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

By Noel O’Dowd

The imperative goal of the path is to supply scholars with a complete realizing of the tension research and fracture mechanics innovations required for describing failure in engineering elements. moreover, the path will clarify easy methods to follow those recommendations in a security evaluate research. The direction offers with fracture lower than brittle, ductile and creep stipulations. Lectures are provided at the underlying ideas and workouts supplied to offer adventure of fixing functional difficulties.

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

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The additional subscript ‘C’ here emphasises that it is the solution for a cracked plate. Often the ‘C’ is left out. For a center cracked plate with crack length 2a and plate width 2W , in tension with a << W , subjected to a load 2P , the limit load under plane stress conditions, is given by PLC = σy (W − a)B. Limit load solutions are commonly used in fracture mechanics. The ratio between load and limit load is a measure of the extent of plasticity and provides a good means of compar2W ing two geometries.

The ratio between load and limit load is a measure of the extent of plasticity and provides a good means of compar2W ing two geometries. For example two different geometries at the same ratio of load to limit load have similar J integral values. 22 1 − W 3 46 2 W 2B . 2L This solution may be compared with that for a small crack under pure bending given earlier. 22 term in the equation is due to a finite sized crack. e. 5(σxx + σyy ) (in plasticity) then for von Mises yield, 2 2σvm = (σxx − σyy )2 + (σxx − σzz )2 + (σyy − σzz )2 √ ⇒ σvm = 3 σ 2 √ At yield σvm = σy , therefore for yielding under tension in plane strain σ = 2σy / 3, so √ the limit load is higher by a factor of 2/ 3 under plane strain conditions compared to plane stress conditions when the yield condition is simply σ = σy .

Here rp is the distance from the crack tip to the plastic zone boundary and σy is the material yield strength. 24(a) shows the numerically calculated elastic-plastic stress fields directly ahead of the crack for a plane strain analysis. Here equivalent (Von Mises) stress, σe , divided by yield strength, σy , is plotted so in the plastic zone σe /σy = 1. The estimated plane strain plastic zone size is indicated on Fig. 24(a). The numerically calculated value is somewhat less than this approximation.

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