Hydrostatic stress

About: Hydrostatic stress is a research topic. Over the lifetime, 1568 publications have been published within this topic receiving 37773 citations.

Optimal lower bounds on the hydrostatic stress amplification inside random two-phase elastic composites

Abstract: Composites made from two linear isotropic elastic materials are subjected to a uniform hydrostatic stress. It is assumed that only the volume fraction of each elastic material is known. Lower bounds on all r th moments of the hydrostatic stress eld inside each phase are obtained for r 2. A lower bound on the maximum value of the hydrostatic stress eld is also obtained. These bounds are given by explicit formulas depending on the volume fractions of the constituent materials and their elastic moduli. All of these bounds are shown to be the best possible as they are attained by the hydrostatic stress eld inside the Hashin{Shtrikman coated sphere assemblage. The bounds provide a new opportunity for the assessment of load transfer between macroscopic and microscopic scales for statistically dened microstructures. Keywords. A Composite materials; B Failure criteria; C Stress concentrations

A Hydrostatic Stress-Sensitive Relationship for Fatigue Under Biaxial Stress Conditions

Abstract: Failure criteria for elastic- and plastic-strain controlled fatigue under biaxial loading are proposed. The criterion for elastic strain is defined in terms of the equivalent strain from the distortion energy theory and that for the plastic part as the corresponding equivalent plastic strain, but modified to include a function of the hydrostatic stress component. These criteria are incorporated into the derivation of a relationship for fatigue life in terms of the principal strain amplitude, analogous to a conventional form for uniaxial loading. An analysis of some limited available data from the literature shows the potential predictive capability of the relationship.

The elastic stability, bifurcation and ideal strength of gold under hydrostatic stress: an ab initio calculation.

Abstract: In this paper, we employ an ab initio density functional theory calculation to investigate the elastic stability of face-centered cubic Au under hydrostatic deformation. We identify the elastic stiffness constant Bijkl as the coefficient in the stress–strain relation for an arbitrary deformed state, and use it to test the stability condition. We show that this criterion bears the same physics as that proposed earlier by Frenkel and Orowan and agrees with the Born–Hill criterion. The results from those two approaches agree well with each other. We show that the stability limit, or instability, of the perfect Au crystal under hydrostatic expansion is not associated with the bulk stiffness modulus as predicted in the previous work; rather it is caused by a shear instability associated with the vanishing rhombohedral shear stiffness modulus. The deviation of the deformation mode from the primary hydrostatic loading path signals a bifurcation or symmetry breaking in the ideal crystal. The corresponding ideal hydrostatic strength for Au is 19.2 GPa at the Lagrangian expansion strain of ~0.06. In the case of compression, Au remains stable over the entire pressure range in our calculation.

Stress sensitivity of porosity and permeability under varying hydrostatic stress conditions for different carbonate rock types of the geothermal Malm reservoir in Southern Germany

Abstract: In geothermal reservoir systems, changes in pore pressure due to production (depletion), injection or temperature changes result in a displacement of the effective stresses acting on the rock matrix of the aquifer. To compensate for these intrinsic stress changes, the rock matrix is subjected to poroelastic deformation through changes in rock and pore volume. This in turn may induce changes in the effective pore network and thus in the hydraulic properties of the aquifer. Therefore, for the conception of precise reservoir models and for long-term simulations, stress sensitivity of porosity and permeability is required for parametrization. Stress sensitivity was measured in hydrostatic compression tests on 14 samples of rock cores stemming from two boreholes of the Upper Jurassic Malm aquifer of the Bavarian Molasse Basin. To account for the heterogeneity of this carbonate sequence, typical rock and facies types representing the productive zones within the thermal reservoir were used. Prior to hydrostatic investigations, the hydraulic (effective porosity, permeability) and geomechanical (rock strength, dynamic, and static moduli) parameters as well as the microstructure (pore and pore throat size) of each rock sample were studied for thorough sample characterization. Subsequently, the samples were tested in a triaxial test setup with effective stresses of up to 28 MPa (hydrostatic) to simulate in-situ stress conditions for depths up to 2000 m. It was shown that stress sensitivity of the porosity was comparably low, resulting in a relative reduction of 0.7–2.1% at maximum effective stress. In contrast, relative permeability losses were observed in the range of 17.3–56.7% compared to the initial permeability at low effective stresses. Stress sensitivity coefficients for porosity and permeability were derived for characterization of each sample and the different rock types. For the stress sensitivity of porosity, a negative correlation with rock strength and a positive correlation with initial porosity was observed. The stress sensitivity of permeability is probably controlled by more complex processes than that of porosity, where the latter is mainly controlled by the compressibility of the pore space. It may depend more on the compaction of precedented flow paths and the geometry of pores and pore throats controlling the connectivity within the rock matrix. In general, limestone samples showed a higher stress sensitivity than dolomitic limestone or dolostones, because dolomitization of the rock matrix may lead to an increasing stiffness of the rock. Furthermore, the stress sensitivity is related to the history of burial diagenesis, during which changes in the pore network (dissolution, precipitation, and replacement of minerals and cements) as well as compaction and microcrack formation may occur. This study, in addition to improving the quality of input parameters for hydraulic–mechanical modeling, shows that hydraulic properties in flow zones largely characterized by less stiff, porous limestones can deteriorate significantly with increasing effective stress.