Prediction of mechanical-hysteresis behavior and complex moduli using the phase field crystal method with modified pressure controlled dynamic equation

Abstract

Damping materials have been used in numerous engineering applications. The important property that plays a key role in this type of material is a damping capacity which is related to mechanicalhysteresis behavior of viscoelasticity. During the last decade, the phase-field-crystal (PFC) model has emerged as a robust tool to predict various material phenomena. This density-functional-type model has the advantage over a conventional phase-field model in terms of atomistic resolution and molecular dynamics in terms of computational expense. In this work, we propose a method to predict mechanical-hysteresis behavior and its related complex moduli parameters using a modifiedpressure-controlled dynamics (MPCD) equation incorporating with the PFC model, denoted as PFC-MPCD method, in a three-dimensional solid structure. We modify the previously proposed pressurecontrolled dynamics (PCD) equation by introducing the pressure-time derivative term which allows us to produce the results consistent with the standard linear solid model (SLS) at the broader frequency range. We apply sinusoidal pressure oscillation and compare the results predicted by both models. The results demonstrate that mechanical-hysteresis behavior and complex moduli parameters predicted by PFC-MPCD method are in good agreement with those of SLS model and consistent with numerous experimental observations whereas the results produced by original PCD equation tends to exhibit inaccurate results at the very frequency. We expect that this new PFC-MPCD method can be extended to a more complex system and still be capable to exhibit the accurate mechanical-hysteresis behavior and complex moduli parameters which results in predicting more reliable damping capacity parameter in damping material design. computational technique that incorporates microstructures which influences the material properties and can reproduce a correct mechanical-hysteresis behavior.During the last decade, the phase-field-crystal (PFC) method has appeared as a promising tool to investigate numerous material phenomena. In the PFC model, its free energy functional is minimized by periodic density field which provides elastic effects and microstructural features e.g. multiple crystal orientations, grain boundary and dislocations which is more appealing than conventional phase field (PF) model in terms of self-consistency. Moreover, this method is restricted to operate on diffusive time-scales which give an advantage over molecular dynamics (MD) in terms of computational expense. The PFC model was first introduced by Elder et al [1] which its free energy functional was minimized by periodic function that found in many physical systems even in crystalline structure. This model that incorporated elastic and plastic properties [2] was used to study various range of material phenomena such as phase transformation [3,4], topological defect dynamics such as crack [2,5], elasticity [6-8] to plasticity [9,10]. This method could also be used to model microstructural defects such as vacancy [11], grain...