Determination of Toughness Characteristics of Concretes

Some numerical models, related to mode I cracking of concretes, use toughness parameter as K_IC or G_IC (in the framework of Linear Fracture Mechanics theory) as main material characteristic [1-3]. The principal problem is the difficulty to determine experimentally these toughness characteristics. Indeed, it has been clearly demonstrated that experimental tests have to be performed on large concrete specimens to get it [1, 4-14]. This is due to the high level of heterogeneity of concrete linked to the larger aggregate size. Thus, the dimension of the process zone at the macrocrack front tip which propagates reaches about 30 cm [14]. In the past, this type of test on large Double Cantilever Beam (DCB) specimen was performed [11, 13, 14]. This DCB specimen had the following dimensions: 3.5m long, 1.1m large and 0.3m width.

It is important to point out that this DCB test on very large spec imen is the only one performed on current concretes (with larger aggregate diameter larger than 10 cm and without fibers) that allowed to get real and intrinsic values of K_IC or G_IC [11-14]. It means that the large majority of the others experimental studies led to K_IC or G_IC that was not intrinsic but scale effect sensitive [11-14]. This type of DCB test on so huge specimen being difficult to perform and time consuming, only one concrete, called concrete 1 in this paper, was studied [11,13,14]. In parallel to this DCB test, 6 standardized compressive and splitting tests (Brazilian tests) were performed on 16 cm (diameter) x 32 cm (length) cylindrical specimens [14]. The objective of the present work is to perform the same program of tests (DCB, compressive and Brazilian tests) on two more concretes very different compared with the previous one and try to find general relations between toughness parameters and tensile and compressive strengths.

The geometry and the loading conditions are given in Figure 1.

The test is controlled by applying a constant notch displacement rate of 25 μm/min. The test is fully detailed in [11, 14]. The load/ notch opening curve is recorded during the test. After the peak load, that corresponds to the macrocrack initiation, several notch closing/ opening cycles are imposed at the same frequency. These cycles permit to follow the stiffness evolution of the specimen that is used to calculate K_IC (mode I critical intensity factor) and G_IC (mode I specific fracture energy) using the classical and well known (in linear fracture mechanics theory) compliance method [11-16].

Table 1 presents the concrete 1 mix design [11, 13, 14]. The average compressive, f_c, and splitting tensile strengths, f_ts, of concrete 1 are given in Table 2.

Table:1Concrete 1 mix design.

Table:2Average compressive and splitting tensile strengths of concrete 1.

*The average young modulus was determined during the compressive tests.

Figure 2 presents the load/notch opening curve related to concrete 1. The analysis of the DCB test by using the compliance method leads to get K_IC versus equivalent crack length curve. This equivalent crack length is the idealized crack length (straight and smooth crack in a linear elastic material) that leads to the same specimen compliance than the experimental one. Very commonly, the evolution of the specimen compliance with the idealized crack length (analytical relation) is obtained by performing linear elastic finite element analysis [11,13,14].

In figure 3, this KIC versus equivalent crack length curve related to concrete 1 is presented. In this Figure, it can be noted that K_IC fluctuates between a minimum and a maximum with a constant evolution. This fluctuation is the result of the material heterogeneity. The fact that a constant evolution of K_IC with the equivalent crack length is observed proves that the DCB specimen used is large enough to get characteristic KIC value. In other words, the length of the crack propagation is so large, more than 1.0 m, that one DCB test is sufficient to get a precise information about the dispersion related to K_IC of a given concrete. It is not necessary, as for others concrete mechanical characteristics, to perform several tests. From the K_IC fluctuation a mean value can be easily determined (Figure 3).

Table:3K_IC and G_IC mean values related to concrete 1.

K_IC and G_IC mean values related to concrete 1 are presented in Table 3.

Note that the relation between K_IC and G_IC is very well known in Linear Elastic Fracture Mechanics:

This relation (1) is relevant for stresses plane conditions that is the case with the DCB specimen.

The same program of tests, described in chapter I, have been performed in this new experimental campaign. The mix design of these two concretes, concrete 2 and concrete 3, are given in table 4.

The average compressive and splitting tensile strengths and young modulus of concretes 2 and 3 are given in Table 5.

Table:4Mix designs of concretes 2 and 3.

Table:5Average compressive and splitting tensile strengths and young modulus of concretes 2 and 3.

Table:6K_IC and G_IC mean values related to concretes 2 and 3.

Figures 4 and 5 present the load/notch opening curves related respectively to concrete 2 and 3. K_IC and G_IC mean values related respectively to concretes 2 and 3 are presented in Table 6.

From tables 2, 3, 5 and 6, it is interesting to draw the following curves:
 K_IC versus f_ts and f_c.  G_IC versus f_ts and f_c.

Figures 6 and 7 present respectively the curves K_IC versus f_ts and K_IC versus f_c.

Figures 8 and 9 present respectively the curves G_IC versus f_ts and G_IC versus f_c. From Figures 6 to 9, it appears that the links between K_IC and G_IC with f_ts and f_c. are strong. From curves 6 to 9 the following relations can be proposed:

All these relations above being the consequence of experimental imprecisions, it is acceptable to simplify them as following:

It is important to recall that these relations have been determined for concretes having:

It can be argued that making a direct link between toughness and compressive or tensile strength is too simplistic because other parameters than compressive (or tensile) strength influence this toughness, such as, for example, the water/cement ratio or the larger aggregate size. In fact, this link is possible and relevant because the physical mechanisms at the origin of these three mechanical characteristics are similar. Indeed, these three mechanical characteristics are the result of the passage from a diffuse microcracking to a localized macrocracking, it means the localization process of the cracking. This is obvious and well known for the compressive and the tensile strengths. Concerning KIC or GIC, it exists a microcracked zone at the front tip of the macrocrack in propagation, called process zone. The macrocrack can propagate only when the total dissipative energy in this process zone (microcracked zone) is achieved. The fact that parameters like water/cement ratio and larger aggregate have the same type of influence on the localization process related to the three mechanical characteristics can explain the good correlation between them and the linear relations obtained, even only three points are concerned. There are no physical and mechanical reasons that prevent extending the domain of validity of relations (6) to (9) to concretes having smaller compressive and tensile strengths. On the other hand, these relations are not valid for fibre reinforced concretes [12].

To conclude this chapter on discussion, it can be affirmed without any ambiguity, that the use of the analytical relations 6 to 9, as simplistic as they are, leads to a better prediction of the toughness of a given concrete than the usual use of small (a lot of smaller than the DCB specimen of the present study) laboratory test specimens.

This paper is related to experimental works concerning the possible link between toughness characteristics (KIC and GIC, determined by performing fracture mechanic test on large DCB specimens) and splitting tensile and compressive strengths (determined by performing tests on standardized cylindrical specimens) of several concretes. These experimental works were carried out during two campaigns of test:
 A past one, yet published, on one type of concrete.
 The present one on two more and different concretes.

These campaigns of test have the following interests:
 They permit to get intrinsic values of the toughness (defined in the framework of the Linear Fracture Mechanics) of three different concretes with different mechanical properties (compressive and tensile splitting strengths).
 They propose load-notch opening curves related to mode I macrocrack propagation over more than one meter. These results are very important and useful for researchers who want to validate their numerical models related to this problem.
 They propose to engineers and/or researchers, using numerical models based on fracture mechanics, simple analytical relations permitting to get real and intrinsic KIC and GIC values from simple and standardized tests.

None.

No conflict of interest.

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