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The phenomenological equation which describes Harper–Dorn creep is = where ρ 0 is dislocation density (constant for Harper–Dorn creep), D v is the diffusivity through the volume of the material, G is the shear modulus and b is the Burgers vector, σ s, and n is the stress exponent which varies between 1 and 3.
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
F.R. Larson and J. Miller proposed that creep rate could adequately be described by the Arrhenius type equation: = / Where r is the creep process rate, A is a constant, R is the universal gas constant, T is the absolute temperature, and is the activation energy for the creep process.
Constitutive equations for the type of mechanism have been developed for each deformation mechanism and are used in the construction of the maps. The theoretical shear strength of the material is independent of temperature and located along the top of the map, with the regimes of plastic deformation mechanisms below it.
Development of thermo mechanical constitutive equations for the mathematical description of the deformation behaviour of metals and rubber (theory and experiments). Professional results: 1953: Constitutive equations for creep and plasticity on the basis of a "fraction model". 1957: Two reaction theory for induction motors.
The equations that govern the deformation of jointed rocks are the same as those used to describe the motion of a continuum: [13] ˙ + = ˙ = = ˙: + = where (,) is the mass density, ˙ is the material time derivative of , (,) = ˙ (,) is the particle velocity, is the particle displacement, ˙ is the material time derivative of , (,) is the Cauchy stress tensor, (,) is the body force density ...
Stress Intensity Equation. As the fibrils in the crack begin to rupture the crack will advance in either a stable, unstable or critical growth depending on the toughness of the material. To accurately determine the stability of a crack growth and R curve plot should be constructed. A unique tip of fracture mode is called stick/slip crack growth.
The standard linear solid (SLS), also known as the Zener model after Clarence Zener, [1] is a method of modeling the behavior of a viscoelastic material using a linear combination of springs and dashpots to represent elastic and viscous components, respectively.