A statistical model of brittle fracture by transgranular cleavage

Lin, Tianyi; Evans, A.G.; Ritchie, Robert O.

doi:10.1016/0022-5096(86)90013-x

Cited by 179 publications

(93 citation statements)

References 21 publications

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“…Work of the Beremin group [17] attains particular relevance here as it introduced the so-called Weibull stress as a local fracture parameter. Similar statistical approaches falling within the scope of micromechanics methodologies have also been described by Wallin, et al [18,19,20], Lin, et al [21], Mudry [22], Bruckner, et al [23,24], Minami, et al [25], Bakker et al [26,27], Ruggieri, et al [28], among others. Dodds and Anderson [29,30] have proposed to quantify the relative effects of constraint variations on cleavage fracture toughness in the form of a toughness scaling model.…”

Section: Introductionmentioning

confidence: 56%

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

1996

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Annual: 10-1-95 to 9-30-96 14.This study describes a computational framework to quantify the influence of constraint loss and ductile tearing on the cleavage fracture process, as reflected by the pronounced effects on macroscopic toughness (J c , Dc). Our approach adopts the Weibull stress, Ow, as a suitable near-tip parameter to describe the coupling of remote loading with a micromechanics model incorporating the statistics of microcracks (weakest link philosophy). Unstable crack propagation (cleavage) occurs at a critical value of Ow which may be attained prior to, or following, some amount of stable, ductile crack extension. A central feature of our framework focuses on the realistic numerical modeling of ductile crack growth using the computational cell methodology to define the evolution of near-tip stress fields during crack extension. Under increased remote loading (J), development of the Weibull stress reflects the potentially strong variations of near-tip stress fields due to the interacting effects of constraint loss and ductile crack extension. Computational results are discussed for well-contained plasticity, where the near-tip fields for a stationary and a growing crack are generated with a modified boundary layer (MBL) formulation (in the form of different levels of applied T-stress). These analyses demonstrate clearly the dependence of Ow on crack-tip stress triaxiality and crack growth. The paper concludes with an application of the micromechanics model to predict the measured geometry and ductile tearing effects on the cleavage fracture toughness, J c , of an HSLA steel. Here, we employ the concept of the Dodds-Anderson scaling model, but.replace their original local criterion based on the equivalence of near-tip stressed volumes by attainment of a critical value of the Weibull stress. For this application, the proposed approach successfully predicts the combined effects of loss of constraint and crack growth on measured Jc-values. ABSTRACTThis study describes a computational framework to quantify the influence of constraint loss and ductile tearing on the cleavage fracture process, as reflected by the pronounced effects on macroscopic toughness (J e , oe). Our approach adopts the Weibull stress, a w , as a suitable near-tip parameter to describe the coupling of remote loading with a micromechanics model incorporating the statistics of microcracks (weakest link philosophy). Unstable crack propagation (cleavage) occurs at a critical value of a w which may be attained prior to, or following, some amount of stable, ductile crack extension.A central feature of our framework focuses on the realistic numerical modeling of ductile crack growth using the computational cell methodology to define the evolution of near-tip stress fields during crack extension. Under increased remote loading (J), development of the Weibull stress reflects the potentially strong variations of near-tip stress fields due to the interacting effects of constraint loss and ductile crack extension.Computational results are dis...

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Section: Introductionmentioning

confidence: 56%

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

1996

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“…For grain size dependence, the yield stress is increased, but the fracture stress is increased more because of k C > k y , and a greater amount of work hardening is required to reach a higher stress intensity, K C . An H-P dependence for K C was shown by Petch and Armstrong to apply for 0.08 carbon steel results reported by Lin et al [82] in tests at −80 and −120 • C.…”

Section: Crack Size In Fracture Mechanicsmentioning

confidence: 63%

Material grain size and crack size influences on cleavage fracturing

Armstrong

2015

Phil. Trans. R. Soc. A.

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A review is given of the analogous dependence on reciprocal square root of grain size or crack size of fracture strength measurements reported for steel and other potentially brittle materials. The two dependencies have much in common. For onset of cleavage in steel, attention is focused on relationship of the essentially athermal fracture stress compared with a quite different viscoplastic yield stress behaviour. Both grain-size-dependent stresses are accounted for in terms of dislocation pile-up mechanics. Lowering of the cleavage stress occurs in steel because of carbide cracking. For crack size dependence, there is complication of localized crack tip plasticity in fracture mechanics measurements. Crack-size-dependent conventional and indentation fracture mechanics measurements are described also for results obtained on the diverse materials: polymethylmethacrylate, silicon crystals, alumina polycrystals and WC-Co (cermet) composites.

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“…The material conditions analysed in this paper are basically brittle, although in notched conditions there are some plastic phenomena prior to the final cleavage instability. The literature presents a number of significant papers (e.g., [30][31][32][33]) dealing with cleavage fracture which are based on an elastic-plastic approach and on the consideration, explicitly or implicitly, of a material characteristic dimension.…”

Section: Finite Elements Modelling and Calibration Of The Critical DImentioning

confidence: 99%

Analysis of notch effect in the apparent fracture toughness and the fracture micromechanisms of ferritic–pearlitic steels operating within their lower shelf

Cicero

Madrazo

García

2014

Engineering Failure Analysis

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The fracture resistance of materials is generally higher in notched conditions that in cracked conditions. In other words, when the notch radius increases there is also an increase in the apparent fracture toughness, which is that exhibited in notched conditions. This paper presents an analysis of the notch effect on two ferritic-pearlitic steels operating within their corresponding lower shelf, and develops an experimental The research is completed with the analysis of the evolution of fracture micromechanisms when the notch radius increases, revealing a direct relation between this evolution and the apparent fracture toughness observations.

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A statistical model of brittle fracture by transgranular cleavage

Cited by 179 publications

References 21 publications

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

Material grain size and crack size influences on cleavage fracturing

Analysis of notch effect in the apparent fracture toughness and the fracture micromechanisms of ferritic–pearlitic steels operating within their lower shelf

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