In the first of its series of four state-of-the-art reports under preparation, the Committee describes the basic concepts of fracture mechanics of concrete, the existing theoretical models, and the methods for determining the material fracture parameters. Chapter 1 offers five reasons for introducing fracture mechanics into certain aspects of design of concrete structures, including some code provisions: (1) a theoretical energy argument; (2) the need to achieve objectivity of finite element solutions, i.e., eliminate spurious mesh sensitivity; (3) the progressive (propagating) nature of failure, implied whenever the load-deflection diagram lacks a yield plateau; (4) the need to rationally predict ductility and energy absorption capability; and most importantly, (5) the effect of structure size on the nominal strength (i.e., nominal stress at maximum or ultimate load) as well as on ductility and energy absorption capability. The size effect is due to stored energy release into the fracture front, and is not governed by Weibulltype statistical theory. Experimental evidence on the existence of the size effect, hitherto ignored in design practice and code provisions, is documented.
Chapter 2 gives a brief review of the necessary basic results of linear elastic fracture mechanics (LEFM). In concrete, departures from this classical theory are caused by the existence of distributed cracking (or damage) in a progressively softening fracture process zone which surrounds the tip of a continuous crack.
In Chapter 3 nonlinear fracture models characterizing the softening stress-displacement or stress-strain relations (such as those of Hillerborg’s fictitious crack model, crack band model, nonlocal strain-softening models, etc.) are described and random particle simulation of aggregate microstructure is discussed. The principles of implementation of these models in finite element programs are also outlined.
Chapter 4 presents simpler nonlinear fracture models which represent adaptations of linear elastic fracture mechanics, such as Jenq and Shah’s model and the R-curve, along with determination of geometry-dependent R-curves from the size effect law proposed by Bazant.
This law, describing the approximate dependence of the nominal stress at maximum load on structure size, is discussed in Chapter 5, and structural response is characterized by the brittleness number.
Chapter 6 presents in considerable detail the current methods for experimental and analytical determination of material fracture parameters, including the quasi-LEFM methods, RILEM (work-of-fracture) method, the Jenq-Shah and Karihaloo-Nallathambi methods, and the size-effect method. Experimental determination of the characteristic length for nonlocal continuum models and the strain-softening properties is then examined, and material parameters for modes II and III, shear fractures and mixed mode fracture are also discussed.
Chapter 7 then proceeds to describe various influencing factors, such as the loading rate, humidity and temperature, as well as the effect of cyclic loading.
Chapter 8 is devoted to the effect of reinforcing bars and their bond slip on fracture propagation, and to fracture of fiber-reinforced concrete.
Chapter 9 deals with more theoretical problems of modeling systems of interacting cracks. Attention is focused on systems of parallel growing cracks. Their stability decides the spacing and width of the cracks from the mechanics viewpoint. It is concluded that, after a decade of rapid progress in research, the time appears ripe for introducing fracture mechanics into design practice. This should not only bring about more uniform safety margins, thus improving safety and economy of design, but also pave the way for safer and more efficient use of high-performance concretes and permit design extrapolations beyond the range of previous experiments and design.
KEYWORDS: Brittleness, concrete, concrete structures, crack spacing and width, cracking, damage mechanics, design codes, ductility, failure, fiber-reinforced concrete, nonlocal continuum models, reinforced concrete, size effect, strain softening, structural design, testing methods, ultimate loads.
Table of Contents
Chapter 1 - Why fracture mechanics?
* Five reasons for fracture mechanics approach
* Is Weibull's statistical theory of size effect applicable?
* Simple energy explanation of size effect
* Experimental evidence for size effect in structures
* Explanation of size effect on ductility
Chapter 2 - Essential results from linear elastic fracture mechanicsStress singularity
* Energy criterion
* Limits of applicability
Chapter 3 - Nonlinear fracture modesl with softening zone
* Softening stress-displacement relations
* Softening stress-strain relations
* Stress-displacement vs. stress-strain softening relations
* Nonlinear triaxial models for strain-softening
* Random particle simulation of microstructure
Chapter 4 - Special nonlinear fracture models based on adaptation of LEFM
* Effective crack models
* Two-parameter model of Jenq and Shah
* Geometry-dependent R-curve determined from size effect law
Chapter 5 -Size effect and brittleness of structures
* Size effect law for maximum nominal stress
* Brittleness number
* Other size effects and limitations
Chapter 6 - Experimental or analytical determination of material fracture parameters
* Notched beam tests
* Wedge-splitting test
* Work-of-fracture method (RILEM, Hillerborg)
* Size effect in work-of-fracture method
* Two-parameter fracture model of Jenq and Shah
* Effective crack model of Karihaloo and Nallathambi
* Determination of material parameters by size effect method
* Size required for applicability of LEFM
* Identification of nonlocal characteristics length
* Identification of tensile post-peak softening stress-strain curve
* Material parameters for Mode II and planar mixed mode fracture
* Material parameters for Mode III fracture
Chapter 7 - Factors influencing fracture parameters
* Effect of loading rate and creep
* Effect of temperature and humidity on fracture energy
* Effect of cyclic loading
Chapter 8 - Effect of reinforcement
* Effect of reinforcing steel bars
* Fracture in fiber-reinforced concrete
Chapter 9 - Crack systems
* Response of structures with interacting growing cracks
* Interacting parallel cracks
* Crack spacing and width in beams
* Interacting microcracks