13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- stress intensity corresponding to maximum load in the test [4]. This method is really an improvement of the classical tests where the maximum load has been combined with the initial crack length (a0) to obtain a nominal fracture toughness value. The challenge with the double-K criterion lies in the reliable detection of the moment of crack initiation, which is almost invisible on the load-displacement record. Also, the estimation of the crack length at maximum load contains an experimental challenge and the necessity to combine both estimates of the crack tip displacement and load displacement. This prevents the method from becoming a simple quality assurance type of fracture toughness estimate. As a compromise to the use of the classical nominal load maximum stress intensity factor, a special size effect expression has been proposed by Bažant. (See e.g. [6]). The Bažant size effect expression is versatile and has been shown to describe well the size effect in load maximum values of concrete and other quasi-brittle materials. The Bažant size effect expression for load maximum (Pmax) can be expressed in the form of Eq. (1). B and W denote the fracture toughness specimen thickness and width and σf corresponds to the tensile stress of the material. The constant c accounts for specimen geometry and W0 is a normalizing constant. The constants c and W0 are determined by fitting to test results from different size specimens of identical geometry. Apparently the only weakness with the size effect expression is that a comparison between different loading geometries is not possible without the inclusion of additional fitting parameters [7]. max 0 1 f c P B W W W σ⋅ = ⋅ + , (1) Here, a LEFM based estimate of the effective stress intensity factor and the effective crack growth at maximum load in a fracture mechanics test is used to obtain a simple power law approximation of the effective K-R curve that is applicable to the description of not only different size specimens, but also specimens with varying geometry. 2. Estimate of Maximum Load In the case of metals, the materials tearing resistance is usually well described with a simple power law expression. Assuming, that the evolution of the fracture process zone and its effect on the effective materials fracture resistance behaves similarly to metals, also the effective stress intensity factor as a function of the effective crack growth should be possible to approximate with a power law in the form of Eq. (2). 1 m Ieff mm eff K K a ≈ ⋅Δ , (2) For metals, when the tearing resistance is expressed in J-integral units, the power m is close to 0.5 or less. Thus, in K units the power should be in the vicinity of 0.25. If the fracture process zone size is very small compared to the crack growth, Δa, the power m will be small. If it is large compared to Δa, the power m should be closer to 0.25 or even above. When the relation between crack growth and fracture process zone no longer exists, the power m is expected to grow uncontrollable. This is not, however, expected to occur until well beyond the maximum load value. The effective stress intensity factor is related to load and the effective crack length by Eq. (3).
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