PSI - Issue 5

472 Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 468–475 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000 5 is schematically shown in Box 1. Notice that the input data must be provided for this algorithm consists of the linear elastic stiffness matrix 0 , external force vector f (according to Equation (1) and a properly defined tolerance, tol. For any given increment i Iteration n

= 0−1 = : ∆ = ∆ = 0 ∆ = +1 + ∆

Displacement field

Stress field

Stress return mapping algorithm

Actualization of variational fields

= − ∫ ∆ Ω Ω [∑ ( ) =1 ] . [∑ ( ) =1 ] −1 ≤ Go to the next load increment

Residual force

Check the condition

If YES

= Go to the next iteration

If NO

End of the test

Box 1. Non-linear solution algorithm.

2. Experimental test An AA6061-T6 Aluminum alloy bi-failure specimen was tested under tensile loading state performed by a standard servo-hydraulic system, MTS-812 machine with a frequency of = 5 ( ) , the geometry of the specimen is indicated in Fig. 1. Prior to performing the experimental test and as a requirement of DIC analysis, the specimen surface was painted in white color and sprinkled with black dots. Specific rods passing through holes positioned in the extremes of the specimen were used to connect the specimen to the MTS machine. A computer device was handled to collect images from two synchronized DIC cameras and the load cell. DIC cameras were hence calibrated with a 12-by-9 calibration pattern, 2.5 (mm). So, the experimental test was executed and the obtained data was accumulated in the DIC software. To analyze this data in the DIC processing software, a pair of points was selected on the central section with the following coordinates, 1 = (12.16, 6.60) and 2 = (12.16, 31.41) . The problem domain and interest points are presented in Fig. 3-a. The vertical displacement variation was thereby calculated on the selected points identified as 2 and 1 . The reaction force received from load cell in terms of the vertical displacement variation ( 21 = 2 − 1 ) was attained as seen in Fig. 3-b.

= 145 ( ) = 115 ( ) = 25 ( ) = 1 ( ) = 4 ( ) = 1.5 ( ) 1 = 3 ( ) 2 = 5 ( )

Fig. 1. A schematic view of the bi- failure specimen with its dimension’s demonstration.