Documents disponibles écrits par cet auteur

Can stirrups suppress size effect on shear strength of RC beams? / Yu, Qiang in Journal of structural engineering, Vol. 137 N° 5 (Mai 2011) 

Public ISBD [article]  in Journal of structural engineering > Vol. 137 N° 5 (Mai 2011) . - pp. 607-617 Titre : Can stirrups suppress size effect on shear strength of RC beams? Type de document : texte imprimé Auteurs : Yu, Qiang, Auteur ; Zdenek P. Bazant, Auteur Année de publication : 2011 Article en page(s) : pp. 607-617 Note générale : Génie Civil Langues : Anglais (eng) Mots-clés : Concrete  design  Size  effect  Shear  reinforcement  Failure  probability  RC  beams Index. décimale : 624 Constructions du génie civil et du bâtiment. Infrastructures. Ouvrages en terres. Fondations. Tunnels. Ponts et charpentes Résumé : This paper demonstrates the size effect on the shear strength of reinforced concrete (RC) beams with stirrups and does so in two separate and independent ways: (1) by fracture mechanics, based on finite-element analysis calibrated by a large beam test; and (2) by purely statistical analysis in which a newly assembled database of 234 tests is filtered to eliminate spurious size effects caused by nonuniformity of secondary influencing parameters. Both ways show that stirrups, whether minimum or heavier, cannot suppress the size effect completely, although they can mitigate it significantly for beam depth d<1  m (39.4 in.). The effect of stirrups is to push the size effect curve in logarithmic scale into sizes larger by about one order of magnitude. For beam depths d<0.5  m, 1, 2, and 6 m (19.7, 39.4, 78.7, and 236.2 in.), the percentages of beams whose shear strength is below the code limit are calculated as 3.5, 6.5, 15.7, and 55.1%, respectively. The corresponding failure probabilities are 10-6, 10-5, 10-4, and 10-3, whereas 10-6 is the generally accepted standard for a tolerable maximum in risk analysis. It follows that, for beams with stirrups having depth >1  m (39.4 in.), the size effect cannot be neglected. DEWEY : 624.17 ISSN : 0733-9445 En ligne : http://ascelibrary.org/sto/resource/1/jsendh/v137/i5/p607_s1?isAuthorized=no [article] Can stirrups suppress size effect on shear strength of RC beams? [texte imprimé] / Yu, Qiang, Auteur ; Zdenek P. Bazant, Auteur . - 2011 . - pp. 607-617. Génie Civil Langues : Anglais (eng) in Journal of structural engineering > Vol. 137 N° 5 (Mai 2011) . - pp. 607-617 Mots-clés : Concrete  design  Size  effect  Shear  reinforcement  Failure  probability  RC  beams Index. décimale : 624 Constructions du génie civil et du bâtiment. Infrastructures. Ouvrages en terres. Fondations. Tunnels. Ponts et charpentes Résumé : This paper demonstrates the size effect on the shear strength of reinforced concrete (RC) beams with stirrups and does so in two separate and independent ways: (1) by fracture mechanics, based on finite-element analysis calibrated by a large beam test; and (2) by purely statistical analysis in which a newly assembled database of 234 tests is filtered to eliminate spurious size effects caused by nonuniformity of secondary influencing parameters. Both ways show that stirrups, whether minimum or heavier, cannot suppress the size effect completely, although they can mitigate it significantly for beam depth d<1  m (39.4 in.). The effect of stirrups is to push the size effect curve in logarithmic scale into sizes larger by about one order of magnitude. For beam depths d<0.5  m, 1, 2, and 6 m (19.7, 39.4, 78.7, and 236.2 in.), the percentages of beams whose shear strength is below the code limit are calculated as 3.5, 6.5, 15.7, and 55.1%, respectively. The corresponding failure probabilities are 10-6, 10-5, 10-4, and 10-3, whereas 10-6 is the generally accepted standard for a tolerable maximum in risk analysis. It follows that, for beams with stirrups having depth >1  m (39.4 in.), the size effect cannot be neglected. DEWEY : 624.17 ISSN : 0733-9445 En ligne : http://ascelibrary.org/sto/resource/1/jsendh/v137/i5/p607_s1?isAuthorized=no

Excessive long-time deflections of prestressed box girders. I / Bažant, Zdeněk P. in Journal of structural engineering, Vol. 138 N° 6 (Juin 2012) 

Public ISBD [article]  in Journal of structural engineering > Vol. 138 N° 6 (Juin 2012) . - pp. 676–686 Titre : Excessive long-time deflections of prestressed box girders. I : Record-span bridge in palau and other paradigms Type de document : texte imprimé Auteurs : Bažant, Zdeněk P., Auteur ; Yu, Qiang, Auteur ; Guang-Hua Li, Auteur Année de publication : 2012 Article en page(s) : pp. 676–686 Note générale : Génie Civil Langues : Anglais (eng) Mots-clés : Prestressed  box  girder  Bridges  Segmental  erection  Shear  lag  Design  standards  Concrete  Relaxation Résumé : The segmental prestressed concrete box girder of Koror-Babeldaob (KB) Bridge in Palau, which had a record span of 241 m (791 ft), presents a striking paradigm of serviceability loss because of excessive multidecade deflections. The data required for analysis have recently been released and are here exploited to show how the analysis and design could be improved. Erected segmentally in 1977, this girder developed a midspan deflection of 1.61 m (5.3 ft) compared with the design camber after 18 years, and it collapsed in 1996 as a consequence of remedial prestressing, after a 3-month delay. Compared with three-dimensional analysis, the traditional beam-type analysis of box girder deflections is found to have errors up to 20%, although greater errors are likely for bridges with higher box-width-to-span ratios than the KB Bridge. However, even three-dimensional finite-element analysis with step-by-step time integration cannot explain the observed deflections when the current American Concrete Institute, Japan Society of Civil Engineers, Comité Euro-International du Béton (or Comité Euro-International du Béton—Fédération internationale de la précontrainte), and Gardner and Lockman prediction models for creep and shrinkage are used. These models give 18-year deflection estimates that are 50–77% lower than measured and yield unrealistic shapes of the deflection history. They also predict the 18-year prestress loss to be 46–56% lower than the measured mean prestress loss, which was 50%. Model B3, which is the only theoretically based model, underestimates the 18-year deflection by 42% and gives a prestress loss of 40% when the default parameter values are used. However, in Model B3, several input parameters are adjustable and if they are adjusted according to the long-time laboratory tests of Brooks, a close fit of all the measurements is obtained. For early deflections and their extrapolation, it is important that Model B3 can capture realistically the differences in the rates of shrinkage and drying creep caused by the differences in the thickness of the walls of the cross section. The differences in temperature and possible cracking of the top slab also need to be taken into account. Other paradigms on which data have recently been released are four bridges in Japan and one in the Czech Republic. Their excessive deflections can also be explained. The detailed method of analysis and the lessons learned are presented in Part II. ISSN : 0733-9445 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29ST.1943-541X.0000487 [article] Excessive long-time deflections of prestressed box girders. I : Record-span bridge in palau and other paradigms [texte imprimé] / Bažant, Zdeněk P., Auteur ; Yu, Qiang, Auteur ; Guang-Hua Li, Auteur . - 2012 . - pp. 676–686. Génie Civil Langues : Anglais (eng) in Journal of structural engineering > Vol. 138 N° 6 (Juin 2012) . - pp. 676–686 Mots-clés : Prestressed  box  girder  Bridges  Segmental  erection  Shear  lag  Design  standards  Concrete  Relaxation Résumé : The segmental prestressed concrete box girder of Koror-Babeldaob (KB) Bridge in Palau, which had a record span of 241 m (791 ft), presents a striking paradigm of serviceability loss because of excessive multidecade deflections. The data required for analysis have recently been released and are here exploited to show how the analysis and design could be improved. Erected segmentally in 1977, this girder developed a midspan deflection of 1.61 m (5.3 ft) compared with the design camber after 18 years, and it collapsed in 1996 as a consequence of remedial prestressing, after a 3-month delay. Compared with three-dimensional analysis, the traditional beam-type analysis of box girder deflections is found to have errors up to 20%, although greater errors are likely for bridges with higher box-width-to-span ratios than the KB Bridge. However, even three-dimensional finite-element analysis with step-by-step time integration cannot explain the observed deflections when the current American Concrete Institute, Japan Society of Civil Engineers, Comité Euro-International du Béton (or Comité Euro-International du Béton—Fédération internationale de la précontrainte), and Gardner and Lockman prediction models for creep and shrinkage are used. These models give 18-year deflection estimates that are 50–77% lower than measured and yield unrealistic shapes of the deflection history. They also predict the 18-year prestress loss to be 46–56% lower than the measured mean prestress loss, which was 50%. Model B3, which is the only theoretically based model, underestimates the 18-year deflection by 42% and gives a prestress loss of 40% when the default parameter values are used. However, in Model B3, several input parameters are adjustable and if they are adjusted according to the long-time laboratory tests of Brooks, a close fit of all the measurements is obtained. For early deflections and their extrapolation, it is important that Model B3 can capture realistically the differences in the rates of shrinkage and drying creep caused by the differences in the thickness of the walls of the cross section. The differences in temperature and possible cracking of the top slab also need to be taken into account. Other paradigms on which data have recently been released are four bridges in Japan and one in the Czech Republic. Their excessive deflections can also be explained. The detailed method of analysis and the lessons learned are presented in Part II. ISSN : 0733-9445 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29ST.1943-541X.0000487

Excessive long-time deflections of prestressed box girders. II / Bažant, Zdeněk P. in Journal of structural engineering, Vol. 138 N° 6 (Juin 2012) 

Public ISBD [article]  in Journal of structural engineering > Vol. 138 N° 6 (Juin 2012) . - pp. 687–696 Titre : Excessive long-time deflections of prestressed box girders. II : Numerical analysis and lessons learned Type de document : texte imprimé Auteurs : Bažant, Zdeněk P., Auteur ; Yu, Qiang, Auteur ; Guang-Hua Li, Auteur Année de publication : 2012 Article en page(s) : pp. 687–696 Note générale : Génie Civil Langues : Anglais (eng) Mots-clés : Kelvin  chain  Design  standards  Segmental  erection  Bridges  Shear  lag  Prestressed  concrete  Relaxation Résumé : As a sequel to Part I, which clarified the causes of the unexpectedly large deflections of the Koror-Babeldaob Bridge in the Pacific island nation of Palau, Part II presents the numerical procedure and reviews the lessons learned. The box girder represents a thick shell that is discretized by eight-node, three-dimensional (3D) finite elements. Except for corrections due to cracking, concrete creep is assumed to follow aging linear viscoelasticity and is modeled by a rate-type law based on the Kelvin chain, the properties of which are adjusted for humidity conditions and temperature. In each time step and at each integration point, Widder’s formula is used to convert the aging compliance function to a continuous retardation spectrum for the current age of concrete, and discretization of the spectrum yields the current elastic moduli of the Kelvin units. The shrinkage strains depend on the environmental humidity and the thickness of each plate in the cross section. The computations proceed according to Bažant’s exponential algorithm, which is unconditionally stable and reduces the problem to a sequence of elasticity problems with an orthotropic effective stiffness of material and nonisotropic inelastic strains, different for each integration point in each time step. These problems are solved by commercial software ABAQUS. The segmental construction sequence is also modeled. The computer results reported in Part I explain the excessive deflections and compare the performance of various material models for creep and shrinkage. Part II formulates the lessons learned and makes recommendations for implementation. ISSN : 0733-9445 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29ST.1943-541X.0000375 [article] Excessive long-time deflections of prestressed box girders. II : Numerical analysis and lessons learned [texte imprimé] / Bažant, Zdeněk P., Auteur ; Yu, Qiang, Auteur ; Guang-Hua Li, Auteur . - 2012 . - pp. 687–696. Génie Civil Langues : Anglais (eng) in Journal of structural engineering > Vol. 138 N° 6 (Juin 2012) . - pp. 687–696 Mots-clés : Kelvin  chain  Design  standards  Segmental  erection  Bridges  Shear  lag  Prestressed  concrete  Relaxation Résumé : As a sequel to Part I, which clarified the causes of the unexpectedly large deflections of the Koror-Babeldaob Bridge in the Pacific island nation of Palau, Part II presents the numerical procedure and reviews the lessons learned. The box girder represents a thick shell that is discretized by eight-node, three-dimensional (3D) finite elements. Except for corrections due to cracking, concrete creep is assumed to follow aging linear viscoelasticity and is modeled by a rate-type law based on the Kelvin chain, the properties of which are adjusted for humidity conditions and temperature. In each time step and at each integration point, Widder’s formula is used to convert the aging compliance function to a continuous retardation spectrum for the current age of concrete, and discretization of the spectrum yields the current elastic moduli of the Kelvin units. The shrinkage strains depend on the environmental humidity and the thickness of each plate in the cross section. The computations proceed according to Bažant’s exponential algorithm, which is unconditionally stable and reduces the problem to a sequence of elasticity problems with an orthotropic effective stiffness of material and nonisotropic inelastic strains, different for each integration point in each time step. These problems are solved by commercial software ABAQUS. The segmental construction sequence is also modeled. The computer results reported in Part I explain the excessive deflections and compare the performance of various material models for creep and shrinkage. Part II formulates the lessons learned and makes recommendations for implementation. ISSN : 0733-9445 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29ST.1943-541X.0000375

Problems with hu-duan boundary effect model and Its comparison to size-shape effect law for quasi-brittle fracture / Yu, Qiang in Journal of engineering mechanics, Vol. 136 N° 1 (Janvier 2010) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 136 N° 1 (Janvier 2010) . - pp. 40-50 Titre : Problems with hu-duan boundary effect model and Its comparison to size-shape effect law for quasi-brittle fracture Type de document : texte imprimé Auteurs : Yu, Qiang, Auteur ; Jia-Liang Le, Auteur ; Hoover, Hristian G., Auteur Article en page(s) : pp. 40-50 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Cracking  Concrete  Structural  failures  Data  analysis  Size  effect. Résumé : Recent disagreements on the mathematical modeling of fracture and size effect in concrete and other quasi-brittle materials are obstacles to improvements in design practice, and especially in design codes for concrete structures. In an attempt to overcome this impediment to progress, this paper compares the Hu-Duan boundary effect model (BEM) expounded since 2000 to the size-shape effect law (SEL) proposed at Northwestern University in 1984 and extended to the geometry (or shape) effects in 1990. It is found that within a rather limited part of the range of sizes and shapes, the fracture energy values identified by BEM and SEL from the test data on maximum loads are nearly the same. But in other parts of the range the BEM is either inferior or inapplicable. The material tensile strength values identified by BEM have a much larger error than those obtained from the SEL after calibration by the cohesive crack model. From the theoretical viewpoint, several hypotheses of BEM are shown to be unrealistic. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/dbt/dbt.jsp?KEY=JENMDT&Volume=136&Issue=1 [article] Problems with hu-duan boundary effect model and Its comparison to size-shape effect law for quasi-brittle fracture [texte imprimé] / Yu, Qiang, Auteur ; Jia-Liang Le, Auteur ; Hoover, Hristian G., Auteur . - pp. 40-50. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 136 N° 1 (Janvier 2010) . - pp. 40-50 Mots-clés : Cracking  Concrete  Structural  failures  Data  analysis  Size  effect. Résumé : Recent disagreements on the mathematical modeling of fracture and size effect in concrete and other quasi-brittle materials are obstacles to improvements in design practice, and especially in design codes for concrete structures. In an attempt to overcome this impediment to progress, this paper compares the Hu-Duan boundary effect model (BEM) expounded since 2000 to the size-shape effect law (SEL) proposed at Northwestern University in 1984 and extended to the geometry (or shape) effects in 1990. It is found that within a rather limited part of the range of sizes and shapes, the fracture energy values identified by BEM and SEL from the test data on maximum loads are nearly the same. But in other parts of the range the BEM is either inferior or inapplicable. The material tensile strength values identified by BEM have a much larger error than those obtained from the SEL after calibration by the cohesive crack model. From the theoretical viewpoint, several hypotheses of BEM are shown to be unrealistic. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/dbt/dbt.jsp?KEY=JENMDT&Volume=136&Issue=1

Size Effect on Strength of Quasibrittle Structures with Reentrant Corners Symmetrically Loaded in Tension / Zdenek P. Bazant in Journal of engineering mechanics, Vol. 132 N°11 (Novembre 2006) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 132 N°11 (Novembre 2006) . - 1168-1176 p. Titre : Size Effect on Strength of Quasibrittle Structures with Reentrant Corners Symmetrically Loaded in Tension Titre original : Classement de l'Effet sur la Force des Structures Quasi-Fragiles avec les Coins de Réentrée Symétriquement Chargés dans la Tension Type de document : texte imprimé Auteurs : Zdenek P. Bazant, Auteur ; Yu, Qiang, Auteur ; Xi, Yunping, Editeur scientifique Article en page(s) : 1168-1176 p. Note générale : Génie Mécanique Langues : Anglais (eng) Mots-clés : Size  effects  Fracture  Concrete  Notches  Stress  concentration  Effet  de  taille  Concret  Entailles  Concentration  d'effort  Ruptures Index. décimale : 620.1 Essais des matériaux. Défauts des matériaux. Protection des matériaux Résumé : The effect of V-notches (or reentrant corners) on fracture propagation has been analyzed for brittle materials, but not for quasi—brittle materials such as concrete, marked by a large material characteristic length producing a strong size effect transitional between plasticity and linear elastic fracture mechanics. A simple size effect law for the nominal strength of quasi—brittle structures with symmetrically loaded notches, incorporating the effect of notch angle, is derived by asymptotic matching of the following five limit cases: (1) Bazant’s size effect law for quasi—brittle structures with large cracks for notch angle approaching zero; (2) absence of size effect for vanishing structure size; (3) absence of size effect for notch angle approaching π; (4) plasticity-based notch angle effect for vanishing size; and (5) the notch angle effect on crack initiation in brittle structures, which represents the large-size limit of quasibrittle structures. Accuracy for the brittle large-size limit, with notch angle effect only, is first verified by extensive finite-element analyses of bodies with various notch angles. Then a cohesive crack characterized by a softening stress-separation law is considered to emanate from the notch tip, and the same finite-element model is used to verify and calibrate the proposed law for size and angle effects in the transitional size range in which the body is not far larger than Irwin’s material characteristic length. Experimental verification of the notch angle effect is obtained by comparisons with Dunn et al.’s extensive tests of three-point-bend notched beams made of plexiglass (polymethyl methacrylate), and Seweryn’s tests of double-edge-notched tension specimens, one set made of plexiglass and another of aluminum alloy. L'effet des entailles en V (ou des coins de réentrée) sur la propagation de rupture a été analysé pour les matériaux fragiles, mais pas des matériaux de quasi fragile tels que le béton, marqué par une grande longueur caractéristique matérielle produisant un effet fort de taille transitoire entre la plasticité et la mécanique élastique linéaire de rupture. Une loi simple d'effet de taille pour la force nominale des structures de quasi fragile avec les entailles symétriquement chargées, incorporant l'effet de l'angle d'entaille, est dérivée par l'assortiment asymptotique des cinq cas suivants de limite : (1) loi d'effet de taille de Bazant’s pour des structures de quasi fragile avec de grandes fissures pour l'angle d'entaille approchant zéro ; (2) absence d'effet de taille pour disparaître la taille de structure ; (3) absence d'effet de taille pour l'angle d'entaille approchant π ; ; (4) effet plasticité-basé d'angle d'entaille pour disparaître la taille ; et (5) l'effet d'angle d'entaille sur le déclenchement de fente en structures fragiles, qui représente la limite de grande taille des structures de quasi fragile. L'exactitude pour la limite de grande taille fragile, avec l'effet d'angle d'entaille seulement, est d'abord vérifiée par des analyses étendues d'élément fini des corps avec de divers angles d'entaille. Alors une fente cohésive caractérisée par une loi se ramollissante de soumettre à une contrainte-séparation est considérée comme émanere du bout d'entaille, et le même modèle d'élément fini est employé pour vérifier et calibrer la loi proposée pour des effets de taille et d'angle en classe de grandeur transitoire dans laquelle le corps n'est pas bien plus grand que la longueur de caractéristique de matériel d'Irwin’s. La vérification expérimentale de l'effet d'angle d'entaille est obtenue par des comparaisons avec Dunn et les essais étendus d'al.’s de trois-point-plient les faisceaux entaillés faits de plexi glass (méthacrylate de polymethyl), et les essais de Seweryn’s des spécimens double-bord-entaillés de tension, d'un ensemble fait de plexiglass et des autres de l'alliage d'aluminium. DEWEY : 620.1 ISSN : 0733-9399 En ligne : z-bazant@northwestern.edu, qiangyu@northwestern.edu [article] Size Effect on Strength of Quasibrittle Structures with Reentrant Corners Symmetrically Loaded in Tension = Classement de l'Effet sur la Force des Structures Quasi-Fragiles avec les Coins de Réentrée Symétriquement Chargés dans la Tension [texte imprimé] / Zdenek P. Bazant, Auteur ; Yu, Qiang, Auteur ; Xi, Yunping, Editeur scientifique . - 1168-1176 p. Génie Mécanique Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 132 N°11 (Novembre 2006) . - 1168-1176 p. Mots-clés : Size  effects  Fracture  Concrete  Notches  Stress  concentration  Effet  de  taille  Concret  Entailles  Concentration  d'effort  Ruptures Index. décimale : 620.1 Essais des matériaux. Défauts des matériaux. Protection des matériaux Résumé : The effect of V-notches (or reentrant corners) on fracture propagation has been analyzed for brittle materials, but not for quasi—brittle materials such as concrete, marked by a large material characteristic length producing a strong size effect transitional between plasticity and linear elastic fracture mechanics. A simple size effect law for the nominal strength of quasi—brittle structures with symmetrically loaded notches, incorporating the effect of notch angle, is derived by asymptotic matching of the following five limit cases: (1) Bazant’s size effect law for quasi—brittle structures with large cracks for notch angle approaching zero; (2) absence of size effect for vanishing structure size; (3) absence of size effect for notch angle approaching π; (4) plasticity-based notch angle effect for vanishing size; and (5) the notch angle effect on crack initiation in brittle structures, which represents the large-size limit of quasibrittle structures. Accuracy for the brittle large-size limit, with notch angle effect only, is first verified by extensive finite-element analyses of bodies with various notch angles. Then a cohesive crack characterized by a softening stress-separation law is considered to emanate from the notch tip, and the same finite-element model is used to verify and calibrate the proposed law for size and angle effects in the transitional size range in which the body is not far larger than Irwin’s material characteristic length. Experimental verification of the notch angle effect is obtained by comparisons with Dunn et al.’s extensive tests of three-point-bend notched beams made of plexiglass (polymethyl methacrylate), and Seweryn’s tests of double-edge-notched tension specimens, one set made of plexiglass and another of aluminum alloy. L'effet des entailles en V (ou des coins de réentrée) sur la propagation de rupture a été analysé pour les matériaux fragiles, mais pas des matériaux de quasi fragile tels que le béton, marqué par une grande longueur caractéristique matérielle produisant un effet fort de taille transitoire entre la plasticité et la mécanique élastique linéaire de rupture. Une loi simple d'effet de taille pour la force nominale des structures de quasi fragile avec les entailles symétriquement chargées, incorporant l'effet de l'angle d'entaille, est dérivée par l'assortiment asymptotique des cinq cas suivants de limite : (1) loi d'effet de taille de Bazant’s pour des structures de quasi fragile avec de grandes fissures pour l'angle d'entaille approchant zéro ; (2) absence d'effet de taille pour disparaître la taille de structure ; (3) absence d'effet de taille pour l'angle d'entaille approchant π ; ; (4) effet plasticité-basé d'angle d'entaille pour disparaître la taille ; et (5) l'effet d'angle d'entaille sur le déclenchement de fente en structures fragiles, qui représente la limite de grande taille des structures de quasi fragile. L'exactitude pour la limite de grande taille fragile, avec l'effet d'angle d'entaille seulement, est d'abord vérifiée par des analyses étendues d'élément fini des corps avec de divers angles d'entaille. Alors une fente cohésive caractérisée par une loi se ramollissante de soumettre à une contrainte-séparation est considérée comme émanere du bout d'entaille, et le même modèle d'élément fini est employé pour vérifier et calibrer la loi proposée pour des effets de taille et d'angle en classe de grandeur transitoire dans laquelle le corps n'est pas bien plus grand que la longueur de caractéristique de matériel d'Irwin’s. La vérification expérimentale de l'effet d'angle d'entaille est obtenue par des comparaisons avec Dunn et les essais étendus d'al.’s de trois-point-plient les faisceaux entaillés faits de plexi glass (méthacrylate de polymethyl), et les essais de Seweryn’s des spécimens double-bord-entaillés de tension, d'un ensemble fait de plexiglass et des autres de l'alliage d'aluminium. DEWEY : 620.1 ISSN : 0733-9399 En ligne : z-bazant@northwestern.edu, qiangyu@northwestern.edu