The fingerprint of deformation in materials at large strains and at high strain rates is the formation of adiabatic shear bands. Adiabatic shear bands lead to unexpected failure of materials during service. This study investigated the possibility of eliminating adiabatic shear bands from materials subjected to severe deformation at high strain rates by post impact heat treatment. Five groups of cylindrical AISI 4340 steel samples were impacted using the Direct Impact Hopkinson Pressure Bar (DIHPB) developed at the University of Manitoba. Selected impacted samples with distinct transformed shear bands were soaked at 350⁰C to 850⁰C for periods ranging from 30 minutes to 4 hours to investigate how temperature and time affects the properties and structure of the shear bands. Annealing the shear bands at 350⁰C resulted in an increase in hardness of the shear bands and the surrounding material outside the shear bands regardless of the heat treatment before impact, amount of deformation, and the time of annealing. Significant decrease in hardness of the shear bands occurred after post impact annealing at 650⁰C for 30 minutes and 2 hours. Hardness of the shear bands reduced to the same level as that of the impacted material outside the shear bands. However, the initial path of the shear bands in the impacted steel samples could be traced through a “signature” left after the annealing. Post-impact annealing of the steel samples at 750⁰C and 850⁰C resulted in a homogenous microstructure with no trace of the shear bands. The “signatures” which were used to trace the path of the shear bands in impacted samples annealed at 650⁰C disappeared and the hardness across the samples became uniform. The observations from this study show that adiabatic shear bands in typical steel can be eliminated by annealing heat treatment. The temperature of annealing is the most critical parameter and the annealing should be performed above 650⁰C.

The initiation and propagation of adiabatic shear bands is analyzed numerically for an impulsively loaded thick-walled steel tube. A circumferential V-notch located at the outer surface of the center of the tube provides a stress concentration. The material is modeled as strain hardening, strain-rate hardening and thermal softening. The dynamic loading conditions considered are pure torsion, axial pressure combined with torsion, and internal pressure combined with torsion. Because of the stress concentration, a shear band will first initiate in an element adjoining the notch tip and propagate radially inwards through the thickness of the tube. The speed of propagation and the amount of energy required to drive a shear band through the material are calculated. The effects of the pressure preload and the depth of the notch are studied. Also, the influence of thermal softening is investigated by modeling it after a relation proposed by Zhou et al. <i>[Vita removed July 18, 2008 CK/GMc 2/2/2012]<i> / Master of Science

This thesis consists of two parts. The first part explores a 2-d edge dislocation model to demonstrate characteristics of Field Dislocation Mechanics (FDM) in modeling single and collective behavior of individual dislocations. The second work explores the possibility of modelling adiabatic shear bands propagation within the timespace averaged framework of Mesoscopic Field Dislocation Mechanics (MFDM). It is demonstrated that FDM reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. The explored questions include the existence of a Peierls stress in translationally-invariant media, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-a-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics. A variety of dislocation pile-up problems are studied, primarily complementary to what can be dealt by existing classical pile-up models. In addition, the model suggests the possibility that the tip of a shear band can be modelled as a localized spatial gradient of elastic distortion with the dislocation density tensor in continuum dislocation mechanics; It is demonstrated that the localization can be moved by its theoretical driving force and forms a diffuse traveling band tip, thereby extending the thin layer of the deformation band. A 3-d, parallel finite element framework of MFDM is developed in a geometrically nonlinear context for the purpose of modelling shear bands. The numerical formulations and algorithm are presented in detail. Constitutive models appropriate for single crystal plasticity response and J2 plasticity with thermal softening are implemented.

The objective of this research project was to simulate the behavior of armor metals at high strain rates and large strains, using the Johnson-Cook visco-plastic model, while incorporating the formation of adiabatic shear bands. The model was then to be applied to three armor metals, namely maraging steel 300, high hardness armor (HHA), and aluminum alloy 5083-H131; supplied by the Canadian Department of National Defense and tested in compression at the University of Manitoba. The Johnson-Cook model can accurately simulate the behavior of BCC metal (steels) up to a point of thermal instability. Conditions for complete shear failure in the model match closely to conditions at which adiabatic shear bands formed in specimens tested experimentally. The Johnson-Cook model is not quite valid for FCC metals, such as aluminum, where strain rate and temperature effects are dependent on the strain while in the Johnson-Cook model, these parameters are separable.

The objective of this research project was to simulate the behavior of armor metals at high strain rates and large strains, using the Johnson-Cook visco-plastic model, while incorporating the formation of adiabatic shear bands. The model was then to be applied to three armor metals, namely maraging steel 300, high hardness armor (HHA), and aluminum alloy 5083-H131; supplied by the Canadian Department of National Defense and tested in compression at the University of Manitoba. The Johnson-Cook model can accurately simulate the behavior of BCC metal (steels) up to a point of thermal instability. Conditions for complete shear failure in the model match closely to conditions at which adiabatic shear bands formed in specimens tested experimentally. The Johnson-Cook model is not quite valid for FCC metals, such as aluminum, where strain rate and temperature effects are dependent on the strain while in the Johnson-Cook model, these parameters are separable.

During high strain rate deformations of metals and metallic alloys, narrow regions of intense plastic deformations have been observed experimentally. The phenomenon is termed strain localization and is usually a precursor to catastrophic failure of a structure. Similar phenomenon has been observed in glassy polymers deformed both at slow and high strain rates. Whereas strain localization is attributed to material softening due to thermal heating in metallic alloys, it is believed to be due to the reorganization of the molecular structure in polymers. Here we numerically study the strain localization in Tungsten Heavy Alloys (WHAs), and glassy polymers. WHAs are heterogeneous materials and thus inhomogeneities in deformations occur simultaneously at several places. Thus strains may localize into narrow bands at one or more places depending upon the microstructure of the alloy. We analyze the strain localization phenomenon during explosion and implosion of WHA hollow cylinders. We have developed a procedure to generate three-dimensional microstructures from planar images so that the two have the same 2-point correlation function. The WHA considered here is comprised of W particulates in a Nickel-Iron (NiFe) matrix, and each constituent is modeled as a heat conducting, strain hardening, strain-rate hardening and thermally softening elastic-plastic material. Furthermore, the porosity is taken to evolve in each constituent and the degradation of material properties due to porosity is incorporated into the problem formulation. It is found that the strain localization initiation in WHA hollow cylinders does not significantly depend on microstructural details during either explosive or implosive loading. However, the number of disconnected regions of localized deformations is influenced by the microstructure. We have generalized constitutive equations for high strain rate deformations of two glassy polymers, namely, Polycarbonate (PC) and poly (methyl methacrylate) (PMMA). These have been validated by comparing computed results with test findings in uniaxial compression at different axial strain rates, and subsequently used to study strain localization in a plate with a through-the-thickness elliptic hole at the centroid and pulled axially at a nominal strain rate of 5,000 /s. For the problems studied, the intensely deformed narrow regions have very high shear strains in WHAs, but large axial strains in glassy polymers. / Ph. D.

Plane strain deformations of an elastoplastic material are studied using numerical methods. In the first chapter, a meshless formulation of the static small strain elastic-plastic problem is formulated using the meshless local Petrov-Galerkin method. The code is validated against the small strain plasticity routines in the commercial finite element code ABAQUS for two basic configurations with loading, unloading, and reloading. The results are found to agree within 5%. The validated code is then used to analyze the stress intensity factor (SIF) in a double edge-cracked plate. Deformations of the plate are studied both with and without exploiting the symmetry conditions. The penalty method is used to enforce the essential boundary condition in the former case. When analyzing the deformations of the entire plate, the diffraction method is employed in order to introduce the discontinuity in the displacement field across the crack faces. The log-log and a higher order extrapolation technique due to Dally and Berger (1996) are used to calculate the SIF. It is found that the penalty method was inadequate to enforce the essential boundary conditions in the vicinity of the crack tip and that in this region the deformations were oscillatory. Consequently, the SIF calculation using the higher order technique was not accurate. It is also found that for a small plastic zone (3% of the cracked length) the SIFs do not differ significantly from their values for the corresponding linear elastic problem. In the second chapter, a finite element formulation of the dynamic deformations of a micro-porous thermoviscoplastic solid is formulated. The heat conduction in a material is assumed to be governed by a hyperbolic heat equation; thus thermal and mechanical waves propagate with finite speeds. The formation and propagation of an adiabatic shear band (ASB) inplane strain tensile deformations is studied for eleven materials. The ASB is assumed to form when the maximum shear stress has been reduced to 80% of its peak value at a point and it is deforming plastically. The materials are ranked according their susceptibility to the formation of an ASB. A parametric study of the effect of the initial defect strength where the defect is assumed through an initially inhomogeneous distribution of porosity, the thermal conductivity, the thermal wave speed, and the applied strain-rate upon the ASB initiation and propagation is conducted. It is found that the susceptibility ranking for this configuration differs somewhat from that previously found for simple shear and torsion of thin-walled tubes. It is also found that thermal conductivity influences ASB initiation and propagation only for materials with large values of · and that for such materials an adiabatic model may not be adequate. The effects of initial defect strength and the nominal strain-rates are both found to be consistent with simple shearing studies except that the ASB propagation speed was found to decrease with increasing nominal strain-rate. It is found that the criterion employed for ASB initiation accurately predicts the onset of the collapse of the total axial load applied to the body. In the final chapter, the formulation from the previous chapter is modified to permit the formation and propagation of brittle and ductile fracture. Deformations of the impact loaded double edge-crack specimen of Kalthoff and Winkler (1987) are studied. The brittle to ductile failure mode transition with increasing impact speed was found. Previous studies have focused on identifying the transition speed and did not allow for crack propagation. In this study, crack propagation is achieved through a nodal release algorithm and interpenetration of the crack surfaces is prevented using stiff-spring contact elements. Brittle fracture is assumed to occur when the maximum tensile principal stress achieves a critical value and the ductile fracture is assumed to occur when the effective plastic strain reaches a critical value. It is found that the transition speed for 4340 steel is approximately 54 m/s. For the brittle failure, the stress field is found to be significantly modified by the propagating crack and in the vicinity of the propagating crack the field is mode-I dominant. The crack formed through brittle fracture is found to completely propagate through the plate. For the ductile failure, the distribution of effective plastic strain about the crack tip is not significantly altered by the formation of the crack. The temperature rise in the vicinity of the ductile crack is found to be approximately 45% of the melting temperature of the material. / Ph. D.

Plane strain transient finite thermomechanical deformations of heat-conducting particulate composites comprised of circular tungsten particulates in nickel-iron matrix are analyzed using the finite element method to delineate the initiation and propagation of brittle/ductile failures by the nodal release technique. Each constituent and composites are modeled as strain hardening, strain-rate-hardening and thermally softening microporous materials. Values of material parameters of composites are derived by analyzing deformations of a representative volume element whose minimum dimensions are determined through numerical experiments. These values are found to be independent of sizes and random distributions of particulates, and are close to those obtained from either the rule of mixtures or micromechanics models. Brittle and ductile failures of composites are first studied by homogenizing their material properties; subsequently their ductile failure is analyzed by considering the microstructure. It is found that the continuously varying volume fraction of tungsten particulates strongly influences when and where adiabatic shear bands (ASB) initiate and their paths. Furthermore, an ASB initiates sooner in the composite than in either one of its constituents. We have studied the initiation and propagation of a brittle crack in a precracked plate deformed in plane strain tension, and a ductile crack in an infinitely long thin plate with a rather strong defect at its center and deformed in shear. The crack may propagate from the tungsten-rich region to nickel-iron-rich region or vice-a-versa. It is found that at the nominal strain-rate of 2000/s the brittle crack speed approaches Rayleigh's wave speed in the tungsten-plate, the nickel-iron-plate shatters after a small extension of the crack, and the composite plate does not shatter; the minimum nominal strain-rate for the nickel-iron-plate to shatter is 1130/s. The ductile crack speed from tungsten-rich to tungsten-poor regions is nearly one-tenth of that in the two homogeneous plates. The maximum speed of a ductile crack in tungsten and nickel-iron is found to be about 1.5 km/s. Meso and multiscale analyses have revealed that microstructural details strongly influence when and where ASBs initiate and their paths. ASB initiation criteria for particulate composites and their homogenized counterparts are different. / Ph. D.

In recent times, application of aluminum alloys is favored in the transportation sectors such as the aerospace and automobile industries where reduced fuel consumption and greenhouse gas emission are major priorities. In these applications, these alloys can be exposed to dynamic shock loading conditions as in the case of car crash and birds’ collision during aircraft’s take-off or landing. This study therefore focused on the deformation and damage mechanisms in AA 2017, AA 2024 and AA 2624 aluminum alloys under both quasi-static and dynamic impact loading conditions. Cylindrical specimens of the selected aluminum alloys were investigated under both quasi-static loading at 3.2 x10-3 s-1 using an Instron R5500 mechanical testing machine and dynamic impact loading using the split Hopkinson pressure bar at strain rates ranging between 2000 and 8000 s-1. The effects of strain rate and temper condition on the microstructural evolution in the alloys during mechanical loading were studied. The electron backscatter diffraction (EBSD) technique was used to investigate the texture of the naturally-aged AA 2017 and AA 2624 alloys before and after dynamic shock loading. The contributions of the major alloying elements such as copper, magnesium and silicon to the microstructural evolution and deformation behavior of the alloys under the dynamic shock loading condition were also studied using the energy dispersive spectroscopy (EDS) technique. Results showed that the morphology and atomic distribution of particles in the investigated alloys are functions of the temper condition. The hardness of all the three alloys was higher in the age-hardened conditions than the annealed ones. Although deformation of the alloy under quasi-static compressive loading was dominated by strain hardening, flow softening leading to strain localization and formation of shear bands occurred once certain critical strain values were reached. Under both quasi-static and dynamic loading, the alloys with low Cu:Mg ratio (AA 2024 and AA 2624) showed higher mechanical strength in age-hardened condition than that with high Cu:Mg ratio (AA 2017). All the alloys in the annealed condition exhibited an enhanced plasticity and formability. Intense strain localization leading to formation of adiabatic shear bands (ASBs) was the principal contributor to failure in the alloys under dynamic impact loading. Both deformed and transformed bands were observed, with cracking occurring mainly along the transformed shear bands. The tendency for formation of adiabatic shear bands is observed to be a function of the alloy composition, temper condition, strain, strain rate and strain hardening rate. In the natural aging condition, AA 2024 showed the highest susceptibility to formation of ASBs followed by AA 2624 and AA 2017 in that order. On the other hand, AA 2024 has the least susceptibility in the artificially-aged condition. Occurrence of bifurcation of transformed bands in dynamic impacted specimens is dependent on temper condition, strain and strain rate. The mechanism of fracture of the precipitation hardened samples is typical of ductile fracture occurring sequentially by nucleation, growth, and coalescence of micro-voids processes within transformed band. Elongated grains were observed to arrest propagating shear band depending on the angle the band makes with elongated grains. The higher the angle of inclination of a shear band to the grain on its path, the higher the tendency of the grain to stop its propagation. Texture analysis of the impacted specimens of AA 2017-T451 and AA 2624-T351 shows that the former has a higher tendency for the evolution of ultra-fine DRX grains within the transformed shear band. High strain rate led to the development of CD//<111> orientations at the expense of CD//<110> orientations. Schmid factor calculations performed on few different orientations in the starting microstructure shows that CD//<110> is less susceptible to slip deformation and consequently underwent rotation to CD//<111>.

High strain rate plastic deformation of metals results in the formation of localized zones of severe shear strain known as adiabatic shear bands (ASBs), which are a precursor to shear failure. The formation of ASBs in a high-strength low alloy steel, namely AISI 4340, was examined based on prior heat treatments (using different austenization and tempering temperatures), testing temperatures, and impact strain rates in order to map out grain size and grain deformation behaviour during the formation of ASBs. In the current experimental investigation, ASB formation was shown to be a microstructural phenomenon which depends on microstructural properties such as grain size, shape, orientation, and distribution of phases and hard particles—all controlled by the heat treatment process. Each grain is unique and its material properties are heterogeneous (based on its size, shape, and the complexity of the microstructure within the grain). Using measurements of grain size at various heat treatments as well as dynamic stress-strain data, a finite element model was developed using Matlab and explicit dynamic software LSDYNA to simulate the microstructural deformation of grains during the formation of ASBs. The model simulates the geometrical grain microstructure of steel in 2D using the Voronoi Tessellation algorithm and takes into account grain size, shape, orientation, and microstructural material property inhomogeneity between the grains and grain boundaries. The model takes advantage of the Smooth Particle Hydrodynamics (SPH) meshless method to simulate highly localized deformation as well as the Johnson-Cook Plasticity material model for defining the behavior of the steel at various heat treatments under high strain rate deformation.The Grain Model provides a superior representation of the kinematics of ASB formation on the microstructural level, based on grain size, shape and orientation. It is able to simulate the microstructural mechanism of ASB formation and grain refinement in AISI 4340 steel, more accurately and realistically than traditional macroscopic models, for a wide range of heat treatment and testing conditions.