Showing papers on "Hydrostatic stress published in 1972"

A general treatment of plastic anisotropy under conditions of plane strain

Abstract: In this paper, the plane strain of a non work-hardening plastic material having a general yield criterion that includes the effects of anisotropy and hydrostatic stress is considered. The stress and velocity equations are reduced to canonical form and an expression for the rate of plastic work is given. Special attention is given to the cases of zero body-force and of a yield condition which is independent of hydrostatic pressure, and the results are discussed in relation to the particular problem of a smooth rigid die indenting a half-space.

Effects of Hydrostatic Stress on the Yielding of Cold Rolled Metals and Fiber-Reinforced Composites

Abstract: Elastic limit denotes the point in a tensile stress-strain curve, beyond which plastic strain occurs. Under combined loadings, the combinations of different stress components giving the start of plastic strain define initial yielding. After the specimen is loaded beyond the initial yielding, and then unloaded, the different combinations of the stress components to give further plastic strain define a SUbsequent yielding. These combinations of stress components plotted in a space with stress components as coordinates give a surface in this space known as yield or loading surface. The relation of these stress components is known as a criterion of yielding. An ordinary piece of poly crystalline metal is composed of many individual crystals. Single crystal tests [1-4 ) show that crystals slide under stress along certain crystallographic directions on certain crystal planes. This slip depends on the shear stress in this direction on this plane and is independent of the normal pressure on this sliding plane. This sliding causes plastic strain. The orientations of crystals in the metal are random. The polycrystal initially has no particular preferred direction nor particularly preferred plane. This polycrystal is initially isotropic and, hence, the initial yielding depends only on the magnitudes of the three principal stresses and not on their directions. This ihitial yield may be expressed in the form

The Effect of Hydrostatic Stress on Creep and the Creep Rupture of Polycrystalline Metals at Elevated Temperatures

Abstract: In the present paper, the analytical and experimental studies on tensile creep of polycrystalline metal under hydrostatic pressure at elevated temperatures were presented, in a series of studies on the influence of hydrostatic stress on plasticity and fracture laws of the metals. From the tests performed of commercial pure aluminum at 200°C, the following conclusion has been derived.(1) The effect of hydrostatic pressure on minimum creep rate at elevated temperature is more intensive than that on tensile flow stress at the same temperature. This is considered to be mainly due to the pressure on the diffusion of vacancies in the creep process.(2) In order to predict the effect of hydrostatic stress on the creep rupture of the metal at elevated temperature from that on the steady state creep at the same temperature, it is required that the pressure effect on the structural change during the tertiary creep, such as inhibition of growth of void as the result of reduction in the diffusion of vacancies will be taken into consideration.

A Diffusion Model for the Effect of Applied Stress on Void and Loop Growth

Abstract: The effect of a general state of stress on swelling has been considered in a theoretical void growth model. Angular-dependent loop growth has been incorporated into the model in order to include the effects of shear stress. It has been found possible to consider the effects of stress on void and loop growth as a relatively simple deformation process. We define the stress effect as follows: ∈ i = (d∈ i /dt)σ- (d∈ i /dt)σ = 0 where (d∈ i /dτ) σ = 0 is the strain rate associated with the isotropic swelling that would occur in stress-free conditions. For an applied stress having both hydrostatic and shear components, the hydrostatic component provides a driving force for isotropic volume swelling and the shear component causes a shape change. The total deformation process (stress-induced volume increase and shear) may be represented by the relation: ∈ i = κ [σ i + ν(σ j + σ k )] where the σ's are applied tensile stresses and the i,j, κ are the principal axes. K and ν are two material parameters that depend upon microstructure (dislocation density, void number density, and void size) but do not depend upon flux. K depends strongly on temperature whereas ν is independent of temperature. The extent to which plastic flow must accompany stress-assisted swelling is governed by the parameter V. As ν approaches ½, the deformation process becomes pure shear. It is found that the value of ν is bounded and lies between -1/3 and +½. Thus, except under the application of purely hydrostatic stress, stress-assisted swelling cannot be completely shear-free. When transmission electron microscopy (TEM) data for neutron-irradiated solution-treated Type 316 stainless steel were used, the values of ν were found to lie between 0 and 0.5. For cold-worked steels, ν is expected to lie in the upper part of the range just given. The significance of the present results becomes evident in the analysis of fuel pin profiles. For isotropic swelling with no plastic flow, the fractional change in fuel pin diameter is 1/3 the fractional isotropic volume change. However, for stress-assisted swelling, the relation may be much different and depends upon the parameter ν. For a biaxial stress state of the type that occurs in pressurized cylindrical tube, for example, ΔD/D 0.7 when ν = 0.1, whereas ΔD/D 1.4 ΔV/V when ν = 0.3.

Nonlinear variation of the induced birefringence of vitreous silica with uniaxial stress to 7 kbar

Abstract: The induced birefringence of vitreous silica for λ 5893 A was measured at uniaxial stress to about 7 kbar with a Babinet compensator. Nonlinear elasticity was used to account for specimen dimension changes. The variation of birefringence with stress is linear within the limits of experimental error, whereas its relation to Lagrangean strain is nonlinear. This is in contrast to the nonlinear piezo‐optic but linear strain‐optic behavior observed in vitreous silica under hydrostatic stress. The difference p‐ q of the Neumann strain‐optic constants and its stress and strain derivatives is also presented.

Applicability of a linear vicoelastic characterization for asphalt concrete

Abstract: The objective of this investigation was to determine the validity of using a linear viscoelastic constitutive equation to characterize asphalt concrete in the design of pavement systems. The investigation was conducted in two phases. In the first phase, creep tests in compression, tension and torsion, and repeated loading tests were performed on cylindrical specimens of asphalt concrete for various axial loads at different confining pressures and different temperatures to determine the response functions, and establish the degree of linearity and evaluate the time-temperature equivalence of the response. On the basis of these tests creep functions and complex modulus values for the asphalt concrete were determined. The second phase of the investigation was conducted to check if the characterization of the asphalt concrete obtained in the first phase of the program could be used to predict the behaviour of asphalt concrete under stress states which are similar to those that might exist in actual pavements by testing beams and slabs and a Winkler foundation. In this paper only the results of the first phase of the investigation are presented and discussed. It was found that the type of test (e.g. uniaxial, triaxial, torsion) influences the magnitude and nature of the viscoelastic functions. For one type of test, the results obtained are consistent. Based on the results of tests under hydrostatic stress states it was observed that the samples exhibited a substantial degree of anisotropy. It is hypothesized that this is due to the method of compaction utilized in preparation of the samples. It was also observed that the volumetric response of asphalt concrete was time dependent and that the usual assumption of incompressibility was questionble. Thermortheological simplicity was found to be a satisfactory assumption for uniaxial compression tests. In order to reduce the influence of stress level, stress state, anisotropy and other effects to a level that will make linear isotropic viscoelasticity an acceptable characterization of asphalt concrete, it has been suggested that a limit be placed on the strain level that can occur in the asphalt concrete. This was done using the experimental data on the basis of a subjective evaluation. It is strongly recommended that sensitivity studies on the basis of pavement performance be conducted to determine the acceptable variations for ideal material characteristics and hence establish the degree of refinement required in the characterization of materials for the design of pavement systems. /AUTHOR/

Effect of hydrostatic pressure on the strength properties of polymer materials

Abstract: On the assumption that the strength characteristics of homogeneous polymer materials depend on the specific volume, equations are derived for the dependence of the strength or high-elastic limit on the hydrostatic component of the stress tensor and temperature. The ultimate strengths in simple tension, compression and shear are considered in relation to brittle and plastic fracture.

Torsional Creep of Polycrystalline Metallic Materials under Hydrostatic Pressure at Room Temperature

Abstract: It has been confirmed by the present authors, as the result of the experimental studies they performed of the creep of pure aluminum and pure iron in the normal temperature range below 0, 5Tm, 1Tm being the absolute melting temperature, that the creep rate of polycrystalline metals tends to decrease with the increase in hydrostatic pressure regardless of such a normal temperature range in which its diffusion mechanism is not to be expected theoretically3)13). It has also been confirmed that the effect of hydrostatic pressure on the flow stress of metals can be described satisfactorily by assuming the formulation of yield condition including the first invariant of stressJ1=σkk, (a) J2'=k(k2+CkJ1+DJ12)1/2, and further that the qualitative explanation of creep rate decreasing with hydrostatic pressure of metals subjected to constant load is given uniformly by this yield condition from a side view of continuum mechanics.Secondly, however, in order to understand better the relationship of hydrostatic pressure to the deformation mechanism in plasticity and creep of metals it is necessary to evaluate quantitatively the difference in the intensity of the influence of hydrostatic pressure between these deformations.In the present study, therefore, it has been aimed at to evaluate numerically the change in the structure of metallic materials, i.e. the effects of hydrostatic pressure on the magnitude both of their plastic and of their creep deformation, and with these ends in view, various hydrostatic tests, creep tests and simple torsion tests, of polycrystalline materials, e.g. pure aluminum, pure iron and pure zinc, have been carried out under several levels of hydrostatic pressure at room temperature. It is to be noticed that the torsion test is found effective in the investigation because its stress condition does not cause the change in the form of the test specimens, nor does it enter into the hydrostatic stress component.The results are summarized as follows:(1) There has been little influence of hydrostatic pressure on the plastic flow stress of pure aluminum but on pure iron there has been effect to some extent after leaving plastic defomation, while remarkable influence appears on pure zinc in an early stage of deformtion. On the whole, such effects grows gradually with advanced deformation.(2) The shape of the yield surface that varies with plastic deformation is determined by replacing the parameters both C and D in the Eq. (a) with numerical values. The calculated values of C and D, without regard to the kind of metal, are nearly zero during the shearing strain between zero and 30% but increases rapidly with the advanced shearing strain.(3) On the creep of metals at room temperature, the confining pressure has a distinctive effect of decreasing the creep rate. The numerical values of C and D in the creep process of pure zinc agree with those in their static plastic flow respectively. Therefore, it is clear that the intensity of the influence of hydrostatic pressure on the creep rate is of the same magnitude as that on the static plastic deformation.

Analytical Study Of Pressurized Elliptical Cavities

Abstract: Plane strain stress distribution and stability analysis of an elliptical cavity in geological media under internal pressure and in situ stress was conducted using finite element analysis. The investigation was conducted for infinite isotropic and transversely isotropic elastic continuum and infinite elastic-elastoplastic isotropic continuum bearing linear (Coulomb) or nonlinear (Torre) forms of Mohr-Coulomb yield envelopes. Both these envelopes are sensitive to hydrostatic stress and neglect the effects of intermediate principal stress. Incremental constitutive relations were used in the elastic-plastic analysis. Failure or instability in the cavities was studied in terms of failure initiation. Suitable maximum tensile strain and maximum shear strain criteria were formulated and used to indicate failure initiation. One of the more significant results was that an elliptical cavity would be unstable both above and below certain critical internal pressures. (37 refs.)