Context. Pulsars show a steady decrease in their rotational frequency, occasionally interrupted by sudden spin-ups called glitches, whose physical origin is still a mystery. One suggested explanation for at least the small glitches are starquakes, that is, failures of the solid neutron star crust, in which the progressive reduction in the centrifugal force deforms the star, stressing the solid until it breaks. This produces a spin-up, dissipating energy inside the star. Aims. We explore this suggestion by analyzing a mostly analytical model in order to understand the possible consequences of starquakes, particularly whether they can explain at least the small glitches. Methods. We analyze the deformations and strains produced by the decreasing centrifugal force, modeling the neutron star with a fluid core and a solid crust, each with uniform density and with the core possibly denser than the crust, as a simple approximation to the strong density gradient present in real neutron stars. Results. The deformation of a star with very different densities in the core and crust is qualitatively different from the previously studied case of equal densities. The former more closely resembles the behavior of a fluid star, in which the core-crust interface is a surface of constant gravitational plus centrifugal potential. Conclusions. Regardless of the uncertain breaking strain, the glitch activity in this model is several orders of magnitude smaller than observed, even if only small glitches are considered. For a large breaking strain, suggested by simulations, glitches due to starquakes could be roughly of the correct size but much less frequent than observed glitches. The energy released in each such glitch is much larger than in the standard model of angular momentum transfer from a faster rotating superfluid in the inner crust. On the other hand, we cannot rule out that the heating produced by small starquakes could trigger glitches by allowing neutron superfluid vortices to move. We also confirm that stresses in the neutron star crust can in principle support an ellipticity much larger than some observational upper limits from pulsar timing and continuous gravitational wave searches.
