Issue 49

S. Pereira et alii, Frattura ed Integrità Strutturale, 49 (2019) 450-462; DOI: 10.3221/IGF-ESIS.49.43 453 Using the boundary conditions (2), one can solve the equation for given pin displacements (W1, W2 and W3). ( ) ( ) 1 0 ' 1 0 0 0 w x w x =   =  (2a) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 1 ' ' 1 1 2 1 '' '' 1 1 2 1 1 w x w x W w x w x w x w x = =   =   =  (2b) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 3 2 ' ' 2 2 3 2 '' '' 2 2 3 2 2 w x w x W w x w x w x w x = =   =   =  (2c) ( ) ( ) ( ) ( ) ( ) ( ) 3 3 4 3 ' ' 3 3 4 3 '' '' 3 3 4 3 3 w x w x W w x w x w x w x = =   =   =  (2d) ( ) ( ) '' 4 4 ''' 4 4 0 0 w x w x  =   =  (2e) Knowing the shape of the deformed beam, the axial strain at any point can be determined by (3): 2 2 x d w z dx  = − (3) where x  is the axial strain, and z is the radial coordinate of the point. If z is the radius of the wire, the resulting strain will be the surface strain (which has the highest absolute value, at each cross-section). With (3), one can reverse the computations and find what pin displacements are needed in order to obtain a constant strain in section 2, [10]. Instead of using the strain, one can also use the radius of curvature of the beam (  ), which can be obtained by: 2 2 1 d w dx  = (4) Uniaxial Tension Test The uniaxial tension tests, with or without a hysteresis cycle, were performed with a nominal strain rate of 1 0.1min  − = and the measurement on the extension, which later was converted to nominal strain, were obtained using a clip gauge. Only the wire of 0.58mm was used in this testing due to the slenderness of the thinner one with 0.25mm. Besides the uniaxial tension test until rupture, the specimen was also subjected to one hysteresis cycle in order to determine their superelastic properties. The full hysteresis cycle can be obtained from loading the specimen in the elastic domain until the full transformation from Austenite into Martensite, and then reversing the process by unloading the specimen Rotary Bending Test The rotary fatigue bending tests were performed in the machine mentioned above and with a rotational speed of 500rpm (8.33 Hz). As it is a rotary fatigue test, the average stress is 0 m  = and the fatigue ratio is 1 min max R   = = − .