PSI - Issue 13

Tomasz Brynk et al. / Procedia Structural Integrity 13 (2018) 1267–1272 Tomasz Brynk/ Structural Integrity Procedia 00 (2018) 000 – 000

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The algorithm allows to determine residual stress even when rigid body movement and rotation are superimposed to displacement fields determined from DIC measurements. Similar algorithm was used in Brynk (2013) to determine stress intensity factor and crack tip position during fatigue crack growth tests with miniaturized samples. 2.2. Displacement fields near drilled hole According to Makino (1994) general equations relating residual stress components with displacement fields are in the form: = ( + ) + [( − ) 2 + 2 2 ] (3) = [( − ) 2 − 2 2 ] (4) For the simplest case of blind hole drilling coefficients A, B and C are determined as following: = 0 2 (1 + ) (5) = 0 2 [4 − (1 + ) 3 ] (6) = 0 2 [2(1 − ) + (1 + ) 3 ] (7) However, there is no analytical solution available for more practical blind hole case. Nonetheless, corresponding A’, B’ and C’ coefficients might be delivered from Finite Element Modelling (FEM) in the way described in Makino (1994). Values of these coefficients are dependent not only on elastic constants but also on the hole shape and distance from the hole centre. FEM model has been developed to calculate A’, B’ and C’ coefficients for three drilling cases (h=0.5d, 0.75d and d). and different distance from the hole center. Model geometry presented in Fig. 1 depicted ¼ of sample gauge section shape and symmetric displacement boundary conditions were applied to appropriate areas. Simulations were done for 500 MPa uniaxial stress. Element death technique has been applied to simulate hole drilling process. FEM displacement field components for points of polar coordinates ( r,0° ) and ( r,45° ), for r= 1.5r 0 , 2 r 0 ….,6 .5r 0 were used to determine A’, B’ and C’ coefficients. According to Makino (1993) these coefficients are valid also for biaxial stress conditions. 2.3. FEM model

Fig. 1. FEM mesh

2.4. Experimental set-up Improved version of experimental set-up previously introduced in Brynk (2017) for samples loaded in bending mode is presented in Fig. 2. Testing set-up for 3D DIC assisted drilling was designed and build using aluminium profiles and appropriate connectors. It consisted on rigid translation table on which sample loading device was fixed. Before testing sample was pretrained to achieve 500 MPa strain based on attached extensometer readings. Two AVT Pike cameras were placed symmetrically to Dremel driller attached to the mechanism allowing to its movement in the direction perpendicular to pretrained sample surface. The mechanism was driven by a stepper motor and steered with Arduino microcontroller which allowed to precisely drill holes of desired depth as well as to remove the drilling head from the cameras observation field during images registration for DIC. High power LED lamp provided lightening of sample surface with speckle pattern applied by white and black paint spraying. Three images registered with approximately one second interval of sample after drilling the hole to desired depth were registered and processed in Vic3D software.