The out-of-plane stress and displacement fields are investigated analytically for mode
I through-the-thickness cracks in an infinite plate of finite thickness within the
first-order plate theory. The developed method is based on the distributed dislocation
approach and an earlier derived three-dimensional solution for an edge dislocation.
Numerical results are obtained through application of Gauss–Chebyshev quadrature
for both finite length and semiinfinite crack cases. The calculated stress and
displacement fields are found to be in good agreement with already published
experimental and finite element studies. Further results for the averaged
through-the-thickness stress intensity factor are given and again found to be in good
agreement with previous finite element values. The developed solutions can therefore
be used in experimental techniques for the assessment of the stress intensity factor
using the out-of-plane displacement measurements, for example by the interferometry
method.