EFFECT OF TEMPERATURE IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDER
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This paper examines the influence of temperature on the creep behavior of an isotropic uniform aluminum matrix composite cylinder under significant mechanical and thermal loads. The study reveals that varying the operating temperature affects stress and strain rates, demonstrating a notable decrease in effective, radial, and tangential strain rates as temperature is reduced. Additionally, it suggests optimizing particle size and content of reinforcement to improve the performance of composite pressure vessels subjected to high-pressure and high-temperature conditions.
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EFFECT OF TEMPERATURE IN ANALYSIS OF CREEP IN AN
ISOTROPIC UNIFORM COMPOSITE CYLINDER
Prof. Vyankatesh S. Kulkarni
Department of Mechanical Engineering,
Solapur University /BIT/Barshi/India
ABSTRACT
The following paper discusses the effect of temperature in analysis of creep in an isotropic
uniform composite cylinder. The paper is a part of the series of papers published under the
analysis of creep in an isotropic uniform composite cylinder.
INTRODUCTION
In 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 significant creep hence reduced service life (Gupta and
Phatak, 2001; Tachibana and Iyoku, 2004; Hagihara and Miyazaki, 2008). As an example, in the
high temperature engineering test reactor, the temperature reaches of the order of 900oC
(Tachibana and Iyoku, 2004). The piping of reactor cooling system are subjected to high
temperature and pressure and may be damaged due to high heat generated from the reactor core
(Hagihara and Miyazaki, 2008). A number of studies pertaining to creep behaviour of the
cylinder assume the cylinder to be made of monolithic material. However, under severe thermo
mechanical loads cylinder made of monolithic materials may not perform well. The weight
reduction achieved in engineering components, resulting from the use of aluminum/aluminum
base alloys, is expected to save power and fuel due to a reduction in the payload of dynamic
systems. However, the enhanced creep of aluminum and its alloys may be a big hindrance in
such applications. Aluminum matrix composites offer a unique combination of properties, unlike
many monolithic materials like metals and alloys, which can be tailored by modifying the
content of reinforcement. Experimental studies on creep under uniaxial loading have
demonstrated that steady state creep rate is reduced by several orders of magnitude in aluminum
or its alloys reinforced with ceramic particles/whiskers like silicon carbide as compared to pure
aluminum or its alloys (Nieh, 1984; Nieh et al, 1988). A significant improvement in specific
strength and stiffness may also be attained in composites based on aluminum and aluminum
alloys containing silicon carbide particles or whiskers. In addition, a suitable choice of variables
such as reinforcement geometry, size and content of reinforcement in these composites can be
used to make the cost-effective components with improved performance. With these
forethoughts, 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](https://image.slidesharecdn.com/1437308851volume2issue7-181127093007/85/EFFECT-OF-TEMPERATURE-IN-ANALYSIS-OF-CREEP-IN-AN-ISOTROPIC-UNIFORM-COMPOSITE-CYLINDER-1-320.jpg)
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developed to describe the steady state creep behavior of the composite cylinder. The developed
model is used to investigate the effect of material parameters viz particle size and particle
content, and operating temperature on the steady state creep response of the composite cylinder.
Fig. Schematic of closed end, thick-walled composite cylinder subjected to internal and
external pressures.
Fig. Free body diagram of an element of the composite cylinder
EFFECT OF TEMPERATURE
The creep in a material is significantly influenced by the operating temperature. Therefore, this
section brings out the effect of varying operating temperature on the stresses and strain rates in a
thick cylinder made of aluminum matrix composite reinforced with 20 vol% of SiCp. Figure 1
shows the variation of radial, tangential, axial and effective stresses in a composite cylinder
operating at three different temperatures i.e. 350 oC, 400 oC and 450 o C. Similar to the effect
observed for particle size (Fig. 2), the radial, tangential and axial stresses do not exhibit sizable
variation with the increase in operating temperature from 350 oC to 450 oC. The effect of
temperature on the stresses is not significant, except for a slight variation noticed for effective
stress. With the decrease in operating temperature from 450 oC to 350 oC, the compressive value
of tangential stress increases a little (around 2.5%) near the inner radius. It is interesting to
observe that in the middle of cylinder, the nature of tangential stress changes from compressive
to tensile. Further, this tensile value of tangential stress increases on moving towards the outer
radius of cylinder with the decrease in operating temperature from 450 oC to 350 oC. The
maximum increase observed is around 3%. The variation of axial stress is similar to that
observed for radial stress. It remains compressive throughout the cylinder, with maximum value](https://image.slidesharecdn.com/1437308851volume2issue7-181127093007/85/EFFECT-OF-TEMPERATURE-IN-ANALYSIS-OF-CREEP-IN-AN-ISOTROPIC-UNIFORM-COMPOSITE-CYLINDER-2-320.jpg)
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at the inner radius and minimum value at the outer radius. On the other hand, the effective stress,
near the inner radius, decreases marginally with the decrease in temperature from 450 oC to 350
oC; but it exhibits a marginal increase towards the outer radius with the decrease in temperature.
The stress difference (σe-σ0) shown in Fig. 3.13, decreases throughout the cylinder with
decreasing temperature. The maximum decrease observed in stress difference is around 12%
over the entire radius when the operating temperature decreases from 450 oC to 350 oC. The
effective, radial and tangential strain rates in the cylinder decreases by about two orders of
magnitude with the decrease in operating temperature from 450 oC to 350 oC. With decrease in
operating temperature, the threshold stress o increases and the creep parameter M decreases
(Table 1), as a result of which the strain rates in the composite cylinder decrease 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
Fig no 1 Variation of creep stresses in composite cylinder for varying temperature (V = 20
vol%, P = 1.7µm).
Fig No. 2 Variation of stress difference in composite cylinder for varying operating
temperature (V = 20 vol%, P = 1.7 µm).](https://image.slidesharecdn.com/1437308851volume2issue7-181127093007/85/EFFECT-OF-TEMPERATURE-IN-ANALYSIS-OF-CREEP-IN-AN-ISOTROPIC-UNIFORM-COMPOSITE-CYLINDER-3-320.jpg)
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Fig no 3 Variation of strain rates in composite cylinder for varying operating temperature
(V = 20 vol%, P = 1.7µm).
SELECTION OF MATERIAL PARAMETERS
It is evident from the above discussion that the creep stresses in a thick composite cylinder do
not vary significantly by varying size and content of reinforcement (SiCp) as compared to the
variation observed in strain rates. From The point of view of designing composite pressure
vessel, operating under elevated temperature, the strain rates are considered to be primary design
parameters. In order to reduce the steady state creep rates in the composite Cylinder, working
under a given set of operating conditions (i.e. operating pressure and temperature) any of the
following three options could be employed: (i) using finer size of reinforcement (SiCp) without
varying its content, (ii) incorporating higher amount of dispersoids (SiCp) without altering its
size, and (iii) simultaneously decreasing the size and increasing the amount of SiCp
reinforcement. The selection of optimum size and content of the reinforcement in a composite
pressure vessel, working under a given set of operating conditions, can be decided by
simultaneously optimizing the cost of composite and the value of maximum strain rate in the
composite cylinder for different combinations of particle size and particle content within the
specified range.
RESULTS AND DISCUSSION
Numerical calculations have been carried out to obtain the steady state creep response of the
composite cylinder for different particle size, particle content and operating temperature.
VALIDATION
Before discussing the results obtained, it is necessary to check the accuracy of analysis carried
out and the computer program developed. To accomplish this task, the tangential, radial and
axial stresses have been computed from the current analysis for a copper cylinder, the results for
which are available in literature (Johnson et al, 1961). The dimensions of the cylinder, operating](https://image.slidesharecdn.com/1437308851volume2issue7-181127093007/85/EFFECT-OF-TEMPERATURE-IN-ANALYSIS-OF-CREEP-IN-AN-ISOTROPIC-UNIFORM-COMPOSITE-CYLINDER-4-320.jpg)
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pressure and temperature, and the values of creep parameters used for the purpose of validation
are summarized in Table 2.
Table no.2 Summary of data used for validation (Johnson
To estimate the values of parameters
at the inner and outer radii of the cylinder by substituting the values of
obtained at these locations, as reported in The study of Johnson
stresses σr σθ and σz and the tangential strain r
and outer radii are substituted in Eqn. we know to estimate the effective strain rates
corresponding radial locations. The effective stresses and effective strain rates thus estimated at
the inner radius σe = 189.83MPa and
1.128x10-9
s-1
of the copper cylinder are substituted in creep law, Eqn. we obtained, to obtain the
creep parameters M and o for copper cylinder as given in Table 3.2. These creep parameters have
been used in the developed software to compute the distribution of tangential strain rate in the
copper cylinder. The tangential strain rates, thus obtained, have been compared wi
reported by Johnson et al (1961). A nice agreement is observed in Fig.
analysis presented and software developed in the current study.
REFERENCES
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mperature, and the values of creep parameters used for the purpose of validation
Summary of data used for validation (Johnson et al
To estimate the values of parameters M and o for copper cylinder, firstly σ e have
at the inner and outer radii of the cylinder by substituting the values of σe σr
obtained at these locations, as reported in The study of Johnson et al (1961). The values of
and the tangential strain rate έθ reported by Johnson et al (1961) at the inner
and outer radii are substituted in Eqn. we know to estimate the effective strain rates
corresponding radial locations. The effective stresses and effective strain rates thus estimated at
= 189.83MPa and έe = 2.168x10-8
s-1
and at the outer radius σ
of the copper cylinder are substituted in creep law, Eqn. we obtained, to obtain the
and o for copper cylinder as given in Table 3.2. These creep parameters have
been used in the developed software to compute the distribution of tangential strain rate in the
copper cylinder. The tangential strain rates, thus obtained, have been compared wi
(1961). A nice agreement is observed in Fig. 3 verifies the accuracy of
analysis presented and software developed in the current study.
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mperature, and the values of creep parameters used for the purpose of validation
et al)
have been calculated
r σθ σz in Eqn. we
(1961). The values of
(1961) at the inner
and outer radii are substituted in Eqn. we know to estimate the effective strain rates at the
corresponding radial locations. The effective stresses and effective strain rates thus estimated at
and at the outer radius σe = 116 MPa έe =
of the copper cylinder are substituted in creep law, Eqn. we obtained, to obtain the
and o for copper cylinder as given in Table 3.2. These creep parameters have
been used in the developed software to compute the distribution of tangential strain rate in the
copper cylinder. The tangential strain rates, thus obtained, have been compared with those
verifies the accuracy of
analysis for the FGM thick
cylinders under combined pressure and temperature loading, American J. of Applied Sci., 5
Analysis and performance of fiber composites,
Concept and P/M fabrication of functionally gradient
Properties of metal matrix composites, in: ASM Handbook, 21:
state creep of a pressurized thick
274.](https://image.slidesharecdn.com/1437308851volume2issue7-181127093007/85/EFFECT-OF-TEMPERATURE-IN-ANALYSIS-OF-CREEP-IN-AN-ISOTROPIC-UNIFORM-COMPOSITE-CYLINDER-5-320.jpg)
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EFFECT OF TEMPERATURE IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDER
- 1. NOVATEUR PUBLICATIONS INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT] ISSN: 2394-3696 VOLUME 2, ISSUE 7, JULY-2015 1 | P a g e EFFECT OF TEMPERATURE IN ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDER Prof. Vyankatesh S. Kulkarni Department of Mechanical Engineering, Solapur University /BIT/Barshi/India ABSTRACT The following paper discusses the effect of temperature in analysis of creep in an isotropic uniform composite cylinder. The paper is a part of the series of papers published under the analysis of creep in an isotropic uniform composite cylinder. INTRODUCTION In 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 significant creep hence reduced service life (Gupta and Phatak, 2001; Tachibana and Iyoku, 2004; Hagihara and Miyazaki, 2008). As an example, in the high temperature engineering test reactor, the temperature reaches of the order of 900oC (Tachibana and Iyoku, 2004). The piping of reactor cooling system are subjected to high temperature and pressure and may be damaged due to high heat generated from the reactor core (Hagihara and Miyazaki, 2008). A number of studies pertaining to creep behaviour of the cylinder assume the cylinder to be made of monolithic material. However, under severe thermo mechanical loads cylinder made of monolithic materials may not perform well. The weight reduction achieved in engineering components, resulting from the use of aluminum/aluminum base alloys, is expected to save power and fuel due to a reduction in the payload of dynamic systems. However, the enhanced creep of aluminum and its alloys may be a big hindrance in such applications. Aluminum matrix composites offer a unique combination of properties, unlike many monolithic materials like metals and alloys, which can be tailored by modifying the content of reinforcement. Experimental studies on creep under uniaxial loading have demonstrated that steady state creep rate is reduced by several orders of magnitude in aluminum or its alloys reinforced with ceramic particles/whiskers like silicon carbide as compared to pure aluminum or its alloys (Nieh, 1984; Nieh et al, 1988). A significant improvement in specific strength and stiffness may also be attained in composites based on aluminum and aluminum alloys containing silicon carbide particles or whiskers. In addition, a suitable choice of variables such as reinforcement geometry, size and content of reinforcement in these composites can be used to make the cost-effective components with improved performance. With these forethoughts, 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
- 2. NOVATEUR PUBLICATIONS INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT] ISSN: 2394-3696 VOLUME 2, ISSUE 7, JULY-2015 2 | P a g e developed to describe the steady state creep behavior of the composite cylinder. The developed model is used to investigate the effect of material parameters viz particle size and particle content, and operating temperature on the steady state creep response of the composite cylinder. Fig. Schematic of closed end, thick-walled composite cylinder subjected to internal and external pressures. Fig. Free body diagram of an element of the composite cylinder EFFECT OF TEMPERATURE The creep in a material is significantly influenced by the operating temperature. Therefore, this section brings out the effect of varying operating temperature on the stresses and strain rates in a thick cylinder made of aluminum matrix composite reinforced with 20 vol% of SiCp. Figure 1 shows the variation of radial, tangential, axial and effective stresses in a composite cylinder operating at three different temperatures i.e. 350 oC, 400 oC and 450 o C. Similar to the effect observed for particle size (Fig. 2), the radial, tangential and axial stresses do not exhibit sizable variation with the increase in operating temperature from 350 oC to 450 oC. The effect of temperature on the stresses is not significant, except for a slight variation noticed for effective stress. With the decrease in operating temperature from 450 oC to 350 oC, the compressive value of tangential stress increases a little (around 2.5%) near the inner radius. It is interesting to observe that in the middle of cylinder, the nature of tangential stress changes from compressive to tensile. Further, this tensile value of tangential stress increases on moving towards the outer radius of cylinder with the decrease in operating temperature from 450 oC to 350 oC. The maximum increase observed is around 3%. The variation of axial stress is similar to that observed for radial stress. It remains compressive throughout the cylinder, with maximum value
- 3. NOVATEUR PUBLICATIONS INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT] ISSN: 2394-3696 VOLUME 2, ISSUE 7, JULY-2015 3 | P a g e at the inner radius and minimum value at the outer radius. On the other hand, the effective stress, near the inner radius, decreases marginally with the decrease in temperature from 450 oC to 350 oC; but it exhibits a marginal increase towards the outer radius with the decrease in temperature. The stress difference (σe-σ0) shown in Fig. 3.13, decreases throughout the cylinder with decreasing temperature. The maximum decrease observed in stress difference is around 12% over the entire radius when the operating temperature decreases from 450 oC to 350 oC. The effective, radial and tangential strain rates in the cylinder decreases by about two orders of magnitude with the decrease in operating temperature from 450 oC to 350 oC. With decrease in operating temperature, the threshold stress o increases and the creep parameter M decreases (Table 1), as a result of which the strain rates in the composite cylinder decrease 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 Fig no 1 Variation of creep stresses in composite cylinder for varying temperature (V = 20 vol%, P = 1.7µm). Fig No. 2 Variation of stress difference in composite cylinder for varying operating temperature (V = 20 vol%, P = 1.7 µm).
- 4. NOVATEUR PUBLICATIONS INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT] ISSN: 2394-3696 VOLUME 2, ISSUE 7, JULY-2015 4 | P a g e Fig no 3 Variation of strain rates in composite cylinder for varying operating temperature (V = 20 vol%, P = 1.7µm). SELECTION OF MATERIAL PARAMETERS It is evident from the above discussion that the creep stresses in a thick composite cylinder do not vary significantly by varying size and content of reinforcement (SiCp) as compared to the variation observed in strain rates. From The point of view of designing composite pressure vessel, operating under elevated temperature, the strain rates are considered to be primary design parameters. In order to reduce the steady state creep rates in the composite Cylinder, working under a given set of operating conditions (i.e. operating pressure and temperature) any of the following three options could be employed: (i) using finer size of reinforcement (SiCp) without varying its content, (ii) incorporating higher amount of dispersoids (SiCp) without altering its size, and (iii) simultaneously decreasing the size and increasing the amount of SiCp reinforcement. The selection of optimum size and content of the reinforcement in a composite pressure vessel, working under a given set of operating conditions, can be decided by simultaneously optimizing the cost of composite and the value of maximum strain rate in the composite cylinder for different combinations of particle size and particle content within the specified range. RESULTS AND DISCUSSION Numerical calculations have been carried out to obtain the steady state creep response of the composite cylinder for different particle size, particle content and operating temperature. VALIDATION Before discussing the results obtained, it is necessary to check the accuracy of analysis carried out and the computer program developed. To accomplish this task, the tangential, radial and axial stresses have been computed from the current analysis for a copper cylinder, the results for which are available in literature (Johnson et al, 1961). The dimensions of the cylinder, operating
- 5. INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT] pressure and temperature, and the values of creep parameters used for the purpose of validation are summarized in Table 2. Table no.2 Summary of data used for validation (Johnson To estimate the values of parameters at the inner and outer radii of the cylinder by substituting the values of obtained at these locations, as reported in The study of Johnson stresses σr σθ and σz and the tangential strain r and outer radii are substituted in Eqn. we know to estimate the effective strain rates corresponding radial locations. The effective stresses and effective strain rates thus estimated at the inner radius σe = 189.83MPa and 1.128x10-9 s-1 of the copper cylinder are substituted in creep law, Eqn. we obtained, to obtain the creep parameters M and o for copper cylinder as given in Table 3.2. These creep parameters have been used in the developed software to compute the distribution of tangential strain rate in the copper cylinder. The tangential strain rates, thus obtained, have been compared wi reported by Johnson et al (1961). A nice agreement is observed in Fig. analysis presented and software developed in the current study. REFERENCES 1. Abrinia, K., Naee, H., Sadeghi, F., and Djavanroodi, F. cylinders under combined pressure and temperature loading, American J. of Applied Sci., 5 (7): 852–859. 2. Aggarwal, B.D., and Broatman, L.J. John Wiley, USA. 3. Akira, M., and Watabane, R. materials, Ceramics Int., 23: 73 4. Alman, D.E. (2001) Properties of metal matrix composites, in: ASM Handbook, 21: Composites, ASM International, Metals Park, Ohio, 5. 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The effective stresses and effective strain rates thus estimated at = 189.83MPa and έe = 2.168x10-8 s-1 and at the outer radius σ of the copper cylinder are substituted in creep law, Eqn. we obtained, to obtain the and o for copper cylinder as given in Table 3.2. These creep parameters have been used in the developed software to compute the distribution of tangential strain rate in the copper cylinder. The tangential strain rates, thus obtained, have been compared wi (1961). A nice agreement is observed in Fig. 3 verifies the accuracy of analysis presented and software developed in the current study. Abrinia, K., Naee, H., Sadeghi, F., and Djavanroodi, F. (2008) new analysis for the FGM thick cylinders under combined pressure and temperature loading, American J. of Applied Sci., 5 Aggarwal, B.D., and Broatman, L.J. (1980) Analysis and performance of fiber composites, Akira, M., and Watabane, R. (1997) Concept and P/M fabrication of functionally gradient materials, Ceramics Int., 23: 73–83. Properties of metal matrix composites, in: ASM Handbook, 21: Composites, ASM International, Metals Park, Ohio, 838–858. Altenbach, H., Gorash, Y., and Naumenko, K. (2008) Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges,Acta Mech., 195: 263–274. NOVATEUR PUBLICATIONS INTERNATIONAL JOURNAL OF INNOVATIONS IN ENGINEERING RESEARCH AND TECHNOLOGY [IJIERT] ISSN: 2394-3696 VOLUME 2, ISSUE 7, JULY-2015 5 | P a g e mperature, and the values of creep parameters used for the purpose of validation et al) have been calculated r σθ σz in Eqn. we (1961). The values of (1961) at the inner and outer radii are substituted in Eqn. we know to estimate the effective strain rates at the corresponding radial locations. 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