Characterization of internal damage in a MMCp using X-ray synchrotron phase contrast microtomography

PII:

Acta mater. Vol. 47, No. 5, pp. 1613±1625, 1999 # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain S1359-6454(99)00024-5 1359-6454/99 $20.00 + 0.00

CHARACTERIZATION OF INTERNAL DAMAGE IN A MMCp USING X-RAY SYNCHROTRON PHASE CONTRAST MICROTOMOGRAPHY J.-Y. BUFFIEÁRE1{, E. MAIRE1, P. CLOETENS2, G. LORMAND1 and R. FOUGEÁRES1 GEMPPM UMR CNRS 5510 INSA LYON, 20 Av. A. Einstein, 69621 Villeurbanne Cedex and 2 ESRF BP 220, 38043 Grenoble, France

1

(Received 3 July 1998; accepted 22 December 1998) AbstractÐThe initiation and development of damage inside a 6061 Al alloy reinforced with SiC particles has been studied during in situ mechanical tests using high resolution synchrotron X-ray tomography. The high coherence of the X-ray beam used improves the detection of reinforcements in the matrix as well as the detection of cracks. Qualitatively, the same damage mechanisms are observed at the surface and in the bulk of the sample, the rupture of the SiC particles being the dominant mechanism for the early stages of plastic deformation. Quantitatively, however, it is found that the geometrical characteristics of surface SiC particles di€er from those of bulk particles and that the damage growth rate is larger inside the sample. This result can be understood in terms of elastic energy and normal stress levels in the SiC particles as calculated by ®nite element method (FEM) analysis. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. ReÂsumeÂÐL'initiation et le deÂveloppement de l'endommagement au sein d'un alliage d'aluminium 6061 renforce par des particules de carbure de silicium ont eÂte eÂtudie au cours d'essais meÂcaniques in situ par tomographie X haute reÂsolution utilisant le rayonnement synchrotron. La forte coheÂrence du faisceau X utilise permet d'ameÂliorer la deÂtection des renforts dans la matrice ainsi que la deÂtection des ®ssures. Qualitativement, les meÂcanismes d'endommagement observeÂs en volume sont les meÃmes que ceux observeÂs en surface; la rupture des particules de SiC eÂtant le meÂcanisme preÂdominant pour les premiers stades de la plasticiteÂ. Quantitativement, toutefois, il apparaõà t que les caracteÂristiques geÂomeÂtriques des particules de SiC en surface di€eÁrent de celles des particules en volume et qu'en outre, l'accroissement de l'endommagement soit plus important en volume qu'en surface. Ce reÂsultat est interpreÂte en terme d'eÂnergie eÂlastique et de contrainte normale au sein des particules aÁ partir de calculs en eÂleÂments ®nis. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Composites; X-ray topography

1. INTRODUCTION

Compared to monolithic metallic materials, metal matrix composites (MMCs) exhibit some advantages, such as a high speci®c strength and sti€ness, an increased creep and wear resistance or a tailorable thermal conductivity, which make them very attractive materials for example in transport applications where a gain in weight is highly desirable. However, the industrial use of MMCs has been greatly restricted, so far, by poor fracture properties which stem from the presence of brittle ceramic particles within a ductile matrix. As a consequence, much attention has been paid, in the scienti®c literature, to the failure mechanisms of MMCs during stress/strain application. In the case of particle reinforced MMCs, those mechanisms can be broadly divided in three classes [1]: particle cracking; {To whom all correspondence should be addressed.

matrix-reinforcement decohesion; matrix ductile failure. As a matter of fact, the ¯ow behaviour of MMCs, can be strongly a€ected by the progressive cracking of the particles during the deformation, especially in tension, and properties such as the maximum tensile stress depend on the extent of this phenomenon. Recent theoretical studies [2±5] have enabled the modelling of this e€ect. In each of these studies an important input parameter is the evolution of the fraction of damaged particles during the test. This parameter is dicult to measure experimentally. The experimental characterization of damage can be achieved by serial sectioning or by fractographic analysis of broken samples [6±8]. Those observations provide valuable information on the damage mechanisms occurring in the bulk of the material, but they are generally time consuming observations not free from artefacts and, besides, they provide very limited indication on the chronology

1613

1614

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

of the damage events. This problem can be overcome by performing in situ characterization of damage during mechanical tests, for example in a scanning electron microscope (SEM). Although this technique has given some very interesting results on the sequence of damage leading to the ultimate failure [5, 9, 10], it has been suggested that the complex stress state which prevails at the surface of the samples (where in situ observation is performed) may bias the determination of the damage mechanisms occurring in the bulk [11]. Therefore, the validity of such in situ surface observations with respect to the bulk damage mechanisms has to be checked. As a matter of fact, di€erent damage extents between the surface and the bulk of strained composites have been reported previously. Humphreys [12], for example, has studied the extent of broken particles ahead of a crack both at the surface and in the bulk of a pre-cracked composite material. His results show that more cracked particles can be observed at the surface of the material than in the bulk. A similar result has been obtained by Mummery and Derby [11] on an Al-5050/SiC pre-cracked composite. Zong and Derby have also studied damage development in Al/SiC samples broken in tension [8]. By analysing longitudinal cross-sections, those authors have quanti®ed the extent of broken particles at the surface and in the bulk of the samples at di€erent distances from the fracture surface. However, no clear evolution of damage between the surface and the bulk can be deduced from their results. In the ®rst case, Humphreys suggested that, within the particles located at the surface of a sample, compressive stresses resulting from the processing and the thermal treatment, should be partially relaxed. Therefore, a greater extent of particle cracking is to be expected at the surface. On the contrary, Mummery and Derby have suggested that stress relaxation at the surface should only occur within a narrow band (as shown by other authors [13]), and that large particles should experience some, if not all, thermal residual stress. Therefore, Mummery and Derby assumed that the di€erence in damage extent they observed between surface and bulk was induced by the matrix plastic deformation which was easier at the surface (plane stress) than in the bulk (plane strain). Some authors have tried to monitor the occurrence of damage in micro-heterogeneous materials using non-destructive techniques like sti€ness measurements [14], density measurements [15], acoustic emission measurements [16], or X-ray computed tomography (XRCT). The two ®rst techniques correspond to non-local measurements which are not necessarily representative of local phenomena [17]. Acoustic emission can provide local information on damage mechanisms such as reinforcement cracking but the precise identi®cation

of the damage for which a signal is detected often requires destructive observations as mentioned above. For the moment, XRCT is the only nondestructive characterization technique which provides direct images of the bulk of the materials. As a result, XRCT has been used, in its classical form based on X-ray attenuation, to characterize, in various materials, defects resulting from processing [18± 20] as well as to assess damage resulting from thermal cycling or from deformation [21±24]. In these studies, defects such as voids, ®bre±matrix debondings or ®bre cracks have been imaged with a resolution varying from tens to 1 mm depending on the kind of X-ray source used, either laboratory sources or synchrotron sources. One of the factors also in¯uencing the resolution of the images obtained by XRCT is the di€erence in X-ray attenuation between the matrix and the phases/features that one wants to observe. This attenuation contrast is sucient in the case of a large void or a crack within a matrix and has enabled some authors, for example, to monitor fatigue crack closure in an Al±Li alloy [25]. However, in the case of Al/SiC composites, the X-ray attenuation coecients of the reinforcement and of the matrix can be very close. Hence the contrast obtained on two-dimensional projections and on reconstructed images is faint. Some recent studies have shown, however, that the large spatial coherence of synchrotron radiation can be used eciently to increase such a faint contrast and also to improve the detection of damage such as strain induced cracks in reinforcements [26, 27] in the form of SiC ®bres or particles. In this paper, we have used this new technique, called the phase contrast technique, for monitoring the deformation of a particle reinforced Al/SiC composite. Damage initiation and growth during straining have been studied in situ in the bulk of the material. Qualitative and quantitative comparisons of damage development in the bulk and at the surface are given. The observed di€erences are discussed on the basis of ®nite element (FE) calculations.

2. EXPERIMENTAL PROCEDURE

2.1. Material The studied composite was a model material made of an Al 6061 alloy reinforced by SiC particles with an average size of 150 mm and an average aspect ratio of 1.6. This rather large size of reinforcing particles, compared to industrial MMC, was chosen in relation to the resolution of the reconstructed images (see below). The volume fraction of the reinforcing phases was 10%. The material was processed through a rheocasting route under nitrogen and was subsequently extruded at 813 K with an extrusion ratio of 16 and a ram displacement rate of 100 mm/s. The extruded bars were solutionized at 803 K for 2 h, quenched in water and

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

Fig. 1. Back scattered electron micrograph of the studied composite. The extrusion axis is horizontal on the micrograph.

matured at room temperature for 2 weeks (T4 heat treatment). Small double shouldered specimens, similar to those used for in situ tensile testing in the SEM [5], were then spark cut from the centre of the bars with their axes parallel to the extrusion direction. The cross-section of those samples was 1.5  1.5 mm2 and their gauge length was 4 mm long. Before testing, the samples were polished using SiC paper (1200 grit) and diamond paste (down to 1 mm) and examined in a SEM operated at 25 keV. The polishing step has been carried out very carefully in order to avoid, as much as possible, inducing some defects in the SiC particles located at the surface of the sample. An example of the microstructure as observed by SEM at the surface of the sample is shown in Fig. 1. 2.2. XRCT characterization High resolution tomographic experiments were performed using a synchrotron X-ray source on line ID19 at the European Synchrotron Radiation Facility (ESRF) in Grenoble. The main characteristics of the beam on this line are the large source/ sample distance (150 m) and a small X-ray source

1615

size (100 mm). Thanks to those two characteristics, the X-ray beam on ID19 shows a high lateral coherence. In our case, the X-ray beam coming out of the ring was monochromated using two silicon single crystals and the beam energy was set at 23 keV (l = 0.5 AÊ). This resulted in a lateral coherence of about 100 mm. The experimental set-up used for the tomographic experiments is shown in Fig. 2. The samples were set on a goniometer allowing a precise positioning of the sample. A scan of the samples consisting of the recording of 600 two-dimensional radiographs was performed during a 1808 rotation along the vertical axis (i.e. one radiograph every 0.38). Those radiographs were recorded on a 1024  1024 CCD camera developed at ESRF and described elsewhere [28]. The average exposure time for a radiograph was 12 s and the whole scan lasted approximately 2 h. The pixel size of the CCD camera being 6.65  6.65 mm2, the whole gauge lengths of the tensile samples were imaged on the radiographs, resulting in an investigated volume of material of about 1.5  1.5  4 mm3. The two-dimensional radiographs were then used to re-construct the volumes of the samples using a three-dimensional extension of the conventional two-dimensional ®ltered back projection algorithm. In classical tomography, the detector is normally set directly behind the sample and the contrast obtained on the two-dimensional projections results from the di€erence of X-ray attenuation by the phases/features encountered by X-rays in the specimen. In our case however, the di€erence in speci®c X-ray attenuation of the matrix and reinforcement is small (m=r ˆ 2:31 and 2.25 cm2/g, respectively) thus, a new method of imaging called phase contrast imaging was used. Fresnel fringes due to the interference between parts of the X-ray wavefront that have experienced slightly di€erent angular deviations associated with di€erent phase gradients, are superimposed on the faint attenuation contrast

Fig. 2. Schematic drawing of the experimental set-up used at ESRF on the ID19 beam line.

1616

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

Fig. 3. Reconstructed images of two di€erent cross-sections of the studied composite obtained by (a) attenuation tomography and (b) phase contrast tomography. On the left image, the SiC particles are hardly visible because of the small di€erence in attenuation coecient between SiC and Al. Reconstruction rings are also visible because the contrast of the image has been enhanced to image the SiC particles. On the right image, the contrast between matrix and reinforcement is enhanced by the presence of bright/dark fringes at each particle/matrix interface. Those fringes are obtained by simply setting the CCD detector at 83 cm behind the sample (see the text for details).

mentioned above simply by setting the detector at a rather large distance from the specimen (83 cm in the present case). This method of imaging, which is experimentally very simple, o€ers two advantages. First, a di€raction contrast appears at the vicinity of particle/matrix interfaces which greatly enhances the detection of the reinforcements as shown in Fig. 3(a) (classical attenuation tomography), and Fig. 3(b) (phase contrast tomography). The agreement between the reconstructed images and the real material remains excellent, as shown elsewhere [26]. Second, thanks to the interference phenomenon, cracks with an opening down to 0.5 mm, i.e. well below the voxel size, can be detected in the SiC particles [26]. Although the reconstruction algorithm employed in this work is normally used in classical tomography, very good results were obtained in the case of phase contrast. A detailed discussion of the phase contrast technique as well as a theoretical justi®cation for the use of a classical reconstruction algorithm can be found elsewhere [26, 29, 30]. With the experimental set-up described above, the size of the voxels in the reconstructed volumes was 6.65  6.65  6.65 mm3. 2.3. Mechanical tests Constant strain rate tensile tests were conducted at room temperature on a specially designed in situ tensile testing machine set directly on the goniometer and experiencing the same rotation as the sample during the scans. In order to avoid the frame of the machine hiding the beam during the 1808 rotation, a PMMA tube was used to transmit the load between the upper mobile grip and the lower grip ®xed on the goniometer. This tube was carefully polished and gave uniform absorption on

the two-dimensional radiographs. The machine could be used in tension or in compression with a maximum load of 1500 N. The force and the crosshead displacement were recorded on a computer and monitored during the test. A crosshead displacement rate of 150 mm/mn was used for all the tests corresponding to an average strain rate of 6  10ÿ4/s. Once the sample was set in the machine, a ®rst scan was performed without any load applied, in order to characterize the initial non-deformed state. At the end of this ®rst scan, the load was increased and another scan was performed while the crosshead position was maintained constant. A stress drop of less than 10% was recorded during the scan. Five scans, corresponding to increasing strain levels, were performed on the same sample. The true total strain et ˆ ln…A0 =Ai †, has been calculated at each deformation stage from the area of undeformed (A0) and deformed (Ai) sections, perpendicular to the applied stress. Given the low value of the elastic strain, this total strain is a good approximation of the true plastic strain ep. The values of A0 and Ai have been measured from a reconstructed section of the sample containing the same particles all along the deformation. The relative error on the maximum plastic strain has been estimated at Dep =ep ˆ 2%. 2.4. Quantitative analysis of the reconstructed images The SiC particles and their evolutions with the strain level have been analysed manually on the reconstructed images of the composite. Although this method was quite tedious and drastically limited the number of particles that could be analysed within a reasonable time, it was preferred at automatic analysis. Indeed, because of the phase contrast, each particle/matrix interface, on the

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

1617

equal to the standard deviation) while it was equal to 1452 48 mm in the case of automatic analysis. The two methods were considered in very good agreement as the observed di€erence on the mean values corresponded roughly to one pixel (6.65 mm) on the reconstructed images. Besides, the distribution of the lengths obtained by the two methods were also in close agreement. The fraction of broken particles in the bulk and at the two surfaces of the sample perpendicular to the z-axis has been determined for each strain level. 3. RESULTS

3.1. Qualitative description of damage events Fig. 4. Schematic drawing illustrating the de®nition of the x-, y- and z-axes of the SiC particles with respect to the tensile axis.

reconstructed images, was underlined by a set of dark/bright fringes, as expected [26]. Besides, given the very similar values of m/r for the SiC and the Al matrix, the grey level within the particles was very similar to that of the matrix. Thus, no reliable automatic detection of the particles could be performed even with advanced thresholding algorithms based on edge detection methods. The results presented in the next section correspond to ®ve tomographic scans of a single sample and are based on the analysis of 950 planar sections of three reconstructed volumes. All the particles at the surface of the sample gauge length have been analysed{ corresponding to 114 particles. In the bulk, 200 particles were analysed corresponding roughly to one third of those actually present in the investigated sample volume. The statistical pertinence of these numbers is analysed further. For each analysed SiC particle, in the bulk and at the surface, the projected lengths along the three x-, y- and z-axes, de®ned in Fig. 4, have been measured manually. From those measurements, the volume of the particles has been calculated, assuming an ellipsoidal or a semi-ellipsoidal shape for particles located in the bulk or at the surface, respectively. For the particles located at the surface of the sample, the measurements along the y-direction have been compared to the results of an automatic image analysis of 500 SiC particles observed on SEM micrographs similar to the one shown in Fig. 1. In the ®rst case, the average value of the particle length along the extrusion direction was found equal to 1372 62 mm (the error is taken {A particle is considered at the surface of the sample when it can be observed on the reconstructed image of the sample surface perpendicular to the z-axis. Thus, all the particles located in a super®cial slice of 6.65 mm thickness are considered as surface particles.

The chronology of damage initiation and development in the interior of the sample, as observed by tomography, is illustrated in Fig. 5 which presents reconstructed images of the same internal section of the sample at ®ve di€erent stages of deformation. In Fig. 5(a), representing the initial non-deformed state, one can ®rst notice a global alignment of the SiC particles due to the extrusion process the direction of which is vertical in the ®gure. Two kinds of damage have been observed in the sample before deformation. First, nearly all matrix/particle interfaces perpendicular to the extrusion direction exhibit some voids [Detail A in Fig. 5(a)]. Those voids were also observed at the surface of the sample during SEM examination, but in a much lower proportion, probably because the majority of them had been ®lled during the polishing process by the ductile Al matrix. Those voids correspond to particle/ matrix decohesions induced by the extrusion process. Second, the analysis of the reconstructed images revealed that 11% of the SiC particles located at the surface of the sample contained a crack at the initial state. In the bulk, however, no initial cracks could be detected in the SiC particles. Figure 5(b) illustrates the damage level obtained in the material for a true plastic strain ep ˆ 5  10ÿ3 , close to the plastic o€set of the conventional material yield stress. At that stage, bright fringes, perpendicular to the stress direction are clearly visible in some SiC particles (Detail B). For the specimen detector distance used, those fringes correspond to cracks open in mode I as shown previously on a similar material [26]. Some broken SiC particles were also observed at the surface for the same strain level. No particle matrix decohesion could be detected at that stage of deformation with the available experimental resolution. The fraction of cracked particles increased with plastic strain, both in the bulk and at the surface [see Figs 5(c) and (d) for the bulk], besides, the white fringes corresponding to cracks, became thicker and eventually appeared in black, when the strain increased. This indicates a steady growth of

1618

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

Fig. 5.

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

the crack opening in the SiC particles when the matrix was deforming plastically. For a given strain level, no obvious di€erence in the opening of the cracks could be detected between the surface and the bulk of the sample. Some multiple cracking of the SiC particles has occasionally been observed, both in the bulk and at the surface, but this is not the dominant cracking mechanism for the investigated deformation levels. For a plastic strain ep ˆ 6  10ÿ2 the ®rst interfacial decohesions are detected [Detail C in Fig. 5(d)] at the surface and in the bulk. At that stage, one can also notice a fuzzy contrast in the matrix on the reconstructed images [Fig. 5(d) and (e)]. This contrast is not observed in the sections corresponding to non-deformed parts of the samples (far from the tensile gauge) and seems to be more pronounced near the SiC particles. Furthermore, in some cases (Detail D), this contrast takes a ``V shape'' typical of the localized plastic deformation observed in the matrix at the vicinity of a cracked SiC particle during in situ mechanical tests in optical microscopy. For all those reasons, this fuzzy contrast has been attributed to the occurrence of localized plastic deformation in the matrix, but further work is required to assess this assumption. In the last stages of deformation, the extrusioninduced voids, present in the initial state, started to grow [Detail E in Fig. 5(e)] and the damage tends to be homogeneously distributed in the material. 3.2. Quantitative analysis Previous experimental studies on MMCs, have shown that geometrical characteristics of the reinforcing particles such as their volume or their aspect ratio play a central role in particle cracking. Therefore those parameters have been ®rst determined from our measurements, in the bulk and at the surface of the sample. The cumulated frequencies of the analysed particle volumes are given in Fig. 6(a). It can be seen from this ®gure that the surface and the bulk volume distributions are di€erent and that the median volume of the particles located in the bulk is approximately twice as large as the median volume of the particles located at the surface. The distributions of the y/x, y/z and z/x aspect ratios of the particles in the bulk and at the surface have been calculated. No signi®cant di€erences are observed

1619

Fig. 6. Cumulated distributions of the particle volume (a) and of the y/z aspect ratio (b) of the particles located at the surface and in the bulk of the material. Particles located in the bulk exhibit, on average, a higher volume and a lower aspect ratio than those located at the surface.

between the surface and the bulk for the y/x and z/ x distribution. However, it can be observed from Fig. 6(b) that the particles located at the surface of the sample do exhibit a larger y/z aspect ratio, with almost 20% of the population showing a y/z aspect ratio larger than 4 (to be compared to 2% for the particles located in the bulk). The evolution of the fraction of broken particles as a function of the true plastic strain is shown in Fig. 7. The broken particles present in the initial state at the surface were not included on the curve corresponding to the surface particles. It can be seen from this ®gure that the fraction of broken particles at the surface increases less rapidly with the plastic strain than the fraction of broken par-

Fig. 5. Reconstructed images of the same internal section of the studied composite at ®ve di€erent stages of plastic deformation (a, initial state; b, ep ˆ 5  10ÿ3 ; c, ep ˆ 3  10ÿ2 ; d, ep ˆ 6  10ÿ2 ; e, ep ˆ 13  10ÿ2 ) which are indicated on the tensile curve of the material. At the initial state, some matrix particle decohesions induced by the extrusion process are visible in the bulk (detail A). At the onset of plasticity, some cracks appear in the SiC particles (detail B). Thanks to the phase contrast technique, those cracks appear as bright fringes which grow thicker when the cracks open. At the later stages of deformation, some particle matrix decohesions become visible in the bulk of the material (detail C). Eventually, the extrusion induced decohesions start to propagate under load (detail E).

1620

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

Fig. 7. Fraction of particles broken by the plastic deformation as a function of the true plastic strain. The fraction of broken particles is found larger in the bulk than at the surface for all the investigated strains.

ticles in the bulk. The ratio between the fraction of broken particles in the bulk and at the surface appears to remain constant after a strain of 3% is reached. Given the limited number of analysed particles, the statistical validity of those results has been checked; 95% con®dence intervals calculated after the method described by Saporta [31] are indicated on the curves. Those intervals are seen to overlap only for the ®rst strain level investigated. In that case, however, a statistical test of the surface and bulk fractions equality, shows that the risk for the measured fraction of broken particles to be equal is less than 8%. 4. DISCUSSION

From a qualitative point of view, the results presented above show that at least three damage mechanisms occur in the studied material, during tensile deformation at room temperature. More precisely, when the plastic strain increases, the observed chronology of damage events can be described as follows: 1. Mode I cracking of the SiC particles. 2. Particle matrix decohesions. 3. Growth of pre-existing extrusion-induced voids. Those damage mechanisms are observed both at the surface and in the bulk of the material. In our case, the phase contrast technique used to monitor damage allows a very good detection of the reinforcement cracking. However, because of the presence of bright/dark fringes at the particle/matrix interfaces, it is likely, that the ®rst stage of particle matrix decohesion is harder to detect. The same remark holds for the growth of the pre-existing extrusion-induced voids at the vicinity of particle/ matrix interfaces. Nevertheless, keeping those considerations in mind, our results show that, for the

composite studied here, particle cracking is the ®rst damage event to occur and it remains the main damage mechanism up to an average true plastic strain of 6%. This is in agreement with the results of Maire et al. [5] and Lewis and Withers [32] who have shown on di€erent composites, that interfacial decohesion occurs only at the later stage of the material deformation. Besides, the large size of the SiC particles used in this study should promote the reinforcement cracking as an important failure mechanism as shown by many studies [14, 32, 33]. In what follows we will therefore focus the discussion on particle cracking and analyse the di€erence in damage growth rate observed between the bulk and the surface of the sample. Our results indicate clearly that, for the material investigated, the cracking of SiC particles during straining is underestimated by mere surface observations. A similar result had already been found using the same characterization technique on a similar material processed through a di€erent route. In that case, the material had not been extruded after rheocasting and the fraction of cracked SiC particles, determined on unloaded strained samples, was also found to be larger in the bulk than at the surface at the onset of plastic deformation [27]. However in this previous work, the presence, in the material, of brittle oxides due to the rheocasting process induced some cracks in the matrix. Those cracks rapidly took over the particle cracking and led to the ®nal rupture, preventing a thorough analysis of the particle rupture all along the tensile curve. For the material investigated in this study, at least three factors can be invoked to account for the di€erence in damage growth rate between surface and bulk:

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

1. The thermal stresses resulting from the material processing and/or heat treatment. 2. The probability of ®nding a critical defect which can induce the rupture of the reinforcement. 3. The stress level induced in the SiC particles by the elastic/plastic incompatibilities between matrix and reinforcement. Each of those three mechanisms is discussed separately in the following paragraphs. 4.1. In¯uence of the thermal stresses It is well established that the processing and the heat treatment of MMCs result in thermal residual stresses in the reinforcements and in the matrix. Those stresses, which are of a compressive nature in the reinforcement in our case because of the ®nal heat treatment (solution treatment followed by a water quench), should be at least partially relaxed at the surface of the material [12]. FEM simulations of thermal residual stresses in a MMC show that, indeed, a relaxation of these compressive thermal stresses does occur below the material surface within a band, the thickness of which is of the order of magnitude of the particle mean size [13]. For this reason, the normal tensile stress levels reached within surface particles should be higher than that of a bulk particle. Hence, the risk of rupture of a surface particle should be higher than that of a bulk particle. For the material investigated in this study, although such a relaxation e€ect is likely to occur, it is probably not the main parameter which controls the rupture of the reinforcements as the number of broken particles is experimentally found to be higher in the bulk of the material where the residual stresses should not be relaxed.

1621

4.2. Probability of ®nding a critical defect which can induce the rupture of the reinforcement The probability of rupture of the SiC particles is also related to the probability of ®nding a critical defect in the particles. This probability is, in turn, related to the volume of the particle itself. Our observations show that this volume is, on average, lower at the surface than in the bulk [cf. Fig. 6(a)]. Therefore one should expect a lower probability of rupture for surface particles, which is con®rmed by our experimental observations. The assumption that the sample preparation does not introduce too much damage in the particles close to the free surface (this would increase the probability of ®nding a defect) is dicult to check experimentally. However, it has been checked that the amount of damage induced in the surface SiC particles was considerably higher when the sample polishing was not carried out carefully. Moreover, it must be pointed out, as shown further, that the external faces of the particles at the free surface are the ones which undergo the strongest stress reduction. 4.3. In¯uence of the stress level induced in the SiC particles by the applied stress because of the elastic/ plastic incompatibilities between matrix and reinforcement Eventually, the probability of rupture of the reinforcements is also related to the stress levels induced in the reinforcements during the deformation of the composite. Those stress levels are likely to be di€erent for a surface particle and for a bulk particle. This has been shown by the work of some authors which have given analytical solutions of the stress ®eld within ellipsoidal inclusions

Fig. 8. (a) Schematic diagram of the three-dimensional FE model which consists of a parallelepiped SiC particle with truncated corners (enlarged by a factor 2 with respect to its actual size), embedded in a large area of material with the average properties of the composite. According to the boundary conditions chosen for the mesh, two cases corresponding to a single particle in the bulk or a pair of particles at the free surface can be simulated. (b) Example of the boundary conditions used, as seen on the (x,y) plane. For modelling a single particle in the bulk, the nodes along the right-hand vertical boundary (solid line hollow triangles) are constrained. For modelling two particles at the surface, the nodes along the left-hand vertical boundary (dashed line hollow triangles) are constrained. The nodes along the horizontal line (full triangles) are constrained in both cases.

1622

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

located at the vicinity of a surface and submitted to a uniform dilatational eigenstrain [34, 35]. Those approaches, however, are restricted to the elastic case. The situation where the particle is cut by the free surface (which is the case in our study) has not been investigated analytically except by Ambroise et al. [36]. In our case, plastic deformation occurs in the matrix; calculations based on the ®nite element method (FEM) have therefore been performed, with the ABAQUS commercial code, to analyse this problem. A three-dimensional mesh using eight-node solid elements has been used to model the studied material. The mesh con®guration used is shown in Fig. 8. A SiC particle is embedded in a block of composite. The SiC particles in the material have been modelled by simple parallelepipeds elongated along the direction of the applied stress with an aspect ratio of 1.6. This shape, close to the actual particle shape, has already been chosen in several two-dimensional numerical calculations [37, 38]. The sharp edges of the modelled particles act as stress concentrators which are unlikely to be present in the actual material. In order to smoothen this e€ect on the stress calculations, the triple corner of the particle in the mesh has been truncated as shown in Fig. 8. A tensile stress is applied along the axis labelled y in Fig. 8. The respective properties of the two constituents used for the calculation were: . SiC: Young's modulus E ˆ 400 GPa, Poisson's ratio  ˆ 0:33 (purely elastic behaviour). . Composite: E ˆ 90 GPa,  ˆ 0:33 (elasto-plastic behaviour). The plastic behaviour of the composite which surrounds the particle in the model, has been ®tted on the experimental tensile curve of the composite with an elastic limit of 100 MPa. It was chosen to treat the case of the interaction between a single particle and a material exhibiting the behaviour of the homogenized composite instead of that of the matrix. Indeed, the ratio between the particle dimensions in the model and those of the composite block is large (1/10). Thus, the global behaviour of the composite block is not signi®cantly di€erent from that of the matrix surrounding the particle. From a local point of view, however, the ``real'' plastic behaviour of the matrix is comprised between that of the global composite and that of a pure 6061 alloy. By performing calculations with the behaviour of the matrix (E ˆ 70 GPa,  ˆ 0:33 and the plastic curve of the 6061 alloy), it was checked afterwards that the initial choice for the plastic deformation law had no in¯uence on the ®nal conclusions. Thanks to the symmetry of the system, only one eighth of the representative volume has to be meshed. By simply changing the boundary conditions on the mesh it is possible to simulate a single particle in the middle of the sample or a pair of particles at the free surfaces of the same sample.

Those boundary conditions are described in what follows (see also Fig. 8): . A single particle in the middle of the sample. This can be achieved by constraining the nodes in each of the three symmetry planes of the particle in the direction normal to these planes. Namely, all the nodes situated in the (x,z) plane cutting the particle in its middle are constrained along the direction y, etc. . A pair of particles at the ``surface'' of the sample. This can be achieved by releasing the nodes of one of the planes in which the particle has the aspect ratio of 1.6 and constraining the nodes of the opposite plane in the sample. When the particle is at the centre of the mesh or at its free surface, its aspect ratio is 1.6 or 3.2, respectively. The ®rst value represents the average y/z aspect ratio of the real particles in the bulk as observed by tomography [see Fig. 6(b)] while the second one is slightly higher than the average y/z aspect ratio observed experimentally for surface particles [see Fig. 6(b)]. For the two mesh con®gurations described above, the normal stress values, away from the particle corners, and the elastic energy stored in the SiC particle are calculated for the di€erent plastic strain levels investigated. Those two quantities were chosen, because they are often used as criteria to analyse the rupture of the SiC particles in mode I as observed in our case. It must be pointed out that the load transfer from the matrix to the surface particles, should be reduced with respect to bulk particles in the real material if the matrix/particle interfaces are damaged during the sample preparation. This e€ect has not been taken into account in the FEM calculation. Therefore, the calculation presented below with a ``perfect interface'' assumption represents a higher bound both for the normal stresses and for the stored energy. The results obtained are shown in Figs 9 and 10, respectively. Figure 9 shows the pro®les of syy along the A±A' path shown in Fig. 8 for a given applied stress (170 MPa). Figure 10 shows the evolutions of the elastic energy stored in the particle with the plastic strain. The results of FEM calculations in terms of maximum normal stresses syy in the SiC particle must be considered with caution because the shape chosen for the SiC particle introduces some stress concentrations at the vicinity of the particle edges (in spite of the truncated shape of the triple corner). Experimentally, the rupture of SiC particles at their corners is not observed either by tomography or during in situ mechanical tests in a SEM. It is likely, therefore, that the stress level away from those ``unrealistic'' stress concentrations should be more representative of the actual stress level inside the particles which justi®es the choice of the path A±A' for studying the evolution of the

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

1623

Fig. 9. Evolution of the normal stress syy along the A±A' line, shown in Fig. 8, for a surface particle and for a bulk particle in the case of an applied external load of 170 MPa (A and A' are located within the particle and within the matrix, respectively).

normal stress in the particle. The stress pro®le for the particle in the bulk (Fig. 9) is in good agreement with the analytical results given by Mura for a cuboidal inclusion [35]. Compared to the wellknown constant value in ellipsoidal inclusions, this stress is slightly varying in cuboidal inclusions with a higher value at the interface. When the particle is now assumed to be cut by the free surface, an extra torque is added to the global stress distribution. This had already been pointed out by Ambroise et al. [36]. This torque tends to bend the particle, reducing strongly the normal stress close to the free surface while increasing slightly the maximum value of this stress close to the internal particle/matrix interface. The stress reduction is so high for the chosen value of the applied stress, that the normal stress is nearly equal to zero close to the free surface. This stress could even become negative for a higher value of the applied stress. A similar inversion close to a free surface has been evidenced analytically by Mura [35] for an ellipsoidal particle.

The volume a€ected by the stress increase is smaller than the one a€ected by the stress decrease. Hence, the probability of ®nding a critical defect in the zones where a stress increase prevails is small. When looking at the rupture from a statistical point of view it is more relevant to investigate the distribution of the syy stress values in the whole particle. When doing so, it is found that the global stress distribution is shifted towards the low values of syy when the particle moves from the bulk of the material towards its free surface. The mean value of the stress distribution, for instance, is 12% lower for a surface particle. Besides, the high stress levels observed near the edges of the modelled particles tend to be reduced when the particle is located at a free surface. In short, the FEM calculation shows that a surface particle is globally less loaded than a bulk particle. Concerning the elastic energy stored in the particle, the results of the calculation are easier to analyse. It can be seen from Fig. 10 that, due to the

Fig. 10. Evolution of the total stored elastic energy in a SiC particle, as modelled by FEM, as a function of the plastic strain of the composite. The evolution is shown for a particle located at the surface or in the bulk of the material.

1624

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE

stress relaxation occurring near the surface, the elastic energy stored in a SiC particle is lower when this one is located at the surface of the material, in spite of the larger aspect ratio. Besides, the ratio of the elastic energy in a SiC particle located at the surface or in the bulk remains roughly constant all along the plastic deformation. This is in agreement with the results of Fig. 7 where it is shown that the probability of rupture of a bulk particle is higher than that of a surface particle and that the ratio of these probabilities remains constant when the plastic strain is increased. It must be said that, in the case of damaged interfaces, one could expect a larger amount of interfacial decohesions at the surface when this damage mechanism is occurring. However, those decohesions are dicult to observe because their contrast in the reconstructed imagesÐa set of fringesÐwill coincide with that of the particle/matrix interfaces. As a consequence, this point could not be veri®ed from our observations. To summarize, FEM calculations show that both the normal stress levels and the elastic energy levels are lower for a SiC particle located at the surface of the material. This ``surface relaxation'' e€ect can account for the lower number of broken particles observed at the surface of our material. It must be pointed out, ®nally, that our observations are opposite to the results of Mummery and Derby [11] and those of Humphreys [12] who have reported a larger damage extent at the surface of their samples. However, in their cases the comparisons between surface and bulk have been made on pre-cracked samples for which the stress state is much more complex than the one described here. A quantitative characterization of damage by tomography on precracked samples would allow a direct comparison with the results mentioned above. This work is currently being carried out. 5. CONCLUSION

The present study shows the interest of X-ray tomography for non-destructive local characterization of damage, in a metal matrix composite during a mechanical test. Thanks to the high lateral coherence of the synchrotron radiation, di€raction by the interface region between the Al matrix and the SiC allows a very good detection of the particles. A good detection of strain induced cracks in the reinforcements is also made possible by this technique. At the initial state, some particle matrix decohesions induced by the extrusion process are detected in the bulk of the material. Those decohesions are hardly visible at the surface due to the sample preparation. In the plastic deformation region, for the experimental conditions investigated, three damage mechanisms have been identi®ed, both in the bulk and at the surface: rupture of the SiC particles, par-

ticle matrix decohesions, growth of extrusioninduced interfacial decohesions. The ®rst mechanism is the one that dominates through the early stages of plastic deformation. The quantitative analysis of the SiC particles shows that surface particles have, on average, a smaller volume and a higher y/z aspect ratio than the bulk particles and, also, that the fraction of particles broken by plastic deformation is higher in the bulk than at the surface. Thus, it appears that the damage growth rate in the SiC particles is strongly in¯uenced by the presence of a free surface. FEM calculations have been used to compute the normal stresses and the elastic energy within a SiC particle embedded in a matrix submitted to a tensile stress. Both the global stress distribution in the particle and the stored elastic energy are found to decrease when the particle moves from the centre of the material towards its free surface. This result, combined with a lower mean volume of surface particles which induces a lower probability of ®nding a critical defect, can account for the higher damage rate observed in the bulk of the material investigated here.

REFERENCES 1. Clyne, T. W. and Withers, P. J., An Introduction to Metal Matrix Composites. Cambridge University Press, Cambridge, 1993. 2. Bao, G., Acta metall. mater., 1992, 40, 10. 3. Kiser, M. T., Zok, F. W. and Wilkinson, D. S., Acta metall. mater., 1996, 44, 9. 4. Martinez, J. L., Llorca, J. and Elices, M., Proc. IUTAM Symposium ``Micromechanics of Plasticity and Damage of Multiphase Materials'', ed. A. Pineau and A. Zaoui. Kluwer Academic, Dordrecht, 1996, p. 59. 5. Maire, E., Verdu, C., Lormand, G. and FougeÁres, R., Mater. Sci. Engng, 1995, A196, 135. 6. Christman, T., Needleman, A., Nutt, S. and Suresh, S., Mater. Sci. Engng, 1989, A107, 49. 7. Manoharan, M. and Lewandowski, J. J., Acta metall. mater., 1990, 38, 3. 8. Zong, Y. and Derby, B., Proc. Euromat 93, ed. R. Pichoir and P. Costa. J. Physique IV Colloque C7, suppleÂment au J. Physique III, 1993, 11, 1861. 9. Manoharan, L. and Lewandowski, J. J., Acta metall. mater., 1990, 38, 489. 10. Da Silva, R., Caldemaison, D. and Bretheau, T., Proc. 9th Int. Symp. Metallurgy and Materials Science RISO, ed. S. I. Andersen, H. Lilholt and O. B. Pedersen, 1988, p. 333. 11. Mummery, P. M. and Derby, B., J. Mater. Sci., 1994, 29, 5615. 12. Humphreys, F. J., Proc. EMAG-MICRO 89. IOP, Bristol, 1990, p. 465. 13. Shouxin, L., Lizbi, S., Zhengming, S. and Zhongguang, W., Scripta metall. mater., 1991, 25, 2431. 14. Lloyd, D. J., Acta metall. mater., 1991, 39, 1. 15. Hunt, W. H., Brockenborough, J. R. and Magnusen, P. E., Scripta metall. mater., 1991, 25, 15. 16. Mummery, P. M., Derby, B., Buttle, D. and Scruby, C. B., Proc. Euromat 91, ed. T. W. Clyne and P. W. Withers, Vol. 2, 1991, p. 863.

BUFFIEÁRE et al.: CHARACTERIZATION OF INTERNAL DAMAGE 17. Mummery, P. M., Anderson, P., Davis, G. R., Derby, B. and Elliott, J. C., Scripta metall. mater., 1993, 29, 1457. 18. Kinney, D. L., Haupt, T. M., Breunig, T. M., Nichols, M. C., Starr, T. L. and Stock, S. R., Proc. 17th Conf. on Composites and Advanced Ceramic Materials, ed. D. C. Cranmer. Am. Ceram. Soc., 1993, p. 1028. 19. Breunig, T. M., Nichols, M. C., Kinney, J. H. and Haupt, D. L., Proc. 17th Conf. on Composites and Advanced Ceramic Materials, ed. D. C. Cranmer. Am. Ceram. Soc., 1993, p. 500. 20. Liu, X. and Bathias, C., Comp. Sci. Technol., 1995, 46, 245. 21. Breunig, T. M., Stock, S. R., Guvenilir, A., Elliott, J. C., Anderson, P. and Davis, G. R., Composites, 1993, 24, 209. 22. Baaklini, G. Y., Bhatt, R. T., Eckel, A. J., Engler, P., Castelli, M. G. and Rauser, R. W., Mater. Eval., 1995, Sept, 1040. 23. London, B., Yancey, R. N. and Smith, J. A., Mater. Eval., 1990, May, 604. 24. Hirano, T., Usami, K., Tanaka, Y. and Masuda, C., J. Mater. Res., 1995, 10, 381. 25. Guvenilir, A., Breunig, T. M., Kinney, J. H. and Stock, S. R., Acta mater., 1997, 45, 5. 26. Cloetens, P., Pateyron-SalomeÂ, M., BueÁre, J.-Y., Peix, G., Baruchel, J., Peyrin, F. and Schlenker, M., J. appl. Phys., 1997, 81, 9.

1625

27. BueÁre, J.-Y., Maire, E., Verdu, C., Cloetens, P., Pateyron, M., Peix, G. and Baruchel, J., Mater. Sci. Engng, 1997, A234±236, 633. 28. Labiche, J. C., Segura-Puchades, J., Van Brussel, D. and Moy, J. P., ESRF Newsletter, 1996, 25, 42. 29. Cloetens, P., Barrett, R., Baruchel, J., Guigay, J.-P. and Schlenker, M., J. Phys. D: Appl. Phys., 1996, 29, 133. 30. Wilkins, S. W., Gureyev, T. E., Gao, D., Pogany, A. and Stevenson, A. W., Letters to Nature, 1996, 384, 335. 31. Saporta, G., ProbabiliteÂs Analyse de DonneÂes et Statistique. TECHNIP, Paris, 1990. 32. Lewis, C. A. and Withers, P. J., Acta metall. mater., 1995, 43, 10. 33. BreÂchet, Y., Embury, J. D., Tao, S. and Luo, L., Acta metall. mater., 1991, 39, 8. 34. Seo, K. and Mura, T., J. appl. Mech., 1979, 46, 568. 35. Mura, T., Micromechanics of Defects in Solids, 2nd edn. Martinus Nijho€, 1987. 36. Ambroise, M. H., Bretheau, T. and Zaoui, A., Phil. Mag. Lett., 1987, 56, 7. 37. Llorca, J., Martin, A., Ruiz, J. and Elices, M., Metall. Trans. A, 1993, 24A, 1575. 38. Levy, A. and Papazian, J. M., Acta metall. mater., 1991, 39, 2255.