On the Optimization of the Fiber Orientation in Cement Based Composite Materials
A. M. Brandt
Appears on pages(s):
cracking (fracturing); fiber reinforced concretes;
glass fibers; metal fibers; optimization.
In the paper the concrete-like composites are considered, composed of brittle cement based matrices and thin chopped fibres of various materials, ex. steel, glass. The volume fraction of fibres is usually low, for instance for steel fibres does not exceed 3% for technological reasons. In such composites large cracks may appear before complete failure, because fibres bridge the cracks and control their propagation. In several types of structural elements made of such materials cracks are admissible provided that the structure can sustain certain load, ex. due to the own weight and other permanent actions. This quality of the fibre reinforced concretes may be correctly evaluated by the ability to absorb the work of external load. The amount of this work is chosen as objective function and it is calculated considering its five different components. These components are evaluated using simplified relations derived from the assumed behaviour of the fibres in the cracked matrix. In the presented problem the angle of the orientation of the parallel fibre system is chosen as the only design variable. The solution is obtained for an element subjected to axial tension using the necessary condition for the maximum of the fracture energy and the optimum orientationangle of fibres with respect to the load direction is determined. In the discussion, several parameters are considered which influence the optimum orientation angle. Taking into account the values of the parameters which correspond to com-monly used materials (steel and concrete) the resulting opti-mum angle is varying in different cases between about 18 and 40". The proposed approach is extensively studied for further applications to more complicated optimization problems of internal structure of fibre reinforced composite materials.