13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 5.2 Crack Growth Laws The practical implementation of a combined fatigue and time dependent crack growth integration scheme using a linear summation model requires use of meaningful crack growth data. Baseline fatigue crack growth data is available in many forms but the combined use with time dependent data is more challenging. The approach used here is the use of isothermal testing to derive temperature dependent growth laws which can be applied for non-isothermal cases. Results for the simulation of the non-isothermal tests using this isothermally derived data can then be compared to the actual non-isothermal TMF test results. A number of authors have reported the use of a rate dependent Arrhenius law for addressing temperature dependency in time dependent crack growth data [12,13]. This type of law has been implemented in Zencrack as a “COMET” crack growth law [10]. This equation (Eq. (5)) takes account of the synergetic interaction of Creep, Oxidation, Microstructure, Environment and Temperature through the definition of the D coefficient. A and B are temperature independent material constants, n is a temperature dependent material parameter and TC is the temperature in °C. A full description of the law and a process for determining A and B is given in [10]. ( )n D K dt da = , ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − = 273.15 Tc B D Ae (5) 6. Application of Simulation Procedure to TMF Test Specimens The geometry for the test specimen is shown in Figure 8. This figure also shows an initial cracked mesh and a typical mesh with an advanced crack position. The specimen contains a central 7mm square cross-section into which the starter crack is located (at the mid-length position). The finite element model is a half symmetry model with the crack introduced at the symmetry plane. An uncracked Abaqus model containing C3D20 elements is created and the crack is introduced by Zencrack. The crack tip is modelled with collapsed crack front elements having quarter point nodes. The load is applied at a single point and distributed onto the cylindrical outer surface of the end of the model using a distributed coupling constraint. The load and temperature time histories are defined using *AMPLITUDE definitions. For these analyses the temperature changes are deemed to be instantaneous throughout the body (i.e. the temperature is uniform through the model at any time instant). The Abaqus *CONTOUR INTEGRAL option is used to calculate energy release rates along the crack front through the time history. The analysis uses temperature dependent Young’s modulus and Poisson ratio for coarse grained RR1000. Temperature dependent Walker coefficients are used for the fatigue law and a COMET law is used for the time dependent growth law. The cracked model is analysed using Abaqus and the full time history results are extracted and processed by Zencrack using the procedure described in section 5. The crack growth is calculated and the mesh updated. This process repeats to simulate crack growth in the specimen. Several TMF load cycles were defined for testing and simulation. The temperature and normalized load variations for the cycles designated 1, 3, 4a, 4b, 4c and 4d are shown in Figure 9. Due to project time constraints not all tests were completed. Simulation results in section 7 are presented for all load cycles with test results available for cycle 1, 3 and 4d. A 400°C isothermal load cycle using the load variation of cycle 3 is also presented in the results.
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