Non-destructive evaluation of the steel fibre content and anisometry in thin UHPFRC elements

The tensile response of ultra-high performance fibre-reinforced composites (UHPFRC) is decisive in many applications and depends on the steel fibre content and orientation. These vary troughout the structural element and may differ from those in the laboratory specimens used to characterize the material behaviour. This work presents the developments on a non-destructive test method based on the measurement of the magnetic inductance, substantiating its use for the determination of the fibre content and orientation in thin UHPFRC elements and allowing the estimation of the directionally dependent post-cracking tensile strength of the material in the structure. Starting from a probabilistic description of the fibre orientation, an existing physical model of the magnetic circuit composed of a U-shaped inductor and the composite is generalized and is used to derive the relations between the magnetic inductance measurements, the fibre volumetric fraction and the fibre orientation factor. A second-order tensor approximation of the relative magnetic permeability of the composite is proposed to determine the in-plane fibre orientation factor along any direction based on any three non-collinear measurements. Experimental evidence is presented supporting the theoretical developments. The factors that may affect the measurements are experimentally quantified. The paper concludes with an application example.