Abstract
Explicit and simple expressions for root compliance coefficients, which can be used to define root rotations and root displacements at the crack tip cross section of orthotropic cracked beams, are derived under general self-equilibrated loading conditions at the crack tip. The effects of both shear deformations and transverse elasticity are taken into account in order to accurately define displacement fields and energy release rate. The derivation builds on and extends one-dimensional formulations in the literature. The employment of the novel analytical expressions requires the determination of one a priori unknown parameter which describes the effects of the transverse elasticity and is determined through matching of well established 2D results in the literature. The one-dimensional model accurately reproduces crack tip effects in symmetric isotropic and orthotropic specimens; shear deformations are included in the formulation for an accurate derivation of the root displacement coefficients; the accuracy reduces in asymmetric specimens where the matching parameter becomes load dependent.
Highlights
I n many problems of fracture in beam-type structures the effects of the transverse elasticity of the intact portion of the specimen ahead of the crack tip are not negligible and must be taken into account when calculating displacements and fracture parameters
This paper deals with the analytical derivation of root compliance coefficients which can be used to define root rotations and root displacements at the crack tip cross section of orthotropic cracked beams
The derivation builds on and extends one-dimensional formulations in the literature and describes the intact part of the specimen as two beams joined by an elastic Winkler type bond. The effects of both shear deformations and transverse elasticity are taken into account; in addition, the continuity condition imposed on the relative sliding displacements of the two beams at their interface to describe the continuity of the intact portion ahead of the crack tip makes the axial and bending problems coupled
Summary
I n many problems of fracture in beam-type structures the effects of the transverse elasticity of the intact portion of the specimen ahead of the crack tip are not negligible and must be taken into account when calculating displacements and fracture parameters. Thouless [10] proposed an approach which links to the original Kanninen's [16] formulation and uses the solution of an elastic and isotropic Euler-Bernoulli beam on an elastic foundation in order to find the relationships between the compliance coefficients describing root rotations and root displacements for a symmetric DCB specimen subjected to transverse point forces. These relationships were used to derive the root displacements for orthotropic specimens. The solution procedure previously followed by the authors to solve the problem of multi-layered systems with imperfect interfaces [19,20,21,22,23,24] is employed and leads to explicit expressions for the root rotation and displacement compliance coefficients under different crack tip loading conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
