Fracture and Size Effect in Concrete and Other Quasibrittle Materials

2019 ◽  
Author(s):  
Zdenĕk P. Bažant ◽  
Jaime Planas
Keyword(s):  
Size Effect ◽  
Quasibrittle Materials

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.

Scaling Of Fracture In Quasibrittle Materials And The Question Of Possible Influence Of Fractal Morphology

1995 ◽  
Vol 409 ◽  
Author(s):  
Zdeněk P. Bažant
Keyword(s):  
Size Effect ◽  
Asymptotic Expansions ◽  
Asymptotic Properties ◽  
Fractal Nature ◽  
Nonlinear Fracture Mechanics ◽  
Quasibrittle Materials ◽  
Large Size ◽  
Nonlinear Fracture ◽  
Nominal Strength ◽  
Asymptotic Matching

AbstractThe paper presents a review of recent results on the problem of size effect (or the scaling problem) in nonlinear fracture mechanics of quasibrittle materials and on the validity or recent claims that the observed size effect may be caused by the fractal nature of crack surfaces. The problem of scaling is approached through dimensional analysis and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are presented, considering not only specimens with large notches (or traction-free cracks) but also structures with no notches. Simple size effect formulas matching the required asymptotic properties are given. Regarding the fractal nature of crack surfaces, it is concluded that it cannot be the cause of the observed size effect.

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.

On geometry dependent R-curve from size effect law for concrete-like quasibrittle materials

2015 ◽  
Vol 15 (4) ◽  
pp. 673-686 ◽  
Author(s):  
Yan-Hua Zhao ◽  
Jian-Mei Chang ◽  
Hong-Bo Gao
Keyword(s):  
Size Effect ◽  
Quasibrittle Materials

scholarly journals Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180617 ◽  
Author(s):  
Zdeněk P. Bažant
Keyword(s):  
Probability Distribution ◽  
Analytical Solution ◽  
Size Effect ◽  
Failure Probability ◽  
Transition Rate ◽  
Microelectromechanical Systems ◽  
Rate Theory ◽  
Weakest Link ◽  
Quasibrittle Materials ◽  
The Mean

The objective in materials or structure design has been to maximize the mean strength. However, as generally agreed, engineering structures, such as bridges, aircraft or microelectromechanical systems must be designed for tail probability of failure less than 10 −6 per lifetime. But this objective is not the same. Indeed, a quasibrittle material or structure with a superior mean strength can have, for the same coefficient of variation, an inferior strength at the less than 10 −6 tail. This tail is unreachable by histogram testing. So, one needs a rational theory, physically based and experimentally verified indirectly, which is feasible by size effect. Focusing on the results at the writer's home institution, this inaugural article (written three years ex post facto ) reviews recent results towards this goal, concerned with quasibrittle materials such as concretes, rocks, tough ceramics, fibre composites, bone and most materials on the micrometer scale. The theory is anchored at the atomic scale because only on that scale the failure probability is known—it is given by the frequency of breakage of bonds, governed by the activation energy barriers in the transition rate theory. An analytical way to scale it up to the macroscale representative volume element (RVE) has been found. Structures obeying the weakest-link model are considered but, for quasibrittle failures, the number of links, each corresponding to one RVE, must be considered as finite. The result is a strength probability distribution transiting from Weibullian to Gaussian, depending on the structure size. The Charles-Evans and Paris laws for subcritical crack growth under static and cyclic fatigue are also derived from the transition-rate theory. This yields a size-dependent Gauss–Weibull distribution of lifetime. Close agreement with numerous published test data is achieved. Discussed next are new results on materials with a well-defined microscale architecture, particularly biomimetic imbricated (or staggered) lamellar materials, exemplified by nacre, a material of astonishing mean strength compared to its constituents. This architecture is idealized as a diagonally pulled fishnet, which is shown to be amenable to an analytical solution of the strength probability distribution. The solution is verified by million Monte Carlo simulations for each of the fishnets of various shapes and sizes. In addition to the classical weakest-link and the fibre-bundle models, the fishnet is found to be the third strength probability model that is amenable to an analytical solution. The nacreous architecture is shown to provide an additional major (greater than 100%) strengthening at the 10 −6 failure probability tail. Finally, it is emphasized that the most important consequence of the quasibrittleness, and also the most effective way of calibrating the 10 −6 tail, is the size effect on the mean structural strength, which permeates all formulations.

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