Full-field representation of discretely sampled surface deformation for displacement and strain analysis

A detailed evaluation of the feasibility of determining displacements and displacement gradients from measured surface displacement fields is presented. An improved methodology for both the estimation and elimination of noise is proposed. The methodology is used to analyze the gradients for three tests: (1) uniform rotation, (2) uniform strain, and (3) crack-tip displacement fields. Results of the study indicate that the proposed methodology can be used to extract the underlying two-dimensional displacements and their corresponding gradients from the noisy data with reasonable accuracy. Specifically, it is shown that (a) the digital correlation method for acquiring displacement fields has an error in strain of approximately 150 strain at each point, (b) the average strain in a region of uniform strain has much less error, typically on the order of 20 strain, (c) the displacement nolse present in digital correlation is very small, approximately 0.01 pixels, (d) the proposed methodology for reducing noise in the data is essential to the accurate evaluation of displacement gradients and (e) the successful evaluation of displacement and displacement gradients for all three cases indicates that the proposed methodology can be used both to quantify the displacement fields and to reasonably estimate the overall gradient trends.