Estimating Material Properties Under Extreme Conditions by Using Bayesian Model Calibration with Functional Outputs

Abstract

Summary Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto‐correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment‐specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.

Multi-megabar Dynamic Strength Measurements of Ta, Au, Pt, and Ir

“…The simulation parameter scalings refer to: (1) global multiplication of the magnetic field boundary condition (ie. drive uncertainty) which has been determined previously [29], (2) the initial strength ( Y 0 ) which propagates linearly to high pressures (see Eq. 8), and (3) the linear anelastic theory constants B(L∕b) 2 and B∕(nb 2 ) described in [20].…”

“…1. Bayesian calibration frameworks are being actively developed specifically for these types of dynamic experiments in which velocimetry is the primary diagnostic and a predictive simulation capability exists [29,30]. There are two features of Bayesian approaches which are appealing for this application.…”

Bayesian calibration of strength parameters using hydrocode simulations of symmetric impact shock experiments of Al-5083

“…In order to maintain a simple and narrow focus for this effort, we do not consider uncertainty (or parameter variations) in all possible aspects of the model. For example, although there is (certainly) uncertainty in the parameters for the equation of state, 25 they were held fixed in this work. We primarily restrict our attention to the variation of model parameters for the Johnson-Cook strength model, although there are a few additionally included variables noted here.…”

“…Presumably, the parameters are often estimated by manually adjusting them until they produce an acceptable visual match. Brown and Hund 25 is a notable exception from the statistics literature. They follow a procedure similar to the one that we use, although they handle the functional nature of the output in a different manner.…”

Modelo matemático multivariante para estimar el valor CTOD en función de propiedades mecánicas, químicas y microestructurales aplicado a uniones soldadas para la industria Offshore = Multivariate analysis to relate CTOD values with material properties in steel welded joints for the Offshore industry

“…La prueba CTOD requiere la preparación de una entalla, con una geometría muy específica, que promueva la nucleación de una grieta estable y uniforme en un área delimitada . El uso de modelos matemáticos predictivos para el estudio de propiedades de los materiales está ampliamente tratado en la bibliografía (García et al, 2008, Rajakumar, 2012, Mohammed et al, 2016, Brown, 2018 (Moskovic, 1993), endurecimiento por acritud, …, etc. En esas pruebas, generalizando, se somete al material a solicitaciones de severidad creciente hasta que la fuerza impulsora de crecimiento de la grieta exceda la resistencia a la fractura del material.…”