By Emmanuel E. Gdoutos (auth.)
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Extra info for Fracture Mechanics: An Introduction
14. An infinite periodic array of equally spaced cracks in an infinite plate subjected to equal uniform stresses u at infinity. Observe that negative values of >. are ignored since they produce infinite displacements at the crack tip. Furthermore, use the result that the total strain energy contained in any circular region surrounding the crack tip is bounded to show that the value >. = 0 should also be excluded from the solution. 2. Show that the Airy stress function U = Cr312 ( cos -0 2 1 30) 2 +3 cos - corresponds to a semi-infinite mode I crack with the crack faces at 0 unloaded.
Theoretical methods are generally restricted to plates of infinite extent with simple geometrical configurations of cracks and boundary conditions. For more complicated situations one must resort to numerical or experimental methods. Description of these methods is outside the scope of the present book. 4]. To obtain an idea of stress intensity factor solutions 28 Chapter 2 y 8 12b A 1 X ~--------2a--------~ Fig. 7. Elliptical crack with axes 2a and 2b. 1. 6]. 6. Three-dimensional cracks So far, attention has been paid only to the problem of a plane crack extending through the thickness of a flat plate.
Fiffi sin (3 cos (3 . 23. 24). fiffi 2 . 47 Linear Elastic Stress Field in Cracked Bodies I I y 1 A~========~B---x l--2a----l I I I I I I I I I I Fig. 24. A crack of length 2a in an infinite plate subjected to a linear stress distribution at infinity. c -----l 1---b-t (] (] T T a---t---a ·I Fig. 25. A crack of length 2a in an infinite plate subjected to a unifonn nonnal stress u and shear stress Tfromx =±btox= ±a. 24. 5 to detennine the stress intensity factor for a crack of length 2a in an infinite plate subjected to unifonn normal stress (J and shear stress r along the upper crack surface from x = b to x = c.
Fracture Mechanics: An Introduction by Emmanuel E. Gdoutos (auth.)