Issue34

A. Campagnolo et alii, Frattura ed Integrità Strutturale, 34 (2015) 190-199; DOI: 10.3221/IGF-ESIS.34.20

For s ≥ 0.25 mm the value of λ calculated from τ xy singularity (Tab. 1). Hence, realistic values of K II can be calculated. For s = 0 mm, in the discs case λ increases as t/a increases, this is in contrast to the plate results where the value of λ has a maximum for t/a = 0.25, and decreases as t/a increases. The values of λ are all significantly less than the theoretical value of 0.598 for a corner point singularity. Realistic values of K II can probably be calculated for t/a ≥ 0.25 mm. Realistic values of K III can be calculated from τ yz for s ≥ 1 mm. The results for s = 0 mm (Fig. 2) show that τ yz is slightly lower than τ xy for small x , and decreases as x increases. Realistic values of K III cannot be calculated. The presence of finite values of τ yz , linked to finite values of K III (Fig. 4), appears because of the appearance of mode I disclinations, which are rotations about the y axis. Differentiating the expression for the displacement U z gives the amount of this rotation which increases towards the crack tip, with a concomitant increase in τ yz at a surface. This accounts qualitatively for the observed distributions of τ yz at a surface. is close to the theoretical value of 0.5 for a stress intensity factor

t/a

s = 0 mm

s = 0.25 mm

s = 1 mm

disc

plate 0.538 0.527 0.523 0.520 0.517 0.515 0.513 0.512 0.510 0.510 0.509 0.508

disc

plate 0.498 0.498 0.498 0.498 0.498 0.498 0.498 0.498 0.498 0.498 0.498 0.498

disc

plate 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 plate 0.507 0.506 0.506 0.506 0.506 0.506 0.506 0.506 0.506 0.505 0.506 0.506

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

0.505 0.520 0.530 0.538 0.544 0.549 0.553 0.556 0.559 0.542 0.545 0.547

0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497

0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.497 0.508 0.506 0.507 0.507 0.506 0.506 0.506 0.506 0.507 0.506 0.506 0.507 disc

Table 1 : Values of λ for τ xy

, s is the distance from the surface in the z direction.

t/a

s = 0 mm

s = 0.25 mm

s = 1 mm

disc

plate

disc

plate

0.25

- - - - - - - - - - - -

- - - - - - - - - - - -

- - - - - - - - - - - -

- - - - - - - - - - - -

0.5

0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Table 2 : Values of λ for τ yz

, s is the distance from the surface in the z direction.

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