13th International Conference on Fracture June 16–21, 2013, Beijing, China -3i) Aluminum, al { } { } al xy xy y al x al al y al y x al al x γ µ τ υ ε ε υ E σ ε υ ε υ E σ = + − = + − = ) (1 ) (1 2 2 ; Stiffness matrix, ii) Resin, r { } { } r xy xy r x y r r y x r y r r x γ µ τ υ ε ε υ E σ ε υ ε υ E σ = + − = + − = ) (1 ) (1 2 2 ; Stiffness matrix, iii) Fibre, f { } { } f xy xy f x y f f y x f y f f x γ µ τ υ ε ε υ E σ ε υ ε υ E σ = + − = + − = ) (1 ) (1 2 2 ; Stiffness matrix, Stiffness matrix of the laminate is obtained from classical theory as follows:- { } = lam M { } { } { } d t d t d t f f r r al al 6 M 12 M 3 M × + × × + × × × For applied stress state over the laminate, { }applied σ = xy applied y x τ σ σ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ , Strain in the laminate, { } applied lam xy lam y x lam σ γ ε ε ε 1 M − = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ = Residual strain (rs) in material layers is written as:- Aluminum,{ }al rs ε , = ( ) ambient cuiring ll tl al y x T T α α α α − × ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ − ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ 0 0 Resin,{ }r rs ε , = ( ) ambient cuiring ll tl r y x T T α α α α − × ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ − ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ 0 0 Fibre,{ }f rs ε , = ( ) ambient cuiring ll tl f y x T T α α α α − × ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ − ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ 0 0 Residual stress in aluminum = { } { } [ ] al rs al ε , M × ; Residual stress in resin = { } { } [ ] r rs r ε , M × ; Residual stress in { } ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − = f f f f f f f f f f f f µ υ E υ υ E υ υ E υ E 0 0 0 1 1 0 1 1 M 2 2 2 2 { } ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − = r r r r r r r r r r r r µ υ E υ υ E υ υ E υ E 0 0 0 1 1 0 1 1 M 2 2 2 2 { } ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − = al al al al al al al al al al al al µ υ E υ υ E υ υ E υ E 0 0 1 1 0 1 1 M 2 2 2 2 0
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