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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4. Numerical Examples

In this section, the numerical results are presented in three dimensional RVEs where the influence of microstruc tural parameters on the plastic deformation and failure behavior of dual-phase steels is addressed shortly. In order to realize this, several cubic polycrystalline RVEs with side length of 100 µ m, including 50 randomly oriented grains, are generated and subjected to uniaxial loading. The input files for ABAQUS are generated through an in-house script as discussed previously. The rate dependent crystal plasticity model which has been presented through equations (1)-(6) with the hardening parameters in Table 1 are assigned to the ferrite phase, while classical J 2 plasticity theory with isotropic hardening as given in equation (7) with the given parameter set in Table 2 is assigned to the martensite phase. Boundary conditions are defined such that RVE analysis can mimic the mechanical response of the material under uni axial loading conditions (see e.g. Yalc¸inkaya et al. (2019) and Yalc¸inkaya et al. (2021)). The applied strain rate is taken to be 0 . 001s − 1 for all the simulations. Once the analyses are completed, stress and stain results are homogenized employing a volumetric averaging method to obtain true stress-strain curves. Initially, four RVEs having the same morphology and martensite volume fraction of 15% are analyzed. For each RVE, crystal orientations of ferrite grains are varied randomly to observe the effect of the grain orientation and microstructure on the plasticity and fracture behavior of the material. Fig. 1 illustrates the resulting homogenized stress-strain curves. The anisotropy in the initial hardening stage is attributed to the low number of ferrite grains used in the analysis. The first observation is that variation in the microstructure of DP-steels has a profound impact on the response of the material. Even though only the ferrite grain orientations are varied among the four RVEs, significantly different decohesion patterns can be observed. Yet, the initial decrease in the stress-strain response, which corresponds to a crack initiation, occurs at around similar strain values for all cases (at 11 = 0 . 05). Furthermore, after the initial drop-off, the softening trends for all the RVEs are different, which indicates dissimilar failure behavior.

Fig. 1: True stress versus true strain curves of 15% volume fraction RVEs with four different orientation sets.

To have more insight into the effect of grain orientation on the stress and damage evolution of the DP-steels, three different orientation sets from Fig. 1 is selected, then their damage and Von Mises stress distribution are plotted at the same cross-section and instant as shown in Fig. 2. It is clear that different orientation sets result in different defor mation and decohesion patterns due to the changes between the grain boundary interactions in the RVE. Martensite cracking has already occurred for the orientation set on the left, while martensite grains are still intact for the orienta tion set on the right. Stress distribution also differs considerably for each set. Fig. 2 verifies that martensite cracking occurs due to high stress partitioned to martensitic islands, as mentioned in Tang et al. (2021).