The geometric phase analysis (GPA) method based on the local high resolution discrete Fourier transform (LHR-DFT) for deformation measurement, defined as LHR-DFT GPA, is proposed to improve the measurement accuracy. In the general GPA method, the fundamental frequency of the image plays a crucial role. However, the fast Fourier transform, which is generally employed in the general GPA method, could make it difficult to locate the fundamental frequency accurately when the fundamental frequency is not located at an integer pixel position in the Fourier spectrum. This study focuses on this issue and presents a LHR-DFT algorithm that can locate the fundamental frequency with sub-pixel precision in a specific frequency region for the GPA method. An error analysis is offered and simulation is conducted to verify the effectiveness of the proposed method; both results show that the LHR-DFT algorithm can accurately locate the fundamental frequency and improve the measurement accuracy of the GPA method. Furthermore, typical tensile and bending tests are carried out and the experimental results verify the effectiveness of the proposed method.
By using the principle of stereovision, 3D digital image correlation (3D-DIC) can determine the 3D morphology and deformation of a target and has been widely used in experimental mechanics as a noncontact 3D measurement technique. To eliminate the limitations of the conventional 3D-DIC system, this study proposes a calibration-free single-lens 3D-DIC system based on a bilateral telecentric lens and a bi-prism. The performance of the proposed system is verified by tests of rigid-body translation along the out-of-plane direction. As a comparison, the same rigid-body translations are measured using a single-entocentric-lens 3D-DIC system. The results show that the measurement accuracy of the proposed system is higher than that of the entocentric-lens-based one. As an application, the proposed system is used to measure the thermal linear expansion of a ceramic plate at elevated temperatures. The reasonable measurement results verify its applicability in deformation measurements, even in high-temperature environments.
Three-dimensional (3D) digital image correlation (DIC) is an effective measurement method to obtain both 3D morphology and displacements of a target. The aim of this study was to investigate the 3D DIC technique using a single camera and a bi-prism so as to benefit from the high accuracy of measurements and the compatibility of the measurement system. A modified virtual point (MVP) model based on the analysis of light refraction in the prism using a backward ray-tracing method was proposed. As applications, the measurements of morphology and rigid-body translations of a cylindrical specimen and the deflection of a cantilever were conducted. The results show that the proposed method is capable of accurate determination of the 3D morphology and displacements. They also verify that the MVP model is feasible and that the designed bi-prism for the single-camera 3D DIC technique is reliable in morphology retrieval and displacement measurements.
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