The effect of transverse shear on the face sheets failure modes of sandwich beams loaded in three points bending

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1 The eect o transverse shear on the ace sheets ailure modes o sandwich beams loaded in three points bending Abstract BOUROUIS FAIROUZ University Mentouri Constantine, Mechanical Department, Algeria amo6@yahoo.r MILI FAYCAL University Mentouri Constantine Faculty o Engineering Science, Laboratory o Mechanics Chaab Ersas 5 Constantine, Algeria Sandwich beams loaded in three points bending may ail in several ways including tension or compression ailure o acings. In this paper, The eect o the transverse shear on the ace yielding and ace wrinling ailure modes o sandwich beams loaded in three points bending have been studied, the beams were made o various composites materials carbon/epoxy, evlar/epoxy, glass/epoxy at sequence [+θ/-θ] s, [ /9 ] s.. The stresses in the ace were calculated using maximum stress criterion and the simple beam theory. The obtained dierent results show that the sandwich beams with carbon/epoxy, and glass/epoxy ace sheets are the best materials, in return the evlar /epoxy acing characterised by low resistance o transverse shear in compression and tensile. Keywords: Beam theory, Maximum stress criterion, Transverse shear, ace wrinling, ace yielding. 1. Introduction Bourouis Fairouz et al. / International Journal o Engineering Science and Technology (IJEST) Sandwich composites consist o two thin ace sheets with high stiness and high strength and a core with low density and low stiness.. Sandwich structures exhibit complex ailure mechanisms including ace sheet compressive, ailure adhesive, bond ailure, indentation ailure, core ailure and acing wrinling. A large number o theoretical and experimental investigations on sandwich structures have been published in the literature, core ailure by shear studied by Allen [1], Hall and Robson [] and Zenert [].Triantaillou [] studied ailure modes o sandwich beams with aluminum ace sheets and a rigid polyurethane oam core. Failure maps or various core densities and span to depth ratios were constructed or ace yielding, ace wrinling,core yield in shear, and core yield in tension and compression. Niu and Tareja [5] presented a model or the analysis o wrinling behavior o sandwich panels in compression. They gave a single expression or the wrinling stress or the single sided ace wrinling stress or the single sided ace wrinling, and the in phase and out phase wrinling.they showed that the wrinling stress in all three cases in almost the same or short wave length wrinling. El sayed and Sridharan [6] used inite element analysis to examine the compressive behavior o sandwich columns with a variety o imperections.kim and Dharam [7] ocused on bucling o the debonded ace sheet and extended the delamination bucling model o Vizzini and Lagace [8] to debonded sandwich specimens.. Three points bending o sandwich beams Consider a simply supported sandwich beam loaded in three points bending. Let l = 18 mm be the beam length between the supports, b = 5 mm the width o the beam, h = 1 mm the core thicness, and t = 6 mm the ace thicness. The mechanical characteristics o the sins composites materials are listed in the table I [9]. ISSN : 9756 Vol. No. April 1 188

2 Table 1 : Mechanical characteristics measured on various unidirectional iber epoxy composite Mechanical characteristics Glass E/epoxy Carbon HR /epoxy Kevlar 9/epoxy Fiber volume raction V Longitudinal young s modulus E l (Gpa) Transverse young s modulus E t (Gpa) Longitudinal shear modulus G lt (Gpa) Poisson ratio lt.1.. The tensile strength in longitudinal direction X t (Mpa) The compressive strength in longitudinal direction X c (Mpa) The tensile strength in the transverse direction Y t (Mpa) 5 15 The compressive strength in the transverse direction Y c (Mpa) 11 5 The in plan shear strength o the layer S (Mpa) We consider the symmetric sandwich beams with two identical sins with orthotropy directions parallel to the direction x and y. The normal stresses are given by relation : Ph * xx D11 11 x (1) b The stresses are maximum or x= l/ and P is the total load applied at middle o beam The transverse stress xz can then be deduced rom equilibrium equation. xx xz x z () xx normal stress o the th layer given by : xz * Ph D z c () b The constants c are determined by setting xz to zero on the upper and lower aces, and by ensuring the continuity o xz rom layer to layer. And D ij The bending stiness, The inverse matrix o ij D11 D1 D16 D ij D1 D D6 () D16 D6 D66 * 1 D given by D D D (5) D6 ij is the determinant o the matrix D, Dij hc ij (6) Cij the stiness coeicients in the upper sins C ij n 1 e z (7) ij ISSN : 9756 Vol. No. April 1 189

The reduced stiness constant o unidirectional or orthotropic composite, o its material directions: Sin 11 11Cos Sin 1 66 Cos Sin Cos Sin 1 11 66 1 Cos SinCos Sin Cos 16 11 1 66 1 66 Sin 11Sin Cos 1

3 The reduced stiness constant o unidirectional or orthotropic composite, o its material directions: Sin 11 11Cos Sin 1 66 Cos Sin Cos Sin Cos SinCos Sin Cos Sin 11Sin Cos 1 66 Cos Sin Cos Sin Cos Sin Cos Sin (8) Cos The preceding relation allow us to express the reduced stiness constants as unctions o the engineering constants in the material directions we obtain: 11 El 1, Et E 11, 1 lt, 66 Glt (9) lt tl l. Failure modes o sandwich materials A sandwich material must have the strength to carry the design loads without ailing in one o the possible ailure modes igure 1 [1]. Fig.1. Some ailure modes a) Face yielding /racture, b) Core shear ailure, c) and d) ace wrinling, e) general bucling, ) ace dimpling, g) local indentation. I the beam ails by ace yielding, the normal stress in the ace at the critical section equal the yield stress o that ace y. (1) y The compression ace o a sandwich beam subject to bending is liely to ail by a particular ind o local instability described as wrinling. The local bucling o wrinling or ace wrinling occurs when the normal stress in the ace reaches the local instability stress. xx w xx (11) ISSN : 9756 Vol. No. April 1 18

4 . Results and discussion In order to study the eect o transverse shear stress in the ace sheets ailure modes o sandwich beams loaded in three points bending, we considered the aces made o various composite laminates ( glass/ epoxy, carbon/epoxy or evlar /epoxy) o stacing sequence [+θ/-θ] s and [ /9 ] s with unidirectional iber reinorced at 6 %...1.The eect o transverse shear on ace yielding and ace wrinling ailure modes in sandwich beams with various ace sheets materials oriented at [ /9 ] s 8, 7, ace wrinling ace yielding 5, Fig.. Variation o transverse shear stress through the thicness in sandwich beams with carbon/epoxy ace sheets oriented at [ /9 ] s 8, 7, (ace wrinling) 5, - -,5 -, -17,5-1 -1,5, -7,5 - -,5, Fig.. Variation o transverse shear stress through the thicness in sandwich beams with glass/epoxy ace sheets oriented at [ /9 ] s 8, 7, 5, (ace wrinling) -,5 -, -17,5-1 -1,5, -7,5 - -,5, Fig..Variation o transverse shear stress through the thicness in sandwich beams with evlar/epoxy ace sheets oriented at [ /9 ] s Figure shows the variation o the transverse shear stress through the thicness o the higher sin o a sandwich beam with carbon/epoxy ace sheets oriented at [ /9 ] s. We notices that the curves represent the six layers have a linear orm and that the value o shear stresses is higher in the ace wrinling ailure mode than ISSN : 9756 Vol. No. April 1 181

5 the ace yielding, we can say that the sandwich beams with carbon/epoxy ace sheets resist better the transverse shear stress in compression than in tensile. Figures and show that the value o transverse shear stress is more signiicant in ace yielding ailure mode than the ace wrinling ailure mode or the sandwich beams with glass/epoxy and evlar/epoxy coatings when we approaches to the core, the value o the transverse shear stress become similar or the two ailure modes. mode 8, 7, (evlar/epoxy) 5, Fig. 5. Variation o transverse shear stress through the thicness with various ace sheets materials oriented at [ /9 ] s in ace wrinling ailure mode 8, 7, ( evlar/epoxy) 5, -,5 -, -17,5-1 -1,5, -7,5 - -,5, Fig. 6. Variation o transverse shear stress through the thicness with various ace sheets materials oriented at [ /9 ] s in ace yielding ailure Figures 5 and 6 show the variation o the transverse shear stress through the thicness o sandwich beams with various ace sheets materials. In the case o the ace wrinling ailure mode ; igure 5 shows that the sandwich beams with coatings carbon/epoxy resist better the eect o transverse shear stress than glass / epoxy and the evlar/epoxy is the least resistant material. Figure 6 shows that the value o transverse shear stress is almost similar or the three materials in ace yielding ailure mode... The eect o transverse shear on ailure modes in sandwich beams with various ace sheets materials oriented at [+θ /-θ ] s The igure 7 shows that or small values o iber orientation rom to the transverse shear stress o sandwich beams with carbon/epoxy ace sheet is very important in ace wrinling ailure mode than in ace yielding ailure mode,and when the iber orientation are between to the transverse shear stress is similar or the two ailure modes and rom to 9, the carbon/epoxy is the best material in ace wrinling than in ace yielding ailure mode. Figure 8 shows that or small values o the iber orientation rom to 7 the value o transverse shear stress is very signiicant in ace yielding than in ace wrinling ailure mode, we notice that the sandwich beams resists the eect transverse shear in tensile than in compression. rom 8 to 9 the transverse shear stress value is almost similar or the two ailure modes. ISSN : 9756 Vol. No. April 1 18

6 - (ace wrinling) Transverse shear stress (N/mm ) - (ace wrinling) Fig.7. Transverse shear stress in sandwich beams at z=h/ with carbon /epoxy ace sheets in ace wrinling and ace yielding ailure modes Fig.8. Transverse shear stress in sandwich beams at z=h/ with evlar /epoxy ace sheets in ace wrinling and ace yielding ailure modes Transverse shear stress (N/mm ) - (ace wriling) Fig.9. Transverse shear stress in sandwich beams at z=h/ with glass /epoxy ace sheets in ace wrinling and ace yielding ailure modes Figure 9 shows that or small values o the iber orientation sandwich beams with glass/epoxy ace sheets resist better the eect o transverse shear in ace yielding than in ace wrinling ailure mode,rom 5 to 6 the value o the transverse shear stress is similar or the two ailure modes. rom 7 to 9 the sandwich beams resist better the eect o transverse shear in compression than in tensile. From igure 1 we distinguishes three zones, the irst relates to the angles between and the value o transverse shear stress is higher or the sandwich beam with carbon/epoxy than with glass/epoxy and the evlar/epoxy coatings. From 5 to 58 the transverse shear stresses value is similar or the sandwich beams with carbon/epoxy and glass/epoxy ace sheets. From 59 to 9 it is always the carbon/epoxy the best material and evlar/epoxy the least resistant material in ace wrinling ailure mode taing the eect the transverse shear. From to 57 igure 11 shows that the value o transverse shear stress is similar or the sandwich beams with glass/epoxy and carbon/epoxy ace sheets, when the iber orientation is between 58 and 9 the three materials have a similar resistance in ace yielding ailure mode taing the eect o transverse shear. ISSN : 9756 Vol. No. April 1 18

7 Transverse shear stress ( N/mm ) - (evlar/epoxy) Fig. 1.Transverse shear stress in sandwich beams at z= h/ with various ace sheets materials in ace wrinling ailure mode Transverse shear stress (N/mm ) 5 - (evlar/epoxy) Fig. 11.Transverse shear stress in sandwich beams at z= h/ with various ace sheets materials in ace yielding ailure mode 5. Conclusion Sandwich structures, constructed by bonding two sti, thin-walled ace sheets to a light weight, relatively lexible thic core, are widely used in various industrial applications demanding a high bending stiness per unit weight. Sandwich beams are now to exhibit a number o possible ailure modes, including ailure o the core in shear, in compression and ailure o aces. In this study, the ace yielding and ace wrinling ailure modes o sandwich beams loaded in three points bending have been studied. The beams were made o various composite materials carbon/epoxy, evlar /epoxy, glass/epoxy at sequence [+θ/ -θ] s, [ /9 ] s. The eect o transverse shear on the acings ailure modes has also been studied in this paper. Results shows that the ace yielding and ace wrinling ailure modes depend on the transverse shear, on the type o loading, constituent materials properties, and the iber orientation o ace sheet materials. Reerence [1] Allen, H.G. (1969). Analysis and design o structural sandwich panels. Pergamon, London. [] Hall,D.J. ; Robbon,B.L. (198): A review o the design and materials evaluation programme or the GRP/oam sandwich composite hull o the RAN mine hunter. composites, 15, pp [] Zenert.D. (1995). An introduction to sandwich construction, Chameleon, London. [] Triantaillon T.C.; Gibson L.J. (1987): Failure mode maps or oam core sandwich beams. Materials Science and Engineering, 95, pp.7. [5] Niu. K.;Talreja.R. (1999): Modeling o wrinling in sandwich panels under compression.j.eng.mech.15, pp [6] El-Sayed, S. ;Sridharam, S. (): Imperection-sensitivity o integral and debonded sandwich beam under compression. J Sandwich Stru Mater,, pp [7] Kim, WC.; Dharam,CKH. (199): Face sheet debonding criteria or sandwich panels under in-plane compression.eng Fract Mech,,pp [8] Vizzini,AJ.;Lagace, PA. (1987): The bucling o a delaminated sublaminate on an elastic oundation.j.compos.mater,1,pp [9] Berthelot, J.Marie.(1996). Mechanical behaviour o composite materials and structures. Masson,Paris. [1] Luassen,D.; Meidell,A. (7).Advanced Materials and structures and their abrication. Processes, Boo manuscript. Navic University college, Hin. ISSN : 9756 Vol. No. April 1 18

DEPENDENCE OF GEOMETRICAL CONFIGURATION ON MECHANICAL BEHAVIOUR OF GFRP COMPOSITE SANDWICHES

DEPENDENCE OF GEOMETRICAL CONFIGURATION ON MECHANICAL BEHAVIOUR OF GFRP COMPOSITE SANDWICHES Antonino Valenza 1, Vincenzo Fiore 1 and Luigi Calabrese 2 1 Dept. o Ingegneria Chimica dei Processi e dei Materiali,