Ij. Beyerlein et al., COMPARISON OF SHEAR-LAG THEORY AND CONTINUUM FRACTURE-MECHANICS FOR MODELING FIBER AND MATRIX STRESSES IN AN ELASTIC CRACKED COMPOSITE LAMINA, International journal of solids and structures, 33(18), 1996, pp. 2543-2574
This study analyzes fiber tensile and matrix shear stresses near the c
rack tip ina transversely cracked, unidirectional, fiber-reinforced la
mina under a remote tensile stress applied in the fiber direction. The
two-dimensional lamina consists of parallel, equally-spaced elastic f
ibers with elastic matrix in-between, and contains a row of up to a fe
w hundred contiguous fiber breaks aligned transverse to the fiber dire
ction forming a central transverse crack. Using the break-influence su
perposition (BIS) technique, a recently developed method for analyzing
a shear-lag model first introduced by Hedgepeth, we calculate the ten
sile and shear stress concentrations in the fibers and matrix, respect
ively. These are compared to tensile and shear stresses calculated usi
ng Linear Elastic Fracture Mechanics (LEFM) and the complete elasticit
y solution both for the continuum limit of a homogeneous, orthotropic
elastic material with a transverse central crack loaded in Mode I. For
the shear-lag model a critical scaling parameter for examining the st
ress behavior away from the crack tip along the fiber direction is roo
t E/G*, where E* and G* are composite in-plane stiffness constants al
ong the fiber direction and in shear, respectively. In addition to the
se parameters, the LEFM and complete elasticity solutions also involve
the effective transverse stiffness and Poisson's ratio. For a sizable
crack (consisting of 100 or more fiber breaks), the fiber tensile str
esses ahead of the crack tip along the crack plane calculated from the
BIS approach achieve excellent agreement with the LEFM solution down
to the scale of one fiber diameter and even better agreement with the
complete solution both in the near crack tip field and far field, rega
rdless of the composite stiffness constants. The profiles of the fiber
tensile and matrix shear stresses along the fiber direction show gene
rally good agreement, with the agreement improving as the composite st
iffness transverse to the fiber direction grows.