Theoretical Analysis of Crack Propagation Measurement for Brittle Materials Based on Virtual Principal Strain Field

The measurement of crack propagation is crucial for revealing the fracture mechanical properties of materials and structures.Based on the virtual principal strain field and Steger’s algorithm,an accurate and automatic method has been proposed for measuring the geometric parameters of crack propagation.The measured geometric parameters of crack propagation include the width,length,and tip location of each crack.The mechanism of the crack-induced virtual principal strain field and the effects of subset,step,and strain window size are analyzed and discussed theoretically.The effectiveness of the derived theoretical equations is verified by the simulation experiments.According to the theoretical equations,it is determined that the distribution of the virtual principal strain field near the crack is similar to the grayscale distribution of the laser fringe image with optimized calculation parameters.Experiments are further conducted to validate the effectiveness of the derived equations.With the optimized calculation parameters,the minimum crack that can be measured is approximately 0.0362 pixel in the laboratory environment,while the measurement error of the crack width is less than 0.025 pixel for two-dimensional digital image correlation(DIC)and 0.020 pixel for three-dimensional DIC.