Showing papers by "Zdenek P. Bazant published in 1993"

Fatigue Fracture of High-Strength Concrete and Size Effect

Abstract: The results of an experimental study of fatigue fracture of geometrically similar high-strength concrete specimens of very different sizes are reported and analyzed. Three-point bend notched beams were subjected to cyclic loading. The number of cycles to failure ranged from 200 to 41,000. It was found that Paris law for the crack length increment per cycle as a function of the stress intensity factor, which was previously verified for normal concrete, is also applicable to high-strength concrete. However, for specimens of different sizes, an adjustment for the size effect needs to be introduced, of a similar type as previously introduced for normal concrete. A linear regression plot estimating the size-adjustment parameters is derived. An LEFM (linear elastic fracture mechanics)-type calculation of the deflections under cyclic loading on the basis of the size-adjusted Paris law yields correct values for the terminal phase but grossly underpredicts the initial deflections. Overall, the results underscore the importance of considering fatigue fracture growth in the case of high-strength concrete structures subjected to large, repeated loads, and taking into account the very high brittleness under fatigue loading.

Why direct tension test specimens break flexing to the side

Abstract: Contrary to the traditional view, unnotched direct tension test specimens of quasi‐brittle materials that exhibit post‐peak strain softening do not deform symmetrically. After passing the peak load, the equilibrium path bifurcates and the secondary postbifurcation branch represents flexing to the side. The bifurcation is shown to be analogous to Shanley's bifurcation in elastoplastic columns. According to the thermodynamic criterion of stable path, the flexing to one side must occur even if the geometry is perfect and if the straightening effect of the moment of the axial force about the centroid of the deflected cross section is taken into account. The lateral flexing favors failure of the specimen at midlength. The phenomenon (which is similar to the recently discovered behavior of notched tensile fracture specimens) is first illustrated using a simple model in which the specimen consists of two rigid bars of unequal lengths, joined by a strain‐softening link. It is shown that flexing to the side is ret...

Nonlocal microplane concrete model with rate effect and load cycles. i: general formulation

Abstract: The nonlocal microplane model for concrete is improved to describe unloading, reloading, cyclic loading, and the rate effect. The differences compared to the previous formulation are: (1) Normal strain component on the microplane is not split into its volumetric and deviatoric parts—rather the normal component is made dependent on the lateral normal strains on the microplane; and (2) instead of considering on each microplane only one shear strain vector parallel to the shear stress vector, the shear strain is represented by two independent components on the microplane. To introduce rate effect, the stress-strain law for each microplane component is described by a generalized Maxwell model—a series coupling of a linear viscous element and an elastoplastic-fracturing element. Nonlinear unloading-reloading hysteresis rules with back- and objective-stresses are developed to introduce hysteresis. The model is then combined with nonlocal theory to enable describing localization phenomena and avoid spurious mesh sensitivity due to strain softening. The numerical implementation in finite-element programs is described. The study consists of two parts; part I deals with the general formulation and part II deals with experimental verification.

Nonlocal microplane concrete model with rate effect and load cycles. II: Application and verification

Abstract: In the first of this 2-part paper, various improvements and extensions of a previously developed microplane model for concrete were presented. This, the second part of the paper, demonstrates its capability to simulate pertinent test data. The details of the study and its results are presented and discussed. It is shown that by contrast with the previous microplane model for concrete, the normal strain component on the microplane is not split into its volumetric and deviatoric parts; instead the lateral strains are considered. The stress-strain relations for a material point were simulated and then the tests were studied in finite element analyses with nonlocal calculation.