Acta mater. ve Pergamon Copyright C 1996 Acta Met 09567151(95003878 Printed in Great Bri 1359-645496 MICROSTRUCTURE-PROPERTY RELATIONSHIPS OF SIC FIBRE-REINFORCED MAGNESIUM ALUMINOSILICATES--II. MECHANICAL PROPERTIES AND FAILURE CHARACTERISTICS A KUMAR+ and K M. KNOWLES University of Cambridge, Department of Materials Science and Metallurgy, P Cambridge CB2 3QZ, England Received 31 October 1994: in revised form 6 September 1995) Abstract--Interfacial frictional shear stresses, flexural properties and failure mechanisms are reported for two magnesium aluminosilicates unidirectionally reinforced with Nicalon SiC fibres Composites A and 00and920°c spcctivcly. High valucs of intcrfacial frictional shear stres inferred from Marshall,'s analysis of the micro-indentation technique could be attributed in part to presence of compressive radial stresses at the fibre-matrix interfaces. Although both comp symmetrical four point bend testing at roo different. Extensive matrix microcracking, fibre failure and then fibre pull-out were commonly observed in composite A. Failure modes in composite B included the formation of a limited number demonstrate that the mechanical properties, the interfacial frictional shear st mechanisms of both composites are governed by their microstructural features, in particular the and structure of the matrix-fibre interfacial region. Copyright c 1996 Acta Metallurgica ine 1 INTRODUCTION microstructural features have been described in Part I [2]. Estimates of the interfacial frictional It is now well established that the structure and shear stress have been made using Marshall's micro properties of the fibre-matrix interf nant role in controlling the mechanical properties ot the failure mechanisms of the composites have been comin ned using a symmetrical four-point bend tes matrix composites[I]. In Part I of this paper [2], it Finally, the properties and the fracture behaviour of was demonstrated that the structure and morphology these composites have been correlated with the of the interfacial layers in two different magnesium microstructure of the composites aluminosilicate glass-ceramic matrices unidirection ally reinforced with SiC fibres were quite complex and different. As a result of this, interpretation of the 2. MATERLALS AND EXPERIMENTAL mechanical properties and fracture process is not as 2.1 Materials straightforward as is often presumed Details of material and processing parameters Several attempts have been made in the past to have been given in Part I of this paper [2 ]. Briefly, estimate the mechanical properties of Sic fibre einforced glass-ceramics. In particular, the Sic/ composite A was hot-pressed at 1500oC,whereas lithium aluminosilicates (Las)and Sic/calci composite B was hot-pressed at 920.C. Composite B aluminosilicates(CAS)systems have received a lot of was ceramed in air at 1150 C for I h, whereas no attention [3-5]. Although the mechanical properties of SiC/magnesium aluminosilicate(MAS)composites posite A. Fibre volume fractions were 0.47 and 0.40 have been reported in the literature, attempts have in composites A and B, respectively not been made to correlate the properties with the microstructural fcaturcs of thc composites [69] 2.2. Experimental The first objective of this paper is to report the 2.2. 1. Microhardness and interfacial friction stres mechanical properties of the composites whose A Vickers diamond on a Leitz microhardness tester was used to indent the fibres for evaluating both the Department of Mechanica hardness and the interfacial friction stress. A load of raduate School. Monterey, CA 93943, 245, 25 mN was used to measure the hardness of the fibres in be mposites. The total indentati 2923
Pergamon 09%7151(95)00387-8 Acta mater. Vol. 44, No. I, Pp. 2923-2934. 1996 Copyright 0 1996 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-6454/96 $15.00 + 0.00 MICROSTRUCTURE-PROPERTY RELATIONSHIPS OF SIC FIBRE-REINFORCED MAGNESIUM ALUMINOSILICATES-II. MECHANICAL PROPERTIES AND FAILURE CHARACTERISTICS A. KUMARt and K. M. KNOWLES University of Cambridge, Department of Materials Science and Metallurgy, Pembroke Street, Cambridge CB2 342, England (Received 31 October 1994; in revised form 6 September 1995) Abstract-Interfacial frictional shear stresses, flexural properties and failure mechanisms are reported for two magnesium aluminosilicates unidirectionally reinforced with Nicalon Sic fibres. Composites A and B were hot-pressed at 1500 and 92O”C, respectively. High values of interfacial frictional shear stresses inferred from Marshall’s analysis of the micro-indentation technique could be attributed in part to the presence of compressive radial stresses at the fibre-matrix interfaces. Although both composites failed non-catastrophically in symmetrical four point bend testing at room temperature, the failure modes were different. Extensive matrix microcracking, fibre failure and then fibre pull-out were commonly observed in composite A. Failure modes in composite B included the formation of a limited number of matrix cracks, the failure of fibres in the matrix crack front and progressive delamination. Our observations demonstrate that the mechanical properties, the interfacial frictional shear stresses and the failure mechanisms of both composites are governed by their microstructural features, in particular the chemistry and structure of the matrix-fibre interfacial region. Copyright 0 1996 Acta Metallurgica Inc. 1. INTRODUCTION It is now well established that the structure and properties of the fibre-matrix interface play a dominant role in controlling the mechanical properties of continuous fibre-reinforced glass and glass-ceramic matrix composites [l]. In Part I of this paper [2], it was demonstrated that the structure and morphology of the interfacial layers in two different magnesium aluminosilicate glass-ceramic matrices unidirectionally reinforced with SIC fibres were quite complex and different. As a result of this, interpretation of the mechanical properties and fracture process is not as straightforward as is often presumed. Several attempts have been made in the past to estimate the mechanical properties of SIC fibrereinforced glass-ceramics. In particular, the Sic/ lithium aluminosilicates (LAS) and Sic/calcium aluminosilicates (CAS) systems have received a lot of attention [3-51. Although the mechanical properties of Sic/magnesium aluminosilicate (MAS) composites have been reported in the literature, attempts have not been made to correlate the properties with the microstructural features of the composites [6-91. The first objective of this paper is to report the mechanical properties of the composites whose TPresent address: Department of Mechanical Engineering, Naval Postgraduate School, Monterey, CA 93943, U.S.A. microstructural features have been described in Part I [2]. Estimates of the interfacial frictional shear stress have been made using Marshall’s microindentation technique [lo]. Flexural properties and the failure mechanisms of the composites have been determined using a symmetrical four-point bend test. Finally, the properties and the fracture behaviour of these composites have been correlated with the microstructure of the composites. 2. MATERIALS AND EXPERIMENTAL 2.1. Materials Details of material and processing parameters have been given in Part I of this paper [2]. Briefly, composite A was hot-pressed at 15OO”C, whereas composite B was hot-pressed at 920°C. Composite B was ceramed in air at 1150°C for 1 h, whereas no post-processing heat-treatment was given to composite A. Fibre volume fractions were 0.47 and 0.40 in composites A and B, respectively. 2.2. Experimental 2.2.1. Microhardness and interfacial friction stress. A Vickers diamond on a Leitz microhardness tester was used to indent the fibres for evaluating both the hardness and the interfacial friction stress. A load of 245.25 mN was used to measure the hardness of the fibres in both composites. The total indentation time 2923
2924 KUMAR and KNOWLES: SIC REINFORCED ALUMINOSILICA'TES-II plates using a high speed diamond saw. The as-cut Indenter stub specially designed for grinding and polishing large composite samples. All four sides of the samples ere first polished with 6 um diamond paste and finally with I um diamond paste. The composite samples were 2 a tiff vo-hydraulic machine with a l kn load cell t investigate their fexural properties and their fracture 2 b behaviour. The tests were carried out with the machine under displacement control. The ramp-rate was 0.025 mm/ mples of dimensions approxi Matrix Matrix mately50×10×06 mm and50×5×3 mm were tes A and B, respectively. The Fig. 1. Schematic of the indentati separation between the inner loading points was (10D). The relevant parameters have been defined in the text. 16 mm for both composites, whereas the separation 10 and 12 mm for composites A and B, respectively. was 30s(15 s for load application and 15s for The exact span to depth ratio varied from sample to dwelling). Diagonals of the indentation impression sample because of small variations in the thicknesses on the fibres and the matrix were measured on the of the samples, but was in the range of 14-16 and 4-5 micrographs recorded using both a scanning electron for composites A and B, respectively microscope(SEM, Camscan-S2)and a Zeiss optical Load-deflection curves were plotted using an x The interfacial frictional shear stress was estimated mechanisms, the test was interrupted at different load sing Marshall's method [10]. The fibres were loaded levels and the samples were examined ex situ in an so that indentation impressions were seen in the optical microscope. A minimum of four samples was matrix(Fig. 1). The equations tested for both composites. The maximum nominal Hat Hexural stress and the elastic modulus were calculated (I) from the linear elastic theory of uniform beams Fracture surfaces were carefully cut and mounted derived by Marshall [10]were used to calcula ( 2) onto an aluminium stub for examination by SEM (b-a)cotψ Sample surfaces were gold coated to reduce specimen in the sem. Th interfacial frictional shear stress. In these equations, SEM was operated in secondary electron mode t is the interfacial frictional shear stress (assumed in this analysis to be constant ), 2a is the mean diagonal of the indentation on the fibre. h is the fibre hard- 3. RESULTS AND INTERPRETATION ess, u is the fibre displacement, 2b is the mean onal of the indentatio on on the matrix 3.1. Microhardness and interface friction stress a(a148 )is the angle between the opposite edges of The values of microhardness obtained using a the indenter, r is the fibre radius and Er is the elastic 245. 25 mn load were 19-24 and 26-32 GPa for modulus of the fibres composites A and B, respectively. An example of According to the suppliers specifications, the elastic micro-indentations used to calculate the micro- modulus of the Nicalon fibres (NL 202) used to hardness of fibres in both composites is shown for fabricate both composites was 184 GPa [11]. This composite B in Fig. 2(a), Debonding at the alue was therefore used to estimate the interfacial fibre-matrix interface was observed when a load frictional shear stresses via equation (1). However, it higher than 245.25 mn was used to indent the fibres should be noted that the values of the elastic modulus in both sites,The fibre hardness obtained of Nicalon fibres reported in the literature vary from experimentally in composite a is lower than that in 182 to 210 GPa [e.g. 12]and that authors often quote composite B and also the hardness in both a value of 200 GPa instead [10, 13]. The interface composites is higher than the typical Nicalon fibre friction stress in equation( 1)is inversely proportional hardness(13 GPa)available in the literature [3, 10 to the elastic modulus of the fibre and therefore a Bleay et al. [ 13] have recently reported a micro- relatively small value assumed for the elastic modulus hardness value of 8.9 GPa for Nicalon fibres, and of the fibres will produce a relatively high frictional although they did not mention the load required shear stress and vice-versa obtain this value. it can be inferred that the load used d fractography. was less than 0.5N, the load used in their work to Samples for flexural testing were cut from composite cause the fibres to slide within the matrix
2924 KUMAR and KNOWLES: SIC REINFORCED ALUMINOSILICATES-II Indenter I ! 2b h 2r ! I * Matrix’ Fibre Matrix Fig. 1. Schematic of the indentation method for measurement of matrix-fibre interfacial friction stress (after Ref. [lo]). The relevant parameters have been defined in the text. was 30 s (15 s for load application and 15 s for dwelling). Diagonals of the indentation impression on the fibres and the matrix were measured on the micrographs recorded using both a scanning electron microscope (SEM, CamscanS2) and a Zeiss optical microscope. The interfacial frictional shear stress was estimated using Marshall’s method [lo]. The fibres were loaded so that indentation impressions were seen in the matrix (Fig. 1). The equations and H2a4 z- n 2ur3E, (1) u =(b -a)cotti (2) derived by Marshall [lo] were used to calculate the interfacial frictional shear stress. In these equations, z is the interfacial frictional shear stress (assumed in this analysis to be constant), 2a is the mean diagonal of the indentation on the fibre, H is the fibre hardness, u is the fibre displacement, 26 is the mean diagonal of the indentation impression on the matrix, 2$(x 148”) is the angle between the opposite edges of the indenter, r is the fibre radius and Ef is the elastic modulus of the fibres. According to the suppliers specifications, the elastic modulus of the Nicalon fibres (NL 202) used to fabricate both composites was x 184 GPa [l 11. This value was therefore used to estimate the interfacial frictional shear stresses via equation (1). However, it should be noted that the values of the elastic modulus of Nicalon fibres reported in the literature vary from 182 to 210 GPa [e.g. 121 and that authors often quote a value of 200 GPa instead [lo, 131. The interface friction stress in equation (1) is inversely proportional to the elastic modulus of the fibre and therefore a relatively small value assumed for the elastic modulus of the fibres will produce a relatively high frictional shear stress and vice-versa. 2.2.2. Mechanical testing and fractography. Samples for flexural testing were cut from composite plates using a high speed diamond saw. The as-cut samples were mounted on a well polished aluminium stub specially designed for grinding and polishing large composite samples. All four sides of the samples were first ground with graded SIC grit papers, polished with 6pm diamond paste and finally with 1 pm diamond paste. The composite samples were tested in symmetrical four point bend on a stiff servo-hydraulic machine with a 1 kN load cell to investigate their flexural properties and their fracture behaviour. The tests were carried out with the machine under displacement control. The ramp-rate was 0.025 mm/min. Samples of dimensions approximately 50 x 10 x 0.6 mm and 50 x 5 x 3 mm were used for composites A and B, respectively. The separation between the inner loading points was 16mm for both composites, whereas the separation between the inner and the outer loading points was 10 and 12 mm for composites A and B, respectively. The exact span to depth ratio varied from sample to sample because of small variations in the thicknesses of the samples, but was in the range of 14-16 and 4-5 for composites A and B, respectively. Load-deflection curves were plotted using an x-y recorder. In order to study the damage initiation mechanisms, the test was interrupted at different load levels and the samples were examined ex situ in an optical microscope. A minimum of four samples was tested for both composites. The maximum nominal flexural stress and the elastic modulus were calculated from the linear elastic theory of uniform beams. Fracture surfaces were carefully cut and mounted onto an aluminium stub for examination by SEM. Sample surfaces were gold coated to reduce specimen charging and to enhance contrast in the SEM. The SEM was operated in secondary electron mode. 3. RESULTS AND INTERPRETATION 3.1. Microhardness and interface friction stress The values of microhardness obtained using a 245.25 mN load were 19-24 and 2632GPa for composites A and B, respectively. An example of micro-indentations used to calculate the microhardness of fibres in both composites is shown for composite B in Fig. 2(a). Debonding at the fibre-matrix interface was observed when a load higher than 245.25 mN was used to indent the fibres in both composites. The fibre hardness obtained experimentally in composite A is lower than that in composite B and also the hardness in both composites is higher than the typical Nicalon fibre hardness (13 GPa) available in the literature [3, lo]. Bleay et al. [13] have recently reported a microhardness value of 8.9 GPa for Nicalon fibres, and although they did not mention the load required to obtain this value, it can be inferred that the load used was less than 0.5 N, the load used in their work to cause the fibres to slide within the matrix
KUMAR and KNOWLES: SiC REINFORCED ALUMINOSILICATES--II 2925 It is likely that the low microhardness of fibres in Values of ise indices for a number of crystalline composite a compared with composite B is due to the ceramics have been given by Sargent [16] and an large-scale diffusion of matrix elements into the fibres explanation of the effect in terms of a mixed elastic- in composite A [2], producing a softening effect which plastic materials deformation response has been given composite B. The size of the Sic grains in the si co by Bull et al.[17]. An ISE index, n, for Nicalon fibres ble. but if Nicalon fibres is on a nanometre level [2], approxi data collected by Sargent for hot-pressed SiC, where ately three orders of magnitude smaller than the n 1.7, can be considered to be a first approximation mean diagonal of the indentations used for estimating to what might be expected for the fibres, a simple the fibre hardness, and so a useful analogy is with the calculation combining the equations for Vickers hardness behaviour of glasses function of hardness with the ISE force-diagonal power law [14] network modifiers [14]. Although the hardness of shows that hardness values H, and H2 measured at crystalline ceramics increases generally with a loads Fi and Fx. respectively, are related through the decrease in grain size because dislocations generated equation by the indenter are blocked by the grain boundaries [5, this effect is clearly not relevant in the present case because of the grain sizes involved de and so if F2/F=4, H,/HR0.784 for n=1.7. Thu discrepancies reported for the experimentally ifferent laboratories were to have used loads measured hardness values of Nicalon fibres: (i) an significantly higher than the ones we have used, some intrinsic variation of hardness between the different of the discrepancies could be explained at least in part batches of fibres; (ii) an indentation-size effect; and by an ISE. However, this is not in accord with the iii) systenatic experimental errors. Neither (i) nor lvads used for measuring fibre hardness reported in ii)can account for the differences we have observed the literature ween the fibres in composites a and b because the It is therefore more likely that a major reason hardness values were taken at a single load and any for the discrepancies in the hardness values of systematic errors inherent in the measurement will be Nicalon fibres lies in the calibration and use of the same for both batches different equipment by various researchers generating When comparing results from different labora- systematic measurement errors. To examine this tories, it is important to recognise that in general the possibility, the hardness of fibres in composite b was microhardness of ceramics is load dependent(known measured on indentation equipment at the School of as the indentation-size effect, ISE)and that in general Materials Science, University of Bath, Claverton it increases with a decrease in applied load [14]. Down, England. In order to obtain a direct compari- a 15m ig. 2. Nomarski interference contrast images showing (a, b) indentations obtained Microhardness tester il cUinpusite B and (b) indentations (indicated b microhardness tester in composite B
KUMAR and KNOWLES: Sic REINFORCED ALUMINOSILICATES-II 2925 It is likely that the low microhardness of fibres in composite A compared with composite B is due to the large-scale diffusion of matrix elements into the fibres in composite A [2], producing a softening effect which reduces the hardness compared with the fibres in composite B. The size of the SIC grains in the SIC-0 Nicalon fibres is on a nanometre level [2], approximately three orders of magnitude smaller than the mean diagonal of the indentations used for estimating the fibre hardness, and so a useful analogy is with the hardness behaviour of glasses as a function of network modifiers [14]. Although the hardness of crystalline ceramics increases generally with a decrease in grain size because dislocations generated by the indenter are blocked by the grain boundaries [15], this effect is clearly not relevant in the present case because of the grain sizes involved. There are three possible reasons for the wide discrepancies reported for the experimentally measured hardness values of Nicalon fibres: (i) an intrinsic variation of hardness between the different batches of fibres; (ii) an indentation-size effect; and (iii) systematic experimental errors. Neither (ii) nor (iii) can account for the differences we have observed between the fibres in composites A and B, because the hardness values were taken at a single load and any systematic errors inherent in the measurement will be the same for both batches. When comparing results from different laboratories, it is important to recognise that in general the microhardness of ceramics is load dependent (known as the indentation-size effect, ISE) and that in general it increases with a decrease in applied load [14]. Values of ISE indices for a number of crystalline :eramics have been given by Sargent [16] and an :xplanation of the effect in terms of a mixed elasticplastic materials deformation response has been given by Bull et al. [17]. An ISE index, n, for Nicalon fibres IS, to the best of our knowledge, not available, but if data collected by Sargent for hot-pressed SIC, where ‘I z 1.7, can be considered to be a first approximation to what might be expected for the fibres, a simple :alculation combining the equations for Vickers hardness with the ISE force-diagonal power law [14] shows that hardness values H, and H, measured at loads F, and F2, respectively, are related through the equation n-2 H, F2 T -=(-> HI F, ’ and so if F,/F, = 4, H,IH, e 0.784 for n = 1.7. Thus, if different laboratories were to have used loads significantly higher than the ones we have used, some of the discrepancies could be explained at least in part by an ISE. However, this is not in accord with the loads used for measuring fibre hardness reported in the literature [lo, 131. It is therefore more likely that a major reason for the discrepancies in the hardness values of Nicalon fibres lies in the calibration and use of different equipment by various researchers generating systematic measurement errors. To examine this possibility, the hardness of fibres in composite B was measured on indentation equipment at the School of Materials Science, University of Bath, Claverton Down, England. In order to obtain a direct compariFig. 2. Nomarski interference contrast images showing (a, b) indentations obtained on the Leitz microhardness tester in composite B and (b) indentations (indicated by arrows) obtained on the Leco microhardness tester in composite B
KUMAR and KNOWLES: SIC KEINFURCED ALUMINOSILICA'TES-II 10 um Fig. 3. No ashed in son with our own measurements the hardness of the were used to calculate these values of interfacial fibres was measured on the optical microscope on frictional shear stresses and the assumption has been their Leco (M-400) microhardness tester (as in the made that there is no indentation size effect in esults quoted by the Bath group [18) using a vickers Nicalon SiC fibres, as other workers in this area have diamond and an indentation load of 245. 25 mN. a assumed implicitly hardness valuc of 10-13 GPa was obtained. these It was observed that most of the fibres at or near hardness values are considerably lower than the the edge of the samples of composite B did not slide values obtained using our own Leitz microhardness in the matrix at 981 mN, suggesting higher interfacial ster. The indentations made on the two different frictional shear stresses at or near the edges in ieces of equipment are shown in Fig. 2. The comparison with the bulk of the sample. Values of indentations made on the Leco arrowed in Fig. 2(b) interfacial frictional shear stresses of 136-158 MPa are representative of those reported elsewhere by the were obtained from those fibres which could b Bath group [19] and are used both for hardness pushed-in at or near the edge of the samples. These measurements and in the relevant Marshall equation apparently high shear stresses can arise because of for interfacial frictional shear stress measurements. It localised oxidation of surface layers during ceraming should be noted that these indentations are not sharp of composite B in air. Similar trends in results have and that the diagonals are longer than the diagonals been reported for a Sic/barium osumilite composite btaincd on the Leitz using the same load morcover by Bleay and Scott [201 the values of diagonals measured on the optical The interfacial frictional shear stresses in these nicroscope on the Leco equipment equipped with an composites are considerably higher than those eye-piece were always higher than the values reported for SiC/LAS composites [10, 21-23]. This measured in a SEM, leading to an underestimate of can be attributed at least in part to the differences in fibre hardness. Thus, it is clear thal, at least for this residual thermal stresses at the fibre-matrix articular comparison, the considerable differences interfaces. Residual thermal stresses arise from the reported in the apparent fibre hardness on the Leitz thermal contraction mismatch between matrix and and the leco equipment are due purely to the system fibre, and also from the unrelaxed volume changes atic errors generated when introducing and then associated with any phase transformation an measuring indentation diagonals using different crystallisation in the matrix, Brun and Singh [22] equipment. have shown that the sliding friction stress is nearly A total load on both the fibre and matrix of zero when the coefficient of thermal expansion of 981 mN was sufficient to push-in all the fibres in both fibre(ar)is greater than the coefficient of thermal composites. A fibre pushed into the matrix in expansion of matrix (am )and that it increases composite A is shown in Fig. 3. Interfacial frictional linearly with the thermal expansion mismatch when shear stresses estimated using equation( 1)were 24-33 a< and 49 71 MPa in composites A and B, respectively. The coefficient of thermal expansion of LAS is The values of fibre hardness measured on the Leitz smaller than that of Nicalon fibres and therefore
2926 KUMAR and KNOWLES: Sic REINFORCED ALUMINOSILICATES-II Fig. 3. Nomarski interference contrast image of a fibre pushed in the matrix in composite A. son with our own measurements, the hardness of the fibres was measured on the optical microscope on their Leco (M-400) microhardness tester (as in the results quoted by the Bath group [18]) using a Vickers diamond and an indentation load of 245.25 mN. A hardness value of l&13 GPa was obtained. These hardness values are considerably lower than the values obtained using our own Leitz microhardness tester. The indentations made on the two different pieces of equipment are shown in Fig. 2. The indentations made on the Leco arrowed in Fig. 2(b) are representative of those reported elsewhere by the Bath group [19] and are used both for hardness measurements and in the relevant Marshall equation for interfacial frictional shear stress measurements. It should be noted that these indentations are not sharp and that the diagonals are longer than the diagonals obtained on the Leitz using the same load. Moreover, the values of diagonals measured on the optical microscope on the Leco equipment equipped with an eye-piece were always higher than the values measured in a SEM, leading to an underestimate of fibre hardness. Thus, it is clear that, at least for this particular comparison, the considerable differences reported in the apparent fibre hardness on the Leitz and the Leco equipment are due purely to the systematic errors generated when introducing and then measuring indentation diagonals using different equipment. A total load on both the fibre and matrix of 981 mN was sufficient to push-in all the fibres in both composites. A fibre pushed into the matrix in composite A is shown in Fig. 3. Interfacial frictional shear stresses estimated using equation (1) were 2433 and 49-71 MPa in composites A and B, respectively. The values of fibre hardness measured on the Leitz were used to calculate these values of interfacial frictional shear stresses and the assumption has been made that there is no indentation size effect in Nicalon Sic fibres, as other workers in this area have assumed implicitly. It was observed that most of the fibres at or near the edge of the samples of composite B did not slide in the matrix at 98 1 mN, suggesting higher interfacial frictional shear stresses at or near the edges in comparison with the bulk of the sample. Values of interfacial frictional shear stresses of 136-l 58 MPa were obtained from those fibres which could be pushed-in at or near the edge of the samples. These apparently high shear stresses can arise because of localised oxidation of surface layers during ceraming of composite B in air. Similar trends in results have been reported for a Sic/barium osumilite composite by Bleay and Scott [20]. The interfacial frictional shear stresses in these composites are considerably higher than those reported for Sic/LAS composites [lo, 21-231. This can be attributed at least in part to the differences in residual thermal stresses at the fibre-matrix interfaces. Residual thermal stresses arise from the thermal contraction mismatch between matrix and fibre, and also from the unrelaxed volume changes associated with any phase transformation and crystallisation in the matrix. Brun and Singh [22] have shown that the sliding friction stress is nearly zero when the coefficient of thermal expansion of fibre (a,) is greater than the coefficient of thermal expansion of matrix (a,) and that it increases linearly with the thermal expansion mismatch when tlf< CI,. The coefficient of thermal expansion of LAS is smaller than that of Nicalon fibres and therefore
KUMAR and KNOWLES: SIC REINHORCED ALUMINOSILICA'TES--Il able 1. Assumed materials parameters and estimated values of residual thermal stresses in composites A and B Composite CC MPa)(MPa ratio, linear thermal exp coefticient and elastic modulus, respectively. The f and m reter to the fibre and matrix respectively. (e.g. the glass transition temperature) and room temperature, m is the res g s moduli of the mullite and glass [26]. whereas the value of a, for composite R is ei residual thermal radial tensile stresses will be present where at the fibre-matrix interface in the Nicalon-LAS composites, consistent with low interfacial frictional Em ve (4) shear stresses. In contrast. the coefficients of thermal expansion of the matrices in both the composites that In these equations, vr and vm are the Poisson's ratios compressive stresses will be present at the r is the radius of the fibres, u the coefficient of fric fibre-matrix interface. It should be noted that if at the fibre matrix interface arro the residual radial either of the composites were to have had only stress at the fibre-matrix interface, and to is a con- a-cordierite in the matrix, there would have been stant sliding resistance term justified by Weihs and residual tensile stresses at the fibre-matrix interface, Nix on the basis of remnant fibre surface roughness rather than compressive stresses, because the co- after fibre-matrix debonding cfficient of thermal expansion of -cordierite is If we assume that the logarithm term in equation smaller than that of Nicalon fibres. As explained in (3)is of the form In(1+x)for small x, equation(3) Part I (2 the matrices in both the composites consist can be rewritten in the form of a-cordierite and other phases. Phases with high coefficients of thermal expansion, such as mullite in (1-2vk composite A and enstatite in composite B, help increase the effective thermal expansion coefficient of The term 2vk is small in comparison with I as it is the matrix in both cases of the order of v?(which is 0.0225 using the value of An estimation of an upper limit to the residual 0.15 for vr quoted for Nicalon fibres [21, 23). If we thermal stresses arising solely from the thermal follow Marshall [10] and let F-2a2H then to a good expansion mismatch can be made using the classical approximation Lame solution of a coaxial fibre and surrounding ix [24, 25]. The relevant cquations are given in H the appendix. The residual stresses estimated assum 1. The residual radial stresses in composites A and b replacing t. Coefficients of friction, H, assumed for at the fibre-matrix interfaces are compressive and SiC/LAS composites, in which there is good evidence comparable in magnitude, .-28 and -27MPa, of a carbon layer at the fibre-matrix interface, are respectively.If,instead of Marshall's simple model quoted in the range 0.01-0.32[21-23). If we therefore [10], the more sophisticated model of the push assume for SiC/MAS that a value of u=0. 2 is not technique of Weihs and Nix [23] is used, in which unreasonable in lieu of any firm experimental data, account is taken not only of a constant sliding then a 6 MPa contribution to any"constant "inter- resistance term, but also of the residual stress arising facial frictional shear stress would arise from the from thermal expansion mismatch and a Poisson on effect, then the displacement of the top of presence of thermal stresses on these calculations and would be independent of errors arising from, in the fibre,u, for a given load F on the fibre takes the particular, the measurement of fibre hardness form The values of interfacial frictional shear stresses calculated in equation()are very sensitive to the F22n:(0+m) values of fibre hardness and any ISE effect, if present Thus, if a hardness value of 10-13 GPa were to have een used instead of 26-32 GPa for the fibres in (3) compositc B in cquation(1), the inter facial frictional hear stresses would be reduced to 8-13 MPa before
KUMAR and KNOWLES: Sic REINFORCED ALUMINOSILICATES-II 2921 Table 1, Assumed materials parameters and estimated values of residual thermal stresses in composites A and B Comuosite Y_ Yr a, x 10-s AT Em Er Qw fl,,m (‘C’) (K) (GPaj (GPa) tMPa) (MPa) A 0.47 0.20 0.15 3.1 4.0 800 110 184 56 -28 B 0.40 0.20 0.15 3.1 4.1 800 80 184 45 -27 Y. G( and E refer to Poisson’s ratio. linear thermal expansion coefficient and elastic modulus, respectively. The subscripts, f and m refer to the fibre and matrix respectively. Vr is the volume fraction of the fibres. AT is the difference in temperature between the temperature at which the composite can be assumed to be stress-free (e.g. the glass transition temperature) and room temperature. o,,, is the residual axial stress in the matrix and Q,,, is the residual radial stress in the matrix at the fibre-matrix interface in a Lam& coaxial cylinder model of the composite [24]. The value of a, for composite A is based on the known linear thermal coefficients of Mg0_Al,O,-SiO, glasses and mullite. the relative volume fractions of mullite and glass and reasonable values for the Young’s moduli of the mullite and glass [26], whereas the value of OL, for composite B is given by the suppliers [I l] residual thermal radial tensile stresses will be present at the fibre-matrix interface in the Nicalon-LAS composites, consistent with low interfacial frictional shear stresses. In contrast, the coefficients of thermal expansion of the matrices in both the composites that we have examined here are higher than that of Nicalon fibres and, therefore, residual radial compressive stresses will be present at the fibre-matrix interface. It should be noted that if either of the composites were to have had only a-cordierite in the matrix, there would have been residual tensile stresses at the fibre-matrix interface, rather than compressive stresses, because the coefficient of thermal expansion of a-cordierite is smaller than that of Nicalon fibres. As explained in Part I [2], the matrices in both the composites consist of cc-cordierite and other phases. Phases with high coefficients of thermal expansion, such as mullite in composite A and enstatite in composite B, help to increase the effective thermal expansion coefficient of the matrix in both cases. An estimation of an upper limit to the residual thermal stresses arising solely from the thermal expansion mismatch can be made using the classical Lame solution of a coaxial fibre and surrounding matrix [24,25]. The relevant equations are given in the Appendix. The residual stresses estimated assuming the various material parameters are given in Table 1. The residual radial stresses in composites A and B at the fibre-matrix interfaces are compressive and comparable in magnitude, -28 and -27 MPa, respectively. If, instead of Marshall’s simple model [lo], the more sophisticated model of the push-down technique of Weihs and Nix [23] is used, in which account is taken not only of a constant sliding resistance term, but also of the residual stress arising from thermal expansion mismatch and a Poisson expansion effect, then the displacement of the top of the fibre, u, for a given load F on the fibre takes the form (1 - 2vrk) F tl= ~ 4 - r t%l+ P%,,) 2pkzr 2p2k’ xln 1 @F ’ +(z,+~(T,,,) 7cr2 II where k = Emvi -w + %I) In these equations, vr and v, are the Poisson’s ratios for the fibre and matrix respectively, E, and Em are the Young’s moduli of the fibre and matrix respectively, Y is the radius of the fibres, p the coefficient of friction at the fibre-matrix interface, orro the residual radial stress at the fibre-matrix interface, and z, is a constant sliding resistance term justified by Weihs and Nix on the basis of remnant fibre surface roughness after fibre-matrix debonding. If we assume that the logarithm term in equation (3) is of the form ln(1 + x) for small x, equation (3) can be rewritten in the form (1 - 2v,k) F= 24% Ef 4712r3(7, + pi,,,)’ (5) The term 2v,k is small in comparison with 1 as it is of the order of vf (which is 0.0225 using the value of 0.15 for vr quoted for Nicalon fibres [21,23]). If we follow Marshall [lo] and let F = 2&H, then to a good approximation, H2a4 70 + w-Jr,, =-. n”ur3Ef This is the same as equation (l), but with 7, + purr0 replacing 7. Coefficients of friction, p, assumed for Sic/LAS composites, in which there is good evidence of a carbon layer at the fibre-matrix interface, are quoted in the range 0.014.32 [21-231. If we therefore assume for SiC/MAS that a value of p = 0.2 is not unreasonable in lieu of any firm experimental data, then a 6 MPa contribution to any “constant” interfacial frictional shear stress would arise from the presence of thermal stresses on these calculations and would be independent of errors arising from, in particular, the measurement of fibre hardness. The values of interfacial frictional shear stresses calculated in equation (1) are very sensitive to the values of fibre hardness and any ISE effect, if present. Thus, if a hardness value of lo-13 GPa were to have been used instead of 2632 GPa for the fibres in composite B in equation (1) the interfacial frictional shear stresses would be reduced to 8-13 MPa before