13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- max 0 2 0 0 0 0 4, 0.1 0.3886 m 0.1963 2 0.00 . 1118 147 m effP a a m a S a m W W W W W W a W a Δ ⎡ ⎤ ≈ ⎢⎣ = ≥ ⎥ ⎦ ⋅ − ⎛ ⎞ ⎛ ⎞ + ⋅ − ⋅ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ − − ⋅ ⋅ , (6) 0 2 2 0 0 max 0 0.1542 8.063 0.8219 2.9 0.6, 0.1 4 effP a m W a a a a H m exp m W W W W W ⋅ ⎧ ⎫ ⎛ ⎞ ⎛ ⎞ + ⋅ ⋅ + − ⋅ ⋅ ⎨ ⎬ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎩ Δ ⎡ ⎤ ≈ = ≥ ⎢ ⎥ ⎣ ⎦ ⎭ , (7) It is important to note that Eqs. (6) and (7) are applicable only for standard specimen geometries. Especially in the case of the SE(B) specimen often different S/W ratios are used in the tests. For such tests, the standard f(a/W) expression can be adjusted e.g. by Eq. (8) [9] to be used together with its derivative in Eq. (5). 2 3 S/W S/W 4 4W a a a a a f f 1 1 0.08 0.24 1 0.28 1 1 S W W W W W = ⎧ ⎫ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎪ ⎪ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ = ⋅ + − + − − − − ⎨ ⎬ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎪ ⎪ ⎝ ⎠ ⎩ ⎭ , (8) The analysis consists of solving the power m and K1mm iteratively by combining Eqs (4) and (5) to provide the correct maximum load values for different size and/or geometry specimens. The result is obtained in the form of the effective K-R curve in the form of Eq. (2) which then can be used for the evaluation of other geometries. For a constant geometry and fixed initial crack size ratio (a0/W), the effective crack growth is directly related to the specimen width (W). The proposed method relies on the assumption that the effective K-R curve up to maximum load can be approximated by a simple power law. Karihaloo and Nallathambi [10] collected a large number of SE(B) data and estimated from the experimental load-displacement traces, the relation between initial crack length and the effective (based on effective compliance) crack length corresponding to maximum load. Their results have been reproduced in Fig. 5. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.2 0.4 0.6 0.8 1.0 m = 0.1 SE(B) specimen S/W = 4 aeff/W a0/W Karihaloo varying S/W m = 0.45 Figure 5. Estimate of effective crack length at maximum load, Eq. (6), compared to Karihaloo and Nallathambi experimental data from SE(B) specimens with varying S/W [10].
RkJQdWJsaXNoZXIy MjM0NDE=