A three-frame digital image correlation (DIC) method for the measurement of small displacements and strains

Digital image correlation (DIC) has become a well-established approach for the calculation of full-field displacement and strains within the field of experimental mechanics. Since their introduction, DIC methods have been relying on only two images to measure the displacements and strains that materials undergo under load. It can be foreseen that the use of additional image information for the calculus of displacements and strains, although computationally more expensive, can positively impact DIC method accuracy under both ideal and challenging experimental conditions. Such accuracy improvements are especially important when measuring very small deformations, which still constitutes a great challenge: small displacements and strains translate into equally small digital image intensity changes on the material's surface, which are affected by the digitization processes of the imaging hardware and by other image acquisition effects such as image noise. This paper proposes a new three-frame Newton–Raphson DIC method and evaluates it from the standpoints of accuracy and speed. The method models the deformations that are to be measured under the assumption that the deformation occurs at approximately the same rate between each two consecutive images in the three image sequences that are employed. The aim is to investigate how the use of image data from more than two images impacts accuracy and what is the effect on the computational speed. The proposed method is compared with the classic two-frame Newton–Raphson method in three experiments. Two experiments rely on numerically deformed images that simulate heterogeneous deformations. The third experiment uses images from a real deformation experiment. Results indicate that although it is computationally more demanding, the three-frame method significantly improves displacement and strain accuracy and is less sensitive to image noise.