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 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.

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.

scholarly journals Aplikasi Size Effect Law Pada Beton Marine dengan Pola Bukaan Tarik

2021 ◽  
Vol 28 (2) ◽  
pp. 143-154
Author(s):  
Fella Supazaein ◽  
Resmi Bestari Muin
Keyword(s):  
Fracture Mechanics ◽  
Size Effect ◽  
Fracture Energy ◽  
High Performance ◽  
High Performance Concrete ◽  
Actual Performance ◽  
Nonlinear Fracture Mechanics ◽  
Nonlinear Fracture ◽  
Sample Height ◽  
Marine Concrete

AbstrakPengembangan infrastruktur di bidang maritim adalah salah satu strategi untuk mengembangkan perekonomian. Beton marine banyak digunakan sebagai material struktur  pada pembangunan infrastruktur di bidang maritim tersebut. Beton marine harus menggunakan beton high performance concrete (HPC). Dengan berkembangnya teknologi beton HPC pengoptimalan efisiensi komponen struktur menjadi lebih signifikan.Pada perencanaan pelaksanaan pembangunan khususnya pada tahap analisa struktur, jarang sekali direncanakan kekuatan terhadap mekanika fraktur yang seharusnya juga didesain agar keruntuhan secara fraktur bisa diatasi. penelitian ini mengkaji aplikasi size effect law pada beton HPC pada balok  dengan berbagai ukuran yang sudah ditentukan (small, medium dan high) untuk memperoleh nilai energy fraktur (Gf). Hasil penelitian ini dapat berkontribusi dalam penerapam metode untuk mendapatkan nilai parameter dari kinerja fraktur. selain itu, data parameter dapat digunakan dalam mengkalibrasi analisa numerik elemen struktur berbasis fraktur energi agar dapat dipastikan kinerja struktur yang sesungguhnya.Hasil pengujian menunjukkan energi fraktur pada benda uji set II (rasio takik terhadap tinggi sample = 1/6) lebih besar 8,4% dari benda uji set I (rasio takik terhadap tinggi sample = 1/3). Factor geometri  dan kemiringan pada garis regresi (A) menurun selaras dengan menurunnya rasio takik. Dari angka keruntuhan nilai  berada pada range 0,1 <  < 10 yang menandakan material didesain harus dengan kriteria nonlinear fracture mechanic.Kata-kata Kunci: Beton marine, mekanika fraktur, size effect law, nonlinear fracture mechanics AbstractInfrastructure development in the maritime sector is one strategy for developing the economy. Marine concrete is widely used as a structural material in infrastructure development in the maritime sector. Marine concrete must use high performance concrete (HPC). With the development of HPC concrete technology, optimization of the efficiency of structural components has become more significant.In the construction implementation planning, especially at the structural analysis stage, it is rare to plan the strength of the fracture mechanics which should also be designed so that fracture collapse can be overcome. This study examines the application of size effect law on HPC concrete on beam of various predetermined sizes (small, medium and high) to obtain the fracture energy value (Gf). The results of this study can contribute to the application of the method to obtain parameter values of fracture performance. In addition, parameter data can be used in calibrating the numerical analysis of energy fracture based structural elements in order to ascertain the actual performance of the structure.The results showed that fracture energy in specimen set II (ratio of notches to depth = 1/6) was 8.4% greater than specimen set I (ratio of notches to sample height = 1/3). The geometric factor  and slope of the regression line (A) decreased in line with the decreasing notch ratio. From the brittleness number, the value of β is in the range 0.1 <β <10 which indicates that the material should  designed with nonlinear fracture mechanic criteria.Key words: marine concrete, fracture mechanics, size effect law, nonlinear fracture mechanics

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.

Complex study of the fracture processes in materials and structures

2018 ◽  
Vol 84 (11) ◽  
pp. 46-51 ◽  
Author(s):  
N. A. Makhutov
Keyword(s):  
Fracture Mechanics ◽  
Crack Resistance ◽  
Scientific Basis ◽  
Intensity Factors ◽  
Nonlinear Fracture Mechanics ◽  
Nonlinear Fracture ◽  
Linear Fracture ◽  
Science Technology ◽  
Fracture Processes

The results of comprehensive studies of multifactor processes, mechanisms and criteria for fracture at a variation of the crack-like defect state, loading conditions and mechanical properties of structural materials carried out in the 20th - 21st centuries are presented on the basis of monographic publications and articles published in the journal “Zavodskaya Laboratoriya. Diagnostika Materialov.” Crack resistance of materials and structures has become a key problem of the material science, technology, design, manufacture and service of structures. Fracture mechanics including estimation of the stress-strain and limiting states in a cracks tip formed a scientific basis of the crack resistance analysis Stress intensity factors (linear fracture mechanics) and strain intensity factors (nonlinear fracture mechanics) are accepted as the basic criteria of those states. The basic computational relations for construction of the fracture diagrammes which link the cracks growth with conditions of a static, cyclic, long-term, dynamic loading are presented. Parameters of computational relations are put into correspondence with the features of fracture processes on nano-, micro-, meso- and macrolevels. Prospects of the research and guidelines of further studing crack resistance are discussed.

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