Advanced Fracture Mechanics: Lectures on Fundamentals of by Noel O’Dowd

By Noel O’Dowd

The primary objective of the direction is to supply scholars with a accomplished realizing of the tension research and fracture mechanics suggestions required for describing failure in engineering parts. furthermore, the path will clarify the way to follow those options in a security overview research. The path offers with fracture less than brittle, ductile and creep stipulations. Lectures are awarded at the underlying ideas and workouts supplied to offer event of fixing functional difficulties.

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Extra info for Advanced Fracture Mechanics: Lectures on Fundamentals of Elastic, Elastic-Plastic and Creep Fracture, 2002–2003

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2 The above is an illustration for perfect plasticity. There are more rigorous proofs, (given in Kanninen and Poplar) which show that in general for a low hardening material, η is close to 1 in tension and 2 in bending. Many crack geometries are loaded by a combination of bending and tension. g. 52(1 − a/W ). 4 η value for a linear elastic material We can also evaluate η for a linear elastic material. 14, Load-displacement curve for a linear elastic material For a linear elastic material: J =G= 1 2 dC(a) P , 2B da where C is the elastic compliance P = J= ∆ ∆ ⇒ P2 = P C C 1 ∆ dC 1 1 dC P = A 2B C da B C da and since the alternative equation for J is J= η A B(W − a) ⇒ ηe = W − a dC C da Thus if the compliance is known, ηe can be determined.

8 Overall J estimation procedure 55 The final form of the GE-EPRI J estimation scheme, is then J = Je (aeff ) + Jp (a, n), with Jp evaluated using the estimation scheme and Je evaluated using the plastic zone correction as discussed above, with ry based on the unmodified crack length, a. A comparison between the numerically calculated J value and the GE-EPRI approximation is shown in Fig. 18 (This figure is adapted from the figure on page 318 of Kanninen and Poplar). The GE-EPRI scheme can be used to estimate J in materials which obey power law hardening in the plastic regime.

5. Thus there is a one-to-one relationship between CTOD and J for a given material and any J based approach can be converted to a CTOD based approach. 7 Conventional definition of crack opening displacement The above equation is consistent with the expression introduced in FFM, δ= G . mσy Here the symbol m is used rather than dn and the elastic energy release rate G is used rather than J. The equivalence between G and J for small scale yielding conditions is discussed next. 4 Relationship between J and G It can be shown that J is in fact equal to the change in potential energy G for a nonlinear elastic material.

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