The corresponding load P vs. In the nonlinear behavior at the crack tip, the fracture criterion is characterized by two parameters: 1. This assumption can be applied to determine the fictitious effective crack extension for complete analysis of fracture process in concrete. It was found that the influence coef- ficients along the crack line did not change appreciably in these cases. Mater Struct 21 l :2I-32. T , cr2 x , and diix. Zfiang X, Xu S 2007 Fracture resistance on aggregate bridging crack in concrete.
The comparison of results obtained using weight function and simplified approach is made with regard to that determined using standard analyti- cal method. Int J Fract 87: 139-149. J Am Concr Inst 58 5 : 591- 610. Size effects in concrete fracture: Part I, experimental setup and observations. The influence of speci- men geometry, loading condition, and softening function on the fracture parameters for the size range 100-600 mm is also investigated. Cem Concr Res 38: 1061-1069.
Eng Fract Mech 21: 1055- 1069. Int J Fract 102: 25-42. Mater Struct 28 4 : 187-194. Behind every accom- plishment, the family plays an important role in sacrificing the precious time of togetherness. Int J Fract 98: 111-149. Eng Fract Mech 35: 87-94.
There are good reasons to believe that the third phase of evolu- tion in the design of concrete structures may probably come by introduction of fracture mechanics parameters. Int J Numer Meth Eng 58: 103-126. Int J Fract 69: 97-105. Mater Struct 22 3 : 185-193. This inspired us to attempt to present a unified view of the theoretical development and applications of these models on concrete. One of the major reasons which possibly inhibit the wide application of the fracture parameters to a common practice is that the concrete fracture parameters are influenced by many factors including softening function of concrete, concrete 4 1 Introduction to Fracture Mechanics of Concrete Strength, specimen size, specimen geometry, geometrical factor like relative size of notch length and the loading condition. This assumption might lead to simplification in numerical computations without affecting much on the final values of fracture parameters.
It was observed that weight function approach yields indistin- guishable difference in the results of Kr curve as compared to those obtained using the analytical method. Comput Concr 1 1 : 47-60. Eng Fract Mech 35: 87-94. In due course of time, a number of nonlinear fracture models have been pro- posed and used to predict the nonlinear fracture behavior of cementitious materials. It is also to be pointed out that weight function method does not involve any specialized numerical technique; moreover, straightforward solu- tion can be obtained in closed-form equation resulting in computational efficiency.
Towards the end, a comparative study between different fracture parameters obtained from various models is presented. At last, the authors would be thankful to the readers and their invaluable suggestions or comments for the further improvement of the book. In the study, it was shown that the predicted fracture loads from both the models for the practical size range of notched concrete beam in three-point bending test configuration are indistinguishable and in the asymptotic limit of infinite size , the predictions differed by about 17%. His research interests are: Structural Health Monitoring, Computational Mechanics and Concrete Technology. Further, the initial fracture toughness and the unstable fracture toughness values are approximately close to the constants when the depth of specimens is larger than 200 and 400 mm for three-point bending beams and wedge splitting specimens, respectively. Concrete is made up of many ingredients such as cement, fine aggregates, coarse aggregates, water, and admixtures in complex arrangements.
The numerical results are compared with the experimental results available in the literature. Later, linear elastic fracture mechanics was extended to elastic-plastic material behavior with well-established theories. Fatigue Fract Eng Mater Struct 33 10 :645- 660. In Fracture Toughness and Fracture Energy: Test Method for Concrete and Rock. However, these numbers can be cho- sen arbitrarily to any value depending upon the memory capacity of the computer.
Mater Struct 25 4 , 212-218. In this book, the authors have taken a small step to present a basic introduction on the various nonlinear concrete fracture models considering the respective fracture parameters. Determination of stress intensity factors for cracks in complex stress fields. The length of the fracture process zone is found to be influenced by the specimen size and the zone length was almost independent of the type of specimen geometry for a given value of relative crack size. Thereafter, extensive experimental and numerical research investigations proved that the classical form of linear elastic fracture mechanics cannot be applied to normal size concrete members. Since , C2 — 5 for all computations in the present work.