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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: r = A ⋅ e − Δ H / ( R ⋅ T ) {\displaystyle r=A\cdot e^{-\Delta H/(R\cdot T)}} Where r is the creep process rate, A is a constant, R is the universal gas constant , T is the absolute temperature , and Δ H {\displaystyle \Delta ...
L. M. Kachanov [5] and Y. N. Rabotnov [6] suggested the following evolution equations for the creep strain ε and a lumped damage state variable ω: ˙ = ˙ ˙ = ˙ where ˙ is the creep strain rate, ˙ is the creep-rate multiplier, is the applied stress, is the creep stress exponent of the material of interest, ˙ is the rate of damage accumulation, ˙ is the damage-rate multiplier, and is ...
The constitutive relation is expressed as a linear first-order differential equation: = + ˙ This model represents a solid undergoing reversible, viscoelastic strain. Upon application of a constant stress, the material deforms at a decreasing rate, asymptotically approaching the steady-state strain.
Schematic diagram of Burgers material, Maxwell representation. Given that one Maxwell material has an elasticity and viscosity , and the other Maxwell material has an elasticity and viscosity , the Burgers model has the constitutive equation
Creep is the tendency of a solid material to slowly move or deform permanently under constant stresses. Creep tests measure the strain response due to a constant stress as shown in Figure 3. The classical creep curve represents the evolution of strain as a function of time in a material subjected to uniaxial stress at a constant temperature.
Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads.