Mech080707.qxd The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 1. Introduction Cylinder made of monolithic material such as metal and concrete (eg. asphalt concrete), is a common compo- nent employed in numerous applications such as pressure vessels (eg. hydraulic cylinders, gun barrels, pipes, boilers and fuel tanks), accumulator shells, emergency breathing cylinders, cylinders for aerospace industries, nuclear reac- tors, military applications and civil structures etc. (Arya, Bhatnagar, 1976; Bhatnagar, et al. 1980; Becht, et al. 2000; Gupta, et al. 2001; Perry and Aboudi, 2003; Buttlar, et al. 2004 and You and Buttlar, 2005). In some of these applications such as pressure vessel for industrial gases or a media transportation of high-pressurized fluids and piping of nuclear reactors, the cylinder has to operate under severe mechanical and thermal loads, causing sig- nificant creep hence reduced service life (Gupta and Pathak, 2001; Tachibana and Iyoku, 2004 and Hagihara and Miyazaki, 2008). As an example, in the high temper- ature engineering test reactor, the temperature reaches of the order of 900 0C (Tachibana and Iyoku, 2004). The piping of reactor cooling system is subjected to high _______________________________________________ *Corresponding author’s e-mail: guptavk_70@yahoo.co.in temperature and pressure and may be damaged due to high heat generated from the reactor core (Hagihara and Miyazaki, 2008). Creep analysis of thick-walled cylinder made of isotrop- ic monolithic material and subjected to internal pressure has been presented by (Weir, 1957; King and Mackie 1967 and Pai 1967) has solved the problem for orthotropic cylinders. In all these analyses it was assumed that the strains are infinitesimal and the deformation is referred with respect to original dimensions of the cylinder. Rimrott, 1959, used generally accepted assumptions of constant density, zero axial strain and distortion energy theory to derive equations for creep rate, creep strains and creep stresses in a, closed end, thick-walled hollow cylin- der subjected to internal pressure. Bhatnagar and Gupta, 1969 obtained the solution for thick walled cylinder made of an orthotropic material and subjected to internal pres- sure. In recent years, the problem of creep in composite cylinders made of Functionally Graded Materials (FGMs) operating at high pressure and temperature has attracted the interest of many researchers. Fukui and Yamanaka, 1992 investigated the effect of gradation of components on strength and deformation of thick-walled Functionally Graded (FG) tubes subjected to internal pressure under Effect of Material Parameters on Steady State Creep in a Thick Composite Cylinder Subjected to Internal Pressure Tejeet Singha and V.K.Gupta*b aDepartment of Mechanical Engineering, S. B.S. College of Engineering and Technology, Ferozepur, 152001, India *b Department of Mechanical Engineering, University College of Engineering, Punjabi University, Patiala-147002, India Received 25 April 2008; accepted 26 October 2008 Abstract: The steady state creep in Al- SiCP composite cylinder subjected to internal pressure was investigat- ed. The creep behavior of the material were described by threshold stress based creep law by assuming a stress exponent of 5. The effect of size and content of the reinforcement (SiCP), and operating temperature on the stresses and strain rates in the composite cylinder were investigated. The stresses in the cylinder did not have significant variation with varying size and content of the reinforcement, and operating temperature. However, the tangential as well as radial strain rates in the cylinder could be reduced to a significant extent by decreas- ing size of SiCP, increasing the content of SiCP and decreasing operating temperature. Keywords: Cylinder, Creep, Composite, Internal pressure, Modeling »∏NGO §¨° d á°Vô©e ᵫª°S áÑcôe áfGƒ£°SE’ º¶àæŸG ∞MõdG ≈∏Y IOÉŸG πeGƒY ÒKCÉJ *GÉàHƒL .∑ h èæ°S äÉé«J áá°°UUÓÓÿÿGG¢SCG ¢VGÎaEÉH ∞MõdG ¿ƒfÉb ≈∏Y á«æÑŸG OÉ¡L’G Iƒb ¢SÉ°SCG ≈∏Y É¡Ø°Uh ” ~b IOÉŸG ∞MR ∑ƒ∏°S ¿EG .»∏NGO §¨° d á°Vô©e áÑcôe áfGƒ£°SC’ º¶àæŸG ∞MõdG á°SGQO ” : á°SGQ~dG äQÉ°TCG ~bh .áÑcôŸG áfGƒ£°S’ÉH ádÉ£à°S’G h OÉ¡L’G ä’~©e ≈∏Y 𫨰ûàdG IQGôM áLQOh ájƒ≤àdG iƒàfih ºé◊G πeÉY ÒKCÉJ á°SGQO ” ~bh Gòg .á°ùªN ÉjhÉ°ùe OÉ¡LE’G π≤J áfGƒ£°SEÓd ájô£≤dG h á«°SɪŸG OÉ¡LC’G ä’~©e ¿CG ~Lh ~≤a ∂dP ™eh .𫨰ûàdG IQGôM áLQOh ájƒ≤àdG iƒàfih äGÒ¨J ™e Rõ©e πµ°ûH ~«≤àJ ’ áfGƒ£°S’ÉH äGOÉ¡LE’G ¿G ¤G .𫨰ûàdG IQGôM áLQO π«∏≤J h iƒàÙG IOÉjR h ºé◊G π«∏≤J ~æY ®ƒë∏e ~M ¤G áá««MMÉÉààØØŸŸGG ääGGOOôôØØŸŸGG.áLò‰ ,≈∏NGO §¨°V ,Öcôe ,∞MR ,áfGƒ£°SG : 21 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 plain strain conditions. Fukui et al. 1993 extended the work to investigate the effect of graded components on residual stresses in a thick walled FG tube under uniform thermal loading. Chen et al. 2007 studied the creep behavior of a thick walled FGM cylinder subjected to internal and external pressures. The asymptotic solutions were obtained on the basis of Taylor expansion series and compared with the results obtained by finite element analysis. You et al. 2007 investigated steady state creep in a thick walled FGM cylinder subjected to internal pres- sure. The effect of variation in material parameters on the stresses induced in cylinder was investigated. Abrinia et al. 2008 obtained the analytical solution for radial and cir- cumferential stresses in a thick FGM cylindrical vessel under the influence of internal pressure and temperature. The study indicated that stresses in FGM cylinder could be lowered by tailoring the material properties along radi- al direction of the cylinder. Under severe thermo-mechanical loads cylinder made of monolithic materials may not perform well. The metal matrix composites (MMCs) such as aluminium/alumini- um alloy matrix reinforced with silicon carbide offer excellent mechanical properties like high specific strength and stiffness along with high temperature stability. Therefore, these are suitable for cylinder applications exposed to high pressure and high operating temperature (Nieh, 1984; Roy and Tsai, 1988; Fukui et al. 1993; Salzar et al. 1996 and Gupta et al. 2004. With these fore- thoughts, it is decided to investigate the steady state creep in a cylinder made of Al- SiCP composite and subjected to high pressure and high temperature. A mathematical model has been developed to describe the steady creep behavior of the composite cylinder. The model developed is used to investigate the effect of material parameters viz particle size and particle content, and operating tempera- tures on the steady state creep response of the composite cylinder. 2. Selection of Creep Law (1) where the symbols A', n, Q, E, R and T denote respective- ly structure dependent parameter, true stress exponent, true activation energy, temperature-dependent Young's modulus, gas constant and operating temperature. The true stress exponent n appearing in Eq. (1) is usu- ally selected as 3, 5 and 8 which correspond to three well- documented creep cases for metals and alloys: (i) n = 3 for creep controlled by viscous glide processes of dislocation, (ii) n = 5 for creep controlled by high temperature dislo- cation climb (lattice diffusion), and (iii) n = 8 for lattice diffusion-controlled creep with a constant structure (Tjong and Ma, 2000). Though, some of the research groups (Mishra and Pandey, 1990; Pandey et al. 1992; Gonzalex-Doncel and Sherby, 1993 and Pandey et al. 1994) have used a true stress exponent of 8 to describe steady state creep in Al-SiCP,W (subscript 'p' for particle and 'w' for whisker) composites but a number of other research groups (Park et al. 1990; Mohamed et al. 1992; Park and Mohamed, 1995; Cadek et al. 1995; Yoshioka et al. 1998; Li and Mohamed, 1997; Li and Langdon, 1997 and Li and Langdon, 1999) have observed that a stress exponent of either ~3 or ~5, rather than 8, provides a bet- ter description of steady state creep data observed for dis- continuously reinforced Al-SiC composites. Keeping this in view, a stress exponent of 5 is used to describe steady state creep behavior of the composite cylinders in this study. The justification regarding choice of stress expo- nent is further elaborated in the next section. 3. Estimation of Creep Parameters The creep law given by Eq. (1) may alternatively be written as: (2) In aluminium based composites, undergoing steady state creep, the effective creep rate, eε , is related to the effective stress, eσ , through well documented threshold stress, 0σ , based cree p law given by (Mishra and Pandey, 1990; Pandey et al. 1992; Gonzalez - Doncel and Sherby, 1993; Pandey et al. 1994; Park et al. 1990; Mohamed et al. 1992; Part and Mohamed, 1995; Cadek et al. 1995; Yoshioka et al. 1998; Li and Mohamed, 1997; Li and Langdon , 1997; Li and Langdon, 1997; Li and Langdon, 1999; Tjong and Ma 2000 and Ma and Tjong, 2001). 0 n Q' eA expe E RT σ σ ε − −⎛ ⎞ ⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ ( )0 nMe eε σ σ⎡ ⎤= −⎣ ⎦ where 11 / nQ'M A exp E RT −⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ and the stress exponent n is chosen as 5. The creep parameters M and so appearing in Eq . (2) are dependent on the type of material and are also affected by the temperature (T) of application . In a composite , the dispersoid size (P) and the content of dispersoid (V) are the primary material variables determining these parameters . In the present study , the values of M and σ0 have been extracted from the expe- rimental creep results reported for Al -SiCP composite under uniaxial loading (Pandey et al. 1992). Though, Pandey et al. 1992 suggested a stress exponent of 8 to describe steady state creep in these composites . But due to the objections pointed by several research groups (Park et al. 1990; Mohamed et al. 1992; Park and Mohamed, 1995; Cedek et al. 1995; Yoshioka et al. 1998; Li and Mohamed , 1997; Li and Longdon , 1997 and Li and Langdon , 1999), we have used a stress exponent of 5 to describe steady state creep in compo- site (Al-SiCP) taken in the study of (Pandey et al. 1992). The individual set of creep data of (Pandey et al. 1992) have been plotted as 1 5/ε versus σ on linear 22 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 scales as shown in Figs. 1(a)-(c). From the slope and inter- cepts of these graphs, the values of creep parameters M and σο have been obtained and are reported in Table-1. This approach of determining the threshold stress σο, is known as linear extrapolation technique (Lagneborg and Bergman, 1976). To avoid variation due to systematic error, if any, in experimental results, the creep results from a single source have been used. The ε1/5 versus σ plots corresponding to the observed experimental data points of Al- SiCP composites (Pandey et al. 1992) for various combinations of particle size, par- ticle content and operating temperature exhibit an excel- lent linearity as evident from Figs.1(a)-(c). The coefficient of correlation for these plots has been reported in excess to 0.916 as given in Table-1. In the light of these results, the choice of stress exponent n = 5, to describe the steady state creep behavior of Al-SiCP composite, is justified. The accuracy of the creep response of the composite cylinder, to be estimated in subsequent sections, will depend on the accuracy associated with prediction of creep parameters M and σο for various combinations of material parameters and operating temperature. To accom- plish this task, the creep parameters given in Table-1 have been substituted in the constitutive creep model, Eq. (2), to estimate the strain rates corresponding to the experi- mental stress values reported by (Pandey et al. 1992) for Al-SiCP composite for the various combinations of mate- rial parameters and temperature as given in Table-1. The estimated strain rates have been compared with the strain rates observed experimentally by (Pandey et al. 1992). Figs. 2(a)-(c) show an excellent agreement between the strain rates estimated from Eq. (2) and those observed experimentally, to inspire confidence in the creep param- eters estimated in this study. 16 20 24 28 32 10o 10-1 10-2 ε1 /5 (s - 1 /5 ) σ (MPa) (1a) 20 30 40 50 60 70 10-1 10-2 ε1 /5 (s -1 /5 ) σ (MPa) (1b) 30 35 40 45 50 55 10-1 10-2 ε1 /5 (s - 1 /5 ) σσ (MPa) (1c) Figure 1. Variation of ε1/5 versus σ in Al-SiCp compo- site for different (a) particle sizes of SiC, (b) vol% of SiC and (c) temperature σ (MPa) (2a) σ (MPa) (2b) 23 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 4. Mathematical Formulation Consider a long, closed end, thick-walled hollow cylin- der made of Al-SiCP composite having inner and outer radii of a and b respectively and subjected to internal pressure p. The coordinates axes r, θ and z are taken respectively along radial, tangential and axial directions of the cylinder. The present analysis is based on the follow- ing assumptions: i. Material of the cylinder is incompressible, isotropic and has uniform distribution of SiCP in aluminium matrix. ii. Pressure is applied gradually and held constant during the loading history. iii. Stresses at any point in the cylinder remain constant with time ie. steady state condition of stress is assumed. iv. Elastic deformations are small and are neglected as compared to creep deformations. (3) (4) (5) Considering the equilibrium of forces on an element of the cylinder in the radial direction, we may write, (Gupta and Pathak, 2001) (6) where σθ is the tangential stress. Since material of the cylinder is assumed to be incom- pressible, therefore, (7) The generalized constitutive equations for creep in an isotropic composite (Gupta et al. 2005), when reference frame is along the principal directions of r, θ and z are given by, (8) (9) (10) where σr, σθ, σz are respectively the radial, tangential and axial stresses. Following Von-Mises yield criterion (Dieter, 1988), the effective stress is given by, (11) σ (MPa) (2c) Figure 2. Comparison of experimental and estimated strain rates in Al-SiCp composite for diff- erent (a) particle sizes of SiC, (b) vol% of SiC and (c) temperature P (µm) T ( 0C) V (Vol %) M (s-1/5/MPa) óo (MPa) Coefficie nt of correlati on 1.7 14.5 45.9 350 10 4.35E-03 8.72E-03 9.39E-03 19.83 16.50 16.29 0.945 0.999 0.998 1.7 350 10 20 30 4.35E-03 2.63E-03 2.27E-03 19.83 32.02 42.56 0.945 0.995 0.945 1.7 350 400 450 20 2.63E-03 4.14E-03 5.92E-03 32.02 29.79 29.18 0.995 0.974 0.916 Table 1. Creep parameters used for Al-SiCp compo- sites in the present study The radial ( rε ) and tangenti al ( θε ) strain rates in the cylinder are respectively given by: r r d u dr ε • = ru rθ ε • = where r du u dt • = is the radial displacement rate and u is the radial displacement. r d r dr θ θ ε ε ε= − r r d r dr θ σ σ σ= − 0r zθε ε ε+ + = where Zε is the strain rate in the axial ( z) direction. 2 2 e r r z e [ ]θ ε ε σ σ σ σ = − − 2 2 e z r e [ ]θ θ ε ε σ σ σ σ = − − 2 2 e z z r e [ ]θ ε ε σ σ σ σ = − − 1 2 2 2 1 2 2 /[( ) ( ) ( ) ]e z z r rσ σ σ σ σ σ σθ θ= − + − + − In a cylinder made of incompressible material with closed end, the plane strain condition exist i.e. the axial strain rate )( zε is zero (Popov 2001). Therefore, Eqs. (3), (4) and (7) on simplifying yields, 24 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 (12) where C is the constant of integration. Substituting Eq. (12) into Eqs. (3) and (4), we get (13) (14) (15) Using Eq. (15) into Eq. (11), one gets (16) Substituting Eqs. (13) and (15) into Eq. (8) we get, (17) (18) where, and, On substituting Eq. (18) into equilibrium Eq. (6) and integrating, we get, (19) where C1 is another constant of integration. The boundary conditions for a cylinder subjected to only internal pressure are given as, (i) At r = a, σr = - P (negative sign implies compressive stress) (20) (ii) At r = b, σr = 0 (21) Applying boundary conditions stated above, in Eq. (19), we get, The values C1 and I1, thus obtained, are substituted in Eq. (19) to get the radial stress, σr, (22) where, Using Eq. (22) in Eq. (18), the tangential stress, σθ, is obtained, (23) Substituting Eqs. (22) and (23) in Eq. (15), we get the axial stress, σz, (24) Based on the analysis presented, a computer program has been developed to calculate the steady state creep response of the composite cylinder for various combina- tions of size and content of the reinforcement (SiCP), and operating temperature. For the purpose of numerical com- putation, the inner and outer radii of the cylinder are taken 25.4 mm and 50.8 mm respectively, and the internal pres- sure is assumed to be 85.25 MPa. The dimensions of cylinder and the operating pressure chosen in this study are similar to those used in earlier work (Johnson et al. 1961) on thick walled aluminum alloy (RR59) cylinder. The radial, tangential and axial stresses at different radial locations of the cylinder are calculated respectively from Eqs. (22), (23) and (24). The distributions of radial and tangential strain rates are computed from Eqs. (8) and (9) respectively. The creep parameters M and σo required during the computation process are taken from Table-1 for the desired combination of particle size, particle content and operating temperature. 5. Results and Discussions Before discussing the results obtained in the present study, it is necessary to check the accuracy of analysis car- ried out and the computer program developed. To accom- plish this task, following present analysis, the tangential, radial and axial stresses have been computed for a copper cylinder, for which the results are available in the litera- ture (Johnson et al. 1961). The dimensions of the cylin- r C u r • = 2r C r ε = − 2 C r θε = Under the assumption of plane strain condition ie. 0=zε , the Eq. (10) becomes, 2 r z σ σθσ + = ( )3 2e r σ σ σθ= − 4 23 Ce r re σ σ σθ ε ⎛ ⎞ ⎜ ⎟− = ⎜ ⎟ ⎝ ⎠ Putting eε and eσ respectively from Eqs. (2) and (16) in the above equation and simplifying, one gets, 1 22 I Ir / nr σ σθ − = + 1 14 2 1 3 n / nCnI M + ⎛ ⎞⎡ ⎤ ⎜ ⎟= ⋅⎢ ⎥ ⎜ ⎟⎣ ⎦ ⎝ ⎠ 2 2 3 I oσ= 1 2 122 In I ln r Cr / nr σ = − ⋅ + + 1 1 222 nI C I ln b / nb = − 2 2 1 2 2 p I ln( a / b ) I / n / nn ( a b ) +⎡ ⎤⎣ ⎦= − −− 2 2 2 / n / nX b r I ln( r / b )rσ − −⎡ ⎤= − +⎢ ⎥⎣ ⎦ 2 2 2 p I ln( a / b ) X / n / n( a b ) +⎡ ⎤⎣ ⎦= − −− 2 2 21 12 r/ n / nX r b I ln n b σθ ⎡ ⎤⎛ ⎞ ⎛ ⎞− −= − ⋅ + + ⋅ +⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎣ ⎦ 1 12 2 2 2 2 r/ n / n / nX b r r I . lnz n b σ ⎡ ⎤ ⎡ ⎤− − −= − + ⋅ + +⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ 25 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 der, operating pressure and temperature, and the values of creep parameters used for the purpose of validation are summarized in Table-2. To estimate the parameters M and σo for copper cylinder, firstly the values of σe have been calculated at inner and outer radii of cylinder by substitut- ing in Eq. (11) the values of σe , σr, σθ and σz at these locations as reported in the study of (Johnson et al. 1961). The values of stresses σr, σθ and σz and the tangential strain rates (εθ) reported in reference (Johnson et al. (1961) at inner and outer radii are substituted in Eqn. (9) to estimate the effective strain rates (εe) at the correspon- ding radial locations. The effective stresses and effective strain rates estimated at the inner (εe = 189.83 MPa and εe = 2.168 x 10-8 s-1 ) and the outer (εe = 116 MPa and εe = 1.128 x 10-9 s-1 ) radii of the copper cylinder are substitut- ed in creep law, Eq. (2), to estimate the creep parameters M and σo for copper, Table-2. The creep parameters have been used in the developed software to compute the distri- bution of tangential strain rate in the copper cylinder. The tangential strain rates thus obtained have been compared with those reported by (Johnson et al. 1961). A nice agreement is observed in Fig. 3, therefore verifying the accuracy of analysis presented and software developed in the current study. 5.1 Effect of Particle Size and Particle Content Figs. 4(a)-(d) show the variation of creep stresses in composite cylinder for varying SiCP size from 1.7 µm to 45.9 µm. The trend of stresses obtained is similar to those reported by (Bhatnagar and Arya 1974). The radial stress, Fig. 4(a), remains compressive over the entire cylinder radius with maximum at the inner radius and zero at the outer radius, due to the imposed boundary conditions given in Eqs. (20) and (21). The tangential stress shown in, Fig. 4(b), remains always tensile and increases on moving from the inner to the outer radius of cylinder. Unlike radial and tangential stresses, the axial stress, Figs. 4(c), decreases from maximum compressive, observed at the inner radius, to reach a maximum tensile value at the outer radius of the cylinder. It is clearly evident from Figs. 4(a)-(c) that the variation in particle size does not have a sizable effect on the stresses. The maximum varia- tion observed in radial and tangential stresses are less than 1% and for axial stress it is around 5% at a radius of 30.5 mm, in cylinders having relatively coarser SiCP of size 14.5 and 45.9 µm. when compared to cylinder having finer SiCP of 1.7 µm size. The variation of effective stress,σe, given by Eq. (11), for varying particle size of SiC is shown in Fig. 4(d). The effective stress shown does not change on varying the particle size near the inner radius; however, towards the outer radius it decreases Cylinder Material : Copper Cylinder dimensions: a = 25.4 mm, b =50.8 mm. Internal Pressure = 23.25 MPa, External Pressure = 0 Operating Temperature = 250 0C Creep parame ters estimated: M = 3.271×10 -4 s-1/5/MPa, óo = 11.32 MPa Table 2. Summary of data used for validation Figure 3. Comparison of tangential strain rates in copper cylinder estimated from current analysis and reported by Johnson et al. r (mm) (4a) r (mm) (4b) 26 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 marginally with increasing particle size. The maximum decrease of about 1% is observed at a radius 40.6 mm in cylinders containing relatively coarser SiCP (14.5µm and 45.9 µm) when compared to cylinder having finer SiCP of 1.7µm size. The strain rates given by Eqs. (8) and (9) are related to the effective strain rate, εe, which ultimately depends upon (σe - σo), as evident from creep law given by Eq. (2). Therefore, to investigate the effect of particle (SiCp) size on the creep rates, the distribution of (σe - σo), is plotted in Fig. 5. Though, the effective stress varies a little with particle size but the threshold, σo, decreases from 19.83 MPa to 16.29 MPa with the increase in particle size from 1.7µm to 45.9 µm, Table 1. Under external load, as the deformation of material reaches to threshold value, the interfacial debonding occurs between particles (SiCp) and the matrix (Al) (Chen et al. 2008). Due to which the stress triaxiality in the matrix near the reinforcement will decrease and the debonded particles are no longer be able to transfer the stress. The damage dissipation caused by interfacial debonding increases with increase in particle (SiCp) size (Chen et al. 2007), thereby decreasing the threshold stress, Table 1. As a result of this, the stress dif- ference (σe - σo) exhibits sizable variation throughout the cylinder with decreasing SiCP size from 45.9 µm to 1.7µm. The decrease observed towards the inner radius are relatively more than those observed near the outer radius. As a consequence, the effective strain rate (εe ) also decreases significantly with decreasing SiCP size as shown in Fig. 6(a). The decrease observed is about two orders of magnitude on decreasing SiCP size from 45.9µm to 1.7 µm. The decrease in effective strain rate may be attributed to decrease in creep parameter M and increase in threshold stress σo with decreasing size of SiCP rein- forcement (Table-1) as evident from creep law given in Eq. (2). The radial (compressive) and tangential (tensile) strain rates, Fig. 6(b), decrease on moving from the inner to the outer radius of the cylinder. Throughout the cylin- der, the radial and tangential strain rates remain equal in magnitude but have opposite nature due to the condition of incompressibility (Eq. 7) and of plane strain condition (εz = 0). The effect of particle size on both the strain rates is similar to those observed for effective strain rate in Fig. 6(a). The tangential and radial creep rates in the cylinder may be reduced to a significant extent by reinforcing finer SiCP particles. The smaller size particles will be larger in number for the same volume fraction of reinforcement, thereby, leading to: (i) more transfer of load to the rein- forcement with a corresponding reduction in the level of effective stress acting on the matrix, and (ii) enhancement of substructure strength, which help in restraining the r (mm) (4c) r (mm) (4d) Figure 4. Variation of creep stresses in composite cylinder for varying particle size of SiC (V = 10 vol%, T = 350oC) r (mm) Figure 5. Variation of stress difference in composite cylinder for varying particle size of SiC (V = 10 vol%, T = 350oC) 27 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 creep flow (Li and Langdon, 1998; Peng et al. 1998; Peng et al. 1999; Han and Langdon, 2002). Further, the thresh- old stress observed for finer particles is higher than those observed for coarser one (Table 1) due to lesser degree of debonding between particles and matrix (Chen et al. 2007). As a result, the load is effectively transferred from the matrix to reinforcement hence reducing the creep rates in cylinder having finer sized SiCp. Figures 7(a) to 7(c) show respectively the variation of radial, tangential and axial stresses in composite cylinder containing different SiCP content ie. 10%, 20% and 30% by volume. The radial stress as shown in Fig. 7(a) does not vary on changing the content of SiCP except for a small variation noticed in the middle of cylinder. Unlike particle size, the increase in particle content leads to some sizable r (mm) (6a) r (mm) (6b) Figure 6. Variation of strain rates in composite cylin- der for varying particle size of SiC (V = 10 vol%, T = 350oC). r (mm) (7a) r (mm) (7b) r (mm) (7c) 28 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 variation in tangential and axial stresses as shown respec- tively in Figs. 7(b) and 7(c). On decreasing the content of SiCP from 30% to 10%, the tangential stress increases near the inner radius but decreases towards the outer radius of the cylinder. The maximum increase and decrease observed in tangential stress are about 8% and 3.5% respectively at the inner and outer radii of the cylin- der. Similar to tangential stress, the tensile values of axial stress as observed in Fig. 7(c), increases near the inner radius but decreases towards the outer radius of the cylin- der on decreasing the content of SiCP from 30% to 10%. However, at the inner radius, the compressive axial stress decreases by about 10% on decreasing the particle content from 30% to 10%. Therefore, by incorporating more amounts of reinforcement (SiCP), the tangential and axial (only tensile values) stresses increases near the inner radius but decreases near the outer radius. The effect of particle content on effective stress, Fig. 7(d), is similar to those observed for tangential stress in Fig. 7(b). The stress difference, (σe - σo), shown in Fig. (8), decreases signifi- cantly over the entire radii with increasing SiCP content. The decrease observed is relatively more prominent towards the inner radius compared to those observed around the outer radius. As expected, the effective strain rate decreases significantly with increasing content of SiCP, Fig. 9 (a). The effective strain rate reduces by about two orders of magnitude on increasing the content of SiCP from 10% to 30%. The reduction in effective strain rate, given by Eq. (2), may be attributed to decrease in creep parameter M and increase in threshold stress σo with increasing content of SiCP (Table-1). The impact of parti- cle content on tangential and radial creep rates, Fig. 9(b), is similar to those observed for effective strain in Fig. 9(a). By increasing the content of SiCP in the composite cylin- der, the inter-particle spacing decreases which cause the increase in threshold stress (Li and Langdon, 1999) but decrease in creep parameter M (Table-1), both these fac- tors contribute in reducing the strain rates significantly. Mishra and Pandey (1990), in their review of uniaxial creep data of Nieh (1984), have also observed that the creep rate in SiC (whisker) reinforced aluminum alloy (6061Al) composite could be reduced significantly by increasing the content of reinforcement. Similar effect of increasing SiC (particle) content on strain rate has been observed by (Pandey et al. 1992) for Al- SiCP composite under uniaxial test. r (mm) (7d) Figure 7. Variation of creep stresses in composite cylinder for varying particle content of SiC (P = 1.7 µm, T = 350o C) r (mm) Figure 8. Variation of stress difference in composite cylinder for varying particle content of SiC (P = 1.7 µm, T = 350 oC) r (mm) (9a) 29 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 5.2 Effect of Temperature The creep in any material is significantly affected by operating temperature. Therefore, this section discusses the effect of varying operating temperature on the stresses and strain rates in a thick cylinder made of aluminium matrix composite containing 20 vol% of SiCP. Figs. 10(a)- (c) show respectively the variation of radial, tangential, axial stresses in a composite cylinder for three different operating temperatures ie. 350 0C, 400 0C and 450 0C. The effect of temperature on the stresses is not significant, except for a slight variation observed in tangential stress, Fig. 10(b). On increasing the operating temperature from 350 0C to 450 0C, the tangential stress increases a little (around 1%) near the inner radius but towards the outer radius of the cylinder it does not change. The effective stress, Fig. 10(d), at the inner radius does not change with varying temperature; however, it exhibits a marginal decrease at the outer radius with increase in temperature. The stress difference, (σe - σo), decreases throughout the cylinder with decreasing temperature, Fig. 11. The effec- tive as well as radial and tangential strain rates observed in Figs. 12(a) and 12(b) respectively increases by about two orders of magnitude on increasing the temperature from 350 0C to 450 0C. With increase in operating temper- ature, the threshold stress σo decreases (Gonzalez and Sherby, 1993; Cadek et al. 1998) and the creep parameter M increases (Table-1), as a result of which the strain rates in the composite cylinder increase to a significant extent. The effect of temperature on the creep rate observed in this study are similar to those reported by (Pandey et al. 1992) for Al- SiCP composites under uniaxial creep test. r (mm) (9b) Figure 9. Variation of strain rates in composite cylin- der for varying particle content of SiC (P = 1.7 µm, T = 350oC) r (mm) (10a) r (mm) (10b) r (mm) (10c) 30 The Journal of Engineering Research Vol. 6, No. 2 (2009) 20-32 6. Conclusions The present study has led to the following conclusions: . The steady state radial, tangential and axial stresses increases on moving from the inner to the outer radius of a thick walled composite cylinder. The stress distri- butions do not vary significantly for various combina- tions of particle size, particle content and operating temperature, except for some sizable variation observed in tangential and axial stresses with varying content of SiCP. . 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