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**Source: **STP36770S

The failure assessment diagram procedure for assessing the integrity of flawed structures evolved from the “two criteria” approach due to Dowling and Townley. The present form of the diagram, also referred to as the R-6 diagram, is due to Harrison, Loosemore, and Milne. Chell and Milne generalized the approach to account for thermal and residual stress and for crack growth problems, respectively. The failure assessment curve is obtained by using the Dugdale solution to interpolate between brittle fracture governed by *K*^{lc} and plastic collapse governed by the limit load *P*^{o}. This leads to a single failure curve in the R-6 approach. However, it should be noted that the Dugdale solution is intended for a finite crack in a thin infinite sheet subjected to remote tension and also assumes that the material is elastic-perfectly plastic.

Failure assessment diagrams can be determined directly using the estimation method and the *J*-controlled crack growth approach. The essential elements for constructing the diagrams are the elastic crack solutions (available in several elastic crack handbooks) and the fully plastic crack solutions for the specific crack configurations. It will be shown that the failure assessment equation can be obtained by rearranging the crack growth equilibrium equation associated with the J^{R}-curve approach. The more precise derivations show that the shape and position of the failure assessment curve depend on crack configuration, the relative size of the crack, type of loading, and material deformation properties. Explicit equations for failure curves are derived for elastic-strain hardening material and for elastic-strain hardening material with saturation stress.

Failure curves are constructed for several fracture test specimens and for axially and circumferentially flawed cylinders. The curves are generated for a practical range of deformation properties and crack length-to-width ratios. The usage of these curves is illustrated with several problems. Load-deformation and crack growth behavior of flawed structures can be determined (albeit indirectly!) from the failure curves for the specific structures being evaluated.

**Keywords:**

elastic-plastic fracture, failure assessment diagram, crack growth, J-integral, thermal stress, residual stress, J, R, -curve

**Author Information:**

Shih, CF *Visiting associate professor of engineering, Brown University, Providence, R.I.*

Kumar, V *Mechanical engineers, Corporate Research and Development, General Electric Co., Schenectady, N.Y.*

German, MD *Mechanical engineers, Corporate Research and Development, General Electric Co., Schenectady, N.Y.*

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP36770S