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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 ...
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.
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.
There are many different models that have been developed in an attempt to understand and explain TMF. This page will address the two broadest approaches, constitutive and phenomenological models. Constitutive models utilize the current understanding of the microstructure of materials and failure mechanisms.
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.
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.
Macroscopic material failure is defined in terms of load carrying capacity or energy storage capacity, equivalently. Li [2] presents a classification of macroscopic failure criteria in four categories: Stress or strain failure; Energy type failure (S-criterion, T-criterion) Damage failure; Empirical failure
Nabbaro–Herring creep does not involve the motion of dislocations. It predominates over high-temperature dislocation-dependent mechanisms only at low stresses, and then only for fine-grained materials. Nabarro–Herring creep is characterized by creep rates that increase linearly with the stress and inversely with the square of grain diameter.