Estimation of the tensile strength of UHPFRC layers based on non-destructive assessment of the fibre content and orientation
Introduction
The tensile response of composite materials reinforced with short and discontinuous steel fibres, such as Ultra High Performance Fibre Reinforced cement based Composite (UHPFRC), is strongly influenced by the fibre orientation with respect to the principal tensile stress direction [1], [2], [3]. While the theoretical fibre content, fibre type and fibre-to-matrix interface bond can be optimized during mix design stage to achieve a targeted tensile performance [4], [5], [6], [7], [8], the preferential orientation of the fibres has been shown to be mostly dictated by extrinsic factors, namely the wall effects near formed surfaces and the flow induced orientation, which depends on the geometry of the element, on the casting process and also on the rheological characteristics of the material in the fresh state [1], [9], [10], [11]. Regarding the latter, it is well established that the fluidity of self-compacting UHPFRC is effective to drive and orient the fibres [1], [11], [12], [13]. Fibres tend to become parallel (in the case of shear flow) or perpendicular (in the case of radial flow) to the flow direction as the flow distance increases. Therefore, it can be stated that it is not possible to define a single, or intrinsic, tensile response for UHPFRC and the in-structure tensile response of the UHPFRC as cast in a given structural element must be used instead. In general, the preferential alignment of the fibres along any direction provides the material with an anisotropic structure, which can be described by the probability distribution function for fibre orientation, by orientation tensors [14] or at least using scalar orientation parameters, such as the orientation number ηθ,i [10], [15]. The latter is related to the direction i defining the normal to a given surface and can be defined as the average value of cosθ:where Nf is the number of fibres crossing the surface and θn is the angle of nth fibre with the i-axis, see Fig. 1 for notation. Besides the fibre orientation, also local variations in the fibre content due to deficient fibre dispersion are responsible for the scatter in the tensile response that is sometimes observed in specimens cut from the same element [2].
These issues are extremely relevant in practical applications and are addressed, for instance, in the French interim recommendation for design with UHPFRC [16], [17]. The K-factor concept is suggested for scaling the tensile strength determined from standardized laboratory specimens to obtain that representative of the UHPFRC cast in the real structure. More fundamental approaches can be developed if the effective fibre content and the orientation of the fibres can be characterized. This requires the application of image recognition algorithms on high-resolution pictures of selected cross-sections [18], [19], [20], X-ray images [21], [22], or even using computerized tomography [3], [23]. These techniques allow not only the determination of the number of fibres crossing a given plane but also their position and the corresponding out-of-plane (θ) and in-plane angles (φ) (see Fig. 1). However, due to the involved labour intensity, time-consumption and cost, the application of these techniques is restricted to research purposes. Recently, more research effort has been put on the development of reliable, time- and cost-effective non-destructive test (NDT) methods for providing indicators of the fibre content and orientation. These can be classified mainly as: electrical methods, based on the effects of the fibres on the resistivity/conductivity of the composite material [24], [25]; and magnetic methods, based on the ferromagnetic properties of steel fibres used in the composite [26], [27], [28], [29]. In a previous work, Nunes et al. [28] developed a magnetic probe for performing inductance measurements. It was demonstrated that the local fibre content can be estimated from the inductance measurements performed along any two orthogonal directions using a calibration line previously established for the same type of fibres. A fibre orientation indicator was also proposed based on the same two inductance measurements, which provides a scalar measure of the anisotropy of the fibre distribution with respect to the two selected orthogonal directions [28].
The main objective of the present work is to develop a procedure for estimating the in-structure tensile strength along the directions of interest of a thin UHPFRC layer avoiding the extraction of cores or samples from the structure. The procedure is based on NDT measurements for estimating the parameters of the underlying physical model. To this end, an experimental campaign was developed involving the production of 25 mm thick UHPFRC plates with fibre contents of 1.5 and 3%, with or without pronounced fibre orientation, covering a wide range of orientation profiles. This was achieved using a new strategy to align the fibres in UHPFRC which relies on the application of an external magnetic field during casting. The tensile response of the specimens was obtained using the DEWS test [30]. An image analysis technique was implemented to characterize the fibre orientation distribution with reference to the fracture surface of selected specimens after tensile testing. In addition to image analysis approach, the magnetic NDT method was applied, in view of a meaningful correlation between the NDT measurements and the orientation numbers determined from the image analysis. The tensile strength estimates based on the results of the image analysis or on the NDT measurements are compared and it is concluded that equivalent accuracy is achieved, thereby validating the use of NDT for this purpose.
Section snippets
NDT method for detection of fibre content and orientation
The magnetic permeability μ is a material property defined as the constant of proportionality between the magnetizing field strength to which the material is subjected and the resultant magnetic flux density inside the material. It can be expressed in terms of relative magnetic permeability μr, which is the factor by which the material permeability exceeds that of vacuum, μ0:
UHPFRC can be regarded as a composite constituted by two phases: the matrix, which is characterized by a relative
Underlying mechanical model
The tensile strength of UHPFRC, fUt,u, is generally governed by fibre debonding followed by fibre pull-out, the latter marking the onset of the softening stage of the stress-displacement curve. Assuming that during the debonding stage the fibre-to-matrix bond shear stress slip relation can be approximated by a rigid-plastic law, and that the average pull-out length is lf/4, it is possible to estimate fUt,u using equation (6) [31]:
In the equation above lf and df are the fibre
Materials and mix designs
Two compositions of UHPFRC were investigated in this work containing a volume fraction (Vf) of fibres of 1.5% and 3.0%, as shown in Table 1. Fibres were incorporated in the mix by replacing an equivalent volume of sand. The mixes were prepared with ternary mixtures of cement, limestone filler and silica fume. The average particle size of cement and limestone filler is 14.6 and 5.36 μm, respectively. The particles of silica fume have a size 50 to 100 times lower than that of cement particles.
DEWS results and selection of specimens for image analysis
Fig. 13 shows the experimental results of 36 DEWS tests in terms of nominal tensile stress (σN) versus crack opening displacement at mid-depth (COD_Mid) curves. The corresponding peak normal stress after cracking (σN,peak) results are presented in Table 3. The test results feature a wide range of material constitutive relationships due to the fact that specimens with two fibre contents and three distinct fibre orientation profiles were tested. The results show that depending on fibre
Conclusions
Based on presented results, the following conclusions can be drawn:
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The developed magnetic orientation method was found to produce strong preferential fibre orientations in laboratory specimens and provides an efficient way for studying the related mechanical effects. The fibre orientation factor and the orientation number ranged from 0.18 to 0.89 and from 0.41 to 0.93, respectively.
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A noticeable difference in the orientation angles distribution characteristics was revealed from the image
Acknowledgements
This work was financially supported by: Project POCI-01-0145-FEDER-007457 - CONSTRUCT - Institute of R&D In Structures and Construction funded by FEDER funds through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI) – and by national funds through FCT - Fundação para a Ciência e a Tecnologia; Project PTDC/ECM/122446/2010 and UID/MAT/00144/2013. Collaboration and materials supply by Concremat, Secil, Omya Comital, Sika and KrampeHarex is gratefully acknowledged.
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2023, Construction and Building MaterialsCitation Excerpt :The measurement was taken in two orthogonal directions: one parallel to the direction of preferential orientation of the fibers, and the other perpendicular to the preferential orientation of the fibers. Based on the relative magnetic permeability of the composites determined by the fiber characteristics, magnetic method have demonstrated its suitability for both laboratory and in-site testing [155]. This convenient and reliable method can quickly and effectively provide reliable information about fiber orientation.