The dislocation free zone model of fracture by symbolic programming

Conference · Mon Sep 01 04:00:00 EDT 1997

OSTI ID:522709

Chang, Shih-Jung

The dislocation free zone (DFZ) model of fracture was developed by Chang and Ohr after a series of experimental observations on the crack tip dislocation structures that invariably showed the existence of the dislocation free region. The DFZ model is a modified BCS crack model that is supplemented with the Rice-Thomson crack tip dislocation emission mechanism. This dislocation emission mechanism imposes a finite energy barrier to the crack tip for emitting dislocations into the plastic zone, in contrast to a zero energy barrier for the BCS model. This finite energy barrier results in the formation of the DFZ and a stress-singular crack tip region. This resistance was expressed in terms of a dislocation emission toughness K{sub e} as a material constant. Because of the emission toughness K{sub e} the crack tip has the choice either to emit dislocation or to fracture in brittle mode. The model, therefore, was first used to explain the fundamental phenomenon of brittle versus ductile fracture. Brittle fracture occurs if K{sub Ic} < K{sub e}, that is, the crack tip breaks before the dislocation can be emitted. Ductile fracture is possible if K{sub Ic} > K{sub e} so that dislocation will be generated before brittle fracture toughness K{sub Ic} is reached. The distribution function for the dislocations was solved from the dislocation pile-up equation. It was expressed in terms of the complete elliptic integrals. Although the analytical nature of the model is clear and precise, the numerical values of the model may not always be obtained readily. Attempts have been made to simplify and approximate the model by elementary mathematical functions. In this paper the distribution function is written in terms of a symbolic programming language MAPLE. The analytical and numerical manipulations can be made easily. An improvement of the program that accounts for the technique of calculating the elliptic integral of the third kind in different regions of the model is presented here.

• Research Organization: Oak Ridge National Lab., TN (United States)
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 522709
• Report Number(s): CONF-970877--1; ON: DE97008471
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
99 GENERAL AND MISCELLANEOUS
BRITTLE-DUCTILE TRANSITIONS
CRACK PROPAGATION
DISLOCATIONS
MATERIALS
NUMERICAL SOLUTION