18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS Estimate the peak load and perforation energy of fibre metal laminates subjected to low velocity impact J. Fan, Z.W. Guan * and W. J. Cantwell School of Engineering, University of Liverpool, Liverpool, United Kingdom * Corresponding author(zguan@liverpool.ac.uk) Keywords : empirical formula, fibre metal laminate, finite element, low velocity impact, peak load Abstract experimental tests, (2) theoretical analysis and (3) numerical modelling. Numerous studies have In this paper, using the validated finite element demonstrated that FMLs combine the superior models, a series of parametric study results of fibre fatigue and fracture characteristics associated with metal laminates subjected to low velocity impact fiber-reinforced composite materials, with the were presented. This covers influences of target size, durability offered by many metals [2-5]. The target thickness, projectile size and projectile analytical approach is mainly based on the striking angle on the peak load and perforation conventional plate or laminate theories and evoluted energy. Based on these parametric study results and from experimental results and/or numerical Timoshenko‘s theory, empirical formulas for circul ar simulations. However, it is very difficult to describe or square plates impacted perpendicularly at the accurately the phenomena occurring during impact target centre by hemi-spherical projectile were [6, 7]. Under low velocity circumstances, the developed. The calculated results from the empirical progression of damage in a polymeric matrix formulas were compared with experimental results laminate is usually made of intralaminar cracks in and numerical simulations. Good correlation was the matrix, fibre failures, and delamination. In FMLs, obtained in terms of load-displacement traces up to the presence of metal sheets, prone to large plastic the peak load and the peak load and perforation deformations and tearing, further complicates the energy. The formulas developed may be used to task [8 – 10]. Caprino et al. [11, 12] provided a assist design of fibre metal laminates subjected to simple way to approach the problem of low velocity low velocity impact. impact response of FMLs. Numerical modelling of FMLs subjected to low velocity impact using finite 1 Introduction element approach has also been carried out extensively [13-15]. Fibre metal laminates (FMLs) are multi-layered materials based on stacked arrangements of In this paper, using the validated finite element aluminium alloy and fibre-reinforced composite models, a series of parametric study results of fibre materials. Currently, FMLs such as GLARE (glass metal laminates subjected to low velocity impact fibre/aluminium) and CALL (carbon were presented. This covers influences of target size, fibre/aluminium) are attracting the interest of a target thickness, projectile size and projectile number of aircraft manufacturers. For example, the striking angle on the peak load and perforation aramid fibre/epoxy system, ARALL, is presently energy. Based on these parametric study results and Timoshenko‘ s theory, empirical formulas for circular being used in the manufacture of the cargo door of the American C-17 transport aircraft whilst GLARE or square plates impacted perpendicularly at the is being used in the manufacture of the upper target centre by hemi-spherical projectile were fuselage of the A380 [1, 2], an aircraft that is developed. The calculated results from the empirical capable of carrying up to 700 passengers. formulas were compared with experimental results and numerical simulations. Good correlation was Research on FMLs subjected to low velocity impact obtained in terms of load-displacement traces up to has been undertaken extensively. There are mainly the peak load and the peak load and perforation three approaches and their combinations, (1) energy. The formulas developed may be used to
assist design of fibre metal laminates subjected to 50 2/1 (4-ply) low velocity impact. Perforation energy (J) 40 3/2 (4-ply) 2 Parametric studies Parametric studies were carried out on fibre metal 30 laminates subjected to low velocity impact using the 20 validated finite element models [15]. The influences of target size, target thickness and projectile size on 10 the peak load are considered. A series of parametric studies were undertaken on 0 circular 2/1 and 3/2 FMLs based on 4-ply composite 0 100 200 300 cores with various plate diameters impacted at their Target size (mm) centre by a hemispherical projectile with a diameter Fig. 1. Relationship between the peak of 10 mm. FE models were developed for 72 mm × load/perforation energy and the target size for the 72 mm square 2/1, 3/2, 4/3, 5/4 and 6/5 FMLs 2/1 and 3/2 FML plates. impacted at the centre by a hemispherical projectile with a diameter of 10mm. The effect of projectile size on impact response was also investigated on 72 3 Development of empirical formulae mm × 72 mm square 2/1 and 3/2 FMLs (based on 4- ply composite cores). Here only the relationships Based on the strain energy method originally between the peak load/perforation energy and target provided by Timoshenko and the equation proposed size for 2/1 (4-ply) and 3/2 (4-ply) FMLs are shown by Caprino et al. [16, 17], the load P for the 3/2 in Fig. 1. 10000 100 8000 80 Perforation energy (J) Peak load (N) 6000 60 4000 40 2000 20 0 0 0 1 2 3 4 5 6 Thickness of FML (mm) Fig. 2. Relationship between the peak load/perforation energy and the thickness of In addition, Fig. 2 gives the variation of the peak FMLs for FMLs based on 4-ply composite cores load and the perforation energy with the thickness of subjected to low velocity impact, data from FE the FMLs for 2/1, 3/2, 4/3, 5/4 and 6/5 FMLs based simulations. on 4-ply composite cores. There were drastic increases in both the peak load and the perforation energy with increasing thickness of the FML. Such FMLs is assumed to be expressed as: increases are highly nonlinear and follow a power 3 law. The increase in the perforation energy is 1 A Eh Eh 2 (1) P C w D w certainly more significant than the increase on the 2 B B a a peak load. where w is the displacement at centre, h is the thickness of the plate, P is the load, a is the plate
ESTIMATE THE PEAK LOAD AND PERFORATION ENERGY OF FIBRE METAL LAMINATES SUBJECTED TO LOW VELOCITY IMPACT where β is estimated to be 2.5, making the diameter, E is the effective elastic modulus of fibre metal laminates, and A and B are constants related to theoretical results agree well with the experimental boundary conditions. C =0.0015 m and D =15 m -1 , data. based on the impact results of the circular FMLs Table 1 Data for Eq. (1). with diameters of 50, 100 and 150mm. C may be taken as equivalent to a deflection and D as a D (m -1 ) A B C (m) curvature related to the side length or radius of the 2/1 FML 0.443 0.217 0.00067 10.0 plate. square 2/1 FML For FMLs, the Young ‘ s modulus E in the above 0.443 0.217 0.00150 15.0 circular equation may be calculated as follows: 3/2 FML 0.443 0.217 0.00067 10.0 square 3/2 FML (2) 0.443 0.217 0.00150 15.0 circular 4/3 FML where E Al and E f are the Young ‘ s moduli of the 0.443 0.217 0.00045 6.7 square aluminium alloy and the glass fibre composite, h Al 4/3 FML 0.443 0.217 0.00100 10.0 and h f are the thicknesses of aluminium alloy and circular glass fibre layers, respectively. 5/4 FML 0.443 0.217 0.00045 6.7 square For a square plate with a length and width equal to 5/4 FML ‗ a ‘, the boundary con dition is similar to a circular 0.443 0.217 0.00100 10.0 circular 2 a . Therefore, the impact plate with a diameter load for a square plate with the above dimensions, Based on the FE simulation results, the peak load should be similar to that for a circular plate with a and perforation energy of the FMLs subjected to a diameter 2 a . Based on Eq. (1) and the impact hemispherical projectile with impact angle α can be results of a square FML, the load P for a 3/2 square estimated using the results of FMLs impacted by a FMLs with length ‗ a ‘ is assumed to be equal to that hemispherical projectile at 90º to the surface of the for a 3/2 circular FML with a diameter 1.5 a and plate: expressed as Equation (1) with C =0.00067 m and D =10 m -1 . o (4) P P 0 (1 ), 45 A 180 For the thick FMLs, the stiffness is underestimated and using Eq. (1) which treats these FMLs as isotropic plates, i.e. without considering their laminated 1.5 nature. To take this into account, the constants C and o (5) E E 1 , 45 A 0 D in Eq. (1) are reduced to 0.001 m and 10 m -1 for 180 the circular plates and 0.00045 m and 6.7 m -1 for the square plates. Table 1 summarises the values of A, P and is the peak load and perforation energy 0 B, C, D in Eq. (1) used for FMLs with different 0 o . corresponding to stacking sequences and shapes. The peak load and perforation energy of the FMLs By taking an average of the ratio of the theoretical subjected to an oval projectile with a projectile head energy up to peak load to the numerical perforation height H , can be estimated from the results of FMLs energy for all of the FMLs, a ratio of approximately impacted by a hemispherical projectile: 40% is obtained. Therefore, the perforation energy may be estimated by: (6) and (3) (7) 3
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