Christopher Sebastian

An approach to the validation of computational solid mechanics models for strain analysis

The need to provide strong evidence of the validity of predictions from computational solid mechanics models used in engineering design decisions is discussed. A new procedure is proposed, based on image decomposition, for reducing the dimensionality of strain field data from models and experiments and then comparing the resultant feature vectors via a simple linear correlation in which validation is deemed to be achieved when the coordinate pairs from the two feature vectors lie within a scatter band defined by the minimum measurement uncertainty. The procedure is illustrated by some simple examples that allow the advantages and drawbacks of the approach to be highlighted. It is anticipated that the procedure could become part of a corporate plan or regulatory process for verification and validation of computational solid mechanics models.

A reference material for establishing uncertainties in full-field displacement measurements

A simple reference material for establishing the minimum measurement uncertainty of optical systems for measuring 3D surface displacement fields in deforming objects is described and its use demonstrated by employing 3D digital image correlation as an exemplar technique. The reference material consists of a stepped bar, whose dimensions can be scaled to suit the application, and that can be clamped rigidly at its thick end to create an idealized cantilever. The cantilever was excited at resonance to generate out-of-plane displacements and, in a separate experiment, loaded statically in-plane to provide in-plane displacement fields. The displacements were measured using 3D digital image correlation and compared to the predicted displacement fields derived from tip deflections obtained using a calibrated transducer that provided traceability to the national standard for length. The minimum measurement uncertainties were evaluated by comparing the measured and predicted displacement fields, taking account of the uncertainties in the input parameters for the predictions. It was found that the minimum measurement uncertainties were less than 3% for the Cartesian components of displacement present during static in-plane bending and less than 3 µm for out-of-plane displacements during dynamic loading. It was concluded that this reference material was more straightforward to use, more versatile and yielded comparable results relative to an earlier design.

Comparison of Numerical and Experimental Strain Measurements of a Composite Panel Using Image Decomposition

Image decomposition is used to address the problem of accurately and concisely describing the strain in an inhomogeneous composite panel that is bolted to a vehicle structure. In-service, the composite panel is subject to structural loads from the vehicle which can cause unintended damage to the panel. Finite element simulations have been performed with the plan to establish their fidelity using full-field optical strain measurements obtained using digital image correlation. A methodology is presented based on using orthogonal shape descriptors to decompose the data-rich maps of strain into information-preserved data sets of reduced dimensionality that facilitate a quantitative comparison of the computational and experimental results. The decomposition is achieved employing the Fourier transform followed by fitting Tchebichef moments to the maps of the magnitude of the Fourier transform. The results show that this approach is fast and reliably describes the strain fields using less than fifty moments as compared to the thousands of data points in each strain map.

Calibration of a Digital Image Correlation System

The use and results of the procedure published by Standardisation Project for Optical Techniques of Strain measurement (SPOTS) for a successful calibration of a digital image correlation (DIC) system are described. The details of the calibration specimen used are discussed together with procedure and criteria that must be met to achieve an acceptable calibration. The DIC system was evaluated over a strain range of 289 to 2110 μstrain, with a resulting calibration uncertainty ranging from 14 to 28.7 μstrain. The optical strain measurements were obtained from images taken directly from the bare metal surface, which had been prepared with grit paper, as opposed to generating a speckle pattern by painting the surface.

Image Analysis for Full-Field Displacement/Strain Data: Method and Applications

Recent advances in measurement techniques, including digital image correlation, automated photoelasticity, electronic speckle pattern interferometry and thermoelastic stress analysis, permit full-field maps of displacement or strain to be obtained easily. They provide large volumes of mostly redundant data, which should be condensed to the essential information to permit straightforward processes such as validations of computational models or damage assessments. A way to do this is by image processing, an important aspect of which is the definition of an orthogonal basis (orthogonal kernel functions). Generally, this is problem dependent and requires some skill from the analyst if the number of image features (the coefficients of the orthogonal basis) is to be restricted to a suitably small number. Advantage may be taken of patterns of symmetry, for example cyclically symmetric patterns are well-suited to treatment by Zernike polynomials and rectangular patterns are well-suited to treatment by Fourier series. The Zernike and Fourier kernels are continuous polynomials with orthogonality properties that require integration and must be discretised. The discrete Tchebichef polynomials are ideal for the treatment of full-field information at multiple discrete data points. In many cases the data field is localised around a particular feature, such as local strain around a hole in a tension-test specimen. In this case, the polynomial basis should similarly be localised by various forms of scaling – this requires the application of the Gram-Schmidt procedure to maintain orthogonality. The image features (sometimes called shape features) are meaningful and may be used to identify particular patterns in the data – e.g. for detecting cracks or other forms of damage. When assembled in a feature vector, the distance between feature vectors from measured and numerical results are useful for refining numerical models. In this paper the principles of image analysis, as applied to full-field displacement/strain data are explained and experimental examples are used to illustrate the practical usefulness of the method. The applications include (i) vibration mode shapes of laminated honeycomb structures and, (ii) strain in an aluminium plate with a central hole in tension.

Stereo-DIC Measurements of Thermal Gradient Effects on the Vibratory Response of Metals

Thermomechanical problems have been much less studied than their room temperature counterparts as challenges arise both with metrology and with interpretation of results. This effort aims to shrink this knowledge gap by investigating the influence of thermal effects on the high frequency vibratory response of metals. The present study concentrates on how an inhomogeneous temperature field (max. 600 °C) affects the vibratory response, and specifically mode shapes and resonant frequencies, of a vibrating plate. A plate made of a nickel-based superalloy, Hastelloy X, was heated by induction heating and the temperature distribution was estimated by measuring the out-of-plane curvature resulting form heating. Harmonic vibratory loading at frequencies exceeding 1 kHz was applied using a programmable shaker. Stereo-vision digital image correlation (stereo-DIC) was used to obtain a full-field representation of the vibrating plate. An image decomposition analysis technique based on Tchebichef polynomials was used to compare room and high temperature mode shapes. Results indicate that there is a small influence of temperature on resonant frequencies, even though mode shapes remain similar between room and high temperature vibration.

Image processing of full-field strain data and its use in model updating

Finite element model updating is an inverse problem based on measured structural outputs, typically natural frequencies. Full-field responses such as static stress/strain patterns and vibration mode shapes contain valuable information for model updating but within large volumes of highly-redundant data. Pattern recognition and image processing provide feasible techniques to extract effective and efficient information, often known as shape features, from this data. For instance, the Zernike polynomials having the properties of orthogonality and rotational invariance are powerful decomposition kernels for a shape defined within a unit circle. In this paper, full field strain patterns for a specimen, in the form of a square plate with a circular hole, under a tensile load are considered. Effective shape features can be constructed by a set of modified Zernike polynomials. The modification includes the application of a weighting function to the Zernike polynomials so that high strain magnitudes around the hole are well represented. The Gram-Schmidt process is then used to ensure orthogonality for the obtained decomposition kernels over the domain of the specimen. The difference between full-field strain patterns measured by digital image correlation (DIC) and reconstructed using 15 shape features (Zernike moment descriptors, ZMDs) at different steps in the elasto-plastic deformation of the specimen is found to be very small. It is significant that only a very small number of shape features are necessary and sufficient to represent the full-field data. Model updating of nonlinear elasto-plastic material properties is carried out by adjusting the parameters of a FE model until the FE strain pattern converges upon the measured strains as determined using ZMDs.

The interaction of fatigue cracks with a residual stress field using thermoelastic stress analysis and synchrotron X-ray diffraction experiments

This article presents an experimental study on the fatigue behaviour of cracks emanating from cold-expanded holes utilizing thermoelastic stress analysis (TSA) and synchrotron X-ray diffraction (SXRD) techniques with the aim of resolving the long-standing ambiguity in the literature regarding potential relaxation, or modification, of beneficial compressive residual stresses as a result of fatigue crack propagation. The crack growth rates are found to be substantially lower as the crack tip moved through the residual stress zone induced by cold expansion. The TSA results demonstrated that the crack tip plastic zones were reduced in size by the presence of the residual compressive stresses induced by cold expansion. The crack tip plastic zones were found to be insignificant in size in comparison to the residual stress zone resulting from cold expansion, which implied that they were unlikely to have had a notable impact on the surrounding residual stresses induced by cold expansion. The residual stress distributions measured along the direction of crack growth, using SXRD, showed no signs of any significant stress relaxation or redistribution, which validates the conclusions drawn from the TSA data. Fractographic analysis qualitatively confirmed the influence on crack initiation of the residual stresses induced by the cold expansion. It was found that the application of single compressive overload caused a relaxation, or reduction in the residual stresses, which has wider implications for improving the fatigue life.