للكاتبين :

M. M. I. Hammouda1 , A. S. Fayed2, I.G. El-Batanony1, M. H. Ata3, and H. E. M. Sallam2

1 Mechanical Eng. Dept., University of Engineering and Technology, Taxila, Pakistan

2 Materials Eng. Dept., Faculty of Eng., Zagazig University, Zagazig, Egypt

3 Mechanical Eng. Dept., Faculty of Eng., Al-Azhar University, Cairo, Egypt


An elastic two dimensional finite element analysis was used to evaluate the crack initiation

angle by calculating the normal and tangential crack tip relative displacement as well as mode

I and mode II stress intensity factors of a shortly kinked central slant crack with frictional

surfaces under compression-tension biaxial elastic loading plate. Three main crack angles

measured from the load direction, 45o, 60o and 75o and crack length to plate width equal to

0.3 with biaxial ratios from -1 to 1 with steps of -0.2 were investigated. The coefficient of

friction between the crack surfaces were 0, 0.25, 0.5, 0.75 and 1. The kink angle was assumed

from the main crack line in a counter clockwise direction and varied in increments of 10o

between -60 and +120o.The ratio of the kink length and the main crack length was

0.0065.The plane strain state was assumed.

The results showed that there was an analogy between the two methods, i.e. maximum mode I

stress intensity factor and maximum crack tip opening displacement, used in prediction the

first crack initiation angle. The variation of relative crack tip displacements and mode I and

mode II stress intensity factors were dependent on the type of the remotely applied biaxial

load and both main crack and kinking angles. In biaxially compression-tension loaded plates,

relatively sliding crack surfaces in contact showed opened crack tips only at positive kink

angles. For the same crack angle, the increase of friction coefficient resulted in a decrease in

crack tip opening displacements and mode I stress intensity factor. Increasing the algebraic

biaxiality ratio had the same effect of decreasing the friction coefficient.

The kink angle, at which mode I was a maximum, remained the same or changed slightly as

friction coefficient and/or biaxiality ratio increased. These measured kink angles were in the

range of 80o and 100o. The present results showed that these kink angles are in a good

agreement with those predicted and experimentally found in the literature.

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