The occurrence of hot tearing during solidification is one of the major factors influencing both the quality and productivity of aluminum castings. In order to reduce the formation of hot tears, quantitative information regarding both hot tearing formation and semi-solid deformation is essential. In this study, the mechanisms of hot tearing and semi-solid deformation have been investigated via two novel techniques: x-ray micro-tomography on material deformed in the semi-solid region, and development of a three phase microstructural model based on a geometry derived from a Voronoi diagram with rounded corners and porosity. Numerical techniques were utilized to quantify both the size evolution and orientation of internal damage relative to void growth. In order to conduct the above research, a new semi-solid tensile deformation methodology was devised which uses a two thermocouple control technique to enable accurate measurement of semi-solid tensile strength and ductility. The experimental work was conducted on the aluminum – magnesium alloy AA5182 in the as-cast and hot isostatic pressing (HIP) states. The x-ray micro-tomography technique was used to observe that semi-solid deformation is accommodated by internal damage via growth of as-cast porosity and the nucleation of new damage-based voids. As the volume fraction of damage increases, the growth of voids occurs in an orientation perpendicular to the loading direction, both through expansion within the grain boundary liquid and via coalescence between voids. The damage then localizes, causing failure. The finite element semi-solid microstructural model was used to explore the effects of fraction solid, fraction porosity, and grain size on semi-solid constitutive behaviour. The simulations revealed that increased grain size and fraction porosity lead to a reduction in flow stress for a given fraction solid. Furthermore, local strain accumulation was linked to hot tearing, since strain localizes in the liquid very early in the deformation process. Based on the model predictions, a new constitutive relationship was developed over the range 0.75 < fs < 0.95. Together, these two techniques have provided powerful new insight, such as the critical role played by as-cast porosity, on the phenomena of hot tearing and semi-solid deformation in aluminum alloys.

Horizontal directional drilling is increasingly used to install pipes without costs and disruptions associated with conventional ‘cut and cover’ installations. This technique, which was developed by industrial innovators, feature complex soil and pipe response which is not well understood. The success of this operation depends on knowledge of the pulling forces applied, level of ground disturbance, ground expansion or fracture from mud pressure, and the effect of the pulling operation on the pipes. Tensile stresses in the pipe vary with time during and after installation, and along the pipe. This applies especially to polymer pipes where the stresses during insertion and those over the service life of the pipe may influence its performance. The main objective of this study is to model the short term and long term response of pipes installed using horizontal directional drilling and to investigate the effect of the time dependent behaviour of polymer pipes, as well as other installation variables on the performance of the pipe during and after installation. The mechanical behaviour of high density polyethylene used to manufacture a significant portion of pipes installed using horizontal directional drilling is investigated and two sophisticated constitutive models are developed to simulate the time-dependent behaviour of high density polyethylene. The interaction between the pipe and the surrounding soil during horizontal directional drilling installations is also investigated and modelled. A FORTRAN algorithm is developed to calculate the short and long term response of elastic and polymeric pipes installed using horizontal directional drilling. The program uses the HDPE constitutive models as well as the pipe-soil interaction model developed in the study. After evaluation, the developed program is employed in a parametric study on the sensitivity of short term and long term pipe response to different parameters, including the effect of overstressing the pipe during installation. As Multiaxial modeling is necessary for accurate analysis of some applications including the swagelining method, a uniaxial constitutive model developed in the current study is generalized to a multi-axial model that can simulate the response to biaxial stress-strain fields. The multi-axial model is implemented in a finite element code and its performance in simulating multiaxial stress-strain fields is evaluated. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2008-06-12 18:03:43.501

In metal powder compaction, density non-uniformity due to friction can be a source of flaws. Currently in industry, uniform density distribution is achieved by the optimization of punch motions through trial and error. This method is both costly and time consuming. Over the last decade, the finite element (FE) method has received significant attention as an alternative to the trial and error method; however, there is still lack of an accurate and robust material model for the simulation of metal powder compaction. In this study, Cam-clay and Drucker-Prager cap (DPC) material models were implemented into the commercial FE software ABAQUS/Explicit using the user-subroutine VUMAT. The Cam-clay model was shown to be appropriate for simple geometries. The DPC model is a pressure-dependent, non-smooth, multi-yield surface material model with a high curvature in the cap yield surface. This high curvature tends to result in instability issues; a sub-increment technique was implemented to address this instability problem. The DPC model also shows instability problems at the intersection of the yield surfaces; this problem was solved using the corner region in DPC material models for soils. The computational efficiency of the DPC material model was improved using a novel technique to solve the constitutive equations. In a case study it was shown that the numerical technique leads to a 30% decrease in computational cost, while degrading the accuracy of the analysis by only 0.4%. The forward Euler method was shown to be accurate in the integration of the constitutive equations using an error control scheme. Experimental tests were conducted where cylindrical-shaped parts were compacted from Distaloy AE iron based powder to a final density of 7.0 g/cm3. To measure local density, metallography and image processing was used. The FE results were compared to experimental results and it was shown that the FE analysis predicted local relative density within 2% of the actual experimental density. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2010-09-23 12:15:27.371

This thesis addressed non-smooth dynamics of lumped parameter systems, and was restricted to Filippov-type systems. The main objective of this thesis was twofold. Firstly, modeling aspects of Filippov-type non-smooth dynamical systems were addressed with an emphasis on the constitutive assumptions and mathematical structure behind these models. Secondly, robust algorithms were presented to obtain numerical solutions for various Filippov-type lumped parameter systems. Governing equations were written using two different mathematical approaches. The first approach was based on differential inclusions and the second approach was based on differential-algebraic equations. The differential inclusions approach is more amenable to mathematical analysis using existing mathematical tools. On the other hand, the approach based on differential-algebraic equations gives more insight into the constitutive assumptions of a chosen model and easier to obtain numerical solutions. Bingham-type models in which the force cannot be expressed in terms of kinematic variables but the kinematic variables can be expressed in terms of force were considered. Further, Coulomb friction was considered in which neither the force can be expressed in terms of kinematic variables nor the kinematic variables in terms of force. However, one can write implicit constitutive equations in terms of kinematic quantities and force. A numerical framework was set up to study such systems and the algorithm was devised. Towards the end, representative dynamical systems of practical significance were considered. The devised algorithm was implemented on these systems and the results were obtained. The results show that the setting offered by differential-algebraic equations is appropriate for studying dynamics of lumped parameter systems under implicit constitutive models.

In humans, taste is one of the five senses, and helps in the recognition of nutritionally important and potentially harmful substances. It triggers innate behaviour to accept or reject food. Humans can sense five basic tastes, which are sweet, umami, bitter, salt and sour. The receptors that mediate bitter, sweet and umami tastes belong to the G protein-coupled receptor (GPCR) superfamily. A group of three receptors sense sweet and umami tastes, whereas bitter taste is sensed by 25 bitter taste receptors (referred as T2Rs). T2Rs are activated by structurally diverse natural and synthetic bitter compounds. Many common pharmaceutical compounds are bitter in taste and these are effective ligands for T2Rs. Recent finding of T2Rs in extra-oral tissues suggests these receptors are also involved in various physiological and pathophysiological processes. To understand the structure and function of these receptors, studies directed at elucidating their mechanisms of activation, and identification of novel ligands including bitter blockers (antagonists and inverse agonists), are required. To obtain mechanistic insights into the role of the highly conserved, and receptor specific residues, two bitter taste receptors (T2R1 and T2R4) were targeted. In this study, a combination of molecular, biochemical and pharmacological approaches were used to identify the amino acids and motifs, important for T2Rs to switch from inactive to active state. A hydrogen-bonding network between transmembrane (TM) helices 1-2-7 was identified as important for T2R activation. Alanine-scan mutagenesis of intracellular loops (ICLs) 2 and 3 identified T2R regions important for G protein binding, and receptor activation. A pharmacological method was developed, to screen potential bitter blockers for T2Rs. Using this method, three novel bitter blockers, which include two natural antagonists and one synthetic inverse agonist for T2R4, were discovered. The role of expression tags in enhancing T2R4 expression was also pursued. T2R4 expression on the cell surface was increased 2.5 fold, when its N-terminus was tagged with rhodopsin N-terminal 33 residues (Rho33- T2R4 chimera). In conclusion, work carried out provides novel insights into the mechanisms of T2R activation, and in the discovery of bitter blockers for T2R4.

Recent advances in computational mechanics have opened the potential of carrying out the analysis and design of concrete structures in a realistic manner with the use of nonlinear concrete models. This encourages the development of more capable and realistic constitutive models, based on a rigorous approach, for the analysis and design of concrete structures. This research focuses on the development of a thermodynamic approach to constitutive modelling of concrete, with emphasis on the rigour and consistency both in the formulation of constitutive models, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the defined model can be derived from two specified energy potentials. In addition, the derivation of a constitutive model within this framework merely follows procedures established beforehand. The proposed constitutive model here is based on continuum damage mechanics, in combination with plasticity theory, hence enabling the macroscopic material behaviour observed in experiments to be appropriately modelled. Damage-induced softening is the cause of many problems in numerical failure simulations based on conventional continuum mechanics. The resolution of these problems requires an appropriate special treatment for the constitutive modelling which, in this study, is based on nonlocal theory, and realized through the nonlocality of energy terms in the damage loading functions. For practical applications in structural analysis, the model requires a minimum number of parameters, which can be identified from experimental tests. All the above features of the model have been incorporated in a unified and consistent thermodynamic approach, which also distinguish the approach from existing ones. Numerical implementation and application are important parts of the study. A suitable implicit scheme is adapted here for the integration of the nonlocal rate constitutive equations. For the solution of systems of nonlinear algebraic equations in finite element analysis, the arc-length method in combination with local constraint equations employing dominant displacements is implemented, and proves its reliability in this study. Application of the proposed constitutive models in the analysis and design of concrete structures is straightforward, with several numerical examples showing the practical aspects of the proposed modelling.

In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space. / In der vorliegenden Arbeit wird eine diffentialgeometrische Formulierung der Elektroelastizitätstheorie entwickelt, die auch thermische und magnetische Einflüsse berücksichtigt. Hierbei wird die Bewegung von Körpern untersucht, die aus einem elastischen Material bestehen und sich durch mechanische Kräfte, Wärmezufuhr und den Einfluss eines äußeren elektromagnetischen Feldes verformen. Dazu werden physikalische Bilanzgleichungen (Massenerhaltung, Impuls-, Drehimpuls- und Energiebilanz) aufgestellt, um mit deren Hilfe eine Gleichung zu formulieren, die die Bewegung des Körpers während der Deformation beschreibt. Dabei werden sowohl der Körper als auch der umgebende Raum als Riemannsche Mannigfaltigkeiten modelliert, wobei zugelassen ist, dass der Körper eine geringere Dimension hat als der ihn umgebende Raum. Auf diese Weise kann man nicht nur - wie sonst üblich - die Deformation dreidimensionaler Körper im dreidimensionalen euklidischen Raum beschreiben, sondern auch die Deformation von Membranen und die Deformation innerhalb eines gekrümmten Raums. Weiterhin werden sogenannte konstitutive Gleichungen formuliert, die die Eigenschaften des verwendeten Materials kodieren. Die Energiebilanz ist eine skalare Gleichung und kann daher leicht auf Riemannschen Mannigfaltigkeiten formuliert werden. Es wird gezeigt, dass die Forderung der Invarianz der Energiebilanz unter der Wirkung von beliebigen Diffeomorphismen auf den umgebenden Raum bereits die restlichen Bilanzgleichungen impliziert. Das verallgemeinert ein Resultat von Marsden und Hughes, das nur für Körper anwendbar ist, die die selbe Dimension wie der umgebende Raum haben und keine elektromagnetischen Felder berücksichtigt. Üblicherweise wird in Arbeiten über Elektroelastizität die Entropieungleichung verwendet, um zu entscheiden, welche Deformationen physikalisch zulässig sind und welche nicht. Sie wird außerdem verwendet, um Einschränkungen für die möglichen Formen von konstitutiven Gleichungen, die das Material beschreiben, herzuleiten. Leider gehen die Meinungen über die physikalisch korrekte Formulierung der Entropieungleichung auseinander sobald elektromagnetische Felder beteiligt sind. Weiterhin ist unklar, wie die Entropieungleichung für den Fall einer Membran, die einem elektromagnetischen Feld ausgesetzt ist, formuliert werden muss. Daher zeigen wir, dass die Benutzung der Entropieungleichung ersetzt werden kann durch die Forderung, dass für einen gegebenen Prozess die Energiebilanz invariant ist unter der Wirkung eines beliebigen Diffeomorphimus' auf den umgebenden Raum und der linearen Reskalierung der Temperatur. Zum einen liefert diese Forderung die gewünschten Einschränkungen für die Form der konstitutiven Gleichungen, zum anderen benoetigt sie viel schwächere Annahmen als die übliche Argumentation mit der Entropieungleichung, die man in der Physikliteratur findet. Unser Resultat ist dabei wieder eine Verallgemeinerung eines Theorems von Marsden und Hughes, wobei es, so wie deren Resultat, nur für Körper gilt, die als offene Teilmengen des dreidimensionalen euklidischen Raums modelliert werden können.

Aluminum alloys are a suitable substitution for heavy ferrous alloys in automobile structures. The purpose of this study was to investigate the flow stress behavior of as-cast and homogenized A535 aluminum alloy under various deformation conditions. A hot compression test of A535 alloy was performed in the temperature range of 473-673 K (200-400˚C) and strain rate range of 0.005-5 s-1 using a GleebleTM machine. Experimental data were fitted to Arrhenius-type constitutive equations to find material constants such as n, nʹ, β, A and activation energy (Q). Flow stress curves for as-cast and homogenized A535 alloy were predicted using an extended form of the Arrhenius constitutive equations. The dynamic shock load response of the alloy was studied using a split Hopkinson pressure bar (SHPB) test apparatus. The strain rate used ranged from 1400 s-1 to 2400 s-1 for as-cast and homogenized A535 alloy. The microstructures of the deformed specimens under different deformation conditions were analyzed using optical microscopy (OM) and scanning electron microscopy (SEM). Obtained true stress-true strain curves at elevated temperatures showed that the flow stress of the alloy increased by increasing the strain rate and decreasing the temperature for both as-cast and homogenized specimens. The homogenization heat treatment showed no effect on the mechanical behavior of the A535 alloy under hot deformation conditions. Hot deformation activation energy for both as-cast and homogenized A535 alloy was calculated to be 193 kJ/mol, which is higher than that for self-diffusion of pure aluminum (142 kJ/mol). The calculated stress values were compared with the measured ones and they showed good agreement by the correlation coefficient (R) of 0.997 and the average absolute relative error (AARE) of 6.5 %. The peak stress and the critical strain at the onset of thermal softening increased with strain rate for both the as-cast and homogenized A535 alloy. Homogenization heat treatment affected the high strain-rate deformation of the alloy, by increasing the peak stress and the thermal softening onset strain compared to those obtained for as-cast specimens. Deformed shear bands (DSBs) were formed in both the as-cast and homogenized A535 alloy in the strain rate range of 2000-2400 s-1.

In an automotive crash event, hot stamped, die quenched martensitic structural components have been shown to provide excellent intrusion resistance. These alloys exhibit only limited ductility, however, which may limit the overall impact performance of the component. The introduction of lower strength and more ductile “tailored” properties within some regions of a hot stamped component has the potential to improve impact performance. One approach being applied to achieving such tailored properties is through locally controlling the cooling rate within the stamping die. The primary motivation for the current work is to understand the role of cooling rate on the as-quenched mechanical response of tailored hot stampings, which has required characterization of the high strain rate mechanical behaviour of tailored hot stamped boron steel. The effect of cooling rate and resulting microstructure on the as-quenched mechanical behavior of USIBOR® 1500P boron steel at strain rates between 10-3 and 103 s-1 was investigated. Specimens quenched at rates above the critical cooling rate (~27 °C/s) exhibited a fully martensitic microstructure with a UTS of ~1,450 MPa. Sub-critical cooling rates, in the range 14°C/s to 50 °C/s, resulted in as-quenched microstructures ranging between bainitic to martensitic, respectively. Tension tests revealed that predominantly bainitic material conditions (14 °C/s cooling rate) exhibited a lower UTS of 816 MPa compared to 1,447 MPa for the fully martensitic material condition (50 °C/s cooling rate) with a corresponding increase in elongation from 0.10 to 0.15 for the bainitic condition. The reduction in area was 70% for the bainitic material condition and 58% for the martensitic material conditions which implied that a tailored region consisting of bainite may be a desirable candidate for implementation within a hot stamped component. The strain rate sensitivity was shown to be moderate for all of the as-quenched material conditions and the measured flow stress curves were used to develop a strain rate sensitive constitutive model, the “Tailored Crash Model (TCM)”. The TCM accurately reproduced the measured flow stress curves as a function of effective plastic strain, strain rate and Vickers hardness (or area fraction of martensite and bainite). The effect of deformation during quenching and the associated shift in the CCT diagram on the subsequent constitutive response was also examined for this material. Specimens were simultaneously quenched and deformed at various cooling rates to achieve a range of as-quenched microstructures that included ferrite in addition to martensite and bainite. Tensile tests conducted on these specimens at strain rates ranging from 0.003 s-1 to ~80 s-1 revealed that the presence of ferrite resulted in an increase in uniform elongation and n-value which increased overall energy absorption for a given hardness level. The strain rate sensitivity was shown to be moderate for all of the as-quenched material conditions and the TCM constitutive model was extended to account for the presence of ferrite. This extended constitutive model, the “Tailored Crash Model II (TCM II)”, has been shown to predict flow stress as a function of effective plastic strain, strain rate and area fraction of martensite, bainite and ferrite. As a validation exercise, uniaxial tension test simulations of specimens extracted from the transition zone of a hot stamped lab-scale B-pillar with tailored properties [1] were performed. The measured hardness distribution along the gauge length of the tensile specimens was used as input for the TCM constitutive model to define the element constitutive response used in the finite element (FE) models. The measured stress versus strain response and strain distribution during loading (measured using digital image correlation) was in excellent agreement with the FE models and thus validated the TCM constitutive model developed in this work. Validation of the TCM II version of the model is left for future work.

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