Stability of parallel cracks in solids reinforced by bars

Investigated is the effect of one layer of steel reinforcement on the instability of a system of parallel equidistant shrinkage or cooling cracks in a concrete halfspace or parallel equidistant cracks due to bending of a beam. The cracks are assumed to propagate along straight lines normal to halfspace surface. The instability mode consists in the closing of every other crack at the expense of an extension and increase of the width of the remaining cracks. The previous formulation of stability conditions in terms of the derivatives of the stress intensity factors with respect to the crack lengths is used and numerical results are obtained by finite elements. It is found that instabilities of cracks in reinforced concrete do exist and are profoundly affected by the presence of reinforcement. Assuming a relatively limited length of bond slip near the crack, one finds that the presence of a reinforcement layer greatly increases the penetration depth of cooling or drying at which the instability occurs, but does not prevent the instability from occurring deeper beneath the reinforcement. A small amount of reinforcement, smaller than that required by the building codes, is sufficient to achieve this effect while a further increase of the reinforcement amount has relatively little effect.