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, energy, release and/or rate:
“Christianity as an organized religion has not always had a harmonious relationship with the family. Unlike Judaism, it kept almost no rituals that took place in private homes. The esteem that monasticism and priestly celibacy enjoyed implied a denigration of marriage and parenthood.”
—Beatrice Gottlieb, U.S. historian. The Family in the Western World from the Black Death to the Industrial Age, ch. 12, Oxford University Press (1993)
“I rather think the cinema will die. Look at the energy being exerted to revive ityesterday it was color, today three dimensions. I dont give it forty years more. Witness the decline of conversation. Only the Irish have remained incomparable conversationalists, maybe because technical progress has passed them by.”
—Orson Welles (19151984)
“As nature requires whirlwinds and cyclones to release its excessive force in a violent revolt against its own existence, so the spirit requires a demonic human being from time to time whose excessive strength rebels against the community of thought and the monotony of morality ... only by looking at those beyond its limits does humanity come to know its own utmost limits.”
—Stefan Zweig (18811942)
“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)