13th International Conference on Fracture June 16–21, 2013, Beijing, China -7Refer Figure 5a). 3D finite element models of all cracked Glare laminates without delaminations were created with 8 noded, solid 185 elements in aluminum and 8 noded, layered solid shell 190 elements in fibre and resin layers. Half of the laminates were only modeled due to symmetry. The bottom nodes representing cracks in all aluminum and resin layers were unconstrained while the nodes of un-cracked fibre layers were constrained in y direction (v = 0) as shown in Figure 5b). Stress-strain data of materials, available in Figure 6, were used in the material models of the software. Fracture stress values, fr y applied σ ) ( , , taken from Table 2, were applied at the top edges of the laminates. Residual stress developing in materials during laminate curing at 160 deg. C, whose values were obtained using cuiring T = 160 deg. C and ambient T = 30 deg. C in Section 3, were introduced over nodes in x and y directions. The residual stress was same in all the laminates. Their values are given below (+ve is tensile and -ve is compressive):- i) Aluminum = 46.17 MPa (+ve) in x dir., 48.36 MPa (+ve) in y dir. ii) Resin = 25.59 MPa (+ve) in x dir., 25.73 MPa (+ve) in y dir. iii)Fibre = 173.92 MPa (-ve) in x dir., 171.02 MPa (-ve) in y dir. Crack energy release rate can be represented by J integral in LEFM. J in x-y plane over cyclic path, P, [4] is defined by the summation of different terms at nodes on the path as follows:- ∫ ∂ ∂ − ∂ ∂ − = P y x e ds x v ds T x u J W dy T ) ( (4) where eW is the strain energy density, xy y x x x n τ n σ T = + and xy x y y y n τ n σ T = + are traction terms with nx and ny in the expressions representing unit vectors in x and y directions and u and v are displacements in stated directions. To estimate the shielding effect at the crack tips, values of J integral, tip J , were found over several paths around crack tip, as shown in Figure 5b), which were then averaged to obtain the final value. Laminates without cracks were also modeled under fr y applied σ ) ( , and residual stress stated above. Their constraints are shown in Figure 5c). Since J integral value does not critically depend upon the mesh type, a simpler mesh scheme was adopted in place of square root singularity mesh type around the crack tips. Figure 5. a) Finite element model of Glare b) Constraints in cracked Glare c) Constraints in un-cracked Glare Al - Aluminum layer Pr - Prepreg Al Pr Al Al Pr b) c) Tip J integral paths a) Cracks Laminate edge P r , ) ( f y applied σ y,v x,u z Constraints (v = 0) X Fine mesh Magnified view at X
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