Dynamic response of circular GLARE fiber—metal laminates subjected to low velocity impact

Abstract

This article deals with the dynamic response of thin circular clamped GLARE fiber—metal laminates subjected to low velocity impact by a lateral hemispherical impactor. Using a spring-mass model, the differential equations of motion corresponding to loading and unloading stages of impact are derived and solved numerically. Internal damage due to delamination is taken into account. Previously published analytical formulas1,2 concerning the indentation of circular GLARE plates are used during the loading stages of impact. In this study, an equation for the unloading path is derived and used during the unloading impact stage. The load—time, position—time, velocity—time, and kinetic energy—time history responses are calculated. In this regard, the position where delamination occurs, the maximum plate deformation and the position where the impact load becomes zero are predicted. Also, the maximum impact load and the total impact duration are determined. The derived differential equations of motion are applied for GLARE 4-3/2 and GLARE 5-2/1 circular plates subjected to low velocity impact. The predicted load—time history response is compared with published experimental data and a good agreement is found. No other solution of this problem is known to the authors.

Influence of the Metal Volume Fraction on the maximum deflection and impact load of GLARE plates subjected to low velocity impact

“…Here, the basic employed equations from reference [7] for our calculations are presented. These equations have been validated by comparisons with experimental data [6,7]. For large plate deflections, the impact load during loading is given by: …”

“…It is noted that the final deflection is equal to the permanent dent depth caused by the impact on the GLARE plate [6]. Analytical expressions to calculate max o w and f o w can be found in reference [7].…”

“…Analytical expressions to calculate max o w and f o w can be found in reference [7]. The coefficients K p and K el are as follows [6][7][8]:…”

“…At this point, due to the elastic strain energy of the prepreg layers, which have been stretched during the loading stage, the plate starts to move toward the opposite direction, until the impact load P becomes equal to zero. Using a spring-mass model, the differential equations of motion corresponding to this physical phenomenon were derived in reference [6] and solved in reference [7]. Here, the basic employed equations from reference [7] for our calculations are presented.…”

“…Hoo Fatt et al [5] employed a spring-mass model to predict the ballistic response of clamped square GLARE panels. In two articles by Tsamasphyros and Bikakis, the differential equations of motion, corresponding to the impact of a hemispherical impactor striking on a circular clamped GLARE plate, were derived using a spring-mass model as well [6] and solved [7].…”