PSI - Issue 31

Artyom Chirkov et al. / Procedia Structural Integrity 31 (2021) 80–85 Artyom Chirkov et al. / Structural Int grity Procedia 00 (2019) 000–000

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Fig. 1. σ − ε diagram with distinguished stages of plastic flow.

According to the experimental results of Zuev and Barannikova (2014), it was found that all stages of plastic flow demonstrate a certain character of strain localization – specific patterns corresponding to di ff erent stages of plastic flow. In this study, we focus on numerical modeling of low-carbon steel loading demonstrating the yield plateau stage which is followed by a linear work hardening stage of plastic flow. The part of the stress-strain curve of such steels is illustrated in Fig. 1. Since the distribution of grain size plays a key role in regularities of plastic flow, the representative volume element (RVE) with a certain distribution of grain size is considered. The inhomogeneity of yield stress due to the di ff erent sizes of grains is in accordance with Hall-Petch dependence. Note, that we do not focus on particular low-carbon steel when the model parameters have to be carefully calibrated against the experimental study. This work rather represents a computational study that demonstrates the general regularities of plastic flow when specific hardening law is assigned.

Nomenclature

density

ρ µ

shear modulus bulk modulus

K

Y h τ

yield stress

hardening factor

equivalent stress σ i j components of stress tensor γ P equivalent plastic strain x i Cartesian coordinates v i components of velocity vector v l loading velocity f ( σ i j ) yield function

2. Material and methods

One of the advanced techniques is the step-by-step packing method which allows simulating the distribution of grains within the computational domain close to the experimentally observed (Romanova and Balokhonov (2019)). In