A novel fuzzy digital image correlation algorithm for non-contact measurement of the strain during tensile tests = Développement et validation d'un algorithme de corrélation d'images numériques utilisant la logique floue pour mesurer la déformation pendant les tests de traction
The present thesis is focused on the non-contact and efficient strain measurement using the Digital Image Correlation (DIC) method, which employs the tracking of random speckle pattern for accurate measurement of displacements on a surface of an object undergoing deformation. Specifically, a more efficient DIC algorithm was successfully developed, implemented, and validated. This thesis consists of five parts related to the novel DIC algorithm: (a) the development and implementation, (b) the numerical verification, (c) the experimental validation, for tensile loading, by comparing to the deformation measurements using the strain gauge technique, (d) the investigation of a novel atomization process to reproducibly generate the speckle pattern for accurate tracking, and (e) the analysis of the error sources in the DIC measurements. Specifically, the DIC algorithm was used to exemplarily examine the mechanical properties of polymethyl methacrylate (PMMA) used in skeletal reconstruction. In the DIC algorithm, images of an object are captured as it deforms. Nonlinear optimization techniques are then used to correlate the speckle on the surface of the objects before and after the displacement. This optimization process includes a choice of suitable initial displacement values. The more accurate the estimation of these initial displacement values are, the more likely and the more efficient the convergence of the optimization process is. The thesis introduced a novel, fuzzy logics based processing technique, approximation of the initial values of the displacement for initializing iterative optimization, which more accurately and efficiently renders the displacements and deformations as results. The mathematical formulation of the novel algorithm was developed and then successfully implemented into MATLAB programming language. The algorithmic verification was performed using computer-generated images simulating rigid body displacements and uniform tensile deformations. Specifically, the rigid motion images simulated (1) displacements of 0.1-1 pixel for the rigid body translation, (2) rotation angles of 0.5-5 ̊ for rigid body rotation and (3) large tensile deformations of 5000-300000µɛ, respectively. The verification processes showed that the accuracy of the novel DIC algorithm, for the simulated displacement types and levels above 99%. The experimental validation was conducted to examine the effectiveness of the novel technique under realistic testing conditions. Normalized PMMA specimens, in accordance to ASTM F3087, were produced, inspected and subjected to tensile loading until failure. The deformation of the specimen surface was measured using (a) the novel DIC, and (b) strain gauge rosette techniques. The mean maximum force and ultimate strength of four specimens were 882.2±108.3 N and 49.3±6.2 MPa, respectively. The mean ultimate deformation from the gauge and DIC groups were 15746±2567µɛ and 19887±3790µɛ, respectively. These large deformations are common in polymeric materials, and the DIC technique has thus far not been investigated for large deformation. The relative mean error of the DIC measurement, in reference to those of the strain gauge technique, was found to be up to 26.0±7.1%. Accordingly, the mean Young's modulus and Poisson's ratio of strain gauge measurement were 3.78±0.07 GPa and 0.374±0.02, and of the DIC measurements were 3.16±0.61 GPa and 0.373±0.08, respectively. The increasing difference of the DIC strain measurements relative to those of the strain gauge technique is likely related to the gradual distortion of the speckle pattern on the surface of the tensile specimen. Subsequently, a Correction Factor (CF) of 1.27 was introduced to correct for the systematic error in the deformation measurements of the DIC group. The corrected ultimate deformation of the DIC measurements became 15712±357µɛ with the relative mean error of -0.5±7.1%, if compared to those measurements of the strain gauge techniques. Correspondingly, the mean Young's Modulus and Poisson's ratio of the DIC and of the strain gauge measurements became 3.8±0.4 GPa and 0.368±0.025, respectively. Using an atomization process, paint speckles were reproducibly generated on the surface of an object. A factorial design of experiments was used to investigate the speckle pattern (grey value distribution and gradient) for the DIC measurement accuracy. Specifically, nine different speckle patterns were generated using the atomization process and tested for rigid body translation and rotation. The results showed the relative mean errors among the nine speckle patterns varied from 1.1±0.3% to -6.5±3.6%. The preferred speckle pattern, which was characterized by a wide range of sharp speckle and of grey values, produced a mean error of 1.1±0.3%. The analysis of errors and relating sources in the DIC measurement was conducted. Three categories of sources including algorithmic sources, processing parameters sources (subset size, number of pixels computed) and physical environment sources (specimen uniformity, speckle pattern, self-heating effect of the CCD camera and lens distortion of the camera, non-linearity error in strain gauge circuit) were investigated and discussed. Finally, the solutions were provided in order to help reduce the systematic and random errors relating to the aforementioned three categories of sources for errors. In conclusion, a novel DIC algorithm for a more accurate approximation of the initial guess and accordingly for an efficient and accurate convergence of the optimization was successfully formulated, developed, implemented and verified for relatively large deformations. The experimental validation surprisingly showed a systematic error of the DIC measurements, if compared to the measurements of the strain gauge technique. The larger the deformation applied to the specimen, the larger the error gradually became. Therefore, the gradual distortion of the speckles on the surface of the object was likely the underlying cause of the error. The error was systematic and therefore corrected. The atomization process allowed generating reproducible speckles on the surface of an object. Using the DIC measurements, the mechanical behavior of polymers, undergoing large deformations, such as polymethyl methacrylate used in skeletal reconstruction can be investigated and, once understood, the knowledge gained can help develop more effective materials.
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