PSI - Issue 42

V. Shlyannikov et al. / Procedia Structural Integrity 42 (2022) 714–721 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

719

6

HRR-theory

CMSG-theory

Pure mode I Point 1

Initial pure mode II Point 1

Mixed mode with initial pure mode II Point 7

Fig. 6. Crack tip plastic deformation zones along crack paths for conventional and strain gradient plasticity theories for Steel P2M.

Fig. 6 shows the plastic deformation zones for several successive positions of the crack tip on a curvilinear path of its growth. The contour plots are shown for steel P2M for pure Mode I, initial Mode II and mixed mode loading conditions. The left row in Fig. 6 shows the contours plastic deformation zones according to the classical plasticity theory, while the right row corresponds results in the framework of the strain gradient plasticity theory. All results are presented in the same range of strain values. Deformation fields at the crack tip obtained as a result of a numerical study (Fig. 6) in good agreement with the experimental results obtained for steel (Fig. 4), aluminum and titanium alloys. Fig. 7 presents a comparison of the radial distributions of equivalent von Mises deformations for Steel P2M obtained during the testing of CTS specimens (DIC) and by finite element method for the two theories of plasticity. The obtained results are expressed as a function of the radial distributions of equivalent von Mises deformations by the distances on the continuation crack tip. The first two figures are related to pure mode I and initial pure mode II. Next picture represents Point 7 that corresponds to the state before the final fracture. The results obtained relate to the region of nonlinearity ( Ϭ 0 / E =0.0016). And the values of the von Mises-equivalent deformations of the HRR solution are an order of magnitude larger than at CMSG. However, as move away from the crack tip the values of the results of DIC and FEM are almost the same and belong to one curve (elastic state). The results obtained using DIC in the plasticity zone are limited by the resolution of the lenses of the Vic-3D cameras. This trend persists for all investigated materials and loading conditions considered.