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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

  • 摘要: 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_\rm I, K_\rm 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.

     

    Abstract: Based on the multi-parameter mathematic model of theelastic stress field near a crack-tip, the influences of the stressintensity factors K_\rm I, K_\rm II, and T-stress on thephotoelastic isochromaticand isoclinic fringe patterns are presented for the mode I, mode II andmixed mode I/II crack, respectively. It is confirmed that T-stressinfluences the radius and rotate direction of the isochromatic fringe loops.The rotated angle of the loop only relates to the T-stress for the mode I orII crack, while to the intensity factors K_\rm I, K_\rm II, and T-stress for themixed mode I/II crack. There are two isotropic points along ±π/3directions in the mode I crack under positive T-stress, while none ofisotropic point under the negative T-stress. For the mode II crack only oneisotropic point appears behind the crack-tip under T-stress. For the mixedI/II crack, three isotropic points with different radius appear at thecorresponding positions under the positive T-stress, however, one pointexists behind the crack-tip for the negative T-stress. Thses isotropic pointsfor the mixed I/II crack comply with rules in the mode I and mode II,respectively.

     

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