PSI - Issue 28

L.V. Stepanova et al. / Procedia Structural Integrity 28 (2020) 1781–1786 Author name / Structural Integrity Procedia 00 (2019) 000–000

1786

6

σ r θ

M =0 p M =0.1 p M =0.2 p M =0.3 p M =0.34 p M =0.4 p M =0.5 p M =0.6 p

0.4

0.2

0

-0.2

M =1 p M =0.889 p M =0.88 p M =0.87 p M =0.84 p M =0.8 p M =0.7 p

-0.4

-0.6

θ

-2

3

-1

1

2

-3

0

(0) r   near the crack tip for different values of the mixity parameter (plane strain condition).

Fig.3. Distributions of the shear stress

4. Conclusions In the paper the refined presentation of the asymptotic stress fields in the vicinity of the crack tip in perfectly plastic Mises materials under mixed mode loading for the full range of the mode mixities is given. At loadings corresponding to the values of the mixity parameter higher than 0.89 the asymptotic solution is determined by the formulae which dovetail with mode I solution for plane strain conditions. Thus, the characteristic feature of the asymptotic solution obtained is the presence of a segment of values of the mixity parameter for which the solution does not depend on the mixity parameter (the solution does not depend on the mixity parameter for the mixity parameter from 0.89 to 1 and the solution coincides with the solution for mode I crack in perfect plastic materials for plane strain conditions). Acknowledgements The work was supported by Russian Foundation for Basic Research (project 19-31-90100). References Chao, Y.J., 1993. On a single parameter controlled fracture of solids under plane stress conditions. Int J Fract 62, R7–R10. Dai, Y., Liu, Y., Qin, F., Chao, Y.J., 2019. A unified method to solve higher order asymptotic crack-tip fields of mode I, mode II and mixed mode I/II in power-law creeping solids. Eng Fract Mech 218, 1–21. Dong, P., Pan, J., 1990a. Asymptotic crack-tip fields for perfectly plastic solids under plane-stress and mixed-mode loading conditions. ASME J App Mech. 57, 635–638. Dong, P., Pan, J., 1990b. Plane-stress mixed-mode near-tip fields in elastic perfectly plastic solids. Eng Fract Mech 37, 43–57. Loghin, A., Joseph, P.F., 2003. Mixed mode fracture in power law hardening materials near mode I. Int J Fracture Mech. 123, 81–106. Loghin A., Joseph P., 2020. Mixed mode fracture in power law hardening materials for plane stress. Journal of the Mechanics and Physics of Solids 139, 103890. Shih, C.F., 1973. Elastic-plastic Analysis of Combined Mode Crack Problems Ph.D. Thesis. Harvard University, Cambridge, MA. Shih, C.F., 1974. Small-scale yielding analysis of mixed-mode plane strain crack problems. Fracture Analysis 560, 187–210 ASTM STP. Shlyannikov, V.N., 2003. Elastic-Plastic Mixed-Mode fracture Criteria and Parameters. Springer-Verlag, Berlin Heidelberg. Stepanova, L., Yakovleva, E.M., 2015. Asymptotic stress field in the vicinity of mixed-mode crack under plane stress conditions for power-law hardening material. J Mech Mater Struct 10 (3), 367–393. Stepanova, L.V., Yakovleva, E.M., 2016. Stress-strain near the crack tip under mixed-mode loading: Asymptotic approach and numerical solutions of nonlinear eigenvalue problems. AIP Conference Proceedings 1785, 030030. Symington, M., Ortiz, M., Shih, C.F., 1990. A finite element method for determining the angular variation of asymptotic crack tip fields. International Journal of Fracture 45, 51–64.