The Maugis analysis is applied to adhesive contact between a cylinder with various wave profiles and a semi-infinite, elastic half-plane. We extend the analysis of Waters, Lee and Guduru, who consider the adhesive contact of a Hertzian indenter on a semi-infinite, elastic half-space with axi-symmetric, wave profiles. This work gives the closed-form contact mechanical solution for continuous, line contact without the need for any approximation. The resulting semi-analytical model serves to complement existing (numerical) models of adhesive line contact with the static load-area response as a reference. Herewith we analyse adhesion-induced loading-unloading hysteresis and contrast semi-analytical and numerical result to assess the limit of the former analysis. We confirm that roughness-induced dissipation vanishes with increasing wave roughness and decreasing Maugis parameter due to an increase in the range of adhesion and cavitation. Instability and cavitation are mutually exclusive at a given load-area locus yet occur successively in the same contact. An interesting result is that the Johnson parameter, that is known to govern the amplification of adhesion in the JKR-limit, bounds the load-area envelope irrespective of Maugis parameter. However, the Johnson parameter does not control the occurrence of roughness-induced dissipation and thus interface toughening.

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Inelastic deformation is a common but often neglected phenomenon in experimental analysis of metal deformation and in contacts. This neglect leads to degraded measurement accuracy of material properties. Therefore a need arises for material models that a priori incorporate inelasticity. These material models must be simple and comprehensive to have the highest impact in society. This thesis addresses three main sources of inelasticity, namely anelasticity and plasticity in metals and viscosity in contacts. Inelasticity is a dissipative mode of deformation that is mechanically recoverable for anelasticity and viscosity, and irrecoverable for plasticity. We connect the fundamental properties and structures of metallic and soft matter constituents with experimentally accessible measures. The presented models will aid in the development of materials with specific properties that meet the needs of industry.

Chapter 2 presents an analytical model of the tensile test tangent moduli and yield points for single-crystallite metals with spatially uniform and nonuniform dislocation distributions across slip systems. The moduli and the onset of plastic flow show a notable dependence on initial dislocation character, spatial dislocation distribution, and loading direction with respect to crystallographic orientations. An improved methodology accounts for elastic compressibility and anisotropy, and the geometric structure of crystal lattices when one measures dislocation network geometry in single metallic crystallites.

Chapter 3 contains a seamless, unified stress-strain treatment of dislocation-driven deformation. This treatment combines the three deformation mechanisms of elastic bond stretching, stable dislocation glide, and unstable dislocation glide. The model’s yield criterion connects the bowing out of local dislocation links and global dislocation multiplication. A semi-empirical relation is constructed for the evolution of the dislocation network structure with uniaxial loading.

Chapter 4 formulates a macromechanical model of the yield point phenomenon under invariant plane conditions. The heterogeneous stress state across the Lüders front and the plastic flow inside the Lüders band are accounted for. The Lüders band orientation with respect to the tensile direction is not unique; the orientation changes with material properties and tensile specimen geometry by the stress concentration at the front. The model serves to approximate constitutive parameters independent of the test conditions.

Chapter 5 elucidates the interplay between adhesion and roughness by modelling the retraction of rigid, wavy indenters from viscoelastic substrates. Viscoelasticity governs adhesive hysteresis across all loading rates, and even in the presence of roughness-induced mechanical instabilities. This confirms the central role that viscoelasticity must play in experimental measurements in the presence of adhesive interfaces in soft matter contacts.

Chapter 6 examines the static, quasi-static, and dynamic trajectories of a base-excited mass-spring-damper system in the presence of friction. The differences between the dynamic and the quasi-static solution in engineering problems with viscous, static, and dry friction are assessed. The omission of inertial contributions will under-predict dissipation at both low and high excitation frequencies. This chapter is a guide for future (multi-scale) numerical modelling efforts on adhesion and interface friction, and the hysteretic deformation of metals.

Chapter 7 is a general discussion on the impact of inelasticity in metals, that follows from Chapters 2 and 3, the measurement of the yield point phenomenon in Chapter 4, and numerical modelling of dissipative contacts in Chapters 5 and 6. The four models as presented in Chapters 2-6 are readily applicable in experimental measurements and future numerical models. The importance of accounting for inelasticity in experimental measurement and modelling of the yield strength in metals, and adhesive dissipation in soft matter contacts is emphasised. Finally, the state of the art in research on the three main sources of inelasticity and potential applications of the presented models are enumerated, which serve as starting points of future research.@en

Modelling dislocation glide over the initial part of a stress–strain curve of metals received little attention up to now. However, dislocation glide is essential to ones understanding of the fundamental relationship between inelastic deformation and the evolution of the dislocation network structure. Therefore, we present a model of dislocation-driven deformation under static loading conditions. We reproduce repeated cyclic uniaxial tensile tests on Interstitial-Free and Low-Alloy steels. The elastic mechanical behaviour is described by isotropic linear elasticity, pre-yield anelastic mechanical behaviour by a dislocation bow-out model with dissipation, and the post-yield evolution of dislocation network structure by a statistical storage model. We hypothesise that when the local anelastic compliance is lower than the global plastic compliance, deformation is mechanically recoverable, and vice versa. This hypothesis is corroborated with the classical Taylor relation. We report the relation between stable and unstable dislocation glide using this prototypical modelling framework. We find four structural variables, that are based on dislocation physics, to describe the stress–strain curve: total dislocation density, average dislocation segment length, dislocation junction formation rate, and average dislocation junction length. Firstly, we quantify the dislocation network evolution during uniaxial monotonic loading, and verify work-hardening by dislocation junction formation and a Taylor-type equation for flow. Finally, we present a semi-empirical relation for the evolution of the dislocation network structure. Which allows us to: refine the physical interpretation of the Taylor relationship, and rationalise experimental observations on apparent modulus degradation by thermomechanical processing. Both these findings circumvent the limitations of current, physics-based hardening models.

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Viscoelasticity and roughness are among the possible causes of the adhesive hysteresis displayed by soft contacts. Viscoelasticity causes an increased effective work of adhesion due to stiffening of the contact, while roughness is responsible for elastic instabilities. Herein, we explore the interplay between viscoelasticity and roughness by simulating in two dimensions the retraction of a rigid cylinder, with wavy surface profile, from a viscoelastic half-space. The wave amplitude and length are varied to induce instabilities in the load–to–area response, while the retraction velocity is increased to promote viscoelasticity. Results show that, in the regime where viscoelasticity is confined to the edges of the wavy contact, the contributions of viscoelasticity and waviness to adhesive hysteresis are nearly independent and additive. At low retraction rates, the instabilities in the load-area curve typical of rough elastic contacts are suppressed by viscoelasticity: the contact stiffens to promote a stable decrease of the contact area with load. This occurs with a minimal change in work of adhesion. However, when the instantaneous limit is met at high retraction rates, mechanical instabilities appear.

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Predicting microstructure and (micro-)texture evolution during thermo-mechanical processing requires the combined simulation of plastic deformation and recrystallization. Here, a simulation approach based on the coupling of a full-field dislocation density based crystal plasticity model and a cellular automaton model is presented. A regridding/remeshing procedure is used to transfer data between the deformed mesh of the large-strain crystal plasticity model and the regular grid of the cellular automaton. Moreover, a physics based nucleation criterion has been developed based on dislocation density difference and changes in orientation due to deformation. The developed framework is used to study meta-dynamic recrystallization during double-hit compression tests and multi-stand rolling in high-resolution representative volume elements. These simulations reveal a good agreement with experimental results in terms of texture evolution, mechanical behaviour and growth kinetics, while enabling insights regarding the effect of nucleation on kinetics and crystallographic texture evolution.

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The volume increase and shape change during austenite to martensite transformation in dual-phase (DP) steels are largely accommodated in the microstructure by the deformation of the surrounding ferrite matrix. Accurate estimation of transformation-induced deformation of ferrite via experiments and modeling is essential for predicting the subsequent mechanical behavior of DP steels. This study aims to illustrate the disadvantages of simplifying the anisotropic transformation deformation of martensite to isotropic dilatation for modeling the transformation-induced deformation of ferrite. A novel methodology is developed comprising sequential experimental and numerical research on DP steels to quantify transformation-induced strains in ferrite. This methodology combines the results of prior austenite grain reconstruction, phenomenological theory of martensite crystallography and electron backscatter diffraction (EBSD) orientation data to estimate variant-specific transformation deformation. Subsequently, by comparison of full-field micromechanical calculation results on a virtual DP steel microstructure with experimental EBSD kernel average misorientation and geometrically necessary dislocation measurement results it is shown that neglecting the shear deformation associated with the martensitic transformation leads to significant underestimation in the prediction of transformation-induced strains in ferrite.

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Intricate knowledge of dislocation networks in metals has proven paramount in understanding the constitutive behaviour of these materials but current experimental methods yield limited information on the characteristics of these networks. Recently, the isotropic anelastic response of metals has been used to investigate complex dislocation networks through the well-known phenomenon that the observed elastic constants are influenced by dislocations. Considering the dependence of the behaviour of a Frank-Read (FR) source on its initial dislocation character and using discerning characteristics of dislocations, i.e. Burgers vector, line sense and slip system, the present paper takes dislocation character, crystal structure and dislocation network geometry into account and obtains the anisotropic mechanical response for a generic Poisson's ratio. In this work, the tensile test tangent moduli and yield points are presented for spatially uniform and nonuniform dislocation distributions across slip systems. First, the reversible shear strain of the FR source is derived as a function of initial dislocation character. The area swept by a mobile and initially straight dislocation segment pinned at both ends is given as an explicit function of the line stress. Secondly, the anisotropic anelastic strain contribution of FR sources to the total pre- and at-yield strain in single crystallites is calculated. For a given normal stress and superposition of the principal infinitesimal linear elastic lattice strain and anelastic dislocation strain, the tangent moduli are presented. The moduli and the inception of plastic flow have a notable dependence on initial dislocation character, spatial dislocation distribution and loading direction.

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The retraction of a cylindrical rigid indenter from a viscoelastic substrate is studied by means of an efficient Green's function method. Hysteresis is observed in the load to area relationship in accordance with experimental results. Although our model relaxes many assumptions posed by LEFM-based analytical theories, the results fall between the limits, at high and low retraction velocities, predicted by the theories. Approaching the high velocity instantaneous limit requires, however, very high velocities or Maugis parameter. The work of adhesion is found to change during retraction. A non-dimensional parameter is proposed to estimate the effect of viscoelasticity in adhesive hysteresis.

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It is well established that, at small loads, a linear relation exists between contact area and reduced pressure for elastic bodies with non-adhesive rough surfaces. In the case of adhesive contacts, however, there is not yet a general consensus on whether or not linearity still holds. In this work evidence is provided, through numerical simulations, that the relation is non-linear. The simulations here presented can accurately describe contact between self-affine adhesive rough surfaces, since they rely on Green's function molecular dynamics to describe elastic deformation and on coupled phenomenological traction-separation laws for the interfacial interactions. The analysis is performed for two-dimensional compressible and incompressible bodies under plane strain conditions. Interfaces with various roughness parameters and work of adhesion are considered.

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The contact mechanical response of various polymers is controlled by the viscoelastic behavior of their bulk and the adhesive properties of their interface. Due to the interplay between viscoelasticity and adhesion it is difficult to predict the contact response, even more when surfaces are rough. Numerical modeling could be of assistance in this task, but has so far mostly dealt with either adhesion or viscoelasticity and focused on simple geometries. Ideally, one would need a model that can concurrently describe viscoelasticity, surface roughness, and interfacial interactions. The numerical technique named Green's function molecular dynamics (GFMD) has the potential to serve this purpose. To date, it has been used to model contact between adhesive elastic bodies with self-affine surfaces. Here, as a first step, we extend the GFMD technique to include the transient contact response of frictionless viscoelastic bodies. To this end, we derive the constitutive equation for a viscoelastic semi-infinite body in reciprocal space, then integrate it using the semi-analytical method, and find the quasi-static solution through damped dynamics of the individual modes. The new model is then applied to study indentation as well as rolling of a rigid cylinder on a frictionless isotropic half-plane that follows the Zener model when loaded in shear. Extension of the method to a generalized viscoelastic model is straightforward, but the computational effort increases with the number of time-scales required to describe the material. The steady-state response of the rolling cylinder was provided analytically by Hunter in the sixties. Here, we use his analytical solution to validate the steady-state response of our model and provide additionally the transient response for bodies with various shear moduli.@en

The relative contact area of rough surface contacts is known to increase linearly with reduced pressure, with proportionality factor κ. In its common definition, the reduced pressure contains the root-mean-square gradient (RMSG) of the surface. Although easy to measure, the RMSG of the entire surface does not coincide, at small loads, with the RMSG over the actual contact area g¯ _r, which gives a better description of the contact between rough surfaces. It was recently shown that, for Hertzian contacts, linearity between area and load is indeed obtained only if the RMSG is determined over the actual contact area. Similar to surface contacts, in line contacts, numerical data are often studied using theories that predict linearity by design. In this work, we revisit line contact problems and examine whether or not the assumption of linearity for line contacts holds true. We demonstrate, using Green’s function molecular dynamics simulations, that κ for line contacts is not a constant: It depends on both the reduced pressure and the Hurst exponent. However, linearity holds when the RMSG is measured over the actual contact area. In that case, we could compare κ for line and surface contacts and found that their ratio is approximately 0.9. Finally, by analytically deriving the proportionality factor using g¯ _r in the original model of Greenwood and Williamson, a value is obtained that is surprisingly in good agreement with our numerical results for rough surface contacts.

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