Turbine Blade Cracking
Turbine Blade Cracking
At the macroscale the turbine blades considered are CMSX series nickel based single crystal super alloy. Chemically the crystals are 2% chromium, 3% cobalt, 0.4% molybdenum, 5% tungsten, 8% tantalum, 6% rhenium, 0.1% niobium, 5.6% aluminum, 0.2% titanium, and 0.03% hafnium (1). The blades are grown from a single crystal and have no grain structure. This lowers the yield strength of the material but improves performance under cyclical fatigue. The largest internal structure is the dendrite structure. The dendrites vary between 20 μm and 200 μm and the chemical make-up varies between the dendrite core and inter-dendrite region. The core is rich in tungsten, chromium, and cobalt precipitates while the inter-dendrite region is rich in aluminum, titanium, and tantalum. These precipitates suspended in the nickel base make up the microscale structure. The precipitates are designed to be approximately 0.5 μm in length (2). Gas-turbine blades are designed to have favorable creep and fatigue properties, especially with regard to temperature, due to the harsh environments in which they operate. This environment includes high temperatures, corrosive chemicals, and cyclical fatigue. This examination is limited to simple crack analysis to facilitate downscaling.
The analysis of crack growth in the macrostructure would require long crack growth information and energies from the mesoscale, the dendrite structure. To determine whether or not these cracks would begin within the inter-dendrite or dendrite core structures analysis would be performed at the microscale. The microscale atomistics simulations, Modified Embedded Atom Method or MEAM, would provide dislocation information for the mesoscale. The MEAM simulations would require interfacial energies between precipitates and the elastic modulus of the materials. These parameters would be calculated from Density Functional Theory, DFT, at the electronic scale.
The multitude of elements present in the microstructure makes it necessary to calculate an elastic modulus for the material. Density Functional Theory would be performed to determine the elasticity and the interfacial energies between the nickel base and precipitates. The calculations would be performed for the dendrite core and inter-dendrite structures as well as the boundaries between them. Experiments would then be conducted to calibrate these simulations. Interfacial energies and the elastic modulus would then be passed up to the microscale.
The atomistic scale would focus on precipitate boundaries and dislocations. A MEAM simulation could be run at the atomistic scale using the parameters provided from the DFT calculations. MEAM would provide information on dislocations at the interfaces of the precipitates. These dislocations would be expected to be mostly climb dislocations due to the high temperatures applied to the material. The MEAM simulation would provide information on where dislocations would occur up to the microscale.
The microscale would consist of precipitates and how dislocations joined. With the dislocation information provided from the MEAM simulation a Finite Element Analysis, FEA, would then be performed to determine crack nucleation locations. This analysis would conclude whether cracks were more likely to nucleate in the inter-dendrite structure or the dendrite core. The joining of the dislocations simulated in MEAM as well as information from the DFT calculations would also allow for small crack growth to be analyzed at this scale.
The mesoscale would be concerned with the dendrite structure. The information of crack nucleation and small crack growth calculated at the microscale would be used to run FEA to simulate crack growth through the dendrite structure. The length of the dendrites varies from 20 μm to 200 μm. How the length of the dendrites effect crack growth through this structure and the energy required to bridge dendrites would be also be calculated at this scale.
The mesoscale FEA analysis would provide information on crack growth through the dendrite structure necessary to calculate long crack growth at the macroscale through FEA. This long crack information would then be used to determine the life cycle of the material.