Just start to learn Fracture Mechanics

Hi Experts,
I am reading "BASIC fracture mechanics" which is a very simple book.
You must know this expression
sigmaY = KI/sqrt(2*pi*r)*cos(thita/2)*(1+sin(thita/2)*sin(3*thita/2))
and I think this is symmetric about thita = 0.
My questions:
Is the expression dirived from a rectangular (infinite or finite)
plate with a crack at the center and under a symmetric load system
case? There are different expressions For other cases, say
non-symmetric cases?
Thank you in advance.
Reply to
victor
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In article , victor writes
Yes, this is for 'Mode I' loading which is a pure opening mode of loading of the crack.
There is no 'geometry' here. The expression you quote is leading term of a mathematical series or expansion for stress in an elastic material that dominates the rest very close to the crack tip, i.e. as r approaches zero. The other terms in the series expansion involve other powers of r such as r^0, r^0.5 and so on, that become negligible as r approaches zero. The crack tip 'knows' about the geometry and loading through KI only. A finite plate with a central crack under tensile loading has a different KI to a plate with an edge crack with the tensile stress.
Yes, the loading of a crack is in general a combination of three modes of loading: symmetric opening or Mode I, as above, asymmetric sliding or Mode II and out of plane tearing or mode III. Modes II and III each have similar expression for the components of stress (and also displacement) that dominate very close to the crack tip. There are associated Mode II and Mode III stress intensity factors: KII and KIII. Hope this helps. Regards, Martin
Reply to
Martin Goldthorpe
Nobody answer me :( The book only shows a crack tip and some expressions including the above one, I want to know if the distribution of the stresses near the crack tip is the same or not for different loading and other conditions.
Reply to
victor
Thak you Martin, your explanation is helpful for me!
Reply to
victor
Thank you again. Can we use the above expression for the stress near the crack tip for all different geometry and loadings cases and the only difference is the KI value?
Reply to
victor
For brittle fracture mechanics, yes. Pierre
Reply to
Pierre Burry
Thank you Pierre!
Reply to
victor

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