The adhesive contact problems of a conical frustum punch indenting a transversely isotropic elastic half space and an orthotropic elastic half space are analytically studied in this thesis work. To solve the problem involving a transversely isotropic half space, the harmonic potential function method and the Hankel transform are employed, which lead to a general closed-form solution for the adhesive contact problem. For the case with an orthotropic half space, the problem of a point load applied on the half space is first solved by using the double Fourier transform method. The solution for the adhesive contact problem is then obtained through integrating the former solutions over the punch surface.

Size-dependent material responses observed at fine length scales are receiving growing attention due to the need in the modeling of very small sized mechanical structures. The conventional continuum theories do not suffice for accurate descriptions of the exact material behaviors in the fine-scale regime due to the lack of inherent material lengths. A number of new theories/models have been propounded so far to interpret such novel phenomena. In this dissertation a few enriched-continuum theories - the adhesive contact mechanics, surface elasticity and strain gradient elasticity - are employed to study the mechanical behaviors of a semi-infinite solid induced by the boundary forces. A unified treatment of axisymmetric adhesive contact problems is developed using the harmonic functions. The generalized solution applies to the adhesive contact problems involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile, and it links existing solutions/models for axisymmetric non-adhesive and adhesive contact problems like the Hertz solution, Sneddon's solution, the JKR model, the DMT model and the M-D model. The generalized Boussinesq and Flamant problems are examined in the context of the surface elasticity of Gurtin and Murdoch (1975, 1978), which treats the surface as a negligibly thin membrane with material properties differing from those of the bulk. Analytical solution is derived based on integral transforms and use of potential functions. The newly derived solution applies to the problems of an elastic half-space (half-plane as well) subjected to prescribed surface tractions with consideration of surface effects. The newly derived results exhibit substantial deviations from the classical predictions near the loading points and converge to the classical ones at a distance far away from those points. The size-dependency of material responses is clearly demonstrated and material hardening effects are predicted. The half-space contact problems are also studied using the simplified strain gradient elasticity theory which incorporates material microstructural effects. The solution is obtained by taking advantage of the displacement functions of Mindlin (1964) and integral transforms. Significant discrepancy between the current and the classical solutions is seen to exist in the immediate vicinity of the loading area. The discontinuity and singularity exist in classical solution are removed, and the stress and displacement components change smoothly through the solid body.

The applications of inflatable membrane structures are increasing rapidly in the various fields of engineering and science. The geometric, material, force and contact non-linearities complicate this subject further, which in turn increases the demand for computationally efficient methods and interpretations of counter-intuitive behaviors noted by the  scientific community. To understand the complex behavior of membranes in biological and medical engineering contexts, it is necessary to understand the mechanical behavior of a membrane from a physics point of view.  The first part of the  present work studies the pre-stretched circular membrane in contact with a soft linear substrate. Adhesive and frictionless contact conditions are considered during inflation, while only adhesive contact conditions are considered during deflation. The peeling of membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. It is observed that the pre-stretch is having a considerable effect on the variation of the energy release rate. In the second part, free and constrained inflation of a cylindrical membrane is investigated. Adhesive and frictionless contact conditions are considered between the membrane and substrate. It is observed that the continuity of principal stretches and stresses depend on contact conditions and the inflation/deflation phase. The adhesive traction developed during inflation and deflation arrests the axial movement of material points, while an adhesive line force created at the contact boundary is responsible for a jump in stretches and stresses at the contact boundary. The pre-stretch produces a softening effect in free and constrained inflation of cylindrical membranes. The third part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Both limit points and bifurcation points are observed on equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by an eigen-mode injection method. The occurrence of critical points and the stability of equilibrium branches are determined by perturbation techniques. The relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis. / <p>QC 20150227</p>

The applications of membranes are increasing rapidly in various fields of engineering and science. The geometric, material, force and contact non-linearities complicate their analysis, which increases the demand for computationally efficient methods and interpretation of counter-intuitive behaviours. The first part of the present work studies the free and constrained inflation of circular and cylindrical membranes. The membranes are assumed to be in contact with a soft substrate, modelled as a linear spring distribution.Adhesive and frictionless contact conditions are considered during inflation,while only adhesive contact conditions are considered during deflation. For a circular membrane, peeling of the membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. The second part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Limit points and bifurcation points are observed on primary equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by eigenvectors corresponding to zero eigenvalues at the bifurcation point. Symmetry has major implications on stability analysis of the structures, and the relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis. In the third part, wrinkling in the pressurized membranes is investigated,and robustness of the modified membrane theory and tension field theory is examined. The effect of boundary conditions, thickness variations, and inflating media on the wrinkling is investigated. It is observed that, with a relaxed strain energy formulation, the obtained equilibrium solutions are unstable due to the occurrence of pressure induced instabilities. A detailed analysis of pressure induced instabilities in the wrinkled membranes is described in the thesis. / <p>QC 20160518</p>

Adhesion between solid bodies plays a prominent role in a wide variety of situations ranging from tribological applications to dust coagulation initiating the formation of planets. It can be due to various reasons like capillary, electrostatic, van der Waals, and hydrophobic forces. Among these, adhesion due to van der Waals force| which has its origin in permanent or instantaneous electric dipoles present in all atoms and molecules|is of special significance as it is present in all cases. Computational studies on adhesion due to van der Waals force commonly assume it as a surface force due to its short effective range, which is about a few tens of nanometers, in comparison to the length-scales commonly encountered. However, such restrictions are often violated in various important problems. For example, the characteristic dimensions of asperities| which are the smallest roughness elements interacting to cause friction and wear| are usually of nanometer length-scale. In addition, the assumptions inherent in development of surface force model are exact only when the deformations are small. In all such situations, the van der Waals force must be assumed as distributed over the volume. In this work, a computational model is developed by incorporating van der Waals force and short-range repulsion (steric repulsion or Pauli repulsion) as body forces distributed over the volume in a large deformation, static/transient, finite element framework. First the development of the general formulation is discussed, and then it is specialized for various considerations like handling symmetry and interaction between an elastic body and a rigid half-space, which offer significant computational advantages over the general formulation. The applicability of the model is illustrated by using a number of benchmark and practical problems. The comparison of the analysis results and well-established analytical models are provided, which validates our method. As a specific example, the smooth change of interaction force from a thin-rod model to a at-plate model on increasing the cross-sectional areas of two interacting elastic rods is demonstrated. The impact of elastic bodies in presence adhesion, and the associated energy loss is an important concern in studies regarding the origin of friction. Therefore, adhesive impact of elastic rods and spheres is studied using our formulation. Emphasis of the study is on finding the apparent energy loss during impact, which represents the part of energy lost to elastic stress waves remaining in the body after the impact, and hence not available for rebound motion. In case of impact of elastic rods on a rigid half-space, it is shown that the apparent energy loss is a unique function of the tensile strain energy developed in the rod due to van der Waals attraction. A one-dimensional model is developed for this case to determine the energy loss based on the specified problem parameters, which can be used to predict practically relevant phenomena like capture. In case of impact of elastic spheres, which is often correlated with asperity interactions, the energy loss is found to be significant only if adhesion-induced instabilities occur. The behavior shown by rods and spheres are probably at the two extremes with regards to energy loss during impact of elastic bodies in presence of adhesion. Practical use of the formulation is demonstrated by applying it to the study of amplitude variation and phase shifts in tapping-mode atomic force microscopy. Specifically, the advantage of operating the AFM cantilever just below its natural frequency as compared to operating it just above the natural frequency is demonstrated. Bistable behavior, which is the coexistence of two stable vibration modes under exactly same operating conditions, is shown to be severe when the driving frequency is higher than the natural frequency of AFM cantilever even in the absence of adhesion, which can result in spurious contrast-reversal artifacts during imaging. The hysteresis loop associated with the bistable behavior may lead to erroneous conclusions regarding presence of adhesion. Since this model overcomes the limitations of lumped parameter models and the computational models based on surface force approximation, the results can be used for much more realistic interpretation of experimental data. Computational framework developed in this study achieves the capability for analysis of adhesive contact problems directly from van der Waals interaction and steric repulsion. Such a model can be used for revisiting the fundamental problems in contact mechanics, as well as for providing better insights into experimental observations.

The main purpose of this project is to investigate different tool steels in terms of their ability to withstand material transfer buildup, so-called galling, occurring in SMF (sheet metal forming) operations. The ability to withstand galling is vital to optimize cost-effectiveness and increase the work tool’s effective operational time. This investigation studies four different tool steels, including a TiN-coating, with the intention of evaluating the microstructures, chemical composition and hardness effect on galling resistance in dry conditions using a slider-on-flatsurface (SOFS) tribo-tester which measures the coefficient of friction during sliding. An OP (optical profilometer) was used to measure the size and geometry of lump growth on the tool and damage on the work sheet. A scanning electron microscope (SEM) was used to identify the interacting tribological mechanisms exhibited at different stages during the slide. The SEM figures confirmed three different types of characteristic patterns exhibited in the tracks after tribo- testing which were categorized as mild adhesive, abrasive and severe adhesive damage. A SEM figure that illustrates a ragged contact surface and an obvious change in the sheet materials plastic behavior is in this report regarded as a sign of severe adhesive contact, the characteristics could possibly be explained by local high temperature and high pressure followed by a sudden pressure drop and creation of hardened welds or solders between the two surfaces which increase the frictional input needed for further advancement. Friction coefficients observed in the initial 100% mild adhesive stage were, μ=0,22-0,26 succeeded by abrasive SEM characteristics often in association with mild adhesive contact and friction values between μ=0,25-0,4 which where sometimes followed by severe adhesive SEM characteristics in 100% of the contact zone with friction values between μ=0,34- 0,9 respectively. The tool material that performed best according to the friction detection criteria was Sv21 closely followed by Sleipner (TiN coated) and Va40 (HRC 63.3). Unfortunately was the friction criteria, a significant raise in friction for defining a sliding length to galling, not adequate for dry conditions due to immediate material transfer succeeded by cyclic changes between partial or 100% abrasive+mild adhesive and severe adhesive contact. The mechanism that change abrasive wear in association with mild adhesive contact, (moderate friction input), to sever adhesive wear, (higher friction input), is dependent on lump shape (lump geometry) and can appear at comparably low speeds 0,04-0,08 [m/s] and low friction energy input (μ=0,34), the magnitude of the change in friction is therefore not always significant and hardly detectable on the friction graph. This was quite unexpected but could be explained by concentration of friction energy rater than the absolute amount. The problem with using friction graphs for galling evaluation was increased even further when a very small lump size and low corresponding rate of material transfer to the tool surface caused a sustainable high raise in friction (μ≈0,3→0,6) on a TiN-coated tool steel called Sleipner. A hardly detectable or similar friction raise for Sv21 and Va40 showed much larger corresponding lump size and rate of material transfer. This means that friction graphs demonstrate a clear problem with quantifying lump size [m3] and rate of  material transfer [m3/s]. Another phenomenon called stick slip behavior, material transfer and lump growth followed by a sudden decrease in lump size and transfer of material back to the work sheet, is also not possible to detect on a friction graph. Because a drop in friction can easily be a change in contact temperature and lump attack angle due to a growing lump and not a decreasing lump.   The conclusion, a friction graph is not suited for galling evaluation and ranking in dry SOFS conditions. A ranking should primarily be based on dimensional OP measurements of the cross section of formed tracks and scratches or preferably by repeated OP measurements of the tool surface during a single test, the last revel the exact lump growth history and true lump growth even in the sliding direction. / civilingenjörsexamen

<p>The main purpose of this project is to investigate different tool steels in terms of their ability to withstand material transfer buildup, so-called galling, occurring in SMF (sheet metal forming) operations. The ability to withstand galling is vital to optimize cost-effectiveness and increase the work tool’s effective operational time. This investigation studies four different tool steels, including a TiN-coating, with the intention of evaluating the microstructures, chemical composition and hardness effect on galling resistance in dry conditions using a slider-on-flatsurface (SOFS) tribo-tester which measures the coefficient of friction during sliding.</p><p>An OP (optical profilometer) was used to measure the size and geometry of lump growth on the tool and damage on the work sheet. A scanning electron microscope (SEM) was used to identify the interacting tribological mechanisms exhibited at different stages during the slide. The SEM figures confirmed three different types of characteristic patterns exhibited in the tracks after tribo- testing which were categorized as mild adhesive, abrasive and severe adhesive damage.</p><p>A SEM figure that illustrates a ragged contact surface and an obvious change in the sheet materials plastic behavior is in this report regarded as a sign of severe adhesive contact, the characteristics could possibly be explained by local high temperature and high pressure followed by a sudden pressure drop and creation of hardened welds or solders between the two surfaces which increase the frictional input needed for further advancement. Friction coefficients observed in the initial 100% mild adhesive stage were, μ=0,22-0,26 succeeded by abrasive SEM characteristics often in association with mild adhesive contact and friction values between μ=0,25-0,4 which where sometimes followed by severe adhesive SEM characteristics in 100% of the contact zone with friction values between μ=0,34- 0,9 respectively. The tool material that performed best according to the friction detection criteria was Sv21 closely followed by Sleipner (TiN coated) and Va40 (HRC 63.3). Unfortunately was the friction criteria, a significant raise in friction for defining a sliding length to galling, not adequate for dry conditions due to immediate material transfer succeeded by cyclic changes between partial or 100% abrasive+mild adhesive and severe adhesive contact. The mechanism that change abrasive wear in association with mild adhesive contact, (moderate friction input), to sever adhesive wear, (higher friction input), is dependent on lump shape (lump geometry) and can appear at comparably low speeds 0,04-0,08 [m/s] and low friction energy input (μ=0,34), the magnitude of the change in friction is therefore not always significant and hardly detectable on the friction graph. This was quite unexpected but could be explained by concentration of friction energy rater than the absolute amount. The problem with using friction graphs for galling evaluation was increased even further when a very small lump size and low corresponding rate of material transfer to the tool surface caused a sustainable high raise in friction (μ≈0,3→0,6) on a TiN-coated tool steel called Sleipner.</p><p>A hardly detectable or similar friction raise for Sv21 and Va40 showed much larger corresponding lump size and rate of material transfer. This means that friction graphs demonstrate a clear problem with quantifying lump size [m3] and rate of  material transfer [m3/s]. Another phenomenon called stick slip behavior, material transfer and lump growth followed by a sudden decrease in lump size and transfer of material back to the work sheet, is also not possible to detect on a friction graph. Because a drop in friction can easily be a change in contact temperature and lump attack angle due to a growing lump and not a decreasing lump.</p><p> </p><p>The conclusion, a friction graph is not suited for galling evaluation and ranking in dry SOFS conditions. A ranking should primarily be based on dimensional OP measurements of the cross section of formed tracks and scratches or preferably by repeated OP measurements of the tool surface during a single test, the last revel the exact lump growth history and true lump growth even in the sliding direction.</p><p> </p> / civilingenjörsexamen