Mean Stress Distribution Research Articles

Oil reservoirs in foreland basins charged by thrustbelt source rocks: insights from numerical stress modelling and geometric balancing in the West Carpathians

Abstract The West Carpathian thrustbelt advanced northeastwards over the European Platform. Its thrust sheets comprise sediments of the Early Cretaceous rifts that evolved on a passive margin of the European Platform, the Late Cretaceous-Paleocene basins formed by rift inversion, and the Eocene-Oligocene flexural basin. Geochemical analyses established a clear link between pooled oils in the foreland and the Oligocene Menilite Formation inside the thrustbelt. In order to understand the driving forces for this oil migration scenario, finite-element models of fault-propagation and fold-bend folds are used to study the mean stress distribution in the thrust sheets and the foreland. Mean stress has a profound control on the pore fluid pressure through the relationship affected by sediment porosity, and sediment skeleton and fluid compressibilities. Modelling results suggest that only fault-propagation folds are capable of generating foreland-directed mean stress gradients as they are characterized by a large foreland area of decreased mean stress, by coupled increased/decreased mean stress areas on advancing/receding sides of the ramp tip, and an overall mean stress decrease inside the thrust sheet in the direction towards the foreland. This interpretation is in accordance with the dominant fold-and-thrust style in the Western Carpathians inferred from balanced cross-section restoration. It shows that frontal fault-propagation folding was active during the late Oligocene-Early Miocene, providing an effective tectonic driving force for hydrocarbon migration from source rocks inside the thrustbelt towards reservoirs in the foreland.

Influence of particulate reinforcements on 6061 materials in extrusion modeling

The comparative extrudabilities of 6061 alloy, 10% Al 2 O 3 /6061 and 20% Al 2 O 3 /6061 were estimated by finite element methods with DEFORM™ software. The direct axisymmetric extrusion was modeled with a square die and sticking friction in tooling that was rigid and preheated. The materials were treated as rigid-plastic with dependence of flow stress on temperature and strain rate determined by torsion testing at 300–500 °C and 0.01–5 s −1 . The extrusion ratio, billet temperature and ram speed were varied to study their effects on the load–stroke diagram and find equivalent conditions for alloy and composites. In addition the distribution of velocities, strain, strain rate, temperature and mean stress were calculated and compared to physical simulation; the dependencies of their maximum values on the control parameters were examined. The distributions of the internal variables permit estimation of surface cracking and of extrudate microstructure. Comparison is made with modeling results from other materials.

Numerical simulation of the high Reynolds number slit nozzle gas–particle jet using subgrid-scale coupling large eddy simulation

Large eddy simulation (LES) model in which the effect of the particle existence on subgrid-scale flows have been taken into account is proposed. The kinetic energy of the subgrid-scale flow to obtain a turbulent viscosity coefficient of the subgrid-scale flow in the LES has been calculated in assuming that the interaction terms between the gas and particles, the turbulent production term and the viscous dissipation term were balanced with each other in the kinetic energy equation of the subgrid-scale turbulent flow. Using this model, three-dimensional Navier–Stokes equations and the Lagrangian particle motion equations are simultaneously solved to describe the high Reynolds number ( Re=10 4) gas–particle jet flow and the effect of particle existence on it. The calculated results of air and particle turbulent characteristics which are mean velocity, turbulent intensity and Reynolds stress distributions are in good agreement with experimental data measured by a laser Doppler velocimeter. The existence of particles usually reduces the grid-scale turbulence in the high Reynolds number developed turbulent jet. On the other hand, the particle existence which is some kind of flow disturbance produces grid-scale fluctuations in the initial and the transitional regions of the jet and then it increases the air turbulent intensity. When particle size is much smaller than the grid size, the particle existence reduces the subgrid-scale turbulence. However, when the product of the gas and particle relative velocity and the particle concentration gradient is very large, the particle existence is able to increase the subgrid-scale turbulence.

Extrusion Modelling of Aluminum Particulate Composites

Particulate Al matrix composites inexpensively fabricated into large billets by liquid metal mixing receive final fabrication into components by mechanical forming, notably at high temperatures to minimize cracking and particle-matrix degradation. A hot torsion project on alloys 6061, A356, 7075 and 2618 with 10 to 20% of Al 2 O 3 or SiC determined hot strength and ductility, constitutive constants and microstructural evolution. The substructure is very heterogeneous exhibiting regions of subgrains, non-cellular masses of dislocations and small highly misoriented cells. The modeling of extrusion of the various particulate metal matrix composites was conducted by finite element analysis to develop strain rate, mean stress and temperature distributions. The relative load-stroke curves and extrudability were compared.

Prediction of Fracture-Induced Permeability and Fluid Flow in the Crust Using Experimental Stress Data

The results of a series of two-dimensional photoelastic experiments on dilational jogs cut in PERSPEX™ sheets have been used to determine the second-order fracture patterns and fluid-flow network associated with tectonically loaded dilational jogs. The stress data derived from these experiments, orientation of the principal stresses, and the distributions and magnitudes of the differential stress and the mean stress are used in combination with the theory of brittle failure to predict the orientation, approximate distribution, and likelihood of formation of second-order brittle structures associated with the modeled jog geometries. The orientations of brittle structures predicted compare favorably with those found in natural large-scale dilational jogs, such as the Vienna basin, the Dead Sea basin, and the Brawley jog (California), as well as in mesoscopic examples and those formed in analog models. From the experimental results it is possible to determine areas of high and low mean stress, and by assuming that fluid migration occurs in response to mean stress gradients it is possible to predict the fluid migration associated with the development of a dilational jog. In this way, it is possible to show that the intrajog region of underlapping and neutral dilational jogs will not be favorable sites for fluid ingress. When the jog has an overlapping geometry, the intrajog region is a mean stress low and, consequently, fluid ingress into the jog is more likely. In addition, as the fault overlap increases the distribution of mean stress, and thus the associated fluid flow, in the intrajog region increases in complexity. By combining the predicted second-order fracture patterns and the mean stress distribution derived from the photoelastic analysis, it is possible to construct a map showing sites of likely fluid accumulation and mineralization. These sites correspond to regions of low and high fluid throughflow, respectively. Predictions based on this model compare well with natural examples of fluid accumulation and mineralization in dilational jogs.

Application of the finite element method to powdered metal compaction processes

A plasticity theory is summarized for a powdered metal compact. The constitutive equation is applied to the variational principle and its discretization is developed. The discretized formulation has been implemented into the finite element code and the program has been tested and applied to simulations of axisymmetric die pressings with copper powders. The simulation includes single-action and double-action pressings of solid cylinders as well as cylindrical rings. Predictions are made for density distributions, mean stress distributions, load-stroke relationships, average density as function of height, average density as function of radius, pressure distributions along die-walls and punches, and force fraction transmitted to the stationary punch. Some of the predicted solutions are compared with experimental observations from the literature. It was found that the results from the finite element analysis, in general, agree very well with the experimental observations.

Analysis of forward extrusion by the grid method. Application of Lagrange's method of undetermined multipliers.

The usual gird method has the serious defect that the stress solution depends on the numerical integration path of stress derivatives. In this study, a new method, independent of the numerical integration of the stress derivatives, is developed for steady state axisymmetric extrusion; that is, on every small plastic region, mean stress distribution is approximated with a second order polynomial with respect to r and z, and considering the continuity of mean stress, unknown coefficients of all of these polynomials are evaluated with the least squares method of the mean stress derivatives. Lagrange's method is applied to this procedure together with the unit division method, which is similar to that used in the finite element method and as a result, the stress solution can be uniquely determined in a short calculation time.

Analysis of forward extrusion by grid method (Application of Lagrange's method of undetermined multipliers)

Usual grid method has such serious defect that the stress solution depends on the path for numerical integration of stress derivatives. In this study, a new method which derives stress distributions independently of their numerical integrations is devised for steady state axisymmetric extrusion ; that is, on every small plastic region the mean stress distribution is assumed with second order equation with respect to γ and z, and considering the continuity of the mean stress, the unknown coefficients of all of those assumed equations are evaluated with the least squares method of mean stress derivatives. The above Lagrange's method is applied to this procedure, together with the unit division method, for shortening the calculation time, in a way which is similar to that used in the finite element method. As a result, the stress solutions can be uniquely determined in a short calculation time.

Polarization scrambling by the glass windows of a Raman cell up to 18 kbar

The scrambling of the polarization of a light beam by the glass windows of a 25-kbar hydrostatic Raman cell increases quadratically with the pressure up to 18 kbar, as expected from the theory of the photoelastic effect. When the laser beam passes along the cylinder axis of the window, the degree of scrambling by one window is 0.0022 at 18 kbar, but increases greatly as the laser beam shifts from the center of the window. The theory of the photoelastic effect was specialized to small depolarizations, and from it the mean stress distribution in the window was determined empirically from the degree of scrambling as a function of the radius. The effect of the scrambling on a Raman measurement, which needs a much larger aperture for the exit window than for the exciting laser beam, was estimated for two 90°-scattering geometries by using the empirical stress distribution. The geometry Z(YZ)Y is particularly suitable because the inlet window produces a weak X-polarized signal, which is largely rejected by the analyzer, and the strong Y-polarized signal produces no scattering along the Y direction. The calculated degree of scrambling is <10−3 at 18 kbar. The depolarization of the symmetric stretching bands of carbon tetrachloride up to 1 kbar and of carbon disulphide up to 10 kbar has been measured and confirms this conclusion.

The influence of mean stress and amplitude distribution on random load fatigue crack growth

Random load fatigue crack growth tests have been conducted on a low alloy steel, Q1N, under varying conditions of mean stress and probability density function (pdf). The results show that Q1N is insensitive to the pdf, but that a mean stress effect is measurable. This mean stress dependence is not found in constant amplitude tests on the same material. A modified form of the Fonnan equation was found to fit the data adequately.

The finite element method in tectonic processes

The powerful method of finite elements permits almost all problems of stress analysis and analysis of finite deformations of geological structures to be presented in a mathematical form suitable for solution on a digital computer. A plane strain analysis of a boudinage structure in elastic materials brings out the barrel shape so characteristic of many natural boudins. The fill-in of newly grown minerals in the gap between boudins is afforded a plausible explanation from the mean stress distribution of the structure. Laterally compressed multilayers of rocks tend to develop folds with a characteristic wavelength. Beginning with folds of the dominant wavelength in a five-layer system with a small amplitude/wavelength ratio, the successive changes in geometry and stress distribution were analysed for small increments in nodal velocities. The geometry of folds and the stress distribution was found to be very sensitive to changes in compressibility of the materials involved. An application of the method to isostatic adjustment was tested on a two-layer system consisting of a light layer with sinusoidal deflection at its free surface overlying a dense half space. The flattening of the free surface and the generation of a second wave at the interface as functions of time were considered to agree quite satisfactorily with theory and model experiments. Most of the characteristics of the mid-Atlantic ridge indicate that the mechanism of spreading should be searched for at a shallow depth. Modelling a cross section of the ridge down to 100 km depth gives a surface deflection undulation with sagging and thinning of the basement layer of about 1 cm/y. High values of tensile and shear stresses are concentrated in the basement layer at the crestal zone. The theory of ridge formation caused by the injection of buoyant bodies relatively close to the surface of the ocean bottom and now slowly spreading laterally finds strong support in the results of the finite element analyses.

Perturbation Solution of Plane Stress Problems in Anisotropic Elasticity

The problem on the approximate determination of the mean stress distribution across a thin crystal plate by the method of perturbation is considered. The plate is free from surface tractions and body forces, but is stressed under the action of prescribed self-equilibrating edge forces. The anisotropic elastic compliance matrix $S_{IJ} $ is written in the form $S_{IJ} = S_{IJ}^0 + \epsilon S_{IJ}^ * $, where $S_{IJ}^0 $, is the isotropic elastic compliance matrix nearest to $S_{IJ} $. A power series expansion in $ \epsilon $ is then assumed for the Airy stress function from which the stress components may be derived. The problem of the zeroth order in $ \epsilon $ is that of an isotropic plate. The perturbed problems satisfy nonhomogeneous differential equations and vanishing stress boundary values. The 7090/94 Ibsys Formac programming is used to handle some of the tedious algebraic and analytic routines involved in developing the perturbation solutions. Application of the perturbation method is carried out explicitly for a circular plate.

鋼の疲労変形について(続報)

In the preceeding report, the authors explained the fatigue deformation of various kinds of steels. In the present report, the authors intend to explain how the fatigue deformation should be treated analytically in view of distribution of stress within the specimen.Results obtained are as follows:(1) A useful equation was introduced for expressing the magnitude of fatigue deformation under uniform distribution of stress. Two constants, included in this equation, may be determined from the fatigue test and take the same values in both cases of normal and shear stresses.(2) It was cleared that the mean stress distribution within the specimen after fatigue deformation under uneven stress distribution can be obtained by calculation by using the above equation. By this treatment, the magnitude of fatigue deformation in this case can be also determined.(3) Analytical treatment to obtain the magnitude of fatigue deformation was introduced for the specimens having residual stress or being work-hardened by prestressing.(4) Analytical results have shown favorably agreement with the experimental ones for every cases of performed experiments.

疲労と応力分布

This investigation was performed to clarify the diagram of endurance limit of notched specimens under repeated torsion. The materials used were of two kinds of carbon steels, and specimens had V-grooves of two or three kinds of sharpness.Results obtained are as follows:(1) In this experiments the authors defined the fatigue limit as a maximum reversed stress at which cracks do not yield at the root of notch. Such a determination of fatigue limit is more appropriate theoretically than such case that a maximum reversed stress, at which the specimen does not break down, is defined as the fatigue limit. By such determination, the diagrams of endurance limit under reversed torsion were procured for a few notched specimens.(2) The effect of mean stress in the diagram of endurance limit was much considerable in this experiments than in early experiments basing upon whether the specimen break down or not. Further it was cleared from this results that the diagram of endurance limit of notched specimens under reversed torsion becomes a line drawn from the completely reversed fatigue limit, on the ordinate, to a point on the abscissa, obtained from dividing the torsional strength of unnotched specimen into the stress concentration factor α.(3) Above tendency was understood from consideration of the distribution of mean stress in the specimen during the fatigue tests.

疲労と応力分布

This investigation was made in order to compare the diagram of torsional endurance limit of solid specimen with that of thin-walled hollow specimen. And it was clarified that the stress amplitude at the endurance limit is scarcely affected by the mean stress in the solid specimen as well-known and it decreases fairly with the increasing of the mean stress in the hollow specimen. This dissimilarity of the diagram of endurance limit due to the form of specimen was explained from variation of the distribution of mean stress during the fatigue test in the solid specimen.