Thursday 8:00 AM

May 25, 2017

Room: Salon I

Location: Ann Arbor Marriott Ypsilanti at Eagle Crest

Pole figures and Electron backscatter diffraction (EBSD) scans are an important input for ICME models of thermomechanical processes. We derive an exact analytical formulation for uncertainty quantification (UQ) in material properties due to variability in microstructural measurements. The measurements are acquired from a set of Titanium alloy samples obtained by compressing a beta forged ingot followed by annealing. The samples were taken from different regions of the original ingot creating variability in the resulting microstructure. The joint multivariate probability distributions of the computed orientation distribution function (ODF) is found using the method of characteristic functions based on a Gaussian model of the pole figures. We also present an analytical solution to compute the uncertainty in linear elastic properties using the method of characteristic functions. Non-linear properties are treated analytically using direct transformation of random variables in the homogenization approach. Analytical methods provide a considerable reduction in computational times compared to numerical UQ methods. Thus, it is recommended that the presented approach be used as a first step to verify more advanced UQ models.

A critical aspect of ICME is the development of tools that predict the impact of microstructure on various physical parameters such as thermal conductivity and fracture. However, those tools are only useful if we can predict their uncertainty and validate their predictions. In this work, we use the DAKOTA code to predict the uncertainty of thermal conductivity and fracture models in the Multiphysics Object Oriented Simulation Environment (MOOSE). These uncertainties are then used to facilitate statistical validation of the models using microstructure data.

The Integrated computational materials science/engineering (ICME) initiative aims to establish the microstructure-property-processing relationships in challenging material design and component development. Variations of microstructure induced by liquid-solid interaction from laser fusion welding are responsible for the property scatter in the welded joints. In this paper, a process map-based ICME approach is developed to generate a design space for laser fusion welding of Ti-6Al-4V alloys. To rationalise the process variability, underlying physical effects at the mesoscale are simulated, and combined to provide a mesoscopic description for the process and hence feed into a mechanical simulation at the macroscale. Rapid melting, weld solidification microstructure, defect formation and micromechanics are modelled using representative temporal and spatial distributions to obtain the statistical information required to construct a property function for the macroscale simulation. A dislocation density based crystal plasticity model is then used to understand the flow behaviour of the weld microstructure using the representative volume elements (RVE) approach. It is demonstrated that scatter in material properties within the welded region has a significant impact on the weld structural integrity. The implications for the established process map, accounting for this property variation is discussed in relation to achieving a minimal-waste manufacturing route and the design criteria needed to obtain the functional integrity.

Crystal plasticity material models capture the anisotropic mechanical response of crystalline matter under load. Their underlying constitutive material descriptions have varying degree of rigorousness from purely phenomenological to dislocation mechanics-based. All such models include adjustable parameters that determine their efficacy in prediction. With increasing applications of structural materials in small scale applications where crystal plasticity material models play a vital role in predicting material deformation behavior, determination of their constitutive parameters becomes quintessential. A successful methodology of estimating model parameters has been through the inverse analysis which involves an optimization algorithm to minimize the error between simulated and experimental response. Moreover, these parameters are at the single crystal level, thus motivating such a comparison based on nanoindentation experiments that can capture the single crystal behavior efficiently. Even though this methodology has been of increased interest lately, a few questions remain unanswered: importance of the fitness function, stability and reproducibility of the methodology with crystal orientation, and the effect of the optimization algorithm selected. In this study, we aim to answer such questions. This work is supported by NSF grant DMR-1411102.

Texture induced strong anisotropy has impeded further application of wrought Mg alloys. This strong anisotropy cannot be fully captured by only macroscopic constitutive modeling with directional distortional hardening. Thus, a multi-scale modeling characterizing anisotropic mechanical behavior for Mg alloys was developed based on the concept of ICME in the current work. A bottom-top approach was employed to obtain material parameters from lower scale to neighboring larger scale to connect nano-, micro-, meso- and macro-scales. More precisely, molecular dynamics simulation in nano-scale was applied to obtain the coefficients for dislocation mobility in micro-scale; the hardening parameters of the crystal plasticity model in meso-scale were obtained by the dislocation dynamics simulation; stress-strain responses for wrought Mg alloy under non-proportional loading were computed by a CPFEM model in meso-scale, and further employed to verify a macro-scale internal state variable (ISV) model for characterization of anisotropic behavior. This multi-scale modeling was validated by comparison between evolution of yield surfaces and experimental observations under non-proportional loading for AZ31 Mg alloy sheet.

A physically-based, multiscale modeling approach has been applied, in tandem with uncertainty quantification, to simulate three-point bending of pure nickel. Downscaling requirements are driven by the complex stress state induced by the three-point bend, which is experimentally obtained as a force-displacement. Those requirements are then met by upscaling from the atomistic length scale to the macroscale. Density functional theory was utilized at the electronic principal’s scale to determine the lattice parameter and equilibrium energy of nickel (Ni), which were then upscaled to the atomistic scale. At the atomistic length scale the Modified Embedded Atom Method was used to calibrate the nickel energy potential curve, which was then used to simulate the motion of a dislocation and, subsequently, to determine the dislocation velocity. The dislocation velocity was then upscaled to the microscale to evaluate the hardening constants of nickel by utilizing Multiple Dislocation Dynamics Plasticity simulations. The hardening constants are upscaled as parameters used in Crystal Plasticity simulations to obtain the stress-strain curves for the three stress states, compression, tension, and shear. The stress-strain curves are upscaled to the macroscale and calibrated using the MSU-ISV Plasticity-Damage Model. The macroscale calibration is fed into Abaqus as a user material model in order to accurately replicate the three-point bending of a thin sheet of pure nickel. Uncertainty was quantified at each length scale as well as propagated throughout the length scales. The force-displacement data obtained from Abaqus is in good agreement with the experimental result.