Investigation of Viscoelastic-Creep and Mechanical-Hysteresis Behaviors of Hydrostatically Stressed Crystal Using the Phase Field Crystal Method

J Em-Udom,N Pisutha-Arnond

doi:10.1155/2020/2821402

Abstract

The phase field crystal (PFC) method is a density-functional-type model with atomistic resolution and operating on diffusive time scales which has been proven to be an efficient tool for predicting numerous material phenomena. In this work, we first propose a method to predict viscoelastic-creep and mechanical-hysteresis behaviors in a body-centered-cubic (BCC) solid using a PFC method that is incorporated with a pressure-controlled dynamic equation which enables convenient control of deformation by specifying external pressure. To achieve our objective, we use constant pressure for the viscoelastic-creep study and sinusoidal pressure oscillation for the mechanical-hysteresis study. The parametric studies show that the relaxation time in the viscoelastic-creep phenomena is proportional to temperature. Also, mechanical-hysteresis behavior and the complex moduli predicted by the model are consistent with those of the standard linear solid model in a low-frequency pressure oscillation. Moreover, the impact of temperature on complex moduli is also investigated within the solid-stabilizing range. These results qualitatively agree with experimental and theoretical observations reported in the previous literature. We believe that our work should contribute to extending the capability of the PFC method to investigate the deformation problem when the externally applied pressure is required.

Highlights

The phase field crystal (PFC) method has emerged as a computational model with atomistic resolution and diffusive time scale
The method has an advantage over molecular dynamics (MD) in terms of the time scale that is not restricted by lattice vibration time; this is due to the specification of the order parameter as the local-time-average atomic number density and the evolution of the order parameter through dissipative dynamics
We show the viscoelastic-creep behavior exhibited by the PFC-pressure controlled dynamic (PCD) model and demonstrate the dependence of this behavior on ΔP0 and Lfedreefn

Summary

Introduction

The phase field crystal (PFC) method has emerged as a computational model with atomistic resolution and diffusive time scale. The PFC method was interpreted and derived according to the classical density functional theory (CDFT) of the freezing point of view [4] This derivation provided an additional field variable which extended the capability of the PFC method to investigate the material phenomena in a more complex situation such as phase transformation [4, 17] and segregation-induced grain-boundary premelting [18] in binary alloys. The density periodic field φ can be expressed in terms of Fourier expansion of the form φðr, ρÞ = ρ + 〠AjeiGj⋅r + c:c:, ð2Þ j where Gj is a reciprocal lattice vector (RLV), Aj is an amplitude of the density wave corresponding to Gj, ρ is an average atomic number density, and c.c. denotes a complex conjugate. To simplify the expressions in Equation (1), one can nondimensionalize the variables by using the following substitutions [2]:

Objectives

Methods

Results

Conclusion