Reconstruction of Residual Stress in a Welded Plate Using the Variational Eigenstrain Approach

We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stress-strain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.Comment: 16 pages, 17 figure

Numerical simulation and experimental validation of texture in extruded wires of a bcc metal

We present a comparison between a viscoplastic crystal plasticity finite element simulation of the extrusion process applied to a bcc polycrystal and the experimental evaluation of the preferred orientation (texture) in a tungsten wire by monochromatic synchrotron X-ray diffraction with an area detector. We perform a numerical simulation of sample texture evolution during large extrusion deformation with the elongation factor up to the value of fifty. By matching the predicted Orientation Distribution Functions (ODF) and the pole figures generated on the basis of the simulations to the experimental observations, the extrusion strain experienced by the sample during processing can be estimated

Eigenstrain boundary layer modelling of the yttria-partially stabilised zirconia–porcelain interface in dental prostheses

The exceptional strength and appealing aesthetics of porcelain veneered yttria partially stabilised zirconia (YPSZ) dental prostheses, has led to the widespread adoption of these materials. However, near-interface chipping of the porcelain remains the primary failure mode. Advanced experimental techniques have recently revealed significant variations in residual stress and YPSZ phase distribution at the YPSZ–porcelain interface. Therefore, in order to improve existing understanding and effectively optimise the production of these devices, an enhanced model of the YPSZ coping that includes these newly discovered phenomena is presented in this study. Macroscale stresses are shown to arise through the uneven temperatures within the coping during the sintering process and the coefficient of thermal expansion mismatch with the porcelain during veneering. In contrast, microscale stresses are driven by the YPSZ phase transformation and the associated volumetric expansion. The eigenstrain approach proposed here was found to demonstrate a good match between the phase variation determined experimentally, and the corresponding residual stress distribution showed an effective comparison with the empirical measurements. The proposed technique is a straightforward but powerful method for simulating this dominant mechanical behaviour, with significant potential to combine the resulting expressions into existing models. These enhanced simulations are the only viable approach for the precise, reliable and systematic optimisation of prosthesis production parameters that are needed to significantly reduce prosthesis failure rates.</p

Analytical computation of the lattice rotations induced by 3D dislocation loops

This paper presents the derivation of expressions for the lattice rotations induced by a triangular dislocation loop in an isotropic, elastic medium, based on the classical displacement field solution for a triangular dislocation loop. Using the simple example of a triangular dislocation loop with one segment of edge character, one segment of screw character and a mixed character segment, a comparison of the 3D lattice rotation fields with those predicted for straight, infinitely long 2D dislocations is made. Agreement is excellent. As an illustration of the utility of the rotation solution, the lattice rotations induced by a Frank-Read Source are studied at different stages during its evolution. The dislocation segment positions were computed using the discrete dislocation dynamics code ParaDiS. Post-processing of the lattice rotation maps in terms of lattice orientation spread reveals preferential lattice misorientation or streaking which is consistent with the single active slip system in the simulation. Streaking is a feature frequently observed in micro-diffraction measurements. The availability of the lattice rotation solution makes it possible to evaluate the lattice rotations arising from any 3D distribution of dislocation segments. This allows the computation of predicted diffraction patterns from computed dislocation substructures for direct comparison with experimental measurements. It also makes the inclusion of lattice rotations into 3D dislocation dynamics codes possible. This effect has thus far been treated as small, but was shown to be important in 2D dislocation dynamics simulations

Multi-scale characterisation of the 3D microstructure of a thermally-shocked bulk metallic glass matrix composite

Bulk metallic glass matrix composites (BMGMCs) are a new class of metal alloys which have significantly increased ductility and impact toughness, resulting from the ductile crystalline phases distributed uniformly within the amorphous matrix. However, the 3D structures and their morphologies of such composite at nano and micrometre scale have never been reported before. We have used high density electric currents to thermally shock a Zr-Ti based BMGMC to different temperatures, and used X-ray microtomography, FIB-SEM nanotomography and neutron diffraction to reveal the morphologies, compositions, volume fractions and thermal stabilities of the nano and microstructures. Understanding of these is essential for optimizing the design of BMGMCs and developing viable manufacturing methods

Intragranular residual stress evaluation using the semi-destructive FIB-DIC ring-core drilling method

Titanium aluminide (TiAl) is a lightweight intermetallic compound with a range of exceptional mid-to-high temperature mechanical properties. These characteristics have the potential to deliver significant weight savings in aero engine components. However, the relatively low ductility of TiAl requires improved understanding of the relationship between manufacturing processes and residual stresses in order to expand the use of such components in service. Previous studies have suggested that stress determination at high spatial resolution is necessary to achieve better insight. The present paper reports progress beyond the current state-of-the-art towards the identification of the near-surface intragranular residual stress state in cast and ground TiAl at a resolution better than 5 μm. The semi-destructive ring-core drilling method using Focused Ion Beam (FIB) and Digital Image Correlation (DIC) was used for in-plane residual stress estimation in ten grains at the sample surface. The nature of the locally observed strain reliefs suggests that tensile residual stresses may have been induced in some grains by the unidirectional grinding process applied to the surface. © (2014) Trans Tech Publications, Switzerland

The Principle of Strain Reconstruction Tomography: Determination of Quench Strain Distribution from Diffraction Measurements

Evaluation of residual elastic strain within the bulk of engineering components or natural objects is a challenging task, since in general it requires mapping a six-component tensor quantity in three dimensions. A further challenge concerns the interpretation of finite resolution data in a way that is commensurate and non-contradictory with respect to continuum deformation models. A practical solution for this problem, if it is ever to be found, must include efficient measurement interpretation and data reduction techniques. In the present note we describe the principle of strain tomography by high energy X-ray diffraction, i.e. of reconstruction of the higher dimensional distribution of strain within an object from reduced dimension measurements; and illustrate the application of this principle to a simple case of reconstruction of an axisymmetric residual strain state induced in a cylindrical sample by quenching. The underlying principle of the analysis method presented in this paper can be readily generalised to more complex situations.Comment: 10 pages, 6 figure

The Principle of Strain Reconstruction Tomography: Determination of Quench Strain Distribution from Diffraction Measurements

Evaluation of residual elastic strain within the bulk of engineering components or natural objects is a challenging task, since in general it requires mapping a six-component tensor quantity in three dimensions. A further challenge concerns the interpretation of finite resolution data in a way that is commensurate and non-contradictory with respect to continuum deformation models. A practical solution for this problem, if it is ever to be found, must include efficient measurement interpretation and data reduction techniques. In the present note we describe the principle of strain tomography by high energy X-ray diffraction, i.e. of reconstruction of the higher dimensional distribution of strain within an object from reduced dimension measurements; and illustrate the application of this principle to a simple case of reconstruction of an axisymmetric residual strain state induced in a cylindrical sample by quenching. The underlying principle of the analysis method presented in this paper can be readily generalised to more complex situations.Comment: 10 pages, 6 figure

The Principle of Strain Reconstruction Tomography: Determination of Quench Strain Distribution from Diffraction Measurements

Evaluation of residual elastic strain within the bulk of engineering components or natural objects is a challenging task, since in general it requires mapping a six-component tensor quantity in three dimensions. A further challenge concerns the interpretation of finite resolution data in a way that is commensurate and non-contradictory with respect to continuum deformation models. A practical solution for this problem, if it is ever to be found, must include efficient measurement interpretation and data reduction techniques. In the present note we describe the principle of strain tomography by high energy X-ray diffraction, i.e. of reconstruction of the higher dimensional distribution of strain within an object from reduced dimension measurements; and illustrate the application of this principle to a simple case of reconstruction of an axisymmetric residual strain state induced in a cylindrical sample by quenching. The underlying principle of the analysis method presented in this paper can be readily generalised to more complex situations.Comment: 10 pages, 6 figure