Showing papers by "Zdenek P. Bazant published in 1991"

Size effect on diagonal shear failure of beams without stirrups

Abstract: The paper presents the results of recent tests on diagonal shear failure of reinforced concrete beams without stirrups. The results indicate a significant size effect and show a good agreement with Bazant's law for size effect. Scatter of the test results is much lower than that previously found by studying extensive test data from the literature, which have not been obtained on geometrically similar beams. The tests also show that preventing bond slip of the longituudinal bars causes an increase of the brittleness number of the beam. It is concluded that the current design approach, which is intended to provide safety against the diagonal crack initiation load, should be replaced or supplemented by a design approach based on the ultimate load, in which a size effect of the fracture mechanics type, due to release of stored energy must be taken into account.

Why Continuum Damage is Nonlocal: Micromechanics Arguments

Abstract: The paper presents two micromechanics arguments showing that continuum damage caused by microcracking ought to be nonlocal, defined by a spatial integral. Argument I is an analysis of a simplified model in which the microcracks are of such size, density, and arrangement that that they do not interact. The release of stored energy caused by the formation of one microcrack is calculated as a function of the associated relative displacement across the cell, which corresponds to the average strain of the macroscopic continuum. After imposing two homogenizing conditions, it is shown that damage is a nonlocal variable that is a function of the averaged (nonlocal) strain from a certain neighborhood of the given point. Argument II is an analysis of a body with arbitrary interacting cracks. The local damage is proportional to the forces applied on the cracks to replace the stresses before cracking. Crack formation changes the openings of the neighboring cracks, which represents an interaction described by crack in...

Size Effect in Fatigue Fracture of Concrete

Abstract: Crack growth caused by load repetitions in geometrically similar notched concrete specimens of various sizes is measured by means of the compliance method. It is found that the Paris law, which states that the crack length increment per cycle is a power function of the stress intensity factor amplitude, is valid only for one specimen size (the law parameters being adjusted for that size) or asymptotically, for very large specimens. To obtain a general law, the Paris law is combined with size-effect law for fracture under monotonic loading, proposed previously by Bazant. This leads to a size-adjusted Paris law, which gives the crack length increment per cycle as a power function of the amplitude of size-adjusted stress intensity factor. The crack growth is also characterized in terms of the nominal stress amplitude.

Size Effect in Brazilian Split-Cylinder Tests: Measurements and Fracture Analysis

Abstract: The size effect in the split cylinder (Brazillian) tensile test is studied experimentally and analyzed theoretically. Tests of a very broad size range, 1:26, were conducted on cylindrical discs of constant thickness made from concrete with aggregate of a maximum size of 5 mm. The results confirm the existence of size effect and show that up to a certain critical diameter d, the curve of nominal strength versus diameter approximately agrees with the law proposed by Bazant for the size effect caused by energy release due to fracture growth. For larger sizes, there appears to be a deviation from the size-effect law. These and other study findings are discussed.

Statistical Size Effect in Quasi-Brittle Structures: I. Is Weibull Theory Applicable?

Abstract: The classical applications of Weibull statistical theory of size effect in quasi-brittle structures such as reinforced concrete structures, rock masses, ice plates, or tough ceramic parts are being reexamined in light of recent results. After a brief review of the statistical weakest-link model, distinctions between structures that fail by initiation of macroscopic crack growth (metal structures) and structures that exhibit large macroscopic crack growth prior to failure (quasi-brittle structures) are pointed out. It is shown that the classical Weibull-type approach ignores the stress redistributions and energy release due to stable large fracture growth prior to failure, which causes a strong deterministic size effect. Further, it is shown that, according to this classical theory, every structure is equivalent to a uniaxially loaded bar of variable cross section, which means that the mechanics of the failure process are ignored. Discrepancies with certain recent test data on the size effect are also pointed out. Modification of the Weibull approach that can eliminate these shortcomings is left for a subsequent paper.

Geometric damage tensor based on microplane model

Abstract: An appealing approach to formulate constitutive models for characterizing distributed damage due to microcracks and voids is continuum damage mechanics with the concepts of effective stress and strain equivalence. In that approach, in which damage is imagined to characterize the reduction of the net stress‐transmitting cross‐section area of the material, the constitutive model is separated into two independent parts, one for damage and the other for elastic and inelastic behavior (rheology) other than damage, which, if combined appropriately, give the overall constitutive behavior. However, the existing multidimensional formulations for damage are quite complex, and practical implementations capable of fitting experimental data are hard to obtain. The microplane models, by contrast, provide conceptual simplicity and close fits of multiaxial test data for concrete, soils, etc., although, as formulated in the past, various kinds of physical phenomena were mixed in the definition of the microplane stress‐str...

New method of analysis for slender columns

Abstract: The paper presents a simple new method to calculate column-interaction diagrams, which takes into account slenderness effects. The method consists of a simple incremental loading algorithm that traces the load-deflection curve at constant eccentricity of the axial load. The column failure is defined for design purposes as the peak of the diagram of axial load versus midlength bending moment at constant load eccentricity. The tangent modulus load is found to be apporximately equal to the peak load of column with load eccentricity 0.01 of the cross-sectional thickness and represents a lower bound for the maximum loads at still smaller eccentricities. Strain irreversibility at unloading can be taken into account but its effect is very small. The method is compared with the ACI moment magnification method and with the CEB Model column method based on moment-curvature relations. The agreement with the CEB method is very close, but with respect to the ACI method there are large discrepancies.

Cracks Interacting with Particles or Fibers in Composite Materials

Abstract: Micromechanics analysis of damage in heterogeneous media and composites cannot ignore the interactions among cracks as well as between cracks and inclusions or voids. Previous investigators can to this conclusion upon finding that states of distributed (diffuse) cracking (damage) cannot be mathematically represented merely as crack systems in a homogeneous medium, even though stable states with distributed damage have been experimentally observed in heterogeneous materials such as concrete. This paper presents a method for modeling interactions between a crack and many inclusions. Based on the Duhamel‐Neuman analogy, the effect of the inclusions is equivalent to unbalanced forces acting on the contour of each inclusion in an infinite homogeneous solid. The problem is solved by superposition; it is decomposed into several standard problems of elasticity for which well‐known solutions are available. The problem is finally reduced to a system of linear algebraic equations similar to those obtained by Kachano...