Structures with Notches or Cracks
The size effect law was originally verified (Bazant 1983, 1984a) by comparisons with the tests of Walsh (1972), whose results are summarized in Fig. 1.5.2. Walsh used single-edgc-notchcd beams in three-point bending (SEN-TPB, see Table 1.5.1 and Fig. 1.5.1, test series Al-6). Walsh was apparently first to plot. the test results as loga^u vs. log D, but did not try to describe this plot mathematically or generalize it. Walsh’s classical tests, however, were of limited range, too short for the scatter obtained, and included only one type of fracture specimen, and so the comparisons were not completely conclusive.
A stronger experimental verification was presented by Bazant and Pfeiffer (1986, 1987), covering a broader size range and four very different types of specimens : SEN-TPB, double-edge-notched in eccentric compression (DEN-EC), double-edge notch in eccentric compression (DEN-EC), and doubleedge notch in shear (DEN-S); see Table 1.5.1 and Fig. 1.5.1, test series В1—4 and Cl-^t. The research included tests on concrete (series Bl-4) and on mortar (scries Cl-4). The test results and their optimum fits by the size effect law are shown in Fig. 1.5.3. Obviously, the comparison provides a strong justification for the size effect law (for statistical comparisons, see the original paper). The data points in Fig. 1.5.3 refer to individual tests.
An experimental size effect study of high strength concrete has been conducted by Gettu, Bazant and Karr (1990), using SEN-TPB. The results are shown in Fig. 1.5.4, again in comparison with the optimum fits by the size effect law and its asymptotes.
Figure 1.5.4 Size effect results of Geltu, Bazant and Karr (1990). Results of Bazant and Pfeiffer (1987) for ordinary concrete are also included for comparison.
For concrete, the foregoing results have been complemented by the extensive size effect data for SHN – TPB specimens published hy Bazant and Gcttu (1992). These tests (as well as similar tests of fracture of limestone by Bazant, Bai and Geltu 1993), however, also included a systematic investigation of the effect of the loading rate, and, therefore, the presentation of these data is better postponed to Chapter 11. Further, it has been shown (Bazant, Kim and Pfeiffer 1986) that the size effect law agrees well with the results of the size effect tests by Jcnq and Shah (1985a, b), although a good fitting was not possible because the size range was too limited compared to the scatter obtained.
The ability of the size effect law (1.4.10) to describe the strength variation of notched specimens in materials other than concrete has been investigated, too, particularly for rocks and ceramics. Moving from coarser grained rocks to ceramics, Fnthy (1992) tested marble and granite; Bazant, Gcttu and Kazemi (1991) limestone; and McKinney and Rice (1981) slip-cast fused silica (SiC>2) and nilridized silicon carbide (SiC CN-137 and SiC CN-137). Fig. 1.5.5 summarizes their test results. It can be seen that the size effect law describes the various results acceptably well.
Recent experimental data indicate a similar degree of agreement for composites and for ice. Bazant, Daniel and Li (1996) tested in tension both single – and double-edge notched specimens of highly orthotropic carbon-epoxy fiber laminates and they found good agreement with the size effect law for a 1:8 range of sizes. Adamson et al. (1995) and Mulmule, Dempsey and Adamson (1995) performed various series of tests on sea ice using various specimen geometries. In one of the scries, square plates with a notch subjected to opening forces at the notch mouth were tested with a size ratio of 1; 160 (the specimens ranged from 0.5 to 80 m in size)? This is the test series of wider size range known to date. The results showed a very good agreement with the size effect law.