T应力对光弹性条纹影响的理论分析

THEORETICAL ANALYSIS OF T-STRESS EFFECTS ON PHOTOELASTIC FRINGE PATTERNS IN CRACKS

以裂尖弹性应力场的多参数模型为基础,研究Ⅰ型、Ⅱ型以及Ⅰ/Ⅱ混合型裂纹参数对光弹性条纹的影响.T应力的存在和符号影响着等色线条纹环的半径大小和旋转方向,对于纯Ⅰ型或Ⅱ型裂纹而言,条纹环的旋转角度只与T应力有关;而对于Ⅰ/Ⅱ混合型裂纹,条纹环旋转角度与K_Ⅰ,K_Ⅱ和T应力有关.T应力的存在使得Ⅰ型裂纹在裂尖±π/3方向上出现2个各向同性点(T应力为正时),使得Ⅱ型裂纹在裂尖后的裂纹面上出现1个各向同性点.对于Ⅰ/Ⅱ混合型裂纹而言,当T应力为正时等倾线出现距裂尖半径不等的3个各向同性点;反之,T应力为负时在裂尖后只存在1个各向同性点,这些各向同性点分别与Ⅰ型和Ⅱ型裂纹情况具有相同的规律.

Based on the multi-parameter mathematic model of the elastic stress field near a crack-tip,the influences of the stress intensity factors K_Ⅰ,K_（Ⅱ）,and T-stress on the photoelastic isochromatic and isoclinic fringe patterns are presented for the modeⅠ,modeⅡand mixed modeⅠ/Ⅱcrack,respectively.It is confirmed that T-stress influences the radius and rotate direction of the isochromatic fringe loops.The rotated angle of the loop only relates to the T-stress for the modeⅠorⅡcrack,while to the intensity factors K_Ⅰ,K_（Ⅱ）,and T-stress for the mixed modeⅠ/Ⅱcrack.There are two isotropic points along±π/3 directions in the modeⅠcrack under positive T-stress,while none of isotropic point under the negative T-stress.For the modeⅡcrack only one isotropic point appears behind the crack-tip under T-stress.For the mixedⅠ/Ⅱcrack,three isotropic points with different radius appear at the corresponding positions under the positive T-stress,however,one point exists behind the crack-tip for the negative T-stress.Thses isotropic points for the mixedⅠ/Ⅱcrack comply with rules in the modeⅠand modeⅡ,respectively.