Relationship To Energy Release Rate and J-integral
The strain energy release rate for a crack under mode I loading is related to the stress intensity factor by
where is the Young's modulus and is the Poisson's ratio of the material. The material is assumed to be an isotropic, homogeneous, and linear elastic. Plane strain has been assumed and the crack has been assumed to extend along the direction of the initial crack. For plane stress conditions, the above relation simplifies to
For pure mode II loading, we have similar relations
For pure mode III loading,
where is the shear modulus. For general loading in plane strain, the relationship between the strain energy and the stress intensity factors for the three modes is
A similar relation is obtained for plane stress by adding the contributions for the three modes.
The above relations can also be used to connect the J integral to the stress intensity factor because
Read more about this topic: Stress Intensity Factor
Famous quotes containing the words relationship to, relationship, energy, release and/or rate:
“Women, because of their colonial relationship to men, have to fight for their own independence. This fight for our own independence will lead to the growth and development of the revolutionary movement in this country. Only the independent woman can be truly effective in the larger revolutionary struggle.”
—Womens Liberation Workshop, Students for a Democratic Society, Radical political/social activist organization. Liberation of Women, in New Left Notes (July 10, 1967)
“Every man is in a state of conflict, owing to his attempt to reconcile himself and his relationship with life to his conception of harmony. This conflict makes his soul a battlefield, where the forces that wish this reconciliation fight those that do not and reject the alternative solutions they offer. Works of art are attempts to fight out this conflict in the imaginative world.”
—Rebecca West (18921983)
“But often the presence of mind and energy of a person remote from the spotlight decide the course of history for centuries to come.”
—Stefan Zweig (18811942)
“The steel decks rock with the lightning shock, and shake with the
great recoil,
And the sea grows red with the blood of the dead and reaches for his spoil
But not till the foe has gone below or turns his prow and runs,
Shall the voice of peace bring sweet release to the men behind the
guns!”
—John Jerome Rooney (18661934)
“If you could choose your parents,... we would rather have a mother who felt a sense of guiltat any rate who felt responsible, and felt that if things went wrong it was probably her faultwed rather have that than a mother who immediately turned to an outside thing to explain everything, and said it was due to the thunderstorm last night or some quite outside phenomenon and didnt take responsibility for anything.”
—D.W. Winnicott (20th century)