Attempts to apply linear elastic fracture mechanics (LEFM) to concrete have been made for several years. Several investigators have reported that when fracture toughness, Klc, is evaluated from notched specimens using conventional LEFM (measured peak load and initial notch length) a significant size effect is observed. This size effect has been attributed to nonlinear slow crack growth occurring prior to the peak load. A two parameter fracture model is proposed to include this nonlinear slow crack growth. Critical stress intensity factor, KIcS, is calculated at the tip of the effective crack. The critical effective crack extension is dictated by the elastic critical crack tip opening displacement, CTODc. Tests on notched beam specimens showed that the proposed fracture criteria to be size independent. The proposed model can be used to calculate the maximum load (for Mode I failure) of a structure of an arbitrary geometry. The validity of the model is demonstrated by an accurate simulation of the experimen...

Two Parameter Fracture Model for Concrete

The purpose of this review is to discuss the development and the state of the art in dynamic testing techniques and dynamic mechanical behaviour of rock materials. The review begins by briefly introducing the history of rock dynamics and explaining the significance of studying these issues. Loading techniques commonly used for both intermediate and high strain rate tests and measurement techniques for dynamic stress and deformation are critically assessed in Sects. 2 and 3. In Sect. 4, methods of dynamic testing and estimation to obtain stress–strain curves at high strain rate are summarized, followed by an in-depth description of various dynamic mechanical properties (e.g. uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness) and corresponding fracture behaviour. Some influencing rock structural features (i.e. microstructure, size and shape) and testing conditions (i.e. confining pressure, temperature and water saturation) are considered, ending with some popular semi-empirical rate-dependent equations for the enhancement of dynamic mechanical properties. Section 5 discusses physical mechanisms of strain rate effects. Section 6 describes phenomenological and mechanically based rate-dependent constitutive models established from the knowledge of the stress–strain behaviour and physical mechanisms. Section 7 presents dynamic fracture criteria for quasi-brittle materials. Finally, a brief summary and some aspects of prospective research are presented.

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A Review of Dynamic Experimental Techniques and Mechanical Behaviour of Rock Materials

Highly dispersed carbon nanotube-reinforced cement-based materials

One of the fundamental aspects in cohesive zone modeling is the definition of the traction-separation relationship across fracture surfaces, which approximates the nonlinear fracture process. Cohesive traction-separation relationships may be classified as either nonpotential-based models or potential-based models. Potential-based models are of special interest in the present review article. Several potential-based models display limitations, especially for mixed-mode problems, because of the boundary conditions associated with cohesive fracture. In addition, this paper shows that most effective displacement-based models can be formulated under a single framework. These models lead to positive stiffness under certain separation paths, contrary to general cohesive fracture phenomena wherein the increase of separation generally results in the decrease of failure resistance across the fracture surface (i.e., negative stiffness). To this end, the constitutive relationship of mixed-mode cohesive fracture should be selected with great caution.

Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces

Due to their exceptional mechanical properties, carbon nanotubes (CNTs) are considered to be one of the most promising reinforcing materials for the next generation of high-performance nanocomposites. In this study, the reinforcing effect of highly dispersed multiwall carbon nanotubes (MWCNTs) in cement paste matrix has been investigated. The MWCNTs were effectively dispersed in the mixing water by using a simple, one step method utilizing ultrasonic energy and a commercially available surfactant. A detailed study on the effects of MWCNTs concentration and aspect ratio was conducted. The excellent reinforcing capabilities of the MWCNTs are demonstrated by the enhanced fracture resistance properties of the cementitious matrix. Additionally, nanoindentation results suggest that the use of MWCNTs can increase the amount of high stiffness C–S–H and decrease the porosity. Besides the benefits of the reinforcing effect, autogenous shrinkage test results indicate that MWCNTs can also have a beneficial effect on the early strain capacity of the cementitious matrix, improving this way the early age and long term durability of the cementitious nanocomposites.

Multi-scale mechanical and fracture characteristics and early-age strain capacity of high performance carbon nanotube/cement nanocomposites

Failure of Structures. Principles of Linear-Elastic Fracture Mechanics. Principles of Nonlinear Fracture Mechanics. Structure and Fracture Process of Concrete. Nonlinear Fracture Mechanics for Mode I Quasi-Brittle Fracture. Test Methods to Determine Mode I Fracture Properties for Concrete and Rock. Fracture Resistance Curves (R-Curves) for Quasi-Brittle Materials. Fracture Mechanics for Other Deformation Modes. Applications of Fracture Mechanics to Concrete Structures. Fracture Mechanics and Compressive Failure. Damage Mechanics and Fracture Mechanics. Other Areas in Application of Fracture Mechanics. Problems. Index.

Fracture Mechanics of Concrete: Applications of Fracture Mechanics to Concrete, Rock and Other Quasi-Brittle Materials

Fracture of Concrete and Rock

Fracture and tensile characteristics of asphalt concrete mixtures affect the structural performance of pavements, particularly under low-temperature conditions. This paper reports a study of the tensile and fracture properties of asphalt-rubber (AR) concrete mixtures that formed the basis for the recommendation of an optimum asphalt mixture design incorporating crumb rubber from scrap tires. The work involved a full-factorial experiment with three different rubber contents (19, 22, and 24%), and three different AR binder contents (6, 7.5%, and 9%) in a surface mixture. Fracture and indirect tension tests were performed on AR concrete beams and Marshall test samples, respectively, at two different test temperatures of 25 and 5°C. The variables studied were indirect tensile strength, peak center-point load carried, load-point displacement, and unit fracture energy. The results show that higher mean values of indirect tensile strength and fracture energy were obtained corresponding to the highest AR binder c...

Fracture and Tensile Characteristics of Asphalt-Rubber Concrete

Keynote speaker invited lecture experimental measurements failure localization and damage model micromechanics of geological materials ceramics, ice dynamic study I - response interface mechanics dynamic study II - energy release mechanisms micromechanics of concrete.

Micromechanics of failure of quasi-brittle materials

The method of compliance measurement is sometimes used to determine the length of cracks in fatigued metal specimens. This paper considers an application of this method to plain, concrete beams subjected to sinusoidal loading in three point bending. Three beams, prenotched by cutting with a concrete saw, were used to determine a compliance calibration curve. This curve was then used to determine the extent of cracking in eight beams that were fatigue loaded. Of the beams precracked by fatigue loading, six were subsequently statically loaded to failure. A method for estimating the effective fracture toughness based on a test procedure for metal specimens was used to obtain experimental data as input to a finite element model. Results, including fracture surface appearance, indicate that the compliance method is a convenient and suitable testing technique for monitoring crack growth in concrete beams due to fatigue.

Stuart E. Swartz

Papers

Fracture Mechanics of Concrete: Applications of Fracture Mechanics to Concrete, Rock and Other Quasi-Brittle Materials

Fracture of Concrete and Rock

Fracture and Tensile Characteristics of Asphalt-Rubber Concrete

Micromechanics of failure of quasi-brittle materials

Compliance Monitoring of Crack Growth in Concrete