A modified Johnson–Cook model for the plastic behavior of metals in ultrasonic vibration-assisted upsetting processes

Abstract

In this work, we present a constitutive description of the plastic behavior of the metals and alloys under Ultrasonic Vibration (UV). When UV is imposed, it induces a softening effect on the plastic deformation of metals and alloys, referred to as the acoustoplastic phenomenon. The volumetric softening mechanism of the acoustoplasticity must consider stress superposition and acoustic softening. Taking the Johnson–Cook (JC) constitutive model as the reference for metal thermo-plasticity, the flow stress reduction due to UV is introduced by three types of softening terms: subtractive, multiplicative, and coupled. Those different configurations will be quantified via physical and phenomenological assumptions. For the study and validation of the proposed constitutive models, we focus on a well-known material, 6063 aluminum alloy. The ultrasonic vibration is modeled by an assisted upsetting process of an aluminum billet and compared with experiments. The impact of variations of the strain rate, ultrasonic amplitude, and frequency on the softening behavior of the models are analyzed and compared with available experimental results. We find out that the subtractive and coupled models agreed well with the experimental results showing the errors ranging from 2.4–4.8% and 4.4%–8%, respectively. However, the predictive ability of the multiplicative model exhibits large discrepancies at the low stage of strains following the acceptable predictions at high stains. By understanding the impact of the UV on the acoustoplastic deformation of the metals and alloys we can establish a reliable theoretical framework for prospective numerical studies of the UV-assisted manufacturing processes which is the goal of the current research presented here.