PSI - Issue 52

Tomislav Polančec et al. / Procedia Structural Integrity 52 (2024) 348 – 355 Tomislav Polančec, Tomislav Lesičar, Jakov Rako / Structural Integrity Procedia 00 (2019) 000 – 000

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Numerical model of the test specimen is represented in Fig. 1b. The same geometry is taken in 2D and 3D setting. 2D model of the specimen is discretized by 74766 first-order quadrilateral finite elements, with refinement in the expected fracture process zone (FPZ). In 2D setting, assumption of plane strain and plane stress is adopted. 3D model of the specimen is discretized by 97100 first-order hexahedral finite elements, where also mesh refinement within FPZ is applied. Loading of the specimen is imposed by applying displacement on the upper edge. As concluded in author’s previous work [30], Astaloy Mo+0.2C obeys quasi-brittle behaviour. The grains of ferrite and bainite are ductile, but the pores at the microstructural scale serve as damage initiators, which coalesce during loading, leading to the quasi-brittle fracture. Linear elastic parameters are easily obtained for the linear part of the stress- strain curve, as well as Poisson’s ratio, which are 98000MPa E = and 0.28  = , respectively. Based on the experimental results, nonlinear isotropic hardening is assumed according to the relation ( ) p ekv 0 1 , b y y Q e    −  = + − (9) where 0 y  represents the elasticity limit, Q  is the saturation limit, b represents the saturation exponent and p eqv  is the equivalent plastic strain. Although monotonic loading is applied, nonlinear kinematic hardening is also adopted, as a basis for future extension towards fatigue behaviour. The nonlinear kinematic hardening evolution law is ( ) ( ) p ekv p ekv p ekv k k k k y C       − = − σ α α α . (10) In Eq. (10), k α represents the backstress tensor, k C and k  are material parameters, y  is yield stress and  σ the effective (non-degraded) Cauchy stress tensor. For the sintered steel examined in this paper, only one back-stress tensor is taken, 1 k = . The initial values of the elastoplastic parameters are obtained by fitting the experimental stress-strain curve using Eqs. (9) and (10) via least squares method. The initial values have been used in numerical simulations. Importantly, calibration of the plastic hardening parameters is conducted without considering softening of the material. After few iterations, the final elastoplastic material parameters given in the Table 1.

Table 1. Elastoplastic material parameters. Elastoplastic material parameters

Value





0 MPa

y 

165

  MPa Q 

50.9

  - b   1 -  

315.313 253.162 14802.035



1 MPa C

For the PF calibration, the length scale parameter chosen is 0.1mm l = . The initial value of the energetic threshold c  is read from the experimental stress-strain curve (the area below the curve). After few numerical simulations, the final value of the threshold is c 2.41MPa  = . Based on the brittle fracture which occurs in the specimen, the critical fracture energy density which gives the best agreement to the experimental investigation is c 0.75N/mm G = . Figs. 2 and 3 represent comparison of the numerically and experimentally obtained force-displacement and stress-strain curves.