Solution
The last question in this section of the tutorial illustrates the concept of superposition of stress intensity factors, which has already been invoked in dealing with pressure vessels. For internal defects in pressurised vessels, we had to take account of the stress intensity arising from the internal pressure
on the crack faces, as well as that due to the membrane stresses in the shell.
This particular case also demonstrates the application of LEFM to ice, a glass-like material.
It should take around 10 minutes to complete.
The figure below shows stress intensity factors corresponding to two load cases for a vertical edge crack in an infinite body. Case A represents uniform tension, while Case B illustrates a linearly increasing tensile load with depth into the body. The two stress intensity equations are:
Consider a surface crevasse in a wide, thick glacier, which is subject to a uniform longitudinal stress of 200 kN/m2. Determine the depth to which this vertical crack can grow, given that the density of ice is 0.92 x 103 kg/m3 and the gravitational constant is g =
9.81 m/s2.
Answer: The crack will
reach a depth of about 36.34 m.
This problem illustrates simple superposition stress intensity factors, but requires a bit of thought in relating the cases shown, with what is required by the physics of the problem. Both stress intensity solutions shown are tensile but, clearly, this circumstance cannot directly apply to the crack in
the glacier, or it would not arrest. The crack in the glacier is stated to be
subject to tensile loading (and this, presumably, is true or the glacier would not move forwards!).
For the crack to arrest, this tensile loading must be opposed by a compressive loading, which arises from hydrostatic pressure in the ice. Hydrostatic loading will induce a linear compressive stress gradient identical with the one shown in Case B, but opposite in sign. Although compressive K values have no physical meaning, positive and negative stress intensity factors can be algebraically added. Hence the crack will arrest when:<
KA - KB = 0
The answer is obtained by substituting the appropriate values into the two equations, noting that:
Hence we get:
TOP
Close Window