ON LINEAR ELASTIC STRAIN ENERGY-RELEASE RATE AND THE J-INTEGRAL
ON LINEAR ELASTIC STRAIN ENERGY-RELEASE RATE AND THE J-INTEGRAL
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Date
1986
Authors
ALIYU, ABDU ABDULLAHI,
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Abstract
A brief review of the trend in Fracture Mechanics
studies was provided. Some solutions of elementary
fracture mechanics problems were re-investigated. Many
of those solutions were shown to have some limitations.
These limitations were in the form of introducing some
unrealistic stress and displacement distributions. The
general applicability of the strain energy-release rate
and the J-integral as crack tip parameters are based on
viewing the stress and strain fields at the crack tip
with an appropriate rationale. Therefore, based on the
elementary problems considered and their reported
solutions, some inconsistencies in the application and
interpretation of the Irwin crack extension force, G
and the J-integral as crack tip parameters, were pointed
out.
For the purpose of eliminating some of the limitations
noted in the review, a plane quasi-static problem
was reconsidered. By employing the well-known Kolosov-
Muskhelishvili equations, some new formulae were derived.
The new formulae are, in fact, the generalized Westergaard
formulae. It was furthermore proved that the
new formulae satisfy all necessary equations of motion
and conditions of plane elasticity.
Applying the new formulae, some special problems in
both the main body of the thesis and the appendix, were
solved. From the problems considered, the crack extension
force, G, was evaluated from the new solutions developed.
Furthermore, a new crack tip characterizing parameter, denoted by I,
(after G.R. Irwin) was developed. The effect of biaxial loading
on the Irwin crack tip parameter, I, was investigated.
It was furthermore shown that characterization via
the crack extension force concept is equivalent to
crack tip characterization via the Irwin parameter.
Also from the problems considered, the J—integral
was investigated. For all the cases considered, it
was shown that the J-integral at a crack tip is not
equal to the Irwin crack extension force, G, at the
same crack tip. From the solutions again, by consi—
dering some appropriate rationale, the J-integral was
shown to yield unrealistic results for some loadings.
Finally, some experiments were conducted on glass
to determine its fracture toughness values. All the
experiments were conducted at room temperature and a
loading rate of 2.0 cm/min. From the different
experiments conducted, consistent values of the
fracture toughness values were obtained. A critical
strain energy-release rate, G1 = 6.93 N/m and a
critical Irwin parameter, I1c = 997.6 x 103 N/m1/for the glass were obtained.
Description
ALIYU, ABDU ABDULLAHI (B.Eng.Mechanical,
A.B.U.; M.Eng. Mechanical, A.B.U.; M.Sc.
Mechanical, I.I.T., Chicago).
Submitted in Partial Fulfillment of
the Requirements for the Degree of Doctor
of Philosophy (Ph.D.) in Mechanical Engineering
of Ahmadu Bello University, Zaria, Nigeria.
1986
Keywords
LINEAR,, ELASTIC,, STRAIN,, ENERGY-RELEASE,, J-INTEGRAL