Four-Point Flexural Tests on the Unnotched Beams
For many years ASTM C1018 (ASTM 1997) was the most common testing method for evaluating the toughness of fibre reinforced concrete. As shown in Fig. 2.9, a four-point loading is carried on an unnotched beam of 350 x 100 x 100 mm. The specimen net mid-span deflection is used to control the rate of increase of deflection using a closed-loop, servo-controlled testing system. The deflection of specimen at the mid-span increases at a constant rate within the range of 0.05-0.10 mm/min.
The toughness indexes were defined in terms of the ratio of the area under the load versus deflection curve out to some specified deflection to the area under the curve out to the point of first crack. As shown in Fig. 2.10, the toughness index I5, I10, and I30 are the numbers obtained by dividing the area up to a deflection of 3, 5.5 and 15.5 times the first-crack deflection (Sf) respectively by the area up to first crack.
Fig. 2.9 Typical four-point flexural tests based on ASTM C1018 (ASTM 1997)
Fig. 2.10 Definition of ASTM C1018 toughness parameters (Gopalaratnam et al. 1991)
The first crack point is defined as ‘the point of the load-deflection curve at which the form of the curve first becomes non-linear’. When using first crack deflection as part of a method for characterising toughness, an objective, accurate, and practical definition for the first crack point is important. However, the location of this point in practice is ambiguous and depends upon the resolution of the recording device and the judgement of the operator. Thus, errors can be introduced due to the difficulty of accurate definitions of the first crack point (Mindess et al. 1994). Moreover, these errors can be propagated and magnified when this deflection is multiplied by several numerical factors to calculate the toughness indexes. Equally important is an exact determination of the beam deflections both before and after the first crack. However, this is often difficult, due to various extraneous deflections that may occur due to machine deformations and seating of the specimen on the supports (El-Ashkar and Kurtis 2006). Other limitations include: the wide range of parameters that have been used to interpret test results (Banthia and Trottier 1995), the greater variation in the recorded deflections in four-point bending tests compared with three-point bending tests (Taylor et al. 1997), and the influence of size effects on the test results (Gopalaratnam et al. 1991). As a result of these problems, ASTM C1018 was withdrawn in 2006.