PSI - Issue 61

Berkehan Tatli et al. / Procedia Structural Integrity 61 (2024) 12–19 B. Tatli et al. / Structural Integrity Procedia 00 (2024) 000–000

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where τ and ˙ γ are the shear stress and plastic slip rate in each sip system, respectively. For the classical J2 plasticity framework, the following definition is used, ˙ W J 2 p = σ eq ˙ ε p eq (12) where σ eq is the von Mises equivalent stress and ˙ ε p eq is the rate of the equivalent plastic strain. The model is implemented in ABAQUS software through user subroutines (UMAT and HETVAL). A similarity between the heat transfer equation and the phase field strong form is exploited to facilitate the use of coupled temp displacement elements with temperature behaving as a stand-in for the phase field parameter as demonstrated in Navidtehrani et al. (2021). This section presents the numerical findings within three-dimensional RVEs and o ff ers a brief examination of how microstructural factors impact the plastic deformation and failure behavior of dual-phase steels. To achieve this, square, thin-plate, polycrystalline RVEs with a side length of 100 µ m and thickness of 1 µ m are generated by a Voronoi-based tessellation generator Neper (Quey et al. (2011)). Each RVE is composed of approximately 300 randomly oriented grains and all examples involve a single crystal in the thickness direction. Two di ff erent marten site volume fractions are considered (15%, 37%) with various morphologies and random crystallographic orientation sets. As outlined in Section 2.1, the ferrite phase is characterized by the rate-dependent crystal plasticity framework, implemented through a user-material subroutine (UMAT) and utilizing the hardening parameters presented in Table 1. Simultaneously, the martensite phase is defined by the J 2 plasticity model, employing a user-material subroutine (UMAT) as discussed in Section 2.1. By exploiting the similarity between the strong form of the phase field fracture and heat transfer equations, the phase field fracture framework is implemented through a heat-generation subroutine (HETVAL). This integration is achieved by coupling the heat-generation subroutine with the user-material subroutines of each phase, e ff ectively combining crystal plasticity and conventional plasticity with phase field fracture to capture transgranular cracking in each phase individually. In the finite element calculations, eight-noded coupled temperature displacement brick elements (C3D8T) are utilized, enabling the temperature degree of freedom to serve as a surrogate for the phase field parameter. The boundary value problem is defined such that 3D thin-plate RVEs are restricted at 3. Numerical Examples

Fig. 1. Phase Field Distribution (Top) and Engineering Stress-Strain Response (Bottom) of VF15-Morpho1-Oriset1 and VF15-Morpho1-Oriset2.