Microsoft Word - Benarbia_ed_r3.doc ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 3, 2013, 429-432 429 www.etasr.com Benarbia et al.: Two-dimensional Analysis of Cracks Propagation in Structures of Concrete Two-dimensional Analysis of Cracks Propagation in Structures of Concrete Djamila Benarbia Dpt of Engineering Mechanics Djillali Liabes University of Sidi Bel Abbes, Algeria d_benarbia@yahoo.com Mohamed Benguediab Dpt of Engineering Mechanics Djillali Liabes University of Sidi Bel Abbes, Algeria benguediabm@gmail.com Soumia Benguediab Dpt of Civil Engineering Djillali Liabes University of Sidi Bel Abbes, Algeria Benguediabs@yahoo.com Abstract— In this article we present a numerical simulation that allows describing and studying the damage of concrete works subjected to various stress types. In this study, the propagation of cracks in the concrete is analyzed as of their appearance, which requires having a thorough knowledge of the mechanical behavior of the material. The mechanical approach which leads to better understanding of fracture phenomena and can give satisfactory results, is that of the elastic linear mechanics of failure. The interest in this study is focused in the development processes of the cracks from a phenomenological point of view. The analysis is carried out by using fracture criteria while being based on the determination of the critical stress intensity factors, for each case of the several elaborate tests of indirect tensile per bending and Brazilian Disc. The analysis is carried out in a two- dimensional medium by the finite element method by using the ABAQUS software. The results obtained are compared with experimental data obtained analytically from other authors. Keywords- crack propagation; stress intensity factor; three- points bending beam test; Brazilian disc; fractures mechanics; two-dimensional medium. I. INTRODUCTION The analysis of the behavior of any structure under different loads until its fracture, is an essential component of structural design. The classic methods of collapse designing are based on the research of acceptable fracture diagrams, and on the calculation of ultimate balance in the critical sections. Thus, dimensioning of concrete works is done considering ultimate constraints corresponding to the crushing of the concrete or the plasticization of reinforcement‘s steels. With the development of numerical calculation techniques and finite element methods, it is currently possible to analyze the details of state of equilibrium in various points of the structure. Models using the criterion of crack propagation based on the going beyond of the maximum stress of traction have been developed but are not sufficient to give an account of the harmfulness of the defect [1, 2, 3]. Other models have also been developed [2, 4-8] using the criterion of the breaking process that give a report on the modeling of the cracks by redefining the networks of the elements to each step of propagation. The elastic linear mechanics of the failure is applied to study the crack propagation in concrete not reinforced with massive structures. This approach is adapted to analyze large-sized structures focusing on the influence of structure’s dimension on its behavior [9, 10, 11]. The utilization of a criterion of crack propagation, based on linear mechanics of the failure, imposes the determination of the stress intensity factors. This paper studies crack propagation in concrete structures, using the criterion of failure based on the determination of the stress intensity factors. Two approaches were proposed, an approach based on an analytical approach where the stress intensity factor is calculated starting from the functions weight [12] and a numerical approach where the stress intensity factor is calculated by the finite element method using the ABAQUS software. II. MODEL USED A. Hypothesis of bases The numerical model used within the framework of our study, combines a criterion of the linear elastic mechanics of the failure and a distributed model of cracking that leads to taking into account the singularity of the stress field at the peak of a crack and the influence of the geometrical parameters on the development of cracking and fracture behavior. This model adopts a certain number of basic assumptions: • The not fissured concrete is regarded as an isotropic homogeneous material with an elastic linear behavior describing its mechanics. • The micro crack zones and the nonlinear behavior of the material at the point of the cracks are neglected. B. Analytical and numerical analyses It is a question of determining, for the load patterns considered in this work, the values of the stress intensity factor KI and KII and which are expressed [9] starting from the following relation: ETASR - Engineering, Technology & Applied Science Research Vol. 3, �o. 3, 2013, 429-432 430 www.etasr.com Benarbia et al.: Two-dimensional Analysis of Cracks Propagation in Structures of Concrete I K Fσ π α= ⋅ (1) II K Fτ π α= ⋅ (2) Where: α is the length or half-length of the crack, σ and τ are respectively the normal and shear stresses applied to the structure, F is the geometrical Functions. Two types of tests are used: • Three-points bending test: The geometrical data and the principle of the test are schematized in Figure 1: Fig. 1. Three Bending Beam Tests. The specimen subjected to the bending test is a not reinforced concrete beam where its length is 2L and its width is w, receiving a load P with an eccentricity d. The beam is supposed to have an initial crack of length α located in the middle of the beam. • Brazilian disc test: The geometrical data are illustrated in Figure 2. Fig. 2. Description of the Brazilian disc. The specimen submitted for testing is not reinforced concrete, whose dimensions are shown in Table II. The surface of the disc is supposed to be notched (half- length of the crack α ). The crack forms an angle θ with the vertical axis of the disc. In the numerical study, the values of the stress intensity factors KI and KII are numerically given by finite element modeling in a two-dimensional medium by the ABAQUS software. The models used during the simulation are represented in Figures 3 and 4. Fig. 3. Geometrical representation by ABAQUS of three points bending test . Fig. 4. Geometrical representation by ABAQUS of the Brawilian disc. TABLE I. SUMMARY OF GEOMETRIC DATA 3-PT BB L The length of the beam Varies from 320 to 800 mm w Beam width equal to 160 mm α length of the initial crack Varies from 8 to 64 mm d Eccentricity of load 0≤ d