Atomic-Scale Study of Plastic-Yield Criterion in Nanocrystalline Cu at High Strain Rates

Abstract

Large-scale molecular dynamics (MD) simulations are used to understand the macroscopic yield behavior of nanocrystalline Cu with an average grain size of 6 nm at high strain rates. The MD simulations at strain rates varying from 10 9 s À1 to 8 9 10 9 s À1 suggest an asymmetry in the flow stress values in tension and compression, with the nanocrystalline metal being stronger in compression than in tension. The tension-compression strength asymmetry is very small at 10 9 s À1 , but increases with increasing strain rate. The calculated yield stresses and flow stresses under combined biaxial loading conditions (X-Y) gives a locus of points that can be described with a traditional ellipse. An asymmetry parameter is introduced that allows for the incorporation of the small tension-compression asymmetry. The biaxial yield surface (X-Y) is calculated for different values of stress in the Z direction, the superposition of which gives a full threedimensional (3-D) yield surface. The 3-D yield surface shows a cylinder that is symmetric around the hydrostatic axis. These results suggest that a von Mises-type yield criterion can be used to understand the macroscopic deformation behavior of nanocrystalline Cu with a grain size in the inverse Hall-Petch regime at high strain rates.

Strengthening Behavior and Tension–Compression Strength–Asymmetry in Nanocrystalline Metal–Ceramic Composites

“…The plots suggest higher values for elastic modulus, macroscopic yield stress and flow stress values with an increase in the volume fraction of the reinforcing nanocrystalline Si particles as observed experimentally [5]. The flow stress (oy) is defined as the peak value of the stress in the stress-strain curve [6,7]. The values for the flow stress for the nanocrystalline Al/Si composite for various volume fractions are tabulated in Table 1 for conditions of tensile and compressive loading, respectively.…”

“…The grain size of 6 nm considered here belongs to the inverse Hall-Petch regime (d< 15 nm), where GB sliding/rotation dominates the deformation behavior as compared to dislocations [31]. Recent MD simulations of deformation behavior of nanocrystalline metals at this grain size suggest that higher strain rates result in higher strengths of the nanocrystalline metal as well as a larger asymmetry in the strength values in tension and compression with the nanocrystalline metal being stronger in compression than in tension [6,7]. The higher strain rates further reduce the limited GB sliding/rotation behavior during plastic deformation and thereby render higher flow stress values.…”

“…The reduction in the GB sliding/rotation behavior is greater for loading in compression as compared to tension and thus results in an increased asymmetry at higher strain rates. This strength asymmetry needs to the accounted for in order to use the von Mises type of criterion for the prediction of macro scale behavior at high strain rates [7]. Nanocrystalline Si, on the other hand, has contributions only from the diffusion of disordered atoms at the grain boundaries to plasticity (GB sliding is not observed).…”

Computational Plasticity

“…Atomic-scale study of plastic-yield criterion in nanocrystalline CU is given by Dongare et al (2010). Initial configuration of nanocrystalline Cu with an average grain size of 6nm.…”

“…System consists of approximately 1.2 million atoms arranged in 122 grains, as shown in Fig. In the work of Dongare et al (2010), the biaxial yield surface is calculated by plotting the yield/limit stresses during loading of the nanocrystalline metal by equal/unequal amounts in the X and Y directions and keeping the stress in the Z direction constant (ı x =ı 1 , ı y =ı 2 , and ı 3 =ı z =0). Molecular dynamics (MD) simulations for yield surface are presented.…”