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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3. The subject under study and material properties Numerical solutions are obtained for a single edge tension (SET) specimen under uniaxial tension. The load is prescribed by imposing a displacement on the pins. The geometry and loading conditions of the specimen, as well as the vicinity of the crack tip, are shown in Figure 1. Wide range of the crack curvature radius was used in computations, namely ρ = 0 (mathematical notch); ρ = 25nm, ρ = 30nm, ρ = 60nm and ρ = 100nm. The load corresponded to the value of the elastic stress intensity factor К 1 =7.4 / MPa m . Numerical analyses of the stress-strain state of SET specimen are implemented in the present study for the following material properties, the yield stress is σ y =200MPa, Young's modulus is E = 100000MPa, and the Poisson's ratio is υ = 0.3. For each value of the crack tip radius, the strain hardening exponent varied N = 0.075 to N = 0.4. The value of the Taylor’s length parameter l is usually in the range from 1μm to 10μm. The strain gradient plasticity coincides with the classical plasticity at l = 0 by definition. In present work, stress analysis by CMSG plasticity was performed for two values of l = 1μm and l = 10μm.

Fig. 1. Specimen geometry and crack tip area

Finite element analysis was conducted using the ANSYS Multiphysics Campus Solution to determine the stress strain state parameters of SET specimen under plane strain. Constitutive equations (4,7,8) are implemented in ANSYS by a user material subroutine USEMAT to realized CMSG plasticity by Shlyannikov (2021). Considered SET specimen (Fig.1) has a width W = 80mm, a height h = 140mm, the ratio between the crack length to the width a/W = 0.5. The crack tip was modeled as a mathematical notch with ρ = 0 and as a notch with a finite root radius ρ = 25nm, ρ = 30nm, ρ = 60nm, and ρ = 100nm. With the aim of accurately characterizing the influence of the plastic strain gradients, a highly refined mesh is used near the crack tip. A mesh sensitivity analysis of Shlyannikov (2021) showed that a characteristic element size below 5nm delivers mesh-independent results. Thus, in present paper a characteristic element size equal to 3.5 nm is chosen, ensuring mesh-independent results. 4. Results and discussion 4.1. Crack tip fields In this study the results are presented in the form of radial stress distributions in crack growth direction ( θ =0). Figure 2 shows the hoop (Fig.2a) and equivalent (Fig.2b) stress distributions obtained by the classical HRR-model. Stress components are normalized by the yield stress. The results are presented for two type of material with strain hardening exponent N =0.075 (dashed lines) and N = 0.4 (solid lines) and five values of the crack tip radius. The crack curvature radius has a significant effect on the stress distributions in the range of the relative crack tip distance 0 < rσ y /J <0.2. At rσ y /J >0.2 finite root radius does not affect the stress distribution. It can be concluded that the crack curvature radius in the considered range (0 < ρ <100nm) does not affect the stress fields in the HRR fields