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CONTACT FATIGUE BEHAVIOUR OF AN EPOXY THERMOSET M. C. DUBOURG, N. HADDAR Laboratoire de Mécanique des Contacts, INSA de Lyon, 69622 Villeurbanne, FRANCE; e-mail: [email protected] A. CHATEAUMINOIS Laboratoire de Physico-Chimie Structurale et Macromoléculaire, ESPCI, 75005 Paris, FRANCE; e-mail: [email protected] M. KHARRAT Ecole Nationale d'Ingénieurs de Sfax, 3018 Sfax, TUNISIA; e-mail: [email protected] SUMMARY The contact fatigue behaviour of an epoxy thermoset has been investigated under small amplitude oscillating micro-motions, i.e. fretting. Under such a loading, the development of a network of fatigue cracks was observed within a few thousands cycles, without any significant wear processes. Crack initiation and propagation processes within the epoxy substrate have been monitored from in situ microscopic observations of the contact area and from measurements of the tangential contact stiffness. The experimental data regarding crack initiation sites and initial growth directions have been successfully interpreted in the light of a theoretical model based on specific mechanical parameters linked to the Mode I and Mode II propagation driving forces.
Keywords: Contact Fatigue, Epoxy, Cracking, Fretting
1 INTRODUCTION Fatigue wear models have been largely derived in order to account for the wear resistance of polymers substrates sliding against rigid counterfaces which are insufficiently rough for the elastic limit of the polymer to be exceeded during asperity deformation [1, 2]. Direct experimental evidence of such contact fatigue processes, however, are scarce: propagating cracks in polymers are difficult to detect on an asperity scale because of the elastic recovery. As a result, the exact nature of the contact damage micro-mechanisms (crack orientation, propagation rates…) and the way they relate to the fatigue properties of the bulk material remains largely to be established.
In this investigation, the cracking micro-mechanisms within an epoxy counterface contacting a smooth glass counterface have been studied under small amplitude oscillating micro-motions, i.e. fretting. Due to the reduced sliding amplitude within the contact area, such a contact loading allowed the generation of fatigue cracks at the scale of a macroscopic contact, without the complications arising from particle detachment and wear [3]. Accordingly, the fretting contact under con-sideration may be viewed as a model single asperity contact simulating, at an observable scale, the contact fatigue processes. The development of the cracking network during the fretting tests was investigated from in situ observations of the contact area and from the measurement of the tangential contact stiffness. These experimental data have been analysed by means of a theoretical contact mechanics approach focused on the initiation sites and the initial crack growth directions.
2 FRETTING EXPERIMENTS
2.1 Materials and experimental conditions The polymer under investigation was an epoxy thermoset obtained by curing a stoichiometric mixture of a bisphenol-A prepolymer (DGEBA) with isophoron diamine (IPD). The counterface was a smooth (Ra<2 nm) glass hemisphere with a 48 mm radius. The fretting tests have been carried out using a specific device which has been fully described elsewhere[3, 4]. For all the experiments to be reported, the normal load, P, was set to 100 N, while an imposed oscillating tangential displacement in the micrometer range (from ±40 µm to ±60 µm) was applied to the flat polymer counterface. Under these conditions, the average diameter of the contact area was 2.1 mm, which yield an average contact pressure pm=32 MPa. In addition to the continuous monitoring of the tangential load, Q, and displacement, δ, the fretting device allowed performing in situ microscopic observations of the contact area through the glass counterface.
2.2 Cracks development within gross-slip regime A typical example for the development of a contact fatigue crack network is shown in Fig.1. This experiment was carried out using an imposed displacement amplitude (δ∗ = ± 60 µm) which ensured the development of a gross-slip contact condition during the entire fretting test. The initiation and the propagation of cracks were detected at the surface of the epoxy specimens by means of the in situ optical observations. In addition, a continuous monitoring of the tangential contact stiffness, K, was also performed in order to provide information regarding the propagation of the
cracks through the depth of the epoxy substrate. As shown in Fig. 1, the contact stiffness was determined from the initial slope of the tangential displacement/load fretting loops. Accordingly, this measurement is carried out when the sliding direction is reversed, i.e. under a quasi-stick contact condition. As a result, the tangential
stiffness is mainly a measure of the elastic accommodation of the epoxy substrate. The value of K can therefore be supposed to be sensitive to crack propagation, by virtue of the resulting accommodation of the imposed displacement through the opening and the closing of the cracks during the fretting cycle.
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Figure 1: Crack initiation and propagation within the gross-slip regime.
Pictures (except the last one) obtained from in situ observation of the contact area during the fretting test. The white arrows indicate the locations of the cracks
After about 300 fretting cycles, two cracks were detected close to the edge of the contact and at two approximately symmetrical locations along the sliding direction. The propagation of these cracks occurred within a few tens of cycles, in a quasi-brittle manner, as indicated by the optical observations and the rapid decrease in the measured tangential stiffness. As the
number of cycles was increased, secondary cracks developed close to the semi-elliptical initial cracks, but they resulted in a more limited and progressive decrease in contact stiffness. Once the two initial cracks have propagated, their neighbouring areas are unloaded as a consequence of crack flank movements and due to the reduction in the specimen stiffness. As a result, the
mechanical parameters inducing crack initiation and propagation become less efficient in the vicinity of the initial cracks. Such an effect can probably account for the observed reduced crack growth rate of the secondary cracks.
Cross-sections of the epoxy substrates at the end of the fretting tests showed that the depths of the two initial cracks were comparable to the radius of the contact. These observations tend to demonstrate that the arrest of the main cracks is due to the vanishing of the contact stress field as these cracks propagate through the thickness of the epoxy substrate.
Similar crack networks were observed within the whole range of imposed tangential displacement (i.e. from δ* = ±40 µm to δ* = ±60 µm). As indicated by a syste-matic observation of the specimen cross-sections, the initial growth direction of the two main cracks was oriented to about 11 degrees with respect to a direction perpendicular to the contact interface. Slightly higher growth directions were observed for the neighbouring secondary cracks, but it must kept in mind that the latter propagated within a contact stress field which was strongly modified after the early propagation of the main cracks. In the subsequent part of this paper, the theoretical analysis will be focused on the initiation of the initial cracks, on the basis of a continuum stress field analysis which was carried out within the subsurface epoxy layer. 3 THEORETICAL APPROACH The initial growth of the main cracks was analysed using a two steps procedure. In a first stage, the three-dimensional contact stress distribution within the epoxy substrate was calculated within the frame of linear elasticity. The use of an elastic approach was justified by the low viscoelasticity of the glassy epoxy polymer at the frequency and temperature of the fretting tests (tanδ <0.005 at 1 Hz and 25 °C). In addition, the application of a modified Von Mises criterion taking into account the effects of hydrostatic pressure revealed that the polymer was strained below yield [5]. The contact problem was solved as a unilateral contact problem obeying a Coulomb's friction law. By means of a Kalker's algorithm [6], the contact area, the contact pressure distribution and the internal stresses were determined under a gross-slip contact condition. The magnitude of the corresponding tangential load was determined from the experimental value of the co-efficient of friction within the gross slip regime (µ = 1.2).
In a second stage, the initial crack propagation processes were analysed in the meridian plane of the contact, y=0 (Fig.2), where cracks first initiate. The crack initiation mechanisms have been considered theoretically in the light of a simple dislocation dipole model that was initially introduced for metallic materials [7, 8]. Two sets parameters, based on the amplitude of the shear stress, τm, along the crack path and the amplitude of the tensile stress, σm, perpendicular to the crack path have been considered. In order to take into account the strong
stress gradient close to the contact interface, τm and σm have been averaged over a finite length (20 µm) from the polymer surface.
In previous investigations using aluminium alloys[9], the choice of these parameters was justified from physical arguments based on the growth of dislocations from the surface of the crystalline material. Although the material under investigation is an amorphous polymer, a previous fretting analysis [10] tends to demonstrate that, regarding contact fatigue cracks, the mechanical loading prevail on the micro-structural factors. Within the context of this study, the sets of parameters based on τm
and σm will, however, be used without any underlying assumptions regarding the nature of the microscopic processes involved in crack initiation. They will just be used as tools to discriminate between predominant Mode I or Mode II crack propagation driving forces.
The values of σm and τm have been calculated as a function of the crack orientation (angle α; Fig. 2) and the location within the contact, during the various steps of a discrete tangential loading. In the present simulation, the sliding amplitude was set to two discretisation steps, i.e. 240 µm.
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meridian plane y = 0. 2a is the contact diameter.
In Fig.3, the maximum value, ∆σm*, of the effective
amplitude of the average tensile stress has been reported as a function of the orientation. ∆σm
* is defined as the amplitude of the positive values of the average tensile stress (i.e. σm>0), which is assumed to represent the driving force regarding the opening of tensile fatigue cracks. Due to the loading symmetry and for the sake of clarity, only the results corresponding to one half of the contact have been presented. It can be seen that the maximum value of ∆σm
* corresponds to the edge of the contact (x/a = -1), where the initial cracks were experimentally detected. The orientation of the corresponding crack plane is 7°, which is a value very close to the experimental one (11°). On the opposite, the
orientation of the maximum amplitude of the average shear stress at the contact edge (α = 53°) do not correspond to the orientation of the experimental cracks. The simulation therefore tends to establish that the initial cracks nucleated close to the contact edge correspond to tensile fatigue cracks. Under such conditions, the propagation driving force is assumed to be the maximum amplitude of crack opening.
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Figure 3: Changes in the effective maximum values of the amplitude of the tensile stress, ∆σm
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Figure 4 : Changes in the maximum values of the am-plitude of the shear stress, ∆τm, and in the orientation of the corresponding crack plane as a function of the location from the centre of the contact area.
The contact fatigue data can interestingly be compared to the plain fatigue data obtained for the epoxy material under investigation. Under a three-point bending fatigue loading, it was found that the lifetime of the bulk epoxy is about 300 cycles for σmax = 70 MPa [3], i.e. a tensile stress corresponding the maximum value of ∆σm
*. As reported in Fig.1, very similar crack initiation and propagation times were observed under contact fretting conditions. Although the fatigue conditions were different for the two kinds of loading (R = 0.1 and F =10 Hz for plain fatigue tests; R = -1.2 and F = 1 Hz for fretting tests), these results tend to demonstrate that plain fatigue data are relevant for the prediction of
contact fatigue cracking under predominantly tensile loading. 4 CONCLUSION The experimental analysis of the contact fatigue behaviour of an epoxy thermoset contacting a glass counterface showed that the material response is dominated by the early propagation of cracks at the edge of the contact. From a contact mechanics theoretical analysis, it was demonstrated that the initial cracks propagated under predominantly tensile stress conditions. Moreover, the associated lifetimes were found to be consistent with the values predicted from plain fatigue data and from the calculation effective amplitude of the tensile stress perpendicular to the crack plane. 5 REFERENCES [1] Jain, V. K. and Bahadur, S. Development of a wear equation for polymer-metal sliding in terms of the fatigue and topography of the sliding surfaces., Wear, 1980, 60, 237-248. [2] Lancaster, J. K. Materials-specific wear mechanisms: relevance to wear modelling, Wear, 1990, 141, 159-183. [3] Chateauminois, A., Kharrat, M. and Krichen, A. (2000). Analysis of Fretting Damage in Polymers by Means of Fretting Maps. Fretting Fatigue : Current Technology and Practices, ASTM STP 1367. V. Chandrasekaran and C. B. Elliott. West Conshohocken, American Society for Testing and Materials, 325-366. [4] Kharrat, M., Krichen, K. and Chateauminois, A. Analysis of the fretting conditions in a contact between an epoxy thermoset and a glass counterface., Trib. Trans., 1999, 42, N°2, 377-384. [5] Kharrat, M. (1996). . Ecully, Ecole Centrale de Lyon: 192. [6] Kalker, J. J. (1990). Three dimensional elastic bodies in rolling contact. Dordrecht, Kluwer Academic Publishers. [7] Tanaka, K. and Mura, T. A dislocation model for fatigue crack initiation, J. Appl. Mech., 1981, 47, 111-113. [8] Yamashita, N. and Mura, T. Fatigue crack initiation under repated oblique force, Wear, 1983, 91, 235-250. [9] Lamacq, V. and Dubourg, M. C. Modelling of initial crack growth and crack branching under fretting conditions., Fatigue & Fracture of Eng. Mat.and Struct., 1999, 22, N°6, 535-542. [10] Lamacq, V., Dubourg, M. C. and Vincent, L. (1996). Fretting fatigue crack growth analysis - Experimental photoelastic method combined with numerical model. ECF 11, Poitiers, 1387-1392.
