  In this paper, Neumann cracks in elastic bodies are considered. We establish
a rigorous asymptotic expansion for the boundary perturbations of the
displacement (and traction) vectors that are due to the presence of a small
elastic linear crack. The formula reveals that the leading order term is
\epsilon^2 where \epsilon is the length of the crack, and the \epsilon^3-term
vanishes. We obtain an asymptotic expansion of the elastic potential energy as
an immediate consequence of the boundary perturbation formula. The derivation
is based on layer potential techniques. It is expected that the formula would
lead to very effective direct approaches for locating a collection of small
elastic cracks and estimating their sizes and orientations.
