(山東大學 機械工程學院，濟南 250061)
摘 要: 采用裂紋柔度法測試殘余應力時，柔度函數(shù)的計算和插值函數(shù)階數(shù)的合理選擇對計算結(jié)果的精確性有著較大影響。采用有限元法計算得到測試試樣的裂紋柔度函數(shù)；考慮應力計算不確定度兩個主要的來源：應變測量數(shù)據(jù)的隨機誤差以及模型誤差，基于應力總不確定度的最小化目標，確定最優(yōu)的插值函數(shù)階數(shù)，進而計算得到鋁合金預拉伸板7050-T7451內(nèi)部殘余應力的分布規(guī)律。結(jié)果表明：采用9階勒讓德多項式能較好地擬合此鋁合金板材內(nèi)部殘余應力的分布，不確定度的均方根值為2.797 MPa，預拉伸板內(nèi)部殘余應力呈明顯的外壓內(nèi)拉的“M型曲線”分布規(guī)律。
關(guān)鍵字: 級數(shù)擴展；殘余應力；裂紋柔度法；預拉伸鋁合金板；不確定度
pre-stretched aluminum alloy plate using crack
compliance method
（School of Mechanical Engineering, Shandong University, Ji’nan 250061, China）
Abstract:In the evaluation of the residual stresses by the crack compliance method, the calculation of compliance functions and the choice of the order of interpolation function are important to calculation results. The compliance functions were calculated by using finite element method. An optimal expansion order was obtained based on minimizing the total stress uncertainty which was evaluated by considering the two main sources in the calculation of stress uncertainty: the random errors in strain data and model error. Then the residual stress depth profiles in pre-stretched aluminum alloy plate 7050-T7451 were determined. The results reveal that Legendre polynomials that the fit order is 9 can evaluate accurately through-thickness residual stresses of thick plate, and the root-mean-square average over uncertainty is only 2.797 MPa. It is also shown that the residual stresses distribution in pre-stretched aluminum alloy plate can be revealed by “M type curves”, that is, the exteriors are residual compressive stress and the interiors are residual tensile stress.
Key words: series expansion; residual stresses; crack compliance method; pre-stretched aluminum alloy plate; uncertainty
