International Journal of Fracture 57: 269-280, 1992. ~., 1992 Kluwer Academic Publishers. Printed in the Netherlands. 269 An integral formulation of C t for use in creep crack growth evaluation AN-YU KUO, 1 KUAN-LUEN CHEN, 1 ASHOK SAXENA 2 and ARVIND NAGAR 3 1Structural Integrity Associates, Inc. San Jose, California 95118, USA 2Mechanical Properties Research Laboratory, Georgia Institute of Technology, Atlanta, Georgia 30332-0245, USA aFlight Dynamics Laboratory, Wright-Patterson AFB, Ohio 45433, USA Received 10 March 1991; accepted in revised form 17 February 1992 Abstract. Ct has been found to be an effective parameter to characterize steady-state and transient creep crack growth rates. An integral formulation for computing Ct numerically is proposed in this paper, which complements existing Ct formulation used in laboratory measurements. 1. Introduction The C, parameter defined by Saxena [1] is a generalization of C* but is different from the C(t)-integral [2]. Ct generalizes upon the energy rate interpretation of C* as follows. Consider several identical pairs of cracked specimens. Within each pair, one specimen has a crack length a and the other has an incrementally larger crack length a + Aa. The specimen of each pair are loaded to various constant load levels P1, P2, P3, -.., Pi, etc. at elevated temperatures, and the load-line deflection as a function of time is recorded (Fig. la). The loadline deflection due to creep is Vc. It is assumed that no crack extension occurs in any of the specimens and the instantaneous response is linear elastic. At a fixed time, the load versus deflection rate f'c behavior is plotted for all specimens. A schematic of the expected behavior is shown in Fig. lb. Several such plots can be generated from these tests by varying time. The area between the P - f'c, curves for specimens with crack length a and a + Aa, is called AU* (the subscript denotes that this value is at a fixed time t). The Ct parameter is given by the following equation 1 ~U* Ct- BOa' (1) r~ y I s s~ - .- )5> v2>)i +A a _k ct=-~ ao Vo t Fig. 1. (a) Load line deflection, vc, as a function of time for bodies of crack lengths a and a + Aa at various load levels, and (b) the definition of the Ct parameter.