Fractal theory of a propagating crack in austenitic stainless steel

Abstract

Classical fracture mechanics have limitation when it comes to solving real world applications. Factors such as material properties, probabilistic aspects make it difficult for classical fracture mechanics to be used in fatigue life prediction on working components. The introduction of fractal theory provides a better alternative tool for fatigue life prediction. Therefore, this research aims to investigate the relationship between stress intensity factor range, !J.K and local fractal dimension on the crack surface, Df . Compact tension (C(T)) specimen was used for fatigue crack growth rate test in accordance to ASTM E647 to obtain crack length against number of cycles i.e. "a vs N" curve. In the constant growth rate stage ranging from 2.0 (10. 8) to 2.5 (10.7 ) m/cycle, the crack growth rate behavior can be represented by Paris Law equation with coefficient of3.0 (10.12 ) and 3.2851. This linear region ranging from !J.K 16 Ml'avm to 28 Ml'avm will be considered for fractal dimension evaluation. Fractal dimension evaluation was conducted using the Box-counting method. The process was made for different sampling sizes, !J.x to find the optimum range for this method. Results have shown that for every sampling size, increment of Df is fairly consistent with the value of 0.065. We can also deduce that a correlation can be made between Df and !J.K where a linearly increasing relationship was obtained. This shows that the crack tip driving force leaves behind a local uniqueness on the crack surface which varies along the crack length. If was also found that sampling sizes ranging from 0.025mm to 0.055mm have achieved the best consistency for evaluating Df . Fractal dimension for this range only varies from 1.7274 to 1.7293. It contributes to only 5% of the entire Df range that was tested. Improvement to achieve a single value (lower percentage) for Df could be possible if the mentioned recommendations will be considered for future works.