Shape Memory Alloys

Dr. Mohammad Tawfik

SMA Constitutive Relations

Martensite/Austenite Transformation

• In the absence of stresses, the martensite fraction is a function of the temperature only

• In the following we will present approximate expressions for the fraction in terms of temperature

Martensite/Austenite Transformation

• Let’s define the fraction of the martensite phase in the SMA as follows:

• For the range of

15.0

fs

f

MM

MTCos

sf MTM

Martensite/Austenite Transformation

• Similarly, we may write an expression for the transformation

15.0

sf

s

AA

ATCos

fs ATA

Martensite/Austenite Transformation

• For an arbitrary starting point, we may write the expression:

15.0

of

oo

TA

TTCos

ff ATM

Effect of Stresses

• Experiments have shown that the characteristic temperatures of the SMA are affected by the stresses.

• The effects are assumed linear as shown in the figure.

Effect of Stresses (AM)

• Thus, the expression for the martensite fraction may be written as:

• Where, CM is the slope of the linear relation for the Martenite temperature

o

fs

Mf

oMM

CMTCos

1

/15.0

fMSM MTCMTC

Effect of Stresses (MA)

• And, the expression for the martensite fraction may be written as:

• Where, CA is the slope of the linear relation for the Austenite temperature

1

/5.0

sf

Aso

AA

CATCos

sAfA ATCATC

Linear Region

SMlin MTC

A

SM

A

linlin

E

MTC

E