Matthew P. Miller

Far-field high-energy diffraction microscopy: a tool for intergranular orientation and strain analysis

The far-field high-energy diffraction microscopy technique is presented in the context of high-energy synchrotron x-ray diffraction. For each grain in an illuminated polycrystalline volume, the volume-averaged lattice orientations, lattice strain tensors, and centre-of-mass (COM) coordinates may be determined to a high degree of precision: better than 0.05°, 1 × 10−4, and 0.1 pixel, respectively. Because the full lattice strain tensors are available, corresponding mean stress tensors may be calculated unambiguously using single-crystal elastic moduli. A novel formulation for orientation indexing and cell refinement is introduced and demonstrated using two examples: first, sequential indexing and lattice refinement of a single-crystal ruby standard with known COM coordinates; and second, indexing and refinement of simulated diffraction data from an aggregate of 819 individual grains using several sample rotation ranges and including the influence of experimental uncertainties. The speed of acquisition and penetration depth achievable with high-energy (that is, >50 keV) x-rays make this technique ideal for studies of strain/stress evolution in situ, as well as for residual stress analysis.

Modeling large strain multiaxial effects in FCC polycrystals

Abstract Results from compression, torsion, compression-followed-by-torsion and torsion-followed-by-tension experiments are presented for 304L stainless steel at room temperature. Very distinct stress state-dependent loading compared to uniaxial compression at the same uniaxial equivalent strain. Secondary axial effects are measured during torsional loading as well. Pertinent inelastic deformation processes are discussed and explanations are offered for the observed stress state-dependent phenomena, including morphological changes of both texture and deformation substructure. We review basic micro- and macro-scale model frameworks for modelling large deformation stress-strain behavior. Efforts to capture stress state-dependent phenomena using such formulations are presented. A macro-scale model framework is proposed which uses the third invariant of overstress, J 3 ∗ , to delineate stress state effects.

Experimental measurement of lattice strain pole figures using synchrotron x rays

This article describes a system for mechanically loading test specimens in situ for the determination of lattice strain pole figures and their evolution in multiphase alloys via powder diffraction. The data from these experiments provide insight into the three-dimensional mechanical response of a polycrystalline aggregate and represent an extremely powerful material model validation tool. Relatively thin (0.5mm) iron/copper specimens were axially strained using a mechanical loading frame beyond the macroscopic yield strength of the material. The loading was halted at multiple points during the deformation to conduct a diffraction experiment using a 0.5×0.5mm2 monochromatic (50keV) x ray beam. Entire Debye rings of data were collected for multiple lattice planes ({hkl}’s) in both copper and iron using an online image plate detector. Strain pole figures were constructed by rotating the loading frame about the specimen transverse direction. Ideal powder patterns were superimposed on each image for the purpos...

A direct method for the determination of the mean orientation-dependent elastic strains and stresses in polycrystalline materials from strain pole figures

A salient manifestation of anisotropy in the mechanical response of polycrystalline materials is the inhomogeneous partitioning of elastic strains over the aggregate. For bulk samples, the distributions of these intergranular strains are expected to have a strong functional dependence on grain orientations. It is then useful to formulate a mean lattice strain distribution function (LSDF) over the orientation space, which serves to characterize the micromechanical state of the aggregate. Orientation-dependent intergranular stresses may be recovered from the LSDF via a constitutive assumption, such as anisotropic linear elasticity. While the LSDF may be determined directly from simulation data, its experimental determination relies on solving an inverse problem that is similar in character to the fundamental problem of texture analysis. In this paper, a versatile and robust direct method for determining an LSDF from strain pole figures is presented. The effectiveness of this method is demonstrated using synthetic strain pole figures from a model LSDF obtained from the simulated uniaxial deformation of a 1000-crystal aggregate.

Development of automated real-time data acquisition system for robotic weld quality monitoring

Abstract The lack of reliable non-contact, non-destructive, online sensors with the ability to detect defects as they form and with the capacity to operate at high temperatures and in harsh environments is a big obstacle to fully automated robotic welding. This paper presents a non-contact automated data acquisition system for monitoring a robotic gas–metal arc welding process based on laser ultrasonic technology. While a robot welds between two 1040 steel strips, a Nd:YAG Q-switched pulse laser generates ultrasound on one side of the weld by ablation, and a non-contact electro-magnetic acoustic transducer (EMAT) placed on the opposite side of the weld detects ultrasound transmitted through the weld bead. Ablation is employed because high temperature specimens require strong signals to compensate for attenuation within the bulk of the material. The data is then analyzed to determine the time required for ultrasound to travel from the laser source to the EMAT, termed as the time of flight (ToF). When experimental ToF is compared to theoretical ToF, it is determined that surface waves are detected by this system. Therefore, this system can measure weld bead reinforcement distance. In most cases, weld bead geometry is an indication of the weld quality, and can be used as feedback to control a welding process.

Yield Strength Asymmetry Predictions From Polycrystal Elastoplasticity

Since the 1960s, it has been known that elastoplastic polycrystal models predict asymmetries in the yield strength for polycrystals that have been prestrained. After prestraining in tension, a model polycrystal exhibits Bauschinger-like behavior in that it yields in compression at a lower stress magnitude than in tension. Furthermore, the knee of the reloading stress-strain curve is more gradual for compression than for tension. The origins of these behaviors reside in the assumption that links the macroscopic deformation to the deformations in individual crystals. More precisely, the reloading response is biased by the residual stress field which is induced with plastic straining by the anisotropy of the single crystal yield surface. While the earlier work pointed to the polycrystalline origins of the asymmetry, it did not resolve the degree to which the particular linking assumption affects the amount of asymmetry. However, due to the strong influence of the linking assumption on the crystal stresses, the sensitivity of the asymmetry to the linking assumption is expected to be appreciable. In this paper we examine the influence of the linking assumption on the magnitude of the computed yield strength asymmetry of prestrained polycrystals. Elastoplastic polycrystal simulations based on upper bound (Taylor) and lower bound (equilibrium-based) linking assumptions are compared to finite element computations in which elements constitute individual crystals. The finite element model maintains compatibility while satisfying equilibrium in a weak sense and treats the influence of neighboring crystals explicitly. The strength of the predicted Bauschinger effect does depend on the linking assumption, with ‘compatibility first’ models developing stronger yield strength asymmetries.

On the mechanical behaviour of AA 7075-T6 during cyclic loading

The mechanical behavior of an aluminum alloy during uniaxial cyclic loading is examined using finite element simulations of aggregates with individually resolved crystals. The aggregates consist of face centered cubic (FCC) crystals with initial orientations assigned by sampling the orientation distribution function (ODF) determined from the measured crystallographic texture. The simulations show that the (elastic) lattice strains within the crystals evolve as the number of cycles increases. This evolution is attributed to the interactions between grains driven by the local plasticity. Under constant amplitude strain cycles, the average (macroscopic) stress decays with increasing number of cycles in concert with the evolution of the lattice strains. Further, the average number of active slip systems also decreases with increasing cycles, eventually reaching zero as the material response becomes totally elastic at the grain level. During much of the cyclic history only a single slip system is activated in most grains. The simulation results are compared to experimental data for the macroscopic stress and for lattice strains in the unloaded state after 1, 30 and 1000 cycles.

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.

Reverse yield experiments and internal variable evolution in polycrystalline metals

Abstract In this work, sequences of reverse yield experiments are used to measure the evolution of the directionally-dependent contribution to strain-hardening in OFHC copper. It is shown that based upon a 50 microstrain offset definition of yielding, a strength asymmetry commonly known as the Bauschinger effect develops and increases with prestrain. From the perspective of macroscale isotropic/kinematic hardening models, these data imply an increase in the kinematic hardening component of the yield strength. Hardening model parameters are determined by integrating the evolution equations and correlating the experimental data. Consistency between these modeling results and other data on the same heat of OFHC copper is then explored. It is found that while the reverse yield tests show the kinematic hardening variable, α , increasing in magnitude for uniaxial strains up to 20%, the tensor must very quickly change direction in stress space when the straining path is altered. Stress relaxation experiments were conducted and strain rate effects including the decomposition of the rate dependence between the flow rule and the evolution equations are investigated.

Influence of slip system hardening assumptions on modeling stress dependence of work hardening

Abstract Due to the discrete directional nature of processes such as crystallographic slip, the orientation of slip planes relative to a fixed set of loading axes has a direct effect on the magnitude of the external load necessary to induce dislocation motion (yielding). The effect such geometric or textural hardening has on the macroscopic flow stress can be quantified in a polycrystal by the average Taylor factor M . Sources of resistance to dislocation motion such as interaction with dislocation structures, precipitates, and grain boundaries, contribute to the elevation of the critically resolved shear strength τcrss. In continuum slip polycrystal formulations, material hardening phenomena are reflected in the slip system hardness equations. Depending on the model, the hardening equations and the mean field assumption can both affect geometric hardening through texture evolution. In this paper, we examine continuum slip models and focus on how the slip system hardening model and the mean field assumption affect the stress-strain response. Texture results are also presented within the context of how the texture affects geometric hardening. We explore the effect of employing slip system hardnesses averaged over different size scales. We first compare a polycrystal simulation employing a single hardness per crystal to one using a latent hardening formulation producing distinct slip system hardnesses. We find little difference between the amplitude of the single hardness and a crystal-average of the latent hardening values. The geometric hardening is different due to the differences in the textures predicted by each model. We also find that due to the high degree of symmetry in an fcc crystal, macroscopic stress-strain predictions using simulations employing crystal- and aggregateaveraged hardnesses are nearly identical. We find this to be true for several different mean field assumptions. An aggregate-averaged hardness may be preferred in light of the difficulty encountered in experimentally verifying slip system strength in a polycrystal. We also examine model performance under different stress states. We find that, due to a higher degree of geometric softening in torsion, the latent hardening model more closely correlates oxygen free high conductivity copper compression and torsion data than the aggregate-averaged model. Both models predicted similar material hardening rates in torsion and compression, however. Finally, we propose an aggregate-averaged hardening equation with a heightened dependence on the Taylor factor as defined by the average crystal shearing rate that predicts a higher material hardening rate in compression as compared to torsion to correlate the data. We then use the model to predict compression followed by torsion results.