Analysis of a non-linear crack model

Andersson, Hans; Bergkvist, Hans

doi:10.1016/0022-5096(70)90011-6

Cited by 51 publications

(6 citation statements)

References 11 publications

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“…Andersson and Bergkvist (1970) showed that the length/thickness ratio of a fully developed process region increases with the ratio between the slopes (absolute values) of the cohesive and decohesive parts, which were assumed to be linear in their investigation. The ratio between the slopes increases with d max ad D .…”

Section: Significance Of Cohesion-decohesion Characteristicsmentioning

confidence: 99%

The cell model of materials

Broberg

1997

Computational Mechanics

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The cell is regarded as the smallest material unit that contains reasonably suf®cient information about crack growth in the material. A cell is either in a cohesive state or in a decohesive state, the latter implying instability at load control. It is characterized by its linear size and its cohesion-decohesion relation. The reference case of a uniaxially loaded, originally cubic, cell exhibits the cohesive strength and the elongations at which decohesion starts and ends. These quantities in¯uence the size and shape of the process region at a crack edge and also the energy required for crack growth. A body can be modelled by an aggregate of cells, but such modelling is needed only in regions where cells are expected to reach the docohesive state. The cell model is a model of the material and is not necessarily connected to a particular computational method. However, the cells can be ®tted into a ®nite element or ®nite difference formulation. For dynamic cases such as fast crack growth the cell model can be used to qualitatively reproduce experimental results which could hardly be obtained by means of continuum models.

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Section: Significance Of Cohesion-decohesion Characteristicsmentioning

confidence: 99%

The cell model of materials

Broberg

1997

Computational Mechanics

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“…Such a process in which the inelastic dissipation is subsequent to the advancement of the cracking front resembles those cases frequently encountered in brittle composites reinforced with discrete ®bres of a given length¯c (Argon 2000). The mechanism of the advance of such a process zone in which a characteristic traction±separation process, illustrated in ®gure 9 (b),`processes' unbroken solid into fully separated crack¯anks, has been considered in detail by Andersson and Bergkvist (1970). We adopt the ®ndings of their model to our phenomenon.…”

Section: Fractures Across Grain Boundaries Above the Cleavage To Mixementioning

confidence: 97%

Cleavage cracking resistance of large-angle grain boundaries in Fe-3 wt% Si alloy

Argon¹,

Qiao²

2002

Philosophical Magazine A

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A bstractLarge-angle grain boundaries in steel o er an important resistance to the propagation of cleavage cracks that a ects the fracture toughness and can modulate the ductile-to-brittle transition temperature of fracture downwards. This behaviour has been studied in bicrystals of Fe±3 wt% Si alloy in detail. It was noted that the twist misorientation across a large-angle boundary has a more profound e ect on cleavage fracture resistance than the tilt misorientation does. Speci®c measurements of such resistance at ¡ 20°C over a random selection of large-angle grain boundaries in bicrystals and associated fractographic studies have led to quantitative models of this resistance. The study has also revealed a transition from pure cleavage to mixed cleavage at around 0°C for this alloy, above which the observed increment of fracture work could be associated with the sigmoidal plastic bending and rupture of ligaments left between separate primary cleavage strips in the adjoining grain.

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“…The mechanism of the advance of such a process zone in -12-which a characteristic traction-separation process, illustrated in Fig. 9b, "processes" unbroken solid into fully separated crack flanks has been considered in detail by Andersson and Bergkvist (1970). We adopt the findings of their model to our phenomenon.…”

Section: Work Of Cleavage In a Grainmentioning

confidence: 99%

Brittle to Ductile Transition in Cleavage Fracture of Alpha-Iron: Experiments and Modeling of Mechanisms

Argon¹

2002

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Washington Headquarters Service, Directorate for Information Operations and Reports. 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188) Washington, DC 20503. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) 15- PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Massachusetts Institute of Technology 77 Massacusetts Avenue Cambridge, MA 02139 145 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)Office of Naval Research, Materials Science Prg ONR Code 331 800 N. Quincy Street, Balston Tower 9 Arlington VA 22217-5000 SPONSOR/MONITOR'S ACRONYM(S) ONR SPONSORING/MONITORING AGENCY REPORT NUMBER 99R00006-01 DISTRIBUTION AVAILABILITY STATEMENTONR Program Officer Dr. George Yoder; Administrative Grants Office; Director NRL; DTIC Othrewise Unlimited 13. SUPPLEMENTARY NOTES ABSTRACTIn this research the mechanisms of the brittle to ductile transition of fracture initiated primarily by crack tip processes under both quasi-static as well as dynamic conditions was studied experimentally, and mechanistically modeled. Additional experiments and modeling included the role of grain boundariesin resisting cleavage cracking among grains in Fe-3%Si alloy, also associated with modeling. Reproduction in whole, or in part, is permitted for any purpose of the United States Government.This document has been approved for public release and sale, its distribution is unlimited. BRITTLE TO DUCTILE TRANSITION IN CLEAVAGE FRACTURE OF ALPHA-IRON: EXPERIMENTS AND MODELING OF MECHANISMS I. Summary of Research Carried out under the ProgramThe research results reported here in this final technical report are a continuation of an earlier program supported by the ONR Mechanics Division under Contract #N00014-92-J-4022 where the emphasis was on an experimental study of the brittle-to-ductile transition of fracture in silicon single crystals by thermal crack arrest and on modeling of dislocation emission from crack tips. Similarly, the research initiated under the ONR Program reported here, supported by the Materials Science Division and studying the role of grain boundaries in the crack growth resistance is now being continued under NSF support.The principal thrust in the completed research program under ONR support was on two experimental studies. One thrust was the completion of earlier research on the study of brittle to ductile fracture transition in silicon single crystals as stated above, while the second thrust was on a study of the role of grain boundaries in the enhancement of cleavage crack-gr...

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Analysis of a non-linear crack model

Cited by 51 publications

References 11 publications

The cell model of materials

The cell model of materials

Cleavage cracking resistance of large-angle grain boundaries in Fe-3 wt% Si alloy

Brittle to Ductile Transition in Cleavage Fracture of Alpha-Iron: Experiments and Modeling of Mechanisms

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