56 H. T. Nguyen et al. the standard fracture test specimens used for concrete, typically the three-point-bend specimen, there is also no significant compression parallel to the notch, and so these tests give no information on its possible effect. Presented here is a simple modification of the standard notched three-point-bend fracture test that can provide experimental information on the effect of crack-parallel compression. The idea is to apply the compressive load through plastic pads, which exhibit near-perfect plastic yielding with a long yield plateau, and install the end support with a gap that engages only after the compression load has reached the yield plateau. This approach avoids using for compression separate jacks, which is the common way to apply additional loads in structural engineering labs. The self-weight and support of such jacks would make the test evaluation complicated and ambiguous. It will also be shown that the crack band model coupled with microplane constitutive model M7 can match the tests results well. Based on this validation, computer simulations with model M7 will be trusted to extend the understanding of crack-parallel normal stress effects beyond the limited range of the present experiments. A feature of the microplane model that is important for the present problem is that it can capture separately the frictional slip of microcracks of various orientations (modeling internal friction as interaction between the first and second invariant makes no distinction among various orientations of frictional slip). 8.2 Background Normal concrete of specific compression strength f c = 27.58 MPa (4000 psi) at 28 days of age was utilized for the experiments. To minimize the scatter of mechanical properties, all the specimens were cast within a few hours from the same batch of concrete delivered by a ready-mix supplier (Ozinga Co.). The specimens for material characterization and model calibration include: cylinders and square prisms for compression tests; cylinders and prisms for splitting tests; beams for fracture tests, geometrically scaled, were of three sizes: small D (height of the notched beam) =101.6 mm, medium D=203.2 mm, and large D=404.6 mm. The elasto-plastic loading pads had sizes S of ratio S/D=1/4. All the samples were cured for 1 year in a fog room and then tested within 3 weeks. This testing period was sufficiently short to avoid appreciable properties change due to hydration. To produce additional compressive stress parallel to the crack, elasto-plastic polypropylene pads (Fig. 8.1a) were placed adjacent to the crack mouth (Fig. 8.1a), exactly symmetric with the steel loading pads on the opposite side. Figure 8.1 shows that the pads are almost elastic-perfectly plastic, exhibiting a long yield plateau (strictly speaking there is a very small but negligible hardening slope). A bending moment can then be applied while keeping simultaneous constant compressive stress parallel to crack. To obtain a different value of the applied compressive stress (with no shortening of the yield plateau), holes are drilled through the pads to weaken their yield strength (this also reduces the elastic stiffness). The polypropylene is stiff enough to reach the yield strength without bulging of the pad, and the yielding of the pad results from the growth of shear bands across its body. The complete setup can be seen in Fig. 8.1a (right). The testing procedure for beams with crack-parallel compression is described in Fig. 8.1b. First, the plastic pads are placed under the beam and the cylindrical supports at beam ends are placed to have a 2–4 mm gap below the bottom surface; Fig. 8.1b-I. Until the gap closes, such elasto-plastic pads produce only the crack-parallel compression with no bending. As the load point displacement increases, the pad deforms first elastically and then yielding begins (Fig. 8.1b-II). Strictly speaking, there is a slight hardening (Fig. 8.1c) due to mild expansion of contact area, but this can be neglected. For a while, the cylindrical end supports are not yet engaged in contact. Once they get in contact, bending begins, and the bending moment M increases at constant crack-parallel compression (Fig. 8.1b-III), which eventually triggers crack growth (Fig. 8.1b-IV). In Fig. 8.1c, this is manifested by an increase of load departing from the yield plateau. This was confirmed to not have any impact on the overall stiffness of the entire beam and fracture analysis but to allow cracks to initiate and propagate at the main crack tip area. After reaching the peak load, the specimen gets fractured completely, leaving two separate beams under compressive loads. This causes the load to drop down to the yield plateau of the load-displacement curve. From that up and down the portion of the curve, one can extract some of the material response under crack-parallel compression; Fig. 8.1d. A typical load-displacement curve in the whole test is shown in Fig. 8.1c, and the extracted curve of load versus crack tip opening displacement (CTOD) curve is shown in Fig. 8.1d. 8.3 Analysis To quantify the variation of the fracture energy Gf caused by crack-parallel compression, the size effect method [2] is used. In this method, it suffices to measure the maximum loads, P, of notched specimens of several sufficiently different sizes. Geometrically similar notched three-point-bend beams of three sizes, have been used. To determine Gf, one must obtain first
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