Keywords: GLARE, aluminum-glass-epoxy laminate, static load-indentation response, tensile fracture.

This paper deals with the static response of thin circular fully clamped GLARE fiber-metal laminated plates under the action of a lateral hemispherical indentor located at the center of the plate. In reference [1] Vlot used an elastic-plastic impact model to solve this problem numerically. Hoo Fatt et al. [2] modeled analytically the response of fully clamped square GLARE plates. In this paper we develop an analytical model for the calculation of static load-indentation curve and first failure due to glass-epoxy tensile fracture applicable to circular plates. No analytical solution of this problem is known to the authors.

In order to obtain analytical expressions for the load-indentation curve we idealize the material behaviour of aluminum as rigid-perfectly plastic and the glass-epoxy as linear elastic. The aspect ratio is assumed high so that the shear deformation and local indentation are negligible. We also assume stress distributions corresponding to fully plastic bending and membrane states for aluminum layers. Furthermore, we assume that deflections are large, in-plane deformations are negligible compared to the transverse deflections and that the strains are finite.

From the experimental data of reference [1] it is concluded that GLARE plates undergo very large deflections before first failure occurs. Since deflections are large and the plates are thin, we first consider the case of membrane only resistance and then the case of both bending and membrane resistance.

The Ritz method is employed in association with suitable approximation functions. Formulas corresponding to one, two and three-parameter Ritz approximations have been derived. First, the strain energy is calculated. Then the total potential energy functional is derived and minimized. The minimization yields a system of algebraic equations from which the Ritz coefficients can be determined for a specific value of indentation load. Since deflections are very large, we ignore bending strains and assume that all glass-epoxy layers break simultaneously when the membrane strain reaches the limit value of the prepreg. By calculation of the maximum value of the tensile strain we derive a condition that must be satisfied by the Ritz coefficients. When this happens, the indentation load has reached the critical value and the corresponding first failure displacement is calculated for those Ritz coefficients.

We apply the derived formulation to calculate the load-indentation curve and the first failure for GLARE 2-2/1-0.3. It is shown that the results based on the three-parameter Ritz approximation converge satisfactorily. The best prediction (failure load and deflection within 7% and 3% of experimental values respectively) corresponds to the three-parameter Ritz approximation that takes into account bending and membrane stiffness of the plate. Also, the governing role of the membrane in comparison with bending stiffness for this problem is demonstrated.

1

A. Vlot, "Impact loading on fibre metal laminates", Journal of Impact Engineering, 18(3), 291-307, 1996. doi:10.1016/0734-743X(96)89050-6

2

M.S. Hoo Fatt, C. Lin, D.M. Revilock Jr., D.A. Hopkins, "Ballistic impact of GLARE^TM fiber-metal laminates", Composite Structures, 61(1-2), 73-88, 2003. doi:10.1016/S0263-8223(03)00036-9

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