scholarly journals Scaling of Structural Failure

1997 ◽  
Vol 50 (10) ◽  
pp. 593-627 ◽  
Author(s):  
Zdeneˇk P. Bazˇant ◽  
Er-Ping Chen
Keyword(s):  
Size Effect ◽  
Process Zone ◽  
Material Behavior ◽  
Constitutive Law ◽  
Cohesive Crack ◽  
Crack Model ◽  
Rate Dependent ◽  
Quasibrittle Materials ◽  
History Of ◽  
Material Fracture

This article attempts to review the progress achieved in the understanding of scaling and size effect in the failure of structures. Particular emphasis is placed on quasibrittle materials for which the size effect is important and complicated. After reflections on the long history of size effect studies, attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, nonlocal finite element models and discrete element models. Extensions to compression failure and to the rate-dependent material behavior are also outlined. The damage constitutive law needed for describing a microcracked material in the fracture process zone is discussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber composites, rocks and ceramics are presented. There are 377 references included in this article.

State-of-the-Art Review on Concrete Softening Curve

2010 ◽  
Vol 168-170 ◽  
pp. 669-673
Author(s):  
Zhi Fang Zhao ◽  
Zhi Gang Zhao ◽  
Xiao Jie Feng ◽  
Ming Li
Keyword(s):  
Constitutive Law ◽  
Cohesive Crack ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Direct Tension ◽  
Tension Softening ◽  
Nonlinear Form ◽  
Determination Methods ◽  
Relationship Of ◽  
Inverse Analysis Method

The cohesive crack model is widely employed to the fracture analysis of concrete for mode I crack. The tension softening relationship is a very important constitutive law in the cohesive crack model. The determination methods of tension softening relationship of concrete are introduced in this paper which are direct tension methods, J-integral method and inverse analysis method. Meanwhile, those simplified softening curves including linear form and nonlinear form are summarized.

A Comparison of Cohesive Crack Model and Crack Band Model in Concrete Fracture

2012 ◽  
Vol 170-173 ◽  
pp. 3375-3380
Author(s):  
Liang Wu ◽  
Ze Li ◽  
Shang Huang
Keyword(s):  
Fracture Process ◽  
Fracture Process Zone ◽  
Process Zone ◽  
Crack Opening ◽  
Cohesive Crack ◽  
Band Model ◽  
Crack Model ◽  
Concrete Fracture ◽  
Cohesive Crack Model ◽  
Crack Band

The cohesive crack model and the crack band model are two convenient approaches in concrete fracture analysis. They can describe in full the fracture process by the different manner: The entire fracture process zone is lumped into the crack line and is characterized in the form of a stress-displacement law which exhibits softening; or the inelastic deformations in the fracture process zone are smeared over a band of a certain width, imagined to exist in front of the main crack. The correlation of the two models is developed based on a characteristic width of crack band. The analysis shows that they can yield about the same results if the crack opening displacement in the cohesive crack model is taken as the fracturing strain that is accumulated over the width of the crack band model. Some basic problems are also discussed in finite element analysis.

Cohesive Crack Model for Geomaterials: Stability Analysis and Rate Effect

1994 ◽  
Vol 47 (6S) ◽  
pp. S91-S96 ◽  
Author(s):  
Zdeneˇk P. Bazˇant ◽  
Yuan-Neng Li
Keyword(s):  
Stability Analysis ◽  
Stability Problem ◽  
Good Description ◽  
Maximum Load ◽  
Cohesive Crack ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Opening Displacement ◽  
Cohesive Stress ◽  
Quasibrittle Materials

The cohesive (or ficticious) crack model, characterized by softening stress-displacement relations, provides a good description of fracture of quasibrittle materials such as conrete, rock, or tough ceramics. The cohesive crack model is formulated in terms of compliance influence functions and the failure is analyzed as a stability problem. The size effect is determined by means of an eigenvalue problem. In this problem, the structure size for which a given relative crack length yields the maximum load is the eigenvalue. The model is further generalized to time dependence. The opening displacement is considered as a function of the cohesive stress and the opening rate of the crack. Finally, applications to rock and concrete are discussed.

scholarly journals Critical comparison of the boundary effect model with cohesive crack model and size effect law

2019 ◽  
Vol 215 ◽  
pp. 193-210 ◽  
Author(s):  
Christian Carloni ◽  
Gianluca Cusatis ◽  
Marco Salviato ◽  
Jia-Liang Le ◽  
Christian G. Hoover ◽  
...  
Keyword(s):  
Size Effect ◽  
Boundary Effect ◽  
Cohesive Crack ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Critical Comparison ◽  
Effect Model

scholarly journals The role of the material fracture properties in the size-effect law of concrete structures

1996 ◽  
Vol 18 (1) ◽  
pp. 40-48
Author(s):  
V. Tran Tu
Keyword(s):  
Size Effect ◽  
Process Zone ◽  
Crack Opening ◽  
Concrete Structures ◽  
Fracture Propagation ◽  
Fracture Properties ◽  
Nominal Strength ◽  
Material Fracture ◽  
General Size

The size effect of the nominal stress at failure in concrete structures is dealt within general. An existence of a rather large fracture process zone in front of crack tip is proved to be the main reason leading to the size effect of the nominal strength. On the basis of the new general size-effect law and numerical results of fracture propagation, a particularly proposed size effect law for beams in bending is developed, in which the role of each material fracture characteristic, especially the shape of the stress - crack opening curve, is elaborated clearly.

scholarly journals Scaling of Quasi-Brittle Fracture and the Fractal Question

1995 ◽  
Vol 117 (4) ◽  
pp. 361-367 ◽  
Author(s):  
Zdeneˇk P. Bazˇant
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Process Zone ◽  
Asymptotic Properties ◽  
Material Strength ◽  
Fractal Nature ◽  
Quasibrittle Materials ◽  
Large Size ◽  
Fracture Simulation ◽  
Nominal Strength

The paper represents an extended text of a lecture presenting a review of recent results on scaling of failure in structures made of quasibrittle materials, characterized by a large fracture process zone, and examining the question of possible role of the fractal nature of crack surfaces in the scaling. The problem of scaling is approached through dimensional analysis, the laws of thermodynamics and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are given, for specimens with large notches (or traction-free cracks) as well as zero notches, and simple size effect formulas matching the required asymptotic properties are reported. The asymptotic analysis is carried out, in general, for fractal cracks, and the practically important case ofnonfractal crack propagation is acquired as a special case. Regarding the fractal nature of crack surfaces in quasibrittle materials, the conclusion is that it cannot play a signification role in fracture propagation and the observed size effect. The reason why Weibull statistical theory of random material strength does not explain the size effect in quasibrittle failures is explained. Finally, some recent applications to fracture simulation by particle models (discrete element method) and to the determination of size effect and fracture characteristics of carbon-epoxy composite laminates are briefly reviewed.

scholarly journals Size Effect of Cohesive Delamination Fracture Triggered by Sandwich Skin Wrinkling

2007 ◽  
Vol 74 (6) ◽  
pp. 1134-1141 ◽  
Author(s):  
Zdeněk Bažant ◽  
Peter Grassl
Keyword(s):  
Size Effect ◽  
Impact Analysis ◽  
Cohesive Crack ◽  
Crack Model ◽  
Element Analysis ◽  
Simple Description ◽  
Nominal Strength ◽  
Delamination Fracture ◽  
Special Cases ◽  
Asymptotic Matching

Because the observed size effect follows neither the strength theory nor the linear elastic fracture mechanics, the delamination fracture of laminate-foam sandwiches under uniform bending moment is treated by the cohesive crack model. Both two-dimensional geometrically nonlinear finite element analysis and one-dimensional representation of skin (or facesheet) as a beam on elastic-softening foundation are used. The use of the latter is made possible by realizing that the effective elastic foundation stiffness depends on the ratio of the critical wavelength of periodic skin wrinkles to the foam core thickness, and a simple description of the transition from shortwave to longwave wrinkling is obtained by asymptotic matching. Good agreement between both approaches is achieved. Skin imperfections (considered proportional to the the first eigenmode of wrinkling), are shown to lead to strong size dependence of the nominal strength. For large imperfections, the strength reduction due to size effect can reach 50%. Dents from impact, though not the same as imperfections, might be expected to cause as a similar size effect. Using proper dimensionless variables, numerical simulations of cohesive delamination fracture covering the entire practical range are performed. Their fitting, heeding the shortwave and longwave asymptotics, leads to an approximate imperfection-dependent size effect law of asymptotic matching type. Strong size effect on postpeak energy absorption, important for impact analysis, is also demonstrated. Finally, discrepancies among various existing formulas for critical stress at periodic elastic wrinkling are explained by their applicability to different special cases in the shortwave-longwave transition.

scholarly journals Size Effect in Fracture of Concrete Specimens and Structures: New Problems and Progress

10.14311/608 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
Z. P. Bažant ◽  
Q. Yu
Keyword(s):  
Size Effect ◽  
Fracture Energy ◽  
Damage Model ◽  
Apparent Size ◽  
Shear Capacity ◽  
Cohesive Crack ◽  
Smooth Transition ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Nominal Strength

Presented is a concise summary of recent Northwestern University studies of six new problems. First, the decrease of fracture energy during crack propagation through a boundary layer, documented by Hu and Wittmann, is shown to be captured by a cohesive crack model in which the softening tail slope depends on the distance from the boundary (which causes an apparent size effect on fracture energy and implies that the nonlocal damage model is more fundamental than the cohesive crack model). Second, an improved universal size effect law giving a smooth transition between failures at large cracks (or notches) and at crack initiation is presented. Third, a recent renewed proposal that the nominal strength variation as a function of notch depth be used for measuring fracture energy is critically examined. Fourth, numerical results and a formula describing the size effect of finite-angle notches are presented. Fifth, a new size effect law derivation from dimensional analysis coupled with asymptotic matching is given. Finally, an improved code-type formula for shear capacity of R.C. beams is proposed. 

scholarly journals CHARACTERIZATIONS ON FRACTURE PROCESS ZONE OF PLAIN CONCRETE

2019 ◽  
Vol 25 (8) ◽  
pp. 819-830
Author(s):  
Yuxiang Tang ◽  
Hongniao Chen
Keyword(s):  
Fracture Process ◽  
Fracture Process Zone ◽  
Process Zone ◽  
Speckle Pattern ◽  
Plain Concrete ◽  
Cohesive Crack ◽  
Electronic Speckle Pattern Interferometry ◽  
Crack Model ◽  
Fe Model ◽  
Durability Analysis

The fracture property of concrete is essential for the safety and durability analysis of concrete structures. Investigating the characteristics of the fracture process zone (FPZ) is of great significance to clarify the nonlinear fracture behaviour of concrete. Experimental and numerical investigations on the FPZ of plain concrete in pre-notched beams subjected to three-point bending were carried out. Electronic speckle pattern interferometry (ESPI) technique was used to observe crack evolution and measure the full-field deformation of the beams. The development of the FPZ were evaluated qualitatively and quantitatively based on the in-plane strain contours and displacement field measured by ESPI, respectively. By integrating the cohesive crack model and finite element (FE) model, various tension softening curves (TSCs) were employed to simulate the fracture response of concrete beams. By comparing the deformation obtained by FE simulation and experiments, the TSCs of plain concrete were evaluated and most suitable TSCs of concrete were recommended.

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