Fracture mechanics crack extension modes

Available theoretical solutions in dynamic fracture are few, and limited to finite or semi-infinite cracks in an infinite solid for Mode I, self-similar crack extension. Despite the above limitations, short of conducting detailed numerical analysis of the crack tip state of stress, these solutions must be used to deduce the characteristics of the crack tip state of stress, as well as to extract the dynamic stress intensity factor for elastodynamic fracture mechanics. In the following sections, a brief description of available theoretical solutions is presented. 

Fracture mechanics tests were conducted on an Instron-type displacement controlling test machine (Sanwa Testing Machine Co., Toyohashi, Japan) under a crosshead speed of 0.05 mm/min. All the fracture tests were made in three-point flexural modes. A stable crack extension was observed for all the specimens with the relative notch depth ao/Ws 0.4. However, the crack extension was always unstable for oo/W < 0.4. The apparent fracture toughness, Kq, at the onset of crack initiation for the critical load Pc was determined by... 

From studies of service behavior and from extensive laboratory investigations, the well-established terms stress-corrosion cracking (SCC) and corrosion fatigue have been shown to relate to a continuum of failure modes classified as environment-sensitive fracture. In many environments, the addition of stress, with associated strains, introduces a variable that can result in brittle failure in the sense of very limited plastic flow in otherwise ductile materials such as the stainless steels. Environment-sensitive fractures propagate at an advancing crack tip at which, simultaneously, the local stresses can influence the corrosion processes, and the corrosion can influence the crack-opening processes. Since these processes proceed by kinetic mechanisms, they are time and stress dependent with the result that the crack propagation rate can become very sensitive to the stress application rates. Conventional SCC usually has been associated with static stress, but this is seldom realized... 

The above solution can also be used if cr is an applied uniaxial compressive stress. In this case, the maximum tensile stress is — cr and the minimum is 3cr. Thus, plates can fail in a tensile mode, even if the plate is in compression. This idea is used extensively in rock mechanics, as most rocks are in a state of compression but can undergo a tensile failure in the vicinity of holes and pores. In general, pores in brittle materials are not expected to be bounded by a smooth surface and the stress concentrations can be much larger. Consider what would happen to the stresses if another circular hole with a much smaller radius was placed at 6= ttI2. This process could be repeated to approximate surface roughness or holes with sharp radii of curvature. It is clear from such a process that the stress concentration would quickly exceed lOcr. As will be shown in Chapter 8, the ability of cracks to concentrate stress is a key aspect in understanding the fracture process. 

---