### STP1189: Developing *J-R* Curves Without Displacement Measurement Using Normalization

Lee, K

*Graduate assistant and professor, University of Tennessee, Knoxville, TN*

Landes, JD

*Graduate assistant and professor, University of Tennessee, Knoxville, TN*

Pages: 35 Published: Jan 1993

**Abstract**

The method of normalization is used in a new inverse way to develop *J-R* curves from test records that contain only load-versus-crack length values with no measure of displacement. These data may represent a special case where measurement of crack length is easier experimentally than the measurement of displacement. The method of normalization uses the principle of load separation to relate the three variables of load, displacement, and crack length. This relationship is expressed by a functional form so that, given any of the two variables, the third can be determined. Previously, the method of normalization has been used to determine crack length when given only load and displacement; however, it can also be applied to determine displacement when given only load and crack length.

In this new way of applying normalization, some problems arise; namely, the calibration points needed to evaluate the functional form of normalized load are not available. A major thrust of this paper is to solve the problem of how to determine these calibration points. To do this, the method is first applied to data for which all of the three variables have been already determined. The displacement is assumed to be missing and the *J-R* curves are determined from only the load and crack length values; these *J-R* curves are then compared with the ones generated for the data with all of the variables available. Three methods of determining calibration points were used in the comparison. Of the three, an approach called the power law fit is the best for determining the calibration points. The method is then applied to data for which there are only load-versus-crack length data. The results of this study show that the method of normalization works well for developing *J-R* curves from load-versus-crack length data.

**Keywords:**

fracture mechanics, fatigue (materials), J-R, curve, normalization, fracture toughness, displacement, loads, crack length, empirical formula, power law

**Paper ID:** STP24268S

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP24268S

ASTM International is a member of CrossRef.