DOUBLY PERIODIC ARRAYS OF BRIDGED CRACKS AND SHORT-FIBER-REINFORCED CEMENTITIOUS COMPOSITES

This paper presents a superposition approach for studying the influenc e of bridging forces upon the opening of multiple cracks in elastic so lids under unidirectional tensile loading. The bridging forces may be purely elastic and proportional to the crack-opening displacements, bu t an elasto-plastic bridging law is more likely to represent reality i n a short fibre-reinforced solid. The fibres debond from the elastic m atrix at a certain critical crack-opening and thereafter provide a res idual bridging force due to frictional pull-out. From a mathematical p oint of view, the elasto-plastic bridging law introduces an additional (logarithmic) singularity at the point of discontinuity in the bridgi ng force, besides the square root singularity at the crack tips. These singularities have been analytically isolated, so that only regular f unctions are subjected to numerical integration. The double infinite s ummations necessary for the solution of multiple cracks have been foun d to be divergent in earlier studies. The superposition procedure deve loped in this paper eliminates double infinite series and thus the pro blem of divergence. The mathematical solutions are used to study the i nfluence of varying amounts of short fibre reinforcement upon the comp lete tensile macroscopic response (including strain hardening and tens ion softening) of two fibre-reinforced cementitious composites: a conv entional fibre-reinforced cement and a high-performance fibre-reinforc ed (DSP) cement. It is shown hat the model of multiple bridged cracks accurately predicts the prolonged nonlinear strain-hardening and the i nitial tension-softening response of both these cementitious composite s. Copyright (C) 1996 Elsevier Science Ltd.