Dislocation Density-Based Finite Element Method Modeling of Ultrasonic Consolidation

Abstract

A dislocation density based constitutive model has been developed and implemented into a crystal plasticity quasi‐static finite element framework. This approach captures the statistical evolution of dislocation structures and grain fragmentation at the bonding interface when sufficient boundary conditions pertaining to the Ultrasonic Consolidation process are prescribed. Hardening is incorporated using statistically stored and geometrically necessary dislocation densities (SSDs and GNDs), which are dislocation analogs of isotropic and kinematic hardening respectively. The GND considers strain‐gradient and thus renders the model size‐dependent. The model is calibrated using experimental data from published refereed literature and then validated for the Aluminum 3003 alloy. Introduction As a direct result of ongoing research efforts in ultrasonic consolidation (UC) worldwide [1], it has become apparent that a new approach to modeling of UC bonding is needed. A model which provides a better understanding of the effects of process parameter changes on grain refinement, plastic deformation and bonding during UC will better enable researchers to predict which materials will bond, how the mechanical properties of UC-produced parts can be improved, and how to better design the next generation of UC equipment. The continuum properties of parts made using UC are strongly dependent upon the micromechanics of the bonded interface [1]. Interfacial-scale microstructures can be studied fundamentally using electron microscopy [1] and can be used to correlate atomic and mesoscopic mechanisms of deformation to their continuum counterparts. A dislocation density-based crystal plasticity Finite Element Model (FEM) can capture the statistical distribution of dislocations, partials and various deformation mechanisms at the bonding interface as inputs to predict macroscopic deformation profiles as a function of energy input characteristics. These input characteristics are a function of the process parameters used in a UC machine, namely vibration amplitude, normal force, ultrasonic frequency, welding speed, sonotrode geometry and temperature. Problem Formulation It has been shown that material sheets subjected to UC undergo inhomogeneous plastic deformation through their thickness [1]. Classical continuum plasticity theories do not fully explain this phenomenon [2]. Therefore, a study of strain localization and grain refinement at the material interfaces during UC bonding is required. The following steps lead to the calculation of these localized strains and their effects. Large Deformation Quasi-Static Crystal Plasticity Description The deformation map in space and time is described by the total deformation gradient tensor F (Figure 1). Applying the Kroner-Lee assumption, F is decomposed into elastic Fe and plastic gradient Fp tensors using multiplicative operator theory