Fracture mechanics, stress intensity, fracture toughness

[DJ2019]

Homework Statement

7. A ship’s deck is provided with longitudinal strips of high toughness material for crack arrest purposes. The strips are welded in the deck and of equal thickness to it. The strip material has toughness 170 MN m-3/2 and yield stress 550 MPa, while the deck plate has toughness 55 MN m-3/2 and yield stress 320 MPa. If the highest “yearly wave” encountered produces a deck stress of 95 MPa:
(i) What size crack in the deck plate will cause fracture thereof?
(ii) How far apart should the crack arrest strips be placed to be safe? Ignore dynamic effects and assume the deck is wide.

Relevant Equations

Fracture toughness

I've been giving this some thought. It's clear that the stiffners will increase the resistance of the material so that the energy release is no longer high enough to cause further fracture. I'm just not sure what formula I can use to take into account the new resistance. I suspect part 1 of the question is just looking for use of the fracture intensity formula using the fracture toughness value as K. Could it be that simple?

 

[haruspex]

Homework Statement:: 7. A ship’s deck is provided with longitudinal strips of high toughness material for crack arrest purposes. The strips are welded in the deck and of equal thickness to it. The strip material has toughness 170 MN m-3/2 and yield stress 550 MPa, while the deck plate has toughness 55 MN m-3/2 and yield stress 320 MPa. If the highest “yearly wave” encountered produces a deck stress of 95 MPa:
(i) What size crack in the deck plate will cause fracture thereof?
(ii) How far apart should the crack arrest strips be placed to be safe? Ignore dynamic effects and assume the deck is wide.
Homework Equations:: Fracture toughness

I've been giving this some thought. It's clear that the stiffners will increase the resistance of the material so that the energy release is no longer high enough to cause further fracture. I'm just not sure what formula I can use to take into account the new resistance. I suspect part 1 of the question is just looking for use of the fracture intensity formula using the fracture toughness value as K. Could it be that simple?

You might have better luck posting this in the engineering homework forum.

 

[berkeman]

You might have better luck posting this in the engineering homework forum.

Moved.