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Characterization by ultra-micro indentation of an oxidized epoxy polymer: Correlation with the predictions of a kinetic model of oxidation
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Polymer Degradation and Stability 93 (2008) 489e497 www.elsevier.com/locate/polydegstab
Characterization by ultra-micro indentation of an oxidized epoxy polymer: Correlation with the predictions of a kinetic model of oxidation L. Olivier, N.Q. Ho, J.C. Grandidier, M.C. Lafarie-Frenot* Laboratoire de Me´canique et Physique des Mate´riaux, UMR CNRS No. 6617, ENSMA, BP 40109, 86961 Futuroscope-Chasseneuil Cedex, France Received 8 October 2007; received in revised form 29 October 2007; accepted 11 November 2007 Available online 22 November 2007
Abstract This study aims to understand better the influence of thermo-oxidation on the degradation of an epoxy resin used as the matrix of aeronautical composite laminates. Neat epoxy resin plates have been aged at 150 C, under vacuum and ambient air. Using an instrumented ultra-micro indentation device, modifications of mechanical properties due to oxidation at elevated temperature are characterized through the measurements of elastic indentation modulus, Vickers hardness and indentation creep. By using a kinetic model of oxidation developed specifically for this epoxy resin, the local values of oxidation product concentration are calculated and correlated to experimental indentation measurements. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Epoxy resin; Thermo-oxidation; Oxidized layer; Indentation; Kinetic modelling
1. Introduction In the aerospace industry, widespread use is made of long fibre carbon/epoxy laminates, as they possess very interesting specific mechanical properties. Nowadays, such materials are used in structural parts subjected to rather severe thermal conditions. Therefore, in the presence of oxygen, oxidation reactions of the polymer can take place and threaten the integrity of the composite material. Thus, an increased demand for long lifetime requires better understanding of the oxidation processes and their consequences in terms of mechanical degradation, to have better predictive tools at one’s disposal. In that context, many studies concerned thermoset polymers, and continuous carbon fibreethermoset matrix composites (Lafarie-Frenot and Rouquie [1], Lafarie-Frenot [2], Lafarie-Frenot et al. [3], Rouquie et al. [4], Johnson et al. [5], Schoeppner et al. [6], Tandon et al. [7]). In particular, it was found that in carbon/epoxy composite laminates, * Corresponding author. E-mail address: [email protected] (M.C. Lafarie-Frenot). 0141-3910/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymdegradstab.2007.11.012
oxidation induces some matrix shrinkage which generates high local stresses, leading to fibreematrix debonding and matrix cracking (Fig. 1) (Lafarie-Frenot and Rouquie [1]). For aeronautical engineers, with the objective of assessing the durability of structural components, the very difficult challenge is to take into account the ‘local’ modifications of mechanical properties due to oxidation on the microscale, in ‘global’ structural simulations on the mesoscale. On one hand, scientists have exerted themselves to elaborate multiscale predictive models and to propose numerical tools useful for ‘virtual material testing’ (Lubineau et al. [8], Schieffer et al. [9]). On the other hand, this approach needs some predictive kinetic model of oxidation. For many years, Verdu and coworkers have elaborated a kinetic model derived from a radical chain oxidation mechanism, including reactionediffusion coupling; recently, the parameters of this model have been identified for the 977-2 epoxy-amine resin, which is the material of the present study (Colin et al. [10e12]). In its present form, the model predicts, at every time t and for every elementary thickness layer at the distance x from the surface, various quantities among which are weight and density variations.
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Fig. 1. SEM observations on a [03/903]S C/epoxy laminate subjected to 100 thermal cycles in air (Lafarie-Frenot and Rouquie [1]).
Because the thermo-oxidation of epoxy resin is diffusion controlled, one can observe in a specimen which experienced some thermal ageing in air, an oxidized layer, the thickness of which varies more or less with test conditions (temperature and duration) (Tandon et al. [7], Colin et al. [10], Bowles et al. [13]). This layer could be characterized by optical observations (Colin et al. [10], Bowles et al. [14]), white light interferometry (Putthanarat et al. [15]), atomic force microscopy (Johnson et al. [5]), pinpoint DMA (Dole and Chauchard [16]), and instrumented ultra-micro indentation (Ho et al. [17]), the latter techniques allowing study of the local evolution of mechanical properties inside the oxidized layer at any given oxidation level. Also, in composite materials, the matrix shrinkage due to oxidation is expected to generate high stress gradients that could be evaluated only if the local mechanical properties are known. Furthermore, global measurements have been obtained from methods such as dynamic mechanical analysis (Bowles et al. [14]). The work presented in this paper tries to establish a relationship between the local structural state of an oxidized epoxy network and its mechanical properties. The first part consists in an experimental investigation of the material behaviour changes due to oxidation. Ultra-micro indentation measurements are used to describe the main characteristics of these modifications. In a second part, the model of oxidation developed by Verdu et al. is used to predict the evolution of some chemical parameters of our resin and to associate them with the experimental results presented in the first part. Taking into account the excellent agreement between model predictions and measurements, we propose a phenomenological correlation between the chemical state of the oxidized epoxy matrix and its mechanical properties, a correlation which will be useful to carry out some numerical modelling of composite specimens (work in progress).
and processed by CCR-EADS (Corporate Research Centre e Francee of the European Aeronautic Defence and Space Company). The plates had been prepared according to a specific polymerization cycle, optimized for obtaining a material stable during thermal ageing. This polymerization cycle is constituted by a 3 h time of gelation at 150 C, a 2 h long cure at 180 C, followed by a post-cure under vacuum of 1.5 h at 210 C to obtain supplementary cross-linking. The epoxy resin under consideration was obtained by mixing two aromatic epoxy pre-polymers (diglycidylether of bisphenol F e DGEBF, triglycidylether of p-aminophenol e TGPAP) crosslinked with an aromatic diamine (diaminodiphenylsulphone e DDS) (Fig. 2). In addition, this resin contains some thermoplastic polymer to enhance its impact resistance (the nature and proportions of this constituent are not given by the supplier). However, according to Colin (Colin [18]), these thermoplastic polymers do not contain aliphatic hydrocarbon groups susceptible to compete with the epoxy network oxidation. As the aim of this study is to characterize the mechanical behaviour modifications due to oxidation, the analysis will not concern these thermoplastic additives. Isothermal ageing tests have been carried out on neat epoxy resin plates at 150 C, under vacuum and atmospheric air, their maximal duration being 1000 h. During tests, at different ageing times, some plates have been taken out from thermal chamber; samples have been cut off with appropriate dimensions and characterized with an instrumented ultra-micro indentation device.
2. Material and experimental conditions 2.1. Material In order to study the influence of oxidation, plates of 977-2 epoxy/amine resin (1 and 2 mm thick) were provided
Fig. 2. Chemical components of pre-polymers and hardener (Johnson et al. [5]).
L. Olivier et al. / Polymer Degradation and Stability 93 (2008) 489e497
2.2. Instrumented ultra-micro indentation The ultra-micro indentation device FischerscopeÒ H100C was used to characterize the modifications of the material mechanical properties, on the microscopic scale. This device being instrumented, the testing force ‘‘F’’ and the penetration depth ‘‘h’’ pffiffiffiare recorded during the test. The analysis of the curves ‘‘ F vs h’’ leads to some local mechanical properties, according to 14577 ISO standard, with a micrometer order spatialpresolution. In Fig. 3 is shown a typical ‘‘square testing ffiffiffi force F vs indentation depth h’’ curve obtained with such a test, here with a Vickers diamond indenter. The curve can be described as follows: Between t0 and t1: application of testing force to the maximum level. The plastic and elastic deformations contribute to the hardness indentation. The hardness calculation is carried out only in this time interval. The Vickers hardness HV is the quotient obtained by dividing the load Fmax expressed in Newton by the surface area of the indentation expressed in square millimetres: Fmax As Between t1 and t2: the maximum test force is kept at a constant level for a duration that can be pre-selected. The change in penetration depth indicates the creep properties of the material. The ‘‘indentation creep CIT1’’ is defined as the relative variation of penetration depth: HV ¼
CIT1 ¼
h2 h1 100% h1
where h1 and h2 are, respectively, the indentation depths at t1 and t2. Between t2 and t3: unloading of the testing force. The ‘‘indentation elastic modulus’’ is calculated from the slope of the curve at Fmax:
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pffiffiffiffi pðdF=dhÞ pffiffiffiffiffi EIT ¼ 2b Ap where b depends of the indenter type (b ¼ 1.013 for a Vickers indenter) and Ap is the contact area between the indenter and the sample, projected on a plane perpendicular to the indenter axis. 2.3. Particular law of micro-hardness, effect of the applied load For a Vickers diamond indenter, the plane angle of the pyramid is equal to 136 , leading to the fundamental formula for Vickers Hardness (HV): HV ¼
2cos 22 Fmax d2
where d is the diagonal of the projected area of the print. For a given material, standard macro-hardness tests give e in the range of the experimental scattering e a single hardness value, whatever be the value of the applied load. In that case, the applied load F and the imprint diameter obey a quadratic relation: F ¼ ad2, and the factor ‘‘a’’ is a material constant that characterizes the hardness of the tested material: HV ¼ 2cos 22 a¼ 1:854a On another hand, in the micro-hardness domain, and particularly in the ultra-micro-hardness one, the measured parameters F and d do not follow such a parabolic law: they obey an empirical relation F ¼ adn. Writing HV as a function of F, gives: 2 n2 HV ¼ 2cos 22 a2=n Fð1nÞ ¼ Cl F n
Then, Vickers micro-hardness is not a ‘material constant’ because it depends on the applied load. In most cases, n < 2 and the hardness value increases with load (Bu¨ckle [19]). For the material under consideration, preliminary qualifying tests of the method have effectively shown an influence of the applied load on the measured value of the elastic modulus EIT, one of the ‘‘intrinsic’’ parameters obtained by indentation. Tests have been carried out with different loading levels (5, 10 and 20 mN) and pffiffiffidifferent creep durations (20, 60 s), with a constant ratio d F=dt. In Table 1 measured elastic modulus values are shown according to the indentation test conditions. It can be noted Table 1 Virgin epoxy resin, indentation elastic modulus for different load levels (5,10 and 20 mN) and different creep durations (20, 60 s) Load (mN)/loading duration (s)
Creep duration (s)
EIT (MPa)
5/20
20 60 20 60 20 60
4083 4078 3780 3787 3708 3723
10/28 20/40 Fig. 3. Description of a ‘‘load versus indentation depth’’ indentation curve.
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Fig. 4. Epoxy resin samples, coating procedure and microscopic observation of indentation prints.
here that the EIT values significantly depend on the applied load level: the higher the applied load, the lower the elastic modulus value. On the contrary, for a given load level, the creep duration does not show any influence. As the objective of our study is to highlight an evolution of the mechanical properties on our material after a thermal treatment, we will use the same experimental conditions for all indentation tests: same maximal load and same creep duration. Therefore, the obtained values will make it possible to characterize the variations of the mechanical properties due to ageing. 2.4. Cutting and coating samples for indentation Prior to ultra-micro indentation tests, specimens were cut and coated, then polished by a semi-automatic polishing machine (a recent study on PMR-15 showed that the polishing time does not influence the measurement of the elastic modulus (Putthanarat et al. [15])). Because of the difference in
hardness between the epoxy resin and the coating, an edge roundness effect may happen during polishing and lead to important errors in indentation measurements. To avoid this unwanted effect, two specimens are put side-by-side and polished at the same time (Fig. 4a). An observation under optical microscope shows that, using this procedure, we can get a very plane surface at the interface between the two coated samples (Fig. 4b). The ultra-micro indentation device used in that study has a testing load range from 0.4 to 1000 mN. Preliminary tests have been done in order to determine the optimal indentation conditions allowing a good precision of the measurement and a good spatial resolution. So, a maximum load of 5 mN has been chosen, leading to an average size of prints around 6 mm, and a minimum distance between two indentations of 20 mm, which is approximately three times longer than the print diameter, in order to have no interaction between two measurements (Fig. 4b).
Fig. 5. Instrumented ultra-micro indentation, initial characteristics of the epoxy resin: Vickers Hardness HV, elastic modulus EIT, and creep CIT1.
L. Olivier et al. / Polymer Degradation and Stability 93 (2008) 489e497 Table 2 Instrumented ultra-micro indentation, mechanical properties of the initial epoxy resin Initial resin
HV (N/mm2)
EIT (MPa)
CIT (%)
Mean value Standard deviation Range
43.9 2.89 37.2e53.6
4070 107 3791e4245
5.03 0.81 2.87e7.34
Then the conditions of all the indentation tests were as follows: e loading from the minimum load (close to 0 mN) to 5 mN in 20 s; e application of the 5 mN maximum load during 20 s; e unloading at the same speed as the loading.
2.4.1. Characterization of mechanical properties by instrumented ultra-micro indentation 2.4.1.1. Initial epoxy resin. In order to have some reference values of the mechanical characteristics of the material before any thermal ageing, 200 indentation measurements were made on a ‘as received’ epoxy resin sample. In Fig. 5 are presented the measurement distributions obtained, respectively, for the Vickers hardness HV, the indentation elastic modulus EIT and the indentation creep CIT1. In outline, Fig. 5 shows that the initial resin mechanical properties are homogeneous: hardness and elastic modulus values are very little scattered, but creep measurements present a little more variability. In Table 2 are gathered the statistical characteristics of these measurements.
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specimen) for different durations of thermal ageing, under vacuum or in air. Each value plotted in this figure corresponds to the average of three lines of measurements far away from specimen corners. In this figure, the hatched zone corresponds to the extent of the 200 EIT values obtained for the virgin material and presented in the above section. First of all, it can be noticed in this figure that the thermal ageing under vacuum, even after 1000 h, does not lead to any noticeable variation of the elastic modulus: indeed, values obtained either on the edge or in the centre of that sample are included in the dispersion range of the initial elastic modulus (mean value 4070 MPa and standard deviation of 107 MPa). In contrast, after 100 h of isothermal ageing in air, we observe a small increase of the elastic modulus close to the edge of the specimen. This increase is more important at 600 h and 1000 h, the later case leading to a relative increase of the elastic modulus up to 35%: 5500 MPa at the edge of the aged sample compared to the initial value of 4070 MPa. In a superficial layer of the specimen, 200 mm thick, the elastic modulus increases progressively with time, which could be due to the internal antiplasticization of the epoxy network as proposed by Verdu in Ref. [21] (Pascault et al.). Indentation measurements can offer other results, such as the Vickers Hardness and creep of indentation. In Fig. 8a, the comparison of the HV values for specimens that sustained 1000 h of thermal ageing according to the environment (air or vacuum), reveal a hardness gradient induced by thermo-oxidation in the oxidized layer. Fig. 8b shows a similar gradient of the indentation creep deformation. These measurements show that thermooxidation leads to an increase in hardness and a decrease in the creep deformation capability of the polymer. 3. Analysis e comparison to oxidation model
2.4.1.2. Aged epoxy resin. Epoxy resin specimens were aged at 150 C under vacuum and in ambient air, for different durations (100 h, 600 h, 1000 h). In Fig. 6 are presented two samples aged for 600 h, either under vacuum (on the left), or in air (on the right). A difference of colour can be observed: the sample that experienced thermal ageing under vacuum has kept its initial colour (yellow amber), whereas in air, the specimen has become very black. Apparently, an opaque oxidized layer was formed during the thermal ageing in air. The same phenomenon has been observed for all samples aged for 1000 h in air. According to Buch and Shanahan [20] the change of colour of the epoxy polymer specimens subjected to heat treatments in air would be an indication of the chemical modifications of the material due to its thermo-oxidation. In Fig. 7 the indentation elastic modulus values are plotted against the distance from the edge (0 mm and 500 mm correspond, respectively, to the edge and to the centre of the
Fig. 6. Epoxy resin specimens after 600 h at 150 C under vacuum (left) and in air (right).
3.1. Oxidation model (Colin [10]) For epoxy resins, Verdu and coworkers have developed a kinetic model of oxidation coupled with the equations of oxygen
Fig. 7. Isothermal ageing at 150 C of epoxy resin specimens, indentation elastic modulus vs distance from the edge. Comparison is done according to test environment (vacuum or air) and ageing duration.
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Fig. 8. Epoxy resin, evolutions of Vickers hardness and deformation by creep CIT1 due to ageing.
diffusion. This closed loop mechanistic scheme can be described by six equations, corresponding to three steps: initiation, propagation and termination. Starting from this scheme, a differential system describing the variations in concentrations of the different reacting species can be obtained thanks to some model constants that can be identified from experiments (Lafarie-Frenot et al. [3], Decelle et al. [22], Colin et al. [23]). Moreover, it is assumed that the oxygen diffusion in the polymer material follows Fick’s second law. Then, the variation rate of the oxygen concentration C at any point (x, y, z) and any time t can be written as (cf. Fig. 9): vC v2 C v2 C ðx; y; z; tÞ ¼ DX 2 ðx; y; z; tÞ þ DY 2 ðx; y; z; tÞ vt vx vy v2 C þ DZ 2 ðx; y; z; tÞ RðCðx; y; z; tÞÞ vz where DX, DY, and DZ are the diffusion coefficients of oxygen in the polymer, respectively, in the x, y and z directions (DX ¼ DY ¼ DZ in the case of a pure isotropic resin), and R(C ) is the oxidation rate (defined thanks to the reduced variables according to Verdu et al. (Colin et al. [12])): 2 RðCÞ ¼ k2 C P0 k6 PO02 the k2 standing for the rate constant for oxygen addition to radicals and k6 being the PO02 þ PO02 termination rate constant. For many years, Verdu and coworkers have developed numerical tools to solve the differential equations of the model, in the case of unidirectional diffusionereaction problems. In this study, the system of differential equations has been set in a specific finite element (ABAQUS software), so as to solve the coupled diffusionereaction problem on a global 3D structure. In Fig. 9, a section of an epoxy resin specimen has been considered, far from the edges in the z direction, for which it is not necessary to take into account the DZ diffusion (Note: this section corresponds to the one where indentation tests have been done). Then, the coupled diffusion-chemical 3D problem can be reduced to 2D one. Let us consider, in the xey plane, a corner of dimensions 500 mm 500 mm (Fig. 9). This section is discretised along
the directions x1 and y1 (121 nodes for the 2D mesh), and the model is numerically solved, thanks to the method proposed by Rosenbrock for such differential equation systems [24]. This numerical approach makes it possible to obtain, for every point in the mesh and for different ageing durations, the concentration of each reactive species. Then, as proposed in (Colin [18]), the following parameters can be calculated at any given point (x1, y1) and for any ageing duration tf: e the concentration in reaction products Q: Ztf Qðx1 ; y1 ; z1 Þ ¼ RðCÞdt t¼0
e the relative mass loss Dm/m0 obtained as the mass difference between the mass gain due to oxygen sorption and the mass loss due to the escape of water and volatile elements. e the density r of the oxidized polymer, inferred from the mean atomic mass Ma by an empirical relation (Colin and Verdu [25]). NOTE e this model has been identified and validated for different thermosetting polymers in many experimental conditions (Colin et al. [10]). It is still improved by Verdu et al. in order to better describe the complex chemical processes; the version used in this work can be found in the PhD thesis of Colin (Colin [18]).
Fig. 9. Geometry of the model used in the bidimensional calculus of oxidation.
L. Olivier et al. / Polymer Degradation and Stability 93 (2008) 489e497
Fig. 10. Epoxy resin, prediction of concentration of the oxidation products Q after 1000 h of isothermal ageing at 150 C, under air.
3.2. Comparison between predictions and experimental measures Isothermal ageing tests have been carried out at 150 C, in air with the atmospheric pressure, and compared to corresponding predictions of the finite element model. In this configuration, the oxygen concentration at the surface of the sample CS is equal to 3.3 103 mol/l and that value is used as a limit condition. Furthermore, the constants used to solve the system of differential equations, identified during a previous study for the same epoxy resin have been taken from the literature (Lafarie-Frenot et al. [3], Colin et al. [23]). In Fig. 10 the concentration of oxidation products is presented, as predicted by the model for 1000 h of ageing at 150 C in air. For the considered section, oxygen diffuses along the two main directions x1, y1 and the concentration of the reactive species depends on the local level of oxygen. At the corner of the model (500 mm, 500 mm), an edge effect can be noticed, due to the superposition of the two oxygen fluxes, which leads to a higher value of concentration in oxidation products at that point. Far from the corner, diffusion can be considered as unidirectional. For example, along the axis x1 ¼ 0, it can be observed that the concentration in oxidation products is higher close to the edge
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(around 5.7 mol/l) and that it decreases rapidly to the centre of the model. In Fig. 11a, simulation results far from the edge of the specimen are presented, as a function of the x space variable, for three ageing times (100 h, 600 h, 1000 h). An ‘‘oxidised’’ layer, characterized by the presence of oxidation products, is observed from 100 h of ageing. Despite the fact that the thickness of this layer is mostly constant in the range of ageing durations studied, the concentration in oxidation products at the edge (x ¼ 0) increases with time. For comparison, in Fig. 11b, the values of the measurements of indentation elastic moduli are recalled. One observes that the oxidized layer thickness obtained by the numerical model does correspond to the one observed by ultra-micro indentation (around 200 mm in each case).
3.3. Correlations If measured values of the indentation elastic modulus (EIT) are plotted against the predicted values of concentration in oxidation products (Q) (Fig. 11), one can notice a very good correlation between those two parameters (Fig. 12), whatever the sample and the oxidation level be. Indeed, in Fig. 12 all the values experimentally obtained, for different samples and for different ageing durations, are gathered; they all fit the same curve, whatever the corresponding space (x) and time (t) variables be. In the range of low concentration values (Q < 1.5 mol/l), we get a quasi-linear relation between the elastic modulus and the concentration of oxidation products. However, when the concentration of the oxidation products is higher (Q > 1,5 mol/l), the general correlation between EIT and Q can be approximated by an exponential expression: this result shows that the indentation elastic modulus would tend to saturate when the concentration of oxidation products increases in long-term ageing tests. Moreover, this mathematical correlation gives a value of EIT equal to 4000 MPa for a zero value of Q, which is very similar to the mean value
Fig. 11. Epoxy resin, prediction of the concentration of oxidation products Q (a) and elastic modulus obtained by ultra-micro indentation (b), in the oxidized layer after 100 h, 600 h and 1000 h of isothermal ageing at 150 C, under atmospheric air.
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Acknowledgements The authors acknowledge the financial support of the French Research Department, the French Transport Department, and EADS (CCR Suresnes, France) for supplying the composite plates and samples.
References
Fig. 12. Correlation between the elastic modulus EIT measured by indentation and the concentration of oxidation products Q calculated.
obtained for the virgin material, before any ageing (4070 MPa in Table 2).
4. Conclusions In this study, we performed numerical modelling of the thermo-oxidation of an epoxy resin, which is used as the matrix of aeronautical CFRP composites. A new finite element method has been specifically developed, including coupling between diffusion and oxidation, thanks to the kinetic model of Verdu et al. Simulations have been made in the case of an isothermal ageing of a non-reinforced resin sample (150 C, air, atmospheric pressure). The main results are: the kinetic model of oxidation can predict the concentration of oxidation products at any given point and any given time; moreover, it was shown that the oxidized layer can be characterized by the region corresponding to a nonzero value of concentration in oxidation products. On the other hand, a simple mathematical correlation was found between the measured values of indentation elastic modulus and the calculated ones of concentration of oxidation products, whatever the values of space and time variables be. This correlation will be useful to carry out some mechanical calculations of stresses induced by oxidation in composite materials subjected to longterm ageing in similar environmental conditions. However, even if the kinetic model used makes it possible to predict the chemical parameter values for other temperatures, other oxygen concentrations etc., it will be necessary to validate the mathematical correlation obtained in that study, since it is not based on theoretical demonstration. At that point, the numerical model using the finite element method needs to be developed, in order to include coupling effects with mechanical behaviour, so as to simulate the local evolution of the matrix in aeronautical laminates during oxidation. Hence, from the calculated local stress field, and with appropriate failure criteria, this model could be used to predict the lifetime of a complex composite laminate before any matrix cracking and contribute to enhanced control of the durability of aeronautical structures.
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Characterization by ultra-micro indentation of an oxidized epoxy polymer: Correlation with the predictions of a kinetic model of oxidation L. Olivier, N.Q. Ho, J.C. Grandidier, M.C. Lafarie-Frenot* Laboratoire de Me´canique et Physique des Mate´riaux, UMR CNRS No. 6617, ENSMA, BP 40109, 86961 Futuroscope-Chasseneuil Cedex, France Received 8 October 2007; received in revised form 29 October 2007; accepted 11 November 2007 Available online 22 November 2007
Abstract This study aims to understand better the influence of thermo-oxidation on the degradation of an epoxy resin used as the matrix of aeronautical composite laminates. Neat epoxy resin plates have been aged at 150 C, under vacuum and ambient air. Using an instrumented ultra-micro indentation device, modifications of mechanical properties due to oxidation at elevated temperature are characterized through the measurements of elastic indentation modulus, Vickers hardness and indentation creep. By using a kinetic model of oxidation developed specifically for this epoxy resin, the local values of oxidation product concentration are calculated and correlated to experimental indentation measurements. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Epoxy resin; Thermo-oxidation; Oxidized layer; Indentation; Kinetic modelling
1. Introduction In the aerospace industry, widespread use is made of long fibre carbon/epoxy laminates, as they possess very interesting specific mechanical properties. Nowadays, such materials are used in structural parts subjected to rather severe thermal conditions. Therefore, in the presence of oxygen, oxidation reactions of the polymer can take place and threaten the integrity of the composite material. Thus, an increased demand for long lifetime requires better understanding of the oxidation processes and their consequences in terms of mechanical degradation, to have better predictive tools at one’s disposal. In that context, many studies concerned thermoset polymers, and continuous carbon fibreethermoset matrix composites (Lafarie-Frenot and Rouquie [1], Lafarie-Frenot [2], Lafarie-Frenot et al. [3], Rouquie et al. [4], Johnson et al. [5], Schoeppner et al. [6], Tandon et al. [7]). In particular, it was found that in carbon/epoxy composite laminates, * Corresponding author. E-mail address: [email protected] (M.C. Lafarie-Frenot). 0141-3910/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymdegradstab.2007.11.012
oxidation induces some matrix shrinkage which generates high local stresses, leading to fibreematrix debonding and matrix cracking (Fig. 1) (Lafarie-Frenot and Rouquie [1]). For aeronautical engineers, with the objective of assessing the durability of structural components, the very difficult challenge is to take into account the ‘local’ modifications of mechanical properties due to oxidation on the microscale, in ‘global’ structural simulations on the mesoscale. On one hand, scientists have exerted themselves to elaborate multiscale predictive models and to propose numerical tools useful for ‘virtual material testing’ (Lubineau et al. [8], Schieffer et al. [9]). On the other hand, this approach needs some predictive kinetic model of oxidation. For many years, Verdu and coworkers have elaborated a kinetic model derived from a radical chain oxidation mechanism, including reactionediffusion coupling; recently, the parameters of this model have been identified for the 977-2 epoxy-amine resin, which is the material of the present study (Colin et al. [10e12]). In its present form, the model predicts, at every time t and for every elementary thickness layer at the distance x from the surface, various quantities among which are weight and density variations.
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Fig. 1. SEM observations on a [03/903]S C/epoxy laminate subjected to 100 thermal cycles in air (Lafarie-Frenot and Rouquie [1]).
Because the thermo-oxidation of epoxy resin is diffusion controlled, one can observe in a specimen which experienced some thermal ageing in air, an oxidized layer, the thickness of which varies more or less with test conditions (temperature and duration) (Tandon et al. [7], Colin et al. [10], Bowles et al. [13]). This layer could be characterized by optical observations (Colin et al. [10], Bowles et al. [14]), white light interferometry (Putthanarat et al. [15]), atomic force microscopy (Johnson et al. [5]), pinpoint DMA (Dole and Chauchard [16]), and instrumented ultra-micro indentation (Ho et al. [17]), the latter techniques allowing study of the local evolution of mechanical properties inside the oxidized layer at any given oxidation level. Also, in composite materials, the matrix shrinkage due to oxidation is expected to generate high stress gradients that could be evaluated only if the local mechanical properties are known. Furthermore, global measurements have been obtained from methods such as dynamic mechanical analysis (Bowles et al. [14]). The work presented in this paper tries to establish a relationship between the local structural state of an oxidized epoxy network and its mechanical properties. The first part consists in an experimental investigation of the material behaviour changes due to oxidation. Ultra-micro indentation measurements are used to describe the main characteristics of these modifications. In a second part, the model of oxidation developed by Verdu et al. is used to predict the evolution of some chemical parameters of our resin and to associate them with the experimental results presented in the first part. Taking into account the excellent agreement between model predictions and measurements, we propose a phenomenological correlation between the chemical state of the oxidized epoxy matrix and its mechanical properties, a correlation which will be useful to carry out some numerical modelling of composite specimens (work in progress).
and processed by CCR-EADS (Corporate Research Centre e Francee of the European Aeronautic Defence and Space Company). The plates had been prepared according to a specific polymerization cycle, optimized for obtaining a material stable during thermal ageing. This polymerization cycle is constituted by a 3 h time of gelation at 150 C, a 2 h long cure at 180 C, followed by a post-cure under vacuum of 1.5 h at 210 C to obtain supplementary cross-linking. The epoxy resin under consideration was obtained by mixing two aromatic epoxy pre-polymers (diglycidylether of bisphenol F e DGEBF, triglycidylether of p-aminophenol e TGPAP) crosslinked with an aromatic diamine (diaminodiphenylsulphone e DDS) (Fig. 2). In addition, this resin contains some thermoplastic polymer to enhance its impact resistance (the nature and proportions of this constituent are not given by the supplier). However, according to Colin (Colin [18]), these thermoplastic polymers do not contain aliphatic hydrocarbon groups susceptible to compete with the epoxy network oxidation. As the aim of this study is to characterize the mechanical behaviour modifications due to oxidation, the analysis will not concern these thermoplastic additives. Isothermal ageing tests have been carried out on neat epoxy resin plates at 150 C, under vacuum and atmospheric air, their maximal duration being 1000 h. During tests, at different ageing times, some plates have been taken out from thermal chamber; samples have been cut off with appropriate dimensions and characterized with an instrumented ultra-micro indentation device.
2. Material and experimental conditions 2.1. Material In order to study the influence of oxidation, plates of 977-2 epoxy/amine resin (1 and 2 mm thick) were provided
Fig. 2. Chemical components of pre-polymers and hardener (Johnson et al. [5]).
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2.2. Instrumented ultra-micro indentation The ultra-micro indentation device FischerscopeÒ H100C was used to characterize the modifications of the material mechanical properties, on the microscopic scale. This device being instrumented, the testing force ‘‘F’’ and the penetration depth ‘‘h’’ pffiffiffiare recorded during the test. The analysis of the curves ‘‘ F vs h’’ leads to some local mechanical properties, according to 14577 ISO standard, with a micrometer order spatialpresolution. In Fig. 3 is shown a typical ‘‘square testing ffiffiffi force F vs indentation depth h’’ curve obtained with such a test, here with a Vickers diamond indenter. The curve can be described as follows: Between t0 and t1: application of testing force to the maximum level. The plastic and elastic deformations contribute to the hardness indentation. The hardness calculation is carried out only in this time interval. The Vickers hardness HV is the quotient obtained by dividing the load Fmax expressed in Newton by the surface area of the indentation expressed in square millimetres: Fmax As Between t1 and t2: the maximum test force is kept at a constant level for a duration that can be pre-selected. The change in penetration depth indicates the creep properties of the material. The ‘‘indentation creep CIT1’’ is defined as the relative variation of penetration depth: HV ¼
CIT1 ¼
h2 h1 100% h1
where h1 and h2 are, respectively, the indentation depths at t1 and t2. Between t2 and t3: unloading of the testing force. The ‘‘indentation elastic modulus’’ is calculated from the slope of the curve at Fmax:
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pffiffiffiffi pðdF=dhÞ pffiffiffiffiffi EIT ¼ 2b Ap where b depends of the indenter type (b ¼ 1.013 for a Vickers indenter) and Ap is the contact area between the indenter and the sample, projected on a plane perpendicular to the indenter axis. 2.3. Particular law of micro-hardness, effect of the applied load For a Vickers diamond indenter, the plane angle of the pyramid is equal to 136 , leading to the fundamental formula for Vickers Hardness (HV): HV ¼
2cos 22 Fmax d2
where d is the diagonal of the projected area of the print. For a given material, standard macro-hardness tests give e in the range of the experimental scattering e a single hardness value, whatever be the value of the applied load. In that case, the applied load F and the imprint diameter obey a quadratic relation: F ¼ ad2, and the factor ‘‘a’’ is a material constant that characterizes the hardness of the tested material: HV ¼ 2cos 22 a¼ 1:854a On another hand, in the micro-hardness domain, and particularly in the ultra-micro-hardness one, the measured parameters F and d do not follow such a parabolic law: they obey an empirical relation F ¼ adn. Writing HV as a function of F, gives: 2 n2 HV ¼ 2cos 22 a2=n Fð1nÞ ¼ Cl F n
Then, Vickers micro-hardness is not a ‘material constant’ because it depends on the applied load. In most cases, n < 2 and the hardness value increases with load (Bu¨ckle [19]). For the material under consideration, preliminary qualifying tests of the method have effectively shown an influence of the applied load on the measured value of the elastic modulus EIT, one of the ‘‘intrinsic’’ parameters obtained by indentation. Tests have been carried out with different loading levels (5, 10 and 20 mN) and pffiffiffidifferent creep durations (20, 60 s), with a constant ratio d F=dt. In Table 1 measured elastic modulus values are shown according to the indentation test conditions. It can be noted Table 1 Virgin epoxy resin, indentation elastic modulus for different load levels (5,10 and 20 mN) and different creep durations (20, 60 s) Load (mN)/loading duration (s)
Creep duration (s)
EIT (MPa)
5/20
20 60 20 60 20 60
4083 4078 3780 3787 3708 3723
10/28 20/40 Fig. 3. Description of a ‘‘load versus indentation depth’’ indentation curve.
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Fig. 4. Epoxy resin samples, coating procedure and microscopic observation of indentation prints.
here that the EIT values significantly depend on the applied load level: the higher the applied load, the lower the elastic modulus value. On the contrary, for a given load level, the creep duration does not show any influence. As the objective of our study is to highlight an evolution of the mechanical properties on our material after a thermal treatment, we will use the same experimental conditions for all indentation tests: same maximal load and same creep duration. Therefore, the obtained values will make it possible to characterize the variations of the mechanical properties due to ageing. 2.4. Cutting and coating samples for indentation Prior to ultra-micro indentation tests, specimens were cut and coated, then polished by a semi-automatic polishing machine (a recent study on PMR-15 showed that the polishing time does not influence the measurement of the elastic modulus (Putthanarat et al. [15])). Because of the difference in
hardness between the epoxy resin and the coating, an edge roundness effect may happen during polishing and lead to important errors in indentation measurements. To avoid this unwanted effect, two specimens are put side-by-side and polished at the same time (Fig. 4a). An observation under optical microscope shows that, using this procedure, we can get a very plane surface at the interface between the two coated samples (Fig. 4b). The ultra-micro indentation device used in that study has a testing load range from 0.4 to 1000 mN. Preliminary tests have been done in order to determine the optimal indentation conditions allowing a good precision of the measurement and a good spatial resolution. So, a maximum load of 5 mN has been chosen, leading to an average size of prints around 6 mm, and a minimum distance between two indentations of 20 mm, which is approximately three times longer than the print diameter, in order to have no interaction between two measurements (Fig. 4b).
Fig. 5. Instrumented ultra-micro indentation, initial characteristics of the epoxy resin: Vickers Hardness HV, elastic modulus EIT, and creep CIT1.
L. Olivier et al. / Polymer Degradation and Stability 93 (2008) 489e497 Table 2 Instrumented ultra-micro indentation, mechanical properties of the initial epoxy resin Initial resin
HV (N/mm2)
EIT (MPa)
CIT (%)
Mean value Standard deviation Range
43.9 2.89 37.2e53.6
4070 107 3791e4245
5.03 0.81 2.87e7.34
Then the conditions of all the indentation tests were as follows: e loading from the minimum load (close to 0 mN) to 5 mN in 20 s; e application of the 5 mN maximum load during 20 s; e unloading at the same speed as the loading.
2.4.1. Characterization of mechanical properties by instrumented ultra-micro indentation 2.4.1.1. Initial epoxy resin. In order to have some reference values of the mechanical characteristics of the material before any thermal ageing, 200 indentation measurements were made on a ‘as received’ epoxy resin sample. In Fig. 5 are presented the measurement distributions obtained, respectively, for the Vickers hardness HV, the indentation elastic modulus EIT and the indentation creep CIT1. In outline, Fig. 5 shows that the initial resin mechanical properties are homogeneous: hardness and elastic modulus values are very little scattered, but creep measurements present a little more variability. In Table 2 are gathered the statistical characteristics of these measurements.
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specimen) for different durations of thermal ageing, under vacuum or in air. Each value plotted in this figure corresponds to the average of three lines of measurements far away from specimen corners. In this figure, the hatched zone corresponds to the extent of the 200 EIT values obtained for the virgin material and presented in the above section. First of all, it can be noticed in this figure that the thermal ageing under vacuum, even after 1000 h, does not lead to any noticeable variation of the elastic modulus: indeed, values obtained either on the edge or in the centre of that sample are included in the dispersion range of the initial elastic modulus (mean value 4070 MPa and standard deviation of 107 MPa). In contrast, after 100 h of isothermal ageing in air, we observe a small increase of the elastic modulus close to the edge of the specimen. This increase is more important at 600 h and 1000 h, the later case leading to a relative increase of the elastic modulus up to 35%: 5500 MPa at the edge of the aged sample compared to the initial value of 4070 MPa. In a superficial layer of the specimen, 200 mm thick, the elastic modulus increases progressively with time, which could be due to the internal antiplasticization of the epoxy network as proposed by Verdu in Ref. [21] (Pascault et al.). Indentation measurements can offer other results, such as the Vickers Hardness and creep of indentation. In Fig. 8a, the comparison of the HV values for specimens that sustained 1000 h of thermal ageing according to the environment (air or vacuum), reveal a hardness gradient induced by thermo-oxidation in the oxidized layer. Fig. 8b shows a similar gradient of the indentation creep deformation. These measurements show that thermooxidation leads to an increase in hardness and a decrease in the creep deformation capability of the polymer. 3. Analysis e comparison to oxidation model
2.4.1.2. Aged epoxy resin. Epoxy resin specimens were aged at 150 C under vacuum and in ambient air, for different durations (100 h, 600 h, 1000 h). In Fig. 6 are presented two samples aged for 600 h, either under vacuum (on the left), or in air (on the right). A difference of colour can be observed: the sample that experienced thermal ageing under vacuum has kept its initial colour (yellow amber), whereas in air, the specimen has become very black. Apparently, an opaque oxidized layer was formed during the thermal ageing in air. The same phenomenon has been observed for all samples aged for 1000 h in air. According to Buch and Shanahan [20] the change of colour of the epoxy polymer specimens subjected to heat treatments in air would be an indication of the chemical modifications of the material due to its thermo-oxidation. In Fig. 7 the indentation elastic modulus values are plotted against the distance from the edge (0 mm and 500 mm correspond, respectively, to the edge and to the centre of the
Fig. 6. Epoxy resin specimens after 600 h at 150 C under vacuum (left) and in air (right).
3.1. Oxidation model (Colin [10]) For epoxy resins, Verdu and coworkers have developed a kinetic model of oxidation coupled with the equations of oxygen
Fig. 7. Isothermal ageing at 150 C of epoxy resin specimens, indentation elastic modulus vs distance from the edge. Comparison is done according to test environment (vacuum or air) and ageing duration.
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Fig. 8. Epoxy resin, evolutions of Vickers hardness and deformation by creep CIT1 due to ageing.
diffusion. This closed loop mechanistic scheme can be described by six equations, corresponding to three steps: initiation, propagation and termination. Starting from this scheme, a differential system describing the variations in concentrations of the different reacting species can be obtained thanks to some model constants that can be identified from experiments (Lafarie-Frenot et al. [3], Decelle et al. [22], Colin et al. [23]). Moreover, it is assumed that the oxygen diffusion in the polymer material follows Fick’s second law. Then, the variation rate of the oxygen concentration C at any point (x, y, z) and any time t can be written as (cf. Fig. 9): vC v2 C v2 C ðx; y; z; tÞ ¼ DX 2 ðx; y; z; tÞ þ DY 2 ðx; y; z; tÞ vt vx vy v2 C þ DZ 2 ðx; y; z; tÞ RðCðx; y; z; tÞÞ vz where DX, DY, and DZ are the diffusion coefficients of oxygen in the polymer, respectively, in the x, y and z directions (DX ¼ DY ¼ DZ in the case of a pure isotropic resin), and R(C ) is the oxidation rate (defined thanks to the reduced variables according to Verdu et al. (Colin et al. [12])): 2 RðCÞ ¼ k2 C P0 k6 PO02 the k2 standing for the rate constant for oxygen addition to radicals and k6 being the PO02 þ PO02 termination rate constant. For many years, Verdu and coworkers have developed numerical tools to solve the differential equations of the model, in the case of unidirectional diffusionereaction problems. In this study, the system of differential equations has been set in a specific finite element (ABAQUS software), so as to solve the coupled diffusionereaction problem on a global 3D structure. In Fig. 9, a section of an epoxy resin specimen has been considered, far from the edges in the z direction, for which it is not necessary to take into account the DZ diffusion (Note: this section corresponds to the one where indentation tests have been done). Then, the coupled diffusion-chemical 3D problem can be reduced to 2D one. Let us consider, in the xey plane, a corner of dimensions 500 mm 500 mm (Fig. 9). This section is discretised along
the directions x1 and y1 (121 nodes for the 2D mesh), and the model is numerically solved, thanks to the method proposed by Rosenbrock for such differential equation systems [24]. This numerical approach makes it possible to obtain, for every point in the mesh and for different ageing durations, the concentration of each reactive species. Then, as proposed in (Colin [18]), the following parameters can be calculated at any given point (x1, y1) and for any ageing duration tf: e the concentration in reaction products Q: Ztf Qðx1 ; y1 ; z1 Þ ¼ RðCÞdt t¼0
e the relative mass loss Dm/m0 obtained as the mass difference between the mass gain due to oxygen sorption and the mass loss due to the escape of water and volatile elements. e the density r of the oxidized polymer, inferred from the mean atomic mass Ma by an empirical relation (Colin and Verdu [25]). NOTE e this model has been identified and validated for different thermosetting polymers in many experimental conditions (Colin et al. [10]). It is still improved by Verdu et al. in order to better describe the complex chemical processes; the version used in this work can be found in the PhD thesis of Colin (Colin [18]).
Fig. 9. Geometry of the model used in the bidimensional calculus of oxidation.
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Fig. 10. Epoxy resin, prediction of concentration of the oxidation products Q after 1000 h of isothermal ageing at 150 C, under air.
3.2. Comparison between predictions and experimental measures Isothermal ageing tests have been carried out at 150 C, in air with the atmospheric pressure, and compared to corresponding predictions of the finite element model. In this configuration, the oxygen concentration at the surface of the sample CS is equal to 3.3 103 mol/l and that value is used as a limit condition. Furthermore, the constants used to solve the system of differential equations, identified during a previous study for the same epoxy resin have been taken from the literature (Lafarie-Frenot et al. [3], Colin et al. [23]). In Fig. 10 the concentration of oxidation products is presented, as predicted by the model for 1000 h of ageing at 150 C in air. For the considered section, oxygen diffuses along the two main directions x1, y1 and the concentration of the reactive species depends on the local level of oxygen. At the corner of the model (500 mm, 500 mm), an edge effect can be noticed, due to the superposition of the two oxygen fluxes, which leads to a higher value of concentration in oxidation products at that point. Far from the corner, diffusion can be considered as unidirectional. For example, along the axis x1 ¼ 0, it can be observed that the concentration in oxidation products is higher close to the edge
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(around 5.7 mol/l) and that it decreases rapidly to the centre of the model. In Fig. 11a, simulation results far from the edge of the specimen are presented, as a function of the x space variable, for three ageing times (100 h, 600 h, 1000 h). An ‘‘oxidised’’ layer, characterized by the presence of oxidation products, is observed from 100 h of ageing. Despite the fact that the thickness of this layer is mostly constant in the range of ageing durations studied, the concentration in oxidation products at the edge (x ¼ 0) increases with time. For comparison, in Fig. 11b, the values of the measurements of indentation elastic moduli are recalled. One observes that the oxidized layer thickness obtained by the numerical model does correspond to the one observed by ultra-micro indentation (around 200 mm in each case).
3.3. Correlations If measured values of the indentation elastic modulus (EIT) are plotted against the predicted values of concentration in oxidation products (Q) (Fig. 11), one can notice a very good correlation between those two parameters (Fig. 12), whatever the sample and the oxidation level be. Indeed, in Fig. 12 all the values experimentally obtained, for different samples and for different ageing durations, are gathered; they all fit the same curve, whatever the corresponding space (x) and time (t) variables be. In the range of low concentration values (Q < 1.5 mol/l), we get a quasi-linear relation between the elastic modulus and the concentration of oxidation products. However, when the concentration of the oxidation products is higher (Q > 1,5 mol/l), the general correlation between EIT and Q can be approximated by an exponential expression: this result shows that the indentation elastic modulus would tend to saturate when the concentration of oxidation products increases in long-term ageing tests. Moreover, this mathematical correlation gives a value of EIT equal to 4000 MPa for a zero value of Q, which is very similar to the mean value
Fig. 11. Epoxy resin, prediction of the concentration of oxidation products Q (a) and elastic modulus obtained by ultra-micro indentation (b), in the oxidized layer after 100 h, 600 h and 1000 h of isothermal ageing at 150 C, under atmospheric air.
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Acknowledgements The authors acknowledge the financial support of the French Research Department, the French Transport Department, and EADS (CCR Suresnes, France) for supplying the composite plates and samples.
References
Fig. 12. Correlation between the elastic modulus EIT measured by indentation and the concentration of oxidation products Q calculated.
obtained for the virgin material, before any ageing (4070 MPa in Table 2).
4. Conclusions In this study, we performed numerical modelling of the thermo-oxidation of an epoxy resin, which is used as the matrix of aeronautical CFRP composites. A new finite element method has been specifically developed, including coupling between diffusion and oxidation, thanks to the kinetic model of Verdu et al. Simulations have been made in the case of an isothermal ageing of a non-reinforced resin sample (150 C, air, atmospheric pressure). The main results are: the kinetic model of oxidation can predict the concentration of oxidation products at any given point and any given time; moreover, it was shown that the oxidized layer can be characterized by the region corresponding to a nonzero value of concentration in oxidation products. On the other hand, a simple mathematical correlation was found between the measured values of indentation elastic modulus and the calculated ones of concentration of oxidation products, whatever the values of space and time variables be. This correlation will be useful to carry out some mechanical calculations of stresses induced by oxidation in composite materials subjected to longterm ageing in similar environmental conditions. However, even if the kinetic model used makes it possible to predict the chemical parameter values for other temperatures, other oxygen concentrations etc., it will be necessary to validate the mathematical correlation obtained in that study, since it is not based on theoretical demonstration. At that point, the numerical model using the finite element method needs to be developed, in order to include coupling effects with mechanical behaviour, so as to simulate the local evolution of the matrix in aeronautical laminates during oxidation. Hence, from the calculated local stress field, and with appropriate failure criteria, this model could be used to predict the lifetime of a complex composite laminate before any matrix cracking and contribute to enhanced control of the durability of aeronautical structures.
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