With the focus of the automotive industry on decreasing vehicle weight and improving fuel efficiency, aluminum is being used for structural components in automobiles. Given the high strain rates associated with vehicle impact, it is necessary to understand the rate sensitivity of any potential alloy (eg. AA5754) in order to accurately predict deformation behaviour. Furthermore, the magnitude and strain path associated with the residual strains remaining after forming of the component also play a major role in how the material will behave. It has been found that AA5754 sheet exhibits negative rate sensitivity up to a strain rate of 0.1/s, and positive strain rate sensitivity at strain rates between 0.1/s and 1500/s. Increasing the strain rate also has the effect of increasing the yield stress as well as the ductility. When a strain path change is involved between the prestrain stage and subsequent uniaxial loading, it has the effect of reducing the rate sensitivity of the material as well as reducing the overall flow stress. A rate-sensitive adaptation of the Voce material model was successfully implemented in LS-DYNA and used to predict the response of AA5754 sheet in bending for applied strain rates of 0.001/s and 0.1/s. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2008-09-23 20:11:30.829

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Dans le cadre de cette étude, l’influence de la pré-déformation sur l’anisotropie du comportement plastique et sur la ténacité d’un acier API X100 pour pipeline a été abordée. Une étude expérimentale approfondie de la microstructure, des propriétés mécaniques et de l’endommagement du matériaux a été mise en oeuvre. Un modèle phénoménologique anisotrope combinant les écrouissagesisotrope et cinématique a été développé dans l’objectif de rendre compte du comportement ductile de cet acier à haute résistance. De plus, un modèle d’endommagement anisotrope a été établi pour représenter l’effet de pré-déformation sur la ductilité et la ténacité de cet acier. L’application des modèles à la flexion sous contrainte illustre, par exemple, l’effet négatif de la pré-déformation sur la charge limite (Moment de flexion maximum) supportée avant flambement du pipe. / In this thesis the influence of prestrain on anisotropic ductility and fracture toughness has been evaluated for API grade X100 line pipe steel. A omprehensive experimental investigation of microstructure, mechanical properties and fracture mechanisms has been carried out. A phenomenological model combining isotropic and kinematic hardening with anisotropic yield function has been developed, in order to represent anisotropic hardening behavior of the high strength steel. Additionally, a damage model incorporating anisotropic damage has been established for representation of prestrain effect on ductility and toughness of the X100 steel. The developed models could predict the bending capacity and the ductile fracture toughness of the cold-formed line pipes.

Cette thèse traite des effets de pré-écrouissage, monotone ou cyclique, sur le comportement cyclique et la durée de vie en fatigue (traction-compression à température ambiante). Les matériaux utilisés sont un alliage de nickel-chrome (80-20%), un acier inoxydable austénitique 316L et du cuivre pur. Ils présentent une aisance croissante au glissement dévié ; un paramètre considéré comme majeur pour expliquer les écarts de sensibilité aux effets de mémoire de pré-écrouissage existants entre ces matériaux.Des courbes d'écrouissage cyclique obtenues suite à des chargements multi-paliers sur des échantillons pré-écrouis sont comparées à celles des matériaux vierges. Cette comparaison permet de tracer des cartographies d'effet mémoire. Différents effets y sont observés et leurs origines discutées via une approche par partition de contrainte. Enfin, des essais de fatigue sont effectués pour chaque domaine de mémoire de pré-écrouissage et leurs conséquences sur la durée de vie sont discutées / This work focuses on the effect of a pre-hardening, either monotonic or cyclic, on the cyclic behavior and the fatigue life during tension-compression tests at room temperature. Materials used are a nickel-chromium alloy (80-20%), a 316L austenitic stainless steel and OFHC pure copper. They present an increasing ease to the cross-slip : a deformation mechanism identified as a key parameter to understand the distinct memory effect sensibilities existing between materials.Cyclic stress-strain curves obtained from sequential loadings on prestrained samples are compared to the ones of virgin materials. Such comparison allows plotting memory effect maps. According to these memory plots, different pre-hardening effects exist and their origins are discussed through a stress-partition analysis. Finally, fatigue tests are carried out for each domain of the prestrain memory and their consequences on fatigue life are discussed

In summary, this thesis focuses on developing an a priori theory for geometric finite element discretizations of a Cosserat rod model, which is derived from incompatible elasticity. This theory will be supported by corresponding numerical experiments to validate the convergence behavior of the proposed method. The main result describes the qualitative behavior of intrinsic H1-errors and L2-errors in terms of the mesh diameter 0 < h ≪ 1 of the approximation scheme. Geometric Finite Element functions uh with its subclasses Geodesic Finite Elements and Projection- based Finite Elements as conforming path-independent and objective discretizations of Cosserat rod configurations were used. Existence, regularity, variational bounds and vector field transport estimates of the Cosserat rod model were derived to ob- tain an intrinsic a-priori theory. In the second part, this thesis concerns the derivation of the Cosserat rod from 3D elasticity featuring prestress together with numerical experiments for microheteroge- neous prestressed materials.

Instrumented nanoindentation techniques have been widely used in characterizing mechanical behavior of materials in small length scales. For defect-free single crystals under nanoindentation, the onset of elastic-plastic transition is often shown by a sudden displacement burst in the measured load-displacement curve. It is believed to result from the homogeneous dislocation nucleation because the maximum shear stress at the pop-in load approaches the theoretical strength of the material and because statistical measurements agree with a thermally activated process of homogeneous dislocation nucleation. For single crystals with defects, the pop-in is believed to result from the sudden motion of pre-existing dislocations or heterogeneous dislocation nucleation. If the sample is prestrained before nanoindentation tests, a monotonic decrease of the measured pop-in load with respect to the increase of prestrain on Ni and Mo single crystals is observed. A similar trend is also observed that the pop-in load will gradually decrease if the size of indenter tip radius increases. This dissertation presents a systematic modeling endeavor of energetics and kinetics of defect initiation in the stressed volume at small scales. For homogeneous dislocation nucleation, an indentation Schmid factor is determined as the ratio of maximum resolved shear stress to the maximum contact pressure. The orientation-depended nanoindentation pop-in loads are predicted based on the indentation Schmid factor, theoretical strength of the material, indenter radius, and the effective indentation modulus. A good agreement has been reached when comparing the experimental data of nanoindentation tests on NiAl, Mo, and Ni, with different loading orientations to theoretical predictions. Statistical measurements generally confirm the thermal activation model of homogeneous dislocation nucleation, because the extracted dependence of activation energy on resolved shear stress is almost unique for all the indentation directions. For pop-in due to pre-existing defects, the pop-in load is predicted to be dependent on the defect density and the critical strength for heterogeneous dislocation nucleation. The cumulative probability of pop-in loads contains convoluted information from the homogenous dislocation nucleation, which is sensitive to temperature and loading rate, and heterogeneous dislocation nucleation due to the unstable change of existing defect network, which is sensitive to the initial defect distribution.

This thesis, gathering four papers, concerns the enhancement in understanding and modelling of the audible dynamic stiffness of vibration rubber isolators including experimental measurements. Paper A studies the performances of three different types of vibration isolator using an indirect measurement technique to estimate the blocked dynamic transfer stiffness of each specimen. The measurements are performed over a wide audible frequency range of 200 to 1000 Hz in a specially designed test rig enabling the investigation of arbitrary preload influences. Paper B addresses the modelling of the audible-frequency stiffness of the rubber conical mount experimentally appraised in Paper A accounting for preload effects. The model is based on a simpliflied waveguide approach approximating the nonlinearities attributed to the predeformations by adopting shape factor considerations. The carbon black filled rubber is assumed incompressible, displaying a viscoelastic behavior based on a fractional derivative Kelvin-Voigt model efficiently reducing the number of required material parameters. In Paper C the focus is on the axial dynamic stiffness modelling of an arbitrary long rubber bushing within the audible frequency range. The problems of simultaneously satisfying the locally non-mixed boundary conditions at the radial and end surfaces are solved by adopting a waveguide approach, using the dispersion relation for axially symmetric waves in thick-walled infinite plates, while fulfilling the radial boundary conditions by mode-matching. The results obtained are successfully compared with simpliflied models but display discrepancies when increasing the diameter-to-length ratios since the influence of higher order modes and dispersion augments. Paper D develops an effective waveguide model for a pre-compressed cylindrical vibration isolator within the audible frequency domain at arbitrary compressions. The original, mathematically arduous problem of simultaneously modelling the preload and frequency dependence is solved by applying a novel transformation of the pre-strained isolator into a globally equivalent homogeneous and isotropic configuration enabling the straightforward application of a waveguide model to satisfy the boundary conditions. The results obtained present good agreement with the non-linear finite element results for a wide frequency range of 20 to 2000 Hz at different preloads. / QC 20101001

The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium—a property that makes such objects relevant for the fabrication of active and functionalmaterials. In this paperwe studymicroheterogeneous, prestrained plates that feature non-flat equilibriumshapes. Our goal is to understand the relation between the properties of the prestrained microstructure and the global shape of the plate in mechanical equilibrium. To this end, we consider a three-dimensional, nonlinear elasticity model that describes a periodic material that occupies a domain with small thickness. We consider a spatially periodic prestrain described in the form of a multiplicative decomposition of the deformation gradient.By simultaneous homogenization and dimension reduction, we rigorously derive an effective plate model as a Γ-limit for vanishing thickness and period. That limit has the form of a nonlinear bending energy with an emergent spontaneous curvature term. The homogenized properties of the bending model (bending stiffness and spontaneous curvature) are characterized by corrector problems. For a model composite—a prestrained laminate composed of isotropic materials—we investigate the dependence of the homogenized properties on the parameters of the model composite. Secondly, we investigate the relation between the parameters of the model composite and the set of shapes with minimal bending energy. Our study reveals a rather complex dependence of these shapes on the composite parameters. For instance, the curvature and principal directions of these shapes depend on the parameters in a nonlinear and discontinuous way; for certain parameter regions we observe uniqueness and non-uniqueness of the shapes. We also observe size effects: The geometries of the shapes depend on the aspect ratio between the plate thickness and the composite period. As a second application of our theory, we study a problem of shape programming: We prove that any target shape (parametrized by a bending deformation) can be obtained (up to a small tolerance) as an energy minimizer of a composite plate, which is simple in the sense that the plate consists of only finitely many grains that are filled with a parametrized composite with a single degree of freedom.