Time-dependent Constitutive Equations Research Articles

Constitutive Equations for Tensile and Creep Behavior of a 9 Cr-1 MO Steel

This paper describes an investigation of the tensile and creep properties of annealed 9 Cr-1 Mo steel. Tensile tests were conducted at temperatures from 70 to 1050 F while creep tests were conducted at 750, 850, 950, and 1050 F with stresses from 4 to 52 ksi. From the tensile test data, a constitutive equation was developed for the stress-plastic strain relationship. This equation was based on a two-stage hardening mechanism and combined power law and exponential functions. From the creep test data, isochronous stress-strain curves were constructed out to 104 hr. These curves were extrapolated to 105 hr and to lower stresses using a parametric analysis procedure. Additionally, a creep constitutive equation capable of describing the total creep curve, including the tertiary region, was developed. This equation, having three stress and temperature dependent parameters predicted creep curves which were in good agreement with the actual curves. Both the time-independent (tensile) and time-dependent (creep) constitutive equations are suitable for use in finite element stress analysis computer programs.

Analytical Determination of Pressure on Formwork

A method is presented for determining the distribution of form pressure during the pouring of a vertical slab from a chemically hardening material such as concrete. The pressure distribution against the form surfaces results from the interaction of gravity with the progressive hardening and shrinkage of the material. Essential aspects of the formulation include time-dependent constitutive equations for the solidifying material which incorporate the effects of shrinkage, and a transformation to a moving coordinate system which handles the motion of the pouring surface. Hardening occurs as the consequence of the conversion of the material from an initial liquid-like condition into an elastic solid, where intermediate states during hardening are represented by a mixture of two components having the initial and final properties of the solidifying material. Graphical comparisons of results obtained from the analytical formulation are shown and examined in relation to experimental data and recommended design practice.

125. Time-dependent constitutive equations for RVD graphite at elevated temperatures

125. Time-dependent constitutive equations for RVD graphite at elevated temperatures

Migration of Particles to a Hole Wall in a Drilling Well

Abstract The rate at which a particle will migrate from the rotating drill pipe to the hole wall was calculated as functions of the mud properties, pipe rotational speed, and hole size. The information can be used to estimate the relative carrying capacity of one mud compared to another Then the changes that need to be made when a hole. is not cleaning can be determined. An adaptive control process for field use is suggested Two major simplifying assumptions are that axial flow does not influence the liquid viscosity and that the viscous resistance to particle movement in the radial direction is proportional to the particle's velocity. The calculations assume a power model liquid, spherical cuttings, and concentric pipe in a round hole. A concept of "theoretical zones" where the calculations are valid interspersed with areas where the particles are uniformly redistributed, is used to relate the simplified theory to actual hole conditions. Introduction This theoretical study was conducted to improve the understanding of hole cleaning and how various drilling conditions and muds influence the ability to lift cuttings to the surface. The primary object of the study was to see how fast a particle might move from the drill pipe to the hole wall and how factors of drilling and liquid properties influence the rate of radial movement. The rate of movement may be important as the centrifugal force set up by the rotating drill pipe tends to force the particle toward the hole wall, an area of low vertical mud velocity and, therefore, poor lifting. PRIOR WORK Removal of cutting from a drilling well by circulating a structured liquid such as bentonite-water is a physically complex operation. Explicit prediction of the path of a cutting requires the ability to calculate the velocity of the particle relative to the liquid and the velocity field of the liquid. Various phases have been investigated. Williams and Bruce showed experimentally the path of particles in a laboratory wellbore and developed slip correlations for turbulent flow. Many investigations have been made for drag coefficients of particles settling in stationary Newtonian liquids under conditions of laminar and turbulent flow. The only work with inclined discs is with very low Reynolds numbers, an area of little interest in hole cleaning. Some investigations with drag coefficients in non-Newtonian liquids and the only work with structured liquids indicates the drag coefficient is different in stationary liquid from the drag coefficient in moving liquid. Various methods of predicting slip velocities are available, as well as correlations of hole cleaning based on experimental well tests. Bentonite drilling muds are generally a shear thinning liquid in which stress-rate relation at a fixed time depends on past history. Most rheological work is done under steady-state conditions to show the influence of chemical additives and temperature changes. There has been little work on dynamic response such as has been done with viscoelastic liquids to select time dependent constitutive equations or experiments with shear in two directions. Most pressure drop calculations for field use are based on annular flow without rotating drill pipe, and radial migration of particles and angular liquid velocities are neglected. Savins and Wallick calculated annular pressure drops, including rotating drill pipe, for a liquid described by a three constant Oldroyd model. The calculations were based on a viscosity relation for one-dimensional flow but used the vector sum of the longitudinal and angular components of stress to calculate the viscosity. This procedure was shown correct for a viscoelastic liquid. SPEJ P. 147ˆ