Cohesive zone models and the plastically deforming peel test

The peel test is a popular test method for measuring the peeling energy between flexible laminates. However, when plastic deformation occurs in the peel arm(s) the determination of the true adhesive fracture energy, G c , from the measured peel load is far from straightforward. Two different methods of approaching this problem have been reported in recently published papers, namely: (a) a simple linear-elastic stiffness approach, and (b) a critical, limiting maximum stress, σ max , approach. In the present article, these approaches will be explored and contrasted. Our aims include trying to identify the physical meaning, if any, of the parameter σ max and deciding which is the better approach for defining fracture when suitable definitive experiments are undertaken. Cohesive zone models Fracture mechanics Laminates Peel tests Plastic deformation     

The Mechanical Behaviour of Polyimide/Copper Laminates Part 2: Peel Energy Measurements

The mechanical peel behaviour of laminates consisting of polyimide films adhered to copper foil using a modified acrylic adhesive has been studied over a wide range of test rates and temperatures. The laminates were prepared from polyimide films which had been subjected to either a “high-thermal history” or a “low-thermal history” treatment during the production of the film. The measured peel energies of the laminates could be superimposed to give a master curve of peel energy versus the reduced rate of peel test, Ra_T, where R is the rate of peel test and a_T is the time-temperature shift factor. The appropriate shift factors were a function of the test temperature and were mainly deduced from tensile tests conducted on the bulk adhesive. The “high-thermal history” laminates gave higher peel energies and the locus of failure of the laminates was mainly by cohesive fracture through the adhesive layer. At low values of log₁₀ Ra_T, i.e. Low rates of peel and high test temperatures, the “low-thermal history” laminates also failed in the adhesive layer and possessed similar peel energies to those measured for the “high-thermal history” laminates. However, at high log₁₀ Ra_T values, the peel energies measured for the “low-thermal history” laminates were lower and showed a wider scatter. These arose from a different locus of failure occurring in these “low-thermal history” laminates when tested under these conditions. Namely, it was found that most of these laminates failed in a weak boundary layer in the outer regions of the “low-thermal history” polyimide film.     

Interfacial and Bulk Contributions to Peeling Energy

Thin polyurethane films, having low adhesion to dried protein, were developed as candidate materials for non-adhesive surgical dressings. In order to model wound-adhesion, gelatine was cast from solution on to the film and allowed to dry. The film was peeled from the gelatine at 180° peel angle, and the peel force measured as a function of the temperature of test. The dynamic mechanical properties of the films were measured over the range -90°C to 110°C and values of tan δ were determined at the temperatures employed for peeling. Thus, a correlation was obtained between peeling energy and tan δ for each of eight films.

The generalised theory of fracture mechanics states that the adhesive failure energy is given by the product of an interfacial energy term and a “loss function” involving the hysteresis ratio of the material. If the strains are small the hysteresis ratio is proportional to tan δ. The experimental results show excellent agreement with the theory, but the interfacial term turns out to be much greater than the true interfacial energy (or thermo-dynamic work of adhesion). The reason for this result is discussed.     

Application of the Island Blister Test for Thin Film Adhesion Measurement

The island blister test has recently been proposed as an adhesion test which allows the peel of thin, well-adhered films without exceeding the tensile strength of the film. The island blister test site is a modification of the standard blister test site, consisting of a suspended membrane of film with an “island” of substrate at the film center. The membrane support and island are secured to a rigid plate and the film is pressurized, peeling the film inward off the island. A model for this inward or “annular” peel indicates that even for systems of good adhesion, peel can be initiated at low enough pressures to prevent film failure by making the center island sufficiently small relative to the size of the film.

We have fabricated island blister test sites using micromachining techniques and have used them to measure the debond energy of polymer films on various substrates. The peel data obtained from these island sites match well to the behavior predicted by a simple fracture mechanics analysis. This paper reports the fabrication of the island test sites, the experimental verification of the test, and the results of application of the test to polyimide films on metallic and polymeric substrates.     

Protocols for the Measurement of Adhesive Fracture Toughness by Peel Tests

This article reports on the work of the European Structural Integrity Society Technical Committee 4 (ESIS TC4) and its activities in the development of test protocols for peel fracture. Thirteen laboratories have been working on peel test methods in ESIS TC4 since 1997 and their activities are ongoing.

The aim of the work is to develop robust and credible test methods for the determination of adhesive fracture toughness by peel tests. Several geometric configurations have been used, namely, multi-angle fixed arm peel, T-peel, and roller assisted peel in the form of a mandrel test.

The starting point of their work is an established analysis of a peel method that is often developed from a global energy approach. The adopted analysis is combined with an experimental approach in order to resolve ambiguities in the determination of adhesive fracture toughness (G_A). The test methods involve the measurement of peel strength in order to calculate the total input energy for peel (G) and the calculation of the plastic bending energy (G_P) during peel. The latter is often obtained from a measurement of the tensile behaviour of the peel arm. Adhesive fracture toughness is then G - G_P.

Four ESIS TC4 projects are described. The first relates to fixed arm peel whilst the second and third involve both fixed arm and T-peel. The fourth project combines mandrel peel and fixed arm peel. Each project uses different types of polymeric adhesives in the form of quite different laminate systems. The selection of the laminate system enables all characteristics of laminate property to be embraced, for example, thin and thick adhesive layers, polymeric, and metallic peel arms and a range of flexibility in the laminates.

The development of the enabling science required to establish the test protocols is described and software for conducting all calculations is referenced.     

Evaluation of the Constrained Blister Test for Measuring Adhesion

The constrained blister test (CBT) was evaluated as a method for measuring adhesion using a model system, electrical tape bonded to polystyrene. Pressure is applied through a circular inlet hole in the substrate, causing the adhesive to “blister” up and peel radially away from the substrate. A glass constraint, placed some distance above the adhesive, limits deformation of the adhesive in the vertical direction and promotes radial peel. By operating at low spacer height (the distance of the constraint above the adhesive) and very low growth rates, the energy spent for deformation of the adhesive and viscoelastic dissipation is minimized. Blister radial growth was linear with time, and growth rate increased linearly with the second power of the energy input. An intrinsic, rate-independent adhesion energy was obtained by extrapolation to zero crack growth rate. The CBT was compared with two peel tests. The dependence of the growth rate on energy input was different, but the extrapolation to zero growth rate gave the same value of the intrinsic adhesion energy.     

The Use of Large Diameter Monofilament for Improving Peel Resistance of a Brittle High Temperature Adhesive

Peel force measurements as a function of adherend thickness are reported for adhesively bonded specimens based on a cyanate ester resin and aluminium adherends. It has been demonstrated that by incorporating large diameter (0.28mm) PTFE monofilament within the adhesive bond then the peel force and associated fracture energy can be increased significantly over that for specimens based on adhesive alone. Fracture energy measurements are derived for specimens with peeling adherend thickness of up to about 0.6 mm using the 90° peel test. Fracture energies are also derived for peeling of more practically-representative 1.6mm thickness adherends using a single cantilever beam experiment. In-situ photoelasticity and SEM microextensomctry experiments are reported which show the stress fields and displacements associated with the presence of the monofilament. It is believed that the reported increase in measured fracture energy is partly due to the crack pinning effect of the monofilament, and partly due to the monofilament creating a “load shadowed” region between adherend and monofilament which prevents the interfacial crack from propagating between adherend and adhesive.     

The Interlaminar Bond Strength of Flexible Polymer-Metal Laminates

An alternative test method to the traditional 180° “T” peel test has been developed for the measurement of interlaminar bonding in three-ply (polyester/aluminium/polypropylene) flexible-packaging, laminate materials. The new test is thought to involve mixed mode I (opening) and mode II (shearing) failure, and takes into account the yielding of the polypropylene layer during testing. The method allows more direct comparisons between materials to be made, and allows the measurement of strong bonds, where a peel test would result in yield or fracture of the substrate arms before debonding.     

The Fracture Mechanics of the Pin and Collar Test for High Temperature Anaerobic Adhesives

A mechanical test method for the studies of high-temperature anaerobic adhesives has been established, based on fracture mechanics, by modifying the standard test method of collar and pin test. Linear Elastic Fracture Mechanics approach was applied to the establishment of the relationship between adhesive fracture surface energy “R”, fracture load and crack length. Hence, from the joints containing a given artificial flaw the adhesive fracture surface energy can be determined; alternatively, from the strength of the joints without artificial flaws the inherent flaw size “a_i” can be calculated to account for the decrease of joint strength.

The experimental techniques were applied to examine the mechanical behaviour of the joint system based on high temperature anaerobic adhesives. It was found that the joints cured at room-temperature had higher adhesive fracture surface energy but lower joint strength than the joints postcured at high temperatures. The “a_i” data explained this interesting phenomenon. The joints cured at room-temperature had extraordinarily large “a_i”, which was found to be formed by the uncured adhesive near the edges of the joints and the adhesive further cured in the postcure processes to reduce the “a_i”. Also, the growth of intrinsic flaw was found to be responsible for the deterioration of the joints in a short-term, high-temperature ageing process.     

The effect of flexible substrates on pressure-sensitive adhesive performance

The adhesive fracture energy (fracture toughness) of tapes during globally elastic unpeeling is often calculated from the relation “G=P/b(1−cos θ)”. We show that while this expression is correct for elastic peeling from rigid substrates, it gives misleading results when peeling from reversible flexible substrates. A two-dimensional analysis is presented for peeling from non-linear elastic substrates that give consistent fracture energies from experimental data.     

Protocols for the Measurement of Adhesive Fracture Toughness by Peel Tests

This article reports on the work of the European Structural Integrity Society Technical Committee 4 (ESIS TC4) and its activities in the development of test protocols for peel fracture. Thirteen laboratories have been working on peel test methods in ESIS TC4 since 1997 and their activities are ongoing.

The aim of the work is to develop robust and credible test methods for the determination of adhesive fracture toughness by peel tests. Several geometric configurations have been used, namely, multi-angle fixed arm peel, T-peel, and roller assisted peel in the form of a mandrel test.

The starting point of their work is an established analysis of a peel method that is often developed from a global energy approach. The adopted analysis is combined with an experimental approach in order to resolve ambiguities in the determination of adhesive fracture toughness (G _A ). The test methods involve the measurement of peel strength in order to calculate the total input energy for peel (G) and the calculation of the plastic bending energy (G _P ) during peel. The latter is often obtained from a measurement of the tensile behaviour of the peel arm. Adhesive fracture toughness is then G – G _P .

Four ESIS TC4 projects are described. The first relates to fixed arm peel whilst the second and third involve both fixed arm and T-peel. The fourth project combines mandrel peel and fixed arm peel. Each project uses different types of polymeric adhesives in the form of quite different laminate systems. The selection of the laminate system enables all characteristics of laminate property to be embraced, for example, thin and thick adhesive layers, polymeric, and metallic peel arms and a range of flexibility in the laminates.

The development of the enabling science required to establish the test protocols is described and software for conducting all calculations is referenced.     

Wave Phenomena in Low Angle Peeling

The angular dependence of peeling has been investigated over a wide range of peel angles for a rubber strip peeled from glass. At low peel angles the peel front becomes “V”-shaped, wave phenomena are often observed and the peel energy can increase by an order of magnitude or more. A tentative theory, which appears to give the correct magnitude in a worked example, is advanced to account for the energy increase. The influence of factors such as electrostatic charge, deformation and rate on the observed phenomena are discussed.     

THE DEVELOPMENT OF A MANDREL PEEL TEST FOR THE MEASUREMENT OF ADHESIVE FRACTURE TOUGHNESS OF EPOXY–METAL LAMINATES

A mandrel peel test is established for measuring the adhesive fracture toughness of a metal/rubber-toughened epoxy laminate system. By adopting an energy balance analysis it is possible to determine directly both adhesive fracture toughness and plastic work in bending the peel arm around the mandrel. The suitability of the procedure is examined for various types of metal peel arms, which are classified in terms of their ability to deform plastically during the test. The plastic work is also predicted theoretically, and comparisons are made between the measured and calculated values. The fracture energies determined from the mandrel tests are compared with those obtained from 90° fixed-arm peel tests. For the calculations of plastic work in bending in the fixed arm test, various options are used when modelling the tensile stress-strain behaviour of the peel arm material. In addition, the adhesive layer thickness is considered in terms of its influence on the calculation of adhesive fracture toughness.     

THE DEVELOPMENT OF A MANDREL PEEL TEST FOR THE MEASUREMENT OF ADHESIVE FRACTURE TOUGHNESS OF EPOXY-METAL LAMINATES

A mandrel peel test is established for measuring the adhesive fracture toughness of a metal/rubber-toughened epoxy laminate system. By adopting an energy balance analysis it is possible to determine directly both adhesive fracture toughness and plastic work in bending the peel arm around the mandrel. The suitability of the procedure is examined for various types of metal peel arms, which are classified in terms of their ability to deform plastically during the test. The plastic work is also predicted theoretically, and comparisons are made between the measured and calculated values. The fracture energies determined from the mandrel tests are compared with those obtained from 90° fixed-arm peel tests. For the calculations of plastic work in bending in the fixed arm test, various options are used when modelling the tensile stress-strain behaviour of the peel arm material. In addition, the adhesive layer thickness is considered in terms of its influence on the calculation of adhesive fracture toughness.     

Studies on The Modification of Epoxy Resin with Silicone Rubber

In order to find a compatibilizer for epoxy resin/silicone rubber systems, interfacial tension of epoxy resin mixed with modified silicone oils which had the compatible groups to epoxy resin was measured against RTV silicone rubber and silicone oil. From the results, it was found that one of polyether modified silicone oils (EtMPS) had strong interfacial activity. Then using the EtMPS as the compatibilizer, RTV silicone rubber or silicone diamine was filled in epoxy resin. The effects of silicone content of these materials on impact fracture energy and on peel strength were investigated. The impact fracture energy of epoxy resin was increased by the addition of RTV silicone rubber up to two times that of unmodified resin while silicone diamine had almost no effect which might be due to the small molecular weight. T-peel strengths of aluminium plates bonded by epoxy resin filled with RTV silicone rubber and with silicone diamine effectively increased with the increasing of silicone content showing the maximum at 10 ∼ 20 phr. The fracture surfaces after the mechanical tests of these materials were observed by a scanning electron microscope. Many particles of silicone rubber in the size of 1 ∼ 20 μ were observed over the fracture surface.     

Cohesive Zone Models of Polyimide/Aluminum Interphases

The fracture energy required to delaminate PMDA/ODA polyimide films from aluminum substrates was determined using the circular blister test. Films were prepared by spin coating the polyamic acid of PMDA and ODA onto polished aluminum substrates, by vapor co-deposition of PMDA and ODA monomers onto polished aluminum substrates, or by spin-coating the polyamic acid onto polished aluminum substrates that were first coated with thin layers of γ-aminopropyltriethoxysilane (γ-APS). Elastic and elastoplastic analyses were used to extract the fracture energies from the blister test results. Elastoplastic analysis provided fracture energies that ranged from 579 J/m² for spin-coated films on polished substrates to 705 J/m² for vapor-deposited films on polished substrates and to 750 J/m² for spin-coated films on silanated substrates. These values were intermediate between those provided by the two different elastic analyses. Differences in fracture energy determined by the three different analysis methods were related to plastic deformation in the films and, in the case of the two elastic analyses, to differences in the approach used to extract the fracture energy from experimental results. Failure of specimens prepared by spin-coating PMDA/ODA films onto aluminum substrates occurred cohesively within the polymer, near the interface between well imidized polymer in the bulk of the films and poorly imidized polymer in a layer near the aluminum surface. For the case of specimens prepared by vapor codeposition of PMDA and ODA monomers, failure occurred within the vapor deposited films, close to the aluminum/film interface. Failure of spin-coated films on silanated substrates occurred mostly within the γ-APS but leaving 'islands' of polyimide and silane on the aluminum.     

Calorimetric Measurements of The Heat Generated by The Peel Adhesion Test

The peel test is a simple mechanical test commonly used to measure the adhesion of flexible films bonded to rigid substrates. When the film is deformed elastically during peeling, the peel force is a direct measure of the strength of the interface. However, when plastic deformation takes place, the work of detachment is much larger than the thermodynamic work of forming the fracture surfaces. Simultaneous mechanical and calorimetric measurements of the work of detachment and the heat generated during the peeling of polymeric films from metal substrates and metal films from polymeric substrates have been made. An energy balance for peeling has been proposed. Most of the work of peeling was consumed by plastic deformation. The peeled polymer dissipated approximately one half of the work of peeling as heat and most of the remainder was stored in the peeled material. The peeled metal dissipated most of the work of peeling as heat.     

Strain energy release rates of a pressure sensitive adhesive measured by the shaft-loaded blister test

The elastic solution to the shaft-loaded blister test (SLBT) was adopted to measure the applied strain energy release rate ( G ) of Kapton® pressure sensitive adhesive (PSA) tape bonded to a rigid substrate. The substrates used were either aluminum or Teflon®, a high-energy surface and low-energy surface, respectively. The values of G were calculated from three different equations: (1) load-based, (2) hybrid, and (3) displacement-based. An experimental compliance calibration was utilized to measure the film's effective tensile rigidity, ( Eh ) eff , the results of which are presented in an appendix. Plastic deformation at the contact area of the shaft tip and adhesive results in an overestimated displacement ( w 0 ) (relative to the elastic model), leading to disagreement among the values of G calculated. Estimation of the effective membrane stress in the film, ( N eff ), as well as the reasonable agreement between the value of ( Eh ) determined from a stress-strain experiment and the compliance calibration, suggest that, in spite of the plastic deformation, the assumption of linear elasticity in the crack growth region and hence the validity of the model, is reasonable. The compliance calibration has been shown to improvethe agreement among the values of G calculated from the three equations. Using the load-based equation, the assumed "correct" value of G may be obtained for a thin adhesive coating independent of the film's stiffness even in the presence of plastic deformation at the shaft tip. Comparing the value of G obtained by a pull-off test and the 90° peel test for a single ply indicates that the value of G obtained by the SLBT is of reasonable magnitude, being less than that obtained by the more firmly established pull-off test, and also that undesirable plastic deformation is reduced relative to the 90° peel test. An experimental configuration for studying the effects of liquids on the fracture energy has been demonstrated for the SLBT. This study indicates that the SLBT is an attractive and convenient test method for measuring the strain energy release rate of adhesive films, because of the insensitivity of the load-based equation to the coating stiffness, plus the independence of the value of G on the plastic deformation at the shaft tip, and the reduced plastic deformation at the crack front relative to the 90° peel.     

STRAIN ENERGY RELEASE RATES OF A PRESSURE SENSITIVE ADHESIVE MEASURED BY THE SHAFT-LOADED BLISTER TEST

The elastic solution to the shaft-loaded blister test (SLBT) was adopted to measure the applied strain energy release rate ( G ) of Kapton® pressure sensitive adhesive (PSA) tape bonded to a rigid substrate. The substrates used were either aluminum or Teflon®, a high-energy surface and low-energy surface, respectively. The values of G were calculated from three different equations: (1) load-based, (2) hybrid, and (3) displacement-based. An experimental compliance calibration was utilized to measure the film's effective tensile rigidity, ( Eh ) eff , the results of which are presented in an appendix. Plastic deformation at the contact area of the shaft tip and adhesive results in an overestimated displacement ( w 0 ) (relative to the elastic model), leading to disagreement among the values of G calculated. Estimation of the effective membrane stress in the film, ( N eff ), as well as the reasonable agreement between the value of ( Eh ) determined from a stress-strain experiment and the compliance calibration, suggest that, in spite of the plastic deformation, the assumption of linear elasticity in the crack growth region and hence the validity of the model, is reasonable. The compliance calibration has been shown to improvethe agreement among the values of G calculated from the three equations. Using the load-based equation, the assumed "correct" value of G may be obtained for a thin adhesive coating independent of the film's stiffness even in the presence of plastic deformation at the shaft tip. Comparing the value of G obtained by a pull-off test and the 90° peel test for a single ply indicates that the value of G obtained by the SLBT is of reasonable magnitude, being less than that obtained by the more firmly established pull-off test, and also that undesirable plastic deformation is reduced relative to the 90° peel test. An experimental configuration for studying the effects of liquids on the fracture energy has been demonstrated for the SLBT. This study indicates that the SLBT is an attractive and convenient test method for measuring the strain energy release rate of adhesive films, because of the insensitivity of the load-based equation to the coating stiffness, plus the independence of the value of G on the plastic deformation at the shaft tip, and the reduced plastic deformation at the crack front relative to the 90° peel.     

A New Approach to the Copper/Epoxy Joint Using Atmospheric Pressure Glow Discharge

A new approach for adhering copper to an epoxy resin was studied. In this new approach, the copper surface was first treated with hydrogen plasma generated by the atmospheric pressure glow (APG) discharge. Then a thin film of γ-aminopropyltriethoxysilane (γ-APS) was formed on the treated copper surface. The copper oxide formed by air on the copper surface deteriorated the adhesion by forming a weak boundary layer, part of which could separate from the surface. This oxide layer was reduced when an APG hydrogen plasma was applied for a couple of minutes at a frequency of 13.56 MHz and a power input of 200 W. The resulting peel strength at the copper/epoxy interface increased up to ca. 0.9 Kg/cm. Curing temperature of γ-APS was also an important factor in obtaining good adhesion at the copper/epoxy interface, with the highest value of peel strength occurring at a curing temperature of 120°C.