Issue 29

M. Marino, Frattura ed Integrità Strutturale, 29 (2014) 96-110; DOI: 10.3221/IGF-ESIS.29.10

     







d 

0

if

d   





 

max 2   Loading ε [0,ε ] : ( ) 



d   

d 





if

<

(26)

D





D

 

if > 

d 





1

D

     





r 

1 if

>



  

r 

 



max 2   Unloading ε [ε ,0] : ( ) 







r 





r 

if

<

(27)

R





R

 

r   





0 if

R

with . The behavior of the alloy, as obtained from Eq. (24-27), is fully strain-rate independent. Moreover, due to the phase diagram in Fig. 1, reverse transformation occurs at positive stresses at high-temperature (namely, ( )> 0 r T   for > ro T T ), reproducing the characteristic pseudo-elastic behavior of SMAs in initial austenitic microstructure. Compression loading-unloading : 1 1 [2 , 4 ] t t   . In this case, the behavior of the alloy in terms of the stress-strain relationship and alloy composition is analogous to the traction behavior. In fact, it can be obtained from previous relationships by replacing 2  with 3  , D   with D   , R   with R   , d   with d   , r   with r   . It is worth pointing out that, in the compressive regime, = d de   is associated with loading conditions, and = d de  with un-loading ones. The full SMA stress-strain constitutive response, obtained by addressing the traction-compression loading-unloading cycle in Eq. (17) for 1 [0, 4 ] t   at high temperature 2 > > af ro T T T , is depicted in Fig. 5a. 1 2 ( )=1 ( )     

(a)

(b) Figure 5 : Stress  vs. strain  predicted by present model in a tensile-compressive loading-unloading test obtained from applied strain as in Fig. 2 at the high temperature 2 T (a) and at the low temperature 1 T (b) .

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