13th International Conference on Fracture June 16–21, 2013, Beijing, China -4fibre = { } { } [ ] f rs f ε , M × Stress developing in material layers (Induced stress), { }induced σ = xy induced y x τ σ σ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ , is determined as follows:- { } al induced σ , ={ } { } [ ] al rs al lam ε ε , M × + ; { } r induced σ , ={ } { } [ ] r rs r lam ε ε , M × + ; { } f induced σ , ={ } { } [ ] f rs f lam ε ε , M × + In the case of cracked Glare, stress state around cracked aluminum and affected fibre zone differs from the induced stress due to the presence of crack and onset of the process of fibre bridging. These effects are assessed numerically in Section 5. Plane stress fracture toughness or induced stress intensity parameter of Glare, at fracture (fr), containing cracks of length, c, in aluminum layers is obtained from the following expression pertaining to Linear Elastic Fracture Mechanics (LEFM) c CF π σ K al fr y induced C lam × × = ) ( , , , (1) where configuration factor, CF, for an edge crack is empirically given by ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ + ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ − ⎠ ⎞ ⎜ ⎝ ⎛ + = − 4 3 2 30.39 21.72 1.12 0.23 10.55 w c w c w c w c CF and , w, is the width of the laminate. For cracked plain aluminum alloy specimen, the expression takes the form, c CF π σ K fr y applied C al × × = ) ( , , , term al fr y induced σ ) ( , , used in the laminate being replaced by fr y applied σ ) ( , since load redistribution does not take place in plain specimen. In the case of a thin plain specimen, plane strain fracture toughness, IC,al K , is estimated from plane stress toughness value, C,al K , by the following expression [3] 2 1 4 2 , 1.4 1 ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + = al IC,al IC al C,al Y K p K K (2) where p is the thickness of the specimen. Knowing IC,al K , plane stress toughness of hypothetical plain aluminum alloy specimen, d C,al K , with higher thickness, d, equal to that of Glare laminate, is again obtained from Eq. (2). The following condition holds good in Glare at fracture br tip C lam K K K = + , or br d C,al C lam K K K+ = , since d C al tip K K , = (3) where tip K is the crack tip stress intensity parameter and br K is the bridging stress intensity parameter. Fulfillment of the conditions, 2 , 2.5 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ < al IC al al Y K t and 2 , 2.5 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ < al IC al Y K p , supports plane stress conditions in cracked aluminum of Glare and of plain specimen respectively. 4. Experimental work Starter notches were machined across the interfaces of all material layers at the edges of Glare laminates. Mode I cracks, nucleated at notch tips by fatigue cycles, were made to grow up to
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