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- All Subjects: multiaxial fatigue
- Creators: Liu, Yongming
Description
A new critical plane-energy model is proposed in this thesis for multiaxial fatigue life prediction of homogeneous and heterogeneous materials. Brief review of existing methods, especially on the critical plane-based and energy-based methods, are given first. Special focus is on one critical plane approach which has been shown to work for both brittle and ductile metals. The key idea is to automatically change the critical plane orientation with respect to different materials and stress states. One potential drawback of the developed model is that it needs an empirical calibration parameter for non-proportional multiaxial loadings since only the strain terms are used and the out-of-phase hardening cannot be considered. The energy-based model using the critical plane concept is proposed with help of the Mroz-Garud hardening rule to explicitly include the effect of non-proportional hardening under fatigue cyclic loadings. Thus, the empirical calibration for non-proportional loading is not needed since the out-of-phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature and it is shown the proposed model can work for both proportional and non-proportional loadings without the empirical calibration. Next, the model is extended for the fatigue analysis of heterogeneous materials integrating with finite element method. Fatigue crack initiation of representative volume of heterogeneous materials is analyzed using the developed critical plane-energy model and special focus is on the microstructure effect on the multiaxial fatigue life predictions. Several conclusions and future work is drawn based on the proposed study.
ContributorsWei, Haoyang (Author) / Liu, Yongming (Thesis advisor) / Jiang, Hanqing (Committee member) / Oswald, Jay (Committee member) / Arizona State University (Publisher)
Created2016
Description
A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM) in which the dislocations are modelled according to the Volterra dislocation model. Interior discontinuities are introduced across dislocation glide planes using enrichment functions and the resulting boundary value problem is solved through the standard finite element variational approach. The level set method is used to describe the geometry of the dislocation glide planes without any explicit treatment of the interface geometry which provides a convenient and an appealing means for describing the dislocation. A method for estimating the Peach-Koehler force by the domain form of J-integral is considered. The convergence and accuracy of the method are studied for an edge dislocation interacting with a free surface where analytical solutions are available. The force converges to the exact solution at an optimal rate for linear finite elements. The applicability of the method to dislocation interactions with inclusions is illustrated with a system of Aluminium matrix containing Aluminium-copper precipitates. The effect of size, shape and orientation of the inclusions on an edge dislocation for a difference in stiffness and coefficient of thermal expansion of the inclusions and matrix is considered. The force on the dislocation due to a hard inclusion increased by 8% in approaching the sharp corners of a square inclusion than a circular inclusion of equal area. The dislocation experienced 24% more force in moving towards the edges of a square shaped inclusion than towards its centre. When the areas of the inclusions were halved, 30% less force was exerted on the dislocation. This method was used to analyse interfaces with mismatch strains. Introducing eigenstrains equal to 0.004 to the elastic mismatch increased the force by 15 times for a circular inclusion. The energy needed to move an edge dislocation through a domain filled with circular inclusions is 4% more than that needed for a domain with square shaped inclusions.
ContributorsVeeresh, Pawan (Author) / Oswald, Jay (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Arizona State University (Publisher)
Created2016
Description
Two fatigue life prediction methods using the energy-based approach have been proposed. A number of approaches have been developed in the past five decades. This study reviews some common models and discusses the model that is most suitable for each different condition, no matter whether the model is designed to solve uniaxial, multiaxial, or biaxial loading paths in fatigue prediction. In addition, different loading cases such as various loading and constant loading are also discussed. These models are suitable for one or two conditions in fatigue prediction. While most of the existing models can only solve single cases, the proposed new energy-based approach not only can deal with different loading paths but is applicable for various loading cases. The first energy-based model using the linear cumulative rule is developed to calculate random loading cases. The method is developed by combining Miner’s rule and the rainflow-counting algorithm. For the second energy-based method, I propose an alternative method and develop an approach to avert the rainflow-counting algorithm. Specifically, I propose to use an energy-based model by directly using the time integration concept. In this study, first, the equivalent energy concept that can transform three-dimensional loading into an equivalent loading will be discussed. Second, the new damage propagation method modified by fatigue crack growth will be introduced to deal with cycle-based fatigue prediction. Third, the time-based concept will be implemented to determine fatigue damage under every cycle in the random loading case. The formulation will also be explained in detail. Through this new model, the fatigue life can be calculated properly in different loading cases. In addition, the proposed model is verified with experimental datasets from several published studies. The data include both uniaxial and multiaxial loading paths under constant loading and random loading cases. Finally, the discussion and conclusion based on the results, are included. Additional loading cases such as the spectrum including both elastic and plastic regions will be explored in future research.
ContributorsTien, Shih-Chuan (Author) / Liu, Yongming (Thesis advisor) / Nian, Qiong (Committee member) / Jiao, Yang (Committee member) / Arizona State University (Publisher)
Created2021
Description
Extensive efforts have been devoted to understanding material failure in the last several decades. A suitable numerical method and specific failure criteria are required for failure simulation. The finite element method (FEM) is the most widely used approach for material mechanical modelling. Since FEM is based on partial differential equations, it is hard to solve problems involving spatial discontinuities, such as fracture and material interface. Due to their intrinsic characteristics of integro-differential governing equations, discontinuous approaches are more suitable for problems involving spatial discontinuities, such as lattice spring method, discrete element method, and peridynamics. A recently proposed lattice particle method is shown to have no restriction of Poisson’s ratio, which is very common in discontinuous methods. In this study, the lattice particle method is adopted to study failure problems. In addition of numerical method, failure criterion is essential for failure simulations. In this study, multiaxial fatigue failure is investigated and then applied to the adopted method. Another critical issue of failure simulation is that the simulation process is time-consuming. To reduce computational cost, the lattice particle method can be partly replaced by neural network model.First, the development of a nonlocal maximum distortion energy criterion in the framework of a Lattice Particle Model (LPM) is presented for modeling of elastoplastic materials. The basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. Then, two multiaxial fatigue models are proposed for random loading and biaxial tension-tension loading, respectively. Following this, fatigue cracking in homogeneous and composite materials is studied using the lattice particle method and the proposed multiaxial fatigue model. Bi-phase material fatigue crack simulation is performed. Next, an integration of an efficient deep learning model and the lattice particle method is presented to predict fracture pattern for arbitrary microstructure and loading conditions. With this integration, computational accuracy and efficiency are both considered. Finally, some conclusion and discussion based on this study are drawn.
ContributorsWei, Haoyang (Author) / Liu, Yongming (Thesis advisor) / Chattopadhyay, Aditi (Committee member) / Jiang, Hanqing (Committee member) / Jiao, Yang (Committee member) / Oswald, Jay (Committee member) / Arizona State University (Publisher)
Created2021