An approximate method of stress analysis in elastic solids with multiple cracks is
proposed to improve the accuracy of the Kachanov method in analyzing closely
spaced cracks. Classical Kachanov method assumed that traction in each crack can
be represented as the sum of a uniform component and a nonuniform one, and that
the interaction among the cracks is only due to the uniform components. The
assumptions simplify considerably the mathematics. However, they may not be valid
when the cracks are very close and overlap along the direction of load, because
each crack may be embedded in the stress-amplifying region as well as the
stress-shielding region of the other cracks at this time. To improve the accuracy of
the Kachanov method, a new asymptotic method, in which the influence on
a crack of the quadratic parabola pseudotractions (QPPTs) rather than
the average ones on the other crack are taken into account, is proposed.
Applications to the problem of three collinear cracks and two offset parallel
closely spaced cracks are considered to validate the accuracy of the new
method.
