Atomistic simulations of high-temperature creep in nanotwinned TiAl alloys
Introduction
Creep is a time-dependent plastic behavior of materials under sustained stress at elevated temperature and may result in unexpected deformation and even failure of materials or structures [1], [2], [3]. Creep behaviors are significantly related to external conditions, such as applied stress and temperature. In recent years, nanocrystalline (NC) materials have attracted much attention due to their high strength. A large number of experimental, computational and theoretical studies have been performed on NC metals and alloys [4]. Creep is an important issue encountered in practical high-temperature applications of NC materials. Currently, the creep mechanisms of NC metals have been extensively investigated through experiments and simulations [2], [3], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Previous molecular dynamics (MD) simulations elucidated that the typical creep mechanisms include grain boundary (GB) diffusion, GB sliding, and dislocation nucleation, and they are activated under different levels of applied stress [3], [16], [17]. The well-known classic Bird–Dorn–Mukherjee equation [18] has been widely used to describe the creep behaviors of NC materials and comprehensively reflects the effects of applied stress, temperature and grain size on the creep behaviors. This equation is expressed as [18] where is the steady-state creep strain rate, A is a dimensionless constant, is the diffusion coefficient, G is the shear modulus of materials, b is the magnitude of the Burgers vector, is Boltzmann’s constant, T is the absolute temperature, d is the mean grain size of polycrystalline materials, is the applied stress, n is the stress exponent reflecting the strain-rate sensitivity of yielding/flow stress, p is the grain size exponent and Q is the activation energy for a specific thermally activated creep mechanism. Both the stress exponent n and grain size exponent p are important for the creep mechanism. Generally, different exponents correspond to different creep mechanisms. When the stress exponent , creep is dominated by diffusion. For this case, if the grain size exponent p is equal to 2, vacancy diffusion occurs through the crystalline lattice, which is called Nabarro–Herring diffusion [8]. If , vacancy flow occurs along the GB, which is termed GB diffusion (or Coble diffusion) [13]. Therefore, for and , creep is referred to as Nabarro–Herring creep, while for and , creep is called Coble creep. For , the creep mechanism is mainly GB sliding [11], [17], [19]. Note that GB diffusion always occurs simultaneously with GB sliding according to previous studies [16], [17]. For n 4, dislocation gliding and climbing are mechanisms controlling creep [17]. Therefore, the creep process for n 4 is called dislocation creep, in which the dislocation density and velocity are two critical parameters used to determine the creep rate. The dislocation velocity is mainly influenced by the resistance from the lattice and the dislocation-defect or dislocation–dislocation interactions.
Nanotwinned (NT) metals/alloys exhibit ultrahigh strength and good ductility due to the presence of a high density of nanoscale twins [20], [21], [22], [23], [24], [25], [26]. Due to the low energy and good stability of the twin boundary (TB), NT materials also exhibit better thermal stability than NC materials [27], [28], implying their great potential in high-temperature applications. Previous MD simulations and experiments [2], [16], [29] have been performed on creep in NT metals and revealed that because TBs can block the motion of dislocations and further suppress creep, the creep rate significantly decreases with increasing TB density. Therefore, NT metals have a higher resistance to creep than their NC counterparts [2], [16]. Sanders et al. conducted creep experiments on NT Cu at temperatures of 0.24–0.64 (where is the melting temperature) and reported that a high density of TBs in NT Cu can induce a very low creep rate over the tested temperature range [29]. Recently, Jiao et al. performed MD simulations for high-temperature creep in NC Cu [16] and showed that creep in NT metals with very small twin thicknesses at a high applied stresses is accommodated by TB migration. A combination of experiments and MD simulations recently confirmed that nanoscale twins can effectively improve the creep property of pure metals and further verified the modified Bird–Dorn–Mukherjee equation involving the stress conjugated activation volume [2].
Because TiAl alloys possess a low density, a high specific strength and good ductility at elevated temperatures, they have been used for high-temperature applications in aerospace and automotive industries. Recently, a type of new polysynthetic twinned TiAl single crystal with a twin thickness of approximately 10 nm was successfully fabricated by directional solidification without the use of complex seeding methods [30]. This new NT TiAl alloy exhibited an average tensile ductility of 8.1% and a yield strength of 637 MPa at 900 °C [30]. More importantly, such an NT TiAl alloy has superior creep resistance, i.e., its creep lifetime and minimum creep rate are better than those of commercial polycrystalline TiAl alloys by more than one order of magnitude [30]. However, the creep mechanism of such NT TiAl alloys remains poorly understood. In this paper, we performed a series of large-scale MD simulations to systematically investigate the creep behaviors of NC and NT TiAl alloys with various grain sizes and twin thicknesses under different external conditions (such as different applied stresses and temperatures) and to reveal the underlying creep mechanisms of NT TiAl.
Section snippets
Methods
We performed a series of large-scale MD simulations for high-temperature creep of quasi-three-dimensional NC and NT -TiAl alloys via large-scale atomic/molecular massively parallel simulator (LAMMPS) [31]. The NC sample is compared with NT samples. The simulated NC and NT samples contain randomly oriented columnar grains constructed by the Voronoi method. We constructed two types of samples: one type of sample with dimensions of 50502.8 nm3 and a mean grain size varying from 3.1 nm to
Creep behaviors of nanocrystalline and nanotwinned samples
Fig. 2(a) and (b) show the evolution of creep strain with time in NC and NT samples with under constant applied stress at the same temperature of 1200 K. The typical creep curves obtained from our MD simulations include two stages: primary creep and steady-state creep. In the primary creep stage, the creep strain rapidly increases but the creep strain rate (i.e. tangential slope of creep strain vs. time curve) gradually decreases with increasing of time, reflecting an instantaneous
Conclusion
In summary, we performed a series of large-scale MD simulations for high-temperature creep in NC and NT TiAl alloys and systemically investigated the influences of grain size, temperature, applied stress and twin thickness on their creep behaviors and mechanisms. The simulation results showed that for the NC and NT TiAl alloys, the creep mechanisms in the low-, moderate- and high-stress regimes were diffusion, GB sliding and dislocation activities, respectively, which is consistent with
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
X.L. gratefully acknowledges the Beijing Natural Science Foundation, China (Grant No. Z180014) and the National Science and Technology Major Projec, China (Grant No. 2017-VI-0003-0073). All the simulations were performed on the TianHe-1 supercomputer at the National Supercomputer Center in Tianjin.
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