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Analysis: Crack propagation and loads have a direct correlation.
For example mode one is obvious as perpendicular loads try to open the crack and torsional load leads to tearing.
Note the second example is not obvious but if we write the stress state, it becomes easy to reckon that it is in mode II
Mixed crack propagation
Mixed-mode Three situations are shown for each type of loading. There could be a mixed-mode that would have a combination of the two modes. For example, the cylinder is subjected to axial pulling and torsion, mode I and mode III could be coupled. Stress intensity factors are defined for each mode and are designated as K1 K2 and K3.
Box crack propagation is because of the mixed mode because of axial load it is opening mode and because of the torque it is second mode.
If the box is subjected to a perpendicular force and also an axial torque then the situation becomes a mixed-mode situation
Irwin’s equation could be used for mixed-mode by the following formula, which is based on energy conservation.
This is because we assume, K1C≅K2C. As nature takes the path of least resistance, in a mixed-mode situation crack propagates in a direction that is of maximum hoop/tangential /circumferential
Determine the life of the component in seconds. Details of the situation are tabulated below:
Machine component has the following details
We must calculate the final crack length beyond which the crack propagation rates become practically unacceptable
Observation: Linear fracture mechanics is very close to practice. Though we calculate the cycles ideally using Paris law some times large loads bring about crack tip plasticity hence propagation may be halted.
Note: Using the fracture toughness, find the maximum crack length reached before failure, meaning, the rate of crack propagation becomes large