No abstract

Purpose The purpose of this paper is to introduce a new numerical approach for studying a cantilever bar having a transverse crack. The crack is modeled by an elastic longitudinal spring with a stiffness K according to Castiglione’s theorem. Design/methodology/approach The bar is excited by different longitudinal impulse forces. The considered problem based on the differential equation of motion is solved by the method of characteristics (MOC) after splitting the second-order motion equation into two first-order equivalent equations. Findings In this study, effects of the crack size and crack’s position on the reflected waves from the crack are investigated. The results indicate that the presence of the crack in the cantilever bar generates additional waves caused by the reflection of the incident wave by the crack. Originality/value A numerical approach developed in this paper is used for detecting the extent of the damage in cracked bars by the measurement of the difference between the dynamic response of an uncracked bar and a cracked bar.

In this study, interaction between a main crack and a surrounding layer of micro cracks is considered. A stress field distribution induced during these interactions is obtained using Muskhelshvili’s complex variables formalism which relies on the Green's functions. The effect of amplification and shielding on the resulting stress field is shown, herein, through a study of mode I Stress Intensity Factor (SIF). To quantify these effects, orientations as well as positions of microcracks with respect to the main crack is taken into consideration. Obtained results are compared and agreed with those of other researchers.

PurposeIn this paper, an approximate analytical approach is developed for the determination of natural longitudinal frequencies of a cantilever-cracked beam based on the Lagrange inversion theorem.Design/methodology/approachThe crack is modeled by an equivalent axial spring with stiffness according to Castigliano's theorem. Thus, an implicit frequency equation corresponding to cantilever-cracked bar is obtained. The resulting equation is solved using the Lagrange inversion theorem.Findingseffect of different crack depths and crack positions on natural frequencies of the cracked beam is analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. Furthermore, approximate analytical results are compared with those obtained numerically as well as from experimental tests.Originality/valueA new approximate analytical expression of a fundamental longitudinal frequency, as a function of crack depth and crack location, is obtained.

Abstract. The present study evaluates the Stress Intensity Factor (SIF) during the propagation of a crack interacting with a nearby circular dislocation. The problem is formulated using a numerical approach such as FEM along with the software (ABAQUS). The stress field and the SIF are determined for different crack's length. A brittle material such as a glass having an equivalent elasticity modulus and a Poisson rain this research work. Besides, the proposed model is a rectangular specimen with an edge crack subjected to tensile stresses according to the mode 1 opening. Obtained results are compared and agreed with those determined by other researchers.