Three-Point Flexural Tests on the Notched Beams
The stress-strain relation from the four-point flexural test on the unnotched beams is considered to be the most desirable since it can be directly used in engineering calculations. However, it does not represent the actual post-cracking behaviour of fibre reinforced concrete and cannot be retrieved directly from a characterisation
Fig. 2.14 Load-deflection curve of ASTM C1609 (ASTM 2011b)
test. Moreover, during the test, there is a momentary loss of stability when the concrete matrix cracks, even under displacement control, and while using relatively stiff conventional testing machines (Barr et al. 1996). Therefore, the unnotched beams through a four-point flexural test normally have a great variation in the recorded deflections.
Notched beam tests offer a promising alternative to characterise toughness of fibre reinforced concrete. The tests avoid many of the problems associated with the four-point test on the unnotched beams, and thus guarantee stability throughout the tests even for unreinforced and high-strength low fibre-content concretes (Shaheen and Shrive 2007). A mid-point loading configuration is obviously more appropriate for notched beam specimens than the four-point loading (Ding 2011).
For the notched mid-point loaded specimen, crack initiates at the notch-tip and propagates along the notch plane and hence, deformation is always localised at the notch-plane and the rest of the beam does not undergo significant inelastic deformations (Mahmud et al. 2013). This minimises the energy dissipated over the entire volume of the specimen and, therefore, all the energy absorbed can be directly attributed to fracture along the notch plane. Consequently, the energy dissipated in these tests can be directly correlated to material response (i.e. fibre reinforcement) (Stynoski et al. 2015). Moreover, the stress-crack opening relation from the tests naturally expresses the real post-cracking behaviour of fibre reinforced concrete. The stress-crack opening properties are also independent of the structural member size (de Montaignac et al. 2012). Therefore, three-point flexural test on the notched beams are considered as the best way of studying toughness, crack propagation and the associated fibre reinforcement.
Crack Tip Opening Displacement (CTOD) and Crack Mouth Opening Displacement (CMOD) tests are common three-point flexural tests on the notched beams. According to ASTM E1290 (ASTM 2008b), CTOD is the displacement of the crack surfaces normal to the original (unloaded) crack plane at the tip of the fatigue precrack. However, due to inherent difficulties in the direct determination of CTOD, CMOD test is a preferred test to assess post-cracking performance of fibre reinforced concrete (Zhijun and Farhad 2005). According to BS EN 14651:2005 +A1:2007 (BSI 2007), CMOD test measures the opening of the crack at mid-span using a displacement transducer mounted along the longitudinal axis.
During the last ten years many laboratories have been using closed-loop servo-hydraulic machines to test concrete specimens in the fracture tests. In such machines the opening of crack mouth is used to control the tests. In such tests, the CMOD can be used directly as a measure of the response of the beam, thus eliminating the need to monitor the actual central deflection of the test specimens via a ‘yoke’ arrangement (Aslani and Bastami 2015). The load-CMOD curves directly represent the deformation of the critical section. Though this requires more sophisticated testing equipment than that required for load-displacement curves, such testing equipment results in stable post-peak response and avoids the effects of energy dissipation outside the cracking zone (Bordelon et al. 2009). Therefore, in our research CMOD tests were carried out to study the reinforcing effects of the recycled plastic fibres in concrete, rather than using the four-point flexural tests on the unnotched beams.
Figure 2.15 shows the test set-up and the schematic of the controls. A CMOD transducer monitors the crack opening displacement and supplies the feed-back signal to the servo-controller, as shown in Fig. 2.15(a). A Japanese yoke is mounted around the specimen to record the net deflections so that the extraneous deflections resulting from settlement of supports, crushing at load points, and load-fixture deformation are automatically eliminated. Averaged data from two LVDTs placed on either side of the specimen are used to record the net deflection of the beam at the mid-span (de Montaignac et al. 2012), as shown in Fig. 2.15(b). A load-CMOD relationship can be obtained from the test. Using this type of relationship, the load at the limit of proportionality and the residual flexural tensile strength parameters can be obtained.