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RESEARCH PAPERS

Deformation and Life Estimates for a Metal Matrix—Spherical Particulate Subjected to Thermomechanical Loading

[+] Author and Article Information
Russell J. McDonald

Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61820rjmcdona@uiuc.edu

Peter Kurath

Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61820

J. Eng. Mater. Technol 128(3), 401-418 (Jan 25, 2006) (18 pages) doi:10.1115/1.2209649 History: Received February 14, 2005; Revised January 25, 2006

Thermal cycling has been experimentally demonstrated to diminish the performance of many reinforced materials. The coefficient of thermal expansion mismatch is the driving force for the development of high self-equilibrating stresses and strains in the vicinity of the reinforcement. To glean the magnitude of these stresses, a simple geometry, a spherical particulate (SiC) in a spherical domain (aluminum W319) was investigated. A set of partitioned strain rate equations considered temperature dependent material properties for thermal, elastic, mechanical plastic, and creep plastic deformation. The mechanical plasticity model utilized an improved Armstrong-Fredrick kinematic hardening algorithm and a Fisher type rate dependent yield criteria. A hyperbolic sine relation proposed by Dorn (1954, “Some Fundamental Experiments on High Temperature Creep  ,” J. Mech. Phys. Solids, 3, pp. 85–116) was used to model creep deformation. A multidimensional residual stress state due to cooling from the molten state was considered in the simulations. Two damage parameters, Findley and equivalent plastic strain, were employed to estimate cyclic damage. While the life estimates are crude, they both predict finite lives for reasonable service temperature ranges.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Particulate’s temperature dependent coefficient of thermal expansion for alumina and silicon carbide (see Ref. 46)

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Figure 2

Particulate’s temperature dependent elastic modulus and Possion’s ratio for alumina and silicon carbide (see Ref. 46)

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Figure 3

Aluminum W319 matrix elastic modulus versus temperature

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Figure 4

One block of the strain control in an incremental step test

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Figure 5

Shear yield strength (obtained from incremental step tests) versus Fisher parameter with the optimized parameter values (dashed line)

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Figure 6

Temperature dependent backstress values, r(i) for i=1–3

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Figure 7

Relaxation tests with results from an optimized hyperbolic sine curve fit

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Figure 8

Effect of a ±10% variation in the activation energy for fully constrained uniaxial thermomechanical loading

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Figure 9

Lower center: Residual stress field of a composite simulation with a cooling time of 100,000s and a volume fraction of 0.1%. Upper left: A typical cycling history showing the current point of interest as the circle. Upper right: A trace of the cyclic stress versus mechanical strain at the material interface.

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Figure 10

Lower center: Residual strain field of a composite simulation with a cooling time of 100,000s and a volume fraction of 0.1%. The dashed lines indicate circumferential strains while solid lines indicate radial strain components. Upper left: A typical cycling history showing the current point of interest as the circle. Upper right: A trace of the cyclic stress versus mechanical strain at the material interface.

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Figure 11

Effect of cooling time on the initial residual stress field with a volume fraction of 0.1%

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Figure 12

Effect of cooling time on the residual strain components with a volume fraction of 0.1%. The x-axis range is smaller than other figures.

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Figure 13

Effect of volume fraction on the initial room temperature residual radial stress field with a cooling time of 100,000s

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Figure 14

Effect of volume fraction on the initial room temperature residual circumferential stress field with a cooling time of 100,000s

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Figure 15

Effect of the volume fraction on the initial room temperature residual deviatoric stress field with a cooling time of 100,000s. See Figs.  1314 for legends.

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Figure 16

Lower center: Stress field of a composite simulation after two complete cycles between room temperature and 400°C with a volume fraction of 0.1%

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Figure 17

Lower center: Residual strain field of a composite simulation after two complete cycles between room temperature and 400°C with a volume fraction of 0.1%. The dashed lines indicate circumferential strains while solid lines indicate radial strain components.

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Figure 18

Hysteresis loops at the material interface of a composite simulation with a volume fraction of 0.1%. The solid lines are radial stress and dashed lines are circumferential stress.

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Figure 19

Hysteresis loops at the material interface of a composite simulation with a volume fraction of 0.1%. The solid lines are radial stress and dashed lines are circumferential stress.

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Figure 20

Influence of volume fraction on the hysteresis loop at the material interface for the first two cycles

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Figure 21

Influence of volume fraction on the hysteresis loop at the material interface for the first two cycles

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Figure 22

Experimental isothermal fatigue results using the Findley parameter with a kf=0.3

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Figure 23

Experimental isothermal fatigue results normalized by the rate-temperature dependent shear yield strength, kM, using the Findley parameter

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Figure 24

Normalized Findley damage for composite simulations with various volume fractions and reversal times

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Figure 25

Normalized Findley damage for composite simulations with various volume fractions and reversal times

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Figure 26

Inelastic strain range versus number of cycles to failure for various cast aluminum alloys (see Ref. 54).

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Figure 27

Inelastic strain range for composite simulations with various volume fractions and reversal times

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Figure 28

Inelastic strain range for composite simulations with various volume fractions and reversal times

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Figure 29

Inelastic strain ranges versus cycles to failure for out-of-phase and in-phase thermomechanical fatigue experiments of various cast aluminum alloys (see Ref. 54)

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