Showing papers on "Hydrostatic stress published in 2004"

Calculation of stress in atomistic simulation

Abstract: Atomistic simulation is a useful method for studying material science phenomena Examination of the state of a simulated material and the determination of its mechanical properties is accomplished by inspecting the stress field within the material However, stress is inherently a continuum concept and has been proven difficult to define in a physically reasonable manner at the atomic scale In this paper, an expression for continuum mechanical stress in atomistic systems derived by Hardy is compared with the expression for atomic stress taken from the virial theorem Hardy's stress expression is evaluated at a fixed spatial point and uses a localization function to dictate how nearby atoms contribute to the stress at that point; thereby performing a local spatial averaging For systems subjected to deformation, finite temperature, or both, the Hardy description of stress as a function of increasing characteristic volume displays a quicker convergence to values expected from continuum theory than volume averages of the local virial stress Results are presented on extending Hardy's spatial averaging technique to include temporal averaging for finite temperature systems Finally, the behaviour of Hardy's expression near a free surface is examined, and is found to be consistent with the mechanical definition for stress

Nonlinear rock physics model for estimation of 3D subsurface stress in anisotropic formations: Theory and laboratory verification

Abstract: We develop a rock physics model based on nonlinear elasticity that describes the dependence of the effective stiffness tensor as a function of a 3D stress field in intrinsically anisotropic formations. This model predicts the seismic velocity of both P- and S-waves in any direction for an arbitrary 3D stress state. Therefore, the model overcomes the limitations of existing empirical velocity-stress models that link P-wave velocity in isotropic rocks to uniaxial or hydrostatic stress. To validate this model, we analyze ultrasonic velocity measurements on stressed anisotropic samples of shale and sandstone. With only three nonlinear constants, we are able to predict the stress dependence of all five elastic medium parameters comprising the transversely isotropic stiffness tensor. We also show that the horizontal stress affects vertical S-wave velocity with the same order of magnitude as vertical stress does. We develop a weakanisotropy approximation that directly links commonly measured anisotropic Thomsen parameters to the principal stresses. Each Thomsen parameter is simply a sum of corresponding background intrinsic anisotropy and stressinduced contribution. The stress-induced part is controlled by the difference between horizontal and vertical stresses and coefficients depending on nonlinear constants. Thus, isotropic rock stays isotropic under varying but hydrostatic load, whereas transversely isotropic rock retains the same values of dimensionless Thomsen parameters. Only unequal horizontal and vertical stresses alter anisotropy. Since Thomsen parameters conveniently describe seismic signatures, such as normal-moveout velocities and amplitudevariation-with-offset gradients, this approximation is suitable for designing new methods for the estimation of 3D subsurface stress from multicomponent seismic data.

Shear and compaction band formation on an elliptic yield cap

Abstract: [1] Conditions for shear and compaction localization are examined for stress states on an elliptic yield cap in the space of Mises equivalent shear stress and mean normal compressive stress σ. Localization is predicted to occur when the slope of the hydrostatic stress versus inelastic volume strain curve falls to a critical value kcrit. When applied to the standard triaxial test, the analysis reveals a transition from compaction localization to shear localization as lateral confining stress σc decreases below a particular value. This value also corresponds to the largest value of kcrit, which is zero if normality is satisfied and slightly positive if not, for either shear or compaction bands. For σc larger than the transition value, compaction bands are the only mode of localized deformation predicted, and kcrit becomes increasingly negative with increasing σc. For σc smaller than the transition value, both shear bands and compaction bands are possible, but the value of kcrit is larger for shear bands. These results are consistent with experimental observations of compaction bands on relatively flat portions of the stress versus strain curve, corresponding to kcrit ≈ 0, and with their occurrence in a limited range of σc. As σc is decreased from the transition value, the predicted angle between the normal to the shear band and the maximum compression direction increases rapidly from 0° (for a compaction band) to 20°–30°. This rapid increase provides a possible explanation for the infrequent observation of very low angle shear bands.

Exceptional ideal strength of carbon clathrates.

Abstract: We study by means of ab initio calculations the ideal tensile and shear strengths of the C-46 clathrate phase. While its bulk modulus and elastic constants are smaller than in diamond, its strength is found to be in all directions larger than the critical stresses associated with the diamond {111} planes of easy slip. This can be related to the frustration by the clathrate cage structure of the diamond to graphite instability under hydrostatic stress conditions. The criteria for designing strong materials are discussed.

Piezospectroscopic Study of Residual Stresses in Al2O3–ZrO2 Directionally Solidified Eutectics

Abstract: The residual thermoelastic stresses were studied in Al2O3–ZrO2 (monoclinic zirconia, m-ZrO2) and Al2O3–ZrO2(Y2O3) (tetragonal zirconia, t-ZrO2) fibrous eutectics that were produced via the laser floating zone method, using different piezospectrosocopic probes. The luminescence of the R-lines of ruby (Cr3+ in Al2O3 phase) was used to determine the stresses in the Al2O3 matrix, assuming that the stress state in the fibers was transversally isotropic. The sapphire matrix was subjected to tensile stresses in the Al2O3–m-ZrO2 eutectics. The hydrostatic stress component attained a value of 1.13 GPa in well-ordered regions. In contrast, sapphire was in compression in the Al2O3–ZrO2(Y2O3) fibers, and the hydrostatic stress was −0.37 GPa in both ordered and disordered regions. The influence of the microstructure in the residual stresses was explained through thermoelastic analyses, based on a self-consistent method. In addition, the Raman spectra of m-ZrO2 and the 417 cm−1 Raman mode of Al2O3 were measured in samples that showed different microstructures and thermoelastic stresses. An approximate linear dependence was observed in the tension–compression range between frequency shifts of the Al2O3R-lines and those of the 417 cm−1 Raman mode.

Damage Evolution and Stress Analysis in Zirconia Thermal Barrier Coatings during Cyclic and Isothermal Oxidation

Abstract: The failure mechanisms of air-plasma-sprayed ZrO{sub 2} thermal barrier coatings with various microstructures were studied by microscopic techniques after thermal cycling. The elastic modulus (E) and hardness (H) of the coatings were measured as functions of the number of thermal cycles. Initially, both E and H increased by -60% with thermal cycling because of sintering effects. However, after -80 cycles (0.5 h at 980{sup o}C), the accumulated damage in the coatings led to a significant decrease of -20% of the maximum value in both E and H. These results were correlated with stresses measured by a spectroscopic technique to understand specific damage mechanisms. Stress measurement and analysis revealed that the stress distribution in the scale was a complex function of local interface geometry and damage in the top coat. Localized variations in geometry could lead to variations in measured hydrostatic stresses from -0.25 to -2.0 GPa in the oxide scale. Protrusions of the top ZrO{sub 2} coat into the bond coat were localized areas of high stress concentration and acted as damage-nucleation sites during thermal and mechanical cycling. The net compressive hydrostatic stress in the oxide scale increased significantly as the scale spalled during thermal cycling.

Simulation of hydride-induced steady-state crack growth in metals – Part I: growth near hydrogen chemical equilibrium

Abstract: Hydride-induced sub-critical crack growth in metals is simulated, by taking into account the coupling of hydrogen diffusion, hydride precipitation and material deformation. The terminal solid solubility of hydrogen in a stressed metal is derived analytically for hydrides of any shape with different elastic properties than those of the solid solution. The general relation considers full anisotropy of both hydride and metallic phases. It is shown that a hydrostatic stress plateau develops in the area of hydride precipitation near the crack tip, when crack propagates under conditions approaching hydrogen chemical equilibrium, near the threshold stress intensity factor. The plateau hydrostatic stress depends strongly on remote hydrogen concentration and temperature. However, it is nearly independent of the yield stress and the hardening of the metal. The same hydrostatic stress develops also behind the crack tip in the presence of hydrides. The characteristics of the near-tip field are used for estimating a critical remote hydrogen concentration, below which no hydride precipitation occurs, and the threshold stress intensity factor. The theoretical estimates compare favorably with experimental measurements.

The importance of multiaxial stress in creep deformation and rupture

Abstract: This paper investigates the importance of multiaxial stress states by considering several distinct testing techniques used in assessing both creep deformation and creep damage accumulation. The requirements of testing programmes to determine the necessary data are discussed in respect of sensitivity and interdependence of the principal and hydrostatic stress ratios.

Calibration of Velocity-stress Relationships Under Hydrostatic Stress For Their Use Under Non-hydrostatic Stress Conditions

Abstract: We have computed stress sensitivity parameters for intrinsically transverse isotropic (TI) shales and sandstones under hydrostatic stress using literature data from Wang (2002b). We use the three-parameter non-linear model that relates the whole stiffness tensor and the whole stress tensor. We introduce physical and empirical constraints in the inversion of parameters c111, c112, c123 to compensate for the absence of non-hydrostatic stress data. The constraints c111 < c112 and c155 < c144 ensure respectively that P-waves are dominated by the stress in the polarization direction and S-waves by stresses in the polarization and propagation direction. We confirm the validation of the model for all 16 shale samples and 10 out of 20 sandstone samples (35 MPa stress range) when intrinsic anisotropy is present and greater than 4.5 %. Sand samples show higher stress sensitivity than shale samples. With this methodology, we suggest that velocity-stress relationships can be calibrated in the lab under hydrostatic stress and then used under non-hydrostatic stress conditions.

Determination of intrinsic stresses in textured and epitaxial TiN thin films deposited by dual ion beam sputtering

Abstract: TiN thin films with thickness ranging from 50 to 300 nm were deposited by a dual ion beam sputtering technique, which consisted in sputtering a pure Ti target with primary Ar ions, while an (Ar+N2) gas mixture was used as a secondary assistance beam during deposition. Two different substrates were used: Si wafers covered with native oxide for which TiN films exhibited a fibre-texture, and MgO (001) single crystals for which a cube-on-cube epitaxial growth was observed. The intrinsic stresses in the TiN films were measured by X-ray diffraction using the sin2 ψ method after subtracting the thermal stress contribution at room temperature. The influence of the substrate, energy of primary and secondary ion beam on the strain/stress state of the films have been systematically studied. The stress results are discussed and analysed using a stress model that includes a hydrostatic and biaxial component. For the fibre-textured TiN films deposited on Si wafers at room temperature, large hydrostatic stresses, ranging from 5 to 6 GPa are obtained. For the epitaxial TiN films grown on MgO at 500 °C, the intrinsic hydrostatic stress decreases to 1.7 GPa. We show that this stress analysis satisfactorily accounts for the results obtained in TiN films with mixed (002)+(111) texture.

Evaluation of Damage Evolution in Ceramic‐Matrix Composites Using Thermoelastic Stress Analysis

Abstract: Thermoelastic stress analysis (TSA) has been used to monitor damage evolution in several composite systems. The method is used to measure full-field hydrostatic stress maps across the entire visible surface of a sample, to quantify the stress redistribution that is caused by damage and to image the existing damage state in composites. Stress maps and damage images are constructed by measuring the thermoelastic and dissipational thermal signatures during cyclic loading. To explore the general utility of the method, test samples of several ceramic-matrix and cement-matrix composites have been fabricated and tested according to a prescribed damage schedule. The model materials have been chosen to illustrate the effect of each of three damage mechanisms: a single crack that is bridged by fibers, multiple matrix cracking, and shear bands. It is shown that the TSA method can be used to quantify the effect of damage and identify the operative damage mechanism. Each mechanism is identified by a characteristic thermal signature, and each is shown to be effective at redistributing stress and diffusing stress concentrations. The proposed experimental method presents a new way to measure the current damage state of a composite material.

Micromechanical Modeling of Steady-State Deformation in Asphalt

Abstract: A micromechanical model for the steady-state deformation of idealized asphalt mixes is presented. Triaxial compression tests were conducted on idealized asphalt mixes and the volumetric and deviatoric strains were measured. The specimens were observed to dilate under compressive stresses and the deformation behavior was seen to be dependent on the hydrostatic as well as the deviatoric stresses. A simple model for the nonlinear viscous steady-state behavior of idealized mixes is presented based on a ''shear box'' analogy. Predictions of the model are seen to agree well with experimental measurements for a wide range of conditions. An upper bound is calculated for the steady-state deformation rates within a plane strain half space comprising the idealized asphalt mix subject to a uniform pressure over a finite contact strip. The deformation rate varies nonlinearly with the applied load and is strongly dependent on the hydrostatic stress. Further, the deformation rate is seen to be a maximum at a position about half a contact length below the surface of the half space. These findings are in general agreement with wheel tracking experiments on these idealized mixes.

Modeling the Nonlinear, Strain Rate Dependent Deformation of Shuttle Leading Edge Materials with Hydrostatic Stress Effects Included

Abstract: An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites, such as the Reinforced Carbon Carbon (RCC) material used on the leading edges of the Space Shuttle. In the developed model, the differences in the tension and compression deformation behaviors have also been accounted for. State variable viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear response is independent of the stiffness in the normal directions. The developed equations have been implemented into LS-DYNA through the use of user defined subroutines (UMATs). Several sample qualitative calculations have been conducted, which demonstrate the ability of the model to qualitatively capture the features of the deformation response present in woven ceramic matrix composites.

Concrete Subjected to Triaxial Stress States: Application to Pull-Out Analyses

Abstract: This paper presents the application of three-dimensional (3D) -constitutive models for concrete formulated in the framework of plasticity theory to structural analyses of anchor devices. For this purpose, two commonly employed concrete material models are considered. The first model, the extended Leon model, is based on one yield surface for the description of compressive and tensile failure of concrete. The second material model is a multisurface plasticity model consisting of three Rankine yield surfaces and a Drucker-Prager yield surface. The predictive capability of the models is demonstrated by means of anchor devices, commonly employed in structural engineering for the connection of steel and concrete members. Such devices induce strongly nonuniform triaxial stress states in the surrounding concrete, ranging from tensile, overcompressive, to confined compressive stress states. In the vicinity of the anchor head, even nearly hydrostatic stress states may occur. The numerical simulations on the basis of the employed 3D material models for concrete give insight into the load-carrying behavior of the investigated anchor devices. Two headed studs characterized by different shapes of the anchor head and an undercut anchor are considered. Comparison of the peak loads and failure modes of the respective anchor device predicted by the numerical models with experimental data highlight the strength and weakness of the employed material models. It is shown that some load cases may lead to rather large differences in peak load depending on the choice of material model. These differences are based on the individual properties of the constitutive models for concrete and, hence, detailed knowledge of the model under consideration is essential for giving accurate estimates of the peak load of the anchor device and the failure mode of concrete.

Volumetric Constraint Models for Anisotropic Elastic Solids

Abstract: We study three incompressibility flavors of linearly elastic anisotropic solids that exhibit volumetric constraints: isochoric, hydroisochoric, and rigidtropic. An isochoric material deforms without volume change under any stress system. An hydroisochoric material does so under hydrostatic stress. A rigidtropic material undergoes zero deformations under a certain stress pattern. Whereas the three models coalesce for isotropic materials, important differences appear for anisotropic behavior We find that isochoric and hydroisochoric models under certain conditions may be hampered by unstable physical behavior. Rigidtropic models can represent semistable physical materials of arbitrary anisotropy while including isochoric and hydroisochoric behavior as special cases.

Simulation of hydride-induced steady-state crack growth in metals – Part II: general near tip field

Abstract: Hydride-induced steady-state crack propagation in metals is investigated under conditions of constant temperature, plane strain, small-scale yielding and small-scale hydride precipitation, by taking into account the coupling of the operating physical processes It is shown that the near-tip field depends on a normalized stress intensity factor, which incorporates both effects of the applied stress intensity factor and the crack velocity According to Part I of the present study, when the normalized stress intensity factor tends to zero, the crack-tip field near the threshold stress intensity factor is produced, which is characterized by a constant hydrostatic stress in the hydride precipitation zone As the value of the normalized stress intensity factor increases, the evolution of the near-tip field for crack propagation from stage-I to stage-II regime is produced: the actual size of the hydride precipitation zone decreases, the hydrostatic stress increases, deviating from the level of the plateau, and the near-tip field tends to that of a hydrogen-free metal The near-tip field depends strongly on hydrogen concentration, far from the crack tip The stage-II crack growth velocity is predicted and the experimentally observed effect of metal yield stress and temperature on crack velocity is confirmed

Atomic scale stresses and strains in Ge/Si(001) nanopixels: An atomistic simulation study

Abstract: Recent progress in the growth of nanostructures on nonplanar (patterned) substrates has brought to the forefront issues related to atomic-level surface and subsurface stress and strain field variations, as these govern the process of formation of such nanostructures and strongly affect their physical properties. In this work, we use atomistic simulations to study the atomically resolved displacements, stresses, strains, and the strain energy in laterally finite nanoscale Si(001) mesas, uncovered and covered with the lattice-mismatched Ge overlayers. The spatial variations of the stress are examined both across the surface profile of the mesas and in the direction down to the substrate. We find that the hydrostatic stress and strain at the Ge∕Si interface undergo rapid changes from tensile in the interior of the Si mesa to compressive in the Ge overlayer, with the transition taking place over distances of the order of Si lattice constant. Substantial relaxation of the hydrostatic stress and strain, in both...

Hydrostatic piezoelectric coefficient d h of PZT ceramics and PZN-PT and PYN-PT single crystals

Abstract: The hydrostatic piezoelectric coefficient d h of Pb(Zr x Ti1 − x)O3 ceramics (PZT), and of Pb(Zn1/3Nb2/ 3)O3-PbTiO3 and Pb(Yb1/2Nb1/2)O3-PbTiO3 (PZN-PT, PYN-PT, respectively) single crystals with compositions near to the morphotropic phase boundary (MPB) have been measured using a dynamic hydrostatic method. The effects of DC electric field and static component of hydrostatic stress on d h of PZT ceramics, PZN-PT and PYN-PT single crystals were studied. Changes of the piezoelectric hydrostatic coefficients d h caused by an electric field (DC bias) were observed along with pressure and temperature dependencies. The measurement of the hydrostatic piezoelectric coefficient d h seems to be promising for investigation of intrinsic (single domain) and extrinsic (domain-walls) contributions to piezoelectric behavior of single crystals and ceramic materials.

Hydrostatic Stress Effect on the Yield Behavior of Inconel 100

Abstract: Classical metal plasticity theory assumes that hydrostatic stress has no effect on the yield and postyield behavior of metals. Recent reexaminations of classical theory have revealed a significant effect of hydrostatic stress on the yield behavior of notched geometries. New experiments and nonlinear finite element analyses (FEA) of Inconel 100 (IN 100) equal-arm bend and double-edge notch tension (DENT) test specimens have revealed the effect of internal hydrostatic tensile stresses on yielding. Nonlinear FEA using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (yielding is linearly dependent on hydrostatic stress) yield functions was performed. In all test cases, the von Mises constitutive model, which is independent of hydrostatic pressure, overestimated the load for a given displacement or strain. Considering the failure displacements or strains, the Drucker-Prager FEMs predicted loads that were 3% to 5% lower than the von Mises values. For the failure loads, the Drucker Prager FEMs predicted strains that were 20% to 35% greater than the von Mises values. The Drucker-Prager yield function seems to more accurately predict the overall specimen response of geometries with significant internal hydrostatic stress influence.

The Role of Constraint and Warm Pre-stress on Brittle Fracture in Ferritic Steels

Abstract: This paper presents the results of an experimental and numerical study carried out to investigate the effect of warm pre-stressing on cleavage fracture in ferritic steels using cracked and notched specimens. It is shown that the local approach based on Weibull theory predicts the increase in toughness following warm pre-stressing in highly constrained geometries. The observed effect of pre-loading in low constraint specimens such as round notched bars is less. The local approach could not predict the differences and it is suggested that the variation of triaxiality factor, the ratio of hydrostatic stress to Von Mises, in the plastic zone, is a contributing factor.