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.

Universal size effect of concrete specimens and effect of notch depth

2017 ◽  
Vol 3 (1) ◽  
pp. 47 ◽  
Author(s):  
Sıddık Şener ◽  
Kadir Can Şener
Keyword(s):  
Size Effect ◽  
Crack Length ◽  
Asymptotic Properties ◽  
Experimental Program ◽  
Three Point Bending ◽  
Large Size ◽  
Nominal Strength ◽  
Notch Length ◽  
Point Bend

The universal size effect law of concrete is a law that describes the dependence of nominal strength of specimens or structure on both its size and the crack (or notch) length, over the entire of interest, and exhibits the correct small and large size asymptotic properties as required. The main difficulty has been the transition of crack length from 0, in which case the size effect mode is Type 1, to deep cracks (or notches), in which case the size effect mode is Type 2 and fundamentally different from Type 1. The current study is based on recently obtained comprehensive fracture test data from three-point bending beams tested under identical conditions. In this test, the experimental program consisted of 80 three-point bend beams with 4 different depths 40, 93, 215 and 500mm, corresponding to a size range of 1:12.5. Five different relative notch lengths, a/D = 0, 0.02, 0.075, 0.15, 0.30 were cut into the beams. A total of 20 different geometries (family of beams) were tested. The present paper will use these data to analyze the effects of size, crack length. This paper presents a studying to improve the existing universal size effect law, named by Bazant, using the experimentally obtained beam strengths for various different specimen sizes and all notch depths. The updated universal size effect law is shown to fit the comprehensive data quite well.

UNIVERSAL SIZE EFFECT STUDIES USING THREE POINT BEAM TESTS

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Siddik Şener ◽  
Kadir Can Şener
Keyword(s):  
Size Effect ◽  
Asymptotic Properties ◽  
Main Difficulty ◽  
Fracture Test ◽  
Three Point Bending ◽  
Large Size ◽  
Nominal Strength ◽  
Notch Length

The universal size effect law for concrete is a law that describes the dependence of nominal strength of specimen or structure on both its size and the crack (or notch) length, over the entire of interest, and exhibits the correct small and large size asymptotic properties as required. The main difficulty has been the transition of crack length from 0, in which case the size effect mode is Type 1, to deep cracks (or notches), in which case the size effect mode is Type 2 and fundamentally different from Type 1. The current study is based on recently obtained comprehensive fracture test data from three-point bending beams tested under identical conditions. This paper presents a studying to improve the existing universal size effect law using the experimentally obtained beam strengths for various different specimen sizes and all notch depths. The updated universal size effect law is shown to fit the comprehensive data quite well.

Size Effect and Fracture Characteristics of Composite Laminates

1996 ◽  
Vol 118 (3) ◽  
pp. 317-324 ◽  
Author(s):  
Zdeneˇk P. Bazˇant ◽  
Isaac M. Daniel ◽  
Zhengzhi Li
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Process Zone ◽  
Fiber Composite ◽  
Maximum Load ◽  
Two Dimensions ◽  
Effective Length ◽  
Smooth Transition ◽  
Fracture Characteristics ◽  
Nominal Strength

Measurements of the size effect on the nominal strength of notched specimens of fiber composite laminates are reported. Tests were conducted on graphite/epoxy crossply and quasi-isotropic laminates. The specimens were rectangular strips of widths 6.4, 12.7, 25.4 and 50.8 mm (0.25, 0.50, 1.00 and 2.00 in.) geometrically similar in two dimensions. The gage lengths were 25, 51, 102 and 203 mm (1.0, 2.0, 4.0 and 8.0 in.). One set of specimens had double-edge notches and a [0/922]s crossply layup, and another set had a single-sided edge notch and a [0/±45/90]s, quasi-isotropic layup. It has been found that there is a significant size effect on the nominal strength. It approximately agrees with the size effect law proposed by Bazˇant, according to which the curve of the logarithm of the nominal strength versus the logarithm of size represents a smooth transition from a horizontal asymptote, corresponding to the strength criterion (plastic limit analysis), to an inclined asymptote of −0.5 slope, corresponding to linear elastic fracture mechanics. Optimum fits of the test results by the size effect law are obtained, and the size effect law parameters are then used to identify the material fracture characteristics, particularly the fracture energy and the effective length of the fracture process zone. Finally, the R-curves are also identified on the basis of the maximum load data. The results show that in design situations with notches or large initial traction-free cracks the size effect on the nominal strength of fiber composite laminates must be taken into account.

scholarly journals Size Effect in Fracture of Sandwich Structure Components: Foam and Laminate

2001 ◽  
Author(s):  
Zdeněk P. Bažant ◽  
Yong Zhou ◽  
Drahomír Novák ◽  
Isaac M. Daniel
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Sandwich Structure ◽  
Maximum Load ◽  
Material Strength ◽  
Large Structures ◽  
Nominal Strength ◽  
Sandwich Plates And Shells ◽  
Extensive Test ◽  
Plates And Shells

Abstract In the design of sandwich plates and shells for very large structures, such as ships in the range of 100 m length, it is very important to take the size effect on the nominal strength into account, and do so in a realistic, physically justified, manner. Before the size effect is addressed for a sandwich structure, it must be understood for its components — the foam core and the laminate skins. In the current practice, the size effects are automatically attributed to the randomness of material strength, as described by the Weibull theory. The purpose of this paper is to show that in both the foam and the laminate there are deterministic size effects, which are generally more pronounced. They are caused by stress redistribution and energy release due to the growth of large fractures or large cracking zones prior to attaining the maximum load. This deterministic size effect is verified and calibrated by new tests of notched specimens of rigid close-cell vinyl foam. A combined deterministic-probabilistic theory of size effect of the laminates is proposed and verified by extensive test data.

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.

An approximate analytical model for modification of size effect law for open-hole composite structure under biaxial load

2020 ◽  
pp. 095440622095937
Author(s):  
Mohammed Y Abdellah
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Approximate Model ◽  
Biaxial Stress ◽  
Damage Initiation ◽  
Main Challenge ◽  
Nominal Strength ◽  
Biaxial Stress State ◽  
Cohesive Laws ◽  
Open Hole

Nominal strength prediction remains the main challenge in the field of design and manufacturing of composite laminates. An approximate model to study the stress distribution around a circular hole in composite laminates is derived in this study. This model is constructed using well-known cohesive zone models and mainly depends on the un-notch strength and in-plane fracture toughness. The model attempts to modify and extend the specimen size effect curves, extracted using two-parameter cohesive laws (linear, exponential, and constant), into a biaxial stress state. It successfully predicts the damage initiation, propagation, and fracture of multidirectional composite laminates. Moreover, the stress concentration factor for a composite plate under varying biaxiality is calculated.

scholarly journals Mode I and II Interlaminar Fracture in Laminated Composites: A Size Effect Study

2019 ◽  
Vol 86 (9) ◽  
Author(s):  
Marco Salviato ◽  
Kedar Kirane ◽  
Zdeněk P. Bažant ◽  
Gianluca Cusatis
Keyword(s):  
Size Effect ◽  
Process Zone ◽  
Laminated Composites ◽  
Nonlinear Effects ◽  
Effect Study ◽  
Mode I ◽  
Brittle Behavior ◽  
Linear Elastic ◽  
Nominal Strength ◽  
Significant Difference

This work investigates the mode I and II interlaminar fracturing behavior of laminated composites and the related size effects. Fracture tests on geometrically scaled double cantilever beam (DCB) and end notch flexure (ENF) specimens were conducted. The results show a significant difference between the mode I and mode II fracturing behaviors. The strength of the DCB specimens scales according to the linear elastic fracture mechanics (LEFM), whereas ENF specimens show a different behavior. For ENF tests, small specimens exhibit a pronounced pseudoductility. In contrast, larger specimens behave in a more brittle way, with the size effect on nominal strength closer to that predicted by LEFM. This transition from quasi-ductile to brittle behavior is associated with the size of the fracture process zone (FPZ), which is not negligible compared with the specimen size. For the size range investigated in this study, the nonlinear effects of the FPZ can lead to an underestimation of the fracture energy by as much as 55%. Both the mode I and II test data can be captured very accurately by the Bažant’s type II size effect law (SEL).

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.

Scaling of Sea Ice Fracture—Part I: Vertical Penetration

2001 ◽  
Vol 69 (1) ◽  
pp. 11-18 ◽  
Author(s):  
Z. P. Bazˇant
Keyword(s):  
Fracture Mechanics ◽  
Sea Ice ◽  
Size Effect ◽  
Large Scale ◽  
Load Capacity ◽  
Field Tests ◽  
Material Strength ◽  
In Situ Tests ◽  
Vertical Loading ◽  
Nominal Strength

Based on the premise that large-scale failure of sea ice is governed by fracture mechanics, recently validated by Dempsey’s in situ tests of fracture specimens of a record-breaking size, this two-part study applies fracture mechanics and asymptotic approach to obtain approximate explicit formulas for the size effect in two fundamental problems. In the present Part I, the load capacity of a floating ice plate subjected to vertical load is determined, and in Part II, which follows, the horizontal force exerted by an ice plate moving against a fixed structure is analyzed in a similar manner. The resulting formulas for vertical loading agree with previous sophisticated numerical fracture simulations as well with the limited field tests of vertical penetration that exist. The results contrast with the classical predictions of material strength or plasticity theories, which in general exhibit no size effect on the nominal strength of the structure.

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