PSI - Issue 13

Taiko Aikawa et al. / Procedia Structural Integrity 13 (2018) 104–109 Aikawa/ Structural Integrity Procedia 00 (2018) 000 – 000

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It is well known that brittle fracture surfaces of steel plates exhibit irregularities with typical morphology, known as chevron markings or herring bone patterns (Kies et al., 1950; Boyd, 1953; Tipper, 1957; Carlsson, 1963; Gash, 1971). They attributed the reason of the chevron markings as centrally concentrated crack initiations leading but scalloped crack front. Influence of stress wave reflection was also discussed. It might generally be recognized that brittle fracture surface is smooth at lower temperature and rough and irregular at higher temperature. Another important feature is the formation of shear-lips, which often appear near the plate surfaces (Aihara et al., 2013). It is generally recognized that the shear-lips increase surface energy thereby suppressing crack propagation and increasing crack arrest toughness. It is also said that they reduce stress intensity factor by crack closure force acting on uncracked ligaments, which are yielded, shear-fractured and finally become shear-lips. Formation of the uncracked ligaments are modelled and their effect on crack propagation and arrest were discussed (Shibanuma et al., 2016a, 2016b, 2018). However, their analysis is based on a flat crack and do not take account of the crack surface irregularities. In the present study, a computer simulation model has been developed to reproduce brittle fracture surface morphologies including the chevron markings, uncracked-ligaments and shear-lips. Parameters influencing fracture surface morphologies and crack arrest are discussed based on the developed model. 2. Nomenclature crack arrest toughness − local fracture toughness − local stress intensity factor corresponding to normal stress acting on a cleavage plane plate thickness constant relating with − 3. Modelling Numerical simulations of brittle crack propagation which take account of fracture surface irregularities are not many. Mclintock (1997) proposed a computer simulation model to reproduce irregular cleavage fracture surface at grain-size level. Following his study, Qiao and Argon (2003) proposed a more sophisticated model, in which non uniform cleavage crack propagation in polycrystalline steel microstructure was modeled and compared with observed fracture surface at microscopic level. Shibanuma et al. (2016c) and Yamamoto et al. (2016) extended the model proposed by Aihara and Tanaka (2011) into macroscopic brittle fracture. One of the present authors proposed a numerical simulation model of crack propagation in bcc polycrystalline solids (Aihara and Tanaka, 2011), in which crystal grains were modelled as columnar cells, a flat crack was assumed in each cell and overall fracture surface was constructed as an aggregate of the flat cracks. To determine crack direction in each cell, three {100} planes, having a right angle each other, were assumed randomly. For a cell in front of a crack tip, normal stress acting on each {100} plane is calculated from local stress intensity factors of the mixed mode, { , , } , and the plane having the maximum normal stress was selected as a cleavage plane, see Fig. 1. Because the constructed fracture surface is not flat nor is the crack front straight, it is a laborious task to calculate { , , } for such an irregular crack, accurately. Therefore, approximate formulae were applied. To take the influence of crack front non-straightness, equation developed by Rice (1985) was applied. Also, equations developed by Gao (1992) was applied to take account of the fracture surface irregularity. Ridges between the cells carry shear stress having an effect of crack closure, see Fig.1. Because the ridges are expected to shear-yield just after the crack front passes through, the shear stress acting on the ridge can be assumed equal to the shear-yield stress of the material. Local cleavage fracture criterion is incorporated, i.e. , cleavage crack is assumed to extend in a cell if local stress intensity factor, − , exceeds local fracture toughness, − , − ≥ − . (1) where − is related to the magnitude of normal stress acting on the selected plane in the cell: − = ∑ [ ( )] 3 =1 (2)