PSI - Issue 21

O. Berk Aytuna et al. / Procedia Structural Integrity 21 (2019) 120–129 O. Berk Aytuna et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Stra in-time plots of the ma teria l during testing do not show linear behavior as shown in Fig. 5a . Curves are a lso serra ted due to the stra in jumps from PLC bands. Slopes of the curves after elastic deforma tion are a lso different and stra in-time plot of biaxia l testing shows a steeper stra in rise with time compared to the uniaxia l condition. Fig. 5b and 5c give the stra in changes from each PLC band clearly. For a given time interva l, the number of stra in jumps under uniaxia l loading is higher than the biaxia l condition, highlighting the importance of stra in path for PLC forma tion. Under shear dominated stress sta te (uniaxia l stretching), PLC effects seem to be clearer. Average st ra in jump under uniaxia l stretching is 0.0055 while it is 0.0059 under biaxia l stretching. Towards the end of the test, PLC bands cross each other in biaxia l condition, resulting in h igher stra in jumps than usua l. The stra in increase between two successive bands is only 0.001 under both uniaxia l and biaxia l conditions.

Fig. 6. Strain contribution of PLC bands versus total strain graph under uniaxial and biaxial condition (along ε xx direction).

Fig. 6 represents the stra in contribution of PLC bands to overa ll deforma tion. The contribution of a ll sta in jumps to the overa ll deforma tion in biaxia l and uniaxia l condition are 84% and 75%, respectively. Since the nega tive effects of the PLC bands in the deformation, such as nega tive stra in rate sensitivity, lower formability and poor surface finish, are known; the higher PLC contribution in biaxia l stretching is expected to affect the materia l more nega tively. However, the load-time and load-stra in graphs showed tha t the formability was unaffected with the stra in path change (Fig. 3). Under both conditions, materia l deformed until typica l fracture stra ins. Therefore, even the ma jority of stra in is loca lized to the PLC bands under both conditions; the overa ll formability does not depend on them significantly. Besides the stra in heterogeneity, a more sign ificant drawback of the PLC bands is the forma tion of shear bands. Under uniaxia l tension, the repetitive formation of PLC bands in a particular region of the sample leads to a shear band a t the same region (Fig. 7a). PLC bands create nucleation sites for the shear bands and this is a lso observed by Kang et a l. (2008) and Yoshida and Toyooka (2001). Shear stress sta te in uniaxia l case promotes full-sca le PLC bands that stretch through the whole gage length, whereas in biaxia l they form only to a limited extent because globa l shear stresses are zero (Fig. 4). The loca l resolved shear stresses cause slip and therefore PLC bands in biaxia l case, however they do not grow fully. In uniaxia l case, on the other hand, a collection of full-sca le PLC bands in the same region of the sample ava lanche into a shear band , where further shear stra ins accumulate (Fig. 7a). A single shear band in uniaxia l conta ins multiple PLC bands that appear as surface irregularit ies in Fig. 7a . The shear bands then cross each other, which a lso causes ca tastrophic fa ilure from the same regions. Conversely, there are no surface irregu larities or shear bands observed on the surface after biaxia l deforma tion. Fracture surfaces shown in Fig. 7b prove tha t the fracture and deforma tion mode of the uniaxia l tension is shear-based and rela tively brittle. Shear bands formed due to the PLC bands result in elonga ted sharp dimples. The fracture surface after biaxia l stretching has a typica l ductile fracture structure with round dimples (Fig. 7c).