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Graphical design for specified laminate strain limits. Strictly speaking, strain failure criteria should be applied at ply level rather than at laminate levels. However for in-plane loadings and several ply angles present, it is not unreasonable to use laminate strain limits.
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Graphical design for specified laminate strain limits • Strictly speaking, strain failure criteria should be applied at ply level rather than at laminate levels. • However for in-plane loadings and several ply angles present, it is not unreasonable to use laminate strain limits. • This greatly simplifies the search for the optimum laminate.
Recall A* in terms of lamination parameters • Hooke’s law • From Table 2.1 • What are the expressions for Poisson’s ratio and shear modulus for a quasi-isotropic laminate? • What other laminates will have the same expression for the shear modulus?
Solution for laminate strains • Inverting A* matrix analytically one obtains • Can have partial check by specializing to quasi-isotropic laminate • Does that check? Any other easy checks? • How to change for ?
Other two strain components • Y-strain • Shear strain • Checks? • What property of the laminate is responsible for zero coupling between shear strains and normal stresses?
Example 7.1.1 • Design a graphite/epoxy laminate that will withstand with largest possible . Use strain limits for laminate limits. • Material properties , • From Example 2.4.1 • Would a quasi isotropic laminate do?
Optimum point on Miki’s diagram • Solving for when the strain limits are exactly critical obtain • Optimum at point A,
Possible realization • Easiest is plies with fixed or fixed • For example for • Can do a combination of cross ply and angle ply. • What percentage zeros in cross-plies? • To calculate angle of angle-ply laminate use • To calculate proportions need Eq. 4.2.7, • Point A is at 0.73, what proportion of angle ply laminate?
Textbook alternative • Use laminate. Solve • Two equations, three unknowns? • Get • More easily realizable. Example? • Textbook then checks that this laminate will actually satisfy ply strain limits.
Design of laminates with two fiber orientations • With only two ply orientations, it is possible to derive equations for strain limits and solve for the equations of the curves defining the constraints. • Because quadratic equations are involved one gets two possible solutions. • With at least three constraints for each ply direction, Miki’s diagram gets hairy
Example 7.1.2 • For graphite-epoxy in previous example, but loading of and , • Design a laminate
