The central cracked Brazilian disk (CCBD) specimen is one of the most favored samples to measure the combined mode fracture resistance of brittle materials. The T-stress in this sample has a great influence on the experimental results, which are extensively used in fracture criteria for evaluating the fracture behavior of CCBD specimens for different materials. Due to the errors in geometric dimension and crack inclination angle for CCBD specimens, it becomes essential to conduct error analysis of T-stress. In this work, a closed-form expression of T-stress for a CCBD specimen under radial concentrated force was presented with weight function method. Based on this expression, two error transfer functions were also derived to study the T-stress error caused by the errors of crack length ratio and crack inclination angle. The theoretical analysis indicated that the relative error of T-stress increases with the increase of crack length ratio and crack inclination angle under the combined modes I and II. It was also found that the crack length ratio has a very little impact on the T-stress error for pure mode I loading. Furthermore, T-stress is more sensitive to the impact of crack length ratio than pure mode II stress intensity factor (SIF).

中文翻译：

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巴西圆盘中央裂纹试样T应力的理论误差分析

中央裂纹巴西圆盘 (CCBD) 试样是测量脆性材料的组合模式断裂阻力最受青睐的样品之一。该样品中的 T 应力对实验结果有很大影响，广泛用于评估不同材料 CCBD 试样断裂行为的断裂准则。由于 CCBD 试件的几何尺寸和裂纹倾角存在误差，因此对 T 应力进行误差分析变得至关重要。在这项工作中，采用权函数法给出了 CCBD 试件在径向集中力作用下的 T 应力的闭合表达式。基于该表达式，还导出了两个误差传递函数来研究裂纹长度比和裂纹倾角误差引起的T应力误差。理论分析表明，在I和II组合模式下，T应力的相对误差随着裂纹长度比和裂纹倾角的增加而增大。还发现裂纹长度比对纯模式 I 加载的 T 应力误差影响很小。此外，T 应力对裂纹长度比的影响比纯模式 II 应力强度因子 (SIF) 更敏感。