13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- new facility. Following the initial demonstration, the RR10000 material in a coarse grained condition was also tested and this data is also shown on Figure 5, highlighting the potential benefit from this material, compared with the fine grained variant. All of the crack growth modelling was based upon the coarse grained variant of RR1000 and a range of additional thermal/load cycles were evaluated experimentally and compared with the modelled behaviour below. 5. TMF Crack Growth Simulation Procedure The approach often used for calculating the combined effect of fatigue and time dependent crack growth is a linear summation through the load cycle of the separate fatigue and time contributions to the overall growth [6-8] to give the effective overall growth rate for a single load cycle: time fatigue total dN da dN da dN da ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ + ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ = ⎠ ⎞ ⎜ ⎝ ⎛ (2) The way in which this expression is used in the literature often relates to simple repeated loading waveforms with a single cyclic event e.g. ramp-up, hold time, and ramp-down. [9] presents a summary of approaches used by several authors. However, for a general and complex loading cycle such as the one in Figure 1, the load history and resulting stress intensity factors are defined by a series of data points which do not conform to a simple waveform. It is then necessary to generalize Eq. (2) to account for major and minor fatigue cycle effects within the overall load cycle as well as the time history of load variation. This generalization can be written as: dt dt da dn da dN da load cycle cycles fatigue total ∫ ∑ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟+ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ = ⎠ ⎞ ⎜ ⎝ ⎛ 1 (3) where da/dn is the growth rate due to an individual fatigue cycle within the total load cycle and da/dt is the instantaneous time dependent growth rate at some time t within the total load cycle. Summation of Eq. (3) over multiple load cycles provides the accumulated crack growth history: ∑ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = load cycles total dN da da 1 (4) In order to carry out this summation, two sets of data must be provided to an appropriate integration scheme: (1) the time history of stress intensity factor and temperature for points on the crack front; (2) the crack growth laws for calculating instantaneous da/dn and da/dt values. 5.1 Integration scheme For simple 2D geometries where a handbook K solution is available, it is possible to obtain K vs t with a combination of a spreadsheet and results from finite element analyses of an uncracked component. This procedure is used in-house at Rolls-Royce and has been used to validate the finite element based implementation described below [10]. For general cases with an arbitrary 3D crack front, the finite element method can be used to provide the K solution as a function of time. In using this approach, a finite element model containing a particular crack size is analysed through a full load cycle. The results of the analysis can be used to provide a K vs time history for each crack front node. The time histories can then be cycle counted to extract discrete cyclic events. A typical (normalized) K time history and the cyclic events associated with it are shown in Figure 6.
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