Interaction And Propagation Research Of The Cracks With Unequal Length In Cement Brittle Materials

Cracks with different size exist inevitably in real engineering structures and materials. Some of these cracks are the original cracks in materials and some of these cracks emerge under load. Crack interaction and crack propagation lead to the failure of structures. In order to ensure the safety of structures, the static strength of structures is the first consideration in traditional structural design method. Multiple loads by the safety coefficient which is greater than one as the structural design load. The traditional structural design method is suitable for small structures and low strength materials. It becomes invalid when the material strength is high. The reason is that the resistance ability of high strength materials to crack propagation is worse. Thus, the structure is easy to appear low stress brittle fracture phenomenon and be failure when the load is below the allowable stress. Cement brittle materials refers to materials which take cement as matrix and basic component. Concrete is one of the cement brittle materials. With the development of social productive forces, the requirement of engineering structure on material strength is increasingly high. Cement brittle materials are widely used in various engineering structure and cracks with unequal length exist majority in materials. Researching the interaction and propagation of cracks with unequal length contributes to take effective crack arrest measures to ensure structure safety. Thus, studying the interaction and propagation of cracks with unequal length is of great significance and engineering value.Based on the classic Kachanov method, the stress intensity factor expressions for two unequal collinear cracks and three collinear cracks and two sliding closed cracks in an infinite plate subjected to uniform traction at infinity are derived. Through the stress intensity factor ratio of multiple-cracks and single crack, the influence of geometric parameters such as crack angle, crack distance and crack length on multi-cracks interaction is theoretical quantitative analyzed. Cracks with certain size are often control the crack interaction and the structural stability. In this paper, the cracks with longer length are called the main cracks and the other cracks with shorter length are called the minor cracks. Through the maximum circumferential stress criteria, the initiation angle of the main crack is calculated and the theoretical fracture criteria curve is drawn. The main crack initiation angle of sliding closed cracks is calculated by the strain energy density theory.It mainly studies the propagation of cracks in cement mortar in this paper. To prefabricate unequal cracks by inserting thin steel pieces into cement mortar specimen. The cement mortar specimen subjected to uniaxial compression by 3000kN ultra high rigidity servo testing machine. The high speed movie camera is adopted to collect the image information of the crack propagation process. The crack propagation rule of two unequal collinear cracks and three unequal collinear cracks and two unequal parallel cracks is analyzed by observing the process of crack propagation and the failure of the specimen.The main work and obtained results in this paper are as following:1. Establish crack theoretical models that contain two unequal collinear cracks and three unequal collinear cracks in an infinite plate subjected to uniform tension at infinity and establish crack theoretical models that contain two unequal sliding closed cracks in an infinite plate subjected to uniform compression at infinity. Based on the Kachanov method, the stress intensity factors for multiple-cracks are derived. The pseudo-traction of multiple-cracks is the sum of the crack initial traction and the traction induced by the other cracks. The pseudo-traction in a crack is assumed to be composed of a uniform component and a non-uniform component, the effect of the uniform component on crack interaction is in consideration and the effect of the non-uniform component is ignored. The stress intensity factors for multiple-cracks can be obtained by solving crack interaction coefficient and the average traction in crack surface. Calculate the stress intensity factors ratio of multiple-cracks and single crack under different crack distance and different crack length. The ratio is defined as amplification coefficient of stress intensity factors, and it characterizes the change of stress intensity factors under crack interaction. Through the amplification coefficient of stress intensity factors, the influence of crack geometric parameters on crack interaction is quantitative analyzed. Results show that the I type singular of the two unequal collinear cracks subjected to uniform traction at infinity decreases with the increasing of the crack incline angle and the Ⅱ type singular reaches the maximum when the crack incline angle is 45°. For sliding closed cracks, the crack tips only have the Ⅱ type singular and the stress intensity factors decrease with the increasing of the crack friction. No matter the cracks are loaded by compression or tension, the influence degree of crack interaction on crack stress intensity factor is the same in the case of collinear cracks. A crack almost has no influence on the other crack if the crack distance is larger than the crack length and the influence of the two cracks can be neglected when the crack distance is larger than the main crack length. The influence of the other cracks on the main crack can be neglected if the distance between the main crack and the minor crack is not less than 1.5 times the minor length in the three collinear cracks. When the distance between the two minor cracks is not less than 1.5 times the minor length and the distance between the main crack and the minor crack is larger than half minor crack length, the other cracks almost has no influence on the lateral minor crack, but the middle minor crack is still strong influenced by the other cracks.2. Through the maximum circumferential stress criteria and the strain energy density theory, the main crack initiation angle of unclosed collinear cracks and sliding closed collinear cracks is calculated, respectively. The main crack initiation angle calculated by the maximum circumferential stress criteria shows that the initiation angle of unclosed collinear cracks is only related to the crack incline angle. The main crack initiation angle calculated by the strain energy density theory shows that the initiation angle of sliding closed collinear cracks is related to the Poisson ratio of materials. According to the initiation angle and the stress intensity factors of multiple-cracks, the influence of crack interaction on crack initiation is analyzed. Results show that the crack interaction almost has no influence on the main crack initiation angle no matter the collinear cracks are loaded by tension or compression. The initiation angle of collinear multiple-cracks is as same as the initiation angle of a single crack, but because of the crack interaction, the stress intensity factors at multiple-crack tips is larger, so the collinear multiple-cracks may initiate earlier than a single crack.3. Make cement mortar specimen containing multiple-cracks and observe the process of crack initiation, crack propagation and crack coalescence. Make two and three unequal collinear cracks and two sliding closed cracks by inserting 0.5mm thin steel pieces into the cement mortar specimen. The cement adopted is 425 ordinary Portland cement and the sand particle size is less than 2mm. The mixture ratio (mass ratio) of cement, sand and water is 1:2.35:0.5 and the size of the cement mortar specimen is 110mm×110mm×30mm. Cure the specimen in the constant temperature and humidity curing room for 28 days. The cement mortar specimen are loaded by the 3000kN ultra high rigidity servo testing machine in the state key laboratory of coal resources and safe mining of China university of mining & technology, Beijing. Loading method is displacement control loading method and the loading rate is 0.2mm/min. Use the high speed movie camera to collect image information during the loading process. The resolution of the high speed movie camera is 896×896 and the shooting speed is set as 50fps, so the high speed movie camera will have enough time to record the whole process of crack initiation, propagation, coalescence and failure. By observing the crack failure process, the crack propagation rules can be analyzed. Experimental results show that the coalescence failure of the rock bridge has two modes. One results from the propagation of the secondary cracks initiated at the inner crack tips, the secondary cracks propagation direction is along the extension of the cracks and the rock bridge occurs the shear failure. The other mode results from the crack propagation along the arc and the fracture zone of the rock bridge is round nuclei. When the rock bridge incline angle of the two unequal parallel cracks is more than 90°, the rock bridge failure is often caused by the wing cracks initiated at crack tips. When the rock bridge incline angle of the two unequal parallel cracks is less than 90°, the rock bridge occurs the shear failure or the mixture failure of shear and tensile. When the rock bridge incline angle of the two unequal parallel cracks is just 90°, the rock bridge is not coalescence, the failure of the specimen is mainly caused by the propagation of the main crack. When the crack distance between two unequal collinear cracks reaches the main crack length, the minor crack has no crack initiation or the minor crack and the main crack propagate respectively. The crack interaction almost has no influence on the crack propagation under this circumstance. This experimental result is agreement with the theoretical result. For the three collinear cracks, the propagation paths of the main crack and the outside minor crack are not influenced by crack interaction if the distance between the main crack and the minor crack and the distance between the two minor cracks are both larger than 1.5 times the minor crack length.