13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- 3.Model development In this study, some details of the numerical approach developed by Alderliesten[2] were modified so that the predictions will have a better agreement with the experimental results. The numerical approach is based on a crack opening displacement relationship, as shown in Fig 3. Fig 3 Definition of the crack opening displacement ( ) ( ) ( ) b r f p p v x v x x x (1) where v x and ( ) br v x denote the crack opening displacement due to the remote applied stress and bridging stress in Al layer, respectively. ( ) f x and ( ) pp x are the deformation in the glass/epoxy prepreg and adhesive layers, respectively. The crack opening displacement away from the notch caused by the remote stress can be expressed as below 2 2 2 al al S v x a x E (2) where al E and al S are the elastic modulus and the remote stress of the Al layer, respectively. The crack opening displacement ( ) br v x caused by bridging stress in Al layer can be calculated 0 ( ) ( , ) a br p p v x v x x dx (3) The crack opening displacement ( , )p v x x caused by point load is expressed as equation (4) and (5). If p x x 2 2 2 2 2 , 1 2 2 2 2 2 2 2 2 2 1 (1 ) ( ) 4 2 ( , ) tanh ( ) ( ) ( ) br al p p p p al p b x S dx a x a x v x x E axbx xxbxaxbx (4) and if p x x 2 2 2 2 2 , 1 2 2 2 2 2 2 2 2 2 1 (1 ) ( ) 4 2 ( , ) tanh ( ) ( ) ( ) br al p p al p p p b x S dx a x a x v x x E axbx xxbxaxbx (5) where is Poisson ratio of the Al layer. ( ) b x is the delamination shape function. , br al S is the bridging stress in Al layer. The deformation caused by the elastic fiber extension is expressed as (6) , ( ) ( ) ( ) f br f f f S S x x b x E (6) where f E is the elastic modulus of glass/epoxy prepreg, and , br f S is the bridging stress in glass/epoxy prepreg. f S is the stress in glass/epoxy prepreg at the notched zone. The bridging
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