PSI - Issue 13

F.J. Gómez et al. / Procedia Structural Integrity 13 (2018) 267–272 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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= ( , )

3

(2) Gómez and Elices (2006) checked the validity of the expression (2) in linear elastic materials and showed that introducing a non-dimensional formulation based on the fracture toughness and the characteristic length of the cohesive zone model, leads a function with a weak material dependency. ≈ ∗ ( ℎ ) (3) ℎ = ( ) 2 (4) where f t is the fracture strength. Gómez and Elices (2006) collected failure data of alumina, silicon nitride, monocrystalline and polycrystalline silica, zirconia partially stabilized with magnesia, zirconia partially stabilized with yttria, tetragonal zirconia fully stabilized with yttria, and PMMA at -60°C and demonstrated how the expression (3) reduces the dependency of the material. The experimental results were fitted to the following expression which constitutes itself a phenomenological failure criterion (Gomez et al 2005): = √ 1+0.47392( ℎ ⁄ )+2.1382( ℎ ⁄ ) 2 + /4( ℎ ⁄ ) 3 1+( ℎ ⁄ ) 2 (5) Failure due to U-notches can be explained in a similar way by applying criteria such as the critical strain energy density (Lazzarin and Berto 2005), maximum stress, mean stress (Seweryn and Lukaszewick 2002, Susmel and Taylor 2008) or the theory of cohesive zone model (Gomez et al 2005). All materials considered in Gómez and Elices (2006) had linear elastic behavior until failure. In elastoplastic materials, U-notches can be analyzed in a similar way combining the failure criteria with simplifications or rules that substitute the real elastoplastic behavior by another linear elastic fictitious one. Within this type of approach is the Equivalent Material Concept (EMC) (Torabi 2012 and 2013), which establishes that the modulus of elasticity E and the fracture toughness of the fictitious material as the same than the real material and the fracture stress can be obtained assuming that the energy density developed in a tensile test at maximum load is the same in the real case and the fictitious one. ( ) = 2 2 (6) where SED necking is the strain energy density developed in a tensile test under maximum load (Figure 1) and  f the fictitious fracture strength of the equivalent material. 3. Equivalent material concept To verify the validity of the proposed methodology, failure data of five different materials have been compiled and revised: PMMA, polycarbonate, aluminum alloy, vessel steels and structural steel. Gómez and Elices (2000) studied the failure of PMMA due to notches at room temperature, carrying out an extensive experimental program of fracture tests with different radii, notch depths, sizes and types of solicitation. The fictitious fracture strength of PMMA has been calculated by applying expression (6) to the stress-strain curve measured at room temperature. The non-dimensional critical notch stress intensity factors calculated with the properties of Table 1 are shown in Figure 2. The ratio between the maximum load and the plastic collapse load, L r , (FITNET 2007) has been calculated for the largest radius and the value obtained appears in Table 1. 4. Failure criteria in elastoplastic materials