The equilibrium configurations of a one-dimensional variational model thatcombines terms expressing the bulk energy of a deformable crystal and itssurface energy are studied. After elimination of the displacement, theproblem reduces to the minimization of a nonconvex and nonlocal functional ofa single function, the thickness. Depending on a parameter which strengthensone of the terms comprising the energy at the expense of the other, it isshown that this functional may have a stable absolute minimum or only aminimizing sequence in which the term corresponding to the bulk energy isforced to zero by the production of a crack in the material.