DEVELOPMENT OF PLASTIC ETA FACTORS FOR DEEP AND SHALLOW CRACKED BEND SPECIMENS EMPLOYED IN J-R CURVE TESTING Sebastian Cravero Fracture Mechanics and Structural Integrity Group -- NVFRAC Dept. of Naval Architecture and Ocean Eng., University of São Paulo e--mail: sebastian.cravero@poli.usp.br Claudio Ruggieri Fracture Mechanics and Structural Integrity Group -- NVFRAC Dept. of Naval Architecture and Ocean Eng., University of São Paulo e--mail: claudio.ruggieri@poli.usp.br Abstract. The stable tearing of a macroscopic crack in ductile materials for structural applications is conventionally characterized by crack growth resistance (J--R) curves. Under sustained ductile tearing of the (macroscopic) crack--like defect, large increases in the load-- carrying capacity of the structure, as characterized by resistance curves, are possible beyond the limits given by the crack driving force at theonsetofcrackgrowth.However,structuraldefectsareveryoftensurfacecracksthatformduringfabricationorduringin--serviceopera- tion. These crack configurations generally develop low levels of crack--tip stress triaxiality (crack--tip constraint) which contrasts sharply to conditions present in deeply cracked specimens thereby yielding low resistance curves and increased toughness properties. The above arguments have prompted research efforts to adopt the use of geometry dependent crack growth resistance curves so that crack--tip constraint in the test specimen closely matches the crack--tip constraint for the structural component. However, current standardized meth- ods to determine crack growth resistance properties based upon unloading compliance procedures employing a single specimen, such as ASTM E1820, utilize only bend--type specimens with deep cracks (crack size to specimen width ratios, a/W > 0.5), such as the C(T) and SE(B) specimens. The compliance equations developed for these crackconfiguration do not necessarilyapply to shallow crackspecimens. Consequently, new compliance functions are needed to determine crack growth resistance properties using test specimens with small a/W ratios. Thisworkpresentsthedevelopment ofcomplianceequationsand solutionsof plastic η--factors to evaluate crackgrowth and JInte- gral for shallow crack bend specimens. Very detailed linear and non--linear finite element analyses for plane--strain models provide the evolution of load with increased load--line displacement and crack mouth opening displacement which are needed to determine the com- pliance functions. Keywords: fracture mechanics, compliance, η -factor, J-R curves, ductile tearing 1. Introduction The stable tearing of a macroscopic crack in ductile materials for structural applications is conventionally character- ized by crack growth resistance (J-R) curves. Under sustained ductile tearing of the (macroscopic) crack -like defect, large increases in the load-carrying capacity of the structure, as characterized by resistance curves, are possible beyond the limits given by the crack driving force at the onset of crack growth. Standardized procedures for J-R curve testing require both sufficient specimen thickness to insure predominantly plane strain conditions at the crack -tip and deep cracks (crack size to specimen width ratios, a/W > 0.5) (ASTM E1152, 1995 -ASTM E1820, 2001). Within certain limits on load levels and crack growth, these restrictions insure high levels of stress triaxiality at the crack tip. Since structural defects in com- mon civil and marine strucutres are very often surface cracks that form during fabrication or during in -service operation, the applied driving force needed to the crack grow in laboratory specimens is lower than yhe corresponding drivung force in the structural component. These crack configurations generally develop low levels of crack -tip stress triaxiality (crack - tip constraint) which contrasts sharply to conditions present in deeply cracked specimens thereby yielding low resistance curves and increased toughness properties The above arguments have prompted research efforts to adopt the use of geometry dependent crack growth resistance curves so that crack-tip constraint in the test specimen closely matches the crack-tip constraint for the structural compo- nent. However, current standardized methods to determine crack growth resistance properties based upon unloading com- pliance procedures employing a single specimen, such as ASTM E1152 (1995) or ASTM E1820 (2001), utilize only bend- type specimens with deep cracks (crack size to specimen width ratios, a/W > 0.5), such as the C(T) and SE(B) specimens. The compliance equations developed for these crack configuration do not necessarily apply to shallow crack specimens with much lower crack-tip constraint. Consequently, new compliance functions are needed to determine crack growth resistance properties using test specimens with small a/W ratios. This work presents the development of compliance equations for evaluation of the J Integral and crack growth for shallow cracked bend specimens. The primary objective is to derive plastic η -factors which are applicable to determine J-R curves for a wide range of a/W -ratios and material flow properties. Very detailed linear and non-linear finite element analyses for plane-strain models provide the evolution of load with increased load-line displacement (LLD) and crack mouth opening displacement (CMOD) which are needed to determine the compliance functions. The present results, when