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A theoretical comparison of two possible shape memory processes in shape memory alloy reinforced metal matrix composite

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Abstract

Two possible shape memory processes, austenite to detwinned martensite transformation and twinned martensite to detwinned martensite transformation of a shape memory alloy have been modeled and examined. Eshelby’s equivalent inclusion method with Mori-Tanaka’s mean field theory is used for modeling of the shape memory processes of TiNi shape memory alloy reinforced aluminum matrix composite. The shape memory amount of shape memory alloy, plastic strain and residual stress in the matrix are computed and compared for the two processes. It is shown that the shape memory amount shows differences in a small prestrain region, but the plastic strain and the residual stress in the matrix show differences in the whole prestrain region. The shape memory process with initially martensitic state of the shape memory alloy would be favorable to the increase in the yield stress of the composite owing to the targe compressive residual stress and plastic strain in the matrix.

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Abbreviations

〈σ〉f :

Average stress in the fiber

〈σ〉m :

Average stress in the matrix

σo :

Applied stress

Ω:

Fiber domain

D :

Composite domain

e :

Strain disturbed by the existence of the inhomogeneity

ē:

Average elastic strain in the matrix

e*:

Equivalent eigenstrain of the equivalent inclusion

e c :

Total strain in the composite

e f :

Total strain in the fiber

e m :

Total strain in the matrix

e o :

Strain generated in the matrix without the inhomogeneity by applied stress

RF, RE :

Matrices for expressing the average fiber and matrix stresses

S :

Eshelby tensor

T :

Temperature

ɛTR :

Transformation strain along fiber direction

νf :

Poisson’s ratio of the fiber

〈dmf :

Critical stress at the finish of the conversion of the martensitic variants

〈dms :

Critical stress at the start of the conversion of the martensitic variants

〈f :

Effective stress of SMA fiber

ξTM-DTM :

Volume fraction of detwinned martensite transformed from austenite

ξTM-DTM :

Volume fraction of detwinned martensite transformed from twinned martensite

Δξ:

Incremental martensite volume fraction of the fibers

A f :

Austenite finish temperature

A s :

Austenite start temperature

C A :

Slope of stress and temperature curve for martensite to austenite transformation

C f :

Stiffness matrix of the fiber

C M :

Slope of stress and temperature curve for austenite to martensite transformation

e TR :

Transformation strain in vector notation

f :

Volume fraction of fibers

M f :

Martensite finish temperature

M s :

Martensite start temperature

εP :

Plastic strain along fiber direction

ΔεP :

Small increment of the plastic strain

σmy :

Yield stress of the matrix

σmy,0, K, n:

Constants of Ludwick equation for work-hardening matrix

Δσmy :

Increase in the yield stress of the matrix due to the small increment of the plastic strain

Cm :

Stiffness matrix of the matrix material

eP :

Plastic strain in vector notation

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Catholic University of Daegu, 712-702, Gyeongsansi, Gyeongbuk, Korea

    Jae Kon Lee & Gi Dae Kim

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  1. Jae Kon Lee
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  2. Gi Dae Kim
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Correspondence to Jae Kon Lee.

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Lee, J.K., Kim, G.D. A theoretical comparison of two possible shape memory processes in shape memory alloy reinforced metal matrix composite. J Mech Sci Technol 19, 1460–1468 (2005). https://doi.org/10.1007/BF03023905

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  • DOI: https://doi.org/10.1007/BF03023905

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