**Published:** Jan 2000

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**Source: **STP1360-EB

Recently, Donoso and Landes proposed the existence of a common format equation (CFE) for developing calibration functions for two-dimensional fracture specimens. In the CFE approach, the relation between load, plastic displacement, and uncracked ligament size is expressed as the product of three terms: (1) a constraint factor, (2) a geometry and crack length-dependent function (*G*), and (3) a hardening function (*H*). The history-dependent component of the calibration functions, namely *H*, has been explored by the same authors, using two different hardening functions: a power law and a three-parameter function, designated as the LMN function. For the geometry function *G*, on the other hand, a power-law dependence on normalized ligament length, i.e., *G* ∝ (*b/W*)^{m} (where *W* is the specimen width), is used for all of the classical two-dimensional fracture specimens. This type of behavior for *G* has been derived from the GE EPRI Handbook equations and has also been observed experimentally. From such a relationship, a crack-length independent value of eta plastic, η^{pl} is obtained that is equal to the exponent *m*.

The application of a ductile fracture methodology requires, in addition to the calibration functions, the fracture toughness of the material, usually given by the *J-R* curve. The computation of *J*, according to standard procedures, needs both its elastic and plastic contributions. The elastic component is normally evaluated in terms of *K*, the stress-intensity factor for the geometry and test conditions. The plastic component of *J*, on the other hand, is equal to the area under the load-plastic displacement curve per unit net section area of specimen, multiplied by the plastic eta factor, η^{pl}. The purpose of this work is to extend the use of the CFE approach to the elastic region of the load-displacement curve of standard frac-ture specimens, focusing on both their elastic compliances and their elastic eta factors, η^{el}. The elastic compliances and the *G* functions of the predominantly bend-type geometries, i.e., SE(B), C(T), and SE(T) specimens, are compared, showing that the elastic and the plastic eta factors are practically equal. This allows one to evaluate *J* in these geometries in terms of total displacement. The same does not apply, however, to the tensile M(T) and DE(T) geometries. In addition, *K* factors will be derived for the bend-type geometries based on the dependence of the elastic compliance with ligament size.

**Keywords:**

fracture, elastic, plastic, unifying load, separation

**Author Information:**

Donoso, JR *Universidad Tecnica Federico Santa Maria, Valparaiso,*

Landes, JD *University of Tennessee, Knoxville, TN*

**Paper ID:** STP13393S

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP13393S