Steady State Creep

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T. Mori - One of the best experts on this subject based on the ideXlab platform.

  • Steady-State Creep of a composite
    Mechanics of Materials, 2001
    Co-Authors: A Madgwick, T. Mori, Philip J. Withers, K. Wakashima
    Abstract:

    The termination of composite Creep, when no sliding or diffusion can occur on matrix/inclusion interfaces and plastic volume strain constancy is maintained at every point, is addressed. A Fourier analysis is presented which shows that for a non-uniform distribution of plastic strain the elastic energy increases with increasing macroscopic plastic strain. This indicates that Steady-State Creep is not possible in such a material. Hutchinson's analysis of polycrystalline plasticity is also adapted to reach the same conclusion, by giving some grains an infinitely large flow stress; namely, those grains equivalent to elastic inclusions, on whose interfaces with the matrix neither sliding nor diffusion occurs. The Creep strain, at which Creep in a composite terminates, is determined. If the above conditions are abandoned, Creep can proceed. This is discussed with various examples. Structural changes such as interface debonding and inclusion fracture are discussed as possible causes of continued Creep in a composite. It is also pointed out that sliding and diffusion on matrix inclusion interfaces is also a necessary condition for thermal cycle ratcheting.

  • Model-neutron diffraction strain measurement comparisons for Steady State Creep of metal matrix composites
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2000
    Co-Authors: Ah Madgwick, T. Mori, Philip J. Withers
    Abstract:

    Mori and coworkers have developed a model for the prediction of the Steady State Creep rate of discontinuous composites based on the Eshelby model. This model recognizes that matrix Creep can only achieve Steady State Creep when relaxation processes at the inclusion/matrix interface balance the rate of build up of internal stress. In this paper we follow through the implications of this model for the level of the average matrix stress attained in the Steady State as a function of the applied load. We compare the predictions with direct measurements of the matrix stress by neutron diffraction. The model indicates that the composite Creep exponent should be less than the Creep exponent of the unreinforced matrix provided neither debonding nor inclusion cracking occurs. This is observed experimentally for the composites under the conditions studied.

  • Steady State Creep of a particulate sic 6061 al composite
    Acta Materialia, 2000
    Co-Authors: K. Wakashima, T Moriyama, T. Mori
    Abstract:

    Abstract The Creep behavior of a 10 vol.% silicon carbide particulate reinforced 6061 Al composite produced by powder metallurgy (PM) has been examined by Creep tests in both tension and compression at 400°C. The tensile Creep data covering minimum Creep rates of the orders 10 −9 to 10 −4 /s show an apparent stress exponent n app ≈13, but a comparison with compressive Creep data reveals that some high strain-rate data in tension are due to the transition to the tertiary stage. Analysis of the data is made only for the Steady-State Creep rate, together with that for an unreinforced PM 6061 Al alloy, by incorporating a threshold stress. This gives a stress exponent n =3 for the matrix alloy, whereas the composite data show such a trend that the n value gradually changes from 3 to 1 as the effective stress increases. A new method of Steady-State Creep data analysis is formulated by taking account of the interface-confined diffusional flow and thereby the finding above is reasonably assessed.

  • Steady-State Creep of a particulate SiC/6061 Al composite
    Acta Materialia, 2000
    Co-Authors: K. Wakashima, T Moriyama, T. Mori
    Abstract:

    Abstract The Creep behavior of a 10 vol.% silicon carbide particulate reinforced 6061 Al composite produced by powder metallurgy (PM) has been examined by Creep tests in both tension and compression at 400°C. The tensile Creep data covering minimum Creep rates of the orders 10 −9 to 10 −4 /s show an apparent stress exponent n app ≈13, but a comparison with compressive Creep data reveals that some high strain-rate data in tension are due to the transition to the tertiary stage. Analysis of the data is made only for the Steady-State Creep rate, together with that for an unreinforced PM 6061 Al alloy, by incorporating a threshold stress. This gives a stress exponent n =3 for the matrix alloy, whereas the composite data show such a trend that the n value gradually changes from 3 to 1 as the effective stress increases. A new method of Steady-State Creep data analysis is formulated by taking account of the interface-confined diffusional flow and thereby the finding above is reasonably assessed.

  • Steady-State Creep of a composite analysed by an energy balance method
    Philosophical Magazine Letters, 1998
    Co-Authors: T. Mori, M. Taya, K. Wakashima
    Abstract:

    The purpose of this paper is to analyse Steady-State Creep of a composite with spheroidal inclusions aligned along a tensile direction. It is an extension of a previous study of two-dimensional Creep by Mori et al . (1997, Phil. Mag. Lett ., 75, 359). As in the previous study, interfacial diffusion and sliding play essential roles in inducing Steady-State Creep. A new method of analysis is introduced. Basically, it calculates energy dissipation rates from the rates of diffusional flow and sliding. Both rates are geometrically connected to a Creep rate, in a manner depending on the shape of inclusions. By specifying the matrix Creep law, a simple relation between the Steady-State Creep rate and an external tensile stress is obtained. Coble Creep is also analysed as a simple and extreme case to which the present method can apply: grains in a polycrystal are treated as inclusions and deformation of plastic character is achieved by boundary diffusion and sliding.

Rajiv S. Mishra - One of the best experts on this subject based on the ideXlab platform.

  • Steady State Creep behaviour of an AlAl2O3 alloy
    Acta Materialia, 1997
    Co-Authors: A.b. Pandey, Rajiv S. Mishra, A.g. Paradkar, Y. R. Mahajan
    Abstract:

    Abstract The Al Al 2 O 3 alloy produced by powder metallurgy route has been tested under compression Creep in the temperature range 573–723 K to evaluate the Steady-State Creep mechanisms. The Steady State Creep data covering almost five orders of magnitude in Creep rate shows to distinct regimes of Creep deformation at all the temperatures. In the high stress regime (region-II), the Creep data shows high and variable apparent stress exponents, 25–30 and high apparent activation energy, 372 kJ/mol. However, in the low stress regime (region-I), the lower values of stress exponents, 7–11 and activation energy, 85 kJ/mol are observed. The TEM micrographs of the uncrept and crept specimens exhibit subgrains with Al 2 O 3 particles lying on the subgrain boundaries. The high stress regime data was examined in terms of pipe-diffusion controlled constant substructure Creep model and thermally activated detachment controlled dislocation Creep model. The detachment controlled dislocation model can describe the present data more successfully. The low stress regime data was analyzed according to the thermally activated detachment controlled diffusional Creep model and pipe-diffusion controlled stress dependent substructure model. Thermally activated detachment controlled diffusional Creep mechanism appears to be more appropriate for the present data.

  • Steady State Creep behaviour of particulate-reinforced titanium matrix composites
    Acta Materialia, 1996
    Co-Authors: S. Ranganath, Rajiv S. Mishra
    Abstract:

    Abstract The Steady State Creep behaviour of unreinforced Ti, TiTi 2 C and TiTiBTi 2 C composites has been examined in the temperature range 823–923 K. It is shown that the Creep deformation of unreinforced Ti is governed by climb-controlled Creep mechanism for which the stress exponent is between 4.1 and 4.3 and the activation energy is 236 kJ mol −1 . For composites, the stress exponents are between 6 and 7 at 823 K but are similar to unreinforced Ti at 923 K. The measured Steady State Creep rate of composites is found to be 2–3 orders of magnitude lower than unreinforced Ti in the investigated temperature range. It is then established that the origin of Creep strengthening at 823–923 K is due to the combined effects of increased modulus of composites and the refined microstructure. It is further shown that the change of stress exponent of composites at 823 K is because of the change in Creep mechanism from lattice-diffusion controlled dislocation climb to pipe-diffusion controlled dislocation climb. By analyzing the Creep data, a modification in the dimensionless constant, A = 3.2 × 10 5 exp(−24.2 V r ) for lattice-diffusion regime and A = 9.4 × 10 5 exp(−28.1 V r ) for pipe-diffusion regime, where V r is the volume fraction of reinforcements, is suggested to account for the influence of reinforcements on Creep kinetics.

  • An evaluation of Steady State Creep mechanism in an Al-Mg/26 Al2O3f composite
    Materials Science and Engineering: A, 1995
    Co-Authors: Rajiv S. Mishra, A.b. Pandey, Amiya K. Mukherjee
    Abstract:

    Abstract An analysis of the Steady State Creep data of Al-5Mg/Al 2 O 3f composite shows the substructure invariant Creep mechanism to be operative. This is consistent with the dislocation Creep mechanism map and a previous evaluation of Steady State Creep mechanism in 6061 Al/SiC composites. A temperature dependent threshold stress exists for the Steady State Creep mechanism.

  • Steady State Creep behaviour of a rapidly solidified and further processed al 5 wt ti alloy
    Acta Metallurgica Et Materialia, 1993
    Co-Authors: Rajiv S. Mishra, A.g. Paradkar, K. N. Rao
    Abstract:

    Abstract The Steady State Creep behaviour of rapidly solidified and further processed Al-5 wt% Ti alloy has been studied in the temperature range 573–673 K. The experiememtald ata exhibited apparent stress exponents of 7–8 and an apparent activation energy of 240 kJ mol−1. The results are analyzed using the semi-empirical power law, the substructure invariant model and an exponential law. The semi-empirical power law with a threshold stress and a stress exponent of 5 is found to be the best representation for Steady State Creep of such alloys. By analyzing literature data on the metallic/ intermetallic dispersion strengthened aluminium alloys, a modification in the dimensionless constant, A = 8.3 × 103 exp[−104√(b/L)], is suggested to account for the influence of dispersion on Creep kinetics. It is proposed that the attractive dislocation-particle interaction originates from the dissociation of lattice dislocations into interfacial dislocations when they enter the matrix-particle interface at high temperatures for climb by-pass.

  • Steady State Creep behaviour of a rapidly solidified and further processed Al-5 wt% Ti alloy
    Acta Metallurgica et Materialia, 1993
    Co-Authors: Rajiv S. Mishra, A.g. Paradkar, K. N. Rao
    Abstract:

    Abstract The Steady State Creep behaviour of rapidly solidified and further processed Al-5 wt% Ti alloy has been studied in the temperature range 573–673 K. The experiememtald ata exhibited apparent stress exponents of 7–8 and an apparent activation energy of 240 kJ mol−1. The results are analyzed using the semi-empirical power law, the substructure invariant model and an exponential law. The semi-empirical power law with a threshold stress and a stress exponent of 5 is found to be the best representation for Steady State Creep of such alloys. By analyzing literature data on the metallic/ intermetallic dispersion strengthened aluminium alloys, a modification in the dimensionless constant, A = 8.3 × 103 exp[−104√(b/L)], is suggested to account for the influence of dispersion on Creep kinetics. It is proposed that the attractive dislocation-particle interaction originates from the dissociation of lattice dislocations into interfacial dislocations when they enter the matrix-particle interface at high temperatures for climb by-pass.

K. Wakashima - One of the best experts on this subject based on the ideXlab platform.

  • Steady-State Creep of a composite
    Mechanics of Materials, 2001
    Co-Authors: A Madgwick, T. Mori, Philip J. Withers, K. Wakashima
    Abstract:

    The termination of composite Creep, when no sliding or diffusion can occur on matrix/inclusion interfaces and plastic volume strain constancy is maintained at every point, is addressed. A Fourier analysis is presented which shows that for a non-uniform distribution of plastic strain the elastic energy increases with increasing macroscopic plastic strain. This indicates that Steady-State Creep is not possible in such a material. Hutchinson's analysis of polycrystalline plasticity is also adapted to reach the same conclusion, by giving some grains an infinitely large flow stress; namely, those grains equivalent to elastic inclusions, on whose interfaces with the matrix neither sliding nor diffusion occurs. The Creep strain, at which Creep in a composite terminates, is determined. If the above conditions are abandoned, Creep can proceed. This is discussed with various examples. Structural changes such as interface debonding and inclusion fracture are discussed as possible causes of continued Creep in a composite. It is also pointed out that sliding and diffusion on matrix inclusion interfaces is also a necessary condition for thermal cycle ratcheting.

  • Steady State Creep of a particulate sic 6061 al composite
    Acta Materialia, 2000
    Co-Authors: K. Wakashima, T Moriyama, T. Mori
    Abstract:

    Abstract The Creep behavior of a 10 vol.% silicon carbide particulate reinforced 6061 Al composite produced by powder metallurgy (PM) has been examined by Creep tests in both tension and compression at 400°C. The tensile Creep data covering minimum Creep rates of the orders 10 −9 to 10 −4 /s show an apparent stress exponent n app ≈13, but a comparison with compressive Creep data reveals that some high strain-rate data in tension are due to the transition to the tertiary stage. Analysis of the data is made only for the Steady-State Creep rate, together with that for an unreinforced PM 6061 Al alloy, by incorporating a threshold stress. This gives a stress exponent n =3 for the matrix alloy, whereas the composite data show such a trend that the n value gradually changes from 3 to 1 as the effective stress increases. A new method of Steady-State Creep data analysis is formulated by taking account of the interface-confined diffusional flow and thereby the finding above is reasonably assessed.

  • Steady-State Creep of a particulate SiC/6061 Al composite
    Acta Materialia, 2000
    Co-Authors: K. Wakashima, T Moriyama, T. Mori
    Abstract:

    Abstract The Creep behavior of a 10 vol.% silicon carbide particulate reinforced 6061 Al composite produced by powder metallurgy (PM) has been examined by Creep tests in both tension and compression at 400°C. The tensile Creep data covering minimum Creep rates of the orders 10 −9 to 10 −4 /s show an apparent stress exponent n app ≈13, but a comparison with compressive Creep data reveals that some high strain-rate data in tension are due to the transition to the tertiary stage. Analysis of the data is made only for the Steady-State Creep rate, together with that for an unreinforced PM 6061 Al alloy, by incorporating a threshold stress. This gives a stress exponent n =3 for the matrix alloy, whereas the composite data show such a trend that the n value gradually changes from 3 to 1 as the effective stress increases. A new method of Steady-State Creep data analysis is formulated by taking account of the interface-confined diffusional flow and thereby the finding above is reasonably assessed.

  • Steady-State Creep of a composite analysed by an energy balance method
    Philosophical Magazine Letters, 1998
    Co-Authors: T. Mori, M. Taya, K. Wakashima
    Abstract:

    The purpose of this paper is to analyse Steady-State Creep of a composite with spheroidal inclusions aligned along a tensile direction. It is an extension of a previous study of two-dimensional Creep by Mori et al . (1997, Phil. Mag. Lett ., 75, 359). As in the previous study, interfacial diffusion and sliding play essential roles in inducing Steady-State Creep. A new method of analysis is introduced. Basically, it calculates energy dissipation rates from the rates of diffusional flow and sliding. Both rates are geometrically connected to a Creep rate, in a manner depending on the shape of inclusions. By specifying the matrix Creep law, a simple relation between the Steady-State Creep rate and an external tensile stress is obtained. Coble Creep is also analysed as a simple and extreme case to which the present method can apply: grains in a polycrystal are treated as inclusions and deformation of plastic character is achieved by boundary diffusion and sliding.

  • Steady-State Creep rate of a composite: Two-dimensional analysis
    Philosophical Magazine Letters, 1997
    Co-Authors: T. Mori, M. Taya, Y. Nakasone, K. Wakashima
    Abstract:

    A new method is proposed for calculating the Steady-State Creep rate of a composite, when the inclusion geometry and the matrix Creep law are known. The method is demonstrated in a simple two-dimensional problem. During Steady-State Creep, an increment in plastic strain in the matrix causes a jump in displacement on the interface between the matrix and an individual elastic inclusion. The jump is counterbalanced by that due to diffusion and sliding on the interface. The rate of diffusion is determined by a normal force distributed on the interface and that of sliding by a tangential force. From these forces, the average stress in the inclusions is calculated; it is proportional to the SteadyState Creep rate. From the condition that an external stress is a volumetric average of the stress in the inclusions and that in the matrix, the constitutive equation of stationary Creep of the composite is formulated.

M. M. Mostafa - One of the best experts on this subject based on the ideXlab platform.

  • Steady State Creep during transformation in al 1 wt cu alloy
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2009
    Co-Authors: M. M. Mostafa, M M Elsayed, H A Elsayed, H Abdelaleem
    Abstract:

    Abstract The Steady State Creep of Al–1 wt.%Cu alloy was studied under constant stresses ranging from 10.2 to 12.74 MPa in the temperature range from 553 to 673 K. The strain rate sensitivity parameter (m) varied from 0.2 to 0.42 in the tested temperature range, characterizing the dislocation climb along grain boundaries as the rate controlling mechanism. The activation energy 125.4 kJ/mol obtained in the temperature range from 633 to 653 K characterizes the grain boundary diffusion of Al atoms as the mechanism operating in this temperature range. The variations of the microstructural parameters support the suggested mechanisms to operate in the investigated Steady State Creep stage.

  • Steady State Creep during transformation in Al–1 wt.%Cu alloy
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2009
    Co-Authors: M. M. Mostafa, H. A. El-sayed, M.m. El-sayed, H. Abd-elaleem
    Abstract:

    Abstract The Steady State Creep of Al–1 wt.%Cu alloy was studied under constant stresses ranging from 10.2 to 12.74 MPa in the temperature range from 553 to 673 K. The strain rate sensitivity parameter (m) varied from 0.2 to 0.42 in the tested temperature range, characterizing the dislocation climb along grain boundaries as the rate controlling mechanism. The activation energy 125.4 kJ/mol obtained in the temperature range from 633 to 653 K characterizes the grain boundary diffusion of Al atoms as the mechanism operating in this temperature range. The variations of the microstructural parameters support the suggested mechanisms to operate in the investigated Steady State Creep stage.

  • Steady State Creep characteristics of the eutectic Pb–Sb alloy
    Physica B-condensed Matter, 2004
    Co-Authors: M. M. Mostafa
    Abstract:

    Abstract The change in the Steady State Creep rate of Pb–Sb eutectic alloy is studied under constant stresses ranging from 3.45 to 5.2 MPa and at different temperatures ranging from 433 to 503 K. The strain rate sensitivity parameter (m) varied between 0.33 and 0.46 in the testing temperature range. The activation energy of the Steady State Creep amounted to 96 kJ/mol in the temperature range from 473 to 503 K, characterizing the self-diffusion mechanism of Pb. The analysis of the microstructural variations confirms that the above-mentioned mechanisms are expected to take place during the investigated Steady State Creep stage.

  • Steady-State Creep and Creep recovery during transformation in Al-Zn alloys
    Physica B-condensed Matter, 2003
    Co-Authors: M. M. Mostafa, G.s. Al-ganainy, A.m. Abd El-khalek, R.h. Nada
    Abstract:

    Abstract The Creep and Creep recovery of Al–5 wt%Zn and Al–15 wt%Zn alloys have been investigated under different constant stresses near the transformation temperature. The temperature dependence of Steady Creep rate has shown two different transition points, at 393 K for Al–5 wt%Zn and at 473 K for Al–15 wt%Zn alloy. The stress exponent n was found to change from 6.4 to 4.2 for the first alloy and from 5.4 to 3.6 for the second alloy, respectively, characterising dislocation-slipping mechanism. The energy activating Steady-State Creep of the two alloys in the low and high temperature regions (below and above transformation temperature) characterizing as grain boundary diffusion in Zn and Al atoms, respectively. Microstructure analysis confirmed that the above-mentioned mechanisms took place during Steady-State Creep.

  • MICROSTRUCTURE DEPENDENCE OF Steady State Creep IN Cd-Sn EUTECTIC ALLOY
    Czechoslovak Journal of Physics, 2000
    Co-Authors: M. M. Mostafa
    Abstract:

    The Steady State Creep of Sn–33 wt.% Cd alloy was studied under various constant stresses ranging from 25.56 to 30.85 MPa in the temperature range from 353 to 433 K. The stress exponent n was found to change from 6.25 to 4.55 in the above temperature range. The energy activating the Steady State Creep amounted to 59.3kJ/mol in the temperature range from 353 K to 393 K and to 37 kJ/mol in the temperature range from 413 K to 433 K characterizing the grain boundary diffusion in Cd and in Sn, respectively. Microstructure analysis confirmed that the above mentioned mechanisms took place during Steady State Creep.

Henrik Lund Frandsen - One of the best experts on this subject based on the ideXlab platform.

  • Homogenization of Steady-State Creep of porous metals using three-dimensional microstructural reconstructions
    International Journal of Solids and Structures, 2015
    Co-Authors: Kawai Kwok, Dino Norberto Boccaccini, Åsa Helen Persson, Henrik Lund Frandsen
    Abstract:

    The effective Steady-State Creep response of porous metals is studied by numerical homogenization and analytical modeling in this paper. The numerical homogenization is based on finite element models of three-dimensional microstructures directly reconstructed from tomographic images. The effects of model size, representativeness, and boundary conditions on the numerical results are investigated. Two analytical models for Creep rate of porous bodies are derived by extending the Hashin–Shtrikman bound and the Ramakrishnan–Arunchalam model in linear elasticity to Steady-State Creep based on nonlinear homogenization. The numerical homogenization prediction and analytical models obtained in this work are compared against reported measurements and models. The relationship between Creep rate and porosity computed by homogenization is found to be bounded by the Hodge–Dunand model and the Hashin–Shtrikman Creep model, and closely matched by the Gibson–Ashby compression and the Ramakrishnan–Arunchalam Creep models.

  • computation of effective Steady State Creep of porous ni ysz composites with reconstructed microstructures
    Journal of the American Ceramic Society, 2015
    Co-Authors: Kawai Kwok, Peter Stanley Jørgensen, Henrik Lund Frandsen
    Abstract:

    This paper investigates the effective Steady-State Creep response of porous Ni–YSZ composites used in solid oxide fuel cell applications by numerical homogenization based on three-dimensional microstructural reconstructions and Steady-State Creep properties of the constituent phases. The Ni phase is found to carry insignificant stress in the composite and has a negligible role in the effective Creep behavior. Thus, when determining effective Creep, porous Ni–YSZ composites can be regarded as porous YSZ in which the Ni phase is counted as additional porosity. The stress exponents of porous YSZ are the same as that of dense YSZ, but the effective Creep rate increases by a factor of 8–10 due to porosity. The relationship of Creep rate and volume fraction of YSZ computed by numerical homogenization is underestimated by most existing analytical models. The Ramakrishnan–Arunchalam Creep model provides the closest approximation among all analytical models.

  • Computation of Effective SteadyState Creep of Porous Ni–YSZ Composites with Reconstructed Microstructures
    Journal of the American Ceramic Society, 2015
    Co-Authors: Kawai Kwok, Peter Stanley Jørgensen, Henrik Lund Frandsen
    Abstract:

    This paper investigates the effective Steady-State Creep response of porous Ni–YSZ composites used in solid oxide fuel cell applications by numerical homogenization based on three-dimensional microstructural reconstructions and Steady-State Creep properties of the constituent phases. The Ni phase is found to carry insignificant stress in the composite and has a negligible role in the effective Creep behavior. Thus, when determining effective Creep, porous Ni–YSZ composites can be regarded as porous YSZ in which the Ni phase is counted as additional porosity. The stress exponents of porous YSZ are the same as that of dense YSZ, but the effective Creep rate increases by a factor of 8–10 due to porosity. The relationship of Creep rate and volume fraction of YSZ computed by numerical homogenization is underestimated by most existing analytical models. The Ramakrishnan–Arunchalam Creep model provides the closest approximation among all analytical models.