DEFORMATION-MECHANISM

MAPS

The Plasticity and Creep of Metals and Ceramics

Home Text Symbol Reference Interactive Plots List of Symbols, Definitions and Units Macroscopic Variables Equation Number Other Variables and Constants Equation Number Normal (tensile or compressive strain) 17.7 Force per unit length on a dislocation (N/m) 2.4 Transient strain 17.9 , Fraction of atom sites associated with lattice and core diffusion respectively 2.20 Strain rate (s-1) 1.5 , Gibbs free energy (J/mol) 2.6, 2.10 ,, Principal strain rates (s-1) 1.3 Grain boundary energy (J/m2) — Strain rate tensor (s-1) 1.4 Shear strain (rate); see Macroscopic variables — Shear strain 1.3 Activity coefficient of component A, etc. 2.28 Transient shear strain 17.10 Upper limiting strain rate (taken as 106/s) 17.13 Shear strain rate (s-1) 1.3, 1.4, 1.5 ,, Pre-exponential constants (s-1) 2.9, 2.12, 2.15 ,. . . Shear strain rates of individual mechanisms (s-1) 2.1, 2.9, 2.12, 2.21, 2.23, 2.26, 2.29 Bulk modulus (at 300 K and atmospheric pressure) (MN/m2) 17.37 Shear strain rate caused by low-temperature plastic mechanisms (s-1) 3.1 Work-hardening constant in tension (MN/m2) 17.6 Shear strain rate limited by phonon drag (s-1) 2.14 Work-hardening constant in shear (MN/m2) 17.6 Shear strain rate limited by twinning (s-1) 2.15 Boltzmann's constant (1.381 x 10-23 J/K) — Hydrostatic pressure (MN/m2) 17.37 Thermal conductivity (J/s m K) 17.20 Normal (tensile or compressive) stress (MN/m2) 2.17 Obstacle spacing (m) Table 2.1 ,, Principal stresses (MN/m2) 1.1 Dislocation mobility (m2/Ns) 2.4 Stress tensor (MN/m2) 1.2 Strain hardening exponent 17.6 Shear stress (MN/m2) 1.5 Shear modulus (at 300 K and atmospheric pressure) (MN/m2) 2.1, 2.3, Table 2.1 Deviatoric part of the stress tensor (MN/m2) 1.2 , Creep exponent 2.18, 2.19, 2.26 Time (s) 17.3 Debye frequency (taken as 1012/s) 2.5 Temperature (K) 1.6, 1.12 Material property 1.6 Other Variables and Constants Equation Number Hydrostatic pressure; see Macroscopic variables (MN/m2) 17.37 ,, Power-law creep constants 2.18, 2.19 Dimensionless exponent 2.7 Constant for Harper-Dorn creep 2.23 Atmospheric pressure (0.1 MN/m2) 17.37 Diffusive section of a dislocation core (m2) 2.20 ,, Activation energies for lattice, boundary and core diffusion respectively (kJ/mol) 2.17, 2.20, 2.30 Dimensionless ideal strength 2.1 Activation energy for creep when different from Qv, Qb or Qc (kJ/mol) 2.24 Dimensionless constant for low-temperature plasticity 2.7 Dimensionless exponent 2.17 Constant for power-law breakdown (MN/m2) 2.26 Heat generation rate (J/m3 s) 17.14 Drag coefficient (Ns/m2) 2.13 Gas constant (8.314 J/mol K) — Magnitude of Burgers' Vector (m) 2.2 Dislocation density (m-2) — Burgers' Vector of boundary dislocation (m) 17.25 Density of boundary dislocations (m-1) 17.29 Constant for low-temperature plasticity 2.7 Mobile dislocation density (m-2) 2.3 Constant for power-law breakdown 2.26 State variable (constant initial value) 1.6, 1.10 Specific heat at constant pressure (J/m K) 17.16 Stress; see Macroscopic variables (MN/m2) — Constant for drag-limited glide 17.12 Tensile yield strength (MN/m2) — ,,, etc. Single-crystal moduli (MN/m2) — Absolute temperature; see Macroscopic variables (K) 1.6, 1.12 Boundary diffusion coefficient (m2/s): Db=D0bexp-(Qb/RT) 2.30 Melting temperature (K) — Core diffusion coefficient (m2/s): Dc=D0cexp-(Qc/RT) 2.20 Temperature of surroundings (K) 17.20 Lattice diffusion coefficient (m2/s): Dv=D0vexp-(Qv/RT) 2.17 Time; see Macroscopic variables (s) — Effective diffusion coefficient for power-law creep or diffusional flow (m2/s) 2.20, 2.30 Flow strength (in shear) for obstacle cutting at 0 K (MN/m2) 2.6, 2.7 , Tracer diffusion coefficients for components A and B (m2/s) 2.27, 2.28 Lattice resistance of Peierls stress (in shear) at 0 K (MN/m2) 2.10, 2.12 Chemical interdiffusion coefficient (m2/s) 2.28 Twinning stress at 0 K (MN/m2) 2.15 Grain size (m) 2.29, 2.30 Threshold stress for creep (MN/m2) 17.35 Diffusive thickness of a grain boundary (m) 2.30 , Chemical potential (J/atom) 17.27 Elastic energy of a dislocation (J/m) — , Interface potential barrier (J/atom) 17.24 Normal strain (rate); see Macroscopic variables — Activation volume (m3) 17.49 , Helmholtz free energy (J/mol) 2.6, 2.7, 2.10 , Atom fractions of A and B 2.27, 2.28 Free energy of twin nucleation (J/mol) 2.15 Atomic or molecular volume (m3) 2.17 Average dislocation velocity (m/s) 2.3, 2.5 Ionic volume (m3) 2.29 Average climb velocity (m/s) 2.17