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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, ηpl 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, ηpl. 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, ηel. 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.
fracture, elastic, plastic, unifying load, separation
Universidad Tecnica Federico Santa Maria, Valparaiso,
University of Tennessee, Knoxville, TN