Amir Hosein Mehdizadeh
Lifetime Prediction under High Cycle Fatigue Loading using Finite Element Method based on Continuum Damage Mechanics.
Year: Sept. 2011- Oct. 2014.
Damage is an irreversible process which causes material failure due to mechanical strength gradual degradation. Damage mechanics is a field of solid mechanics which studies mechanical parameters governing material rupture under different loadings. Fatigue is a kind of damage which can lead to sudden fracture of components. Fatigue loading results from cyclic stresses that are less than the ultimate tensile stress, or even the yield stress of the material. The name fatigue is based on the concept that a material becomes tired under repetitive loading and fails at a stress level below the nominal strength of the material. The fatigue life of a component can be expressed as the number of loading cycles required to initiate a crack and to propagate it to critical size. Therefore, it can be said that fatigue failure occurs in three stages: crack initiation; slow-stable crack growth; and rapid fracture. In order for fatigue cracks to initiate, three basic factors are necessary. First, the loading pattern must contain minimum and maximum peak values with large enough variation or fluctuation. The peak values may be in tension or compression and may change over time but the reverse loading cycle must be sufficiently great for fatigue crack initiation. Secondly, the peak stress levels must be of sufficiently high value. If the peak stresses are too low, no crack initiation will occur. Thirdly, the material must experience a sufficiently large number of cycles of the applied stress. The number of cycles required to initiate and grow a crack is dependant on the first to factors. In addition to these three basic factors, there are a host of other variables, such as stress concentration, corrosion, temperature, overload, metallurgical structure, and residual stresses which can affect the propensity for fatigue. Since fatigue cracks generally initiate at a surface, the surface condition of the component being loaded will have an effect on its fatigue life. Surface roughness is important because it is directly related to the level and number of stress concentrations on the surface. Smooth surfaces increase the time to nucleation. Notches, scratches, and other stress risers decrease fatigue life. Surface residual stress will also have a significant effect on fatigue life. Compressive residual stresses from machining, cold working, heat treating will oppose a tensile load and thus lower the amplitude of cyclic loading. In this dissertation, Chaboche-Lemaitre damage evolution model is used to predict failure of components under high cycle fatigue loading uniaxially and multiaxially. Fatigue damage evolution in the model is based on maximum and minimum stresses in each cycle which can be used for anisotropic yield. The Chaboche-Lemaitre damage model takes into account mean stress effect as well as compressive stresses effect making crack to close. In addition, enables damage evolution below the fatigue limit under multilevel loadings. When the values of maximum and minimum stresses are constant, the model is integrated directly and number of cycles to failure is obtained as a closed-form equation. Otherwise, the model is integrated implicitly and implemented as a user material (UMAT) subroutine in Abaqus/Standard software numerically. Also to reduce computation time, Jump-in-Cycles procedure is used based on fatigue loading simulation as a user amplitude (UAMP) subroutine. To verify codified subroutines, first a cubic element is subjected to a fully reversed cyclic loading and the results are compared with Abaqus model for elastoplastic state which show good agreement; then compared to each other with damage and also with/without jump-in-cycles procedure. Subsequently, Unnotched, V-notched and Holed specimens are subjected under fatigue loadings with different stress ratios, and their lifetimes will be compared with experiments and closed-form equation. Eventually as a case study, main rotor spindle of an aircraft blades is subjected under a variable fatigue loading and its lifetime will be compared with practical sample.
Keywords: Continuum Damage Mechanics, High Cycle Fatigue, Life Estimation, Jump-in-Cycles Procedure, Spindle.