Scripta Materialia 162 (2019) 195–199
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Thermally activated twin thickening and solute softening in magnesium alloys - a molecular simulation study Peng Yi a,d,⁎, Michael L. Falk a,b,c,d,⁎⁎ a
Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA d Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD 21218, USA b c
a r t i c l e
i n f o
Article history: Received 29 July 2018 Received in revised form 8 November 2018 Accepted 8 November 2018 Available online xxxx Keywords: Strain rate sensitivity Thermally activated process Plasticity Interface migration Solute hardening
a b s t r a c t Thickening of the tension twin {10 − 12}⟨10 − 11⟩ in Mg-Al and Mg-Y alloys varies systematically with temperature, strain rate and solute concentration. The twin boundary propagates through the nucleation and expansion of twin dislocation loops, a thermally activated process. Solute softening is observed in both alloys. The softening saturates with increasing solute concentration due to solute hardening of twin dislocation loop expansion. With the present interatomic potential, Al solutes are more effective in both softening and hardening than Y solutes. Twin thickening exhibits weak strain rate sensitivity for pure Mg but the strain rate sensitivity increases with solute concentration. © 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Magnesium has great potential as a light-weight structural material. However, due to its low symmetry HCP structure, the slip systems in magnesium are insufficient to accommodate arbitrary homogeneous deformation according to the von Mises requirement. Therefore, twinning is often observed to arise to accommodate the deformation, particularly normal to the c-axis. In the case of magnesium, tension twin {10 − 12}⟨10 − 11⟩ is reported to be activated under low critical resolved shear stresses (CRSS) below 10 MPa, only slightly higher than that for basal slip [1]. It is commonly believed that twin nucleation occurs at grain boundaries [2,3]. Here we focus on the normal propagation of the twin boundary (TB), or twin thickening, in an effort to elucidate some of the basic mechanisms of this process and explain some experimental observations that are not yet fully understood. The fundamental questions we address in this work include the mechanism of twin thickening and the strain rate sensitivity of the twin thickening process. There is a debate regarding whether the dominant mechanism for twin thickening is twin dislocation (TD) migration or local shuffling, although the latter has received a lot of criticisims [4–6]. Several recent experimental studies have also revealed twin boundaries not following a well-defined crystallographic plane in both
⁎ Correspondence to: P. Yi, Maryland Hall 300, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218, USA. ⁎⁎ Correspondence to: M. L. Falk, Shaffer 103, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218, USA. E-mail addresses:
[email protected] (P. Yi),
[email protected] (M.L. Falk).
https://doi.org/10.1016/j.scriptamat.2018.11.021 1359-6462/© 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
pure Mg and Mg alloys [7–9]. In addition, it has long believed that twin thickening is strain rate insensitive when compared to dislocation glide because the flow stress in the twinning-dominant deformation mode has been observed to be strain rate insensitive [10–12]. However, this is an overall effect, and could also arise if the number density of twins and the resolved shear stress of individual twins are both strain rate sensitive, but with opposite signs. Quasi-static mechanical tests indicate that under some conditions the density of twins increases as a function of strain rate, a phenomenon that has been attributed to the higher number of potential twin nucleation sites at increasing levels of applied stress [13]. This would be expected to result in a negative stain rate sensitivity [14]. Dynamic tests, on the other hand, appear to indicate that the strain rate sensitivity increases with strain rate, particularly in the high strain rate regime [15]. The strain rate sensitivity in the high strain rate regime is of great interest to the automobile and aerospace applications because the dynamic response of components must be known for prediction of performance under severe loading conditions, such as impact in order to support failure tolerant design [16]. Twin thickening has been previously studied using computational methods [17,18]. Luque et al. [17] identify the twin thickening mechanism as nucleation and expansion of TD loops. Solute enhances TD loop nucleation but hinders their expansion. A mechanistic model was developed to predict CRSS using the results of first-principle calculations of solute-twin interaction energies as inputs [18]. Based on this model nucleation is predicted to be the controlling mechanism only for solute concentrations less than about 0.1 at.%; and for all commercial
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alloys, the stress for twin plasticity is predicted to be controlled by solute hardening of TD loop expansion. However, this model overestimates the twinning stress for pure Mg. In addition, their own molecular dynamics simulations in Mg-Al alloys exhibit softening for solute concentration up to Al-5 at.%, indicating a much wider composition range for nucleation controlled twin thickening. This discrepancy indicates that a more systematic study that facilitates a reexamination of this concept is warranted. This is true considering the desire to deploy magnesium alloys in applications under which the material would be subjected to extreme strain rate conditions. A more adequate understanding of twin boundary propagation would also shed light on the boundary microstructure, which is important for calculating twin boundarydislocation interactions. In this work, we use molecular simulations to study the solute, temperature, and strain rate effects on the normal propagation of the tension twin in Mg-Al and Mg-Y alloys. Molecular static (MS) and Molecular dynamics (MD) simulations were performed using LAMMPS [19]. Mg alloys were modeled using Kim et al.'s MEAM potentials for Mg/Al [20] and Mg/Y [21], respectively. This MEAM potential has proven to yield good agreement with DFT calculations of more complicated ⟨c + a⟩ dislocation core structures in Mg [22], and has been used for measuring the solute effect on dislocation mobility in our previous studies [23,24]. Simulations were conducted under constant volume conditions. MS simulations were performed by energy minimization using the conjugate gradient method with energy tolerance being 10−14 throughout. For MD simulations, the system was kept thermally isolated, i.e., no thermostat/barostat was used in order to minimize the addition of spurious dissipative dynamics. Since the maximum shear strain applied to the system in our simulation did not exceed 5% for finite temperatures, the maximum temperature rises due to the shear work was no more than 10%. Time was integrated using Verlet algorithm with a time step of 2 fs. The Common Neighbor Analysis (CNA) method [25,26] with a cutoff of 3.8 Å was used to identify the atoms with a non-HCP structure, which constitute the twin boundary.
The simulation box contains a twinned region at the bottom and an un-twinned region on the top, as illustrated by Fig. 1. The edges of the unit cell for the twinned crystal are A = [10 − 11], B = 1/3[−12 − 10] and C = [−1011], and there are (40, 100, 4) unit cells in the (A, B, C) direction, respectively. Similarly the un-twinned crystal has (40, 100, 38) unit cells of edges A = [−1011], B = 1/3[−12 − 10] and C = [−101 − 1]. The lattice constants are obtained through separate equilibration simulations at given temperature and solute concentration at 0 Pa. The A and B vectors of both crystals are chosen to be along the x- and y-directions, respectively, creating an initially flat {10 − 12} twin boundary on the x-y plane. The box dimension is about 32 nm in all three directions and contains 1,344,000 atoms, unless stated otherwise. Periodic boundary conditions were applied on the twin plane. A mixed boundary condition was applied to the zdirection, similar to our previous work [23,24]. Specifically, two slabs were created at the ±z boundaries with thickness dslab. Atoms in each slab comprise a rigid body. In addition, motion of both slabs in the z-direction was prohibited throughout the simulations. The thickness dslab was chosen to be greater than the cutoff distance of the potential. Simple shear was simulated by displacing the +z slab in xdirection, while the −z slab was held fixed. Constant strain rates ε_ between 2 × 106 s−1 to 1 × 108 s−1 were used for the shear simulations. The results presented were obtained using 5 × 107 s−1, unless specified otherwise. To study the solute effect, atoms between the two slabs were randomly substituted with solute atoms at a probability equal to the atomic solute concentration. Temperatures from 0 K to 500 K were studied, as were solute concentration ranges from 1 to 5 at.% for both Al and Y solutes. Softwares Ovito [27] was used for visualization. Simple shear simulations in Mg-Al and Mg-Y alloys were performed at 0 K using MS simulations. The representative stress-strain curves for Mg/Y alloys of different solute concentration are shown in Fig. 2(a) . For pure Mg, yield occurs at a stress of about 1150 MPa, after which the twin boundary starts to propagate in the normal direction by transforming the un-twinned region. The CRSS, or the flow stress, of the twin propagation is calculated by averaging the stress after initial yield. It is also possible to calculate the CRSS by averaging the stress of the peaks in Fig. 2(a) [28]; however, the peaks are hard to identify at high temperatures due to thermal fluctuation. Based on our calculation, the CRSS decreases with increasing solute concentration, demonstrating the solute softening effect. Simple shear simulations in Mg alloys at finite temperatures were also performed and the results are shown in Fig. 2(b) . The CRSS as a function of temperature can be fitted to the Kocks model [29], similar to our previous work on basal dislocation slip [23], 8 >
