PSI - Issue 39

D. Fedotova et al. / Procedia Structural Integrity 39 (2022) 419–431 Author name / Structural Integrity Procedia 00 (2019) 000–000

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It should be noted that with respect to classical HRR solutions, the dependencies of the normalized new plastic SIFs SGP for pure mode I and mixed mode with initial pure mode II fit into one common curve for all tested materials. As a result of our research, we have got approximation equations for normalized distributions of plastic SIFs for SGP at various values of the intrinsic material length l in the following form:

( ) SGP SGP K K f a w   ) (

(13)

1

The main advantage of the new SIF according to the gradient theory of plasticity in comparison with the classical HRR plastic SIF is its sensitivity to changes in the material structure scale parameter l . Acknowledgements The authors gratefully acknowledge the financial support of the Russian Science Foundation under the Project 20 19-00158. Conclusions As a result of experimental and numerical investigations using a CTS specimen made of steels 34X and P2M, titanium Ti-6Al 4V and 7050 aluminum alloys in the pure mode I, pure mode II and subsequent mixed modes loading conditions, the following conclusions were obtained. 1. Series of tests for CTS specimens under pure mode I, mode II and subsequent mixed mode was carried out. As a result of the experiments, curvilinear crack paths for samples made of 34X and P2M steels, Ti-6Al-4V titanium and 7050 aluminum alloys were obtained. 2. The crack tip stress fields along the curvilinear crack path are obtained. It is found from numerical analysis of experimental crack paths that difference between effective dimensionless stresses for conventional classical HRR solutions and SGP theories results are approximately about one order of magnitude. As moving away from the crack tip, the effects of gradient plasticity disappear and the solution gradually moves to the state of a classical singularity of the HRR type. 3. Nonlinear stress intensity factor solutions for classical HRR plasticity and mechanism-based strain gradient plasticity for different experimental crack paths are obtained. It is found that the main advantage of the new SIF according to the gradient theory of plasticity in comparison with the classical HRR plastic SIF is its sensitivity to changes in the material structure scale parameter l . References ANSYS Mechanical APDL Theory Reference Release 14.5// ANSYS, Inc. Southpointe, 275 Technology Drive, CanonBurg, PA 2012. Chang J, Xu J, Mutoh Y. A general mixed-mode brittle fracture criterion for cracked materials. Eng Fract Mech 2006; 73:1249–63. Fleck, N.A., Hutchinson, J.W., 1993. A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41 (12), 1825–1857. Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W., 1994. Strain gradient plasticity: theory and experiment. Acta Metal. Mater. 42, 457 487. Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. Adv. Appl. Mech. 33, 295–361. Fleck, N.A., Hutchinson, J.W., 2001. A reformulation of strain gradient plasticity. J. Mech. Phys. Solids. 49, 2245–2271. Fleck, N.A., Ashby, M.F., Hutchinson, J.W., 2003. The role of geometrically necessary dislocations in giving material strengthening. Scripta Mater. 48, 179–183. Gao, H., Huang, Y., Nix, W.D., Hutchinson, J.W., 1999. Mechanism-based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids. 47, 1239 1263. Guo, S., He, Y., Lei, J., Li, Z., Liu, D., 2017. Individual strain gradient effect on torsional strength of electropolished microscale copper wires. Scr. Mater., 130, 124-127. Huang, Y., Zhang, L., Guo, T.F., Hwang, K.C., 1997. Mixed mode near-tip fields for cracks in materials with strain gradient effects. J. Mech. Phys. Solids. 45, 439–465. Huang, Y., Qu, S., Hwang, K.C., Li, M., Gao, H., 2004. A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plast. 20, 753– 782. Jiang, H., Huang, Y., Zhuang, Z., Hwang, K.C., 2001. Fracture in mechanism-based strain gradient plasticity. J. Mech. Phys. Solids 49, 979 – 993.