George Se Bikakis

Dynamic Response of Circular GLARE Fiber-Metal Laminates Subjected to low Velocity Impact

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.

Quasi-Static Response of Circular Glare Plates Subjected to Low Velocity Impact

The response of circular GLARE fiber-metal laminates subjected to low velocity impact by a hemispherical impactor is treated analytically. Using a quasi-static approach, characteristic impact variables are calculated. A force-deflection relation is determined and employed for the unloading impact stage. Delamination is also considered. Application to GLARE 4-3/2 and GLARE 5-2/1 plates is implemented. The predicted maximum impact load, its application time, and the total impact duration agree well with published experiments. The derived formulas can be used to evaluate impact response of GLARE or other similar hybrid laminates. No other solution of this problem is known to the authors.

FEM analysis and analytical formulas to predict the indentation response of circular simply supported GLARE plates

This article deals with the static response of thin circular simply supported GLAss REinforced fiber-metal laminates subjected to lateral indentation. The indentation response is initially predicted using ANSYS software and a three-dimensional (3D) nonlinear finite element analysis with geometric and material nonlinearities. From this analysis, the load-indentation and the strain energy-indentation curves are calculated. Regression of the obtained Finite Element Method (FEM) results, that takes into account a specific load-indentation relation, and comparison with previously published analytical formulas concerning the indentation of circular clamped GLAss REinforced plates, yields analytical formulas for the prediction of the GLAss REinforced plate indentation load and strain energy as a function of the central plate deflection. The derived analytical formulas are applied for GLAss REinforced 2-2/1-0.3, GLAss REinforced 3-3/2-0.4, and GLAss REinforced 3-3/2-0.3 circular plates with various diameters subjected to lateral indentation. The analytically predicted load-indentation and strain energy-indentation curves are compared with corresponding FEM results and a very good agreement is found.

Response of GLARE fiber–metal laminates under radial in-plane preloading and lateral indentation

This article deals with the static response of thin circular clamped GLAss REinforced (GLARE) fiber–metal laminates subjected to radial in-plane tensile preloading and lateral indentation by a hemispherical indentor simultaneously. The response is initially predicted using ANSYS software and nonlinear analysis. From this analysis, the load-indentation and strain energy-indentation curves are calculated. Regression of the obtained Finite Element Method (FEM) results, using specific load-indentation relation, reveals that the response of the GLARE plates can be predicted with this relation. It also reveals how preloading alters the load-indentation relation of the GLARE plates. Then, analytical formulas are derived to predict the GLARE plate indentation load and strain energy as a function of central plate deflection and the magnitude of preloading. The derived analytical formulas are applied successfully for preloaded GLARE 2-2/1-0.3, GLARE 3-3/2-0.4 and GLARE 3-3/2-0.3 circular plates with various diameters. The analytically predicted load-indentation and strain energy-indentation curves are compared with corresponding FEM results and a very good agreement is found.

Response of circular GLARE fiber–metal laminates subjected to oblique indentation

This article deals with the static response of thin circular clamped GLAss REinforced fiber–metal laminates subjected to oblique indentation. The indentation response is initially predicted using ANSYS software and a three-dimensional nonlinear finite element analysis with geometric and material nonlinearities. From this analysis, the load-indentation and the strain energy-indentation curves are calculated. Postprocessing of the obtained Finite Element Method (FEM) results reveals how GLAss REinforced plates respond to oblique indentation. Then, analytical formulas are derived to predict the GLAss REinforced plate indentation load and strain energy as a function of the oblique indentor’s displacement and the direction of indentation. The derived analytical formulas are applied successfully for circular GLAss REinforced plates with various diameters and indentation directions. The analytically predicted load-indentation and strain energy-indentation curves are compared with corresponding Finite Element Method (FEM) results and a very good agreement is found.

Low-velocity impact response of fiber-metal laminates consisting of different standard GLARE grades

This article deals with the dynamic response of thin circular clamped GLARE (GLAss REinforced) fiber-metal laminates subjected to low-velocity impact by a lateral hemispherical impactor, striking at the center with constant kinetic energy. The laminates have equal total thickness and consist of GLARE 2A-3/2-0.4, GLARE 2A-4/3-0.238, GLARE 3-3/2-0.4, GLARE 4-3/2-0.317, and GLARE 5-3/2-0.233 standard grades. Three different plate diameters are considered for each GLARE grade. Their dynamic response is predicted by solving previously published differential equations of motion corresponding to a spring-mass modeling of the impact phenomenon. The obtained results are analyzed and compared in order to understand and evaluate the performance of the examined material grades along with the effect of different plate radius. With reference to the radius variation, it is found that it affects substantially the overall impact behavior of a GLARE plate. As far as the examined material grades are concerned, similarities and differences related with their impact behavior are recorded and a comparative evaluation is implemented. Characteristic variables associated with the low-velocity impact response of fiber-metal laminates are discussed and pertinent design recommendations are proposed.

Finite element and analytical modeling to predict the frictional oblique indentation response of GLARE fiber–metal laminates:

This article deals with the response of GLARE (GLAss REinforced) fiber–metal laminates subjected to frictional oblique indentation. The indentation response is initially predicted using ANSYS software and a three-dimensional analysis with geometric and material nonlinearities. The classical Coulomb friction model is employed to simulate friction between the contacting surfaces. Then, analytical formulae are derived to predict the GLARE plate indentation load and strain energy as a function of the indentor’s displacement, the friction coefficient, and the indentation direction. These formulae are applied successfully for the GLARE plates with various diameters and indentation directions. The analytical results agree very well with the corresponding finite element analysis results.

Ballistic impact response of steel fiber-metal laminates

In this article, the ballistic impact response of square clamped fiber-metal laminates and monolithic plates consisting of different metal alloys is investigated using the ANSYS LS-DYNA explicit nonlinear analysis software. The panels are subjected to central normal high velocity ballistic impact by a cylindrical projectile. Using validated finite element models, the influence of the mechanical properties of the constituent metal alloy on the ballistic resistance of the fiber-metal laminates and the monolithic plates is studied. Six steel alloys are examined, namely 304 stainless steel, 1010, 1080, 4340, A36 steel and DP 590 dual phase steel. A comparison with the response of GLARE plates is also implemented. It is found that the ballistic limits of the panels can be substantially affected by the constituent alloy. The stainless steel based panels offer the highest ballistic resistance followed by the A36 steel based panels which in turn have higher ballistic resistance than the 2024-T3 aluminum based panels. The A36 steel based panels have higher ballistic limit than the 1010 steel based panels which in turn have higher ballistic limit than the 1080 steel based panels. The behavior of characteristic impact variables during the ballistic impact phenomenon is analyzed.

Loading-unloading response of circular GLARE fiber-metal laminates under lateral indentation

GLARE is a Fiber-Metal laminated material used in aerospace structures which are frequently subjected to various impact damages. Hence, the response of GLARE plates subjected to lateral indentation is very important. In this paper, analytical expressions are derived and a non-linear finite element modeling procedure is proposed in order to predict the static load-indentation curves of circular GLARE plates during loading and unloading by a hemispherical indentor. We have recently published analytical formulas and a finite element procedure for the static indentation of circular GLARE plates which are now used during the loading stage. Here, considering that aluminum layers are in a state of membrane yield and employing energy balance during unloading, the unloading path is determined. Using this unloading path, an algebraic equation is derived for calculating the permanent dent depth of the GLARE plate after the indentor’s withdrawal. Furthermore, our finite element procedure is modified in order to simul...