Analytical solutions for determining residual stresses in two-dimensional domains using the contour method. (English) Zbl 1348.74014
Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 469, No. 2159, Article ID 20130367, 20 p. (2013).
Summary: The contour method is one of the most prevalent destructive techniques for residual stress measurement. Up to now, the method has involved the use of the finite-element (FE) method to determine the residual stresses from the experimental measurements. This paper presents analytical solutions, obtained for a semi-infinite strip and a finite rectangle, which can be used to calculate the residual stresses directly from the measured data; thereby, eliminating the need for an FE approach. The technique is then used to determine the residual stresses in a variable-polarity plasma-arc welded plate and the results show good agreement with independent neutron diffraction measurements.
MSC:
| 74A10 | Stress |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
Keywords:
residual stresses; the contour method; neutron diffraction; semi-infinite strip; finite rectangle; biorthogonality conditionReferences:
| [1] | EXP MECH 50 pp 159– (2010) · doi:10.1007/s11340-009-9228-7 |
| [2] | J COMPOS MATER 38 pp 2079– (2004) · doi:10.1177/0021998304045584 |
| [3] | 108 pp 328– (1986) |
| [4] | Journal of Applied Physiology 88 pp 5487– (2000) · doi:10.1063/1.1313776 |
| [5] | 123 pp 161– (2001) |
| [6] | EXP MECH 50 pp 187– (2010) · doi:10.1007/s11340-009-9280-3 |
| [7] | EXP MECH 51 pp 1123– (2011) · doi:10.1007/s11340-010-9424-5 |
| [8] | SCRIPTA MATER 59 pp 503– (2008) · doi:10.1016/j.scriptamat.2008.04.037 |
| [9] | 443 pp 71– (2003) · doi:10.1016/S0040-6090(03)00946-5 |
| [10] | 60 pp 2337– (2012) · doi:10.1016/j.actamat.2011.12.035 |
| [11] | 205 pp 2393– (2010) |
| [12] | EXP MECH 52 pp 417– (2012) · doi:10.1007/s11340-011-9502-3 |
| [13] | 60 pp 5300– (2012) · doi:10.1016/j.actamat.2012.06.027 |
| [14] | EXP MECH 44 pp 176– (2004) · doi:10.1007/BF02428177 |
| [15] | J NEUTRON RES 11 pp 187– (2003) · doi:10.1080/10238160410001726602 |
| [16] | MATER SCI FORUM 524525 pp 671– (2006) |
| [17] | 54 pp 4013– (2006) · doi:10.1016/j.actamat.2006.04.034 |
| [18] | MATER SCI ENG A 560 pp 518– (2013) · doi:10.1016/j.msea.2012.09.097 |
| [19] | EXP MECH 53 pp 605– (2013) · doi:10.1007/s11340-012-9672-7 |
| [20] | INT J SOLIDS STRUCT 44 pp 4574– (2007) · Zbl 1144.74018 · doi:10.1016/j.ijsolstr.2006.11.037 |
| [21] | EXP MECH 46 pp 473– (2006) · doi:10.1007/s11340-006-8446-5 |
| [22] | J COMP PHYS 80 pp 314– (1989) · Zbl 0659.76037 · doi:10.1016/0021-9991(89)90102-2 |
| [23] | 49 pp 203– (2011) |
| [24] | Q APPL MATH 22 pp 335– (1965) |
| [25] | J APPL MATH 30 pp 107– (1983) |
| [26] | Journal of Elasticity 13 pp 351– (1983) · Zbl 0522.73052 · doi:10.1007/BF00043002 |
| [27] | PROC R SOC LOND A 453 pp 2139– (1997) · Zbl 0891.31003 · doi:10.1098/rspa.1997.0115 |
| [28] | 56 pp 4417– (2008) · doi:10.1016/j.actamat.2008.05.007 |
| [29] | METALL MATER TRANS A 37 pp 411– (2006) · doi:10.1007/s11661-006-0012-3 |
| [30] | 17 pp 43– (1914) |
| [31] | Journal of Applied Crystallography 14 pp 357– (1981) · doi:10.1107/S0021889881009618 |
| [32] | PROC R SOC LOND A 277 pp 385– (1964) · Zbl 0124.40006 · doi:10.1098/rspa.1964.0029 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
