Showing papers on "Hydrostatic stress published in 1991"

The effect of non-singular stresses on crack-tip constraint

Abstract: The effect of the T-stress on the small-scale yielding field of a crack in plane strain conditions has been examined using modified boundary layer formulations. The numerically calculated stresses at the crack tip are represented by slip line fields for small-strain theory. Positive T-stresses cause plasticity to envelop the crack tip and exhibit a Prandtl field, corresponding to the limiting solution of the HRR field for a nonhardening material. Moderate compressive T-stresses reduce the direct stresses within the plastic zone by decreasing the hydrostatic stress by T. This causes a loss of J-dominance, and a stress distribution represented by an incomplete Prandtl field.

Electronic and optical properties of strained Ge/Si superlattices.

Abstract: We present a comprehensive theoretical study of short-period (Ge${)}_{\mathit{n}}$/(Si${)}_{\mathit{m}}$ strained-layer superlattices (SLS's) on Si and Ge [001] substrates, and the ``free-standing'' case, based on ab initio calculations. In order to compensate for the error in the excitation energies inherent to the local-density approximation, we add ad hoc potentials on the atomic sites. With this correction the calculated transition energies compare favorably with quasiparticle calculations and experiment. Special emphasis is placed on the orthorhombic nature of the SLS's with both n and m even, as reflected in both the energy-band structure and the dielectric response ${\mathit{varepsilon}}_{2}$(\ensuremath{\omega}), which is different for all three polarizations along the main axes. The effects of various substrates is examined for the occurring interband transitions, and in some cases reduced to a simple deformation-potential ansatz. A similar approach is taken for the splitting of the top of the valence band due to the internal uniaxial strain, which obeys a simple Vegard-type law; it is shown that confinement effects are negligible up to the values considered, i.e., n+m=12. The SLS's with a period of n+m=10 and sufficiently large strain in the Si layers have a direct gap; the transition from the top of the valence band to the lowest zone-folded conduction band at k=0, however, is only dipole allowed for special cases, such as the superlattices with n,m odd, i.e., for systems with no inversion symmetry. The (Ge${)}_{5}$/(Si${)}_{5}$ SLS is predicted to be a good candidate for optoelectronic devices. A reversal of the two lowest folded conduction states (dipole allowed and forbidden, respectively) is obtained when going from the n=4 to the n=6 case. Recent experiments on 10-monolayer SLS's are discussed in the light of our results.

Macroscopic variables governing the microscopic fracture of pearlitic steels

Abstract: The main macroscopic variables (in the continuum mechanics sense) which govern the microscopic fracture of notched samples of high strength steel are studied. The investigation, performed in inert and aggressive environments, offers therefore a quantitative relationship between the macroscopic and microscopic approaches to fracture, and allows a prediction of the size of the critical microstructural zone by numerical computation. The experimental programme included fracture tests on notched samples covering a broad range of geometries, in air and hydrogen environments. Fractographic analysis of the samples by means of scanning electron microscopy showed the microscopic topographies after failure. The numerical study consisted of elastic-plastic finite-element method computations to determine the distribution of macroscopic variables at the instant of fracture. The critical microstructural region for the tests in air develops by microvoid coalescence and its extension is governed by the stress triaxiality (the ratio of the hydrostatic to the equivalent stress). The tests in hydrogen show a specific microscopic fracture mode, called tearing topography surface whose asymptotic depth extends up to the location of maximum hydrostatic stress.

Calculation of hydrostatic and uniaxial deformation potentials with a self-consistent tight-binding model for Zn-cation-based II-VI compounds.

Abstract: A self-consistent tight-binding (SCTB) calculation of the deformation potentials is performed for ZnTe, ZnSe, and ZnS. Tight-binding bulk parameters reproducing photoemission and reflectivity experiments are given for these compounds. Then the strain effects are considered in the SCTB model, which allows the calculation of the hydrostatic deformation potential and of the nonlinear variation of the fundamental ${\mathit{E}}_{0}$ gap with the relative change in the lattice constant \ensuremath{\Delta}a/${\mathit{a}}_{0}$. The method is applied to the determination of the offset in the strained ZnS-ZnSe system. Results are in good agreement with experimental and other theoretical works.

The nature and determination of stress in the accessible lithosphere

Abstract: Results of stress determination show that stress state is characteristically heterogeneous and apparently unpredictable. Characterization of in situ stress state requires the determination of stress at individual locations and then spatial if not also temporal extrapolation. A variety of different measurements are used as a basis to determine stress state. Thus an adequate understanding of both the nature and origin of rock stress is essential. Representation of the lithosphere as a non-equilibrium, dissipative, dynamical system is shown to be consistent with observations of stress state and fluctuation of crustal displacement. The evolution of rock cores subject to a variety of perturbations in the laboratory can similarly be shown to be consistent with the evolution of a dissipative, dynamical system, driven in part by stored strain energy. These observations are inconsistent with the assumption that rock stress can be adequately represented by superposed traction and internally balanced stresses arising from quasi-static processes. The potential value of analyses of the dynamics of rock stress evolution is emphasized as a means to simplify the apparent complexity arising from present perceptions.

An anisotropic yield function for porous metal

Abstract: In this paper a new yield function for porous metals is proposed. In a similar manner to the function developed earlier by Gurson, yielding is shown to be dependent upon the hydrostatic pressure and volume fraction of voids. At the same time the present model allows for the effect of the spatial distribution of the voids. The model is developed assuming a three-dimensional regular array of ellipsoidal voids, but allowing for variations in spacing along each of the coordinate axes. Yield loci are calculated for two specific types of loading. The first case examined was that of biaxial stressing, and the analysis was reduced to the yielding of a plate with circular holes. The second stress state considered was uniaxial tension under a superimposed hydrostatic stress. For simplicity the voids were assumed to be spherical, but with variable spacing along each of the coordinate axes. A comparison is made with predictions from the Gurson model for each type of loading.

The influence of second-phase dispersions on shear instability and fracture toughness of ultrahigh strength AISI 4340 steel

Abstract: The resistance to shear instability and subsequent flow localization in ultrahigh strength (UHS) steels is dependent upon second-phase particle dispersions and the matrix strain hardening. The effect of the interparticle spacing λ to the geometric mean particle radius R ratio on the shear instability strain of UHS AISI 4340 steel is discussed. Experimental results indicate that a linear relationship exists between shear instability strain and this λ/R ratio. Microvoid nucleation softening associated with second-phase particles appears to be the dominant destabilizing event leading to fracture. The effect of the hydrostatic stress is also discussed. Experimental results of mode I and II fracture toughness testing are compared. A high hydrostatic tension field was found to be the cause for the lower mode I critical stress intensity factor (KIc) than mode II (KIIc). The high hydrostatic tensile stress field induced early microvoid nucleation which promoted flow localization leading to fracture. However, both mode I (KIc) and mode II (KIIc) critical stress intensity factors directly relate to the critical particle parameter λ/R12.

Singular Stress Fields near the Tip of a V-Notch in a Semi-Infinite Plate

Abstract: The stress fields near the tip of a V-notch have singularities. The order of the stress singularity is dependent on the deformation mode. For the I deformation, the stress singurarity is 1/r1-λ1, and for the mode II deformation, it is 1/r1-λ2. Thus, the stress fields around the singular point must be described in terms of two pairs of constants λ1, KI, λ1 and λ2, KII, λ2. Therefore, such numerical stress analysis, in which neither of the stress singularities is taken into account or only one stress singularity is taken into account, are generally not effectiue. In this study, a new method is presented for analyzing the problem of the V-notch in a semi-infinite plate. In this method, the two singular stress fields are taken into account at the same time, and the parameters KIλ1 and KII, λ2 are determined by the solutions of the equations. This method is also applicable to the problem of a composite plate because the stress singularity at the corner of the composite plate is essentially the same one as in the present problem.

Comparison of shear and tensile fracture in high strength aluminum alloys

Abstract: A comparison was made between tensile (mode I) and shear (mode II) fracture characteristics in high strength aluminium alloys (7075-T6 and 6061-T651) using a relatively new mode II fracture specimen to evaluate the critical stress intensity factor. The enlarged plastic zone during mode II fracture required that an increased specimen thickness be used for determining K Hc under a purely plane strain condition. Plane stress conditions prevailed in the mode II fracture of 7075-T6 with a specimen thickness less than 10 mm, while plane strain controlled mode II fracture at a thickness of 10 mm or greater. Fractographic analysis revealed a distinctive difference in the micromechanisms responsible for crack extension. Small dimples were observed only on the mode II fracture surfaces, resulting from a microvoid nucleation fracture mechanism. The mode I fracture surfaces showed a mixed distribution of dimple sizes resulting from a void growth fracture mechanism. Comparing the critical stress intensity factors, the shear mode of failure exhibited a substantially higher value than the tensile mode, resulting from the effect of the sign and magnitude of the hydrostatic stress state on the microvoid nucleation event. Zero hydrostatic tension in the mode II loading configuration helps delay microvoid nucleation, increasing the apparent toughness. The high hydrostatic tension resulting from a mode I loading configuration enhances microvoid nucleation which promotes crack propagation at relatively lower stress intensity factors.

Relaxation kinetics and relaxed stresses caused by interface diffusion around spheroidal inclusions

Abstract: The kinetics of relaxation by interface diffusion around spheroidal inclusions is discussed using the Eshelby method for ellipsodal inclusions and a free energy approach. The relaxation time for the process is derived in the case where the direction of an applied uniaxial stress is parallel to the rotation axis of symmetry of the speroid. The aspect-ratio dependence of the relaxanion time is derived. For prolate inclusions with large aspect ratios, the relaxation time increases proportionally to the aspect ratio. On the other hand, for oblate inclusions with small aspect ratios, the relaxation time becines constant as the aspect ratio approaches zero. The constant value of the relaxation time depends on the elastic moduli of the inclusion but independent of the elastic moduli of the matrix. The hydrostatic stress in the inclusion after the relaxation and its aspect-ratio dependence are also discussed. Although the relaxation time for a rod-like inclusion is longer compared with that for a disk-like inclusion, the relaxed stress in the former is much smaller than that in the latter.

The Proportional Anisotropic Elastic Invariants

Abstract: In this paper we illustrate the six proportional invariants of an orthotropic elastic material using the elastic constants for spruce as the numerical example. The proportional elastic invariants play a role in anisotropic linear elasticity similar to the roles played by the hydrostatic stress and strain and the von Mises stress and strain in isotropic elasticity

On the relationship between crack tip opening displacement at the initiation of a ductile tear in low carbon steel, hydrostatic stress, and void growth

Abstract: The effect of hydrostatic stress on the growth of voids from inclusions located near the tips of deep and shallow notches in three-point bend specimens is analysed using slip-line field theory and the Rice-Tracey void growth model. The analysis explains qualitatively the observed dependence of the crack tip opening displacement δi at the initiation of a ductile tear in low carbon steel on the hydrostatic stress. Although a plot of the experimental values of δi normalised by the inclusion spacing against the inclusion spacing/size ratio do not agree well with the theory, the plot is a promising means of determining experimentally the dependence of δi on hydrostatic stress for any particular steel.

The Effect of Superposed Hydrostatic Stress on the Mechanical Response of Metal-Matrix Composites

Abstract: The effects of a superposed hydrostatic stress on the deformation and failure behavior of whisker reinforced metal-matrix composites are analyzed numerically. The applied loading path consists of the imposition of a hydrostatic stress followed by tension along the fiber axis. Matrix cavitation is the sole failure mechanism analyzed and an elastic-viscoplastic material model is used that accounts for ductile fracture by the nucleation and subsequent growth of voids to coalescence. The effect of the distribution of the whiskers on failure is illustrated. A superposed hydrostatic stress is found to have a much greater effect on ductility when the whiskers are clustered than when they are uniformly distributed in the matrix. The predicted variations in ductility for tensile and compressive superposed hydrostatic stress, and the presence of zones which show highly localized strains, axe in qualitative agreement with available experimental results.

Calculated stress distribution in a PbMo/sub 6/S/sub 8/ wire performing the I/sub c/ vs. epsilon experiment

Abstract: The precompression of the superconducting filament in a PbMo/sub 6/S/sub 8/ monofilamentary wire at 4.2 K. which was experimentally observed as a prestrain in an I/sub c/ vs. epsilon experiment, was simulated with the calculation of the thermal stress distribution using a triaxial elastic stress model. The occurrence of different prestress conditions, due to the choice of different barrier materials (Ta, Nb, and Mo) and as consequence of a varying reinforcing stainless steel content, was investigated by calculations and compared with experimental results. The change of the stress state in the filament with external axial stress shows a significant amount of hydrostatic stress even at the J/sub c/ maximum, which explains the observed degradation of superconductivity. For the presently used Chevrel-phase wire configurations with the unfavorable thermal expansion of the barrier materials, the hydrostatic stress component, e.g. the radial stress in the filament. is important for achieving a good bonding at the layer interfaces and creating the wanted prestress in the filament. If no alternative methods and materials for the barrier are found in the future, enhanced mechanical wire properties can only be obtained by a reduced layer thickness of the barrier, which would additionally improve the overall critical current density of the wire.

Hydrostatic stresses and their effect on the macroflow behavior and microfracture mechanism of two-phase alloys

Abstract: The aspects of the hydrostatic pressure and tension stresses developed as a result of the interaction between hard and soft phases to maintain compatibility are represented for two-phase alloys with different microstructures. It has been theoretically proved that the stress triaxiality, defined as the ratio of the hydrostatic stress to the effective stress (Σ H /Σ e ), causes hardening or softening of the component phases. The average hydrostatic tension and pressure stresses in soft and hard phases developed during monotonic loading make the soft phase harden and hard phase soften. The extent of the hardening and softening increases with the strength ratio of the hard phase to soft phase and the size of the particles and decreasing the phase content. The hardening or softening effect of thein situ constituents has important influence on the flow stress of the composites and is one of the important reasons for deviation from the law of mixtures in prediction of the flow stress of composites based on that of the component phases in bulk. The stress triaxiality distributions in microstructure scale also provide an explicit physical picture of the microfracture mechanisms of the two-phase alloys.

Consolidation, permeability, and strength of crushed salt/bentonite mixtures with application to the WIPP (Waste Isolation Pilot Plant)

Abstract: Three tests were performed to measure the consolidation, permeability, and compressive strength of specimens prepared from bentonite/crushed salt mixtures. Each mixture comprised 30% bentonite and 70% crushed salt based on total dry weight. Brine was added to each mixture to adjust its water content to either 5 or 10% (nominal) of the total dry weight of the mixture. In the consolidation tests, each specimen was subjected to multiple stages of successively higher hydrostatic stress (pressure). During each stage, the pressure was maintained at a constant level and volumetric strain data were continuously logged. By using multiple stages, consolidation data were obtained at several pressures and the time required to consolidate the specimens to full saturation was reduced. Once full saturation was achieved, each specimen was subjected to a final test stage in which the hydrostatic stress was reduced and a permeability test performed. Permeability was measured using the steady flow of brine and was found to range between 1 {times} 10{sup {minus}17} and 5 {times} 10{sup {minus}17} m{sup 2}. After the final test stage, unconfined compressive strength was determined for each specimen and was found to range between 0.5 and 8.1 MPa. Two constitutive models were fitted to the consolidationmore » data. One relatively simple model related volumetric strain to time while the other related instantaneous density to time, pressure, and initial density. 8 refs., 9 figs., 8 tabs.« less

Creep of power-law material containing spherical voids

Abstract: Finite element calculations have been carried out for spherical unit cells containing a concentric spherical hole to characterize the power law creep of a material containing voids. Axisymmetric states of macroscopic stress were applied to the unit cells ranging from purely hydrostatic loading to purely deviatoric stressing. The results of the unit cell calculations are approximated well by a creep potential for the macroscopic behavior of a porous material. This potential agrees with the unit cell results for purely hydrostatic stress and purely deviatoric stress and involves a simple elliptical interpolation in between. The model predicts quite well the ratio of transverse to axial strain rate in uniaxial compression tests.

Comparison of experimental and computational crack-tip deformations using Moire interferometry and finite elements

Abstract: The large plastic deformations at the tip of a crack in a ductile heat treatment of 4340 steel are studied experimentally and numerically to investigate the details of the deformation in a tough material. The specimen is loaded in a three-point-bend arrangement. The finite-element model of the experiment uses a small-strain, incremental plasticity law, with a power-law hardening behavior. Both the in-plane and out-of-plane deformations were measured on the same specimen at the same time. The experimental technique of moire interferometry is used to measure the in-plane displacements. This technique is described in detail, including an analysis of the effect of out-of-plane rotations on the use of the technique. A four-beam interferometer for measuring orthogonal displacement components is described, and its performance analyzed. The three-dimensional, finite-element model has 11913 degrees of freedom, and provides data for comparison with the experiment between 4000 N (linear behavior) up to 73.5 kN (continuous fracture of the steel specimen). The model material properties are determined from a uniaxial test on specimens taken from the same bar as the fracture specimens and with identical heat treatment. This model characterizes the crack as a rounded notch to match the notch in the steel fracture specimen. The effects of tunneling of the crack are introduced through the release of nodes along the crack plane corresponding to measured crack profiles. Results indicate that the numerical model matches the experiment quite well up to a load of 52.3 kN; mismatch at higher loads may be caused by a lack of finite-strain formulation in the code. The finite notch tip negates the singularity in either the stress or strain fields; the HRR field seems to have no region of dominance. However, the function of the J-integral appropriate to the HRR field does normalize the stresses and strains well, indicating that the J-integral is still a good fracture criterion. The effects of the added tunnel indicate that failure of the material depends on both the plastic strain and the hydrostatic stress.

Constant-temperature plastic working method for nial -based intermetallic compound

Abstract: PURPOSE:To improve quality characteristics by subjecting a blank material consisting of an NiAl -based intermetallic compd. to plastic working under the working conditions under which the hydrostatic stress acting on the blank material is within the value of specific times the deformation stress of the blank material and the Z parameter attains a specific value or above at the time of subjecting the blank material to constant-temp. plastic working. CONSTITUTION:The blank material consisting of the NiAl -based intermetalic compd. is subjected to the constant-temp. plastic working at the working temp. and strain rate under which dynamic recrystallization arises. The plastic work ing is executed at the working temp. and strain rate at which the hydrostatic stress acting on the blank material at the time of the working is within the value of =3X10 . The intermediate blank material or product of the NiAl -based intermetallic compd. which is free from working cracks and intergranular corrosion and has the uniform and fine equiaxed crystals and the excellent quality and characteristics is obtd. in this way.

Effects of Hydrostatic Stress and Strain Hardening Exponent on Near-tip Fields Under Mixed Mode Loading.

Abstract: A large deformation finite element analysis has been performed to study the stress and strain fields near the crack-tip under mixed mode conditions. The effects of microvoids on plastic flow are taken into account by using the continuum constitutive model introduced by Gurson. The displacements characterized by the stress intensity factors are imposed at the nodes on a peripheral circle far from a crack tip. Computations are carried out for the case of KII/KI=0 and 1.732 with the plane strain or plane stress condition. In the mixed mode loading, contrastive deformations appear at the upper and lower regions of the crack-tip, i.e., sharpening and blunting. The deformed shape of the crack-tip is influenced by strain hardening exponent. The distributions of the equivalent plastic strain and the void volume fraction near the crack-tip are also influenced by the stress state (plane strain or plane stress) as well as the strain hardening exponent. Based on these numerical results, discussions are made on the experimental observations that under mixed mode loading conditions cracks due to shear fracture initiated at the sharpened corner of the clack tip near the surfaces of the specimen while another crack due to dimple fracture occurred at the blunted corner of the crack tip near the midthickness of the specimen.

Constitutive Law of Porous Viscous Materials

Abstract: This paper examines in the light of Micromechanics the overall behavior of nonlinear viscous materials containing voids. A potential depending on two material parameters is proposed. One coefficient is derived from the hollow sphere problem: a closed form solution for a hollow sphere under hydrostatic stress is established for a compressible matrix. The second coefficient is deduced from a variational bounding of the potential.