stress criterion. For quasi-brittle materials, we derive regression relations that describe the non-classical size effect on strength. This effect is usually treated within nonlinear fracture mechanics but can be naturally captured by SGE. Examples of identification of the length scale parameter $\ell$ based on the established relations and the experimental data for chopped fiber composites and for porous and dense quasi-brittle ceramics are presented.
