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

351

4

u denotes the displacement vector, b represents the volume force vector, t is the surface traction vector and n is the outward-pointing normal vector. The Cauchy stress tensor is denoted as σ and H is the history field parameter included to restrict the unphysical irreversible fracture process of material 0   [16]: ( )   ( ) ( ) 0, : max . e t t D    + = = H (7) Moreover, the evolution of the PF variable described by the Helmholtz type equation (Eq. (5)) can be recast in terms of the crack driving state function D [28] following the TH model: (8) Phase field methodology has been embedded into FE software Abaqus [29] via user subroutines, in the form of a Convergence-Check Phase Field (CCPF) staggered scheme proposed in [25]. The algorithm relies on two layers of finite elements (displacement and PF finite elements), where an additional Convergence-Check Finite Element (CCFE), controls exchange of the variables among mesh layers and controls the stopping criterion in a loading increment. The algorithm has been derived for brittle, as ductile damage in monotonic and cyclic loading regime. 3. Calibration of the material and PF parameters 3 6.5g/cm . The production process consists of sintering process at 1140°C for 30 minutes, cooling to 70°C rapidly, and then cooling to room temperature. Consequently, during this process, the material microstructure is formed by ferrite and bainite phase. Considering the theoretical density of Astaloy powder which is 3 7.8g/cm , it is obvious that the material considered has a porous microstructure [30], more precisely, it consists of 16.7% pores. The experimental testing is performed on the sample presented in Fig. 1a). The quasistatic tensile tests are performed by the Instron servo hydraulic machine, while the displacements of the specimen are measured by the extensometer. More details on the experi mental testing are given in author’s previous work [3 1]. The force-displacement and stress-strain curve obtained are shown in Figs. 2 and 3. e    + + p TH c 1. D = − This paper deals with the low-prealloyed steel powder Astaloy Mo+0.2C whose density is

Fig. 1. Test specimen: (a) geometry and dimensions; (b) numerical model and boundary conditions.