基于传递矩阵的钻孔应变法测量薄板残余应力

针对ASTM E837标准中钻孔应变法测量薄板工件残余应力计算精度低、计算过程复杂的现状,引入弹性力学应变传递矩阵,根据应力叠加原理推导出残余应力与测量应变关系的解析表达式,进而实验研究采用应变传递矩阵计算残余应力的精度。结果表明:与标定值相比,采用传递矩阵计算的残余应力相对误差绝对值均值小于2%,采用ASTM E837标准中校准系数计算的相对误差绝对值均值为5%左右,采用传递矩阵计算残余应力的精度较高。计算残余应力的传递矩阵解析表达式具有严谨的力学理论推导,包含应变花几何尺寸、钻孔直径、泊松比等参数,具有较高的通用性,避免ASTM E837标准中校准系数的有限元标定,简化测量过程,提高残余应力的测量精度。

Hole-drilling strain-gauge method based on transfer matrix for measuring residual stresses of thin plate

Aiming at the low calculation accuracy and complicated calculation process of the residual stress of thin-plate components by the hole-drilling strain-gauge method in ASTM E837, the strain transfer matrix of elastic mechanics is introduced to deduce the analytical expression of the relationship between the residual stress and the measured strain based on the principle of stress superposition. Then the accuracy of residual stress calculated by using strain transfer matrix is studied experimentally. The results show that compared with the experimental calibration value, the residual stress mean of absolute relative error calculated by using the transfer matrix is less than 2%, and the mean of absolute relative error calculated by using the calibration coefficients in ASTM E837 standard is about 5%. Hence the calculation accuracy of residual stress by using strain transfer matrix is higher. The analytical expression of the transfer matrix is derived from a rigorous mechanical theory, and has a high universality including such parameters as the geometric dimensions of strain rosette, the diameter of borehole and Poisson’s ratio, etc. Therefore, this method improves the measuring accuracy of residual stress, and simplifies the measuring process for avoiding the finite element calibration of the calibration coefficients in ASTM E837 standard.