A Multi-Phase Modeling Framework Suitable for Dynamic Applications

Abstract

Under dynamic loading conditions and the associated extreme conditions many metals will undergo phase transformations. The change in crystal structure associated with solid–solid phase transformations can significantly alter the subsequent mechanical response of the material. For the interpretation of experiments involving dynamic loading it is beneficial to have a modeling framework that captures key features of the material response while remaining relatively simple. We introduce a candidate framework and apply it to the metal tin to highlight a range of behaviors that are captured by the model. We also discuss potential extensions to capture additional behaviors that could be important for certain materials and loading scenarios. The model is useful for analysis of results from dynamic experiments and offers a point of departure for more complex model formulations.

Calibration and validation of the foundation for a multiphase strength model for tin

“…This paper calibrates and validates the strength-specific "foundation" for applying the Common Model of Multi-phase Strength and Equation of State (CMMP) 19 to tin (Although the title has changed, this paper is the "in preparation" Ref. 42 in Ref.…”

“…19.). The CMMP 19 framework was recently developed to address the multiphysics problem of simulating multiphase strength along an arbitrary thermomechanical path. To put our work into context for the reader, we outline all the components of the CMMP.…”

“…12,21 Kinetics models for tin are outside of the scope of the experiments presented in this work and have received attention elsewhere. 12,19,22 The next two elements of the CMMP concern strength are controlled by deviatoric (i.e., shear) deformations and are the focus of the calibration efforts in this work. (3) Density and temperature-dependent shear moduli for each solid phase relate elastic deviatoric strains to deviatoric stresses.…”

“…Because of the difficulty of measuring stress-strain curves in non-ambient phases, the multiphase model framework allows a simple description of their strength as a scaled value of the strength model in an ambient phase. 19 The scalar scale factor can potentially be calibrated by simulating high-pressure experiments that are sensitive to strength but do not give explicit calibration data like a stress-strain curve. This pragmatic approach gives some experimental basis for the model but makes simplifying assumptions about hardening and rate-and temperature dependence that should be unique to each phase.…”

“…Preliminary versions of the CMMP calibration presented here were used to model the strength of polycrystalline tin across phase boundaries, 7,12,19 used a framework similar to CMMP, albeit with different constitutive ingredients, including a combined multiphase Birch-Murnagahan equation of state and the Steinberg-Guinan 23 strength model to simulate the longitudinal wave speed 28 and the free surface velocity from plate impact experiments that crossed the β-γ phase boundary in tin. 6 Here, we calibrate a shear modulus model for most solid phases of tin using density functional theory (DFT) calculations.…”