A CRITERION OF TENSILE FAILURE FOR HYPERELASTIC MATERIALS AND ITS APPLICATION TO VISCOELASTIC-VISCOPLASTIC MATERIALS

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1 MTS ADHESIVES PROGRAMME PERFORMANCE OF ADHESIVE JOINTS Project: PAJ1; Failure Criteria and their Application to Visco-Elastic/Visco-Plastic Materials Report 2 A CRITERION OF TENSILE FAILURE FOR HYPERELASTIC MATERIALS AND ITS APPLICATION TO VISCOELASTIC-VISCOPLASTIC MATERIALS A OLUSANYA This report represents part of the deliverable for Task 4, Milestone M15 and Task 5, Milestone M19 April 1997

2 A CRITERION OF TENSILE FAILURE FOR HYPERELASTIC MATERIALS AND ITS APPLICATION TO VISCOELASTIC- VISCOPLASTIC MATERIALS A Olusanya Centre for Materials Measurement & Technology National Physical Laboratory Teddington Middlesex TW11 0LW, UK ABSTRACT Uniaxial tensile tests have been used to investigate the mechanical properties of rubber materials. From the results of these studies it was found that the strength of these materials was related to the energy dissipated by the material during deformation, the hysteresis energy, H B. It has been shown for several rubbers that a simple empirical relationship exists between the energy density to break, U B, and the hysteresis energy at break, H B, where K is a constant of proportionality. 2 /3 U B = KH B (1) This relationship indicates that the more energy a rubber can dissipate on deformation, the more work it can withstand before breaking. This relationship has been investigated as to its applicability to flexible rubbery materials, particularly those used as adhesives. Samples of a commercial flexible polyurethane adhesive, 3M DP609, were extended at a constant extension rate to rupture. A fresh sample was then extended under the same conditions to a load just before rupture. The sample was then retracted at the same rate as the extension cycle. The energy at break, U B, was determined by measuring the area under the load-extension curve and the hysteresis energy at break, H B, from the area between the extension and retraction curves. The initial results indicate that this failure criterion describes the failure in this material between two limits: 1 temperatures above the glass transition temperature where the material tends towards hyperelastic behaviour, and 2 higher temperatures where the hysteresis energy, H B tends to zero, i.e. H B approaches the equilibrium modulus. 2 [L93:CMMTB130]

3 Crown copyright 1997 Reproduced by permission of the Controller of HMSO ISSN National Physical Laboratory Teddington, Middlesex TW11 0LW, UK No extracts from this report may be reproduced without the prior written consent of the Managing Director National Physical Laboratory; the source must be acknowledged. Approved on behalf of Managing Director, NPL, by Dr C Lea Head, Centre for Materials Measurement and Technology 3

4 CONTENTS Abstract Introduction Materials Experimental Results And Discussion The Use Of Energy Density, U b, And Hysteresis Energy, H b, As A Criterion Of Failure Dependence Of The Energy To Break, U b On Temperature Comparison Of Adhesive Data With Rubber Materials Conclusions Further Work References List Of Figures [L93:CMMTB130]

5 1 INTRODUCTION Tensile tests have been widely used to study the mechanical properties of rubber materials by a number of workers (1,2,3,4,5). From the results of these investigations, there have been attempts to establish a criterion of failure. These studies have led to the concept of a 'failure envelope' a unique curve, specific to each rubber that gives the bounds of its safe working limit. These failure envelopes relate the stress at break, (σ b ) to the strain at break, (ε b ), over a wide range of temperature and rate of strain. From these results, Smith (1, 2, 3) concluded that: i) Because the internal viscosity of the polymer varies with temperature, the ultimate properties vary and ii) As the ultimate properties vary with strain rate, as the viscous resistance to network deformation increases with rate. Halpin and Bueche (5) showed that the increase in strength of reinforced rubbers is directly related to the increase in their modulus and that the time and temperature dependence of the ultimate properties is directly related to the time temperature dependence of the modulus. As the failure of reinforced rubber is by tearing or crack propagation within the visco-elastic body, they predicted failure and the time to failure curves from the time dependent mechanical properties of the rubber matrix. However these failure envelopes however do not explain the reasons why a material fails under test. One factor that is known to affect the strength of elastic materials is the energy dissipated by the material during deformation, the hysteresis energy. This hysteresis energy represents the amount of recoverable work that the rubber can dissipate without failure. It has been shown for several rubbers (6, 7) that a simple empirical relationship exists between the energy density to break, U B and the hysteresis energy at break, H B, (the maximum recoverable energy), where K is a constant of proportionality, equation 1. 2 /3 U B = KH B (1) This expression indicates that the more energy a rubber can dissipate on deformation, the more energy it can withstand before failing. The applicability of this equation to filled rubber materials has been investigated (7) dependence of U B, the energy density at break, with temperature has been established (7,8). and the There is a body of information for criteria describing failure in stiff brittle adhesives, such as epoxies (9) that are used in structural applications, however there is a dearth of information with regards to criteria applicable to the flexible rubber type of adhesives. These materials are used in great volumes in the packaging, footwear and automotive sectors. This study examines the applicability of this hysteresis energy failure criterion for rubber materials to describe failure in flexible rubber type adhesives. 5

6 2 MATERIALS The applicability of energy as a failure criterion, Equation 1, was investigated for an elastic polyurethane adhesive. 3M DP609, a two-part polyurethane adhesive (also sold as 3M 3532), was cast as large plates, 200 mm x 250 mm x 1 mm. The material was cured at ambient temperature for 12 hours. The cured material was characterised by measurement of the glass transition temperature, Tg, by dynamic mechanical thermal analysis, DMTA. Only adhesive samples where the Tg was 23 o C ± 5 o C were used for testing. Type B ISO 527-2:1993(E) tensile test specimens as shown in Figure 1 with dimensions as given in Table 1 were then pressed from the selected plates. Figure 1. Type B ISO 527-2:1993(E) tensile test specimen Symbol Description Tensile test specimen dimensions (mm) B (1:2) l 3 Minimum overall length 75 b 2 Width at ends 10 ± 0.5 l 1 Length of narrow parallel portion 30 ± 0.5 b 1 Width of narrow parallel portion 5 ± 0.2 R Minimum radius 30 l 0 Distance between gauge marks 25 ± 0.5 L Initial distance between grips 58 ± 2 h Minimum thickness 2 Table 1: Type B ISO 527-2:1993(E) tensile test specimen dimensions 6 [L93:CMMTB130]

7 3 EXPERIMENTAL The mechanical tests were carried out on an Instron 4505 tensile test machine at an extension rate of 4 mm per minute. The hysteresis and failure stress-strain data were obtained at seven nominal test temperatures; 0, 6, 16, 23, 30, 40, 50 o C. The mean value of the breaking stress and strain was obtained from three tensile tests at each temperature. A fresh test sample was then extended to within 5% of the expected breaking stress as calculated from the failure tests and then retracted to zero stress at the same rate to obtain the hysteresis stress-strain curve. This sample was then reextended to ultimate failure. If the failure stress after a hysteresis cycle exceeded the maximum stress from the failure tests by more than 10%, the hysteresis test was discarded and the test was repeated using a fresh sample. The residual strain in the material after a hysteresis test caused a change in the sample gauge length. This necessitated the normalisation of the strain data to account for the automatic resetting of the gauge length by the Instron software. This was achieved by multiplying the failure strain data following a hysteresis cycle by the factor, (1+ the residual strain value). The energy density on extension to failure, U B, was obtained by measuring the area under the load-extension, stress-strain curve. The hysteresis energy, H B, was obtained by measuring the area bounded by the extension-retraction curves. U B *, the energy density on extension to failure after hysteresis is determined from measuring the area under the load-extension, stress-strain curve after a hysteresis cycle. The graphical plotting package Origin by Microcal was used to calculate the areas representing H B, U B and U B *. 4 RESULTS AND DISCUSSION 4.1 THE USE OF ENERGY DENSITY U B, AND HYSTERESIS ENERGY TO BREAK, H B, AS A CRITERION OF FAILURE Figures 2 and 3 show the engineering stresses and strains to failure at the test temperatures for 3M DP609. The area under these failure curves represents U B, the energy density to break. Figures 4 and 5 show the hysteresis curves and the subsequent stresses and strains to failure at each test temperature. Table 2 summarises the average failure energy density, U B, the failure energy density after an extension cycle, U * B and the average hysteresis energy, H B data at the seven test temperatures from Figures 2 to 5. Temperature ( o C) Maximum energy density U B (MJ/m 3 ) Energy density, after extension U B * (MJ/m 3 ) Hysteresis energy H B (MJ/m 3 )

8 Table 2:Energy density and hysteresis energy for 3M DP609 at seven temperatures A range of test temperatures, above and below the measured Tg of the material were selected in order to test the limits of applicability of the failure criterion. As can be seen from the stress strain curves, Figures 2a, 2b, 2c, the strain to failure data clearly show a element of plastic yield behaviour, the magnitude of which is dependent upon the test temperature. The strain to failure data measured after a single hysteresis cycle, Figures 4a, 4b, 4c and 5a also indicate a large element of nonrecoverable deformation. In practice it was found that the failure energy after a single hysteresis cycle, U B * was less than the failure energy of a fresh sample, U B. This is probably due to the work done on the sample causing microcracks or voids which then initiate failure on subsequent testing. Evaluation of the limited amount of data obtained to date, the correlation of the data with the failure equation is reasonable, as use of the failure energy densities, U B, is effectively proposing the maximum case as U B *, the failure energy density after a hysteresis cycle is less than U B. Figure 6 shows a linear regression plot of the logarithm of the energy density, U B, against the logarithm of hysteresis energy. Table 3 gives the parameters of the linear regression, of a logarithmic plot of U B vs H B. Table 3:Coefficients of failure equation for 3M DP609 polyurethane adhesive ln K Correlation coefficient ± [L93:CMMTB130]

9 Figure 2. 3M DP609 Polyurethane adhesive tested to failure at 4 mm/min at 0, 6, 16 and 23 C 9

10 Figure 3. 3M DP609 Polyurethane adhesive tested to failure at 4 mm/min at 30, 40 and 50 o C. 10 [L93:CMMTB130]

11 Figure 4. 3M DP609 Polyurethane adhesive hysteresis and subsequent failure graphs after testing at 4 mm/min at 6, 16 and 23 o C. 11

12 Figure 5.3M DP609 Polyurethane adhesive hysteresis and subsequent failure graphs after testing at 4 mm/min at 30, 40 and 50 o C. 12 [L93:CMMTB130]

13 Figure 6 Log (Energy density), U B, as a function of Log (hysteresis energy), H B. 4.2 DEPENDENCE OF THE ENERGY TO BREAK, U B ON TEMPERATURE The general expression for defining the temperature dependence of the energy to break, U B, with temperature is given by Equation 2 (7) : ln U B = ln k + C T (2) Figure 7 shows the result of plotting the data in using Equation 2. A regression analysis of the data above the glass transition temperature gives a reasonable correlation to Equation 2. The failure mechanism/s at temperatures near or below the glass transition temperature are complex and may be evaluated by use of criteria proposed for stiff adhesive materials (9). It must be repeated that this is only a preliminary study of this relationship, additional data and repeat testing sufficient to fully evaluate this failure criterion for flexible adhesives is to be performed. 13

14 5 COMPARISON OF ADHESIVE DATA WITH RUBBER MATERIALS Harwood and Payne (7) observed that a maxima occurred in the failure energy density, U B at or near the glass transition temperature of the rubber, U B(max). Table 4 compares the maximum energy density, U B(max) at the glass transition temperature for 3M DP609 polyurethane adhesive with the data obtained by Harwood and Payne (7) for four unfilled rubbers. Material U B(max ) (joules/cm -3 ) T g ( o C) 3M DP609 polyurethane adhesive Styrene-butadiene rubber Acrylonitrile-butadiene rubber Butyl rubber Isomerised natural rubber Table 4:Maximum energy density to break, U B(max) and Tg Table 4 shows that the maximum energy density to break of the polyurethane adhesive is only 25% of the value of a styrene-butadiene rubber and significantly lower than any of the other materials. This lower maximum energy density to break of the polyurethane adhesive is probably due to two effects; 1) a lower chain length than the highly extensible rubbers and 2) the influence of the filler materials on the 3M adhesive. The inextensibility of the filler particles is believed to decrease the energy density to break, U B. Figure 7. Effect of temperature on energy to break U B. 14 [L93:CMMTB130]

15 A factor to explain the effect of filler particles on the strain in rubbers has been used (10). This factor relates the volume concentration of filler particles to the effective increase in modulus in the rubber phase, due to the inextensibility of the filler particles, Equation 3. X = σ E ε 0 E 2 = = c c (3) E 0 where: ε is the strain produced by the stress, σ E 0 is the modulus of the rubber without filler E is the modulus and c is the volume concentration of the filler. A similar expression relating the effect of filler particles to the shear viscosity has also been used (11), Equation 4. η 2 3 = η ( c c c ) 0 (4) where η 0 is the viscosity of the rubber without filler c is the volume concentration of the filler The data reported in the literature use filled rubber materials prepared by addition of a known volume of filler material to a base gum rubber, thus it was simple to define the change in ultimate properties with filler concentration. In this study of this failure criterion, commercial adhesives are being used therefore information on filler concentrations will be required from adhesive manufacturers. One adhesive manufacturer has indicated that this information may be supplied. Testing of an unfilled based material is also required, but if data is available for a material with range of filler concentrations, an estimation the material properties for the unfilled base material may be obtained. 6 CONCLUSIONS A simple empirical relationship exists between the energy to break, U B and the hysteresis energy at break, H B derived from uniaxial tensile tests to failure for rubber materials. This relationship has been investigated using a commercial flexible polyurethane adhesive, 3M DP609. The initial results, Figure 7, indicate that this failure criterion may describe failure in this material between two limits: 1 at temperatures above the glass transition temperature where the material tends towards hyperelastic behaviour, and 2 at higher temperatures where the hysteresis energy, H B tends to zero, H B approaches the equilibrium modulus. 15

16 7 FURTHER WORK This initial study of an energy density failure criterion has yielded promising results. The proposed work programme includes testing bulk specimens of a butadiene/epoxy, a filled butadiene, a rubber toughened epoxy as well as further tests on 3M DP609 polyurethane adhesive to establish the applicability of this criterion for a range of adhesives. Finite element analysis is to be used in this programme of work to model the response of adhesive joints under load. This analysis requires the input of data from additional load configurations, i.e. equibiaxial, shear, as well as uniaxial loading to allow the modelling of the material using a finite element package. The stress-strain data from these additional load cases will also be tested against this energy density failure criterion. This hysteresis, H B /failure energy density, U B, failure criterion in practice represents failure upon the instantaneous application of a critical load. Realistically adhesive joints can sustain loads in excess of the theoretical maximum. It is obvious that other mechanisms are in operation which effectively spread this instantaneously applied critical load across the adhesive joint. This transfer of 'excess' load across joints occurs by creep and stress relaxation mechanisms. This slower time dependent behaviour of adhesives is to be investigated in creep tests to failure. The data from these tests will be used in the finite element modelling of the mechanisms by which adhesive joints can sustain loads greater than the expected failure load. The total energy dissipated in creep to failure tests will also be tested against this proposed failure criterion. The work of Smith (1,3) indicates that if time-temperature superposition is applicable the ultimate tensile properties can be characterised by a failure envelope that is independent of time or strain rate, and temperature. The use of time-temperature superposition will allow the correlation of data from different materials which normally correspond to different relative positions on the characteristic failure envelopes. 16 [L93:CMMTB130]

17 8 REFERENCES 1. Smith, T.L. J. Polymer Sci. A, 1, 3597 (1963). 2. Smith, T.L. J. Appl. Phys., 35, 27 (1964). 3. Smith, T.L., Frederick, J.E. J. Appl, Phys., 36, 2996 (1965). 4. Halpin, J.C. J. Appl. Phys., 35, 3133 (1964). 5. Halpin, J.C., Bueche, F. J. Appl. Phys., 35, 3142 (1964). 6. Grosch, K., Harwood, J.A.C., Payne, A.R. Nature, 212, 497 (1966). 7. Harwood, J.A.C., Payne, A.R. J. Appl. Polymer Sci, 12, 889 (1968). 8. Whittaker, R.E. Polymer 13, 169 (1972). 9. Kinloch, A.J. Review of Adhesive Bond Failure Criteria, MTS Programme , Tests and Measurement Methods on the Performance of Adhesive Joints, Project 2: Failure Modes and Criteria, Report 1, August 1994, AEA-ESD Payne, A.R., Whittaker, R.E. J. Appl. Polymer Sci. 15, 1941 (1971). 11. Mullins, L., Tobin, N.R. J. Appl. Polymer Sci. 9, 2993 (1965). 9 LIST OF FIGURES Figure 1 Figure 2 Type B ISO 527-2:1993(E) tensile test specimen 3M DP609 polyurethane adhesive tested to failure at 4 mm/min at 0, 6, 16 and 23 o C. Figure 3 3M DP609 polyurethane adhesive tested to failure at 4 mm/min at 30, 40 and 50 o C. Figure 4 Figure 5 3M DP609 polyurethane adhesive hysteresis and subsequent failure graphs after testing at 4 mm/min at 6, 16 and 23 o C. 3M DP609 polyurethane adhesive hysteresis and subsequent failure graphs after testing at 4 mm/min at 30, 40 and 50 o C. Figure 6 Energy density, U B, as a function of hysteresis energy, H B. Figure 7 Effect of temperature on energy to break, U B. 17

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