Pub Date : 2021-11-12DOI: 10.1093/oso/9780192846242.003.0008
Z. Bažant, J. Le, M. Salviato
The last chapter briefly sketches the rich century-long history of fracture mechanics, with an additonal quasibrittle focus. The mainstream milestones were Griffith's 1921 introduction of energy criterion of crack propagation, Irwin's 1958 discovery of the relation of the energy release rate to the stress intensity factor of the near-tip singular stress field, Barenblatt's 1959 conception of the cohesive crack model, and Rice's 1966 discovery of the J-integral giving the energy flux into tip crack tip. Progress was spurred by the breakup of welded Liberty ships at sea and of Commet jetliners in flight, and later by many sudden shear failures of RC structures. At the interface with structural safety the main milestone was Weibull's 1939 introduction of his namesake distribution and statistical size effect in brittle failure. Hillerborg's 1976 fictitious crack model for concrete, essentially equivalent to the cohesive crack model, was a boost for computer simulation of concrete fracture. An even stronger impetus was, during 1984-1991, the gradual emergence, during 1976-87, of the crack band and nonlocal models which can capture the tensorial behavior of the FPZ, and of the energetic size effect law. Evolution of quasibrittle fracture mechanics continues until today (2020), e.g., with the recent disruption of established line-crack fracture concepts by the gap test documenting the strong effect of crack-parallel stresses. Fracture mechanics research will doubtless flourish for another century.
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Pub Date : 2021-11-12DOI: 10.1093/oso/9780192846242.003.0003
Z. Bažant, J. Le, M. Salviato
The nonlinearity of fracture mechanics is most easily captured by a line crack model because all the structure volume remains elastic, which means that all the nonlinearity is moved into the boundary conditions, although at the penalty of missing the effect of crack-parallel stresses. The cohesive crack model, originated by Barenblatt, lumps all material nonlinearity into a softening relation between the cohesive stress and the opening displacement. Irwin's material length characterizing the size of the fracture process zone (FPZ) is discussed, equivalent LEFM is introduced, and the R-curves, along with their use in fracture stability analysis and size effect, are presented. The relation of cohesive law to fracture energy and strain softening behavior is described. Boundary integral analysis of the cohesive crack growth is explained. Insensitivity to the crack-parallel stresses and the non-tensorial description of the FPZ are pointed out as a limitation of the cohesive crack model. Finally, direct eigenvalue analysis of peak loads and size effect curves is presented.
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Pub Date : 2021-11-12DOI: 10.1093/oso/9780192846242.003.0004
Z. Bažant, J. Le, M. Salviato
The real fracture process zone (FPZ) in all materials has not only a finite length, but also a finite width, which is particularly important for quasibrittle materials. The width matters, especially in presence of crack parallel stresses. It means that, instead of a scalar stress-displacement relation, fracture needs to be described by a realistic tensorial softening damage constitutive model, for which the microplane model is a particularly effective choice. The easiest way to do that is to use the crack band model, which by now dominates in concrete and aircraft composites in industry. First the need for such a model is established by analyzing bifurcation and stability of equilibrium load-displacement response of a structure, and by demonstrating the necessity of a localization limiter, which represents the effective width of the FPZ dictated by material heterogeneity. For the cases where fracture is known to localize, as is typical for reinforced concrete, simple rules for scaling the postpeak response to preserve the correct energy dissipation are derived, and implementation in FE analysis is outlined. The nonlocal integral and gradient approaches are discussed as alternative models having some advantages and disadvantages. Finally, discrete computational lattice and particle models, with LDPM as a particularly effective choice, are described.
{"title":"Nonlinear Fracture Mechanics—Diffuse Crack Model","authors":"Z. Bažant, J. Le, M. Salviato","doi":"10.1093/oso/9780192846242.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780192846242.003.0004","url":null,"abstract":"The real fracture process zone (FPZ) in all materials has not only a finite length, but also a finite width, which is particularly important for quasibrittle materials. The width matters, especially in presence of crack parallel stresses. It means that, instead of a scalar stress-displacement relation, fracture needs to be described by a realistic tensorial softening damage constitutive model, for which the microplane model is a particularly effective choice. The easiest way to do that is to use the crack band model, which by now dominates in concrete and aircraft composites in industry. First the need for such a model is established by analyzing bifurcation and stability of equilibrium load-displacement response of a structure, and by demonstrating the necessity of a localization limiter, which represents the effective width of the FPZ dictated by material heterogeneity. For the cases where fracture is known to localize, as is typical for reinforced concrete, simple rules for scaling the postpeak response to preserve the correct energy dissipation are derived, and implementation in FE analysis is outlined. The nonlocal integral and gradient approaches are discussed as alternative models having some advantages and disadvantages. Finally, discrete computational lattice and particle models, with LDPM as a particularly effective choice, are described.","PeriodicalId":371800,"journal":{"name":"Quasibrittle Fracture Mechanics and Size Effect","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121933422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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