A methodology to measure the interface shear strength by means of the fiber push-in test

Transcription

1 A methodology to measure the interfae shear strength by means of the fiber push-in test M. Rodriguez a,j.m. Molina-Aldareguia a, C. Gonzalez ab, J. LLora a ' b '* ABSTRACT A methodology is presented to measure the fiber/matrix interfae shear strength in omposites. The strategy is based on performing a fiber push-in test at the entral fiber of highly-paked fiber lusters with hexagonal symmetry whih are often found in unidiretional omposites with a high volume fration of fibers. The mehanis of this test was analyzed in detail by means of three-dimensional finite element simulations. In partiular, the influene of different parameters (interfae shear strength, toughness and frition as well as fiber longitudinal elasti modulus and uring stresses) on the ritial load at the onset of debonding was established. From the results of the numerial simulations, a simple relationship between the ritial load and the interfae shear strength is proposed. The methodology was validated in an unidiretional C/epoxy omposite and the advantages and limitations of the proposed methodology are indiated. 1. Introdution Composite materials ontain a large volume fration of small diameter fibers, whih leads to a very large interfae area per unit volume (of the order of 10 5 m 2 /m 3 in typial arbon fiber omposites). Obviously, omposite properties are ontrolled to large extent by the interfae properties and, in partiular, interfae strength and toughness play a dominant role in the mehanial performane of fiber-reinfored omposites. Despite the importane of this topi, there is no onsensus about the most aurate tehnique to haraterize the interfae mehanial properties and different tests are used for this purpose [1]. They an be broadly divided into two groups depending on whether the measurements are arried out in miroomposites made up of single fibers or fiber tows embedded in the matrix or from the atual omposite samples. The measurement tehniques applied to single-fiber miroomposites inlude the fiber fragmentation test [2], the single fiber ompression test [3], and the fiber pull-out test [4]. They are arried out on miroomposite samples manufatured to this end and the interfae strength is derived by means of simplified load transfer models, suitable for this type of miroomposite [5,2]. Although they were widely used in the past, it was always reognized that the loal environment in these miroomposites was not representative of the mehanial and physio-hemial onditions of atual omposites. For instane, the fiber paking density, the thermal residual stresses and the polymer morphology rosslinking density, rystallite morphology may be very different, leading to signifiant hanges in the interfae properties [6]. The haraterization tehniques used in fiber tows were initially developed for erami- and metal-matrix omposites. They use standard omposite materials and inlude the fiber push-out test [7-13], the slie ompression test [14], and the fiber push-in test [15,6,16-18]. The appliation of the slie ompression test to polymer-matrix omposites is not obvious while the push-out needs a umbersome preparation of a very thin membrane (R±50 urn), leading to the fiber push-in test as the best alternative. Moreover, reording load and displaement during the push-in of an individual fiber on a omposite ross-setion has beome a routine task with the help of a flat-punh nanoindentor. However, the interpretation of experimental results to determine the interfae properties is not straightforward and requires a detailed miromehanial model. The standard approximations are based on the shear-lag model [5,2] or on two-dimensional (axisymmetri) representations of the fiber push-in test [7,17] whih annot take into aount important fators suh as the loal environment (fiber paking) [18], the anisotropi elasti properties of the arbon fibers and the influene of the proessing residual stresses as well as of the fiber-matrix frition after deohesion on the interfae properties.

2 As a result, the experimental tehniques presented above an be applied to rank the interfae properties of idential omposites ontaining fibers with different surfae treatments, but they hardly provide absolute values for the interfae properties. This statement is supported by the inredibly large satter in the interfae properties of idential omposites when they are measured with different tehniques and by the fat that there is no aepted standard to measure interfae properties in omposites [1,19]. This investigation was aimed at overoming these limitations through a detailed simulation of the fiber push-in test appliable to strutural omposites, i.e. unidiretional arbon-fiber omposites ontaining a large volume fration of reinforements. With the help of the numerial analyses, a methodology was established to determine the interfae shear strength by means of push-in tests taking into aount the influene of fiber paking, residual stresses, and frition on the test. The methodology was finally applied to a C/epoxy omposite. 2. Theoretial bakground of the fiber push-in test The push-in test is arried out by loading an individual fiber with a flat-punh nanoindenter until interfae frature takes plae (Fig. la). The applied load, P and the fiber displaement, u, are ontinuously monitored during the test and the orresponding P-u urve is depited in Fig. lb. This urve presents an "S" shape where the initial region orresponds to the zone with imperfet ontat between the punh and the fiber. It is followed by a linear zone (with stiffness S 0 ) due to the elasti deformation of fiber and matrix whih ends with the beginning of interfae failure [18]. The interfae strength, xf, an be determined from the ritial load at the onset of nonlinearity, P a by means of the standard shear-lag model [5,2,6,17] aording to np 2nr 2 (1) where r is the fiber radius and n is a parameter whih depends on the fiber and matrix elasti properties and on the loal fiber volume fration, i.e. the onstraint imposed by the neighboring fibers. Following the shear-lag model, n an be determined from the stiffness of the elasti region in the P-u urve, S 0, as [6,9,18] nre\ where f^ stands for the longitudinal elasti fiber modulus. The interfae strength - aording to the shear lag model - is thus given by, (2) SpP 2n 2 r 3 E{ While this strategy is appealing for its simpliity, it has been shown that the onstraining effet of the surrounding fibers is not aurately taken into aount, leading to very large errors in the ase of omposites with very large fiber volume fration [18]. In addition, the shear-lag model was derived for isotropi elasti fibers while C fibers are extremely anisotropi. Finally, other effets, suh as thermal residual stresses or interfae frition are negleted without proper justifiation. 3. Numerial simulation of the fiber push-in test 3.1. Geometrial model and disretization Following the previous onsiderations, it was deided to arry out a detailed 3D numerial simulation of the fiber push-in test to propose a methodology to haraterize the interfae strength based on this test. Obviously, the numerial simulations annot explore all the loal environments and it was neessary to restrit the analyses to one onfiguration whih ould be easily found and tested experimentally. The ross-setion of a C fiber omposite (Fig. 2) shows that hexagonal pakings formed by one fiber surrounded by its six nearest neighbors are often found in high performane omposites ontaining a large fiber volume fration (>60%). The loal fiber volume fration within these arrangements is very high (lose to the theoretial limit of 91%) and, for this reason, the spatial distribution of the fibers is regular, with very little deviation from the hexagonal symmetry (Fig. 2b). The geometry of the numerial model used to analyze the fiber push-in test is shown in Fig. 3a. It inludes the entral fiber of diameter 2r = 5 urn surrounded by six nearest neighbor fibers in an hexagonal paking. The seven fibers are embedded in the matrix material and this entral region is surrounded by a ring of a homogeneous medium, whih stands for the omposite. The whole model ould have been represented by a wedge of 30 but it was deided to use 60 to aount for indenters with different tip geometries (Berkovih or ube-orner). The radius of the wedge is 32r while the model length parallel to the fibers, L, is 150r. It was heked that these dimensions are large enough so that the load-displaement urve during fiber push-in is insensitive to the wedge dimensions. It should be noted that the entral fiber is not in ontat with the nearest neighbors (Fig. 3b). The minimum (3) * 30 CD O 10 Least Squares Fitting Range Fiber and indenter { not yet in full ontat -i 0 ~r 0 T 600 i Fig. 1. Shemati of the fiber push-in test, (b) Representative load-fiber displaement urve orresponding to a C/epoxy omposite.

3 Fig. 2. Optial mirograph of a ross-setion of a arbon fiber/epoxy matrix omposite. The regions enlosed by irles show hexagonal pakings formed by one fiber surrounded by six nearest neighbors, (b) Sanning eletron mirograph detail of one hexagonal paking showing the regular distribution of the neighbors around the entral fiber. ~2 Fiber ^ Matrix Composite A L# C3D8 Regular Mesh (Central Fiber) C3D8 Non Rleguar Mhes C3D8 Refined Mesh (Near the top) Fig. 3. Geometry of the finite element model to simulate fiber push-in in omposite ross-setions with an hexagonal fiber paking arrangement, (b) Detail of the finite element disretization around the entral fiber. thikness of the matrix layer in between is 0.02r, whih was seleted following the detailed observation of hexagonal fiber lusters in the sanning eletron mirosope and also attending to onvergene problems during the simulations. Matrix, fibers and the homogenized medium have been disretized with 8-node linear brik elements (C3D8) exept for the axis of the entral fiber, in whih wedge elements (C3D6) have been used to ensure a strutured mesh in the rest of the fiber (Fig. 3b).

4 Full numerial integration has been used in both types of elements. Speial are has been taken to obtain a very fine and homogeneous disretization throughout the model to resolve the shear stress gradients at the fiber/matrix interfae during debonding, and the model is refined near the surfae (Fig. 3b). In addition, ohesive surfaes are inserted between the entral fiber and the matrix to aount for interfae deohesion and frition during the push-in test. The number of elements in the model is R±73,000. The density of the mesh as well as the aspet ratio of the elements were seleted on the basis of an exhaustive analysis to ensure that the results were mesh-independent Material properties The model inludes three different solid materials (fibers, matrix and homogenized omposite) and one fiber-matrix interfae. Fibers behaved as thermo-elasti, transversally isotropi solids while the matrix was modeled as an isotropi, elasti solid. The orresponding thermo-elasti onstants an be found in Table 1. The matrix elasti onstants, E m and v m and the fiber elasti modulus in the longitudinal diretion, ^, were provided by the omposite manufaturer, while the thermal expansion oeffiients were obtained from the literature []. The remaining elasti onstants for the fiber were estimated using the Chamis model [21] from the elasti onstants of unidiretional omposite oupons assuming an average fiber volume fration of 67%. Plasti deformation of the matrix was not taken into aount beause detailed numerial analysis revealed that it did not influene the ritial stress at the onset of fiber-matrix debonding for this partiular hexagonal fiber arrangement, in whih interfae frature was mainly ontrolled the high loal fiber volume fration. It should be noted, however, that matrix plastiity should be inluded to ompute the interfae shear strength in the ase of isolated fibers or when the matrix shear flow stress is below 50% of the interfae shear strength. The interfae behavior was haraterized by a ohesive rak model, as in our previous analysis of interfae frature in omposites [12,22,23]. The ohesive model relates the total stress ating on the interfae, t = y{t n ) 2 + t 2 t + t 2, with the orresponding displaement jump, <5 = JS 2, + S 2 + S 2, where t n, t t and t s are, respetively, the normal and tangential stresses transferred by the interfae. {) stand for the Maaulay brakets, whih return the argument if positive and zero otherwise, beause ompressive normal stresses do not open the rak. In addition, <5 n, <5 t and <5 S are, respetively, the normal and tangential displaement jumps aross the ohesive surfae. The simplest onstitutive equation for the ohesive rak is the bilinear model (Fig. 4). In the absene of damage, the interfae behavior is linear with an initial stiffness, K, whih is a numerial parameter large enough to ensure the displaement ontinuity at the interfae and to avoid any modifiation of the stress fields in the absene of damage. The onset of damage is attained when the total stress ating on the interfae reahes a ritial value f given by a quadrati riterion aording to [24], 5 = \/<5n > 2 +<5? + 8? Fig. 4. Constitutive equation of the ohesive rak model for the interfae. where t n and t\ stand for, respetively, the normal and shear interfaial strength. In the simulation of the fiber push-in test, normal stresses are always negligible as ompared with shear stresses at the frature point and it was found that the atual magnitude of t n did not modify the result of the simulations. So, for the sake of simpliity, the ritial values of the normal and shear interfaial strength were set equal to eah other, f n = f t = x, whih will be taken as the atual interfae strength throughout the paper. Damage propagation leads to a progressive redution in the stresses transferred through the interfae as well as in the interfae stiffness (Fig. 4). The atual redution of the stress transferred by the ohesive rak is defined by the slope of the softening region in the onstitutive equation, whih depends on f and the interfae frature toughness r = 0.5^(the area under the urve). It was assumed that the energy neessary to break the interfae was independent of the loading path. One the interfae element was ompletely broken, the tangential sliding between matrix and fiber was opposed by Coulomb frition, haraterized by the frition oeffiient \i Analysis Simulations were arried out using Abaqus/Standard [25] within the framework of the finite deformations theory with the initial unstressed state as referene. The boundary onditions of the wedge (Fig. 3a) were the following: the vertial displaements of the bottom surfae were onstrained, while symmetry boundary onditions were applied on the vertial lateral surfaes, perpendiular to the irumferential diretion. Finally, the vertial surfae perpendiular to the radial diretion as well as the upper surfae of the wedge were stress free. Fiber indentation was simulated by means of the vertial displaement of a rigid, ylindrial flat punh of 3 urn in diameter, similar to the one used in the experiments. Frition between the punh and the fiber was negleted. Additionally, the simulations revealed that the debonding proess is independent of the flat punh radius when the ratio between the indenter and the fiber diameters was equal to or higher than 0.6. Table 1 Thermo-elasti onstants of matrix, fibers and the homogenized omposite. The perpendiular to 1. Material, (GPa) E 2 (GPa) G 12 (GPa) Fiber Matrix 3 Composite stands for the fiber diretion while subindexes 2 and 3 stand for orthogonal axes G 23 (GPa) vj2 «i (!Q- 6 / C) a 2 (!Q- 6 / C)

5 4. Results The 3D model presented above was used to assess the influene of different fators (shear interfae strength and frature energy, uring stresses, and frition) on the P-u urve provided by the push-in test in order to establish a reliable methodology to obtain the interfae properties from this test Effet of the interfae shear strength The first set of simulations was aimed at determining the point of the P-u at whih interfae deohesion began. Curing stresses and frition were negleted and the interfae toughness, r, was set to J/m 2. Analyses with different values of the interfae shear strength 50 MPa < x < 100 MPa were arried out and the orresponding P-u urves are plotted in Fig. 5a. All of them present the same initial elasti stiffness, S 0, followed by a non-linear region whih stands for the propagation of the interfae rak from the upper surfae into the bulk. All the urves onverge to a plateau with onstant load one the steady-state situation for rak propagation has been attained and rak growth is ontrolled by the interfae toughness. The symbols in Fig. 5a indiate the ritial load, P, orresponding to the onset of interfae deohesion for the omposites with different interfae strength. P was determined at the intersetion of the P-u urve with a straight line that passes from two points of the P-u urve determined from two parallel lines with the initial stiffness S 0 drawn with offset displaements of 2% and 10% (Fig. 5b). This definition of the P (somewhat arbitrary) provided very good estimations for the ritial load at the onset of debonding in all the numerial simulations and an be readily applied to an experimental P-u urve. Following this riterion, the atual interfae shear strength, x, is plotted in Fig. 5 as a funtion of the interfae strength omputed aording to the shear lag model, xf, (Eq. (3)) from the values P and S 0 in Fig. 5a. While xf is readily obtained from the push-in test, it seriously underestimates the atual interfae strength in the ase of arbon fiber omposite reinfored with a high volume fration of fibers. It is worth noting, however, that x varies linearly with T SL aording to x = 1.92xf in the range of interfae strengths studied and this opens the possibility to obtain x from xf. To this end, it is neessary to asertain the influene of other fators (interfae T3 CO O r =100 MPa T = 90 MPa r = 80 MPa T = 70 MPa r = 60 MPa T = 50 MPa ~r () a Vffl '' m M /m m - Offset = 10% 50- 'a {=296GPa Offset = 2% Displaement, u P i i i i i i i if (MPa) Fig. 5. Load-fiber displaement urves orresponding to omposites with different interfae strength and J/m 2 of interfae toughness. The symbols stand for the ritial load at the onset of interfae deohesion determined as indiated in (b). (b) Methodology to determine the ritial load at the onset of interfae deohesion, P. () Relationship between the shear interfae strength omputed from the shear-lag model, tf) (Eq. (3)) and the atual shear interfae strength, %.

6 toughness and frition as well as uring stresses) on this relationship o to o ?o I'T /,' ' /' P when rak has fully prop agated along the interfae s A-''' 0./ ' I ' I ' I (b) m m / u 1 r= 100 J/m 2 r= 50 J/m 2 -- /*= J/m 2 -r=10j/m 2 r=4j/m 2 r=2j/m / *' y m-',''' i ' i, Interfae Toughness, /'(J/m ) Fig. 6. Load-fiber displaement urves orresponding to omposites with different interfae toughness and 80 MPa of interfae shear strength. The square symbol stands for the ritial load at the onset of interfae deohesion, P, omputed as indiated in Fig. 5b. The irles at the end of the urve indiate the ritial load for steady-state rak propagation, P ss. (b) Influene of the interfae toughness, r, on the ritial load for steady-state rak propagation, P ss. The broken line stands for a paraboli fitting aording to the energy balane model of Jiang and Penn [26]. Liquid Epoxy (a,>0) Before Curing (180 C) *12 <0 J Solid Epoxy (e <0)! 1 N j r r J \ While the elasti modulus of epoxy resins is always of the order of a few GPa, the longitudinal elasti modulus of arbon fibers may vary signifiantly in the range 150 GPa < ^ < 350 GPa and it was important to assess the influene of this parameter. To this end, a new set of simulations was arried out in whih E{ was redued by half and the orresponding results are plotted in Fig. 5. They show that the relationship between x and %f is not signifiantly influened by the longitudinal modulus of the arbon fiber, whose effet is already inluded in the value of x SL, Eq. (3) Effet of the interfae toughness The P-u urves omputed for an interfae with a ritial shear strength x = 80 MPa and different values of the interfae toughness in the range 2 J/m 2 s r s 100 J/m 2 are plotted in Fig. 6a. Brittle interfaes (r < 10 J/m 2 ) present a maximum in the P-u urve as the stress neessary to initiate the rak is higher than the plateau load under steady-state rak propagation. The non-linear region of the P-u urve and the plateau load, P ss inrease rapidly with r, and it is worth noting that P ss is proportional to VT, in agreement with the energy balane model of Jiang and Penn [26] (Fig. 6b). One important result of these simulations is that the ritial load at the onset of deohesion, P, as defined above, is independent of the interfae toughness and the ratio T C /T^L in Fig. 5 is valid regardless of the interfae toughness Effet of uring stresses and frition Thermal residual stresses develop in omposites upon ooling after uring as a result of the thermal expansion mismath between matrix and fibers. Carbon fibers expand slightly in the longitudinal diretion upon ooling while the matrix shrinks (Fig. 7), and this leads to a build-up of shear stresses along the interfae whih has to be overome during indentation to promote interfae deohesion. In addition, the fiber is lamped within the matrix by ompressive stresses normal to the interfae, whih an inrease frition after deohesion. Both fators are expeted to inrease the indentation load neessary to initiate and propagate the interfae rak and they are analyzed below. The thermal residual stresses were introdued in the model by means of an initial elasti thermal step, in whih the temperature was redued from 180 C to C. Indentation of the fiber was simulated afterwards and the P-u urves with and without uring stresses are plotted in Fig. 8a for a omposite with an interfae with x = 80 MPa, r = J/m 2 and \i = 0. While the residual stresses do not modify the initial stiffness, they inrease the ritial load for the onset of deohesion as well as the plateau load for steady-state rak propagation. As shown in Fig. 8, the influene of the uring stresses on the interfae shear strength is linear and an be aounted for aording to v i \ 1 I 1 After Curing and Cooling (b) M During Push-In Test Fig. 7. Shemati of the development of residual shear stresses at the fiber/matrix interfae during uring, Liquid resin in ontat with the fibers at high temperature, (b) Interfae shear stresses at ambient temperature after uring and ooling, () Interfae shear stresses generated during the push-in test. () r v \ 2*

7 (b) E, o, o to o t»" With Curing Stresses 50 Without Curing Stresses 0 Without Curing Stresses A With Curing Stresses T (MPa) Fig. 8. Influene of uring stresses on the load-fiber displaement urve for a omposite with an interfae shear strength of 80 MPa and an interfae toughness of J/m 2. (b) Influene of uring stresses on the relationship between the shear interfae strength omputed from the shear-lag model, xf) (Eq. (3)) and the atual shear interfae strength, %. T = 1.92tf-0.085AT (5) where AT stands for the temperature hange in C and % and zf are expressed in MPa. Obviously, the uring stresses lamp the fibers and also enhane the energy dissipation by frition after omplete interfae debonding. The influene of these stresses on the P-u urve an be found in Fig. 9 for a omposite with a shear interfae strength and a frature toughness of 80 MPa and J/m 2, respetively. The shear frition is assumed to depend on the normal stress at the interfae, o>, aording to T /r = fia r (6) for different values of the frition oeffiient in the range 0 sg /i < 1. Interfae frition inreases the load neessary to propagate the rak and the plateau orresponding to the self-similar propagation of the rak under steady-state onditions is never ahieved be ^ Fig. 9. Influene of interfae frition on the load-fiber displaement urve for a omposite with an interfae shear strength of 80 MPa and an interfae toughness of J/m 2. ause the larger the debonded zone, the higher the frition ontribution. Fortunately, this effet is only important one the interfae has been broken and the ritial load at the onset of deohesion was not affeted by the frition oeffiient. 5. Methodology to measure the interfae strength by means of the fiber push-in test The numerial simulations presented above show that the shear interfae strength an be determined from fiber push-in tests in omposite materials with high auray under ertain onditions. They are summarized below, together with the test methodology: This methodology to obtain the fiber/matrix interfae strength is appliable to unidiretional fiber-reinfored omposites. Push-in tests on individual fibers have to be arried out in fibers lusters with hexagonal symmetry and a very high fiber volume fration to ensure reproduibility and also to apply the results of the numerial simulations. These regions an be easily found within fiber tows. The ritial load at the onset of fiber/matrix debonding, P, is determined from the load-fiber displaement urve using the onstrution depited in Fig. 5b. The numerial simulations have demonstrated that this value of P oinides with the beginning of deohesion for a wide range of interfae stresses. In addition, the loading stiffness, S 0, an be determined from the slope of the linear region of the P-u urve as indiated in Fig. lb. The interfae strength orresponding to the lassial shear lag model is obtained from Eq. (3) from P, S 0, the fiber radius, r, and the longitudinal fiber modulus, ^. The atual interfae strength, x, is obtained from this value using Eq. (5) to aount for the anisotropy of the fibers and the uring stresses. 5. J. Appliation This methodology has been used to determine the interfae strength in an unidiretional T800 arbon fiber/epoxy omposite. Pre-impregnated sheets of 300 x 300 mm 2 were purhased from Hexel and omposite laminates [0] 4 were onsolidated in

8 70 -r S - a, ro 30 - o 10 - / 0 ~r ' ' 1 r Fig. 10. Experimental load-fiber displaement urve for a C/epoxy omposite. autolave at 180 C and 7 bars for 1 min. They were ooled at 2 C/min releasing the applied pressure at the end of the yle. The total thikness of the laminate was 1 mm and the nominal fiber volume fration was 67%. Cross-setions perpendiular to the fibers were polished on SiC paper to 1000 grit finish followed by a diamond slurry up to 1 urn Fifteen push-in tests were arried out on individual fibers whih were arranged in an hexagonal pattern (Fig. 2). Indentations were performed with a Hysitron TI950 nanoindenter equipped with a flat punh of 3 urn in diameter. Indentations were arried out at a onstant displaement rate of 10 nm/s up to a maximum depth in the range 0 nm to 1 urn. The orresponding P-u urves are shown in Fig. 10: they show very good reproduibility, partiularly in the linear region and at the onset of non-linearity, indiating that the indentation of hexagonal fiber lusters is robust. The initial stiffness S 0 = ±4.5 j.n/nm was determined from the linear region of the P-u urve as indiated in Fig. lb and the ritial load for debonding, P = 24.4 ± 1.7 mn, from the onstrution depited in Fig. 5b. The experimental satter was in both ases below 10%, whih an be onsidered very aurate for this type of tests. The ritial shear strength aording to the shear lag model, xf, was determined from these values from Eq. (3). The atual interfae shear strength, x, taking into aount the anisotropy of the arbon fibers and the influene of the uring stresses, was obtained from Eq. (5), leading to a value of 63 ± 5 MPa, whih is reasonable for these types of omposites and in good agreement with the results in the literature in similar C/epoxy omposites [27,28]. In ontrast, other investigations [29] reported very low values (30-35 MPa) for the interfae strength of similar C/epoxy omposites. Their data was obtained from push-in tests by applying the shear-lag model and very probably underestimated the interfae strength beause neither the elasti fiber anisotropy nor the internal stresses were aounted for. 6. Conluding remarks Three-dimensional finite element simulations were arried out to asertain the influene of interfae properties (strength, toughness and frition), fiber elasti anisotropy and uring stresses on the fiber push-in test. Numerial analyses were restrited to a partiular fiber onfiguration made up of a lose-paked hexagonal fiber arrangement. This onfiguration is often found in rosssetions of unidiretional fiber-reinfored omposites. It was found that the ritial load at the onset of deohesion, P depended on the interfae strength and the uring stresses but was independent of the interfae toughness and frition oeffiient. The interfae strength derived from the P using the lassial shear lag model underestimated (by a fator of «2) the atual interfae strength of the material beause it did not take into aount the influene of the fibers' elasti anisotropy and of the uring stresses. Based on the results of the numerial simulations, a simple orretion of the shear model was derived and a new methodology was proposed to obtain the fiber/matrix interfae shear strength and it was suessfully applied to a high volume fration C/epoxy omposite. The main advantages of the new methodology are that it an be easily performed in standard omposite speimens and an provide quantitative values of interfae shear strength, as opposed to qualitative estimations. Quantitative values are neessary to establish absolute omparisons between interfaes in different materials and are also very useful to feed multisale modeling tools whih attempt to predit the mehanial behavior of omposite plies, laminates and omponents from the properties and spatial arrangement of fiber, matrix and interfaes in the omposite [30]. The numerial simulations also pointed out the limitations of the push-in test to haraterize the interfae properties. Firstly, it does not provide information about the normal interfae strength, whih seems to be ritial for the omposite properties under transverse tension [27,31]. Seondly, it will not be easy to develop a parallel methodology to extrat information about the interfae toughness and frition oeffiient beause of the strong oupling between them and also beause frition is very dependent on the uring stresses, whih are not always easy to estimate. Thus, further developments are required in this area and, in partiular, reent advanes in mehanial testing of miron-sized speimens mehanized from the atual omposite samples using fous ion beam tehniques are very promising to haraterize interfae properties. Aknowledgements This investigation was supported by the Ministerio de Cienia e Innovaion de Espana through the Grant MAT , by the Comunidad de Madrid through the program ESTRUMAT (S09/ MAT-1585), and by the European Community's Seventh Framework Programme FP7/07-13 under grant agreement (MAAXIMUS, M.R. aknowledges the support from the Comunidad de Madrid for the fellowship to arry out his dotoral thesis. Referenes [1 ] Kim J-K, Mai YW. Engineered interfaes in fiber reinfored omposites. Elsevier; [2] Kelly A, Tyson WR. Tensile properties of fibre-reinfored metals: opper/ tungsten and opper/molybdenum. J Meh Phys Solids 1965;13: [3] Broutmari LJ. Measurement of the fiber-polymer matrix interfaial strength. 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