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Crack Growth Threshold Criterion Based on Calculation of Dynamic Stress Intensity Factors in the Mixed Mode (Complex Functions Theory Approach)

In this paper, an analytical method is presented for crack growth threshold criterion based on calculation of dynamic stress intensity factors (DSIF) in the mixed mode. The basis of the method is comparison of DSIF and fracture toughness. The analytical method is grounded on solving two-dimensional wave equations in the frequency domain, using complex functions and mapping technique. Using this method, the J-integrals are calculated and based on relation between the J-integrals and DSIF, these factors are derived. The proposed criterion for crack growth threshold is defined as a comparing calculated DSIF (KI, KII) with fracture toughness (Kc), using complex functions and mapping technique. The mapping technique helps to convert the complicated boundaries geometry into a simple one (unit circle). Finally, since using complex functions theory is an analytical method, the results have a high precision compared with numerical methods.