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# Creep Rupture and the Larson-Miller Approach

February 21, 2017 By: Michael Bak

Creep is time-dependent straining under constant stress.  At high temperatures greater than half the melting point (using absolute temperatures), metals begin to creep.  Creep changes and damages the material and is manifested as overall elongation of a part leading to cracking and failure, as is shown in the turbine blade in Figure 1, above.

Predicting failure due to creep can be challenging. Finite element analyses can be performed using creep material laws that define the creep strain rate of a material as a function of time, temperature, stress and strain. Creep is both time-dependent and nonlinear, and therefore creep analyses can be long running and difficult to converge. A previous blog on Tips & Tricks for FEA Modeling of Creep provides good information for obtaining successful creep analyses. But beyond the challenges of performing complex nonlinear creep analyses, how can the results from a finite element analysis be used to predict failure from creep?

Failure due to creep, also referred to as creep rupture, stress rupture, or creep fracture, can occur for a given material at a combination of stress, temperature and time. If this data exists for your particular combination of stress and temperature, the results from a finite element analysis can use this information to determine when creep failure will initiate. Testing can be performed to determine time to creep rupture using different combinations of stress and temperature, but obviously, testing cannot be done for every combination of stress and temperature, and in some cases testing is not feasible for long time spans.

The Larson-Miller approach can be used to determine creep rupture time for any stress-temperature combination for a given material. The Larson-Miller equation was developed during the 1950s while Miller and Larson were employed by GE performing research on turbine blade life. The parametric relation they developed is used to extrapolate experimental data on creep and rupture life to all temperature-stress combinations and to time spans that would be impractical to reproduce by laboratory testing.

The Larson-Miller expression consolidates many of the variables in creep data. The equation represents a linear expression to calculate a parameter, P, that relates creep time and temperature to a given stress and creep strain level, typically creep rupture. The expression is shown below in equation (1), where t = time in hours, T = temperature in degrees Fahrenheit, and C is an empirical constant.  A value of 20 for C is applicable for low alloy steels, and a factor of 30 is sometimes used in the case of higher alloy steels. Larson-Miller parameter P is sometimes divided by a factor of 1000 for convenience.

If provided a Larson-Miller curve for a given material at creep rupture, one can use the curve to obtain P based on the stress. Once P is known, the equation above can be used to calculate combinations of temperature and time that will produce creep rupture. Although curves can be created for any creep strain value, it is common for Larson-Miller curves to represent creep rupture, the level of creep strain that would cause failure for that material.

As an example, the Larson-Miller curve in Figure 2 represents creep rupture curves for various titanium alloys. One would identify the applied stress on the vertical axis, and using the particular material curve of interest, find the corresponding value of P on the horizontal axis. Once P is known, combinations of temperature and time to cause creep rupture can be calculated from the Larson-Miller equation above.

Figure 2: Larson-Miller Curve for Creep Rupture of Titanium Alloys

## creep-LM-2.jpg

To eliminate the need for any calculations, and to simplify the process, lines representing the Larson-Miller expression written in terms of constant temperature can be superimposed on the plot, and thus a third axis, representing the logarithm of time, can be added as a vertical axis on the right side of the plot. For these curves, the procedure is to start with a stress, find the value of P for that material, determine the intersection of this value with the temperature line, and read the time to reach creep rupture.

To illustrate, assume a low carbon steel is at 1000°F and is subjected to 20 KSI stress, and the creep rupture time is sought.  Referring to Figure 3, point A represents the 20 KSI stress, which intersects the C-Mo Steel Larson-Miller curve at point B. The vertical line at point B represents the parameter P value of about 31 for this stress. The intersection of the vertical line with the 1000°F temperature line will provide the creep rupture time on the right vertical axis at point C of approximately 25 hours.

Figure 3: Reading Creep Rupture Time Directly from a Larson-Miller Plot

## creep-LM-3.jpg

Assuming that the Larson-Miller curve has been generated for your particular material, an estimate of time to reach a given creep strain level based on the stress and temperature can be found in an instant. Or the Larson-Miller expression could be added into a post-processing macro to determine if creep rupture has occurred.

Spending a little time with Larson-Miller curves also provides some insight into creep behavior.  For example, it is readily apparent that creep and creep rupture are very sensitive to temperature. A small increase in temperature can reduce the creep rupture time dramatically.