Three-dimensional Mixed-Mode Crack Propagation Calculations based on a Submodel Technique

Damage tolerant designs are necessary for the continuous operation of aircraft engines which are subjected to harsh environmental influences during operation (e.g. large temperatures, foreign object damage of airfoils). One important aspect of damage tolerance is crack propagation which can be investigated via 3D numerical software. This Master Thesis project focuses on investigating and implementing the submodel technique in MTU Aero Engines' own FEM (Finite Element Method) based in-house crack propagation calculation tool known as Cracktracer 3D. The key points of the project are the theoretical background behind the submodel technique, the changes that have be to made to Cracktracer 3D's Python/C/Fortran based code and the verification and validation of the method by comparing the crack propagation parameters for real engine components with the results of an already established method. It is theorized that the submodel technique will provide more accurate stress intensity factors for complex engineering applications. The need to investigate the capabilities of the submodel technique arises from MTU's desire to have a more reliable alternative to its current method. The findings could have a valuable contribution towards lowering the design safety margin of MTU Aero Engines components. Having a more stable automatic crack propagation calculation routine can also lead to more efficient engine component designs which can directly be translated to weight/cost savings. The side-by-side comparison of two different numerical routines applied on the same examples can also give some valuable insight into the advantages and disadvantages of either methods.The main objective of this thesis project is to reduce the number of test cases in which MTU Aero Engines' crack propagation calculation tool Cracktracer 3D fails to predict the correct crack propagation parameters by investigating the applicability of a submodel method consisting of a pure tetrahedral global model followed by a hexahedral submodel calculation.d to investigate the capabilities of the submodel technique arises from MTU's desire to have a more reliable alternative to its current method. The findings could have a valuable contribution towards lowering the design safety margin of MTU Aero Engines components. Having a more stable automatic crack propagation calculation routine can also lead to more efficient engine component designs which can directly be translated to weight/cost savings. The side-by-side comparison of two different numerical routines applied on the same examples can also give some valuable insight into the advantages and disadvantages of either methods. \\\noindent The main objective of this thesis project is to reduce the number of test cases in which MTU Aero Engines' crack propagation calculation tool Cracktracer 3D fails to predict the correct crack propagation parameters by investigating the applicability of a submodel method consisting of a pure tetrahedral global model followed by a hexahedral submodel calculation.\\\noindent Currently a combined hexahedral-tetrahedral method is used in Cracktracer 3D. The actual initial crack shape is inserted into the structure, thereby automatically re-meshing the neighborhood of the crack in two zones. The first zone consist of a flexible cylindrical tube introduced at the crack tip. This tube contains collapsed hexahedral elements which ensures that the stress singularity at the crack tip is represented correctly. The second zone is located beyond the cylindrical tube and has a tetrahedral mesh created with NETGEN, a free 2D-3D tetrahedral meshing software. In order to determine the crack propagation size and direction, the stress intensity factor concept is applied. CalculiX is used for determining the stresses required by the postprocessor where the actually stress intensity factors are computed and the new crack front is obtained. The complex merging of the two zones together with the intersections of the resulting mesh with the crack shape and with the uncracked domain is the primary reason for the failure of the program.To prevent the failure of the program due to complex crack geometry, an alternative procedure is proposed. The two zones described above are replaced by a coarse mesh containing only tetrahedral elements. The stresses obtained from this purely tetrahedral mesh are not accurate enough to predict the correct stress intensity factors. In order to solve this issue, a submodel is created at the crack front. This submodel consists of a tube-like mesh with collapsed and finer hexahedral elements. The external boundary conditions of this tube are interpolated from the tetrahedral coarse grid resulting into a smaller, but also more accurate problem to obtain the stress intensity factor values at the core of the tube. Such an approach effectively removes the need to merge a hexahedral tube mesh with a tetrahedral one and can thus lead to a much more stable program. The computation time is also decreased. While the underlying principles of this technique are not new, the scope of its applicability, the comparison with another existing technique and the implementation methodology introduced in this thesis are unique.In order to validate such an approach, five different examples are used: a corner crack specimen under Mode I loading, a corner crack specimen under Mode III loading, a torque specimen under Mode I-III loading, a turbine vane carrier under Mode I loading together with thermal stresses and a shrouded turbine blade under mixed mode loading with thermal stresses. The most important crack parameters (e.g. maximum crack size during each increment, maximum equivalent stress intensity factor during each increment) obtained from both methods are compared for 100 crack increments. Generally, the results match very well as the crack shapes are almost identical. There is a slight disagreement occurring for some of the test cases at the free surface due to the tube submodel sticking out of the component which leads to different stress intensity factors being obtained. This difference is caused by interpolation errors. It is well known however that the stress intensity factors are not very accurate at this location even for the original method since the stress singularity changes at the free surface. A study into how fine the submodel mesh and the global tetrahedral mesh need to be is also conducted. The results indicate no significant improvement of a finer tetrahedral mesh but refining the tube submodel mesh does improve the computation of the stress intensity factors since there are more nodes present at the submodel's boundary where the displacements are interpolated. Any type of mesh refinement however comes at the cost of an increase in computation time. The submodel method is capable of computing sufficiently accurate results faster than the original combined hexahedral-tetrahedral method. Many more types of initial cracks can be inserted for the submodel method without forcing the user to increase the tube radius to account for different crack geometries and the complex merging of the meshes as in the original method. The main focus of additional research should be on testing the submodel approach on more complex case studies with multiple load steps in order to ensure that all the relevant features (e.g. concentrated loads, distributed loads, residual stresses) are correctly transferred from the coarse tetrahedral mesh to the submodel. Additionally, a possible combination of both approaches by alternating from one method to the other during the same case study, thereby utilizing each method's strengths when needed, is also worth investigating.Aerospace Engineering | Flight Performance and Propulsio