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This dissertation aims to develop valid numerical approaches to investigate the micromechanics of ductile fracture process and predict the ductile material failure under various loading conditions. As the first portion of this work, a layered unit cell micromechanics model is proposed. This model consists of three void containing material units stacked in the direction normal to the localization plane. Localization takes place in the middle material unit while the two outer units undergo elastic recovery after failure occurs. Thus, a failure criterion is established as the material is considered failure when the macroscopic effective strain of the outer material units reaches the maximum value. Comparisons of the present model with several previous models suggest that the present model is not only easy to implement in finite element analysis but also more suitable to robustly determine the failure strain. A series of unit cell analyses are conducted for various macroscopic stress triaxialities and Lode parameters to investigate the dependency of failure strain on stress state. The analysis results also reveal the effect of the stress state on the deformed void shape within and near the localization band. Additionally, analyses are conducted to demonstrate the effect of the voids existing outside the localization band.Next, the unit cell model is utilized to investigate the effect of hydrogen on ductile fracture demonstrated by its influence on the process of void growth and coalescence. The evolution of local stress and deformation states results in hydrogen redistribution in the material, which in turn changes the material’s flow property due to the hydrogen enhanced localized plasticity effect. The result shows that hydrogen reduces the ductility of the material by accelerating void growth and coalescence, and the effect of hydrogen on ductile fracture is strongly influenced by the stress state experienced by the material, as characterized by the stress triaxiality and the Lode parameter. The predicted material responses of three modified Gurson models are also investigated: GTN model, shear-modified-GTN model, and the shear-modified-GTN applied with anisotropic material model. A single material point test model equivalents to a computational cell of Gurson type models is utilized to demonstrate the effect of damage parameters and its evolution through the loading process when undergoing proportional stress loading. The shear-modified-GTN with anisotropic material model is implemented and calibrated using experimental data of commercially pure titanium, which exhibits complex plastic anisotropy and tension-compression asymmetry. The predicted results show good agreement with the experimental results obtained from various loading applications and specimen geometries. In addition, the predicted results also reveal the important effect of volumetric damage and shear damage under the influence of plastic anisotropy.

Zr-2.5Nb pressure tubes are primary containment components in CANDU (CANada Deuterium Uranium) reactors. One of the important reactor safety concerns is the fracture of the Zr-2.5Nb pressure tubes due to precipitation of circumferential hydrides. In this investigation, ductile fracture initiation with consideration of strain concentration and stress triaxiality near crack fronts in compact tension (CT), pressure tube (PT) and curved compact tension (CCT) specimens of hydrided irradiated Zr-2.5Nb pressure tube materials with split circumferential hydrides is investigated by three-dimensional finite element analyses with submodeling. The stress-strain relation for the irradiated Zr-2.5Nb pressure tube materials is taken as elastic plastic strain hardening with the perfectly plastic behavior at large plastic strains based on the experimental results of transverse tensile tests. A strain-based failure criterion with consideration of stress triaxiality is developed from the Gurson yield model with use of the experimental/computational results of transverse tensile tests and the effective plastic strain of the critical material element in CT specimens without hydride at fracture initiation. The results of the three-dimensional finite element analyses of CT, PT and CCT specimens of irradiated Zr-2.5Nb pressure tube materials without circumferential hydrides suggest that circumferential hydrides ahead of the crack front in the middle of CT, PT and CCT specimens should fracture with the assumption of the hydride fracture stress of 750 MPa for the given load or internal pressure that corresponds to the same fracture toughness (Kc) of the irradiated Zr-2.5Nb pressure tube materials without circumferential hydrides. Based on a strain-based failure criterion with consideration of stress triaxiality, the fracture initiation is determined, respectively, in the middle of the thickness for CT specimens, near the middle of the thickness for PT specimens, and at a quarter of the specimen thickness from the inner specimen surface for CCT specimens. The fracture initiation load or internal pressure corresponding to the same Kc based on the strain-based failure criterion with consideration of stress triaxiality for CCT specimens without hydrides is 2% lower than that for CT specimens without hydrides and is 4.3% lower than that for PT specimens without hydrides. The strain-based failure criterion with consideration of stress triaxiality can be used to describe the slightly higher fracture toughness for a PT specimen due to different constraint conditions and different types of loading, compared with that for a CCT specimen at room temperature. For CT, PT and CCT specimens with split circumferential hydrides with various heights and ligament thicknesses, plastic strain concentration is observed in the middle of the ligament ahead of the crack front when the ratio of the ligament thickness to the hydride height is less than 3. With the strain-based failure criterion with consideration of stress triaxiality, the necessary fraction of the load for crack initiation is about 0.60 to 0.70 to fracture the ligaments when compared to that for CT, PT and CCT specimens without split circumferential hydrides. The computational results can be used to explain the near 35% reduction of the fracture toughness at room temperature obtained from hydrided irradiated PT and CCT specimens when compared with those from unhydrided irradiated ones.

Abstract: Rail breaks, resulting from increasing heavy axle-load operations and harsh environmental conditions, remain a major cause of catastrophic derailment of vehicles in North America. The objective of this research project is to develop convenient testing methods to identify the optimum high-strength rail steels for Canadian weather, which can contribute to reducing derailment risks for the Canadian railway industry. In this research project, both destructive and non-destructive testing methods are developed to quantify the fracture toughness of high-strength rail steels. The project can be broadly divided into two phases. Phase I, which is reported in Chapters 2 and 3, involves establishing an extended strain energy density (SED) model for estimating the fracture toughness of high-strength rail steels at 23, -10, and -40oC. First, the mechanical properties, including the mode I critical stress intensity factor (KIc), constitutive equation, and Vickers hardness, of three types of high-strength rail steels are tested and compared at 23, -10, and -40oC. According to the experimental results, their KIc values and tensile properties are not correlated with each other. Further study in phase I involves investigating the influence of stress triaxiality (defined as the ratio of hydrostatic stress to von Mises stress) on the plastic deformation and fracture behaviour of rail steels. An extended SED model that considers the effect of stress triaxiality on both distortional and dilatational SEDs is proposed for assessing the fracture toughness of high-strength rail steels. The critical SED factor, determined by calculating the product of the critical SED and a characteristic distance ahead of the crack tip, is found to well correlate with the KIc values among the three types of rail steels at 23, -10, and -40oC. The results also confirm that the dilatational energy dissipation (also known as damage energy dissipation) at the crack tip is the primary component to correlate the critical SED factor with the KIc of rail steels. In Phase II, which is reported in Chapters 4 and 5, a more convenient non-destructive indentation technique is developed for estimating the fracture toughness of high-strength rail steels. First, a new constitutive model with coupled stress-triaxiality-dependent plasticity and damage is postulated to describe the mechanisms involved in the plastic deformation and ductile damage to rail steels under different levels of stress triaxiality. Based on the new constitutive model, not only is the independence of the constitutive equation from stress triaxiality explained, but a stress-triaxiality-dependent ductile damage model is also developed to estimate the critical damage parameter (Dcr) at the crack tip. With this ductile damage model, the indentation fracture toughness (KInd) of rail steels is estimated based on the Dcr at the crack tip. In addition, the study in Phase II uses a parameter κ to accommodate the potential difference of the Dcr value in the two loading modes (tensile fracture and indentation compression). The study shows that Dcr is indeed stress-triaxiality dependent and increases with the increase of stress triaxiality. The results also show that the change in KInd based on Dcr either at the crack tip or for the smooth specimen is generally consistent with the difference in the measured fracture toughness (KIc) among the three rail steels. However, for materials that show small difference in KIc, i.e., within the scattering of the measured data, KInd based on the Dcr at the crack tip may show a different trend from that based on the Dcr for the smooth specimen, which depends on the selected κ values. Such an issue needs further investigation using materials that cover a wide range of fracture toughness. Compared to the destructive testing method, the non-destructive indentation technique is more convenient, and has the potential to serve as a tool for the in-field health monitoring of rail steels and for the material evaluation, at an early stage, of the new rail steel under development.

This thesis sought to investigate and develop valid numerical approaches to predict ductile fracture under different stress state and loading conditions. As the first portion of this work, the plastic flow and fracture behaviors of three aluminum alloys (5083-H116, 6082-T6 and 5183 weld metal) under the effects of strain rate and temperature were studied through a series of experiments and finite element analyses. The fracture behavior under the influential factor of stress triaxiality was also studied. The applicability of the Johnson-Cook plasticity and fracture models were investigated with mixed results. For all three materials, the dependency of the failure strain on triaxiality is adequately described.The stress state effect on plasticity and ductile fracture behaviors was further explored for aluminum alloy 5083-H116 through tests on plane strain specimens and torsion specimens, focusing on the third deviatoric stress invariant (lode angle). A stress state dependent plasticity model, J2-J3 model, together with the Xue-Wierzbicki fracture criterion which defined the damage parameter as a function of the stress triaxiality and the Lode angle, was implemented and calibrated with the test data. The calibrated model was utilized to study the residual stress effect on ductile fracture resistance, using compact tension specimens with residual stress fields generated from a local out-of-plane compression approach. Fracture tests with positive and negative residual stresses were conducted on the C(T) specimens. Both experimental and finite element results showed significant effect of residual stress on ductile fracture resistance.In an attempt to predict ductile fracture under shear-dominated conditions, this study combined the damage mechanics concept with the Gurson-Tvergaard-Needleman porous plasticity model that accounts for void nucleation, growth and coalescence. The GTN model was extended by coupling two damage parameters, representing volumetric damage and shear damage respectively, into the yield function and flow potential. The new model was validated through a series of numerical tests in comparison with existing GTN type models, and applied to predict the ductile fracture behaviors of a beta-treated Zircaloy-4. With model parameters calibrated using experimental data, the model was able to predict failure initiation and propagation in various specimens experiencing a wide range of stress states.