Showing papers on "Hydrostatic stress published in 1981"

Radial Distribution Function and Structural Relaxation in Amorphous Solids

Abstract: A method of interpreting radial distribution functions (RDF) of amorphous metals is proposed in which the role of the local atomic structure is emphasized. It is found that the width and height of the peaks of the RDF are related to the second moment of the atomic-level hydrostatic stress distribution $〈{p}^{2}〉$. The results of this analysis are then used to explain the details of the changes that occur in the RDF when structural relaxation takes place. The theoretical ▵RDF is found to be in excellent agreement with the results of a computer study and previous experimental results. It is further proposed that changes in $〈{p}^{2}〉$ may be most easily accounted for in terms of changes in the density of the structural defects defined in terms of the local fluctuations in the hydrostatic stress. In this way the changes that occur in the structure of amorphous metal during structural relaxation, as represented by the RDF, may be explained in terms of the motion and annihilation of these structural defects. It is concluded that the number density of defects which could account for the observed changes in the experimental RDF is 10%. It is also found that while the hydrostatic stress distribution may be significantly changed during structural relaxation, the distribution of the atomic-level shear stresses remains unaltered.

Theoretical Study of the Structural Phase Transition in RbCaF3

Abstract: We have made a first-principles study of the structural phase transition at ${T}_{c}=193$ K in RbCa${\mathrm{F}}_{3}$, using interionic potentials derived by the Gordon-Kim approach, and a new extension of the quasiharmonic approximation for the free energy. The transition is caused by instability of a triply degenerate $R$-point vibration which leads to a coordinated rotation of the Ca${\mathrm{F}}_{6}$ octahedra. We find that, as the lattice contracts, the quasiharmonic frequency of the $R$-point vibrations becomes imaginary at approximately 1280 K: Below this temperature the static lattice energy, as a function of Ca${\mathrm{F}}_{6}$ rotation, has a double minimum. However, the quasiharmonic free energy has no minimum for finite rotations until $T\ensuremath{\lesssim}125$ K. Thus the present theory predicts that ${T}_{c}\ensuremath{\cong}125$ K (cf ${T}_{c}=193$ K, experimental). In the region between 125 and about 1280 K "nests" of modes about the zone edges have imaginary quasiharmonic frequencies. By a simple extension of the quasiharmonic theory their contribution to the free energy has also been included. We also predict that the melting temperature is approximately 1350 K, which agrees very well with the measured value of 1382 K. However, the predicted thermal expansion of the perovskite phase at room temperature is \ensuremath{\sim}17% lower than the observed value. This leads us to argue that the good agreement between theoretical and experimental melting temperatures is, in part, due to a cancellation between neglected anharmonic effects and certain deficiencies in the interionic potentials. We also find that, for the tetragonal phase, the calculated $\frac{c}{a}$ ratio and rotation angle for the Ca${\mathrm{F}}_{6}$ octahedra which minimize the static energy are in good agreement with measured values at low temperature. We also discuss certain more general implications of the present work. Specifically, we suggest that our results indicate that it may be more natural to regard the structural phase transition as arising from the "unfreezing" of the distortion associated with the lower-symmetry phase. Our results also provide a natural explanation for the apparently universal tendency of transition temperatures for zone-boundary instabilities to be raised by hydrostatic stress.

Possible explanation for unexpected departures in hydrostatic tension-fracture strain relations

Abstract: For materials which fail by void coalescence and growth, and possibly for solids failing by other mechanisms, it is commonly held that increasing tensile hydrostatic stress states at fracture produce lower strains to fracture. In tests on sheet material there is a marked change in strain ratio before fracture if plane-strain necking occurs. Then it may be shown that at the instant of fracture the current hydrostatic stress is most tensile for the greatest strains to fracture. These contrary observations may be explained by means of, path-dependent damage functions which involve not only the hydrostatic stress and effective strain but also the current strain ratio.

Fatigue failure criteria for combined cyclic stress

Abstract: Failure criteria for combined cyclic stress are represented in terms of parametric families of failure surfaces in stress space. Quadratic approximations and symmetry arguments are employed in systematic fashion to construct isotropic failure criteria for general three dimensional states of cyclic stress. Particular attention has been directed to the important cases of normal stress-shear stress (bending-torsion) and biaxial stress cyclings. It is shown that failure criteria for cycling with and without mean stress (reversed cycling) have different forms, the latter admitting simpler representations.

Existence and characterization of hydrostatic pressure in finite deformations of incompressible elastic bodies

Abstract: with pI and t prescribed and a~ c an. Conditions for the existence of minimizers of IT for certain choices of the form of a and of the classes of admissible motions on which II is defincd have been established by Ball [2] and aden and Kikuchi [9]. However. the proof that the minimization problem associated with II is in any way equivalent to a boundary-value problem in elastostatics requires that minimizers be characterized as solutions (or weak solutions) of the equilibrium equations. In the case of incompressible materials. the stored energy function determines the stress only to within a scalar-valued function r known as the hydrostatic pressure. Mathematically. p can be interpreted as a multiplier associated with the incompressibility constraint

Observations on the nature of micro-cracking in brittle composites

Abstract: The degree of micro-cracking in BeO-SiC composites due to internal stresses which arise from the mismatch in the coefficients of thermal expansion was monitored by measurements of the thermal diffusivity by the laser-flash technique. The experimental results indicated that micro-cracking was most extensive at approximately 30 and 80 wt% SiC and a minimum at nearly 50 wt% SiC. A theoretical analysis indicated that the magnitude of internal stress increases linearly with SiC content, so that the above observations cannot be attributed to a low internal stress state at ~ 50 wt% SiC. Instead, this effect can be attributed to changes in the statistical variables affecting the brittle fracture as well as the degree of internal stress relaxation. Both these factors are thought to be controlled by the nature of multiaxial stress distribution. At ~ 50 wt% SiC-content, due to anticipated non-hydrostatic triaxial stress distribution, residual stress relaxation is possible in both the components of the composite. However, at low and high fractions of SiC content, such stress relaxation is less likely to occur due to the expected hydrostatic stress distribution in one of the components.

Anisotropic Hardening Of An Initially Isotropic Porous Limestone

Abstract: Anisotropic Hardening of an Initially Isotropic Porous Limestone The work reported in this paper represents an attempt to explain the plastic behavior of a material such as porous rock that compacts or shows a volume decrease as it undergoes plastic deformation, and exhibits a yield strength dependence upon the hydrostatic pressure. Specifically, experimental results are reported for true-triaxial tests conducted on a porous limestone with the objectives of determining the yield surface in stress space, the flow rule, and induced anisotropy. The initial yield surface is obtained by compression tests, extension tests and a hydrostatic stress test. Permanent deformation occurs under a hydrostatic stress for the dry, porous limestone used in these tests, thus the initial yield surface forms a closed surface in stress space. The concept of normality of the strain increment vector with respect to the yield surface is investigated by using different loading paths in stress space. From these different paths of loading the normality principle can be verified. Furthermore, it is found that work hardening along one axis produces changes of the yield stress along the other axes so that a sample was initially isotropic becomes anisotropic as a result of the work hardening.

Triggering of earthquakes by the tidal stress tensor

Abstract: By superimposing the ω-and φ-type general solutions of the equilibrium equation without body force and particular solution of the equilibrium with tidal body force, the tidal stress tensor under free boundary conditions is obtained, and the change of the prineipal stresses and principal stress axes with depth is discussed. In the depth range 0-100km, the deviation of the direction of the principal stress axes in space, may reach a value as high as 10°(when θ=30°).The phase distributions of tidal hydrostatic stress, the maximum tidal shear stress and the tidal shear stress along the dislocation vectors of the faults as related to the origin times of the earthquakes have been studied for 70 earthquakes (Ms≥5.0) occurred in our country since 1957, having correct fault plane solutions.There is no apparent correlation between the phase of tidal, hydrostatic stress and the origin time of the earthquake (pr=0.58), but the maximum tidal shear stress has a certain effect on the triggering of the earthquakes (pr= 8.1×10-2). Tidal shear stress along the dislocation vectors of faults plays an even more prominant part (pr= 5.2×10-2). The phase of the maximum shear stress correlates well with the earthquakes of the oblique-slip type (pr=8.7×10-4).

Constitutive relations describing creep deformation for multi-axial time-dependent stress states

Abstract: A theory of primary and secondary creep deformation in metals is presented, which is based upon the concept of tensor internal state variables and the principles of continuum mechanics and thermodynamics. The theory is able to account for both multi-axial and time-dependent stress and strain states. The wellknown concepts of elastic, anelastic and plastic strains follow naturally from the theory. Homogeneous stress states are considered in detail and a simplified theory is derived by linearizing with respect to the internal state variables. It is demonstrated that the model can be developed in such a way that multi-axial constant-stress creep data can be presented as a single relationship between an equivalent stress and an equivalent strain. It is shown how the theory may be used to describe the multi-axial deformation of metals which are subjected to constant stress states. The multi-axial strain response to a general cyclic stress state is calculated. For uni-axial stress states, square-wave loading and a thermal fatigue stress cycle are analysed.

Crack‐tip plastic zones in glassy polymers under small‐scale yielding

Abstract: Two pressure-modified von Mises yield criteria were used for the determination of the plastic zones developed around cracks subjected to opening-mode loading conditions in glassy polymers. These criteria take into account the particular behavior of glassy polymers expressed by the dependence of their yield locus on the hydrostatic stress component and the difference in their tensile and compressive yield stresses. It was found that both criteria predict larger plastic zones than those obtained by the von Mises criterion which increase as the ratio of the compressive to tensile yield stress also increases. Furthermore, it was established that the differences in the predictions of plastic zones between the two criteria and the von Mises criterion increase with the Poisson's ratio of the material of the cracked plate.

Use of Weight Functions to Determine the Stress Intensity for a Cracked Thick-Walled Cylinder,

Abstract: : The use of weight functions to determine stress intensities for cracked specimens is relatively simple, and, while the initial derivation of a suitable weight function for some specimen geometries may be complex, the technique offers substantial benefits. In particular, stress intensities may be estimated for any initial stress distribution, and variations in stress intensity which result from the introduction of residual stress fields may be handled without the need to perform a full re-analysis for each case. The stress intensity at the tip of a crack which grows through a known stress field has been estimated using a weight function technique. The geometry considered is a thick-walled cylinder (Ro/Ri = 1.8) containing a longitudinal crack along the bore surface, and stress distributions corresponding to a variety of loading arrangements are used as examples. (Author)