# A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS

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2 2 2 FIXED ARM PEEL TEST. 2.1 ANALYSIS OF THE FIXED ARM PEEL TEST. Peel arm (thickness h Peel force P Laminate of width b θ Peel angle Fixed arm of laminate Figure 1 Fixed arm peel test Figure 1 shows the peel of a laminate at a peel angle of θ with a force P acting on the peel arm (width b, thickness h. In order to peel one laer of the laminate from the other, it is necessar to provide energ in the form of external work to the laminate. The energ contributions to a fixed arm peel procedure can be described b a global energ analsis [1]. The input energ to the peel test needs to be resolved into the various deformational energies, elastic, plastic and adhesive fracture energies, at least. G A du ext du s du dt du db = ( 1 bda bda bda bda where G A is the adhesive fracture toughness, U is energ with subscripts ext, s, dt and db referring to external work, strain energ, dissipated tensile energ and dissipated bending energ, respectivel. b is the specimen width and da the peel fracture length. This approach has been applied to a fixed arm peel test [1, 2] in order to convert peel strength (P/b to adhesive fracture toughness: G = G ( 2 A G P G is the input energ after correction for tensile elastic and plastic deformation in the peel arm and G P is the plastic work in bending the peel arm. The tensile corrections are often negligible [1] and then input energ is given b: P G = ( 1 cosθ (3 b θ is the peel angle. In order to calculate the plastic deformation energ associated with the peel arm, it is first necessar to have knowledge of the tensile stress-strain characteristics of the peel arm material. This will include an initial elastic deformation but also a subsequent work hardening, plastic, deformation. The plastic bending in the peel tests ma then be

3 3 modelled using large-displacement beam theor with modifications for plastic bending. Solutions have been formulated for three cases: (i Digitised, where the stress-strain behaviour of the peel arm is digitised and a numerical analsis is used to calculate G P [3]. (ii Bilinear, where a bilinear fit is given to the stress-strain curve and an analtical calculation of G P [4,5]. (iii Power law, where an linear elastic-power law plastic fit is given to the stress-strain curve and an analtical calculation of G P [4,5]. For the bilinear and power law curve fits, the details are as follows where a number of parameters from the stress-strain fits are calculated. N is a constant, α is the ratio of plastic modulus to elastic modulus i.e. E 2 /E 1, σ is ield stress and ε is ield strain. N and α are the respective work hardening coefficients for power law and linear work hardening. When ε ε, σ = Eε ( 3 in both cases, and whenε >, N ε ε σ = σ ( ( 4 ε in the power law work hardening model, and σ = σ + αe( ε ε ( 5 for the bilinear model. For laminates where the adhesive laer thickness (h A is ver small, h A 0, there is no requirement to consider the deformation in the adhesive in conducting the calculations of adhesive fracture toughness [4]. However, when h A >0 the deformation in the adhesive laer should be included in the analsis for which it will be necessar to have knowledge of the modulus of the adhesive material (E A. In all, these various calculations can be complex and whilst a theoretical analsis is given in reference [4], software (ICPeel that can be used to conduct the calculations is available on the Imperial College London website [6]. The digitisation of the stress-strain behaviour also requires a software package as does the subsequent numerical analsis for calculation of G P. This is also provided on the Imperial College London website [6] where the package is called ICPeel (Digitised. In principle, the digitised approach should be the most accurate but it is also the most cumbersome and time-consuming approach. However, the digitised package is quite quick if an approximate solution is used first. This is based on using the stress-strain parameters form the curve fitting procedures prior to conducting an accurate analsis. Therefore, it is necessar to run ICPeel first and ICPeel (Digitised next. Consequentl, it is helpful to use the results from all three cases in the determination of G P and G A. The website includes instructions on how to run the packages. In order to determine G A without neglecting an of the elastic or plastic deformations, two experiments are required:

4 4 (a The peel test with a control of the peel angle. (b A tensile stress-strain measurement of the peel arm up to fracture or at least to a strain magnitude that exceeds the maximum strain in the peel test (this is given in ICPeel and is tpicall 6%. Experimental requirements for both of these measurements are given in section 2.2 and Straight line fitted to elastic curve True Stress (MPa Straight line fitted to initial plastic curve Interception of these lines provides the ield co-ordinates True Strain Figure 2 Definition of ield co-ordinates A critical issue in analsing these curves concerns the definition of the ield co-ordinates (ε, σ. These are obtained from the experimental data b fitting a straight line to the linear elastic region of the curve and a straight line to the initial plastic region of the curve, as shown in Figure 2. The straight line fitted to the initial plastic curve should start beond an approximate ield point and end at approximatel 10 times the ield strain, again as shown in Figure 2. The interception of these two lines defines the ield co-ordinates. The measured stress-strain curve is then modelled to either a bilinear form, as shown in Figure 3 or a power law form as shown in Figure 4. Both fits should be conducted for the purpose of calculation of G P and G A, but also for the ICPeel (Digitised analsis. The fitted curves must compl with these ield co-ordinates (as equations 3-5 indicate. Therefore, once the ield co-ordinates are defined from the experimental curve, then the linear elastic portion for both models is the line between the origin and these co-ordinates. The plastic region then starts beond the ield co-ordinates but for both tpes of model, the fitted curve must pass through the ield co-ordinates. In general, net stress (force/original cross sectional area and net strain (increase in length/gauge length are used. However, if the strain exceeds 10% then a true stress should be used (true stress = net stress [1+ strain].

5 5 250 True Stress (MPa Experimental curve E 1 E 2 Yield co-ordinates (ε,σ True Strain Figure 3 Tensile stress versus strain plot for a peel arm illustrating a bilinear elasticplastic fit and the definition of E 1, E 2 and ield strain 200 True Stress (MPa Experimental curve Yield co-ordinates (ε,σ True Strain Figure 4 An illustration of an elastic region followed b a power law fit for work hardening. Adhesive fracture toughness is determined according to equation 2. Ideall, the corrections for plastic deformation should not be too large otherwise errors for the determination of

6 6 adhesive fracture toughness will become significant. The size of this correction is given b G ( P x100% ; the smaller this correction the better [2]. G These considerations appl equall to the T-peel analsis but can onl be determined for each peel arm separatel. 2.2 EXPERIMENTAL PROCEDURES IN THE FIXED ARM PEEL TEST. Specimens for conducting peel strength should be in the form of rectangular specimens where the two parts of the laminate have alread been adhered but where there is a region of unadhered material (of nominal length 30 mm. The overall dimensions of a peel specimen need not be rigidl defined but for man tests we have found that a length of 100 mm and width 20 mm proves to be quite satisfactor. Three specimens should be tested for each set of conditions. The choice of peel jig is not unique but the apparatus should incorporate a number of facilities. A successful kit is shown schematicall in Figure 5. First, the apparatus should be able to select the peel angle in the range up to 180. Second, the jig is attached to an Instron or similar universal testing machine such that as peel occurs the peel angle is maintained constant b the jig moving along a low friction linear bearing sstem. Third, onl one side of the laminate is allowed to be the peel arm in the test. Of course, the laminate can be reversed so changing the peel arm material in another but separate test. (Consequentl, the composition of the adherends ma or ma not be the same. Adhering one side of the laminate to the peel table is a critical issue. If this laer can separate from the table during the test then the energ involved in that process will increase the measured adhesive fracture toughness value to an erroneousl high level. The means of gluing the laer to the table should be reported. The material used for the peel arm (substrate should be reported, as should the length, width and thickness dimensions of the specimen (h and h A where h is the thickness of the substrate alone (i.e. without an coating of adhesive and h A is the thickness of the adhesive. The peel angle needs to be selected on the basis of ensuring that the peel force is large compared with the resolution of the load cell and the frictional forces in the test. For purposes of the protocol it will be necessar to conduct the test at a range of peel angles between 45 o and 135 o but the peel angle 90 o δ should alwas be one of the angles. A peel test speed ( t of 10 mm/min can be used as a standard speed with the 90 o. However, the peel angle will a influence the peel crack speed (. t δ a = (1 cos θ (6 t t Therefore, when conducting tests over a range of peel angles it us necessar to select a common peel crack speed.

7 7 Figure 5 Fixed arm peel fixture with linear bearing sstem showing a peel angle of 45 o. The force versus displacement curve to initiate and propagate a peel fracture should be recorded. At least 30 mm of peel fracture should be established. The average peel force should then be determined as shown in Figure 6A. If there is a combination of adhesive and cohesive fracture or stick-slip (as illustrated in Figure 6B, then for these occasions, both the mean lowest and the mean highest stead propagation peel force values should then be used to determine the adhesive and cohesive fracture toughness values, respectivel. 400 Peel force (N Onset of peel Average peel force Displacement (mm Figure 6A: Illustrative peel force versus displacement demonstrating how to average the peel force.

8 8 2.5 Cohesive peel force Force N mm Deflection Adhesive peel force Figure 6B Peel force versus deflection in a fixed arm peel test. The higher peel forces relate to cohesive fracture; the lower peel forces relate to adhesive fracture In order to conduct the corrections summarised in equations 2-5 it is necessar to obtain a tensile stress - strain plot on the material of the peel arm. (This should be the substrate material alone i.e. it should not be the substrate with a coating of adhesive material. In order to accommodate current analtical methods for the determination of the plastic work in bending the peel arm, this stress-strain plot will need to be described either as a bilinear function or as a linear elastic-power law plastic function or as a digitised function. The tensile test should be conducted at the same test speed as the peel test and in order to obtain sufficient accurac the test specimen should be a rectangular strip of width 10 mm and length 100 mm. In addition, an extensometer will be required to measure the strain deformations necessar to define the elastic deformations. The extensometer, ideall, should be of a non-contacting tpe, since the peel arms are likel to be of low stiffness. The tensile test should continue in order to enable a clear definition of the plastic region of the deformations b continuing the test to fracture. The comments preceding Figure 3 provide instructions for fitting a bilinear elastic-plastic fit for the stress-strain curve. Five parameters should be obtained, namel E 1, E 2, α (E 2 /E 1, ε and σ. The elastic modulus (E 1 is defined as the slope of the stress-strain curve at small deformations and before ielding has occurred. In order to define the plastic modulus (E 2 it is helpful to allow the tensile specimen to continue extension for as long as possible. If it transpires that the "work hardening" portion of the stress-strain curve exhibits a negative slope, then values of α and E 2 should be made zero (and not negative. In order to construct a linear elastic region followed b a power law work hardening region, the scheme shown in the text preceding Figure 4 should be used. The definition of the elastic region is as above and the power law fit should onl be made for post ield data. The parameters that should be obtained from the analsis are E 1, N, ε and σ. The co-ordinates at ield (as defined in an earlier section are given b the intercept of the elastic line and the plastic region for the experimental curve. Therefore, if the general power law gives N σ = Aε (7 The elastic region is

9 9 σ = E1ε (8 At ield, the stress (σ is σ and the strain (ε is ε. Therefore eliminating σ from equations 7 and 8 gives an expression for ield strain, 1 A 1 N = ( E1 ε (9 and ield stress is σ = E ε ( TEST REPORT FOR THE FIXED ARM PEEL TESTS The following information is required in the test report. General information Name of Laborator Description of laminate Material of peel arm Adhesive used for gluing one arm to the peel table Test equipment Data from tensile test on the peel arm material Test speed (mm/min Bilinear fit Low strain modulus (E 1 (GPa Power law fit Low strain modulus (E 1 (GPa N Yield strain (% High strain modulus (E 2 (GPa Yield strain (% Alpha (E 2 /E 1 Yield stress (MPa Yield stress (MPa Data from the peel test Peel angle ( o Test speed (mm/min Specimen dimensions L (mm b (mm Peel arm thickness h (µm (substrate onl Thickness of adhesive laer h A (µm (if h A > 0 then conduct calculations for two cases h A = 0 and the actual value for h A Value ascribed to the modulus of the adhesive E A (GPa Peel strength (P/b (N/mm Derived results b calculations (for each of the three fits to the stress-strain data G (J/m 2 G P (J/m 2

10 10 G A (J/m 2 Correction factor (% Results should be presented for each specimen. The report should include a plot of the peel curve (i.e. force versus displacement in the peel test. The length of peel growth should be marked on this curve together with a clear indication as to how the peel force used to determine the peel strength is derived from the plot. (Figure 6 shows an illustration of the requirement. In addition, the tensile stress-strain plots with the bilinear and/or power law fits should be reported 3 T-PEEL TEST 3.1 ANALYSIS OF THE T-PEEL TEST. Figure 7 shows the specimen configuration during a T-peel test. When the stiffness of the peel arms is different the peel angles will be φ and θ (rather than 90 o. In Figure 7 the stiffer arm is peel arm 2, therefore φ<90 and θ>90. The analsis proceeds along similar lines to that in the fixed arm peel test (see section 2.1, except that there are now two peel arms to accommodate. However, onl one of the peel angles needs to be considered since φ = π θ:- P G = (1 + cos (6 b 1 φ P G = (1 cos (7 b 2 φ Where the super scripts 1 and 2 refer to the two peel arms, respectivel. The peel toughness terms for elastic corrections are then similar to those in equation (3, except that there are two terms. In a similar manner, there will be two terms for the dissipated energ. Consequentl, there will be two forms for equations (2:- G = G G (8 ( A 1 1 ( P 1 G = G G (9 ( A 2 2 ( P 2

11 11 Peel force P Peel arm Specimen of width b θ φ Peel arm 2 Figure 7: T-Peel Specimen During a Test. The adhesive fracture toughness (G A from the T-peel test is then the sum of the terms from equations (8 and (9, namel:- G + A ( GA 1 ( GA 2 = ( EXPERIMENTAL PROCEDURES IN THE T- PEEL TEST. Specimens for conducting peel strength should be in the form of rectangular specimens where the two parts of the laminate have alread been adhered but where there is a region of unadhered material (of nominal length 30 mm. The overall dimensions of a peel specimen need not be rigidl defined but for man tests we have found that a length of 100 mm and width 20 mm proves to be quite satisfactor. Three specimens should be tested for each set of conditions and care should be taken to ensure that no part of the peel arms can touch the test equipment. There are two configurations for conducting the T-peel tests, as shown in Figure 8. Configuration A has the stiffer peel arm at the bottom, whilst configuration B has the stiffer peel arm at the top. It is likel that the small peel angle for these configurations will not be the same since the stiffer peel arm, which could contain more mass than the less stiff peel arm, will hang differentl. Three specimens tested in either configuration A or B should be conducted and the configuration tpe recorded.

12 12 Peel arm 1 Stiffer arm Peel arm 2 Configuration A Configuration B Figure 8 Specimen configurations for T-peel The materials of the peel arms ma or ma not be the same. The test machine should have the usual capabilities for sufficient resolution of force. Once the peel arms are in tension, the specimen configuration will be similar to one of those shown in Figure 8. During the course of peeling it is necessar to measure one of the peel angles (φ or ϕ and at least three measurements should be made throughout the 30 mm peel fracture; one near the start, one in the middle and one near the end. The average value for the peel angle can then be determined and used in the calculations. A peel test speed of 10 mm/min can be used as a standard. However, if there are large variations in measured peel angle (e.g. > 30 o between specimens or samples then equation 6 should be used to adjust to a common crack speed. (This will be a retrospective judgement. The force versus displacement curve to initiate and propagate a peel fracture should be recorded. At least 30 mm of peel fracture should be established. The average peel force should then be determined unless there is a combination of adhesive and cohesive fracture or stick-slip (as illustrated in Figure 6. For these occasions, the mean lowest and the mean highest stead propagation peel force values should then be used to determine the adhesive and the cohesive fracture toughness values, respectivel. In order to conduct the corrections summarised in equations 6-10, it is necessar to measure tensile stress - strain plots on the material of the peel arms. (Two tensile stress-strain plots will be required if the materials of the peel arms are different. Establishing digitised, bilinear and elastic-power law plastic descriptions of the tensile stress-strain behaviour of the peel arms should be done as previousl described in the section on fixed arm tests. Calculation of the various adhesive fracture toughness terms is then done for each peel arm as described in the section on the fixed arm peel. 3.3 TEST REPORT FOR THE T-PEEL TESTS The information required in a test report is similar to that for the fixed arm test. However, for the T-peel test there will be two peel arms to report and two possible specimen configurations (A and B as well as the measured peel angle. However, there is no requirement to test both tpes of configuration. The information required is as follows:

13 13 General information Name of Laborator Description of laminate Material of peel arm Adhesive used for gluing one arm to the peel table Test equipment Data from tensile test(s on the peel arm material(s This should be provided for both peel arms (1 and 2 if different. Test speed (mm/min Bilinear fit Power law fit Low strain modulus (E 1 (GPa Low strain modulus (E 1 (GPa Yield strain (% N High strain modulus (E 2 (GPa Yield strain (% Alpha (E 2 /E 1 Yield stress (MPa Yield stress (MPa Data from the peel test Specimen configuration (A or B Measured peel angle ( o [The smaller angle should be quoted] Test speed (mm/min Specimen dimensions L (mm b (mm Peel arm thickness h (µm (substrate onl Thickness of adhesive laer h A (µm (if h A > 0 then conduct calculations for two cases h A = 0 and the actual value for h A Value ascribed to the modulus of the adhesive E A (GPa Peel strength (P/b (N/mm Derived results b calculations (for each of the three fits to the stress-strain data To be quoted for each peel arm G (J/m 2 G P (J/m 2 G A (J/m 2 Correction factor (% Overall results G A =(G A 1 +(G A 2 CONCLUDING COMMENTS It would be helpful to use both test methods in order to determine the adhesive fracture toughness. Provided that the correction factor is not too large, then it can be hoped that the values will be the same for both test methods. It is recommended that the software source used for the calculations is quoted in all reports.

14 14 REFERENCES 1 Kinloch, A.J., Lau, C.C. and J G Williams, Int. J. Fract., 66, ( Moore, D.R., Williams, J.G., Fracture of Polmers, Composites and Adhesives, ESIS pub 32, ISBN: , Elsevier, L. F. Kawashita The Peeling of Adhesive Joints PhD thesis Universit of London Georgiou, I., Hadavina, H., Ivankovic, A., Kinloch, A.J., Tropsa, V., Williams, J. G., The Journal of Adhesion, 79, 1-27 ( Lau, C. C., PhD Thesis, Universit of London ( Imperial College London Website,

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