2046 Journal of the American Ceramic Society--Parthasarathy and Kerans Vol. 80. No 8 rom fracture mirrors that are observed in post-mortem frac cludes with a discussion on the design implications for oxida- tography; however, such data is not always available, mal assun motions mand ( Efects of Roughness on Friction IlL. Composite Systems The frictional contribution that is actually measured in tests such as the pushout test is the total friction, an average T value The composite systems that are being considered seriously is then extracted, neglecting the progressive contribution for practical applications can be classified into two group roughness and often assuming a uniform stress distribution non-oxide fiber-based systems and oxide fiber-based systems. However, during progressive debonding, the frictional stress is There is substantially more data in the literature for non-oxide highly nonuniform. The frictional stress that is experienced at reinforced systems. SiC composites reinforced with NicalonTM an arbitrary location on a sliding fiber is illustrated in Fig 3 fiber(Nippon Carbon, Tokyo, Japan) have been the subjects of Poissons effect is neglected for illustration purposes. When numerous investigations into interface, constituent, and com any point on the fiber is in its original position, the normal posite properties, although few studies have been on exactly (clamping)stress is simply the residual stress and the relevant milar materials. This system also is likely to be one in which coefficient of friction is H'(Eq. (1); thus, the friction stress is roughness effects will be larger. because of the stiff matrix μ'[A(△a△D], where A( equal to BE) is a collection of elastic Consequently, the Nicalon-fiber-reinforced SiC matrix com- posite system has been selected as the principal system for ing point of origin on the matrix side of the interface, the local consideration in the present stud clamping stress increases linearly with the displacement, u,as e The roughness amplitude that has been reported in the lit- (u/d)[A(M/R)), where d is the half-period. The rate of increase ture for Nicalon-based composites ranges from -2.5 nm on in clamping stress is linear with e(equal to h/d). When u=d, the as-received fibers to 20-30 nm, which is inferred from the maximum misfit is attained and remains unchanged with indirect measurements. It is believed that, in composites hav further displacement. At that same displacement, the coeffi- ing an interfacial coating, the roughness amplitude can be as cient of friction becomes u, the smooth-fiber value. The fric- high as the coating thickness itself. Thus, for the parametric tion stress for subsequent sliding of the point is then study, the roughness amplitude was varied from zero(smooth H([AAT+(h/R Ii. This value may be higher or lower than fiber)to 30 nm. The fiber strength of Nicalon is usually re- the value at zero displacement, depending on the magnitudes of ported in the range of 2-2.5 GPa(based on a gauge length of u' and h and, thus, on the magnitudes of the roughness param- I in. ) however, processing is expected to weaken the fiber to eters h and d Other shapes of roughness that lead to a nonlinear some extent. The work by Prewo 6 on Nicalon/LASIll co increase in misfit with displacement will result in a nonlinear posites suggests that the fiber strength degrades to -1.7 GPa increase of the clamping stress until u d. The change in after processing in this particular system. Heredia et al. re- frictional stress with relative fiber/matrix displacement can be ported in-situ strengths of 2.2 GPa in a Nicalon/carbon com- expected to be smoother for real surfaces, as illustrated in Fig posite system, Fiber strengths in the range of 1-2 GPa were 3. Although the model captures the key aspects, the magnitude sed in the study of the error that is introduced by the simple form of roughness is unknown V. Results and Discussion A reasonable quantity to consider in seeking insight is the average friction stress along the fiber; this is defined as the total The control set of parameters that were used in this study load on the fiber(less that required for debond initiation) di (listed in Table I) were selected based on the available infor- vided by the debond area. As a fiber begins to slide, the sliding mation and best estimates. One or more of the parameters were length increases as the interfacial crack tip, or the front of then varied systematically, to study the effect of the variable on slippage initiation, propagates down the interface. The dis- friction and debond length placement of the fiber, relative to its original position, increases This section begins with a discussion on the effects of rough- from zero with distance from the crack tip. Similarly, the misfit ness on friction(through defining an average T value); its rel increases as the distance from the crack tip increases until the evance to the measurement of roughness effects during fiber boundary between regions II and Ill is attained Until the slid- pushout tests is presented. This is followed by calculations of ing length exceeds the region Il length, the average friction debond lengths, as functions of roughness parameters, and stress monotonically increases. When the sliding length ex- evaluation of roughness effects relative to other parameters ceeds the region Il length, all additional sliding lengths are Finally, the accuracy of the constant-T approximation is evalu ated, and an alternate piecewise linear approximation is used to predict the composite stress-strain behavior. The paper con- friction H. A zone of region II moves with the crack i oa becomes an ever-smaller fraction of the contribution to the te Table I. Listing of the Control Set of Parameters Used for the Different Composite Systems Studied 密密宽 SCSa/ SCSa/ Fiber modulus(GPa) dulls(GPa) Axial/radial modulus Fiber poisson's ratio 0.l Fiber radius, R(um) Roughness amplitude, h(nm) Roughness period, 2d (um) Friction coefficient Interface toughness, G.(J/m2) Thermal mismatch strain,△a△T(x10-3) Fiber strength(GPa) Fiber volume fraction, f 0.45from fracture mirrors that are observed in post-mortem frac￾tography; however, such data is not always available, making reasonable assumptions mandatory. III. Composite Systems The composite systems that are being considered seriously for practical applications can be classified into two groups: non-oxide fiber-based systems and oxide fiber-based systems. There is substantially more data in the literature for non-oxide reinforced systems. SiC composites reinforced with Nicalon™ fiber (Nippon Carbon, Tokyo, Japan) have been the subjects of numerous investigations into interface, constituent, and com￾posite properties, although few studies have been on exactly similar materials. This system also is likely to be one in which roughness effects will be larger, because of the stiff matrix. Consequently, the Nicalon-fiber-reinforced SiC matrix com￾posite system has been selected as the principal system for consideration in the present study. The roughness amplitude that has been reported in the lit￾erature for Nicalon-based composites ranges from ∼2.5 nm on the as-received fiber35 to 20–30 nm, which is inferred from indirect measurements.12 It is believed that, in composites hav￾ing an interfacial coating, the roughness amplitude can be as high as the coating thickness itself. Thus, for the parametric study, the roughness amplitude was varied from zero (smooth fiber) to 30 nm. The fiber strength of Nicalon is usually re￾ported in the range of 2–2.5 GPa (based on a gauge length of 1 in.); however, processing is expected to weaken the fiber to some extent. The work by Prewo36 on Nicalon/LASIII com￾posites suggests that the fiber strength degrades to ∼1.7 GPa after processing in this particular system. Heredia et al.37 re￾ported in-situ strengths of 2.2 GPa in a Nicalon/carbon com￾posite system. Fiber strengths in the range of 1–2 GPa were used in the study. IV. Results and Discussion The control set of parameters that were used in this study (listed in Table I) were selected based on the available infor￾mation and best estimates. One or more of the parameters were then varied systematically, to study the effect of the variable on friction and debond length. This section begins with a discussion on the effects of rough￾ness on friction (through defining an average
value); its rel￾evance to the measurement of roughness effects during fiber pushout tests is presented. This is followed by calculations of debond lengths, as functions of roughness parameters, and evaluation of roughness effects relative to other parameters. Finally, the accuracy of the constant-
approximation is evalu￾ated, and an alternate piecewise linear approximation is used to predict the composite stress–strain behavior. The paper con￾cludes with a discussion on the design implications for oxida￾tion-resistant composites. (1) Effects of Roughness on Friction The frictional contribution that is actually measured in tests such as the pushout test is the total friction; an average
value is then extracted, neglecting the progressive contribution of roughness and often assuming a uniform stress distribution. However, during progressive debonding, the frictional stress is highly nonuniform. The frictional stress that is experienced at an arbitrary location on a sliding fiber is illustrated in Fig. 3; Poisson’s effect is neglected for illustration purposes. When any point on the fiber is in its original position, the normal (clamping) stress is simply the residual stress and the relevant coefficient of friction is
(Eq. (1)); thus, the friction stress is
[ (T)], where (equal to BEm) is a collection of elastic constants. As the point is displaced relative to the correspond￾ing point of origin on the matrix side of the interface, the local clamping stress increases linearly with the displacement, u, as (u/d)[ (h/Rf )], where d is the half-period. The rate of increase in clamping stress is linear with  (equal to h/d). When u d, the maximum misfit is attained and remains unchanged with further displacement. At that same displacement, the coeffi￾cient of friction becomes , the smooth-fiber value. The fric￾tion stress for subsequent sliding of the point is then { [T + (h/Rf )]}. This value may be higher or lower than the value at zero displacement, depending on the magnitudes of
and h and, thus, on the magnitudes of the roughness param￾eters h and d. Other shapes of roughness that lead to a nonlinear increase in misfit with displacement will result in a nonlinear increase of the clamping stress until u d. The change in frictional stress with relative fiber/matrix displacement can be expected to be smoother for real surfaces, as illustrated in Fig. 3. Although the model captures the key aspects, the magnitude of the error that is introduced by the simple form of roughness is unknown. A reasonable quantity to consider in seeking insight is the average friction stress along the fiber; this is defined as the total load on the fiber (less that required for debond initiation) di￾vided by the debond area. As a fiber begins to slide, the sliding length increases as the interfacial crack tip, or the front of slippage initiation, propagates down the interface. The dis￾placement of the fiber, relative to its original position, increases from zero with distance from the crack tip. Similarly, the misfit increases as the distance from the crack tip increases until the boundary between regions II and III is attained. Until the slid￾ing length exceeds the region II length, the average friction stress monotonically increases. When the sliding length ex￾ceeds the region II length, all additional sliding lengths are under region III conditions: maximum misfit and coefficient of friction . A zone of region II moves with the crack tip but becomes an ever-smaller fraction of the contribution to the total Table I. Listing of the Control Set of Parameters Used for the Different Composite Systems Studied Property System (fiber/matrix/coating) Nicalon/ SiC/ carbon Nicalon/ MAS/ carbon Sapphire/ YAG/ hibonite Nextel/ alumina/ monazite SCS6/ glass SCS6/ RBSN Fiber modulus (GPa) 200 200 465 380 415 415 Matrix modulus (GPa) 400 75 300 400 60 100 Axial/radial modulus 1 1 1.08 1 1 1 Fiber Poisson’s ratio 0.15 0.15 0.25 0.2 0.2 0.2 Fiber radius, Rf (m) 8 8 75 6 71 71 Roughness amplitude, h (nm) 20 20 200 25 25 25 Roughness period, 2d (m) 0.3 0.5 60 1 10 10 Friction coefficient, 0.05 0.04 0.1 0.2 0.1 0.15 Interface toughness, Gc (J/m2 ) 2 2 5 2.5 5 1 Thermal mismatch strain, T (× 10−3) 1 0 0 0.5 0.5 0 Fiber strength (GPa) 1.5 1.5 1.5 1.5 2.5 2.5 Fiber volume fraction, f 0.4 0.45 0.3 0.4 0 0.4 2046 Journal of the American Ceramic Society—Parthasarathy and Kerans Vol. 80, No. 8