X CONGRESO NACIONAL DE MATERIALES COMPUESTOS. Celebrado en Algeciras los días 2, 3, 4 y 5 de julio de 2013The objective of this paper is the design of the adequate geometry of the cruciform specimens to be tested under biaxial transverse loads. To this end Finite Element models have been developed. The analysis of the results provided by the FEM models are used to design a crucifotm geometry that assures that the failure takes place at the central zone of the specimen (the area really subjected to biaxial load) and minimizes undesirable effects such as stress concentrationsMinisterio de Educación y Ciencia TRA2005-06764Ministerio de Educación y Ciencia TRA2006 08077Ministerio de Educación y Ciencia MAT 2009-14022Junta de Andalucía TEP-02045Junta de Andalucía TEP-0405

Barroso Caro, Alberto

Correa Montoto, Elena

París Carballo, Federico

Pérez, M.D.

English

idUS. Depósito de Investigación Universidad de Sevilla

MATERIALES COMPUESTOS 13 117 Design ofa cruciform specimen for biaxial tr·ansverse tests E. Correa, A. Barroso, M.D. Pérez, F. París Group ofElasticity and Strength ofMaterials, Continuum Mechanics Deparlrnent, School ofEngineering, University ofSeville, Spain. ABSTRACT The objective of this paper is the design of the adequate geometry of the crucifotm specimens to be tested under biaxial transverse loads. To this end Finite Element models have been developed. The analysis ofthe results provided by the FEM models are used to design a crucifotm geometry that assures that the failure takes place at the central zone of the specimen (the area really subjected to biaxial load) and minimizes undesirable effects such as stress concentrations. KEYWORDS: Crucifotm specimen, transverse failure, biaxial, FEM models. l. INTRODUCTION The significant use ofcomp osite materials in the industry has been accomp anied, during the last years, by an increase ofthe responsibility ofthese materials in the components they are patt of As a consequence, it seems essential to advance in the knowledge ofthe mechanisms of damage affecting these materials as well as in the prediction of their possible appearance. This work focuses on the transverse failw·e, known as matrix/inter-fibre failw·e at lamina leve!. This failw·e may appear in unidirectional laminates subjected to transverse loads or in multidirectionallaminates subjected, for instance, to im P act loads. The patticular case ofthe inter-fibre failw·e under tension has already been studied at micromechanical leve! by París et al [ lf by means ofBEM models. These numerical studies made it possible to identify the initial phases of the damage growth at micromechanical leve! as well as its latter growth that leads to the macromechanical failw·e. Many ofthe existing proposals for the prediction ofthe inter-fibre failure at lamina leve! are based on the hy P othesis that the failw·e taking place at a plane is govemed by the components ofthe stress vector associated to that plan e. This assumption was revised by París et al [2} and Correa et al [3} for the inter-fibre failure under tension. The results obtained showed that the presence of a secondary tension could alter some aspects ofthe phases of the development of failure previously detected for the uniaxial case; in particular, it was concluded that the presence of a secondary tension (not associated to 118 l\IIA TERIALES COl\IIPUESTOS 13 the plane offailure) could slightly delay the generation offailure. It seems necessary to check the validity of the conclusions derived from the aforementioned micromechanical numerical studies by means of macromechanical experimental tests. In particular, experimental studies must be carry out on specirnens extracted :fi·om unidirectional laminates and subjected to transverse biaxial loads. This task was initiated by the authors in [3} (with the development oftension-compression transverse tests), and continued in Barroso et al [4} (where the initial steps for the development oftension-tension tests where undettaken). In loading situation in which both transverse loads are tensile-type the geomelty ofthe specimen required for the development ofthe experimental tests needs to be cmcifotm in order to be able to introduce the load along two perpendicular axes. The design ofthis specirnen can be perfotmed using FEM models; these models may reproduce the behaviour of the specirnen under the biaxial loading cases to which it would be subjected in the experimental tests. Precisely, the work presented in this paper is a continuation ofthe investigation presented in [4] and is oriented to the development of FEM models that could help in the configuration of the adequate geomelty of the specimen. Results from experimental tests based on the geometries proposed in this paper are presented in Barroso et al [5] l.MODELS The following aspects must be taken into account for the design ofthe specirnen to be subjected to tension-tension transverse biaxial loads: - Development o fa unifotm state ofbiaxial stresses on the specimen under testing. - Maximization ofthe area subjected to biaxialloads. - Minimization of the possible stress concentrations derived from the geometrical configuration. - Failw·e occun·ence in the zone subjected toa unifotm state ofbiaxial stresses. Fig. l. 3D geometrical model including libre orientation. (fype D). The finding ofa geometry that fulfils sirnultaneously with the fotmer requirements is not a simple task. There exists a considerable amount ofstudies in literature about cruciform specirnens though it is not easy to fmd a specifíc design for unidirectional laminates to be subjected to transverse loads (i.e. 9(f specirnens). MATERIALES COMPUESTOS 13 119 In the present work the first geometrical model considered, Type D specimen, is based on Lamkanfi et al [6} and is presented in Figure 1 (applying symmetry only an eighth is presented in the plot). The Type D geometry proposed is composed by a main body, which represents the cmciform specimen itself manufactured from a unidirectional laminate, and 8 reinforcing tabs (one at each side of each "rum" ofthe specimen). The main body presents 2 fillet radii at the central zone and constant thickness; the rums ru·e reinforced with tabs whose slope allows a soft.er transition with the central zone ofthe specirnen. Types A (R=I.5 mm), B (R=6.25 mm), C (R=I9.97 mm) specirnens Type D specirnen Fig. 2. Geometrical proposals: Types A, B, C and D specimens. In order to study the effect ofthe different geometrical features three altemative and simpler geometries are also proposed (fypes A, B and C). These tlm~e geometries presenta single fillet radius whose value varies from zero (fype B), to 19.97mm (fype C) passing tlu·ough the same value adopted for Type D (R=6.25mm, employed in Type A). Figure 2 compares the different geometries proposed. For all types ofspecirnen considered the unidirectionallaminate chosen con·esponds to a cru·bon-epoxy system (AS4/3501-6) whereas tabs ru·e thought to be manufactured fi·om glass fibre +45/45 fabric. Fig. 3. Mesh employed. 120 l\IIA TERIALES COl\IIPUESTOS 13 As explained befare, taking advantage of the symmetries, a FEM model has been prepared for each geomeúy proposed, in order to study the stress state under the combined action oftwo externa! transverse tensions, con·espondingly acting at the ends ofthe horizontal (x axis) and vertical (:y axis) arms. Different loading cases have been considered, al! ofthem corresponding to a ftxed value ofthe extemal tension a0 applied at the edge ofthe horizontal atrn, and different portions of, a 0 , 1 characterized by a coefficient n= 0.25, 0.5, O. 75 and 1) at the edge ofthe vettical one. a 0 has been taken equal to the tensile strength associated to the laminate considered, 48 MPa in this case. A view ofthe mesh employed can be observed in Figure 3 for Type D specimen. 2 FEM RESOLTS The results obtained ft·om the FEl\1 analyses show that axx is the dominant sú-ess (together with arr in the T-T limit case, n =I) for al! specimens and loading cases considered. By way of an example, Figure 4 presents axx distribution for Type D specimen. 350 1 ¡ ¡ ~ X . .. 1 _ . ~T. _.:t. ?-~·• ··~· .~ 250 ~ --"' .,. ...,~-- :d_ --=<'·• - l' 200 il'_: ---11-" :1!~~ - -T~ ...:·~ : .. , .. 1 ' ' 1 -~o ~~~==~~~~~==~ b 100 50 -0-TypeA"'"*""TypeB- TypeC--TypeD D 20 :0 40 50 ncr 0 (1\'IPa) Fig. 4. (a) a~ ditribution for Type D specimen. (b) Maximwn values of a"" versus the secondary external tension. In patticular, for the different biaxial cases analyzed the main features are the following: - Relevant sú-ess concentration is detected for axx at centre ofthe free edge, excepting in Type C, where this concentration is located at the j oint between the tab and the specimen ann This su·ess concentration decreases as n coefficient evolves from n =I to n=O. - axx disuibution at the central zone decreases as the secondary tension increases. - In genet·al, axx distribution at the central zone of the different specimens is quite unifotm. Figure 5 shows the maximum values detected for each type ofspecimen versus the value ofthe secondruy extemal tension. It can be checked ft·om the Figure that the slope ofthe curves presented is quite low. MATERIALES COMPUESTOS 13 121 Although none ofthe four types of specimens considered seem to fulfill the objective proposed, mainly dueto the high stress concentrations at the fi·ee edge, Type D presents the best stress behaviour and thus, it is taken as a basis for futther geometrical modifications. (a) (b) Fig. 6. Geometrical¡>roposals: (a) Ty¡>e MI specimen and (b) Tytle M3 s¡>edmen. The geometrical modifications pw·sue the main objective of reducing the stress concentration at the free edge and also making the stress distribution at the central zone of the specimen (the area nominally subjected to biaxial loads) uniform. These objectives are not achieved in a single step, so that severa! and subsequent models (see Figure 6a where an intetmediate proposal, Type MI is presented), were perfotmed until achieving the fmal model (fype l.\1!3 specimen) presented in Figure 6b. This l.\13 proposal is entirely made on carbon fibre, where the original tabs have been extended to cover the whole specimen. Its thick.ness is larger excepting in the central zone where the failure wants to be located. The transition between the central zone and the outer me is petfotmed by means ofan Fig. 7. Uxx distribution for Tytle M3 specimen. The results provided by this model are quite satisfactot-y although this geometry is not able to completely blur the stress concentration at the free edge, see Figure 7. Nevertheless, this stress concentration has been drastically reduced so that the maximum value of Uxx moves from the free edge to the joint between the central zone and the transition one. Specifically, the concentration factor has been reduced to 1.16 versus 122 l\IIA TERIALES COl\IIPUESTOS 13 2.38 detected in Type D specimen. In addition, the central zone of this Type l\13 specimen is subjected to a quite unifotm stress distribution whose values identifY this zone as the preferential area for failure occmrence. 3. CONCLUSIONS FEM models have been developed in order to design the specimen suitable for the development oftension-tension biaxial transverse tests. Fotu· initial models have been considered, Types A, B, C and D. The mechanical analysis showed that the main inconvenience of these designs is the huge stress concentration that arises in all cases. Based on the fotmer results subsequent geometrical modifications have been petformed on Type D specimen. These alterations have mainly consisted in the increase of the thickness associated to the outet· part of the central zone; besides, the shape of this central zone has finally turned into an ellipse (Type l\13 modification) whose transition zone slope is variable. Stress concentration has been noticeably reduced in this last model, Type M3. In addition, this specimen presents a quite unifotm central stress area. Finally, the maximum axx values take place at the transition zone ofthe central area, and thus, failure occun·ence would be presumably promoted at the biaxial zone. ACKNOWLEDGES This work was supported by the Spanish Ministry ofEducation and Science (Projects TRA2005-06764, TRA2006 08077 and MAT2009-14022) and the Junta de Andalucía (Projects TEP-02045 and TEP-04051). REFERENCES l. PARÍS, F., CORREA, E., MANTIC, V. (2007). Kinking of transvet·se intetface cracks between fibre and matrix. J App Mech, 74(4),pp 703-716. 2 PARÍS, F., CORREA, E., CAÑAS, J. (2003). Micromechanical view offailtu·e of the matrix in fibrous composite materials. Campos Sci Technol, 63,pp 1041-1052. 3. CORREA, E., PARÍS, F., MANTIC, V. (2013). Effect of the presence of a secondary transverse load on the intet·-fibre failure under tension. Eng Fract lvfech, 1 03,pp 17 4-189. 4. BARROSO, A., CORREA, E., FREIRE, J., PÉRFZ, M.D., PARÍS, F. (2012). Biaxial testing of composites in uniaxial machines: manufacturing of a device, analysis of the specimen geometry and preliminary experimental results in Proceedings oj15th Europecm Conforence on Composite Jvfa.Jerials, Venice, Italy. 5. BARROSO, A., CORREA, E., FREIRE, J., VEGA, D., PARÍS, F. (2013). Device for biaxial testing in uniaxial machines. Design, manufacturing and expetimental results using cruciform specimens of composite materials in Proceedings oj MATCOMP2013, Algeciras, Spain. 6. LAMKANFI, E., VAN PAEPEGEM, W., DEGRIECK J., RAMAULT, C., MAKRIS, A, VAN HEI'v1ELRIJCK (2010). Strain distribution in cruciform specimens subjected to biaxial loading conditions. Patt 1: two-dimensional versus three-dimensional fmite element model. Polym Test, 29(1),pp 7-11 

Design of a cruciform specimen for biaxial transverse tests

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Design of a cruciform specimen for biaxial transverse tests

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idUS. Depósito de Investigación Universidad de Sevilla