Measuring internal residual stress in Al-Cu alloy forgings by crack compliance method with optimized parameters

Abstract

Measuring the internal stress of Al alloy forgings accurately is critical for controlling the deformation during the subsequent machine process. In this work, the crack compliance method was used to calculate the internal residual stress of Al-Cu high strength alloys, and the effect of various model parameters of crack compliance method on the calculated precision was studied by combining the numerical simulation and experimental method. The results show that the precision first increased and then decreased with increasing the crack range. The decreased precision when using a high crack range was due to the strain fluctuation during the machining process, and the optimized crack range was 71% of the thickness of forgings. Low orders of Legendre polynomial can result in residual stress curve more smooth, while high orders led to the occurrence of distortion. The Tikhonov regularization method effectively suppressed the distortion of residual stress caused by the fluctuation of strain data, which significantly improved the precision. In addition, the crack compliance method with optimized parameters was used to measure the residual stress of Al-Cu alloy with different quenching methods. The calculated results demonstrated that the distribution of residual stress was obtained accurately.

Keywords

residual stress / crack compliance method / crack range / interpolation orders / Tikhonov regularization method

References

[1] ZhangY-x, YiY-p, HuangS-quan. Influence of quenching cooling rate on residual stress and tensile properties of 2A14 aluminum alloy forgings [J]. Materials science and Engineering A, 2016, 674: 658-665

[2] DongF, YiY-p, HuangC, HuangS-quan. Influence of cryogenic deformation on second-phase particles, grain structure, and mechanical properties of Al-Cu-Mn alloy [J]. Journal of alloy and compounds, 2020, 827: 154300

[3] ZhangT, ZhangS-h, LiLei. Modified constitutive model and workability of 7055 aluminum alloy in hot plastic compression [J]. Journal of Central South University, 2019, 26(11): 2930-2942

[4] HuynhL A T, PhamC H, RasmussenK J R. Mechanical properties and residual stresses in cold-rolled aluminum channel sections [J]. Engineering Structures, 2019, 199109562

[5] ShuklaS. Rapid in-line residual stress analysis from a portable two-dimensional X-ray diffractometer [J]. Measurement, 2020, 157107672

[6] AlinaghianM, AlinaghianI, HonarpishehM. Residual stress measurement of single point incremental formed Al/Cu bimetal using incremental hole-drilling method [J]. International Journal of Lightweight Materials and Manufacture, 2019, 2131-139

[7] WanY, JiangW-c, SongMing. Distribution and formation mechanism of residual stress in duplex stainless steel weld joint by neutron diffraction and electron backscatter diffraction [J]. Materials &; Design, 2019, 181: 108086

[8] SalehiS D, ShokriehM M. Residual stress measurement using the slitting method via a combination of eigenstrain, regularization and series truncation techniques [J]. International Journal of Mechanical Sciences, 2019, 152558-567

[9] Urriolagoitia-SosaG, Romero-AngelesB, Hernandez-GomezL H. Crack-compliance method for assessing residual stress due to loading/unloading history: Numerical and experimental analysis [J]. Theoretical and Applied Fracture Mechanics, 2011, 56(3): 188-199

[10] VaidyanathanS, FinnieI. Determination of residual stresses from stress intensity factor measurements [J]. Journal of Basic Engineering, 1971, 93(2): 242-246

[11] ChengW, FinnieI. The single slice method for measurement of axisymmetric residual stresses in solid rods or hollow cylinders in the region of plane strain [J]. Journal of Engineering Materials and Technology, 1998, 120(2): 170-176

[12] TangZ-t, LiuZ-q, AiXing. Measuring residual stresses depth profile in pre-stretched aluminum alloy plate using crack compliance method [J]. The Chinese Journal of Nonferrous Metals, 2007, 17(9): 1404-1409(in Chinese)

[13] LiJ, SunJuan. Interpolation selection and comparison in the crack compliance method [J]. Journal of Luoyang University, 2005, 20(4): 56-60

[14] OlsonM D, DewaldA T, HillM R. An uncertainty estimator for slitting method residual stress measurements including the influence of regularization [J]. Experimental Mechanics, 2020, 60(1): 65-79

[15] JonesK W, BushR W. Investigation of residual stress relaxation in cold expanded holes by the slitting method [J]. Engineering Fracture Mechanics, 2017, 179: 213-224

[16] ZhangY-x, YiY-p, HuangS-quan. Influence of temperature-dependent properties of aluminum alloy on evolution of plastic strain and residual stress during quenching process [J]. Metals, 2017, 7(6): 228

[17] ChengW, FinnieI. Compliance functions for through-thickness measurement: The FEM approach [M]. Residual Stress Measurement and the Slitting Method, 2007, US, Springer

[18] RobertoR B, ChristofK, TakatsuguY. Composite polymerization stress as a function of specimen configuration assessed by crack analysis and finite element analysis [J]. Dental Materials, 2013, 29101026-1033

[19] TianZ-f, HuL-jian. Comparison of two kinds of interpolation to solve stochastic differential equations [J]. Basic Sciences Journal of Textile Universities, 2003, 16(1): 14-18

[20] PrimeM B, HillM R. Uncertainty analysis, model error, and order selection for series-expanded, residual-stress inverse solutions [J]. Journal of Engineering Materials and Technology, 2006, 128(2): 175-185

[21] CALVETTI D, MORIGI S, REICHEL L. Tikhonov regularization and the L-curve for large discrete ill-posed problems [J]. Journal of Computational &; Applied Mathematics, 123 (1,2): 423–446. DOI: https://doi.org/10.1016/S0377-0427(00)00414-3.

[22] ASTER R C, BORCHERS B, THURBER C H. Tikhonov Regularization [M]. Parameter Estimation and Inverse Problems. Elsevier, 2013. DOI: https://doi.org/10.1016/B978-0-12-385048-5.00004-5.

[23] ZarzerC A. On Tikhonov regularization with non-convex sparsity constraints [J]. Inverse Problems, 2009, 25(2): 025006

[24] NeubauerA. An a posteriori parameter choice for Tikhonov regularization in the presence of modeling error [J]. Applied Numerical Mathematics, 1998, 46507-519