Two shape-sensing algorithms, the calibration matrix (CM) method and the inverse Finite Element Method (iFEM), were compared on their ability to accurately reconstruct displacements, strains, and loads and on their computational efficiency. CM reconstructs deformation through a linear combination of known load cases using the sensor data measured for each of these known load cases and the sensor data measured for the actual load case. iFEM reconstructs deformation by minimizing a least-squares error functional based on the difference between the measured and numerical values for displacement and/or strain. In this study, CM is covered in detail to determine the applicability and practicality of the method. The CM results for several benchmark problems from the literature were compared to the iFEM results. In addition, a representative aerospace structure consisting of a twisted and tapered blade with a NACA 6412 cross-sectional profile was evaluated using quadratic hexahedral solid elements with reduced integration. Both methods assumed linear elastic material conditions and used discrete displacement sensors, strain sensors, or a combination of both to reconstruct the full displacement and strain fields. In our study, surface-mounted and distributed sensors throughout the volume of the structure were considered. This comparative study was performed to support the growing demand for load monitoring, specifically for applications where the sensor data is obtained from discrete and irregularly distributed points on the structure. In this study, the CM method was shown to achieve greater accuracy than iFEM. Averaged over all the load cases examined, the CM algorithm achieved average displacement and strain errors of less than 0.01%, whereas the iFEM algorithm had an average displacement error of 21% and an average strain error of 99%. In addition, CM also achieved equal or better computational efficiency than iFEM after initial set-up, with similar first solution times and faster repeat solution times by a factor of approximately 100, for hundreds to thousands of sensors.

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The present study reports on the evaluation of residual stress field formation and distribution in Central Cut Plies (CCP) specimens. Real-time measurements were performed using a distributed sensing fiber optic system based on Rayleigh Backscattering, which was successfully able to capture strain distribution inside the adhesive layer at every 0.65 mm during the entire curing cycle, for both unidirectional and cross ply laminate configurations. A finite element analysis was also performed to cross-correlate with the experimental residual strain distributions in the proximity of the severed central cut plies. The results outlined in this study demonstrate the presences of tensile residual stresses within the adhesive layer for both configurations. A full field strain distribution and the significance of these findings in relation to the use of the CCP test for fracture mechanics testing will be discussed. Results of this study have shown that residual stresses arise after the curing process for which the amount of longitudinal and transverse residual stresses for the unidirectional CCP laminate are 61% and 19% of the total strength of the adhesive, respectively, while for the cross-ply CCP laminate are 72% and 71%, respectively.@en

The application of strain gauges as recommended by the ASTM standards provides accurate strain measurements in isotropic materials. However, their use in composite materials becomes more challenging due to their anisotropic nature. In this study, we hypothesized that the use of the distributed sensing system and the three-dimensional digital image correlation, which can average strain along a line and surface, respectively, may account for strain variability in composite materials. This study shows an investigation on the mechanical properties of unidirectional, cross-ply, and angle-ply carbon-epoxy specimens using strain gauges, distributed sensing system, and digital image correlation. The Bhattacharyya distance method was used to provide a preliminary evaluation of the closeness of the three different measurement techniques while the B-basis statistical method was used to analyze the experimental data in order to obtain a more conservative and reliable material parameter compared to the conventional averaged value, recommended by ASTM standards. Finally, a finite element model was created in Ansys Workbench™ as a means of evaluating the implication of a single point strain gauges measurement, versus a line or a surface strain measurement. The finite element analysis investigation was performed at a laminae level using the measured experimental elastic modulus and at a lamina–lamina level in which the elastic modulus of the unidirectional case was used as input in all the laminate configurations. The former analysis showed good agreement between the finite element analysis and all the strain measurement systems with an averaged percentage difference below 5%. The latter analysis showed a higher discrepancy in the measured percentage difference. A comparison between the finite element analysis and the strain gauges measurements showed an overall percentage difference between the range of 10% and 26%. Distributed sensing system and three-dimensional digital image correlation measurements provided an overall percentage difference below 10% for all the specimen configurations with a maximum percentage difference recorded for the longitudinal angle-ply case of approximately 9%.

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