Donald E. Boyce

On the influence of crystal elastic moduli on computed lattice strains in AA-5182 following plastic straining

Crystal lattice plane spacing is modified by the application of stress. The changes in spacing can be measured with neutron diffraction and used to determine the elastic strains in loaded crystals. Using finite element methods, elastic strains can be computed under loading that mimics the experiment. The quality of comparisons between the measured and computed strains depends strongly on accurate knowledge of parameters that quantify the single crystal elastic and plastic responses. For one aluminum alloy in particular, we have found that we can improve the match of lattice strains through careful choice of the single crystal elastic moduli. The parameters are selected on the basis of comparisons between the experimental results and a series of simulations in which the single crystal moduli were varied systematically. Good correspondence is obtained for a set of moduli with higher single crystal anisotropy than those of pure aluminum.

A novel optimization-based pole-figure inversion method: comparison with WIMV and maximum entropy methods

An optimization-based method for pole-figure (PF) inversion that utilizes the orientation distribution function (ODF) gradient for conditional control of the solution is presented. The novel PF inversion method, coined the hybrid {\cal H}^1-seminorm minimization (HHSM), is empirically shown to be versatile, general and robust in the presence of simulated experimental errors. Finite elements (FE) and Rodrigues space are used for the representation and parameterization of the orientation space throughout. The versatility of the FE representation is significantly enhanced from previous implementations by introducing a method for obtaining discrete approximations to spherical harmonic modes from the local FE basis functions. A comparative study with similar implementations of the basic WIMV algorithm and the maximum entropy method is undertaken using several model ODFs of varying sharpness and symmetry. Randomly distributed noise is added to the synthetic PFs to simulate experimental errors and assess the stability of each method. Solution consistency is assessed by inverting two sets of measured PFs, one complete, one incomplete, using several meshes on the orientation space with an increasing number of degrees of freedom. The HHSM method is shown to compare favorably in tests with both the WIMV method and the maximum entropy method.

Pole Figure Inversion Using Finite Elements Over Rodrigues Space

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

Modeling Damage Evolution in Friction Stir Welding Process

The evolution of voids (damage) in friction stir welding processes was simulated using a void growth model that incorporates viscoplastic flow and strain hardening of incompressible materials during plastic deformation. The void growth rate is expressed as a function of the void volume fraction, the effective deformation rate, and the ratio of the mean stress to the strength of the material. A steady-state Eulerian finite element formulation was employed to calculate the flow and thermal fields in three dimensions, and the evolution of the strength and damage was evaluated by integrating the evolution equations along the streamlines obtained in the Eulerian configuration. The distribution of internal voids within the material was qualitatively compared with experimental results, and a good agreement was observed in terms of the spatial location of voids. The effects of pin geometry and operational parameters such as tool rotational and travel speeds on the evolution of damage were also examined.

Three‐Dimensional Modeling of Void Growth in Friction Stir Welding of Stainless Steel

The growth of internal voids in the process of friction stir welding of stainless steel was simulated using a damage model that considers both strain hardening and porosity evolution. In the void growth equations, the mean stress (hydrostatic stress) was scaled by the state variable for plastic flow resistance, i. e. strength. The damage model was coupled with the viscoplastic deformation and thermal processes using a steady‐state Eulerian formulation in a finite element scheme. The porosity and strength were calculated by integration of the evolution equations along streamlines of the flow field. The distributions of microvoids as well as the strength within the material were obtained. These distributions were used to model the effects of operational parameters such as the tool rotational and translational speeds as well as the pin threads on the growth of porosity.

Overview of Texture Evolution during Friction Stir Welding of Stainless Steel Using Crystal Plasticity and EBSD

Texture evolution during friction stir welding of stainless steel was investigated using both predictions by crystal plasticity and EBSD measurements. Two- and three-dimensional Eulerian formulations are used to model friction stir welding. Plane strain deformation is assumed in a two-dimensional model, and an initial uniform texture changes into a torsion texture with monoclinic sample symmetry after deformation. Around the tool pin, the texture strengthens, weakens and restrengthens repeatedly. It is found from a simple circular streamline model that the relative magnitudes of the deformation rate and spin along the streamlines decide textural stability. In order to consider more complicated material behaviors, such as movement along the thickness direction due to a threaded tool pin and a tool shoulder, a three-dimensional Eulerian formulation is also implemented. Materials starting under the tool shoulder travel down to the bottom, producing the longest material streamlines. Those material points are predicted to have stronger texture components than others. EBSD results are compared with the predictions.

2‐D Modeling of Friction Stir Welding by Eulerian Formulation

Friction stir welding (FSW) is a solid state joining process that induces large deformations and pronounced heating of two workpieces to accomplish a bond between them. This severe thermomechanical process induces substantial alteration of the microstructure, inducing modification of the crystallographic texture, hardness and grain size. A simplified FSW process based on a 2‐dimensional Eulerian finite element formulation is presented. The formulation couples equations governing the motion, temperature and state evolution to provide a description of the complex thermomechanical process. Texture evolution is predicted using the computed velocity gradients along streamlines of the flow field together with a model for polycrystal plasticity.

Micromechanical Simulation of Deformation of Friction Stir Welded Components

A microstructure‐based finite element formulation for the mechanical response of friction stir welded AL‐6XN stainless steel is presented. The welding process generates regions of substantial variations in material state and properties that contribute to strong heterogeneities in the mechanical behavior of welded components We modeled the system with a multiscale elastoplastic formulation in which polycrystalline behavior is computed as the integrated responses of constituent crystals. Model validation is made through comparisons to post‐test measurements of shape and hardness and to lattice strain measurements from in situ neutron diffraction experiments.