Author ORCID Identifier

Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Chemical and Materials Engineering

First Advisor

Dr. Tongguang Zhai


This study is concerned with using numerical three-dimensional microstructure-based models to quantify the multi-site fatigue crack initiation behaviors by simulating the effects of pores in a cast aluminum alloy, and to analyze the mechanism of fatigue crack branching in thick aluminum alloy plates. It has been recently recognized the three-dimensional effects of pores on fatigue crack initiation, which provide opportunity to quantitatively identify the fatigue weak-link density and strength distribution in aluminum alloy. The stress and strain fields around a micro-pore in an A713 aluminum alloy (an elasto-plastic media) under cyclic loading were quantified as a function of pore position in depth on surface using a 3-D finite element model. The incubation life for the fatigue crack from a pore in surface could be estimated using a micro-scale Manson-Coffin equation. By matching to the experimentally measured fatigue weak-links, the minimum critical pore size for fatigue crack initiation was determined to be 11 μm in diameter at the cyclic maximum stress of 100% yield strength of the alloy.

A quantitative model which took into account the 3-D effect of a pore on the local stress/strain fields was developed to quantify the fatigue weak-link density and strength distribution in the A713 Al alloy. In the model, a digital pore structure was first constructed using single-sized (15 μm in diameter) and multi-sized pores, respectively, that had a total volume fraction same as that of the pores measured experimentally in the alloy. In the sample surface randomly selected by cross-sectioning the simulated pore structure, the size and position in depth of each pore were know in the surface. The rate of fatigue crack initiation at these pores was found to be a Weibull function of the applied stress, which was consistent with the results experimentally measured in the alloy. The density and strength distribution of fatigue weak-links could then be derived and used to evaluate the fatigue crack initiation properties of the alloy. The simulated fatigue weaklink density and strength distribution in the multi-sized pore model were in a good agreement with the experimental results. The difference in the peak of strength distribution between experimentally measured and simulated results was only ~1.8%. It was also found that the average crack incubation life was linearly increased with decrease in the applied cyclic stress. The stochastic behaviors of the multi-site fatigue crack initiation and the reliability of fatigue crack initiation at each applied cyclic stress were quantified in the A713 cast Al alloy. The probability of fatigue crack initiation was characterized by a two-parameter Weibull function, i.e., with 10,000 cyclic loading, the survival probability for crack initiation was 72% at 110% yield strength, and was 99% at 50% yield strength.

A detailed fractographic and microstructural study, using stereo optical and scanning electron microscopy was accomplished to characterize the behavior and mechanisms of fatigue crack branching in a thick commercial 7050-T7651 aluminum plate in the L-S orientation. The SEM fractographies of the middle tension specimen failed in crack growth experiments showed that the transition of the lead crack from a crystallographic (fatigue fracture) to non-crystallographic mode (overloading fracture) of growth at a ΔK of ~17 MPa√m with few non-through thickness branches at the mid-thickness plane. An interior branched crack grew into a through crack at a ΔK greater than 30 MPa√m. The intergranular fracture was observed in the branched cracks, indicating a relationship between crack branching and over-aging state in the alloy. A 3-D finite element model which took into account the effect of both a non-through and through thickness branched crack at the lead crack was consequently developed to simulate the growth behavior with branching. The simulated results demonstrated that the driving force, ΔK, for the lead crack was reduced significantly due to branching at the crack tip, which was responsible for the reduced crack growth rate of the lead crack as observed experimentally. The driving force for crack growth with branching was increased with increasing the lead crack length, which explained the reason why crack branching occurred relatively easily when the lead crack was long. The precipitate-free-zones along grain boundaries were responsible for crack branching parallel to the rolling (L) direction, since the grain structure was stretched in L direction in the Al alloy plate due to hot rolling.

Digital Object Identifier (DOI)