Necking instabilities in elasto-viscoplastic materials
arXiv:1804.04369 · doi:10.1103/PhysRevMaterials.2.073602
Abstract
Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline, polycrystalline and other materials --- feature a predominantly elastic response at small stresses, plasticity onset at a rather well-defined yield stress and rate-dependence. Necking instabilities involve a unique coupling between the system's geometry and its constitutive behavior. We consider generic elasto-viscoplastic constitutive relations involving an internal-state field, which represents the structural evolution of the material during plastic deformation, and study necking in the long-wavelength approximation (sometimes termed the lubrication or slender-bar approximation). We derive a general expression for the largest time-dependent eigenvalue in an approximate WKB-like linear stability analysis, highlighting various basic physical effects involved in necking. This expression is then used to propose criteria for the onset of necking and more importantly for the emergence of strong localization. Applications to strain-softening amorphous plasticity, in the framework of the Shear-Transformation-Zone model, and to strain-hardening crystalline/polycrystalline plasticity, in the framework of the Kocks-Mecking model, are presented. These quantitative analyses of widely different material models support the theoretical predictions, most notably for the strong localization during necking.
arXiv comment15 pages including an Appendix, 5 figures
References in corpus (27)
- Dynamics of Viscoplastic Deformation in Amorphous Solids
- Rheology of Soft Glassy Materials
- Yield Stress Materials in Soft Condensed Matter
- Deformation and Failure of Amorphous Solidlike Materials
- Modeling the mechanics of amorphous solids at different length and time scales
- Shear-transformation-zone theory of plastic deformation near the glass transition
- Strain localization in a shear transformation zone model for amorphous solids
- Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Formulation in Terms of an Effective Disorder Temperature
- Shear banding, aging and noise dynamics in soft glassy materials
- Nonequilibrium Thermodynamics of Amorphous Materials II: Effective-Temperature Theory
- Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles
- Rate dependent shear bands in a shear transformation zone model of amorphous solids
- Microstructural Shear Localization in Plastic Deformation of Amorphous Solids
- Nonequilibrium Thermodynamics of Amorphous Materials III: Shear-Transformation-Zone Plasticity
- Nonequilibrium Thermodynamics of Amorphous Materials I: Internal Degrees of Freedom and Volume Deformation
- Steady-state, effective-temperature dynamics in a glassy material
- Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation II: Analysis of Simulated Amorphous Silicon
- Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
- Tensorial Constitutive Models for Disordered Foams, Dense Emulsions, and other Soft Nonergodic Materials
- Linear Response Theory for Hard and Soft Glassy Materials
- Shear-Transformation-Zone Theory of Linear Glassy Dynamics
- Criterion for extensional necking instability in polymeric fluids
- Notch fracture toughness of glasses: Rate, age and geometry dependence
- Criteria for extensional necking instability in complex fluids and soft solids. Part I: imposed Hencky strain rate protocol
- An Eulerian projection method for quasi-static elastoplasticity
- Age dependent modes of extensional necking instability in soft glassy materials
- Criteria for extensional necking instability in complex fluids and soft solids. Part II imposed tensile stress and force protocols