applied fracture mechanics

Interacting Cracks Analysis Using Finite Element Method 373It also can be seen that I , in,Jiprediction is unable to display the unification of crackinteraction factor, which defined equivalent to fI , ref , BSof single crack. In this case, the, ,prediction is expected to encounter some numerical errors since at lower a/ W 0.07 . Inanalysis, the ratio of crack length and width also define the critical stress field, if the pathindependent radius of J-integral for both crack tips are overlapped, the calculation of J valuemight be overestimated and the stress behavior is equal to behavior of single edge crack infinite body. The path integral line should be always apart and controlled in individualcondition.Based on the FFS codes, the multiple cracks are assumed to be independent as single cracks orcombined cracks, until or unless certain conditions are satisfied. The intersection point that liesin the present I , in,Dprediction trend curve, which intersects with the single crack prediction,shows good agreement with the outlined FFS codes. It is seen that at range of0.05 a/ W 0.15 , the I , in,Dvalue is about to level at 1.072 -1.085. The small changes in theserange indicate that shielding effect is very small and promote the unification in interaction at thepoint of a/ W 0.15 . The smaller the b/a , the faster unification process starts.I in Ji32.82.62.4b/a =1.5Brown & Strawley(1966)Present (ct1)Crack interaction factor, γ I2.221.81.61.41.21 I , in , Jif I , ref , BS0.80.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Crack to width ratio , a/WFigure 6. Variation of I , in,D against a/W for b/ a 1.5 ( , )IinD , , IinDct , , , 1 IinDct , , , 24.2. Mode II fracture behaviorFig. 7 depicts the trend of KI , in,Dand KII , in,Dagainst b/a for a/ W 0.25 0.5 . It can beseen that the increase in b/a results in an increase of KI , in,Dand a decrease of K, ,II in D