The size effects in compression on drilled cylindrical concrete specimens obtained from a unique concrete block over a large scale range (1:19) are analyzed. The experimental results show scale effects on dissipated energy density rather than on the compressive strength. A theoretical explanation for such a phenomenon is presented, assuming a noninteger physical dimension of the subdomain where dissipation occurs. A comparison between experimental and theoretical values is discussed and a renormalization procedure to obtain a scale-independent constitutive law is presented.
Issue Section:
Research Papers
1.
Carpinteri
, A.
, 1981, “Static and Energetic Fracture Parameters for Rocks and Concretes
,” Mater. Constr. (Paris)
0025-5432, 14
, pp. 151
–162
.2.
Carpinteri
, A.
, 1982, “Notch Sensitivity in Fracture Testing of Aggregative Materials
,” Eng. Fract. Mech.
0013-7944, 16
, pp. 467
–481
.3.
Carpinteri
, A.
, 1985, “Interpretation of the Griffith Instability as a Bifurcation of the Global Equilibrium
,” Application of Fracture Mechanics to Cementitious Composites
, S. P.
Shah
, ed., Martinus Nijhoff
, Dordrecht
, pp. 287
–316
.4.
Carpinteri
, A.
, 1989, “Cusp Catastrophe Interpretation of Fracture Instability
,” J. Mech. Phys. Solids
0022-5096, 37
, pp. 567
–582
.5.
Carpinteri
, A.
, 1989, “Size Effects on Strength, Toughness and Ductility
,” J. Eng. Mech.
0733-9399, 115
, pp. 1375
–1392
.6.
Carpinteri
, A.
, 1984, “Stability of Fracturing Process in R.C. Beams
,” J. Struct. Eng.
0733-9445, 110
, pp. 544
–558
.7.
Bažant
, Z. P.
, 1984, “Size Effect in Blunt Fracture: Concrete, Rock, Metal
,” J. Eng. Mech.
0733-9399, 110
, pp. 518
–535
.8.
Carpinteri
, A.
, 1994, “Scaling Laws and Renormalization Groups for Strength and Toughness of Disordered Materials
,” Int. J. Solids Struct.
0020-7683, 31
, pp. 291
–302
.9.
Carpinteri
, A.
, 1994, “Fractal Nature of Material Microstructure and Size Effects on Apparent Mechanical Properties
,” Mech. Mater.
0167-6636, 18
, pp. 89
–101
.10.
Carpinteri
, A.
, Chiaia
, B.
, and Ferro
, G.
, 1995, “Size Effects on Nominal Tensile Strength of Concrete Structures: Multifractality of Materials Ligaments and Dimensional Transition From Order to Disorder
,” Mater. Struct.
1359-5997, 28
, pp. 311
–317
.11.
Holzhausen
, G. R.
, and Johnson
, A. M.
, 1979, “Analyses of Longitudinal Splitting of Uniaxially Compressed Rock Cylinders
,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
0148-9062, 16
, pp. 163
–177
.12.
Nemat-Nasser
, S.
, and Horii
, H.
, 1982, “Compression-Induced Nonplanar Crack Extension With Application to Splitting, Exfoliation and Rockburst
,” J. Geophys. Res.
0148-0227, 87
, pp. 6805
–6821
.13.
Ashby
, M. F.
, and Hallam
, D.
, 1986, “The Failure of Brittle Solids Containing Small Cracks Under Compressive Stress States
,” Acta Metall.
0001-6160, 34
, pp. 497
–510
.14.
Horii
, H.
, and Nemat-Nasser
, S.
, 1986, “Brittle Failure in Compression: Splitting, Faulting and Brittle-Ductile Transition
,” Philos. Trans. R. Soc. London
0962-8428, 319
, pp. 337
–374
.15.
Nemat-Nasser
, S.
, and Hori
, M.
, 1993, Micromechanics: Overall Properties of Heterogeneous Materials
, North-Holland
, Amsterdam
.16.
Bažant
, Z. P.
, and Xiang
, Y.
, 1997, “Size Effect in Compression Fracture: Splitting Crack Band Propagation
,” J. Eng. Mech.
0733-9399, 123
, pp. 162
–172
.17.
Rossi
, P.
, Ulm
, F. J.
, and Hachi
, F.
, 1996, “Compressive Behaviour of Concrete: Physical Mechanisms and Modeling
,” J. Eng. Mech.
0733-9399, 122
, pp. 1038
–1043
.18.
Markeset
, G.
, and Hillerborg
, A.
, 1995, “Softening of Concrete in Compression-Localization and Size Effects
,” Cem. Concr. Res.
0008-8846, 25
, pp. 702
–708
.19.
Slate
, F. O.
, Nilson
, A. N.
, and Martinez
, S.
, 1986, “Mechanical Properties of High-Strength Lightweight Concrete
,” J. Am. Concr. Inst.
0002-8061, 77
, pp. 606
–613
.20.
Carpinteri
, A.
, and Chiaia
, B.
, 1995, “Multifractal Nature of Concrete Fracture Surfaces and Size Effects on Nominal Fracture Energy
,” Mater. Struct.
1359-5997, 28
, pp. 435
–443
.21.
Carpinteri
, A.
, Ferro
, G.
, and Monetto
, I.
, 1999, “Scale Effects in Uniaxially Compressed Concrete Specimens
,” Mag. Concrete Res.
0024-9831, 51
, pp. 217
–225
.22.
van Vliet
, M. R. A.
, and van Mier
, J. G. M.
, 1996, “Experimental Investigation of Concrete Fracture Under Uniaxial Compression
,” Mech. Cohesive-Frict. Mater.
1082-5010, 1
, pp. 115
–127
.23.
Ferro
, G.
, 2006, “Scale Effects on Compressive Tests for Concrete Specimens
,” Eng. Fract. Mech.
0013-7944, 79
, pp. 1510
–1530
.24.
Turcotte
, D. L.
, 1992, Fractals and Chaos in Geology and Geophysics
, Cambridge University Press
, Cambridge
.25.
Carpinteri
, A.
, and Pugno
, N.
, 2002, “A Fractal Comminution Approach to Evaluate the Drilling Energy Dissipation
,” Int. J. Numer. Analyt. Meth. Geomech.
0363-9061, 26
, pp. 499
–513
.26.
Carpinteri
, A.
, and Pugno
, N.
, 2003, “A Multifractal Comminution Approach for Drilling Energy Dissipation
,” Powder Technol.
0032-5910, 131
, pp. 93
–98
.27.
van Mier
, J. G. M.
, et al., 1997, “Report of the Round Robin Test Carried Out by RILEM TC 148-Ssc: Strain-Softening of Concrete in Uniaxial Compression
,” Mater. Struct.
1359-5997, 30
, pp. 195
–209
.28.
van Mier
, J. G. M.
, 1986, “Multiaxial Strain-Softening of Concrete-Part 1: Fracture and Part II: Load-Histories
,” Mater. Struct.
1359-5997, 19
, pp. 179
–200
.29.
Ferro
, G.
, 1994, “Effetti di Scala Sulla Resistenza a Trazione dei Materiali
,” Ph.D. thesis, Politecnico di Torino.30.
Carpinteri
, A.
, Chiaia
, B.
, and Ferro
, G.
, 1997, “A New Explanation for Size Effects on the Flexural Strength of Concrete
,” Mag. Concrete Res.
0024-9831, 49
, pp. 45
–53
.31.
Carpinteri
, A.
, Ciola
, F.
, and Pugno
, N.
, 2001, “Boundary Element Method for the Strain-Softening Response of Quasi-Brittle Materials in Compression
,” Comput. Struct.
0045-7949, 51
, pp. 389
–401
.32.
Carpinteri
, A.
, Ciola
, F.
, Pugno
, N.
, Gobbi
, M. E.
, and Ferrara
, G.
, 2001, “Size-Scale and Slenderness Influence on the Compressive Strain-Softening Behavior of Concrete
,” Fatigue Fract. Eng. Mater. Struct.
8756-758X, 24
, pp. 441
–450
.33.
Turcotte
, D. L.
, 1986, “Fractals and Fragmentation
,” J. Geophys. Res.
0148-0227, 91
, pp. 1921
–1926
.34.
Rittinger
, P. R.
, 1937, Lehrbuch der aufbereitungskunde. Berlin.35.
Kick
, F.
, 1885, Das gesetz der proportionalen widerstande. Leipzig.36.
Stroeven
, P.
, 1991, “Fractals and Fractography in Concrete Technology
,” International Symposium on Brittle Matrix Composities
, Warsaw
, Poland
, pp. 1
–10
.37.
Lee
, Y.-H.
, and Willam
, K.
, 1997, “Mechanical Properties of Concrete in Uniaxial Compression
,” ACI Mater. J.
0889-325X, 94
, pp. 457
–471
.38.
Momber
, A. W.
, 2000, “The Fragmentation of Standard Concrete Cylinders Under Compression: The Role of Secondary Fracture Debris
,” Eng. Fract. Mech.
0013-7944, 67
, pp. 445
–459
.39.
Carpinteri
, A.
, Chiaia
, B.
, and Cornetti
, P.
, 2001, “Static-Kinematic Duality and the Principle of Virtual Work in the Mechanics of Fractal Media
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 191
, pp. 3
–19
.40.
Carpinteri
, A.
, and Ferro
, G.
, 1994, “Size Effects on Tensile Fracture Properties: A Unified Explanation Based on Disorder and Fractality of Concrete Microstructure
,” Mater. Struct.
1359-5997, 27
, pp. 563
–571
.41.
Carpinteri
, A.
, and Chiaia
, B.
, 1996, “Size Effects on Concrete Fracture Energy: Dimensional Transition From Order to Disorder
,” Mater. Struct.
1359-5997, 29
, pp. 259
–266
.42.
Mandelbrot
, B. B.
, 1985, “Self-Affine Fractals and Fractal Dimension
,” Phys. Scr.
0031-8949, 32
, pp. 257
–260
.43.
Carpinteri
, A.
, and Pugno
, N.
, 2002, “Fractal Fragmentation Theory for Shape Effects of Quasi-Brittle Materials in Compression
,” Mag. Concrete Res.
0024-9831, 54
, pp. 473
–480
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