13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- stress in Al layer and glass/epoxy prepreg has a relationship given as(7) 1 1 2 2 , , f f f f br al br f al al n t n t S S n t (7) For the numerical solution, the crack geometry is divided into N elements with equal width s a a w N . The stress intensity factor as a result of the far field stress present in the Al layers follows from the linear elastic theory for monolithic metals farfield al K S a (8) Since the bridging stress in Al layer for a given delamination shape is calculated, the stress intensity factor caused by the bridging stress is expressed as followed 2 , 2 2 2 2 2 2 1 ( ) ( ) 1 2 1 (1 ) 2 ( ) ( ) N br al i i bridging i i i i i S x w b x a K a x b x a a x b x (9) The bridging stress in Al layer impedes the crack growth, so the stress intensity factor at the crack tip is expressed as(10) tip farfield bridging K K K (10) In order to calculate the crack growth rate with Paris equation, an effective stress intensity factor range must be determined. Take the effect of stress ratio and the geometry into consideration, the effective stress intensity factor is expressed as(11) 1.35 1 sec eff tip a K R K W (11) where Wis the width of the specimen. Now, the crack growth rate can be obtained as (12) n cg eff da C K dN (12) 4.Results and conclusions All the equations above are solved by MATLAB. Triangle is chosen as the delamination shape, that is ( ) ( ) 1 s s s x a b x b a a a . ( )s b a is a ratio of maximum delamination length to crack length, which is based on experimental observations. ( )s b a for the FMLs with notch length of 20mm is 0.35 . ( )s b a for the FMLs with notch length of 10mm is 0.35. ( )s b a for the FMLs with notch length of 5mm is 0.175. Bridging stresses distributions in the FMLs with 3 differernt notch sizes along the crack length was plotted in Fig 4 when crack lengths comes to 65mm.The comparisons between experimental and predicted crack growth rates are plotted in Fig 5, Fig 6, Fig 7 when notch length is 20mm,10mm,5mm ,respectively. The fatigue lives of FMLs can be obtained by the equation (13) 0 1 a n cg eff N da C K (13) Using above equations, the fatigue lives for the notched fiber metal laminates can be calculated, as is plotted in Table 1.
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