PSI - Issue 42

Tuncay Yalçinkaya et al. / Procedia Structural Integrity 42 (2022) 1651–1659 Tuncay Yalc¸inkaya et al. / Structural Integrity Procedia 00 (2019) 000–000

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hardening capacity, and low yield to tensile strength ratio. Moreover, they show continuous yielding without the formation of Lu¨ders bands. Due to the two-phase microstructure, the moderate ductility could be a major concern in heavy forming processes, considering the failure mechanisms at the micron scale. Therefore, the influence of microstructure on the ductility/strength balance should be studied at a proper length scale to further understand the micro-plastic, damage and fracture behavior. Depending on the martensite volume fraction, the damage evolution and the crack initiation could occur through ferrite grain boundary decohesion, ferrite/martensite interface decohesion and martensite cracking due to void nucleation (see e.g. Avramovic-Cingara et al. (2009), Zhang et al. (2015), Tang et al. (2021)). Each failure mechanism requires a different analysis technique and a multiscale approach (see e.g. Yalc¸inkaya et al. (2019), Yalc¸inkaya et al. (2021), Acar et al. (2022), Kahveci et al. (2022)) should be implemented to reflect the plastic deformation, damage evolution and crack initiation to the macroscopic response. There are various studies in the literature focusing on the plasticity and ductile failure of dual phase steels at the RVE scale employing both realistic and simplified microstructures (see e.g. Ayatollahi et al. (2016), Pagenkopf et al. (2016)). The ferrite deformation is handled by both phenomenological and crystal plasticity approaches while the martensite is modeled simply by phenomenological models due to the limited ductility. For the modeling of dam age initiation, both uncoupled (see e.g. Luo and Wierzbicki (2010)) and coupled porous plasticity type models (see e.g. Uthaisangsuk et al. (2009)) are implemented and for the crack initiation and propagation cohesive zone ele ments and XFEM frameworks are employed (see e.g. Vajragupta et al. (2012), Sirinakorn and Uthaisangsuk (2018), Hosseini-Toudeshky et al. (2015)). Due to the complicated microstructure, the multiscale frameworks stay mostly at the 2D scale and 3D modeling techniques are quite restricted. In this study, three dimensional RVEs are gener ated using Voronoi tessellations where crystal plasticity and J 2 plasticity frameworks are employed for the ferrite and martensite phases respectively. For the damage and fracture analysis, an uncoupled damage model is employed at martensite phase while cohesive zone elements are inserted for simulating the debonding between martensite and fer rite grains. For the identification of the cohesive zone parameters, an inclusion RVE study and indentation simulations are conducted. Crystal plasticity parameters are also obtained through an RVE study of pure ferrite phase. Finally, polycrystalline DP RVEs are analyzed under axial loading conditions and the failure results are discussed with respect to the observations in the literature. The paper is structured as follows. The constitutive models are explained in Section 2, and the failure frameworks for both ferrite and martensite phases addressed in Section 3. The numerical approach and the obtained results are presented in Section 4, which is followed by concluding remarks in Section 5. A rate-dependent crystal plasticity model is employed for the modelling of the ferrite phase, where the deformation gradient is decomposed multiplicatively into an elastic and a plastic part, F = F e · F p , (1) with F e and F p representing the elastic and plastic deformation gradients respectively. The rate of change of F p is related to the plastic slip rates ˙ γ α of the α slip system via ˙ F p · F − 1 p = α ˙ γ α s α 0 ⊗ m α 0 , (2) where s α 0 and m α 0 represent the slip direction and slip normal in the reference configuration. The left handside of the above equation actually corresponds to the plastic velocity gradient with respect to an intermediate configuration, L p , to be integrated to obtain the plastic deformation gradient, F p . In the finite strain context, the elastic Right Cauchy Green Strain tensor is expressed as C e = F T e · F e , the elastic Green strain tensor as E e = 1 2 ( C e − I ), and the second Piola-Kirchhoff stress tensor as S = C : E e , where I is the second order identity tensor. The fourth order tensor C , whose coefficients are the anisotropic elastic moduli, has cubic symmetry: C i jkl = C jikl = C i jlk = C kli j . Tensor C has three independent constants, namely, C 11 = C 1111 , C 12 = C 1122 and C 44 = C 1212 . Then the relation between the second Piola-Kirchhoff stress and the Kirchhoff stress can be used, S = F − 1 e · τ · F − T e , and projected onto the slip systems τ α = s α · τ · m α = s α 0 · S · C e · m α 0 , (3) 2. Constitutive Models