A. M. Hammad

Correlation between crack tortuosity and fracture toughness in cementitious material

This paper proposes a new technique for the evaluation of fractal dimension (D) of fracture surface and a quantitative correlation between D and fracture toughness of cementitious materials. The experimental program has been performed on compact tension (CT) specimens (600 × 525 × 125 mm) with three different aggregate sizes (dmax=4.7 mm, 18.8 mm and 37.5 mm). The fractal geometry concept is utilized in the evaluation of fracture surface roughness. To avoid indirect or destructive experimental procedures that are prohibitively laborious and time consuming, a new non-destructive technique is presented. Results of the analysis indicate that the concept of fractal geometry provides a useful tool in the fracture surface characterization. The results also suggest that the fracture toughness can be correlated with the fractal dimension of fracture surface.

Assessment and evaluation of fractal dimension of concrete fracture surface digitized images

Abstract Recently, a new non-destructive technique was introduced and tested by the authors [1,2] for the evaluation of fractal dimension of fractured concrete specimens. The objectives of this paper are to expand and eleborate on the advantages of the technique, to provide a basic understanding of fractal geometry and to discuss the potential application of fractal geometry to fracture in cementitious materials. This may eventually lead to a better understanding of the fracture mechanics properties of such materials. Through this technique and the utilization of an Image Analyzer System, the fracture surface was photographed and stored as an image. Different methods of fractal analysis, e.g. modified slit island technique (SIT) and two-dimensional Fourier spectral analyses (2D FFT) were employed. Fractured concrete specimens with a maximum aggregate size of 37.5 mm and a projected fracture area of 367.5 mm long and 125 mm wide were used in the study. Results of the analysis suggest that concrete fracture surface exhibit fractal characteristics over the scales considered. A scaling relation between roughness at different length scales holds only over a limited range of wave lengths. The mean fractal dimension for the modified slit island technique is D=2.21 and the mean stochastic fractal dimension for two-dimensional Fourier spectral analyses is D=2.59. Also, the digitized fracture surface images were found to mimic the actual fracture surfaces.

Fractal dimension as a measure of roughness of concrete fracture trajectories

Abstract In this article, fractal characterization of concrete and mortar fracture trajectories is carried out. These trajectories were either sectioned from a replica of the fracture surface, profiled from a digitized image of the fracture surface, or generated via fractional Brownian motion simulation. Compact tension fractured concrete specimens with three different maximum aggregate sizes ( d max = 4.7, 18.8, and 37.5 mm ) and a projected fracture area (ligament area) of 125 × 367.5 mm were analyzed. Two methods, step divider and variogram, were utilized to evaluate the fractal dimension of the fracture trajectories. The fractal dimensions of concrete fracture trajectories calculated using these methods were in the range of 1.07 to 1.25. The variogram method yielded higher values than the step divider method. Synthetic profiles generated via fractional integrals of Brownian motion showed a good visual similarity to the actual fracture profiles. Advanced Cement Based Materials 1994; 1, 169–177

Fractal characterization of fracture surfaces in mortar

Abstract The objective of this paper is to characterize the fracture surface of mortar specimens in terms of fractal geometry. The specimens were sectioned perpendicular to crack plane and resulting profiles were digitized by using an Image Analyzer. Fractal dimension D for each profile is evaluated by the box counting method. Our results indicate that the concept of fractal geometry provides useful tools for fracture surface characterization. Fractal dimension of the mortar fracture appears to be ∼2.1.

Crack arrest in mortar matrix reinforced with unidirectionally aligned fibers

Abstract This paper presents an investigation on the effects of reinforcement size, reinforcement spacing and specimen size on the fracture parameters of notched mortar specimens reinforced with long aligned steel fibers. A total of 33 specimens of variable fiber size, fiber spacing and specimen size were tested under quasistatic monotonie and cyclic loading conditions. For a constant volume fraction of steel reinforcement, the experimental results indicate an increase in the fracture energy as the size of the reinforcing fibers and the corresponding spacing between the fibers is reduced. Finite element analysis indicates that the closing pressures imposed by the bridging of the fibers in the wake of the crack-tip increase as the spacing between the fibers is decreased, particularly as the spacing approaches approximately 6.25 mm. Within the testing range, the fracture energy (G F ), energy release rate (G Ic ) and stress intensity factor (K Ic ) appear to be independent of the specimen thickness.