The Green's Function

A "FatiguePro Green's Function" is a generic term for a response due to a unit step change in a boundary condition. Several algorithms have been proposed for determining the transient, thermal stress response due to an arbitrary temperature at the boundary of a monitored component. In FatiguePro, thermal stresses are based on finite element analyses to determine the stress response to a unit step in temperature at the surface of a component. The resulting stress-time history, or Green's Function, is integrated over time to determine the actual stress response due to an arbitrary temperature-time history.

Assuming the temperature history consists of sufficiently small step changes, the stress response can be integrated numerically as a summation of those step changes. The Green's Function must be based on conservative material properties and boundary heat transfer coefficients. Often, two different Green's Functions are used for a single location, representing high and low flow conditions.

To develop a Green's Function, a detailed finite element analysis is created and a transient, thermal stress analysis is performed. Once the critical location (region of highest alternating stress intensity) is identified, the stress-time history is discretized every 10 seconds, thereby creating the Green's Function.

SI is experienced in calculating realistic heat transfer coefficients and modeling the interaction between thermal sleeves, interior water gaps and the nozzle.

For a given boundary temperature history, the actual stress response at the critical location may be determined. The stress response for an arbitrary temperature history is shown below:

Thermal shock is the controlling stress component for most monitored locations. Within FatiguePro, any group of instruments may be placed on the same plot as stress or fatigue, making data review easy and intuitive to deal with.