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Journal ArticleDOI

A concept of combined micro and macro fracture mechanics to brittle fracture

01 Sep 1974-International Journal of Fracture (Kluwer Academic Publishers)-Vol. 10, Iss: 3, pp 375-377

AbstractReal materials inevitably contain both stress concentrators as cracks or notches and as dislocations, that is, both macroscopic and microscopic one. From this viewpoint, a concept of combined micro and macro fracture mechanics is proposed for low-stress brittle fracture of steels.

Topics: Fracture mechanics (63%), Brittleness (57%), Fracture toughness (56%)

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Journal ArticleDOI
Abstract: The fracture mechanics stress intensity, K, measured for the cleavage strength of carbon steel by Professor Yokobori and colleagues, at Tohoku University and elsewhere, is shown to follow a Hall-Petch dependence on average grain diameter, l, in accordance with the model-based relationship K = c's 1 2 [σ 0 +kl −1 2 ]; for which c' is a numerical factor, 5 is the effective length of the local plastic zone associated with unstable crack growth, σ0 is a friction stress for appropriate dislocation movement within the polycrystal grains and k is a microstructural stress intensity intermediate between that for the plastic flow or fracture of crack-free material. The separated terms in the K relationship are matched with corresponding Hall-Petch friction stress and microstructural stress intensity measurements for yielding and fracture. In this way, the K relationship is proposed to provide a bridge for the goal set some time ago by Professor Yokobori of combining the microscopic and macroscopic (continuum) viewpoints for understanding the fracture strength properties of engineering materials.

226 citations


Journal ArticleDOI
Abstract: Features of the crack structure of intact rock are systematically investigated by using advanced video microscope, electronic microscope and graphic analysis technology. The fractal effects of the discontinuous structure on the macro-mechanical behavior are discussed. Damage evolution in rocks is described by means of statistical mathematics. Based on the fractal distribution of cracks and on the theory of the weakest link, a general statistical formula of rock strength under a complex stress state has been developed, of which the influence of orientation distribution of cracks and irregularity of crack growth on rock strength has been taken into account. The new expression for rock strength reflects the collective effects of the scale of crack distribution, crack orientation distribution and the irregularity of crack surfaces on rock strength. It relates the macro-strength of rocks to its intrinsic structural properties. It is shown that the Weibull strength formula is a special case of the statistical strength expression when the orientational distribution of cracks is neglected.

44 citations


Journal ArticleDOI
Abstract: The effects of grain size and of crack-tip blunting radius on the fracture toughness of tungsten polycrystals are studied by using a combined dislocation dynamics/cohesive zone model (CZM). Two-dimensional dislocation dynamics are employed to analyze crack-tip plasticity and crack propagation is characterized by a CZM. The geometry of the crack and the corresponding boundary conditions are described by means of a boundary element method with dislocation dipoles as fundamental solution. Grain boundaries are introduced as obstacles for dislocation motion. Numerical experiments reveal that the fracture toughness decreases with grain size, because grain boundaries confine the plastic zone. This effect is particularly pronounced at small loading rates, where the unconfined plastic zone is large. Our results also show that fracture toughness scales with the tip radius as the stress concentration at the crack tip is reduced and the plastic zone is enlarged.

34 citations


Journal ArticleDOI
Abstract: Based on the combined micro- and macro fracture mechanics, the two requisites necessary for the crack propagation, that is, the energy unstable requisite and the critical local stress requisite, are derived for the low-stress brittle fracture of notched specimens. Thus the fracture criterion was obtained. The criterion is compared with the experimental data, such as on the relationships between the fracture stress or the fracture toughness and the grain size diameter, the crack length, the notch tip radius or the yield stress. The good agreement is obtained.

24 citations


Journal ArticleDOI
Abstract: A new approach based on the maximum tangential stress (MTS) criterion has been employed for investigating mixed mode brittle fracture in materials like polycrystalline graphite. The new criterion has been examined using the experimental results reported in the literature for several graphites. The reported experimental data were obtained from fracture tests conducted using the centrally cracked Brazilian disk specimens. It is shown that the values of mixed mode fracture resistance predicted by the new criterion are in good agreement with the experimental results.

8 citations


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