Bayesian Calibration of Material Strength Model for Ti-Al6-V4.*

In multi-physics, dynamic loading simulations, where the system undergoes wide ranges of strain,

strain rate, and temperature, it is crucial to have good understanding of the uncertainties

associated with the material models. The models are extrapolated beyond the regime where

the experimental data are available; hence the treatment of the model form discrepancy becomes nontrivial.

We adopt an approach in which model form discrepancies are projected onto the parameter space

and the uncertainty estimation of the parameters encompasses the sources of error.

We describe three calibration methods based on the Bayesian statistics (pooled, hierarchical, and clustered)

and discuss how they differ in terms of estimated parameter posterior distributions and uncertainties, given the data.

In particular, we demonstrate the flexibility of the hierarchical approach, which also allows incorporating

various types of experimental data in the calibration.

These methods have been implemented in a framework called Impala, at LANL, and it has been applied to

the Preston-Tonks-Wallace (PTW) viscoplasticity model. One feature of Impala we focus on is its capability

to extract the uncertainty bounds from the posterior distribution, at any specified state values of strain,

strain rate, and temperature.

Using Impala and the data from quasi-static (QS), split Hopkins pressure bar (SHPB), and Taylor-cylinder

experiments, we have estimated the optimal and bounding PTW parameter sets for Ti-6Al-4V.

We then applied these parameters to the impact simulations of an impala horn, which is similar to

Taylor cylinder but with a smaller radius at the end point, to demonstrate how the bounding cases

perform and how the uncertainties are manifested.