China
Africa
Explore chapters and articles related to this topic
R-Curve Approach
Published in Alberto Carpinteri, Applications of Fracture Mechanics to Reinforced Concrete, 2018
Chengsheng Ouyang, Barzin Mobasher, Surendra P. Shah
Fracture of concrete and fiber reinforced concrete has been studied for several decades. A primary character of fracture of these materials is the existence of stable crack growth prior to the crack reaching its critical length. Such behavior is often referred to as R-curve behavior. Fracture responses of quasi-brittle material, such as concrete and fiber reinforced concrete are indicated in Fig. 1. For brittle materials, there is no stable crack growth. Whenever the strain energy release rate is equal to the fracture toughness of a material, the material fails. This is represented as a horizontal line in Fig. 1. For concrete, however, crack growth is heterogeneous and tortuous accompanied by grain boundary sliding. The existence of a fracture process zone results in stable crack growth prior to the peak load. This increased energy requirement is represented as a rising R-curve in Fig. 1. For fiber reinforced concrete, the presence of fibers introduces additional toughening, which requires more energy dissipation during crack growth. This is indicated by a second rising R-curve in Fig. 1. Note that this enhanced R-curve refers to the matrix in the fiber reinforced cement composite.
Elastic–Plastic Fracture Mechanics
Published in T.L. Anderson, Fracture Mechanics, 2017
A word of caution is necessary when applying J to elastic–plastic materials. The energy release rate is normally defined as the potential energy that is released from a structure when the crack grows in an elastic material. However, much of the strain energy absorbed by an elastic–plastic material is not recovered when the crack grows or the specimen is unloaded; a growing crack in an elastic–plastic material leaves a plastic wake (Figure 2.6b). Thus the energy release rate concept has a somewhat different interpretation for elastic– plastic materials. Rather than defining the energy released from the body when the crack grows, Equation 3.15 relates J to the difference in energy absorbed by specimens with neighboring crack sizes. This distinction is important only when the crack grows (Section 3.4.2). See Appendix 4A.2 and Chapter 12 for further discussion of the energy release rate concept.
Analysis of rubber components under large deformations
Published in Per-Erik Austrell, Leif Kari, Constitutive Models for Rubber IV, 2017
If a rubber component has an existing sharp crack it is common to study the behavior with fracture mechanics techniques. Usually an energy release rate is evaluated for each crack and the values are compared with fracture toughness values for the material obtained by experiments. Two methods for evaluating the energy release rate are used here. One is the traditional J-integral evaluated with the so-called domain integration method. The formulation is enhanced to take large strains and contact between crack faces into account. The second method is called VCCT – the Virtual Crack Closure Technique. The domain integral method is usually more accurate, but VCCT is simpler and more general since it only involves the force needed to keep the crack together, the crack opening displacement and the geometry around the crack tip. It automatically gives a mode separation of the energy release rate, also for the general nonlinear case. The example in Figure 5 illustrates the usage in a rubber analysis. A rubber block, fixed at the bottom, has an oblique surface crack. A rigid cylinder (the model uses plane strain) is pressed down and slides frictionless along the top part, over the part where the crack is. Figure 6 shows the values of the J-integral as a function of time. The value increases and reaches a peak value just before the cylinder reaches the left hand side part of the crack face, see the upper part of Figure 7. Then when the cylinder is symmetrically over the crack faces the J-integral is almost zero as expected. The figure shows results with and without friction between the crack faces and one can clearly see the effect of including this friction. The peak value with friction is substantially lower since the friction resists the sliding.
Effect of nanocomposites rate on the crack propagation in the adhesive of single lap joint subjected to tension
Published in Mechanics of Advanced Materials and Structures, 2023
Hadj Boulenouar Rachid, Djebbar Noureddine, Boutabout Benali, Mehmet Şükrü Adin
Figure 5a, shows that the maximum von Mises stresses are located at the left edge of the adhesive, and more precisely at the crack front, and this regardless of the quantity of silica nanoparticles. In this region of the adhesive joint, the equivalent stress reaches a maximum value. The energy release rate is the energy required to advance a unit crack length. It corresponds to the decrease in the total potential energy of the cracked medium to go from an initial configuration with a crack length a, to another where the crack is increased by one unit of length da. On passing the crack front, the stresses decrease and are almost zero in the middle of the joint where the assembly is completely relieved, then they rise to the right end of the adhesive under the edge effect. The variation of the maximum von Mises stress at the crack front as a function of the nanosilica content is represented in Figure 5b, it can be seen that the maximum von Mises stresses decrease when the quantity of silica nanoparticles in the adhesive resin is increased. By adding nanoparticles from 2.5% to 30%, we see that the von Mises stress goes from 85.2 MPa to 82 MPa. This reduction in stress is due to the plasticization of the material in the vicinity of the front of the crack. This yielding is caused by stress concentrations
Study on intralaminar crack propagation mechanisms in single- and multi-layer 2D woven composite laminate
Published in Mechanics of Advanced Materials and Structures, 2022
Ping Cheng, Yong Peng, Kui Wang, Yi-Qi Wang, Chao Chen
The strain energy release rate (G) describes the energy required to produce a new crack surface. Thence they reflect the crack propagation status. For the propagation of the plain woven composite mode I crack used in this paper (refer to Figure 2(a)), the equation for GI is as follows [26]: where a11 = 1/E11, a12 = −mu12/E11, a22 = 1/E22, a66 = 1/G12, they are the elasticity of the composite material, respectively. KI is stress intensity factors for mode I, E11, E22 are the elastic modulus in the direction of 11 and 22, G12 is the shear modulus in the direction of 12, mu12 is the Poisson's ratio in the direction of 12. where a is crack length, w is laminate width, is tension stress, is shape factor function [27–29]. The strain energy release rate of the different crack lengths by Eq. (2), the calculating result shown in Figure 11. As the crack length increases, the strain energy release rate increases. The increase of the crack length reduces the load-bearing length of the specimen, and the crack propagates more easily.
Prediction of pavement fatigue cracking at an accelerated testing section using asphalt mixture performance tests
Published in International Journal of Pavement Engineering, 2018
Hasan Ozer, Imad L. Al-Qadi, Punit Singhvi, Jason Bausano, Regis Carvalho, Xinjun Li, Nelson Gibson
In general, crack initiation and propagation involve very complex intertwined mechanisms at different scales. Linear and nonlinear fracture mechanics theories have proposed different criteria to estimate when a crack initiates and how much it propagates under given loading conditions. The stress intensity factor (crack driving force affected by structure and loading) and fracture toughness (crack initiation criteria affected by material properties) are the parameters of linear elastic fracture mechanics and have limited ability to represent cracking in asphalt concrete (AC) materials. Energy release rate and fracture energy are the parameters derived from nonlinear fracture problems; this approach is more applicable to asphalt materials than linear fracture mechanics. In this case, energy release rate is the parameter defining the amount of energy accumulated at the crack fronts that can be considered as a crack driving force. Modulus properties, along with the loading and structure, can determine the amount of energy available for crack growth. On the other hand, fracture energy is a material characteristic somewhat affected by the size of a structure (Bazant and Planas 1997, Anderson and Anderson 2005).