A Statistical Approach for Fracture of Brittle Materials Based on the Chain-of-Bundles Model

Ruggieri, Cláudio; Minami, Fumiyoshi; Toyoda, Masao

doi:10.1115/1.2895934

Cited by 16 publications

(8 citation statements)

References 24 publications

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“…The physical significance is this: ductile tearing increases the crack-tip driving force (a w ) as deformation progresses particularly so for low-constraint configurations, which increases the likelihood of unstable crack propagation by cleavage. The trends shown here are consistent with those obtained in previous numerical analyses [28,29] in that stable crack growth elevates the near-tip stresses and increases the volume of the cleavage fracture process zone. Since a w explicitly incorporates the crack-tip stress field and the volume of the near-tip stressed material, it fully captures the governing features for cleavage fracture in growing cracks.…”

Section: Effects Of Ductile Tearing On the Weibull Stresssupporting

confidence: 81%

“…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: 97%

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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: Effects Of Ductile Tearing On the Weibull Stresssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 97%

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

1996

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“…Convergence of effective transverse Young modulus E eff of FRC ðc ¼ 0:5Þ with a number of realizations N conf increased. approximation of stress distribution by the ''chain of bundles" model (see Gumbel, 1958;Ruggieri et al, 1995) y ¼ expðÀ expðÀkðx À x c ÞÞÞ; where x c ¼ 1:53 and k ¼ 1:59. Claimed by Chen and Papathanasiou (2004) the Weibull's statistics of max stress (dash-dotted line in Fig.…”

Section: Interface Stress Statisticsmentioning

confidence: 99%

Meso cell model of fiber reinforced composite: Interface stress statistics and debonding paths

Кущ

Shmegera

Mishnaevsky

2008

International Journal of Solids and Structures

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The primary goal of this work is to develop an efficient analytical tool for the computer simulation of progressive damage in the fiber reinforced composite (FRC) materials and thus to provide the micro mechanics-based theoretical framework for a deeper insight into fatigue phenomena in them. An accurate solution has been obtained for the micro stress field in a meso cell model of fibrous composite. The developed method combines the superposition principle, Kolosov-Muskhelishvili's technique of complex potentials and Fourier series expansion. By using the properly chosen periodic potentials, the primary boundary-value problem stated on the multiple-connected domain has been reduced to an ordinary, wellposed set of linear algebraic equations. The meso cell can include up to several hundred inclusions which is sufficient to account for the micro structure statistics of composite. The presented numerical examples demonstrate an accuracy and high numerical efficiency of the method which makes it to be a promising tool for studying progressive damage in FRCs. By averaging over a number of random structure realizations, the statistically meaningful results have been obtained for both the local stress and effective elastic moduli of disordered fibrous composite. A special attention has been paid to the interface stress statistics and the fiber debonding paths development, which appear to correlate well with the experimental observations.

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“…Recent efforts in this area have focused on developing transferability models for cleavage fracture toughness. Bakker and Koers 6 Minami et al 7 Ruggieri et al 8 and Koppenhoefer and Dodds 9 assess the effects of specimen thickness, crack length and loading rate on elastic–plastic fracture toughness. Ruggieri and Dodds, 10 Xia and Shih, 11 Xia and Cheng 12 and Gao et al 13 generalize the Weibull stress for stationary and growing cracks to include the coupled effects of constraint loss and ductile tearing on J c ‐values.…”

Section: Introductionmentioning

confidence: 99%

A Weibull stress model to predict cleavage fracture in plates containing surface cracks

Gao

Tregoning

et al. 1999

Fatigue Fract Eng Mat Struct

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This study applies recent advances in probabilistic modelling of cleavage fracture to predict the measured fracture behaviour of surface crack plates fabricated from an A515‐70 pressure vessel steel. Modifications of the conventional, two‐parameter Weibull stress model introduce a non‐zero, threshold parameter (σw‐min ). The introduction of σw‐min brings numerical predictions of scatter in toughness data into better agreement with experimental measurements, and calibration of this new parameter requires no additional experimental data. The Weibull modulus (m) and scaling parameter (σu ) are calibrated using a new strategy based on the toughness transferability model, which eliminates the non‐uniqueness that arises in calibrations using only small‐scale yielding toughness data. Here, the Weibull stress model is calibrated using toughness data from deep‐notch C(T) and shallow‐notch SE(B) specimens, and is then applied to predict the measured response of surface crack plates loaded in different combinations of tension and bending. The model predictions accurately capture the measured distributions of fracture toughness values.

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A Statistical Approach for Fracture of Brittle Materials Based on the Chain-of-Bundles Model

Cited by 16 publications

References 24 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

Meso cell model of fiber reinforced composite: Interface stress statistics and debonding paths

A Weibull stress model to predict cleavage fracture in plates containing surface cracks

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