PSI - Issue 33

V. Di Cocco et al. / Procedia Structural Integrity 33 (2021) 1035–1041 Author name / Structural Integrity Procedia 00 (2019) 000–000

1039

5

a)

b)

Fig. 2. Measured and calculated austenite and martensite quantity for the cycle: a) loading condition, b) unloading condition

In Fig. 2 the measured quantity of austenite and martensite are compared to the model results for cycle 1 in loading and in unloading conditions. It is possible to define a function that returns the amount of austenite that is transforming into martensite simply by deriving equation (2), obtaining the equation (4) � � � � � � �� �� �� ��� � (4) For example, considering only the young modulus of austenite EA, during the transformation the real modulus EAR is reduced by an amount that takes into account the fraction of austenite that is being transformed into martensite as shown in equation 5 �� � ��� � � � � � � � (5) where A is the quantity of austenite (in volume fraction) and KA is an experimental coefficient which considers the real contribution of austenite that is transforming in martensite. In the same way it is possible to define the contribution of the transformation of martensite into austenite. Assuming a parallel stiffness model, the real modulus of elasticity of the shape memory alloy can be expressed as the sum of the contributions due to austenite and martensite as expressed by the equation (6) � ��� � � � � � � � � ��� � � � � �� � (6) where KM is the coefficient associated with the martensite transformation and EM is the young modulus of martensite. In alloys where there is a direct transformation of austenite in martensite or the martensite in austenite without intermediate phases, the derivative of transformation is the opposite values calculated in (4) Using this modeal the camparison between the measured curves in loading and in unloading conditions and the calculated ones is shown in Fig. 3