A very useful way of visualising the stress intensity equation is via the concept of a 'triangle of integrity'. It is clear that the equation:
relates three variables, applied stress (calculated assuming no crack is present), stress intensity K and crack depth a. At the critical condition, where fast fracture occurs, the value of stress intensity is equal to the fracture toughness for the thickness, temperature and strain rate which are relevant to the fracture. Graphically, therefore, we can show a triangular relationship between material toughness, applied stress and crack depth. This is indicated below:
Essentially, these are state properties of the system and we can increase or decrease fracture values of these parameters individually, e.g. we can choose an alloy with a higher toughness and hence withstand either increased stress or increased crack depth, or both. This is part of the function of effective fracture-safe design and, in design terms, we can replace these parameters with their corresponding design/fabrication activity:
The advantage of this triangular representation now becomes clear; we have an inter-dependent relationship between three activities in fracture-safe design, and we can adjust the individual parameters to achieve an optimum result.