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SiC composites
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Acta mater. Vol. 46, No. 18, pp. 6585±6598, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain S1359-6454(98)00297-3 1359-6454/98 $19.00 + 0.00
A NEUTRON DIFFRACTION STUDY OF LOAD PARTITIONING IN CONTINUOUS Ti/SiC COMPOSITES P. J. WITHERS{1{ and A. P. CLARKE}2 Department of Materials Science and Metallurgy, Cambridge University, Pembroke St., Cambridge CB2 3QZ, U.K. and 2Neutron and Condensed Matter Branch, AECL Research, Chalk River, Ontario K0J 1J0, Canada 1
(Received 30 March 1998; accepted 11 August 1998) AbstractÐNeutron diraction measurements are described of the internal strain response of Ti±6Al±4V/ 35 vol.% SiC continuous ®bre composites to loading axial and transverse to the ®bre alignment direction. In the as-fabricated condition large thermal residual strCTains are observed, being equivalent to average axial ®bre and matrix stresses of ÿ840 and 450 MPa, respectively. As one might expect, upon loading there are marked dierences in load sharing according to whether the ®bres are parallel or perpendicular to the loading direction. In the former case, load is transferred towards the ®bres; a process which is accelerated when the matrix deforms plastically, while in the latter case, load is transferred to the ®bres only at very low loads. At higher loads, the process reverses with the reinforcement shedding load back into the matrix. The measurements suggest that this is caused by matrix/®bre interface failure at transverse loads of around 300 MPa. Simple calculations suggest that this would require a non-zero matrix/®bre normal interface strength of around 100 MPa. The measured thermal and load-induced strains are interpreted in the light of Eshelby-based models throughout. # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Although some of the earliest metal matrix composite materials contained continuous ®bres, usually in Cu or Al matrices [1±3], cost factors precluded their widespread application. Recently, however, there has been a resurgence of interest in continuous ®bre composites for aeroengine applications driven by the exceptional properties of Ti-based systems at high temperatures [4]. These materials are capable of higher operating temperatures than conventional Ti-based alloys and are much lighter than Ni-based superalloys. As a result of the dierence in thermal expansion coecients between metallic matrices and ®brous ceramic reinforcements such as SiC mono®laments, Ti/SiC systems often have very large thermal residual stresses after fabrication, which can severely limit their performance in-service. That high thermal stresses are generated during the conventional ®bre/foil lay-up fabrication process, which includes hot pressing of the ®bre foil sandwich at high temperatures (>9008C), is clear from the fact that such lay-ups have been known to delaminate spontaneously upon cooling to room temperature.
While residual stresses in these systems have been the subject of a number of studies [5±8], there have been no reports on partitioning of stress between matrix and reinforcement during loading to date. This is the subject of the current study. Previous studies have been made on Cu±W and Al±W composite systems using X-rays [1±3], but even for these systems the response under transverse loading has not received attention. The transverse loading behaviour is often of crucial importance because transverse strengths are typically far lower than axial strengths, and because in many applications the transverse loads experienced by the component can be signi®cant, for example when used for the hoop reinforcement of rotating parts [4]. In this context, it is clear that the interface is an important parameter in determining the extent to which the ®bres can be loaded. Previous modelling studies have considered the behaviour where the interface strengths are zero [9], around 100 MPa [10] and in®nity [9]. In view of the very poor penetration of X-rays into titanium, neutron diraction is perhaps the best way to evaluate the average ®bre load which can be sustained by the ®bre under transverse loading prior to interface failure. 2. MATERIALS AND EXPERIMENTAL DETAILS
{Present address: Manchester Materials Science Centre, Grosvenor St., Manchester M1 7HS, U.K. {To whom all correspondence should be addressed. }Present address: Microsoft Corporation, Redmond, WA, Seattle, U.S.A.
The composite laminates comprised a Ti±6Al±4V matrix reinforced with 35 vol.% SCS-6 SiC mono®lamentary ®bres. The composite was made by a layup procedure involving the placement of aligned
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arrays of ®bres between thin metallic foils, followed by a hot pressing operation at around 9508C. The laminates were 8-ply (1.8 mm) in thickness. Tensile specimens were cut out from the laminates by computer controlled electro-discharge machining, both with the tensile axis parallel to the alignment direction and perpendicular to it. Great care was exercised not to damage the tensile specimens, and no damage was visible. The samples were of a dogbone geometry having a gauge length of 46 mm and a gauge width of 7.25 mm. For comparison, 2.45 mm thick unreinforced Ti±6Al±4V specimens made by a similar layup route were also included in the study. The loading apparatus was specially designed to ®t within the L3 spectrometer. The load was recorded using a 45 kN load cell, the normal cross-head speed 0.25 mm/min and the strain monitored using an MTS extensometer having a gauge length of 8 mm and attached directly to the edge of the specimen. The neutron diraction experiments were performed on the L3 spectrometer of the NRU reactor, Chalk River, Canada. A neutron wavelength of 2.4330 2 0.0001 AÊ was used, produced by re¯ection from the (113) planes of a Ge single crystal monochromator; this was calibrated using a NIST Si powder standard. The experiments were carried out with a tensile testing machine mounted upon the diraction table so that the axis of loading bisected the incident and diracted beams, i.e. such that strains in the loading direction could be measured. Specimens were strained under load control and the load was maintained at an approximately constant level during the acquisition of the neutron diraction peak data. 3. DIFFRACTION METHOD
Diraction is a well established tool for the evaluation of internal stresses in two-phase materials. Because of the high penetration of neutrons, neutron diraction has found particular use for the examination of metal matrix composites [5, 11]. The principle is simple; changes in the spacing between the atomic lattice planes is deduced from shifts (Dy) in the diraction peak angles (y) and is converted to strain (e) using the relationship e ÿcot y Dy: In the current study, the stress-free reference lattice spacings of the matrix and reinforcement were measured using the unreinforced Ti±6Al±4V alloy reference specimen, and by using free mono®lamentary ®bres. In order to interpret lattice plane strains measured in a single phase material in terms of the internal stresses, a value for the relevant stiness component is required. If the single crystal elastic constants are used then the derived stress will represent the average stress experienced by that family of re¯ecting grains, and it will not necessarily be
equal to the macrostress in that region, i.e. that which could be determined by hole drilling, since intergranular stresses may cause some families of grains to be more highly stressed than others [12]. In a single phase material, the relationship between the overall macrostress and the individual strains recorded by each re¯ection is expressed in terms of diraction elastic constants, determined experimentally. However, with the onset of plasticity this linear relationship is no longer necessarily obeyed. This is because plastic deformation is an inherently inhomogeneous process, especially for low symmetry materials, such as hexagonal Ti±6Al±4V, and this can be the cause of further intergranular stress. Fortunately, it is common in uniaxial straining experiments on a particular alloy for the applied stress/lattice strain relationships of certain re¯ections to remain more or less linear even when plasticity is extensive (e.g. Ref. [13]). It is usually these re¯ections which are the most reliable indicators of the macrostress. X-ray stress measurements on Ti are often based on the analysis of 2133, while Ezeilo et al. [14] used 1011 for neutron work on the basis that they found this re¯ection to be little aected by plastic strain. In our experiments, three Ti alloy peaks ( 1010, (0002) and 1011) and one SiC peak (220) were monitored for the measurements made parallel to the ®bre alignment direction, while for reasons of texture only the Ti 1011 and the SiC(111) and (220) re¯ections could be used for the measurements perpendicular to the ®bre alignment direction. At each load, the diraction peaks were obtained by scanning a single 3He detector in the horizontal plane. The horizontal divergence of the neutron beam was limited to 0.48 using Soller slits, and the spatial widths of the incident and diracted beams were restricted to be approximately 25 mm wide by cadmium masks, so that only the uniformly stressed gauge volume of the specimen was sampled. Each diraction peak pro®le was then ®tted with a Gaussian distribution and a typical result is shown in Fig. 1 for the Ti(0002) re¯ection.
4. RESULTS
4.1. Unreinforced Ti±6Al±4V alloy In order to establish the diraction elastic constants for the matrix, the unreinforced material was loaded and the strain response monitored for the three chosen re¯ections. At certain prescribed levels the loading schedule was interrupted and a series of neutron strain measurements were made at constant load. Measurements were made both below the proportional limit, as well as at larger strains. The macroscopic stress±strain curve is shown in Fig. 2(a) while the lattice strain results are shown in Fig. 2(b)±(d).
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Fig. 1. A typical neutron diraction trace, in this case for the Ti(0002) peak. As shown here, each peak was ®tted with a Gaussian pro®le and the peak centre used to evaluate the strain. Single peak measurement times varied from 15 to 60 min.
For each re¯ection, the gradients of the unloading curves, and of the loading curves up to the proportional limit, are linear and the resulting stinesses are summarized in Table 1. These results show, as one would expect, that the measured elastic constants lie between the single crystal values and the bulk value with the (0002) re¯ection the stiest and the 1010 the most compliant, this is in contrast to the results reported elsewhere [15]. Further, it is clear that, in this case, both the (0002) and 1011 re¯ections are sensitive to the extent of plastic straining, but in contrary senses. This is evidenced by the curvature of the responses at high loads and the residual strains upon unloading. As described above, this arises from the generation of plastic mis®ts and hence stress between neighbouring grains. This is potentially more severe in hexagonal materials than cubic ones because of the limited number of slip systems available for the maintenance of plastic strain compatibility. That it is the (0002) which is the least susceptible to plastic deformation and is thus left residually in tension, while the 1011 is the most susceptible and is residually in compression can be understood in the following terms. Slip for crystallites oriented with the (0002) planes normal to the tensile axis will be particularly resistant to plastic ¯ow due to the diculty of slip on planes other than (0002). This is oset only slightly by the ampli®cation of the applied stress in such crystallites arising from the slightly higher single crystal stiness in that direction (Table 1). As a result of the plastic anisotropy, unthinking application of the diraction elastic constants to the lattice strain data after plastic straining could lead to large errors in the internal stresses. For example, at the end of the experiment one would infer the specimen to be in tension or com-
pression by 70 or ÿ160 MPa according to whether one was to use the (0002) or 1011 re¯ections, respectively. For this reason only the 1010 re¯ection, which appears to be less sensitive to plastic strain, has been used for quanti®cation of the internal stresses in this study. At high loads extensive room temperature ``creep'' was observed to take place. This is evidenced by the 2% creep strain that occurred while the neutron measurements were made with the load at 0900 MPa and by the 4% strain that occurred at 01050 MPa [Fig. 2(a)]. Although the specimen continued to creep throughout the hour it took to acquire the three re¯ections, the greatest part occurred during the ®rst 10 min or so. It was not possible to perform a loading experiment on a single ®bre using the in situ straining rig available at Chalk River. As a result, the axial ®bre stiness was taken to be 415 GPa in the following analyses [4]. 4.2. Thermal residual strain measurements The thermal residual strains were measured parallel and perpendicular to the ®bre alignment direction using the two sets of tensile specimens prior to the application of the load and the unreinforced reference sample and the results are summarized in Table 2. It is clear that the axial residual strains are much larger than those transverse to the ®bres. It is possible that the observed dierences between the 1010, (0002) and 1011 matrix strains are due to the anisotropy in thermal expansion of the matrix; certainly the sense of the dierences is consistent with intergranular stresses having this origin and are much larger than the experimental scatter (0100±200 me). When attempting to interpret these results in the light of simple composite models it
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Fig. 2. (a) The applied stress/engineering strain curve for the unreinforced Ti±6Al±4V alloy. At high loads; the loads at which the neutron measurements were made can be seen by the presence of creep strains at constant load. The applied stress/elastic lattice strain response for (b) the Ti 1010, (c) the Ti(0002) and (d) the Ti 1011 re¯ections. The neutron measurements for these re¯ections were always made under constant load and in this sequence. The thin lines delineate the unloading/reloading stages of the cycle; the ®nal plastic strain of the specimen was in excess of 14%.
could be argued that the Ti 1010 re¯ection might be most representative of the average condition because it is least sensitive to plastic anisotropy, or one could argue that the Ti 1011 re¯ection is more likely to be representative because it has a coecient of thermal expansion which is essentially equal to the bulk value. Given that little plastic ¯ow is expected upon cooling it is probable that the latter is more reliable. As a result the SiC(220) and Ti 1011 strains have been used to infer the phase stresses summarized in Table 2. Despite the uncer-
tainties in both the measurements and their interpretation, these values almost satisfy the necessary balance of internal stress: Th Overall longitudinal stress: 1 ÿ f hsiTh M fhsiF
62 MPa: Th Overall transverse stress: 1 ÿ f hsiTh M fhsiF
53 MPa:
Table 1. Reference data and the stinesses derived for the unreinforced Ti±6Al±4V alloy from Fig. 2 Re¯ection Single crystal stiness (GPa) [16] Measured stiness (GPa) Final residual strain (me)
Specimen
1010
(0002)
1011
Ð 115 140 000
103 104 50
146 134 500
116 111 ÿ1400
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Table 2. The measured residual strains and the inferred phase stresses; the values in parentheses are the Eshelby predictions based on the SiC(220) and the Ti 1011 responses. Experimental uncertainty of around 100 and 200 me was recorded for the axial and transverse measurements, respectively Re¯ection Lattice strains (me) Phase stress (MPa) Thermal exp. coef. [17]
SiC(111) 6to ®bres _ to ®bres 6to ®bres _ to ®bres 10ÿ6/K (293±973 K)
28
These strain measurements compare with axial ®bre and matrix strains of ÿ1900 and 4200 me recorded, respectively, for Ti±14Al±21Nb/35% SCS-6 SiC by neutron diraction [11], and a ®bre strain of ÿ1610 me for Ti±6±4 alloy/35% SCS-6 SiC composite as measured by surface removal [18]. Modelling work by Durodola and Derby [19] using matrix and ®bre CTEs of 4.7 and 9±10.5 me/K predicted the maximum axial ®bre stress{ to be in the range ÿ600 to ÿ800 MPa at 40% reinforcement content for cooling rates in the range 0.1±100 K/s from 9008C. They suggested that a cooling rate of around 0.64 K/s would be representative of cooling after HIPping giving ®bre stresses of around ÿ650 MPa. Nimmer et al. [9] on the other hand predict average matrix (®bre) stresses parallel and transverse to the alignment of 380 (ÿ705) and 250 (ÿ465) MPa, respectively. These FE calculations include plasticity and time-dependent creep and this probably explains the higher transverse stresses predicted compared with the simpler elastic Eshelby-based calculations listed in Table 2. In the previous literature on thermal residual strains a great deal of use has been made of the eectively stress-free temperature (Tesf) representative of the observed residual strains (stresses). This is not the temperature at which the composite was actually stress free, but rather is a measure of the dierential thermal expansion mis®t which can be retained elastically during cooling. In systems which undergo extensive creep or plasticity Tesf is much lower than that at which the composite was fabricated. The main obstacle to determining Tesf in the present case lies in the diculty in obtaining reliable values of the thermal expansion coecients for the two phases. Previously, a very large range 9.5±12.5 me/K has been reported for Ti±6Al±4V [9]. Our recent work suggests that a value of around 11.8 me/K is broadly representative of our matrix material over temperatures appropriate to HIPping and cooling of the composite (293±1173 K) [20]. Taking the expansion coecient for the mono®laments to be 4.8 me/K (in accordance with the supplier) the rate at which residual strains and stresses are generated within the composite per kelvin tem{Finite element models indicate that, in agreement with the assumptions of the Eshelby model, the ®bre strains (stresses) vary little with position across the ®bres.
SiC(220)
Ti 1010
Ti(0002)
Ti 1011
ÿ1500 (ÿ1600) 28 (118) ÿ825 (ÿ840) ÿ340 (ÿ290) 4.8
2600
3600
11.03
13.37
3300 (3100) 230 (ÿ230) 540 (450) 270 (155) 11.81
perature drop are shown in Table 3. Thus assuming an expansion mismatch of 7 me/K, the axial strains (Table 2) are indicative of an eective stress-free temperature drop of around 6758C, i.e. the stresses introduced into the composite as a result of cooling from the hot pressing temperature are equivalent to those that would be caused by cooling from 07008C if the thermal mismatch strains were accommodated completely elastically. Using a lower matrix expansion coecient (9.5 me/K) and a lower matrix stiness (86 GPa), Pickard et al. [6] inferred a similar stress-free temperature drop (6508C) for comparable recorded strain values for Ti±15±3/30% SiC composite. These values are slightly smaller than that deduced experimentally by Saigal et al. [21] who monitored the decrease in thermal residual strains for Ti±14Al±21Nb/35% SCS-6 SiC aligned mono®lament composite as the temperature was increased and found that the strains decreased to zero at a temperature of around 8008C. However, it should be borne in mind that this dierence could be due solely to errors in the thermal expansion coecient used to calculate Tesf. Of course what really matters is the level of retained residual stress (which is surprisingly consistent across all the materials) since it is this which aects the mechanical properties and the size of the clamping eects at the ®bre matrix interface. Electron Back Scatter Patterns (EBSPs) recorded by Pickard and Miracle [18] revealed no discernible plastic zone at the Ti±6Al±4V/SCS-6 SiC ®bre interface after cooling from the fabrication temperature, in contrast to observations on Ti±14Al±21Nb/ SCS-6 SiC. This is consistent with the assertion that little or no local yielding occurs during cooling. Recent work by Watts [20] suggests that high cooling rates (water quenching) can increase the level of retained thermal stresses due to the suppression of creep at high temperatures in agreement with previous modelling work [19]. In view of the limited extent of stress relaxation by plasticity at low temperature and creep at high temperature it is perhaps not surprising that the retained stresses measured for these systems can be represented by a high Tesf (175±85% of the fabrication temperature). 4.3. Axial loading of the composite As can be seen by comparing Fig. 3 with Fig. 2(a), the composite response to axial loading is strongly in¯uenced by the presence of the ®bres.
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Table 3. Eshelby-based predictions of the thermal mis®t, elastic mismatch and plastic mis®t stresses and strains generated in each phase. For the thermal mismatch stresses, the values are those generated per kelvin temperature drop using a thermal expansion mis®t of 7 me/ K. Smaller values of this mis®t would give proportionately lower rates of stress generation. The elastic mismatch stresses are those generated per MPa load applied parallel or transverse to the ®bre direction, while the plastic mismatch stresses are those required to generate an axial residual extension of 1% in the composite Matrix
Thermal strain/K (me/K) Thermal stress/K (MPa/K) Elastic mismatch stress (MPa/MPa6to ®bres) Elastic mismatch stress (MPa/MPa _ to ®bres) Plastic mismatch strain (me/1% axial plastic strain) Plastic mismatch stress (MPa/1% axial plastic strain)
Fibre
6to ®bres
_ to ®bres
6to ®bres
_ to ®bres
4.6 0.67 0.53 ÿ0.12 ÿ18 000 ÿ2070
ÿ0.34 0.23 0.0 0.90 4800 ÿ150
ÿ2.37 ÿ1.24 1.87 ÿ0.22 10 000 4150
0.17 ÿ0.43 0.0 1.18 ÿ2500 270
The maximum load is approximately 250 MPa higher, but the load borne by the reinforcing ®bres means that even at these higher loads the plastic strain (00.22%) is over 50 times smaller than for the unreinforced alloy recorded earlier. The total strain to failure (just under 1%) is dictated by the elastic strain to failure of the ®bres which is normally quoted as being no more than 0.9%. The failure strains observed here also compare well with the 1% failure strain observed by Pickard et al. [6] for Ti±15±3/30% SCS-6 SiC. The composite stiness taken from the unloading curves is around 205 GPa (Table 3), which is in excellent agreement with the rule of mixtures prediction of stiness (220 GPa) calculated using the bulk Ti±6Al±4V value (115 GPa) and an axial SiC ®bre stiness of around 415 GPa [4, 22]. In addition to the reduced plastic straining, the presence of the ®bres has signi®cantly reduced the extent of room temperature ``creep'' deformation at load compared with the unreinforced alloy. A typi-
cal creep curve measured over the two and a half hours required to acquire the three Ti and one SiC re¯ection is shown in Fig. 4. The discontinuities in the data are associated with the activation of the load control system whenever the load fell out of the permissible range (25 MPa of the target load). This curve is well ®tted by a log ®t over the data acquisition period. The creep rate appears to decrease continuously, due to the gradual transfer of load from the matrix towards the ®bres, in accordance with conventional creep models [4] and previous experimental observations on other continuous systems [23]. When interpreting the neutron diraction lattice strain measurements, it should be remembered that they will not be very sensitive to the rapidly creeping portion of the curve because of the considerable time required to acquire each diffraction peak (15±60 min). The internal strain responses for both phases, for all the measured re¯ections, are shown in Fig. 5. In the following discussion attention is focused primar-
Fig. 3. The stress/engineering strain response of the composite to a load applied parallel to the ®bre alignment direction; the thin lines delineate the unloading/reloading stages of the cycle.
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Fig. 4. The occurrence of room temperature creep for the Ti±6Al±4V/35% SiC composite under an axial load of 1354 MPa.
Fig. 5. The applied stress/lattice strain response for (a) the Ti 1010, (b) the Ti(0002), (c) the Ti 1011 and (d) the SiC(220) re¯ections; the thin lines delineate the unloading/reloading stages of the cycle.
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Table 4. A comparison between the unloading gradients (210 GPa) observed in Fig. 5 and those predicted using a Reuss-like assumption for the partitioning of load between the matrix grains Re¯ection (Lattice strain/unit applied stress)ÿ1 (GPa) Predicted gradients (GPa)
Composite
SiC(220)
Ti
Ti(0002)
Ti 1011
205 220
219 220
214 208
243 268
213 201
ily on the SiC(220) and Ti 1010 re¯ections. The latter was chosen because it is least sensitive to plastic anisotropy (Fig. 2). Because the SiC mono®laments deform elastically, and are continuous from one end of the specimen to the other, one would expect their elastic strain behaviour to match the engineering strain response of the specimen as a whole, provided the interfaces remain intact. In this respect it is reassuring to ®nd that the elastic gradients of the two curves are indeed very similar (Table 4). While at a macroscale the load partitions between the two bulk phases according to the equal strain criterion, the load within the matrix is unevenly distributed between dierently oriented grains. This is evidenced by the fact that the gradients of the individual matrix re¯ections lie almost half way between the Voigt equal strain model (which would give all the grains the same gradient) and the Reuss-like predictions shown in Table 4 (i.e. gradients in proportion to their diraction-derived stinesses given in Table 1). This indicates that the load within the matrix partitions between the individual grains approximately according to the Kroner model, i.e. those grains with their stier orientations aligned with the loading direction bear more of the load than those with their more compliant directions aligned with the loading axis. The strain recorded by the clip gauge departs from the linear elastic line at loads as low as 100 MPa. This is evidenced by the unloading/ reloading responses in Fig. 3. This premature curvature of the loading response could arise from the sensitivity of the clip gauge to a slight realignment of the specimen as the load was ®rst applied, or it could be due to microplasticity or matrix/®bre slippage. Use of clip gauges on both sides of the specimens would have avoided this ambiguity, but this would have interfered with the line of sight access of the neutron beam to the sample. Since the ®bres are continuous and essentially elastic, the SiC re¯ection provides an internal composite strain gauge which should be directly comparable with the clip gauge. Its response is essentially linear until the load is in excess of 800 MPa [Fig. 5(d)]. This would suggest that the initial curvature of the composite response is probably an artefact and that the dashed line in Fig. 3 having a gradient equal to the unloading/reloading areas (205 GPa) is more representative. Indeed, the dashed line is more in line with the response commonly recorded for these materials in the testing laboratory. Furthermore, the
composite and ®bre residual strains should be equal unless signi®cant ®bre matrix slippage has occurred. Prior to correction the clip gauge records a plastic strain of around 0.2% (Fig. 3) as compared to a residual ®bre strain of around 0.1% [Fig. 5(d)]. Besides, the early activation of microplasticity or interface sliding might be expected to give rise to residual phase microstrains in Fig. 5(a)±(d) after the early unloading cycles. It is clear from Fig. 5 that as loading progresses into the plastic regime, the lattice strain responses become non-linear indicative of load redistribution towards the ®bres. This curvature also gives rise to residual strains upon unloading, with the ®bres in increasing residual tension and the matrix re¯ections in increasing compression with increased plastic straining. Neglecting the early inelastic straining as being due to specimen alignment it would seem reasonable to take the plastic strain of the composite to be around 0.1% (1000 me). Application of the Eshelby model (a one-dimensional model is nearly as good) predicts (Table 3) that the residual elastic strains in the matrix and ®bres would be ÿ1800 and 1000 me, respectively, in excellent agreement with the strains observed in Fig. 5(a) and (d). This further corroborates the conclusion that the specimen had straightened slightly as the load was ®rst applied. Converting these strains to stresses indicates that load transfer has caused a decrease in the matrix load of ÿ207 MPa and an increase in the ®bre load of 415 MPa. Incorporating the initial thermal residual strains which were excluded from the ®gure the total axial matrix and ®bre residual strains after deformation are A Th A heiM heiTh M heiM and heiF heiF heiF heiM ÿ 1800 2600 800 me and
heiF ÿ 1500 1000 ÿ500 me: The latter change is similar to that (heiA F ÿ1760, 976 giving hei ÿ784 me) recorded for Ti± heiTh F F 14Al±21Nb/35% SCS-6 SiC [18] for which the total composite strain was about 0.8% (compared with 0.9% here). The knees observed in the matrix and ®bre phase curves at an applied load of around 900 MPa suggest that the matrix yields macroscopically at this applied stress level. Initially this might seem surprising in view of the 450 MPa tensile matrix residual stresses and the fact that the unreinforced alloy yielded at around 850 MPa. However, the
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axial stress in the matrix at an applied load of 900 MPa is approximately A M hsiTh s M BM s 450 0:53 900 927 MPa
leading to a principal stress dierence of around 775 MPa. In other words plastic yielding in the matrix occurs at nearly the same matrix stress in the composite as for the unreinforced alloy. This is due to the counterbalancing eects of the thermal residual stress and the elastic load transfer to the ®bres arising from the stiness mismatch (i.e. the elastic mismatch term in Table 3 is much less than one). It is also of interest to deduce the average axial matrix ( sM ) and ®bre ( sF ) stresses at the point of failure: Pl A M hsiTh s M hsiM BM s and Pl A F hsiTh s F hsiF BF s Pl where hsiTh M is the thermal residual stress, hsiM the A A plastic load transfer term and Bs ( s hsiA M) the elastic mismatch stress arising from the applied load. Referring to Table 3, the overall axial matrix and ®bre stresses at the ultimate load (sA=1360 MPa) are inferred to be
M 450 ÿ 207 0:53 1360 and s F ÿ 840 415 1:87 1360 s M 960 MPa and s F 2120 MPa: s As one might expect, the axial matrix stress lies between the unreinforced matrix yield stress and the
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matrix failure stress, since failure of the composite initiates in the ®bres. 4.4. Transverse loading of the composite As one would expect, the loading response transverse to the ®bre direction (Fig. 6) is very dierent from both the unreinforced and the axial composite tests [Fig. 2(a) and Fig. 3]. The stress±strain curve becomes non-linear at around 150 MPa. The stiness over this part of the curve is around 165 GPa; in very good agreement with the Eshelby prediction of 170 GPa. The observation that the unloading gradient decreases as the loading sequence progresses suggests that damage is initiating progressively with increased loading. In addition, the absence of signi®cant plastic strain upon unloading would indicate that, for the range of strains studied, most of the curvature of the stress±strain curve is due to changes in the load partitioning, rather than due to conventional macroscopic plastic ¯ow. The lattice strain responses measured parallel to the loading direction, but perpendicular to the ®bres, are shown in Fig. 7 for both phases and for all the measured re¯ections. In this orientation the SiC ®bres are not continuous from one end of the specimen to the other, and thus one would expect, and indeed one ®nds, the SiC to be strained less than the composite as a whole (i.e. the lattice strain gradients are steeper than the engineering strain gradientÐTable 5). However, more striking is the tendency for the SiC strains to curve in a direction indicative of load shedding, especially above 300 MPa, and at the same time for the response of the Ti re¯ection to curve in the contrary direction.
Fig. 6. The stress/engineering strain response of the composite to a load applied normal to the ®bre alignment direction; the thin lines delineate the unloading/reloading stages of the cycle.
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Fig. 7. The applied stress/lattice strain response for (a) the Ti 1011, (b) the SiC(111) and (c) the SiC(220) re¯ections measured parallel to the loading direction, but normal to the ®bre direction; the thin lines delineate the unloading/reloading stages of the cycle.
This is indicative of a very drastic change in the partitioning of load away from the ®bres and towards the matrix and is in agreement with the reduced composite stiness observed in Fig. 6. The results indicate that the ®bres unload signi®cantly above applied loads of around 300 MPa, and furthermore that the Ti alloy matrix is able to take up the increased load without generalized plastic deformation. This is corroborated by the absence of residual lattice strain in the matrix after each of the loading/unloading cycles (Fig. 7).
It is not possible to determine from the neutron data whether each ®bre has partially unloaded, or whether some of the ®bres have unloaded completely while others continue to bear some load. In any event, a simple consideration of the strains measured at 300 and 450 MPa in the two phases gives a simple view of the development of load transfer (neglecting the small amount of true plastic straining that occurs and the stresses transverse to the applied load). At 300 MPa the matrix and ®bre microstrains are approximately 2400:850, respect-
Table 5. A comparison between the observed (210 GPa) and predicted slopes for the strains measured in the loading direction, but transverse to the ®bre direction for the various re¯ections. The predicted slopes were calculated assuming that the slopes of the matrix re¯ections are in proportion to their unreinforced stinesses. The gradual increase in the loading/unloading slopes for the SiC re¯ections with increasing load and the corresponding decrease in slope of the Ti re¯ection makes it dicult to derive reliable values Re¯ection ÿ1
(Lattice strain/unit applied stress) Predicted gradients (GPa)
(GPa)
Composite
SiC(220)
SiC(111)
Ti 1011
165 170
325 303
360 330
140 160
WITHERS and CLARKE: NEUTRON DIFFRACTION
ively, giving phase stresses of around 275:350 (this is close to the ratio 270:352 taken from the values in Table 3 based on a perfect bond). But at 475 MPa the matrix and ®bre strains of 5020:700 correspond to stresses of around 580:290 (this is very dierent from the 425:560 ratio predicted for a perfect bond). When the initial transverse thermal residual stresses given in Table 2 are included in the calculation the average stresses become M 275 155 430 MPa and s s F 350 ÿ 290 60 MPa at 300 MPa and M 575 155 730 MPa and s F 290 ÿ 290 0 MPa at 475 MPa: s This would suggest that unloading of the ®bres is more or less complete at 475 MPa. Furthermore, the tensile (positive) value of the ®bre stress at sA=300 MPa suggests that the Ti±6±4/SCS-6 SiC interface does have some normal strength. The most probable cause of the load shedding is interfacial debonding. The ®bre interface is known to be fairly weak due to the presence of a graphitic interface layer used both to protect the ®bres during handling prior to fabrication and to control the interface chemistry. At low loads, one would expect the ®bre and matrix to remain in contact even if the interfacial bond strength were zero, because of the clamping eect of the thermal residual stresses. But at higher stresses decohesion would seem to be occurring. Direct observation of the broken test specimens indicates that ®nal fracture occurs by localized ductile failure of the Ti±6±4 matrix in the near ®bre ligaments combined with interface failure [Fig. 8(a)]. That the interface is fairly weak is evident from the absence of signi®cant amounts of matrix remaining adhered to the ®bres. Except in the vicinity of the fracture surface itself there was no evidence of ®bre/matrix interface separation after failure [Fig. 8(b)]. Recent observations of transverse loading undertaken within a scanning electron microscope suggest that at free surfaces, at least, interfacial debonding is occurring prior to failure. This is especially pronounced at the poles of the ®bres, i.e. the interface opens normal to the applied load. 5. DISCUSSION
Modelling work on similar composite systems by Nimmer et al. [9] indicates that, for interfaces of zero strength, debonding would initiate at an applied load of around 200 MPa, while Jansson et al. [24] quote a value of 140 MPa. Both these values are lower than the load at which the ®bres begin to shed load signi®cantly and would seem to con®rm a non-zero interface strength in this case. An important concern, given the testing geometry, is the eect
6595
of the free ®bre ends. Recently, experimental work by Warrier et al. [10] has done much to delineate the eect of free surfaces on interface failure. Their work is based on calculations by Kurtz and Pagano [25] which suggests that there is a tensile radial interface stress singularity at the free surface even with no externally applied stress, and that the stress remains tensile up to about one ®bre diameter from the surface. Of course this tensile region has a negligible eect on the neutron measurements since it is very small, but it does mean that the ®bres are probably already debonded at the ®bre ends even prior to loading. As the transverse stress increases one would expect the debond crack to grow inwards from the free surface. Indeed, in experiments in which strain gauges were placed side-byside from edge to centre the onset of stress±strain curvature was found to occur at progressively higher loads towards the centre indicative of inward debond growth [26], and it was deduced that this debonding process became signi®cant at loads of around 230 MPa. This is consistent with the initial departure from the elastic gradient observed in Fig. 7(a) and (b) at around 250 MPa. Further work using cruciform specimens in which the deforming section had no free ®bre ends has indicated that debonding occurs at a normal interface load of 115 MPa [10]. Returning to our observations, because the ®bre strains would be expected to vary little with lateral position within the ®bres, the average ®bre strain is a good indicator of the normal interface stress at the ®bre pole for transverse loading. Our results indicate that the ®bre begins to debond noticeably at an applied stress of around 300 MPa; presumably this progresses inwards from the free surfaces. At this load the average ®bre stress is around 60 MPa. Given that this is an average value and includes both the unbonded (and unstressed) ®bre end segments and the still bonded and highly stressed (central) sections of each ®bre it is not consistent with the idea that the interface has no normal strength, but is consistent with an interface strength of around 115 MPa (see Fig. 9). In view of the fact that even if all the ®bres were to debond completely (i.e. to behave as holes) the matrix would be able to sustain the applied load of 480 MPa at ultimate failure (the average matrix stress would then be 480/0.65 = 740 MPa), one would not expect extensive plastic deformation. This localization of the plastically deformed region to the matrix ligaments between ®bres is accentuated by the high and low matrix volume fraction regions caused by the sandwich structure of the composite [Fig. 8(b)]. The lack of any evidence of debonded interfaces at ®bre poles in polished sections, except near the failure location Fig. 8(b), is further evidence that little generalized matrix plasticity occurred prior to failure in that the clamping thermal residual stresses are able to maintain contact between the matrix and ®bre across the
6596
WITHERS and CLARKE: NEUTRON DIFFRACTION
Fig. 8. (a) Scanning electron micrograph of the fracture surface for a transversely tested specimen (loaded left to right), (b) a close-up taken near the failure location, at a load just below that required for failure. After unloading interface failure could only be observed in the immediate vicinity of the fracture surface. Note the localized interface failure in (b) both between the ®bre and the carbon coating and between the matrix and the carbon coating (point A). At point B local cracking of the matrix can also be seen.
Fig. 9. Schematic showing how the transverse ®bre stress might vary as the applied load is increased.
WITHERS and CLARKE: NEUTRON DIFFRACTION
debonded interface after unloading. That contact between the matrix and the ®bre poles is reestablished upon unloading may be responsible for the increase in the unloading gradients of both the matrix and composite unloading curves at low loads (Figs 6 and 7) and the absence of signi®cant residual lattice strains. 6. CONCLUSIONS
Our work on unreinforced Ti±6Al±4V indicates that plastic anisotropy caused by intergranular stresses is signi®cant and that the 1010 diraction peak is the least aected by plastic strain. Uncorrected use of the (0002) and 1011 peaks in our case would have lead to considerable errors. The measured thermal residual mismatch stresses were found to be very large (ÿ825 to ÿ840 MPa and 450 to 540 MPa in the axial direction for ®bre and matrix, respectively, and ÿ340 to ÿ290 MPa and 155 to 270 MPa in the transverse direction). These values are in good agreement to those already quoted in the literature. An eective stressfree temperature drop of around 6758C was calculated to be representative of the thermal stresses and indicates that little of the thermal mismatch generated on cooling from the fabrication temperature is inelastically accommodated, either by creep at high temperatures or plastic yielding at low temperatures. When tested in the direction of the ®bres, the composite was approximately 25% stronger and very much more resistant to plastic deformation than the unreinforced alloy. The observed load partitioning during elastic deformation could be well explained in terms of Rule of Mixtures or Eshelby models. At failure, matrix plasticity had resulted in a transfer of load towards the ®bres of about 415 MPa. Our direct measurements of internal stress partitioning during transverse loading corroborate the inferences made by Warrier et al. [27] in that the ®bre/matrix interface has a non-zero normal strength of around 100±120 MPa. This, when combined with initial thermal residual clamping forces of around ÿ340 to ÿ290 MPa at the interface means that, debonding near the free ®bre ends begins to become signi®cant at applied loads in excess of 250 MPa. Debonding is complete ( sF 10) when the applied load is around 475 MPa. Despite load shedding from the ®bres which occurs when the interface fails, the matrix deforms predominantly elastically because the matrix yield stress is still greater than the average matrix stress. In the cruciform tests undertaken by Warrier et al. debonding was found to occur at an applied stress of 330 MPa. This is in good agreement with the current results. With respect to the in¯uence of the free ends, it is important to ask whether one should always carry out tests in which the free ®bre ends are prevented from initiating debonding so as to
6597
measure the ``true'' ®bre matrix/interface strength. Often it is not feasible or realistic to test specially fabricated single ®bre cruciform specimens. Besides, it is probable that in many applications free ®bre ends will be present. Even in cases such as hoopwound aeroengine components there may be ®bre ends within the material arising from fabrication or ®bre fracture, and so it is important to be able to understand the debonding process under these conditions. AcknowledgementsÐWe are grateful to Rolls Royce for the provision of experimental composite material, especially to Colin Small, Diana Cardona and Philip Doorbar. P.J.W. would like to thank Tom Holden and Brian Powell for enabling his visit to Chalk River and to the EPSRC for funding the visit as well as the research programme of which this was a part. Part of this programme was also funded by the European Community under Brite EuRam project No. BRE2-CT92-0156 and the paper was ®nished with funding from the EPSRC/MOD joint project grant scheme. The assistance of David Nicolls and Mike Watts in preparing Fig. 8 is also acknowledged. Thanks are also expressed to Dan Miracle for many helpful discussions on this paper.
REFERENCES 1. Cheskis, H. P. and Heckel, R. W., Metal Matrix Composites, ASTM STP 438. American Soc. for Testing of Materials, 1968, pp. 76±91. 2. Cheskis, H. P. and Heckel, R. W., Metall. Trans., 1970, 1, 1931. 3. Lilholt, H., Acta metall., 1977, 25, 571. 4. Clyne, T. W. and Withers, P. J., An Introduction to Metal Matrix Composites, Cambridge Solid State Series. Cambridge University Press, Cambridge, 1993. 5. Withers, P. J., Key Engng Mater.ÐCeram. Matrix Composites, 1995, 108-110, 291. 6. Pickard, S. M., Miracle, D. B., Majumdar, B. S., Kendig, K. L., Rothen¯ue, L. and Coker, D., Acta metall. mater., 1995, 43(8), 3105. 7. James, M. R., ICRS 2, Nancy, 1988. 8. Cox, B. N., James, M. R., Marshall, D. B. and Addison, R. C., J., Metall. Trans. A, 1990, 21A, 2701. 9. Nimmer, R. P., Bankert, R. J., Russel, E. S., Smith, G. A. and Wright, P. K., J. Comp. Tech. Res., 1991, 13(1), 3. 10. Warrier, S. G., Gundel, D. B., Majumdar, B. S. and Miracle, D. B., Metall. Mater. Trans., 1996, 27A, 2035. 11. Kupperman, D. S., Majumdar, S., Singh, J. P. and Saigal, A., in Measurement of Residual Stress Using Neutron Diraction, NATO Conference, ed. M. T. Hutchings, 1992, pp. 439±450. 12. Noyan, I. C. and Cohen, J. B., in Materials Research and Engineering, ed. B. Ilschner and N. J. Grant. Springer, New York, 1987. 13. Clansen, B., Lorentzen, T. and Leers, T. Acta mater., 1998, 46, 3087. 14. Ezeilo, A. N., Webster, G. A., Webster, P. J. and Wang, X., Physica B., 1992, 180, 1044. 15. Bruno, G. and Dunn, B. D., Meas. Sci. Technol., 1997, 8, 1244. 16. Smithell, Smithell's Metals Reference Book, 7th edn, ed. E. A. Brandes. Butterworth, London, 1993, pp. 14-3±14-27. 17. Berry, R. L. P. and Raynor, G. V., Res. Lond., 1953, 6, 21S.
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18. Pickard, S. M. and Miracle, D. B., Mater. Sci. Engng, 1995, 203, 59. 19. Durodola, J. F. and Derby, B., Acta metall. mater., 1994, 42(5), 1525. 20. Watts, M. R., The analysis of diraction measurements of internal strains in metal matrix composites. Ph.D. thesis, Cambridge University, 1998. 21. Saigal, A., Kupperman, D. S. and Majumdar, S., Mater. Sci. Engng, 1992, A150, 59. 22. Coker, D., Ashbaugh, N. E. and Nicholas, T., in ASTM STP 1186, ed. H. Sehitoglu. American Soc. for Testing of Materials, 1993.
23. Endo, T., Chang, M., Matsuda, N. and Matsuura, K., Risù 12th Int. Conf. on Metal Matrix CompositesÐ Processing, Microstructure and Properties, Roskilde, Denmark, 1991, p. 323. 24. Jansson, S., Dal Bello, D. J. and Leckie, F. A., Acta metall. mater., 1994, 42(12), 4015. 25. Kurtz, R. D. and Pagano, N. J., Composites Engng, 1991, 1, 13. 26. Miracle, D. B., Private communication, 1996. 27. Warrier, S. G., Gundel, D. B., Majumdar, B. S. and Miracle, D. B., Scripta metall. mater., 1996, 34, 293.
Acta mater. Vol. 46, No. 18, pp. 6585±6598, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain S1359-6454(98)00297-3 1359-6454/98 $19.00 + 0.00
A NEUTRON DIFFRACTION STUDY OF LOAD PARTITIONING IN CONTINUOUS Ti/SiC COMPOSITES P. J. WITHERS{1{ and A. P. CLARKE}2 Department of Materials Science and Metallurgy, Cambridge University, Pembroke St., Cambridge CB2 3QZ, U.K. and 2Neutron and Condensed Matter Branch, AECL Research, Chalk River, Ontario K0J 1J0, Canada 1
(Received 30 March 1998; accepted 11 August 1998) AbstractÐNeutron diraction measurements are described of the internal strain response of Ti±6Al±4V/ 35 vol.% SiC continuous ®bre composites to loading axial and transverse to the ®bre alignment direction. In the as-fabricated condition large thermal residual strCTains are observed, being equivalent to average axial ®bre and matrix stresses of ÿ840 and 450 MPa, respectively. As one might expect, upon loading there are marked dierences in load sharing according to whether the ®bres are parallel or perpendicular to the loading direction. In the former case, load is transferred towards the ®bres; a process which is accelerated when the matrix deforms plastically, while in the latter case, load is transferred to the ®bres only at very low loads. At higher loads, the process reverses with the reinforcement shedding load back into the matrix. The measurements suggest that this is caused by matrix/®bre interface failure at transverse loads of around 300 MPa. Simple calculations suggest that this would require a non-zero matrix/®bre normal interface strength of around 100 MPa. The measured thermal and load-induced strains are interpreted in the light of Eshelby-based models throughout. # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Although some of the earliest metal matrix composite materials contained continuous ®bres, usually in Cu or Al matrices [1±3], cost factors precluded their widespread application. Recently, however, there has been a resurgence of interest in continuous ®bre composites for aeroengine applications driven by the exceptional properties of Ti-based systems at high temperatures [4]. These materials are capable of higher operating temperatures than conventional Ti-based alloys and are much lighter than Ni-based superalloys. As a result of the dierence in thermal expansion coecients between metallic matrices and ®brous ceramic reinforcements such as SiC mono®laments, Ti/SiC systems often have very large thermal residual stresses after fabrication, which can severely limit their performance in-service. That high thermal stresses are generated during the conventional ®bre/foil lay-up fabrication process, which includes hot pressing of the ®bre foil sandwich at high temperatures (>9008C), is clear from the fact that such lay-ups have been known to delaminate spontaneously upon cooling to room temperature.
While residual stresses in these systems have been the subject of a number of studies [5±8], there have been no reports on partitioning of stress between matrix and reinforcement during loading to date. This is the subject of the current study. Previous studies have been made on Cu±W and Al±W composite systems using X-rays [1±3], but even for these systems the response under transverse loading has not received attention. The transverse loading behaviour is often of crucial importance because transverse strengths are typically far lower than axial strengths, and because in many applications the transverse loads experienced by the component can be signi®cant, for example when used for the hoop reinforcement of rotating parts [4]. In this context, it is clear that the interface is an important parameter in determining the extent to which the ®bres can be loaded. Previous modelling studies have considered the behaviour where the interface strengths are zero [9], around 100 MPa [10] and in®nity [9]. In view of the very poor penetration of X-rays into titanium, neutron diraction is perhaps the best way to evaluate the average ®bre load which can be sustained by the ®bre under transverse loading prior to interface failure. 2. MATERIALS AND EXPERIMENTAL DETAILS
{Present address: Manchester Materials Science Centre, Grosvenor St., Manchester M1 7HS, U.K. {To whom all correspondence should be addressed. }Present address: Microsoft Corporation, Redmond, WA, Seattle, U.S.A.
The composite laminates comprised a Ti±6Al±4V matrix reinforced with 35 vol.% SCS-6 SiC mono®lamentary ®bres. The composite was made by a layup procedure involving the placement of aligned
6585
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WITHERS and CLARKE: NEUTRON DIFFRACTION
arrays of ®bres between thin metallic foils, followed by a hot pressing operation at around 9508C. The laminates were 8-ply (1.8 mm) in thickness. Tensile specimens were cut out from the laminates by computer controlled electro-discharge machining, both with the tensile axis parallel to the alignment direction and perpendicular to it. Great care was exercised not to damage the tensile specimens, and no damage was visible. The samples were of a dogbone geometry having a gauge length of 46 mm and a gauge width of 7.25 mm. For comparison, 2.45 mm thick unreinforced Ti±6Al±4V specimens made by a similar layup route were also included in the study. The loading apparatus was specially designed to ®t within the L3 spectrometer. The load was recorded using a 45 kN load cell, the normal cross-head speed 0.25 mm/min and the strain monitored using an MTS extensometer having a gauge length of 8 mm and attached directly to the edge of the specimen. The neutron diraction experiments were performed on the L3 spectrometer of the NRU reactor, Chalk River, Canada. A neutron wavelength of 2.4330 2 0.0001 AÊ was used, produced by re¯ection from the (113) planes of a Ge single crystal monochromator; this was calibrated using a NIST Si powder standard. The experiments were carried out with a tensile testing machine mounted upon the diraction table so that the axis of loading bisected the incident and diracted beams, i.e. such that strains in the loading direction could be measured. Specimens were strained under load control and the load was maintained at an approximately constant level during the acquisition of the neutron diraction peak data. 3. DIFFRACTION METHOD
Diraction is a well established tool for the evaluation of internal stresses in two-phase materials. Because of the high penetration of neutrons, neutron diraction has found particular use for the examination of metal matrix composites [5, 11]. The principle is simple; changes in the spacing between the atomic lattice planes is deduced from shifts (Dy) in the diraction peak angles (y) and is converted to strain (e) using the relationship e ÿcot y Dy: In the current study, the stress-free reference lattice spacings of the matrix and reinforcement were measured using the unreinforced Ti±6Al±4V alloy reference specimen, and by using free mono®lamentary ®bres. In order to interpret lattice plane strains measured in a single phase material in terms of the internal stresses, a value for the relevant stiness component is required. If the single crystal elastic constants are used then the derived stress will represent the average stress experienced by that family of re¯ecting grains, and it will not necessarily be
equal to the macrostress in that region, i.e. that which could be determined by hole drilling, since intergranular stresses may cause some families of grains to be more highly stressed than others [12]. In a single phase material, the relationship between the overall macrostress and the individual strains recorded by each re¯ection is expressed in terms of diraction elastic constants, determined experimentally. However, with the onset of plasticity this linear relationship is no longer necessarily obeyed. This is because plastic deformation is an inherently inhomogeneous process, especially for low symmetry materials, such as hexagonal Ti±6Al±4V, and this can be the cause of further intergranular stress. Fortunately, it is common in uniaxial straining experiments on a particular alloy for the applied stress/lattice strain relationships of certain re¯ections to remain more or less linear even when plasticity is extensive (e.g. Ref. [13]). It is usually these re¯ections which are the most reliable indicators of the macrostress. X-ray stress measurements on Ti are often based on the analysis of 2133, while Ezeilo et al. [14] used 1011 for neutron work on the basis that they found this re¯ection to be little aected by plastic strain. In our experiments, three Ti alloy peaks ( 1010, (0002) and 1011) and one SiC peak (220) were monitored for the measurements made parallel to the ®bre alignment direction, while for reasons of texture only the Ti 1011 and the SiC(111) and (220) re¯ections could be used for the measurements perpendicular to the ®bre alignment direction. At each load, the diraction peaks were obtained by scanning a single 3He detector in the horizontal plane. The horizontal divergence of the neutron beam was limited to 0.48 using Soller slits, and the spatial widths of the incident and diracted beams were restricted to be approximately 25 mm wide by cadmium masks, so that only the uniformly stressed gauge volume of the specimen was sampled. Each diraction peak pro®le was then ®tted with a Gaussian distribution and a typical result is shown in Fig. 1 for the Ti(0002) re¯ection.
4. RESULTS
4.1. Unreinforced Ti±6Al±4V alloy In order to establish the diraction elastic constants for the matrix, the unreinforced material was loaded and the strain response monitored for the three chosen re¯ections. At certain prescribed levels the loading schedule was interrupted and a series of neutron strain measurements were made at constant load. Measurements were made both below the proportional limit, as well as at larger strains. The macroscopic stress±strain curve is shown in Fig. 2(a) while the lattice strain results are shown in Fig. 2(b)±(d).
WITHERS and CLARKE: NEUTRON DIFFRACTION
6587
Fig. 1. A typical neutron diraction trace, in this case for the Ti(0002) peak. As shown here, each peak was ®tted with a Gaussian pro®le and the peak centre used to evaluate the strain. Single peak measurement times varied from 15 to 60 min.
For each re¯ection, the gradients of the unloading curves, and of the loading curves up to the proportional limit, are linear and the resulting stinesses are summarized in Table 1. These results show, as one would expect, that the measured elastic constants lie between the single crystal values and the bulk value with the (0002) re¯ection the stiest and the 1010 the most compliant, this is in contrast to the results reported elsewhere [15]. Further, it is clear that, in this case, both the (0002) and 1011 re¯ections are sensitive to the extent of plastic straining, but in contrary senses. This is evidenced by the curvature of the responses at high loads and the residual strains upon unloading. As described above, this arises from the generation of plastic mis®ts and hence stress between neighbouring grains. This is potentially more severe in hexagonal materials than cubic ones because of the limited number of slip systems available for the maintenance of plastic strain compatibility. That it is the (0002) which is the least susceptible to plastic deformation and is thus left residually in tension, while the 1011 is the most susceptible and is residually in compression can be understood in the following terms. Slip for crystallites oriented with the (0002) planes normal to the tensile axis will be particularly resistant to plastic ¯ow due to the diculty of slip on planes other than (0002). This is oset only slightly by the ampli®cation of the applied stress in such crystallites arising from the slightly higher single crystal stiness in that direction (Table 1). As a result of the plastic anisotropy, unthinking application of the diraction elastic constants to the lattice strain data after plastic straining could lead to large errors in the internal stresses. For example, at the end of the experiment one would infer the specimen to be in tension or com-
pression by 70 or ÿ160 MPa according to whether one was to use the (0002) or 1011 re¯ections, respectively. For this reason only the 1010 re¯ection, which appears to be less sensitive to plastic strain, has been used for quanti®cation of the internal stresses in this study. At high loads extensive room temperature ``creep'' was observed to take place. This is evidenced by the 2% creep strain that occurred while the neutron measurements were made with the load at 0900 MPa and by the 4% strain that occurred at 01050 MPa [Fig. 2(a)]. Although the specimen continued to creep throughout the hour it took to acquire the three re¯ections, the greatest part occurred during the ®rst 10 min or so. It was not possible to perform a loading experiment on a single ®bre using the in situ straining rig available at Chalk River. As a result, the axial ®bre stiness was taken to be 415 GPa in the following analyses [4]. 4.2. Thermal residual strain measurements The thermal residual strains were measured parallel and perpendicular to the ®bre alignment direction using the two sets of tensile specimens prior to the application of the load and the unreinforced reference sample and the results are summarized in Table 2. It is clear that the axial residual strains are much larger than those transverse to the ®bres. It is possible that the observed dierences between the 1010, (0002) and 1011 matrix strains are due to the anisotropy in thermal expansion of the matrix; certainly the sense of the dierences is consistent with intergranular stresses having this origin and are much larger than the experimental scatter (0100±200 me). When attempting to interpret these results in the light of simple composite models it
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WITHERS and CLARKE: NEUTRON DIFFRACTION
Fig. 2. (a) The applied stress/engineering strain curve for the unreinforced Ti±6Al±4V alloy. At high loads; the loads at which the neutron measurements were made can be seen by the presence of creep strains at constant load. The applied stress/elastic lattice strain response for (b) the Ti 1010, (c) the Ti(0002) and (d) the Ti 1011 re¯ections. The neutron measurements for these re¯ections were always made under constant load and in this sequence. The thin lines delineate the unloading/reloading stages of the cycle; the ®nal plastic strain of the specimen was in excess of 14%.
could be argued that the Ti 1010 re¯ection might be most representative of the average condition because it is least sensitive to plastic anisotropy, or one could argue that the Ti 1011 re¯ection is more likely to be representative because it has a coecient of thermal expansion which is essentially equal to the bulk value. Given that little plastic ¯ow is expected upon cooling it is probable that the latter is more reliable. As a result the SiC(220) and Ti 1011 strains have been used to infer the phase stresses summarized in Table 2. Despite the uncer-
tainties in both the measurements and their interpretation, these values almost satisfy the necessary balance of internal stress: Th Overall longitudinal stress: 1 ÿ f hsiTh M fhsiF
62 MPa: Th Overall transverse stress: 1 ÿ f hsiTh M fhsiF
53 MPa:
Table 1. Reference data and the stinesses derived for the unreinforced Ti±6Al±4V alloy from Fig. 2 Re¯ection Single crystal stiness (GPa) [16] Measured stiness (GPa) Final residual strain (me)
Specimen
1010
(0002)
1011
Ð 115 140 000
103 104 50
146 134 500
116 111 ÿ1400
WITHERS and CLARKE: NEUTRON DIFFRACTION
6589
Table 2. The measured residual strains and the inferred phase stresses; the values in parentheses are the Eshelby predictions based on the SiC(220) and the Ti 1011 responses. Experimental uncertainty of around 100 and 200 me was recorded for the axial and transverse measurements, respectively Re¯ection Lattice strains (me) Phase stress (MPa) Thermal exp. coef. [17]
SiC(111) 6to ®bres _ to ®bres 6to ®bres _ to ®bres 10ÿ6/K (293±973 K)
28
These strain measurements compare with axial ®bre and matrix strains of ÿ1900 and 4200 me recorded, respectively, for Ti±14Al±21Nb/35% SCS-6 SiC by neutron diraction [11], and a ®bre strain of ÿ1610 me for Ti±6±4 alloy/35% SCS-6 SiC composite as measured by surface removal [18]. Modelling work by Durodola and Derby [19] using matrix and ®bre CTEs of 4.7 and 9±10.5 me/K predicted the maximum axial ®bre stress{ to be in the range ÿ600 to ÿ800 MPa at 40% reinforcement content for cooling rates in the range 0.1±100 K/s from 9008C. They suggested that a cooling rate of around 0.64 K/s would be representative of cooling after HIPping giving ®bre stresses of around ÿ650 MPa. Nimmer et al. [9] on the other hand predict average matrix (®bre) stresses parallel and transverse to the alignment of 380 (ÿ705) and 250 (ÿ465) MPa, respectively. These FE calculations include plasticity and time-dependent creep and this probably explains the higher transverse stresses predicted compared with the simpler elastic Eshelby-based calculations listed in Table 2. In the previous literature on thermal residual strains a great deal of use has been made of the eectively stress-free temperature (Tesf) representative of the observed residual strains (stresses). This is not the temperature at which the composite was actually stress free, but rather is a measure of the dierential thermal expansion mis®t which can be retained elastically during cooling. In systems which undergo extensive creep or plasticity Tesf is much lower than that at which the composite was fabricated. The main obstacle to determining Tesf in the present case lies in the diculty in obtaining reliable values of the thermal expansion coecients for the two phases. Previously, a very large range 9.5±12.5 me/K has been reported for Ti±6Al±4V [9]. Our recent work suggests that a value of around 11.8 me/K is broadly representative of our matrix material over temperatures appropriate to HIPping and cooling of the composite (293±1173 K) [20]. Taking the expansion coecient for the mono®laments to be 4.8 me/K (in accordance with the supplier) the rate at which residual strains and stresses are generated within the composite per kelvin tem{Finite element models indicate that, in agreement with the assumptions of the Eshelby model, the ®bre strains (stresses) vary little with position across the ®bres.
SiC(220)
Ti 1010
Ti(0002)
Ti 1011
ÿ1500 (ÿ1600) 28 (118) ÿ825 (ÿ840) ÿ340 (ÿ290) 4.8
2600
3600
11.03
13.37
3300 (3100) 230 (ÿ230) 540 (450) 270 (155) 11.81
perature drop are shown in Table 3. Thus assuming an expansion mismatch of 7 me/K, the axial strains (Table 2) are indicative of an eective stress-free temperature drop of around 6758C, i.e. the stresses introduced into the composite as a result of cooling from the hot pressing temperature are equivalent to those that would be caused by cooling from 07008C if the thermal mismatch strains were accommodated completely elastically. Using a lower matrix expansion coecient (9.5 me/K) and a lower matrix stiness (86 GPa), Pickard et al. [6] inferred a similar stress-free temperature drop (6508C) for comparable recorded strain values for Ti±15±3/30% SiC composite. These values are slightly smaller than that deduced experimentally by Saigal et al. [21] who monitored the decrease in thermal residual strains for Ti±14Al±21Nb/35% SCS-6 SiC aligned mono®lament composite as the temperature was increased and found that the strains decreased to zero at a temperature of around 8008C. However, it should be borne in mind that this dierence could be due solely to errors in the thermal expansion coecient used to calculate Tesf. Of course what really matters is the level of retained residual stress (which is surprisingly consistent across all the materials) since it is this which aects the mechanical properties and the size of the clamping eects at the ®bre matrix interface. Electron Back Scatter Patterns (EBSPs) recorded by Pickard and Miracle [18] revealed no discernible plastic zone at the Ti±6Al±4V/SCS-6 SiC ®bre interface after cooling from the fabrication temperature, in contrast to observations on Ti±14Al±21Nb/ SCS-6 SiC. This is consistent with the assertion that little or no local yielding occurs during cooling. Recent work by Watts [20] suggests that high cooling rates (water quenching) can increase the level of retained thermal stresses due to the suppression of creep at high temperatures in agreement with previous modelling work [19]. In view of the limited extent of stress relaxation by plasticity at low temperature and creep at high temperature it is perhaps not surprising that the retained stresses measured for these systems can be represented by a high Tesf (175±85% of the fabrication temperature). 4.3. Axial loading of the composite As can be seen by comparing Fig. 3 with Fig. 2(a), the composite response to axial loading is strongly in¯uenced by the presence of the ®bres.
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WITHERS and CLARKE: NEUTRON DIFFRACTION
Table 3. Eshelby-based predictions of the thermal mis®t, elastic mismatch and plastic mis®t stresses and strains generated in each phase. For the thermal mismatch stresses, the values are those generated per kelvin temperature drop using a thermal expansion mis®t of 7 me/ K. Smaller values of this mis®t would give proportionately lower rates of stress generation. The elastic mismatch stresses are those generated per MPa load applied parallel or transverse to the ®bre direction, while the plastic mismatch stresses are those required to generate an axial residual extension of 1% in the composite Matrix
Thermal strain/K (me/K) Thermal stress/K (MPa/K) Elastic mismatch stress (MPa/MPa6to ®bres) Elastic mismatch stress (MPa/MPa _ to ®bres) Plastic mismatch strain (me/1% axial plastic strain) Plastic mismatch stress (MPa/1% axial plastic strain)
Fibre
6to ®bres
_ to ®bres
6to ®bres
_ to ®bres
4.6 0.67 0.53 ÿ0.12 ÿ18 000 ÿ2070
ÿ0.34 0.23 0.0 0.90 4800 ÿ150
ÿ2.37 ÿ1.24 1.87 ÿ0.22 10 000 4150
0.17 ÿ0.43 0.0 1.18 ÿ2500 270
The maximum load is approximately 250 MPa higher, but the load borne by the reinforcing ®bres means that even at these higher loads the plastic strain (00.22%) is over 50 times smaller than for the unreinforced alloy recorded earlier. The total strain to failure (just under 1%) is dictated by the elastic strain to failure of the ®bres which is normally quoted as being no more than 0.9%. The failure strains observed here also compare well with the 1% failure strain observed by Pickard et al. [6] for Ti±15±3/30% SCS-6 SiC. The composite stiness taken from the unloading curves is around 205 GPa (Table 3), which is in excellent agreement with the rule of mixtures prediction of stiness (220 GPa) calculated using the bulk Ti±6Al±4V value (115 GPa) and an axial SiC ®bre stiness of around 415 GPa [4, 22]. In addition to the reduced plastic straining, the presence of the ®bres has signi®cantly reduced the extent of room temperature ``creep'' deformation at load compared with the unreinforced alloy. A typi-
cal creep curve measured over the two and a half hours required to acquire the three Ti and one SiC re¯ection is shown in Fig. 4. The discontinuities in the data are associated with the activation of the load control system whenever the load fell out of the permissible range (25 MPa of the target load). This curve is well ®tted by a log ®t over the data acquisition period. The creep rate appears to decrease continuously, due to the gradual transfer of load from the matrix towards the ®bres, in accordance with conventional creep models [4] and previous experimental observations on other continuous systems [23]. When interpreting the neutron diraction lattice strain measurements, it should be remembered that they will not be very sensitive to the rapidly creeping portion of the curve because of the considerable time required to acquire each diffraction peak (15±60 min). The internal strain responses for both phases, for all the measured re¯ections, are shown in Fig. 5. In the following discussion attention is focused primar-
Fig. 3. The stress/engineering strain response of the composite to a load applied parallel to the ®bre alignment direction; the thin lines delineate the unloading/reloading stages of the cycle.
WITHERS and CLARKE: NEUTRON DIFFRACTION
Fig. 4. The occurrence of room temperature creep for the Ti±6Al±4V/35% SiC composite under an axial load of 1354 MPa.
Fig. 5. The applied stress/lattice strain response for (a) the Ti 1010, (b) the Ti(0002), (c) the Ti 1011 and (d) the SiC(220) re¯ections; the thin lines delineate the unloading/reloading stages of the cycle.
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WITHERS and CLARKE: NEUTRON DIFFRACTION
Table 4. A comparison between the unloading gradients (210 GPa) observed in Fig. 5 and those predicted using a Reuss-like assumption for the partitioning of load between the matrix grains Re¯ection (Lattice strain/unit applied stress)ÿ1 (GPa) Predicted gradients (GPa)
Composite
SiC(220)
Ti
Ti(0002)
Ti 1011
205 220
219 220
214 208
243 268
213 201
ily on the SiC(220) and Ti 1010 re¯ections. The latter was chosen because it is least sensitive to plastic anisotropy (Fig. 2). Because the SiC mono®laments deform elastically, and are continuous from one end of the specimen to the other, one would expect their elastic strain behaviour to match the engineering strain response of the specimen as a whole, provided the interfaces remain intact. In this respect it is reassuring to ®nd that the elastic gradients of the two curves are indeed very similar (Table 4). While at a macroscale the load partitions between the two bulk phases according to the equal strain criterion, the load within the matrix is unevenly distributed between dierently oriented grains. This is evidenced by the fact that the gradients of the individual matrix re¯ections lie almost half way between the Voigt equal strain model (which would give all the grains the same gradient) and the Reuss-like predictions shown in Table 4 (i.e. gradients in proportion to their diraction-derived stinesses given in Table 1). This indicates that the load within the matrix partitions between the individual grains approximately according to the Kroner model, i.e. those grains with their stier orientations aligned with the loading direction bear more of the load than those with their more compliant directions aligned with the loading axis. The strain recorded by the clip gauge departs from the linear elastic line at loads as low as 100 MPa. This is evidenced by the unloading/ reloading responses in Fig. 3. This premature curvature of the loading response could arise from the sensitivity of the clip gauge to a slight realignment of the specimen as the load was ®rst applied, or it could be due to microplasticity or matrix/®bre slippage. Use of clip gauges on both sides of the specimens would have avoided this ambiguity, but this would have interfered with the line of sight access of the neutron beam to the sample. Since the ®bres are continuous and essentially elastic, the SiC re¯ection provides an internal composite strain gauge which should be directly comparable with the clip gauge. Its response is essentially linear until the load is in excess of 800 MPa [Fig. 5(d)]. This would suggest that the initial curvature of the composite response is probably an artefact and that the dashed line in Fig. 3 having a gradient equal to the unloading/reloading areas (205 GPa) is more representative. Indeed, the dashed line is more in line with the response commonly recorded for these materials in the testing laboratory. Furthermore, the
composite and ®bre residual strains should be equal unless signi®cant ®bre matrix slippage has occurred. Prior to correction the clip gauge records a plastic strain of around 0.2% (Fig. 3) as compared to a residual ®bre strain of around 0.1% [Fig. 5(d)]. Besides, the early activation of microplasticity or interface sliding might be expected to give rise to residual phase microstrains in Fig. 5(a)±(d) after the early unloading cycles. It is clear from Fig. 5 that as loading progresses into the plastic regime, the lattice strain responses become non-linear indicative of load redistribution towards the ®bres. This curvature also gives rise to residual strains upon unloading, with the ®bres in increasing residual tension and the matrix re¯ections in increasing compression with increased plastic straining. Neglecting the early inelastic straining as being due to specimen alignment it would seem reasonable to take the plastic strain of the composite to be around 0.1% (1000 me). Application of the Eshelby model (a one-dimensional model is nearly as good) predicts (Table 3) that the residual elastic strains in the matrix and ®bres would be ÿ1800 and 1000 me, respectively, in excellent agreement with the strains observed in Fig. 5(a) and (d). This further corroborates the conclusion that the specimen had straightened slightly as the load was ®rst applied. Converting these strains to stresses indicates that load transfer has caused a decrease in the matrix load of ÿ207 MPa and an increase in the ®bre load of 415 MPa. Incorporating the initial thermal residual strains which were excluded from the ®gure the total axial matrix and ®bre residual strains after deformation are A Th A heiM heiTh M heiM and heiF heiF heiF heiM ÿ 1800 2600 800 me and
heiF ÿ 1500 1000 ÿ500 me: The latter change is similar to that (heiA F ÿ1760, 976 giving hei ÿ784 me) recorded for Ti± heiTh F F 14Al±21Nb/35% SCS-6 SiC [18] for which the total composite strain was about 0.8% (compared with 0.9% here). The knees observed in the matrix and ®bre phase curves at an applied load of around 900 MPa suggest that the matrix yields macroscopically at this applied stress level. Initially this might seem surprising in view of the 450 MPa tensile matrix residual stresses and the fact that the unreinforced alloy yielded at around 850 MPa. However, the
WITHERS and CLARKE: NEUTRON DIFFRACTION
axial stress in the matrix at an applied load of 900 MPa is approximately A M hsiTh s M BM s 450 0:53 900 927 MPa
leading to a principal stress dierence of around 775 MPa. In other words plastic yielding in the matrix occurs at nearly the same matrix stress in the composite as for the unreinforced alloy. This is due to the counterbalancing eects of the thermal residual stress and the elastic load transfer to the ®bres arising from the stiness mismatch (i.e. the elastic mismatch term in Table 3 is much less than one). It is also of interest to deduce the average axial matrix ( sM ) and ®bre ( sF ) stresses at the point of failure: Pl A M hsiTh s M hsiM BM s and Pl A F hsiTh s F hsiF BF s Pl where hsiTh M is the thermal residual stress, hsiM the A A plastic load transfer term and Bs ( s hsiA M) the elastic mismatch stress arising from the applied load. Referring to Table 3, the overall axial matrix and ®bre stresses at the ultimate load (sA=1360 MPa) are inferred to be
M 450 ÿ 207 0:53 1360 and s F ÿ 840 415 1:87 1360 s M 960 MPa and s F 2120 MPa: s As one might expect, the axial matrix stress lies between the unreinforced matrix yield stress and the
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matrix failure stress, since failure of the composite initiates in the ®bres. 4.4. Transverse loading of the composite As one would expect, the loading response transverse to the ®bre direction (Fig. 6) is very dierent from both the unreinforced and the axial composite tests [Fig. 2(a) and Fig. 3]. The stress±strain curve becomes non-linear at around 150 MPa. The stiness over this part of the curve is around 165 GPa; in very good agreement with the Eshelby prediction of 170 GPa. The observation that the unloading gradient decreases as the loading sequence progresses suggests that damage is initiating progressively with increased loading. In addition, the absence of signi®cant plastic strain upon unloading would indicate that, for the range of strains studied, most of the curvature of the stress±strain curve is due to changes in the load partitioning, rather than due to conventional macroscopic plastic ¯ow. The lattice strain responses measured parallel to the loading direction, but perpendicular to the ®bres, are shown in Fig. 7 for both phases and for all the measured re¯ections. In this orientation the SiC ®bres are not continuous from one end of the specimen to the other, and thus one would expect, and indeed one ®nds, the SiC to be strained less than the composite as a whole (i.e. the lattice strain gradients are steeper than the engineering strain gradientÐTable 5). However, more striking is the tendency for the SiC strains to curve in a direction indicative of load shedding, especially above 300 MPa, and at the same time for the response of the Ti re¯ection to curve in the contrary direction.
Fig. 6. The stress/engineering strain response of the composite to a load applied normal to the ®bre alignment direction; the thin lines delineate the unloading/reloading stages of the cycle.
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WITHERS and CLARKE: NEUTRON DIFFRACTION
Fig. 7. The applied stress/lattice strain response for (a) the Ti 1011, (b) the SiC(111) and (c) the SiC(220) re¯ections measured parallel to the loading direction, but normal to the ®bre direction; the thin lines delineate the unloading/reloading stages of the cycle.
This is indicative of a very drastic change in the partitioning of load away from the ®bres and towards the matrix and is in agreement with the reduced composite stiness observed in Fig. 6. The results indicate that the ®bres unload signi®cantly above applied loads of around 300 MPa, and furthermore that the Ti alloy matrix is able to take up the increased load without generalized plastic deformation. This is corroborated by the absence of residual lattice strain in the matrix after each of the loading/unloading cycles (Fig. 7).
It is not possible to determine from the neutron data whether each ®bre has partially unloaded, or whether some of the ®bres have unloaded completely while others continue to bear some load. In any event, a simple consideration of the strains measured at 300 and 450 MPa in the two phases gives a simple view of the development of load transfer (neglecting the small amount of true plastic straining that occurs and the stresses transverse to the applied load). At 300 MPa the matrix and ®bre microstrains are approximately 2400:850, respect-
Table 5. A comparison between the observed (210 GPa) and predicted slopes for the strains measured in the loading direction, but transverse to the ®bre direction for the various re¯ections. The predicted slopes were calculated assuming that the slopes of the matrix re¯ections are in proportion to their unreinforced stinesses. The gradual increase in the loading/unloading slopes for the SiC re¯ections with increasing load and the corresponding decrease in slope of the Ti re¯ection makes it dicult to derive reliable values Re¯ection ÿ1
(Lattice strain/unit applied stress) Predicted gradients (GPa)
(GPa)
Composite
SiC(220)
SiC(111)
Ti 1011
165 170
325 303
360 330
140 160
WITHERS and CLARKE: NEUTRON DIFFRACTION
ively, giving phase stresses of around 275:350 (this is close to the ratio 270:352 taken from the values in Table 3 based on a perfect bond). But at 475 MPa the matrix and ®bre strains of 5020:700 correspond to stresses of around 580:290 (this is very dierent from the 425:560 ratio predicted for a perfect bond). When the initial transverse thermal residual stresses given in Table 2 are included in the calculation the average stresses become M 275 155 430 MPa and s s F 350 ÿ 290 60 MPa at 300 MPa and M 575 155 730 MPa and s F 290 ÿ 290 0 MPa at 475 MPa: s This would suggest that unloading of the ®bres is more or less complete at 475 MPa. Furthermore, the tensile (positive) value of the ®bre stress at sA=300 MPa suggests that the Ti±6±4/SCS-6 SiC interface does have some normal strength. The most probable cause of the load shedding is interfacial debonding. The ®bre interface is known to be fairly weak due to the presence of a graphitic interface layer used both to protect the ®bres during handling prior to fabrication and to control the interface chemistry. At low loads, one would expect the ®bre and matrix to remain in contact even if the interfacial bond strength were zero, because of the clamping eect of the thermal residual stresses. But at higher stresses decohesion would seem to be occurring. Direct observation of the broken test specimens indicates that ®nal fracture occurs by localized ductile failure of the Ti±6±4 matrix in the near ®bre ligaments combined with interface failure [Fig. 8(a)]. That the interface is fairly weak is evident from the absence of signi®cant amounts of matrix remaining adhered to the ®bres. Except in the vicinity of the fracture surface itself there was no evidence of ®bre/matrix interface separation after failure [Fig. 8(b)]. Recent observations of transverse loading undertaken within a scanning electron microscope suggest that at free surfaces, at least, interfacial debonding is occurring prior to failure. This is especially pronounced at the poles of the ®bres, i.e. the interface opens normal to the applied load. 5. DISCUSSION
Modelling work on similar composite systems by Nimmer et al. [9] indicates that, for interfaces of zero strength, debonding would initiate at an applied load of around 200 MPa, while Jansson et al. [24] quote a value of 140 MPa. Both these values are lower than the load at which the ®bres begin to shed load signi®cantly and would seem to con®rm a non-zero interface strength in this case. An important concern, given the testing geometry, is the eect
6595
of the free ®bre ends. Recently, experimental work by Warrier et al. [10] has done much to delineate the eect of free surfaces on interface failure. Their work is based on calculations by Kurtz and Pagano [25] which suggests that there is a tensile radial interface stress singularity at the free surface even with no externally applied stress, and that the stress remains tensile up to about one ®bre diameter from the surface. Of course this tensile region has a negligible eect on the neutron measurements since it is very small, but it does mean that the ®bres are probably already debonded at the ®bre ends even prior to loading. As the transverse stress increases one would expect the debond crack to grow inwards from the free surface. Indeed, in experiments in which strain gauges were placed side-byside from edge to centre the onset of stress±strain curvature was found to occur at progressively higher loads towards the centre indicative of inward debond growth [26], and it was deduced that this debonding process became signi®cant at loads of around 230 MPa. This is consistent with the initial departure from the elastic gradient observed in Fig. 7(a) and (b) at around 250 MPa. Further work using cruciform specimens in which the deforming section had no free ®bre ends has indicated that debonding occurs at a normal interface load of 115 MPa [10]. Returning to our observations, because the ®bre strains would be expected to vary little with lateral position within the ®bres, the average ®bre strain is a good indicator of the normal interface stress at the ®bre pole for transverse loading. Our results indicate that the ®bre begins to debond noticeably at an applied stress of around 300 MPa; presumably this progresses inwards from the free surfaces. At this load the average ®bre stress is around 60 MPa. Given that this is an average value and includes both the unbonded (and unstressed) ®bre end segments and the still bonded and highly stressed (central) sections of each ®bre it is not consistent with the idea that the interface has no normal strength, but is consistent with an interface strength of around 115 MPa (see Fig. 9). In view of the fact that even if all the ®bres were to debond completely (i.e. to behave as holes) the matrix would be able to sustain the applied load of 480 MPa at ultimate failure (the average matrix stress would then be 480/0.65 = 740 MPa), one would not expect extensive plastic deformation. This localization of the plastically deformed region to the matrix ligaments between ®bres is accentuated by the high and low matrix volume fraction regions caused by the sandwich structure of the composite [Fig. 8(b)]. The lack of any evidence of debonded interfaces at ®bre poles in polished sections, except near the failure location Fig. 8(b), is further evidence that little generalized matrix plasticity occurred prior to failure in that the clamping thermal residual stresses are able to maintain contact between the matrix and ®bre across the
6596
WITHERS and CLARKE: NEUTRON DIFFRACTION
Fig. 8. (a) Scanning electron micrograph of the fracture surface for a transversely tested specimen (loaded left to right), (b) a close-up taken near the failure location, at a load just below that required for failure. After unloading interface failure could only be observed in the immediate vicinity of the fracture surface. Note the localized interface failure in (b) both between the ®bre and the carbon coating and between the matrix and the carbon coating (point A). At point B local cracking of the matrix can also be seen.
Fig. 9. Schematic showing how the transverse ®bre stress might vary as the applied load is increased.
WITHERS and CLARKE: NEUTRON DIFFRACTION
debonded interface after unloading. That contact between the matrix and the ®bre poles is reestablished upon unloading may be responsible for the increase in the unloading gradients of both the matrix and composite unloading curves at low loads (Figs 6 and 7) and the absence of signi®cant residual lattice strains. 6. CONCLUSIONS
Our work on unreinforced Ti±6Al±4V indicates that plastic anisotropy caused by intergranular stresses is signi®cant and that the 1010 diraction peak is the least aected by plastic strain. Uncorrected use of the (0002) and 1011 peaks in our case would have lead to considerable errors. The measured thermal residual mismatch stresses were found to be very large (ÿ825 to ÿ840 MPa and 450 to 540 MPa in the axial direction for ®bre and matrix, respectively, and ÿ340 to ÿ290 MPa and 155 to 270 MPa in the transverse direction). These values are in good agreement to those already quoted in the literature. An eective stressfree temperature drop of around 6758C was calculated to be representative of the thermal stresses and indicates that little of the thermal mismatch generated on cooling from the fabrication temperature is inelastically accommodated, either by creep at high temperatures or plastic yielding at low temperatures. When tested in the direction of the ®bres, the composite was approximately 25% stronger and very much more resistant to plastic deformation than the unreinforced alloy. The observed load partitioning during elastic deformation could be well explained in terms of Rule of Mixtures or Eshelby models. At failure, matrix plasticity had resulted in a transfer of load towards the ®bres of about 415 MPa. Our direct measurements of internal stress partitioning during transverse loading corroborate the inferences made by Warrier et al. [27] in that the ®bre/matrix interface has a non-zero normal strength of around 100±120 MPa. This, when combined with initial thermal residual clamping forces of around ÿ340 to ÿ290 MPa at the interface means that, debonding near the free ®bre ends begins to become signi®cant at applied loads in excess of 250 MPa. Debonding is complete ( sF 10) when the applied load is around 475 MPa. Despite load shedding from the ®bres which occurs when the interface fails, the matrix deforms predominantly elastically because the matrix yield stress is still greater than the average matrix stress. In the cruciform tests undertaken by Warrier et al. debonding was found to occur at an applied stress of 330 MPa. This is in good agreement with the current results. With respect to the in¯uence of the free ends, it is important to ask whether one should always carry out tests in which the free ®bre ends are prevented from initiating debonding so as to
6597
measure the ``true'' ®bre matrix/interface strength. Often it is not feasible or realistic to test specially fabricated single ®bre cruciform specimens. Besides, it is probable that in many applications free ®bre ends will be present. Even in cases such as hoopwound aeroengine components there may be ®bre ends within the material arising from fabrication or ®bre fracture, and so it is important to be able to understand the debonding process under these conditions. AcknowledgementsÐWe are grateful to Rolls Royce for the provision of experimental composite material, especially to Colin Small, Diana Cardona and Philip Doorbar. P.J.W. would like to thank Tom Holden and Brian Powell for enabling his visit to Chalk River and to the EPSRC for funding the visit as well as the research programme of which this was a part. Part of this programme was also funded by the European Community under Brite EuRam project No. BRE2-CT92-0156 and the paper was ®nished with funding from the EPSRC/MOD joint project grant scheme. The assistance of David Nicolls and Mike Watts in preparing Fig. 8 is also acknowledged. Thanks are also expressed to Dan Miracle for many helpful discussions on this paper.
REFERENCES 1. Cheskis, H. P. and Heckel, R. W., Metal Matrix Composites, ASTM STP 438. American Soc. for Testing of Materials, 1968, pp. 76±91. 2. Cheskis, H. P. and Heckel, R. W., Metall. Trans., 1970, 1, 1931. 3. Lilholt, H., Acta metall., 1977, 25, 571. 4. Clyne, T. W. and Withers, P. J., An Introduction to Metal Matrix Composites, Cambridge Solid State Series. Cambridge University Press, Cambridge, 1993. 5. Withers, P. J., Key Engng Mater.ÐCeram. Matrix Composites, 1995, 108-110, 291. 6. Pickard, S. M., Miracle, D. B., Majumdar, B. S., Kendig, K. L., Rothen¯ue, L. and Coker, D., Acta metall. mater., 1995, 43(8), 3105. 7. James, M. R., ICRS 2, Nancy, 1988. 8. Cox, B. N., James, M. R., Marshall, D. B. and Addison, R. C., J., Metall. Trans. A, 1990, 21A, 2701. 9. Nimmer, R. P., Bankert, R. J., Russel, E. S., Smith, G. A. and Wright, P. K., J. Comp. Tech. Res., 1991, 13(1), 3. 10. Warrier, S. G., Gundel, D. B., Majumdar, B. S. and Miracle, D. B., Metall. Mater. Trans., 1996, 27A, 2035. 11. Kupperman, D. S., Majumdar, S., Singh, J. P. and Saigal, A., in Measurement of Residual Stress Using Neutron Diraction, NATO Conference, ed. M. T. Hutchings, 1992, pp. 439±450. 12. Noyan, I. C. and Cohen, J. B., in Materials Research and Engineering, ed. B. Ilschner and N. J. Grant. Springer, New York, 1987. 13. Clansen, B., Lorentzen, T. and Leers, T. Acta mater., 1998, 46, 3087. 14. Ezeilo, A. N., Webster, G. A., Webster, P. J. and Wang, X., Physica B., 1992, 180, 1044. 15. Bruno, G. and Dunn, B. D., Meas. Sci. Technol., 1997, 8, 1244. 16. Smithell, Smithell's Metals Reference Book, 7th edn, ed. E. A. Brandes. Butterworth, London, 1993, pp. 14-3±14-27. 17. Berry, R. L. P. and Raynor, G. V., Res. Lond., 1953, 6, 21S.
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18. Pickard, S. M. and Miracle, D. B., Mater. Sci. Engng, 1995, 203, 59. 19. Durodola, J. F. and Derby, B., Acta metall. mater., 1994, 42(5), 1525. 20. Watts, M. R., The analysis of diraction measurements of internal strains in metal matrix composites. Ph.D. thesis, Cambridge University, 1998. 21. Saigal, A., Kupperman, D. S. and Majumdar, S., Mater. Sci. Engng, 1992, A150, 59. 22. Coker, D., Ashbaugh, N. E. and Nicholas, T., in ASTM STP 1186, ed. H. Sehitoglu. American Soc. for Testing of Materials, 1993.
23. Endo, T., Chang, M., Matsuda, N. and Matsuura, K., Risù 12th Int. Conf. on Metal Matrix CompositesÐ Processing, Microstructure and Properties, Roskilde, Denmark, 1991, p. 323. 24. Jansson, S., Dal Bello, D. J. and Leckie, F. A., Acta metall. mater., 1994, 42(12), 4015. 25. Kurtz, R. D. and Pagano, N. J., Composites Engng, 1991, 1, 13. 26. Miracle, D. B., Private communication, 1996. 27. Warrier, S. G., Gundel, D. B., Majumdar, B. S. and Miracle, D. B., Scripta metall. mater., 1996, 34, 293.