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Engineering Fracture Mechanics

Available online 30 April 2018
Engineering Fracture Mechanics

Influence of the width of the specimen on the fracture response of concrete notched beams

https://doi.org/10.1016/j.engfracmech.2018.04.045Get rights and content

Highlights

  • For smaller depth beams, the width of specimens influences the size effect.

  • For larger widths of the specimen, the effect of friction might be relevant.

  • The curing conditions must be the same for all specimens in order to study the width effect.

  • The shape of the FPZ is study by means of DIC analysis.

Abstract

This work presents an experimental study performed to investigate the influence of the width and size of the specimen on the fracture response of concrete notched beams. Twenty-eight beams with six cross-sections has been tested using a three-point bending (TPB) test setup, which is designed according to the draft of a report developed by Joint ACI/ASCE 446 Technical Committee. Two depths (70 mm and 150 mm) and three widths (35 mm, 70 mm and 150 mm) of the beam are considered. 3D digital image correlation (DIC) is employed for 18 specimens. The load-deflection response obtained from DIC is compared with the load-deflection response obtained from the readings of two linear variable displacement transformers (LVDT). Load responses, peak loads, strain profiles, and failure modes of TPB tests are presented and discussed. The authors observe that a potential width effect is combined with the well-known size effect. In addition, the evaluation of the fracture energy from the load response might be influenced by the width of the beam. Finally, the strain profiles along the notched cross-section obtained from DIC suggest that the evaluation of the fracture energy from the load response might be misleading.

Introduction

Since the early 70s [1], it is well-known that linear elastic fracture mechanics (LEFM) does not fully capture the fracture phenomenon in concrete elements. Pioneering results by Walsh [2] indicated that if notched beams of different sizes are tested, the plot of the nominal stress σN [3] deviates from the straight line of slope -1/2 in a double logarithmic plot. This is one proof that LEFM does not apply for concrete, at least for a vast set of sizes, as it is easily proven that, if LEFM holds, similar notched beams of different sizes exhibit a variation of the nominal stress σN that depends on the inverse of the square root of one of the dimensions D of the beams [3]. A new impetus in the study of fracture of concrete came from Hillerborg et al. [4], who introduced the cohesive crack model for concrete. The concept of the cohesive crack model builds on the original works by Bareblatt [5] and Dugdale [6]. The key ingredient of the cohesive crack model is the presence of a non-linear softening zone at the crack tip, which is called fracture process zone (FPZ). Hillerborg et al. [4] assumed that the crack is a zero-width line (fictitious crack model) that opens by an amount w (known as separation or opening displacement) while still transferring stresses σ through it. The softening function σ=f(w) is the identity document of the material. The area under the curve is the fracture energy GF, which can be obtained from tests by employing the concept of work of fracture [7], [8], [9], [10]. It should be pointed out that an alternative model to the one proposed by Hillerborg et al. [4], but to some extent equivalent, was proposed by Bazant [11], [12]. In addition, the cohesive crack model applies to other materials [13], [14] and interfaces between the materials [15], [16], [17], [18] .

Because of its behavior, concrete is typically defined as a quasibrittle material [3]. Many researchers have contributed to the development of the cohesive crack model and therefore to the study of concrete as a quasibrittle material. In this brief introduction, only few key contributions are reported for the sake of brevity [7], [19], [20], [8], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32].

One interesting aspect of the behavior of concrete is how the size effect deviates from what it is observed in LEFM. Size effect itself is a quite intriguing phenomenon. It simply states that, contradicting what predicted by strength of materials, structural members of different sizes would fail at different stress levels. As mentioned above, LEFM is able to predict the size effect. However, if a material like concrete has a large FPZ with respect to the dimensions of the structural element, LEFM does not apply. A first analytical attempt to investigate the size effect in concrete is reported in [33]. Bazant also proposed a simple size effect formula [34], [12] that allows also to determine the material fracture properties as the peak loads of specimens of different sizes are available. As often happens, the experimental evidence of the size effect is fundamental to develop an analytical approach. Typically, notched beams of different sizes are tested and the peak load is used to represent the size effect in terms of nominal stress versus one of the dimensions of the beam. The peak load has been proven to be associated with the first portion of the softening curve [30]. However, as testing different sizes could become cumbersome, most researchers have agreed over the years that while the depth D should be scaled with the length L of notched beam, the width B of the specimens could be kept constant. The width effect is partially studied in the literature and certain phenomena, such as the wall effect, hydration, shrinkage, are known to contribute to the width effect. Nevertheless, to the best of the authors’ knowledge, a robust study of the width effect is not present in the literature [35]. This paper investigates the width effect as a possible coupled problem with the size effect. Notched beams with two different depths and three different widths were tested using a three-point bending test setup. As pointed out in [36], [9], [37], [38], [39], particular care was paid to obtain a series of specimens that were carefully cast from the same batch, cured under the same conditions, and tested at virtually the same age under the same environmental conditions. Few specimens (named DRY specimens), left to cure outside the lime-saturated bath until testing, showed the importance of the curing regimen adopted. The peak load was used to plot in a double logarithmic scale the nominal stress versus the depth. A width effect was observed for smaller depth specimens. In addition, from the experimental point of view, it was noted how the measurement devices used to obtain the load–displacement curves could influence the calculation of the fracture energy. The presence of friction, even though expedients were put in place to reduce its effect, could be relevant for larger (and wider) specimens, and thus should be carefully considered. Finally, three dimensional digital image correlation (3D-DIC) measurements were used to discuss the shape and length of the FPZ.

Section snippets

Materials

All concrete specimens tested in this experimental work, including cubes and cylinders employed for material characterization, were cast from the same batch of portland cement concrete. The mixture proportions by weight of the constituents used were: cement (1.00): water (0.43): coarse aggregate (3.00): fine aggregate (3.00). The maximum aggregate size da was equal to 15 mm. Within the same batch of concrete, specimens were cast at different times. For this reason, concrete specimens were

Load responses

This section presents the results of the fracture mechanics tests performed on 28 notched concrete beams. Two depths and three widths were considered. Two graphs are plotted for each specimen that features the load (P) per unit width (B) on the vertical axis, and the point load displacement δ or the CMOD on the horizontal axis.

Figure 4a-b and Figure 4c-d-e-f show the responses for 70 mm-depth specimens and 150 mm-depth specimens, respectively. Figure 4a-c-e shows the load per unit width P/B

Fracture energy

The fracture energy, GF, of concrete was evaluated from the area under the load-deflection response as proposed by [7], [8], [9], [10]. The value of GF was adjusted to include the work done by the self-weight, P0, of the specimen, as shown in Figure 7a. In the evaluation of the work done by the self-weight P0, it is assumed that the area referred to as A2 in Figure 7 is equal to the area referred to as A3 in Figure 7 [45]. The self-weight, P0, is considered as a concentrated load [46], and is

Conclusions

In this paper, a preliminary study of the possible coupling of the width and size effects in the determination of the fracture properties of concrete is presented. Notched beams with two different depths and three different widths were tested with a three-point bending set-up. The key aspects of this study can be summarized as follows:

  • 1)

    The double logarithmic plots of the nominal stress versus depth indicated that for smaller depth beams, the width effect might be relevant.

  • 2)

    Larger widths, however,

Uncited references

[51], [52], [53], [54], [55], [56], [57]

Acknowledgements

Technicians of the laboratory LISG (Laboratory of Structural and Geotechnical Engineering) at University of Bologna are gratefully acknowledged.

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