NEW PROCEDURE TO CALCULATE COMPRESSION STRENGTH OF FRP USING THE SERIAL/PARALLEL MIXING THEORY

X. MARTINEZ; S. OLLER; A. BARBAT; F. RASTELLINI

Conferencia; 8th International Symposium on Fiber Reinforced Polymer Reinforcement for Concrete Structures, FRPRCS-8; 2007

The use and applications of fibre reinforced polymers (FRP) to reinforce and retrofit existing structures has increased exponentially in last decades. Nowadays, these composite materials can be found as tensile reinforcements, shear reinforcements, column wrapping, etc. Although FRP reinforcements are not recommended to be used to resist compressive forces (Rabinovich [1]), there are many situations in which this load state can be found. This aspect is of special relevance in the case of structures subjected to seismic loads, where the sign of the load is reversed as the earthquake evolves, in case of fatigue loads or when a strengthened element is unloaded. Thus, a procedure to obtain the compression strength of FRP composites is required in order to take into account this sort of situations.The main failure cause of compressed FRP is the fibre buckling phenomenon. Fibres are very slender elements and their second order effects are avoided by the matrix elastic restrain. However, as damage in matrix evolves, fibre restrain becomes weaker and fibre buckling occurs.First studies about fibre buckling correspond to Rosen [2], who defined two different buckling modes: extensional and shear buckling. He also defined the compression stress at which this buckling occurs. This stress value is defined by the matrix shear strength and by the amount of fibres found in the composite. From this initial approximation, different authors have developed new models in order to obtain a better prediction of composite compression strength due to fibre buckling. Among different existing studies, it is worth to mention the works by Barbero and Tomblin [3], Balacó de Morais and Torres Marques [4] and Drapier et al. [5]. All these authors consider composites as a single orthotropic material. Using energetic equilibrium, they develop micro-mechanical models from which the finalcompression stress in the composite is obtained. The expressions found in all different models agree in the dependence of the critical compression stress on three main parameters: (a) Matrix shear strength, (b) Fibre initial misalignment and (c) Proportion between fibre and matrix in the composite.Hence, the limit compression stress of these new formulations depends on the same parameters pointed out by Rosen and on a new one: fibre initial misalignments. According to Jochum and Grandidier [6], fibre misalignments are produced in the composite manufacturing process, during the matrix curing. These misalignments are regular along the whole fibre and can be represented by a sinusoidal shape.The fibre buckling formulation proposed in this paper appears in the context of FRP reinforcement and retrofitting simulations using numerical techniques. These simulations are made using a finite element code which deals with composite materials using the serial/parallel rule of mixtures developed by Rastellini [7]. This theory allows obtaining the composite behaviour from the response of its constituents, each one computed with its own constitutive law. The developed simulations have proved the accuracy of the proposed numerical method, which is able to obtain the different effects produced by different FRP reinforcements in the same structure, the behaviour of the structure if it is reinforced or if it is retrofitted, etc. The code has been validated using experimental values. Some of the simulations realized are exposed in Martinez et al. [8].This paper includes a brief description of the serial/parallel (S/P) rule of mixtures as well as its use in the simulation of FRP reinforcements of existing structures. Afterwards, the new formulation proposed to obtain the compression strength of composite materials is exposed. Finally, the new formulation is validated.