Showing papers by "Zdenek P. Bazant published in 1992"

Rate Effects and Load Relaxation in Static Fracture of Concrete

Abstract: Reports an experimental study of the fracture of concrete at \"arious crack mouth opening displacement (CMOD) rates with time to peak loads ranging from about 1 sec to 3 days (over five orders of magnitude). Tests were conducted on three-point bend specimens of three sizes in the ratio 1:2:4. Quasi-elastic fracture analysis, based on the effective modulus jrom creep theory, is used to evaluate the results according to the size effect method. The fracture toughness is found to decrease in agreement with the trend known for the dynamic range. The effective length of the fracture process zone is found to decrease with increasing rate, which implies increasing brittleness and a shift toward linear elastic fracture mechanics behavior for slow loading. Load relaxation at constant CMOD in the prepeak and post-peak stages of fracture tests was also investigated. The response tends to a straight line in the logarithm of elapsed time, and the post-peak relaxation is nearly twice as strong as the linear viscoelastic relaxation of unnotched specimens, The difference between these two relaxations must be caused by time-dependent processes in the fracture zone. The results reveal that in concrete there is a strong interaction between fracture and creep, which might cause the load-carrying capacity of structures with cracks to decrease significantly with load duration. However, extrapolations to loads beyond several days of duration would be speculative.

Microplane Model for Cyclic Triaxial Behavior of Concrete

Abstract: A recently proposed microplane model, which describes not only cracking but also general nonlinear triaxial response, is extended to cyclic loading and the rate effect, and is implemented in a three‐dimensional finite element code. The material properties are characterized separately on planes of various orientations within the material, called the microplanes, on which no tensorial invariance requirements need to be observed. The state of each microplane is described by normal deviatoric and volumetric strains, and by shear strain. To avoid spurious localization instabilities due to strain softening and the consequent mesh‐sensitivity problems, the concept of nonlocal continuum with local strain is adopted. The rate effect is introduced by combining the damage model on each microplane with the Maxwell rheologic model. The results of finite element analysis of some basic cases on the material level, as well as of plain concrete specimens loaded in bending and compression, are demonstrated. The calculated ...

Compression Failure of Quasibrittle Material: Nonlocal Microplane Model

Abstract: The previously presented constitutive model of microplane type for nonlinear triaxial behavior and fracture of concrete is used in nonlocal finite element analysis of compression failure in plane strain rectangular specimens. For specimens with sliding rigid platens there is a bifurcation of the loading path at the beginning of postpeak softening; a symmetric (primary) path exists but the actual (stable) path is the nonsymmetric (secondary) path, involving an inclined shear‐expansion band that consists of axial splitting cracks and is characterized by transverse expansion. The secondary path is indicated by the first eigenvalue of the tangent stiffness matrix but can be more easily obtained if a slight nonsymmetry is introduced into the finite element model. In specimens with bonded rigid platens there is no bifurcation; they fail symmetrically, by two inclined shear‐expansion bands that consist of axial splitting cracks. The transverse expansion produces transverse tension in the adjacent material, which...

Deformation of progressively cracking partially prestressed concrete beams

Abstract: Deflections of partially prestressed concrete beams are analyzed on the basis of bending theory with plane cross sections, taking into account not only plasticity of steel and nonlinearity of concrete in compression, but also the tensile strain softening of concrete. However, their effect is not very large and is much less than found in a previous analysis of nonprestressed concrete beams. The effect of tensile strain softening is found to be significant only in the initial post-cracking response and vanish near the ultimate load. The effect of tension stiffening of steel due to the surrounding concrete and the associated bond slip is neglected, since the discrepancy from test data which could be ascribed to this phenomenon is quite small and adequate agreement with tests in the initial post-cracking stage is found without tension stiffening. Comparisons are also made with the I-effective method of Branson and Trost, although generally these predictions are softer than measured and become unacceptable near the ultimate load. Comparisons of calculations as well as measurements between beams with bonded and unbonded reinforcement show a relatively small difference.

Why direct tension specimens flex and break at midlength

Abstract: In a direct tension test, unnotched specimens of quasibrittle materials that exhibit post-peak strain softening do not deform symmetrically. The equilibrium path bifurcates and the thermodynamic criterion of stable path requires the specimen to flex to one side, 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. In absence of rotational restraints at the ends, the specimen fails right after the peak load. But if the attachments to the loading machine exert a sufficient restraint against rotation, the flexing to the side is retarded and failure occurs at midlength. The phenomenon (which is similar to the recently discovered behavior of notched tensile fracture specimens) is illustrated using a simple model in which the specimen consists of two bars of unequal length, joined by a strain-softening link.

Nonlinear analysis of strain-softening damage under monotonic and cyclic loading

Abstract: The paper reviews the modeling of damage by the microplane model and presents extensions required for cyclic loading. The general microplane constitutive model is implemented in a three-dimensional finite element code and used in damage and bifurcation analysis of various structures. The results of the analysis are compared with test results and some of the comparisons are shown in the present paper.