FREE EDGE DELAMINATION ONSET CRITERION

Transcription

1 FREE EGE ELAMINATION ONSET CRITERION G. MARION now, 2, formerl 3, R. HARRY 2, and F. LECUYER MEYSYS, 29 rue J. Rostand, 9873 ORSAY CEEX, FRANCE 2 Laboratoire de Génie Mécanique, IUT Bordeaux I, 3345 TALENCE CEEX, FRANCE 3 BERTIN & Cie, 59 rue P. Curie, PLAISIR, FRANCE SUMMARY : This paper shows the results of a theoretical and experimental stud of the free edge delamination on carbon-epox laminates. Edge delamination tests have been made on different stacking sequences to make specimens delaminate under various modes (interlaminar tension, shear or combinations of the two). The tests give results which are necessar to validate a criterion. The thickness influence on the delamination onset stress is used to identif the parameter of the criterion. This method provides good results for the shear delamination. One set of parameters is sufficient to predict the onset delamination stress for [±θ]s, with θ=, 2 and 3. KEYWORS: LAMINATE, ELAMINATION ONSET, CRITERION, EGE ELAMINATION TEST

2 INTROUCTION Various approaches have been investigated in order to predict delamination. Regarding to the propagation, energetic methods are often used. When studing the onset, stress criteria can be of great interest []. This is the approach chosen here. The calculations use an asmptotic method to provide interlaminar stresses. Based on CLT, it consists of a local correction of the plane stresses, which allows the boundar conditions to be correct on the edge of the laminate. The present stud consists of a confrontation of a model with test results. The criterion parameters are identified b a least square method using test results and model predictions. Each term of the criterion is studied separatel. Specific tests were made for this stud. TESTS ifferent specimens were tested to validate the model. The are made of carbon-epox T8/94. The specimens have been cut with a diamond wheel. Their dimensions are 3 2 mm 2, with aluminium tabs. delamination fig : edge delamination test The mechanical properties of U pl are given in table. E xx E G x ν x E (Gpa) (GPa) (GPa) (GPa) (GPa) (GPa) 59 8,4 4,,33 8,4 4, 2,8,33,33 Identified figures Extrapolated figures table : T8/94 properties Tests were lead at a speed of.5 mm/min until 8% of the delamination onset load, then it was dropped down to.5 mm/min to get more accurac to detect the damage phenomenon. G G z ν zx ν z laminate Interface Mode [± n ] s +/- shear [±2 n ] s +2/-2 shear [±3 n ] s +3/-3 shear [25 2n /-25 2n /9 n ] s inside the 9 pl tension [5 2n /9 n /-5 2n ] s 5/9 tension and shear [3 2n /9 n /-3 2n ] s 3/9 tension and shear table 2 : ET specimen The theoretical stud of the criterion is based on thickness influence. For each specimen tpe, several thicknesses were tested (n= to 5, and 8 for [± n ] s ). Five specimens of each tpe and each thickness were tested. An acoustic emission sstem was used to detect the first macroscopic damage. The information from AE were confirmed b enhanced Xra radiograph.

3 [±θ n ] s θ=, 2 and 3 These specimens were often used in previous works. The are known to delaminate in a unstable wa. Here, some tests have been stopped after delamination onset and before whole failure. Figure 2 shows a [±3]s specimen with a delamination at both +3/-3 interface. figure 2 : edge of a delaminated [±3]s specimen figure 3 : X radiograph of a delaminated [±3]s specimen When θ=3, specimens exhibit a non linear behaviour. [25 2n /-25 2n /9 n ] s elamination of these laminates is stable (fig. 4). figure 4 : edge of a delaminated [±25 2 /9]s specimen gages figure 5 : X radiograph of a delaminated [±25 2 /9]s specimen [5 2n /9 n /-5 2n ] s and [3 2n /9 n /-3 2n ] s Acoustic emission increases and some small cracks were observed with microscop. However the were too small to be photographed : when polishing the edge to have a good surface, cracks vanish because of their ver small depth. Fig. 6 shows what could be seen on the edge of a [5 2n /9 n /-5 2n ] s laminate. figure 6 : edge of a [5 2n /9 n /-5 2n ] s specimen It is difficult to know which crack, interlaminar or intralaminar (transverse cracks with an angle of 45 ), occurs first and whether the interlaminar criterion is likel to predict this failure.

4 Results of the tests are summarised in table 2. Laminate nb of nb of nb of average (Mpa) specimens onsets failures stress (Mpa) [±] s [± 2 ] s [± 3 ] s [± 4 ] s [± 5 ] s [± 8 ] s [±2] s [±2 2 ] s [±2 3 ] s [±2 4 ] s [±2 5 ] s [±3] s [±3 2 ] s [±3 3 ] s [±3 4 ] s [±3 5 ] s [±25/9 /2 ] s [±25 2 /9] s [±25 3 /9 3/2 ] s [±25 4 /9 2 ] s [±25 5 /9 5/2 ] s [5 2 /9/-5 2 ] s [5 4 /9 2 /-5 4 ] s [5 6 /9 3 /-5 6 ] s [5 8 /9 4 /-5 8 ] s [5 /9 5 / ] s [3 4 /9 2 /-3 4 ] s table 3 :tests results elamination tpe (onset or failure) is given. Except for the[±25 2 /9] s, the failure stress is ver close to the delamination onset stress. When no onset was detected, the failure stress has been used.

5 ANALYSIS Classical laminate theor is an efficient approach for the stud of laminates. Its basic assumptions provide fast and good results, owing to the fact that thickness is small compared with others dimensions. However, the boundar conditions are not accurate enough to show edge effects. Stress calculation Lecuer [2] achieved an interlaminar stress calculation using appropriate boundar conditions and an asmptotic method. Applied to a linear elastic behaviour laminate, it provides the exact full stress tensor on a bidimensional domain. z h Fig. 7 It consists of adding a tensor to the laminate solution to make the full solution resolve the true boundar conditions. The calculation uses a finite element method in the thickness direction (z) and solves an eigen value problem in the direction normal to the edge (). The solution can be expressed quasi-analticall b the following expression : = ij N k= k λ h ae k () x where ij is the stress at a given z location, h is the laminate thickness, a k is related to the eigen vector corresponding to the eigen value λ k ; none of them depends of h, N is related to the number of nodes in the finite element mesh. The dependence of ij to h is explicit. The out of plane stresses can be singular at the edge of the laminates. Criterion The following expression was used as stress criterion : z 2 (2) It is supposed that onl interlaminar stresses act in the delamination process. A critical length,, is used to take the average stress on this distance. It stands for the distance on which the micro-damages occur, where the stress is redistributed. It is supposed to be characteristic of the interlaminar material (eg resin, fibres and their orientations in adjacent plies) [].

6 There are two critical lengths, and, which correspond to interlaminar shear and interlaminar tension modes. = d (3) where i can be x or. iz = iz d (4) Parameters identification Parameters et have to be found from appropriate test results. Each term (tension or shear) is studied separatel and associated parameters are identified from specific test results. interlaminar shear : [±θ n ]s specimens (5 <θ<35 ) delaminate under interlaminar shear stress [3]. elamination occurs between +θ and -θ laers. The criterion can be written : Eqn, 4 et 5 give the delamination onset : (5) N k = λk h ae k = (6) and doesn't depend on nor h. Hence the curves plotting N k = ae k λ k h versus and for various h (specimens of various thicknesses were tested) must intersect in one point. Edge delamination tests give the applied stress at the delamination onset, and allows the calculation of the left term in Eqn. 6. Fig. 8 shows these curve for a [±3]s laminate. This figure shows how it is difficult to have one intersection point because of dispersion on test results. A least square method was used to avoid such uncertainties.

7 strength (MPa) h=.5mm h=mm h=.5mm h=2mm h=2.5mm interlaminar tension 5,5,,5,2 (mm) fig 8 : identification for a [±3]s [±25 n /9 n/2 ]s laminates can exhibit delamination in the middle of the 9 pl under tension onl [4]. The criterion becomes : (7) The same method than for the shear term could be used to identif the corresponding parameters. However here, the delamination occurs in the middle of the 9 pl. It has been shown that this kind of "interface" has different properties than θ/θ2 interface [5]. No stacking sequence has been found (does it exist?) to make interlaminar tension without shear at a θ/θ2 interface. In order to identif the tension parameters and, specimens under interlaminar tension and shear have been tested. interlaminar tension and shear [5 2n /9 n /-5 2n ] s ET specimens under tension exhibit interlaminar tension and shear. The tension term of the criterion can be related to shear terms, whose parameters are supposed to be known : z 2 (8) The method described can be applied to identif the tension parameters process adds the uncertainties of the shear identification to the tension one.. This

8 RESULTS Shear Tests on [±θ]s, θ=, 2 et 3, have been made to learn whether the parameters and depend on θ. Their value identified once with the three sets of experimental results are : = 6 Mpa and =.6 mm. Figure 9 shows the model prediction with these parameters. delamination onset stress (MPa) h (mm) Fig. 9 : model and tests results, [±θ]s, θ=, 2 et 3 The theoretical curves give a good approximation of the results of the tests. combined mode th 2 th 3 th exp 2 exp 3 exp The identification of the tension parameters and gives unreasonable values. A quick conclusion is to sa that the criterion is unable to give good results for these laminates, owing to the laminate or the criterion itself. However, a comparison has been made between the results of the tests and predictions of the criterion with the following parameters : = 5 Mpa, which corresponds to the intralaminar transverse strength, and =.6 mm, the same as shear critical length. It is interesting to note, on fig., that the variations of this theoretical curve versus the thickness are similar to those of test results, with an offset of 35 MPa. Note that a classical criterion gives a constant value whatever the thickness. This remark allows one to think that it is possible to reproduce the test results b the use of edge stresses. It ma be necessar to appl a full criterion (intra and interlaminar). This point could be confirmed b the inclination of traverse cracks in 9 plies of [±25 n /9 n/2 ]s.

9 delamination onset stress (MPa) th exp h (mm) Fig. : model and tests results, [5 2 /9/-5 2 ] s CONCLUSION Onset delamination stresses on different stacking sequences are available. Edge delamination specimens exhibit different failure behaviour : unstable ([±θ]s, θ=, 2 et 3 ), stable ([±25 n /9 n/2 ] s ) or unstable after a small onset ([5 2 /9/-5 2 ] s ). The criterion provides a good prediction of the results of the tests for interlaminar shear. Parameters values = 6 Mpa and =.8 mm have been identified on the three sets of results ([±θ]s, θ=, 2 et 3 ). Identification of the tension parameters based on results of tests on [5 2 /9/-5 2 ] s laminates gives bad results. However, it seems important to take into account the edge effect, and the influence of the thickness of specimens. A full criterion is to be tested. REFERENCES. BREWER J. C. et LAGACE P. A., "Quadratic stress criterion for initiation of delamination", Journal of Composite Materials, 22, 988, pp LECUYER F., "Etude des effets de bord dans les structures minces multicouches", PH thesis, Université P. et M. Curie, Paris, SONI S. R. and KIM R. Y., "elamination on composite laminates stimulated b interlaminar shear". In Composite Materials : Testing and esign. ASTM-STP-893, CROSSMAN F. W. and WANG A. S.., "The dependence of transverse cracking and delamination on pl thickness in graphite/epox laminates", In amage in Composite Materials, ASTM STP 775, Reifsnider K. L. Ed., pp ALLIX O., LEVEQUE. and PERRET L., "On the identification of an interface damage model for the prediction of delamination initiation and growth". First International Conference on amage and Failure of Interfaces. FI, Sept. 997, Vienna.