Statistical calibration and uncertainty quantification of complex machining computer models

Finite element based machining process models are used in research and industry for process design and optimization. These models require a constitutive description of the material behavior to accurately model and predict process responses such as cutting forces, temperatures, and residual stress. Calibration of these models to low-strain uniaxial dynamic compression experiments can be troublesome since the machining process generally imposes much larger strains than uniaxial compression. Calibration of finite element models directly to machining data is generally difficult since the models are computationally expensive and nonlinear optimization methods for estimating the unknown calibration parameters yield non-unique solutions and require many iterations. In this work we utilize a nonstationary Gaussian Process surrogate model to emulate the finite element response and calibrate to experimental orthogonal cutting tests using a Bayesian inference framework. We assume that the material yield behavior can be described by the Johnson-Cook material flow model. We find that the nonstationary Gaussian Process model is an good surrogate for the complex finite element model. Cutting forces measured from orthogonal tube turning experiments were used for calibration. Validation is performed using a separate response variable - the cut chip thickness. Calibration results illustrate a preference for material models with low hardening rates, which alleviates issues such as over-prediction of strain hardening behavior when using the Johnson-Cook material flow model. The Bayesian formulation also captures the uncertainty in the Johnson-Cook parameters, which can be used to quantify the uncertainty in the machining process responses. The methods presented here are general and can be used for more complex constitutive and tribological models for machining and other complex manufacturing processes.