Theoretical Equation

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Norman Brown - One of the best experts on this subject based on the ideXlab platform.

  • A fundamental theory for slow crack growth in polyethylene
    Polymer, 1995
    Co-Authors: Norman Brown
    Abstract:

    Abstract The following Theoretical Equation has been obtained for measuring the rate of slow crack growth in polyethylene in terms of the crack opening displacement rate δ: δ = α y (1−y 2 ) 2 ηd o E 2 α 2 c K 4 Here δy is the yield point, K is the stress intensity, η is the intrinsic viscosity of the fibrils in the craze, E is Young's modulus, δc is the stress to produce a craze, d0 is the primordial thickness from which the craze originates and γ is Poisson's ratio. The Theoretical Equation agrees with the experimental observation: δCK4e-−Q/RT Thus, for the first time, the dependence of δ on stress and notch depth have been derived in fundamental terms and the physical parameters that constitute the factor C have been identified. The intrinsic viscosity η can be calculated from the theory using specific experimental data. For example at 42°C, the fibrils in a craze in a homopolymer have an intrinsic viscosity of 3 × 1011 Pas. This is much larger than the melt viscosity of the amorphous region, which is about 105–106 Pas. Thus, the resistance of polyethylene to slow crack growth is governed by the crystals and not by the amorphous region.

  • dependence of slow crack growth in polyethylene on butyl branch density morphology and theory
    Journal of Polymer Science Part B, 1991
    Co-Authors: Yan-ling Huang, Norman Brown
    Abstract:

    A Theoretical Equation has been developed to describe the rate of slow crack growth in an ethylen-hexene copolymer in terms of the spacing of the butyl branches, number of tie molecules, and the thickness of the lamellar crystal. The model of slow crack growth is based on the rate of disentanglement of the tie molecules. The rate of disentanglement varies inversely with the number of tie molecules and directly with the number of tie molecules that are not pinned by the branches

Hiroyoshi Murakami - One of the best experts on this subject based on the ideXlab platform.

  • Formulating stress corrosion cracking growth rates by combination of crack tip mechanics and crack tip oxidation kinetics
    Corrosion Science, 2010
    Co-Authors: Tetsuo Shoji, Zhanpeng Lu, Hiroyoshi Murakami
    Abstract:

    A Theoretical Equation for stress corrosion crack growth rate of austenitic alloys in high temperature water is reformulated based on crack tip asymptotic fields and crack tip transient oxidation kinetics. A general oxidation kinetic law is introduced, emphasizing the role of mass transport through solid oxide film at the crack tip. The effects of several parameters on crack growth rate are evaluated. The results are compared with available experimental data and other Equations. A good prediction of the effect of K on stress corrosion cracking growth rate of typical austenitic alloys in simulated light water reactor environments has been achieved.

Tetsuo Shoji - One of the best experts on this subject based on the ideXlab platform.

  • Formulating stress corrosion cracking growth rates by combination of crack tip mechanics and crack tip oxidation kinetics
    Corrosion Science, 2010
    Co-Authors: Tetsuo Shoji, Zhanpeng Lu, Hiroyoshi Murakami
    Abstract:

    A Theoretical Equation for stress corrosion crack growth rate of austenitic alloys in high temperature water is reformulated based on crack tip asymptotic fields and crack tip transient oxidation kinetics. A general oxidation kinetic law is introduced, emphasizing the role of mass transport through solid oxide film at the crack tip. The effects of several parameters on crack growth rate are evaluated. The results are compared with available experimental data and other Equations. A good prediction of the effect of K on stress corrosion cracking growth rate of typical austenitic alloys in simulated light water reactor environments has been achieved.

Zhanpeng Lu - One of the best experts on this subject based on the ideXlab platform.

  • Formulating stress corrosion cracking growth rates by combination of crack tip mechanics and crack tip oxidation kinetics
    Corrosion Science, 2010
    Co-Authors: Tetsuo Shoji, Zhanpeng Lu, Hiroyoshi Murakami
    Abstract:

    A Theoretical Equation for stress corrosion crack growth rate of austenitic alloys in high temperature water is reformulated based on crack tip asymptotic fields and crack tip transient oxidation kinetics. A general oxidation kinetic law is introduced, emphasizing the role of mass transport through solid oxide film at the crack tip. The effects of several parameters on crack growth rate are evaluated. The results are compared with available experimental data and other Equations. A good prediction of the effect of K on stress corrosion cracking growth rate of typical austenitic alloys in simulated light water reactor environments has been achieved.

Haim Kalman - One of the best experts on this subject based on the ideXlab platform.

  • acceleration pressure drop analysis in horizontal dilute phase pneumatic conveying system
    Powder Technology, 2018
    Co-Authors: Naveen Mani Tripathi, A Levy, Haim Kalman
    Abstract:

    Abstract In pneumatic conveying pipelines, there are specific periods and distances where particles start to accelerate or deaccelerate from specific velocity to steady state. This phenomenon attributes an additional loss of energy also invoke as acceleration pressure drop. The total acceleration pressure drop is defined by measuring the pressure difference between two points at the acceleration zone. The pressure drop of steady state flow for the same length is then reduced from the previous measurement to find acceleration only energy loss. Theoretical Equation of momentum change, a material physics, has used to explain the acceleration pressure drop in horizontal pipe. Experimental results have compared with the values of Theoretical Equation. Results indicated that predicted pressure drop is deviating from the experimental results. Hence, the problem was realized that there was need to precisely predict steady state (collision and friction) pressure drop in this zone, which in classical way of prediction would be used to do just by extrapolation up to the acceleration zone. Hence, a novel factor α has derived by the authors to accurately predict steady state loss in this zone. Experiments have conducted by using different kinds of materials (Bottom ash, Glass beads, Semolina etc.) at different conveying conditions. To view point of design engineers, contribution of acceleration pressure drop in total pipeline has demonstrated by comparing 10 m and 100 m long horizontal pipe. To a simplest case of conveying criteria, acceleration loss contribute 25% of total pipeline pressure drop for 10 m pipe and it reduced to 4% for 100 m pipeline. It has concluded that acceleration pressure drop, between any two velocities, would be predicted with momentum change Equation and there is need to accurately predict the steady state pressure drop by factor alpha (α) to predict total pressure drop in acceleration zone.