Micromechanical modelling of strain hardening and tension softening in cementitious composites |
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Authors: | B L Karihaloo J Wang |
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Affiliation: | (1) Institute of Mechanical Engineering, University of Aalborg, DK-9220 Aalborg, Denmark, DK;(2) Department of Aeronautics, Imperial College of Science, Technology and Medicine, London SW7 2BY, U.K., GB |
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Abstract: | This paper will describe a procedure for modelling the complete macroscopic response (including strain hardening and tension
softening) of two short fibre reinforced cementitious composites and show how their microstructural parameters influence this
response. From a mathematical point of view it is necessary to examine how bridging forces imposed by the fibres alter the
opening of multiple cracks in elastic solids under unidirectional tensile loading.
The strain hardening is essentially due to elastic bridging forces which are proportional to crack opening displacements.
After a certain critical crack opening displacement is reached, some fibres progressively debond from the elastic matrix and
thereafter provide a residual bridging force by frictional pull-out, while others continue to provide full bridging. This
results in a kind of elasto-plastic bridging law which governs the initial tension softening response of the composite.
Besides the usual square-root singularity at crack tips, the elasto-plastic bridging law introduces a logarithmic singularity
at the point of discontinuity in the bridging force. These singularities have been analytically isolated, so that only regular
functions are subjected to numerical integration. Unbridged multiple crack problems have in the past been solved using double
infinite series which have been found to be divergent. In this paper a superposition procedure will be described that eliminates
the use of double infinite series and thus the problem of divergence. It is applicable to both unbridged and bridged multiple
cracks.
The paper will end by showing how the model of multiple bridged cracks can accurately predict the prolonged nonlinear strain
hardening and the initial tension softening response of two cementitious composites. |
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