Derivation of 'gamma' parameter from limit load expression of cracked component to evaluate J-R curve

Experimental evaluation of the J-integral requires the 'eta (pl)' function, proposed by Rice et al. [Progress in flaw growth and fracture toughness te sting (1973) 231], to multiply the area under the load vs. plastic load-lin e-displacement curve. However, the J-integral, thus evaluated, requires mod ification if crack growth occurs. A 'gamma' term was proposed by Hutchinson and Paris [Elastic-plastic fracture (1979) 37] and later generalised by Er nst et al. [Fracture mechanics (1979) 581] and Ernst and Paris [Techniques of analysis of load-displacement records by J-integral methods (1980)] to c orrect the J-integral to account for crack growth. The eta (pl), and gamma functions are available for very few geometries under specific loading cond itions. A limit load-based general expression of eta (pl) was given by Roos et al. [Int J Pres Ves Piping 23 (1986) 81], but no such expression is ava ilable for gamma functions. The advantage of having limit load-based genera l expressions for eta (pl) and gamma functions is that the limit load for a particular geometry subjected to a specific loading condition is easily av ailable in the open literature. In the present paper, a limit load-based ge neral expression for the gamma function is derived. The general expression is then validated by deriving the known gamma functions of various geometri es subjected to various loading conditions, which are available in the open literature. The general expressions are then used to derive new eta (pl) a nd gamma functions for same pipe and elbow geometries with various crack co nfigurations under different loading conditions, for which no solutions are available in the open literature. Finally, experiments have been carried o ut on 200 mm. nominal bore (NB) elbows with throughwall circumferential cra cks under in-plane bending moment. The proposed new expressions of eta (pl) and gamma functions for this geometry are used to obtain the J-R curve fro m the experimental load vs. load-line-displacement and load vs. crack growt h data. (C) 2001 Elsevier Science Ltd. All rights reserved.