2012力学专业英语课件-5.pptx

1;2;3;4;5;6;7;8;9;Unit 5 Stress Analysis of Cracked Components;11;?;Where A represents the crack area, and is equal to 2aB for the system shown in Fig.1. Here B is the thickness of the plate containing the crack and denotes the crack surface area growth rate per unit time. Note that the total crack surface area is twice the area of one crack surface. Therefore equation (1) can be rewritten as ;Equation (3) indicates that the reduction of potential energy is equal to the energy dissipated in plastic work and surface creation.;Where g represents the energy required to form unit new material surface area. The factor 2 in the above equation refers to the two new material surfaces formed during crack growth. Simply, the above equilibrium equation means that sufficient potential energy must be available in the system to overcome the surface energy of the material. In general, for an elastic body containing a crack, we can define a crack-extension force, G, ;Note that A=a·B when there is only one crack tip (e.g. edge cracked component) and A=2a·B for center cracked system. It is important to note the distinction between crack area and surface area. Since a crack includes two matching surfaces, the crack surface area is twice that of the projected crack area, and is equal to 2aB in the present case. We can also define the total energy of the system, which contains three parts: (1)the amount of work done by the applied loads, (2)the elastic energy, and (3) the energy required to form the crack surface. The total energy is ;According to linear elasticity theory, a body under constant applied loads obeys;Griffith used the stress solutions by Inglis (1939) to show that the increase in strain energy due to the elliptic cavity (zero radius) in an infinite plane is given by;A schematic drawing of the above equation is shown in Fig.2, which exhibits a maximum at the following crack length, ;Clearly the critical crack length below which the crack would remain stable decreases quick