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.

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

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.

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?

PolyTech Forum website is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.