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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through the densification of material. As an example, 92% of relative density can be achieved by a single step pressing [4], while 96% of relative density can be achieved by the Hipaloy [5] powder concept. For the future PM process development, production of the sintered materials for highly dynamically loaded mechanical components is currently investigated. The pores in the material microstructure of the sinter steel denote the critical areas, where during loading cracks are initiated [6]. Because of the irregular pore shapes and non-homogeneous material within, they act as stress concentrators. During the sintering process, the highest proportion of porosity is located near the surface, which is caused by friction among die walls and metal powder. Therefore, in this area coalescence of the pores occurs, which leads to the formation of the macro-cracks from micro-cracks [7]. Moreover, cracks can propagate within the metallic phase, across the boundaries of the phases, or between them [7]. In order to describe the fracture process in materials, the numerical methods are mostly utilized. One of the most commonly used methods in the literature is Cohesive zone modelling (CZM) developed in [8] and [9]. CZM belongs to discrete methods for describing the failure process. However, the issue of discrete methods is crack tracking, which creates numerical problems with stress singularities, mesh size, and orientation in the process of crack initiation and propagation. In [10] and [11], extended finite element method (XFEM) is developed, with enriched finite elements to accurately describe crack path. On the other hand, the problem of crack tracking is facilitated by very popular phase-field method (PFM), which belongs to the smeared approaches for describing the fracture process. The crack tracking is replaced by a diffusive band, which eliminates problem of stress singularity in the crack tip and crack orientation. The phase-field method is based on Griffith’s theory, wh ere the local failure of material emerges when the specified fracture energy reaches the critical energy release rate [12]. The generalization of the Griffith criterion is implemented in [13], while in [14] is regularized through the variational formulation. Integrating PFM into FEM demands fine mesh discretization within the softening band. To circumvent this problem, the strategy of adaptive mesh refinement is integrated in [15]. The key contribution of PFM is presented in [16], modelling the quasi-static brittle fracture phenomena. Except for brittle fracture [17 – 19], the PFM can also describe the ductile fracture phenomena as well [20 – 22]. The PFM integration into FEM reveals the problems of its numerical robustness. Hence, algorithmic PFM integration is divided into monolithic and staggered solution approaches. In the monolithic approach, the displacements and the phase-field variable are calculated simultaneously, which causes instabilities during crack propagation because of the non-convexity of regularized free energy functional [19]. In contrast, the staggered solution scheme separates the calculation of the displacement field and the PF variable. Therefore, the decoupling of the weak formulation on two equations can be solved in an iterative way, where many approaches in the literature have been proposed. In a single iteration procedure [16], the algorithm demands small-scale increments, which causes a computationally and time-consuming process. Other class of algorithms includes several iterations during one loading increment, which is restricted by the stopping criterion [23,24]. The goal of this paper is calibration of the macroscale material parameters of isotropic hardening and brittle damage for numerical modelling of damage behaviour of sintered steel Astaloy Mo+0.2C with density 6.5 g/cm 3 . In numerical simulations, the staggered PFM scheme proposed in [25] has been utilized. Numerical results are compared to the experimentally conducted uniaxial tests. Numerical simulations are conducted assuming plane strain and plane stress, as 3D setting.

Nomenclature

Abbreviations

saturation exponent

CCFE CCPF CZM

convergence check finite element convergence check phase-field

b b

prescribed body force vector kinematic hardening modulus

cohesive zone model

k C

D E

spatial derivative matrix Young's modulus degradation function

FE

finite element

FPZ

fracture process zone

( ) g 

PF

phase-field

Griffith’s critical energy release rate

PFM PDE PM UEL

phase-field method

c G

length scale parameter

partial differential equation

l

n

normal vector

powder metallurgy

saturation coefficient

user-element

Q 