Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Abstract

Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.

Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods

“…It is natural to propose the average of an ensemble of material properties extracted from the microstructures tω pnq u N n"1 to approximate the expected value in (1). Since the sequence of microstructure RVEs are i.i.d.…”

“…The variability in microstructure mainly contributes to the aleatory uncertainty of the prediction, whereas the numerical approximations in the ICME models bridging the structure-property relationship mainly contribute to the epistemic uncertainty. This manuscript is mainly concerned with rigorously addressing the aleatory uncertainty that is induced from the microstructure perspective, while acknowledging that the epistemic uncertainty work is also addressed elsewhere [1].…”

The multifaceted nature of uncertainty in structure-property linkage with crystal plasticity finite element model

“…In this section, we highlight our recent effort [8] in quantifying epistemic uncertainty associated with initial yield behaviors, which are characterized by yield strength 𝜀 Y and yield stress 𝜎 Y at 0.2% offset. In this approach, we impose a uniform prior for all constitutive model parameters.…”

“…A set of five constitutive parameters is used to parametrize a phenomenological constitutive model for stainless steel 304L. At any time, 12 CPFEM simulations are performed concurrently, where the batch configuration is set as (8,4,0). To account for the aleatory uncertainty, we average the loss function over an ensemble of 5 SERVEs, where the mesh of 5 × 5 × 5 is used.…”