Grain boundary strengthening of FCC polycrystals

Abstract

The effect of grain size on the flow strength of FCC polycrystals was analyzed by means of computational homogenization. The mechanical behavior of each grain was dictated by a dislocation-based crystal plasticity model in the context of finite strain plasticity and takes into the account the formation of pile-ups at grain boundaries. All the model parameters have a clear physical meaning and were identified for different FCC metals from dislocation dynamics simulations or experiments. It was found that the influence of the grain size on the flow strength of FCC polycrystals was mainly dictated by the similitude coefficient K that establishes the relationship between the dislocation mean free path and the dislocation density in the bulk. Finally, the modelling approach was validated by comparison with experimental results of the effect of grain size on the flow strength of Ni, Al, Cu and Ag.

A criterion for slip transfer at grain boundaries in Al

“…Nevertheless, this approach does not take into account the geometry of slip and of the GB, which are known to play a critical role in slip transfer. More recently, the effect of grain boundaries on the response of polycrystals was simulated using a dislocation-based crystal plasticity model in which the rate of dislocation storage is not constant within the grain but increases as the distance to the GB decreases, simulating the formation of pile-ups [8][9]. This approach provided good predictions of the effect of grain size on the strength of FCC polycrystals but tended to overestimate the strengthening for small grain sizes (< 20 µm) because it was assumed that slip transfer was blocked in all GBs.…”

Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization

“…This is not the case for the SGCP model, where the density of GNDs is not affected by the annihilation distance. As a result, the predictions of the simulations in (Rubio et al, 2019) are in better agreement with the experimental data for large strains and small grain sizes although they also tend to overestimate the flow stress under these conditions. Another reason why the flow strength is overestimated by the SGCP model can be found in the presence of slip transfer between neighbour grains.…”

“…The similitude coefficient K is a dimensionless constant that arises from the experimental observation (known as the similitude principle) that relates the flow stress τ with the average wavelength of the characteristic dislocation pattern d according to τ = Kµb/d in the case of FCC metals. The actual values of the similitude coefficient K were identified by Haouala et al (2018) and Rubio et al (2019) for Cu , Al, Ni and Ag from the experimental data in Sauzay and Kubin (2011), and are given in Table 2. Finally, the effective annihilation distance, y c , was assumed to be the average between the mean annihilation distance of edge dislocations (≈ 6b (Martinez-Mardones et al, 2000)) and screw dislocations.…”

Effect of slip transmission at grain boundaries in Al bicrystals

“…Lim et al (2011Lim et al ( , 2014 presented another approach in which the information from polycrystal simulations using a dislocation-based crystal plasticity model was used at another length scale to enforce local slip transmission criteria at the GBs depending on the orientation and on the GB strength. More recently, Haouala et al (2018) and Rubio et al (2019) have developed a dislocation-based model in which the rate of dislocation storage is not constant within the grain but increases as the distance to the GB decreases. This results in dislocation accumulation at boundaries and hence, higher stresses develop near GBs.…”

“…This is the main objective of this investigation, which is inspired by the experimental evidence of slip transfer across a GB in pure Al presented in section 2. The behavior of the GBs in various bycrystals -representative of the experimental conditions as well as of idealized conditions -is analyzed by means of dislocation-based crystal plasticity model in (Haouala et al, 2018) and (Rubio et al, 2019), which was modified to take into account the effect of slip transfer along particular SS. It should be noted that this type of physically-based CP models based on classic continuum mechanics are able to account for many of the phenomena of interest related to dislocation evolution in the grain such as slip, reproduction of hardening stages, thermal activation of deformation mechanisms, etc., in a simple manner.…”