Inelastic Deformation in Metals and Contacts: Comprehensive Treatises on Yielding and Hardening, the Yield Phenomenon and Dissipation

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.