裂纹柔度法插值函数选择和实验对比

在应用裂纹柔度法计算残余应力的过程中,插值函数对计算结果有较大的影响,分别用勒让德多项式、傅立叶级数和幂级数作为插值函数,用有限元法计算了7075铝合金板固溶处理和矩形梁弯曲后的残余应力,对计算结果作了对比分析,给出了在不同残余应力分布条件下插值函数的最佳收敛阶和计算误差,利用梁弯曲对上述插值函数的特点和应用范围作了进一步说明,为裂纹柔度法的应用提供理论依据.

Interpolation Selection and Comparison in the Crack Compliance Method

In the case of residual stresses measurement by the crack compliance method (CCM) , the interpolations and their fit order are important to the calculation results. In this paper, the residual stresses distributed both in 7075 aluminum alloy plate and bent beam were calculated by CCM using Legendre polynomials, Fourier expansion and power series, respectively. In order to determine a appropriate fit order for each interpolation in different residual stresses distribution, both standard deviation and endpoint stability from the results were discussed and compared. It was concluded that the calculations using Legendre polynomials with fit order of 9 and 6 appeared excellent results in the case of 7075 aluminum alloy plate and bent beam. The standard deviation in bent beam test using cosine series was 0.58 MPa. It was shown that Fourier series was less susceptible than polynomials to endpoint instability. The conclusion from this work can be used to detect residual stress profile in thick metallic plate more accurately and efficiently.