PSI - Issue 32

N.V. Boychenko et al. / Procedia Structural Integrity 32 (2021) 326–333 Boychenko N.V./ Structural Integrity Procedia 00 (2019) 000 – 000

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Figure 3 presents the hoop (Fig.3a,c) and equivalent stress (Fig. 3b,d) distributions obtained on the base of the CMSG plasticity theory. The results are shown for two types of material with strain hardening exponent N =0.075 (Fig. 3a,b) and N = 0.4 (Fig. 3c,d) and five values of the crack curvature radius. The data presented in Fig. 3 were determined for the value of specified intrinsic parameter value l = 1μm. It is obvious that the crack curvature radius has a significant influence on the stress distributions. Moreover, a material with higher plasticity ( N =0.075) is characterized by a wider range of stress variation depending on the value of the crack tip radius. The influence of the crack curvature radius in the range under consideration (0 < ρ <100nm) is realized in a small zone in the crack vicinity within the distance less than 0.1 r/l , that is in the strain gradient plasticity dominated zone. Thereby, attention should be focused on understanding what crack root radius should be used for strain gradient plasticity problems. The stress distributions for l =5μm have a similar character.

а)

b)

c) d) Fig.4. Comparison of HRR and CMSG stress distributions for l = 5μm

Figure 4 shows the radial distributions of hoop (Fig.4 a,c) and equivalent stresses (Fig.4 c,d), normalized by the yield stress, depending on the crack curvature radius. Stress distribution corresponds to the CMSG plasticity is indicated by solid lines, the classical plasticity is shown by the dotted line. The results are presented for two values of the strain hardening exponent N = 0.075 (Fig.4 a,b) and N = 0.4 (Fig.4 c,d). As shown in Fig. 4 the CMSG plasticity leads to a significant increase in the values of the stress components. Strain gradient plasticity effects diminish with distance from the crack tip, and CMSG solution is gradually approaching the classical HRR-fields. It should be noted that the influence of the crack curvature radius is realized in a local area within 0.1r/l for both CMSG and HRR plasticity.