中心裂纹圆盘裂纹形状尺寸对应力强度因子的影响

Effect of Crack Shape and Size on Stress Intensity Factorsof Central Cracked Circular Disk

采用有限元数值分析方法 ,分析了由脆性材料制成的中心裂纹圆盘试件 ,在复合模式加载条件下裂纹形状尺寸 ,尤其是裂纹宽度和中心小孔半径对应力强度因子的影响 .结果表明 :槽式和槽孔组合式裂纹圆盘试件 ,其I型无量纲应力强度因子FⅠ均比按理想裂纹推出的解析解大 ,而Ⅱ型无量纲应力强度因子FⅡ 均比解析解小 ;随着加载角度增加 ,FⅠ 的数值解与解析解的差值逐渐变小 ,而FⅡ 的差值逐渐变大 ;同时 ,随着裂纹槽宽度或中心小孔半径的增加 ,应力强度因子数值解与解析解之差逐步增加 .依据数值分析的结果 ,给出了这两类试件相对于理想中心裂纹圆盘试件应力强度因子解析解的修正公式 .

Under the mixed-mode loading, the FEM numerical method is employed to investigate the effect of crack shape and size, especially crack width and the radius of the central hole, on the stress intensity factors for the central cracked circular disk specimen made from brittle materials. The computation results show that the Mode-Ⅰ normalized stress intensity factor of the central cracked circular disk specimens with a notched crack or holed-notched crack is always greater than the corresponding analytic result which calculated from the closed-form formulas of the central cracked circular disk with an ideal crack, while the Mode-Ⅱ normalized stress intensity factor is always less than the corresponding analytic result. The difference of the analytic result and numerical result of Mode-Ⅰ normalized stress intensity factor becomes smaller and smaller as the loading angle increases, while the difference of Mode-Ⅱ normalized stress intensity factor becomes greater and greater. On the other hand, the differences of the analytic result and numerical result of the normalized stress intensity factors increase gradually with the increase of the crack width or the radius of the central hole. Based on the obtained results, the modified formulas for the stress intensity factors, which are derived from the central cracked circular disk with an ideal crack, are presented for the two kinds of specimens with a notched crack or holed-notched crack, respectively.