Application of a hybrid finite element method to determine stress intensity factors in unidirectional composites

Abstract

In this paper a hybrid finite element method is applied in evaluation of the stress intensity factors K I and KII of unidirectional fiber reinforced composites. In order to satisfy the stress singularity at the crack tip a singular super-element based on a modified complementary energy principle is developed. The stress and displacement fields in the super-element are expressed in terms of polynomials of two complex variables ~1 and ~ in the transformed ~-plane. The stiffness matrix of the super-element was determined by using a line integral along the boundary of the super-element. The displacement vector was expressed in terms of the element nodal displacement vector (q } and a properly selected shape function defined along the element boundary.Numerical results for K 1 and K n of glass-epoxy and graphite-epoxy unidirectional composites with cracks along the diameter of a circular cut out as well as elliptical cut outs were evaluated.

Thermoelastic determination of crack-tip coordinates in composites

“…The stress and displacement fields around the crack-tip can be composed by these parameters. This method was first used to develop a singular element for cracked composite problems (Khalil et al, 1986), its reliability has been substantiated by comparing against results from the J-integral approach (Ju, 1996), and subsequently applied to determine stress intensity factors in orthotropic composites (Ju, 1996;Ju and Rowlands, 2003a,b).…”

Simulating stress intensity factors for anisotropic materials by the least-squares method

“…Khalil et al [ 1 ] showed that the displacements near the crack tip in an anisotropic material can be…”

“…Khalil et al [1] generated a hybrid finite element to evaluate the stress intensity factors of anisotropic materials. Chen and Atluri [2], and Lee and Wang [3] presented the finite element method to determine weight functions for orthotropic cracked bodies, and then the stress intensity factors were calculated using the weight functions.…”

“…Very near the crack tip the stresses are dominated by the two stress constants/31 and/31+n which can be related to stress intensity factors KI and Kn[1],…”

Hybrid singular elements in fracture mechanics

“…However, independent of these difficulties and due to their sound theoretical bases, the equilibrium hybrid elements as used in fracture mechanics have been used with success in several areas. Among these areas, one can cite composite and anisotropic material applications [44,45], thermo-elastic applications [46], and determination of the T-stress factor [47] and three-dimensional analysis [48].…”