General expressions for the stress intensity factor of a one-point bend beam

Abstract

The aim of this work is to find general expressions to determine the stress intensity factor of a one point bend beam like specimen, whether from the measurement of the applied load or the crack mouth opening displacement. The expressions, obtained by applying the superposition principle, involve the decomposition of the general case into three auxiliary problems. The solution of two of them (pure bending and three point bending) is well known, while the solution of the third (one point bending) is developed in the present work. The proposed expressions are compared to numerical results obtained by the finite element method and their accuracy is equal to or better than available expressions published elsewhere.

Importance of Material’s Dynamic Stress Intensity Factor Calculation in the Design of High Strenght Structures

“…Nishioka et al [9] derived a formula for determining the dynamic stress intensity factors directly from crack mouth opening displacements in a dynamic teartest specimen. Villa et al [10] in their work derived general expressions to calculate the stress intensity factor for a one-point bend beam specimen. It was either from the measurement of the applied load or the crack mouth opening displacement, using finite-element code ABAQUS.…”

“…Villa et al [10] demonstrated that the stress intensity factor can be evaluated from the measurement of CMOD, while assuming that the relationships between stress intensity factor and CMOD that are used in the quasi-static loading also apply to the dynamic case. Villa et al [10] calculated dynamic stress intensity factor by CMOD. They performed the dynamic tests on a modified Hopkinson pressure bar and measured CMOD using a high speed camera that was coupled with the fracture specimens.…”

“…Then they obtained critical stress intensity factor from the critical CMOD at the time the crack started to grow. Villa et al [10] also proposed a simplified method for the calculation of stress intensity factor, based on load-point displacement obtained by analysis of the Timoshenko cracked beam. Rubio et al [11] suggested that once the input load, the load-point displacement and the CMOD are experimentally obtained using the appropriate instrumentation.…”

Forced Vibration Analysis in the Context of Dynamic SIFs in Impact Bending Tests

“…It is possible to determine DSIF using loading history as external excitation for an analytical model of the specimen. Villa et al (2007) have studied motion of a beam with edge crack through superposition principle by decomposition of the beam into three segments. They have presented closedform expressions for DSIF for a one-point bend specimen.…”