Void growth and coalescence in single crystal nickel
Molecular dynamics simulations using Modified Embedded Atom Method (MEAM) potentials were performed to analyze material length scale influences on damage progression of single crystal nickel. Damage evolution by void growth and coalescence was simulated at very high strain rates (108–1010/s) involving four specimen sizes ranging from _5000 to 170,000 atoms with the same initial void volume fraction. 3D rectangular specimens with uniform thickness were provided with one and two embedded cylindrical voids and were subjected to remote uniaxial tension at a constant strain rate. Void volume fraction evolution and the corresponding stress–strain responses were monitored as the voids grew under the increasing applied tractions. The results showed that the specimen length scale changes the dislocation pattern, the evolving void aspect ratio, and the stress–strain response. At small strain levels (0–20%), a damage evolution size scale effect can be observed from the damage-strain and stress–strain curves, which is consistent with dislocation nucleation argument of Horstemeyer et al. playing a dominant role. However, when the void volume fraction evolution is plotted versus the applied true strain at large plastic strains (>20%), minimal size scale differences were observed, even with very different dislocation patterns occurring in the specimen. At this larger strain level, the size scale differences cease to be relevant, because the effects of dislocation nucleation were overcome by dislocation interaction. This study provides fodder for bridging material length scales from the nanoscale to the larger scales by examining plasticity and damage quantities from a continuum perspective that were generated from atomistic results.
Author(s): G.P. Potirniche, Mark F. Horstemeyer, G.J. Wagner, and P.M. Gullett
Corresponding Author: Mark F. Horstmeyer
Initial geometry and BCs
At macroscale, engineering materials fail by nucleation, growth and coalescence of voids. Accumulation of such voids, cavities, or cracks inside of the material is called a damage, or porosity or void volume fraction. The formula that defines damage is given by: Φ = Vv/V, where Vv is the volume of voids, and V is the volume of the aggregate material. New voids are introduced in the material due to increased effective stress. The increment of void volume fraction is due to void nucleation, void growth and void coalescence. This study is focused on void growth and void coalescence. The study on single void growth and multiple voids coalescence at the nanoscale is performed using molecular dynamics simulations with MEAM potentials. Molecular dynamics(MD) is a powerful computational method to simulate elastoplastic deformation and material failure at the nanoscale.
The study for was performed for four specimens of increasing size in FCC single crystal nickel. Figure 1 shows the geometry and boundary conditions for the study of single void growth in nickel single crystal. The specimen is a plate with a central hole subjected to uniaxial strain rate. In MD, the specimens contained a number of atoms ranging from N = 4408 atoms to N = 171,376 atoms. Similarly, Figure 2 shows the geometry and boundary conditions for the study of voids coalescence. The specimens contained two voids with initial void volume fraction equal to that of one-void specimens. The number of atoms in the specimens ranges from N = 5052 atoms to N = 175,172 atoms. The geometrical dimensions for both one-void and two-void specimens ranged from a few nanometers to tens of nanometers.
Results and Discussion
The void growth phenomena were captured in the study using molecular dynamics principles. For the purpose of studying void growth mechanisms, a strain rate of 1010/s was considered. The specimens were loaded with uniaxial tension until total applied strain reached 41% true strain. The failure of material was seen in both single void and two void specimens. Figure 3 shows the stress-strain curve of the one-void nickel specimen with N = 4,408 atoms indicating the stages of the specimens' internal evolution of damage. From Fig. 3, it can be observed that uniaxial stress-strain response for one-void specimen at the lowest material length comprises an elastic portion up to a true strain 14.5% and a value of the yield strength of about 20.5 GPa. Void nucleation and void growth lead to the increase of void volume fraction. The stress resistance of specimen decreased significantly to about 5 GPa at the final true strain of 41%. The necking starts at about 25% strain level. Figure 4 presents the stress-strain response for the one-void specimen and the next largest specimen size (N = 18,448 atoms). Fig. 4< shows that the dislocation pattern for the larger specimen is different than the dislocation pattern for smallest material length scale. The point of dislocation nucleation varies as the material length scale is changed. Another observed feature is the change in aspect ratio of the changing void.
Triaxility variations with uniaxial applied strain, at the smallest and the largest specimen sizes are presented in Fig. 12(a) and (b) for the one-void and two-void specimens, respectively. The fluctuation in triaxiality values around 0.8 was observed for both cases. Similarly, Figure 11(a) shows that for the one-void specimens, the yield stress increased from 15 to 20.5 GPa as the strain rate was increased two orders of magnitude. The same qualitative conclusion apply to the analysis of the stress-strain responses for two-void specimens as seen in Fig. 12(b).
Molecular dynamics simulations showing damage evolution at four increasing specimen sizes were performed to study the evolution of void growth and coalescence under very high strain rates. One-void specimens and two-void specimens were increased in size to represent an increasing length scale. Given that only uniaxial tension of one crystalline orientation free of initial defects was used, the main conclusions are the following:
The authors are grateful to the Center for Advanced Vehicular Systems at Mississippi State University for supporting this study. The work of G.J. Wagner and P.M. Gullett is supported by U.S. DOE Contract AC04-94AL85000.