Showing papers on "Hydrostatic stress published in 1999"

Influence of hydrostatic stress on failure of axisymmetric notched specimens

Abstract: To investigate the role of the hydrostatic stress on failure, some static and dynamic tensile tests on mild steel axisymmetric notched specimens are described in this paper. Finite–Element results and experimental data indicate that the failure site, for specimens having a small notch radius, occurs in regions of low triaxiality. Comparisons are made between Finite–Element and Bridgman analyses. The influence of some material parameters on the triaxiality levels is explored.

Statistical Mechanics of Stress Transmission in Disordered Granular Arrays

Abstract: We give a statistical-mechanical theory of stress transmission in disordered arrays of rigid grains with perfect friction. Starting from the equations of microscopic force and torque balance we derive the fundamental equations of stress equilibrium. We illustrate the validity of our approach by solving the stress distribution of a homogeneous and isotropic array.

On singular surfaces in isotropic linear thermoelasticity with initial stress

Abstract: It will be shown that the theory of a fundamental paper of Chadwick and Powdrill on singular surfaces, propagating in a linear thermoelastic body which is stress-free, homogeneous, and isotropic, also holds when the medium is subjected to hydrostatic initial stress provided the two characteristic speeds are suitably changed. The result is obtained by using Biot’s linearization of the constitutive law for the stress.

Three-phase elliptical inclusions with internaluniform hydrostatic stresses

Abstract: For an elastic inclusion embedded within an elastic matrix, it is the interfacialstresses that control mechanical integrity of the inclusion/matrix system. To eliminate the stresspeaks at the interface, the uniform hydrostatic stress state within the inclusion is of particularinterest because it achieves both uniform normal stress and vanishing tangential stress along theentire interface. Motivated by practical significance of interphase layer, the present paper studiesthe internal stress state of a three-phase elliptic inclusion which is bonded to an infinite matrixthrough an intermediate elastic layer. What is essential is that the interfaces of the three-phaseelliptic inclusion considered are two confocal ellipses. A simple condition is found that ensuresthat the internal stress state within the elliptic inclusion is uniform and hydrostatic. For givenremote stresses and material parameters, this condition gives a simple relationship between thethickness of the interphase layer and the aspect ratio of the elliptic inclusion. The exact stressfield is obtained in elementary form when this condition is met. In particular, the hoop stress inthe interphase layer is found to be uniform along the entire interphase/inclusion interface. It isbelieved that the availability of this condition relies on the confocal character of the ellipticinterfaces.

Residual stresses in convoluted oxide scales

Abstract: Alumina scales that grow during oxidation of FeCrAl alloys can develop a convoluted morphology. Although convolution relieves the overall growth stress, high thermal stresses develop locally and can be detrimental to the scale or interface integrity. Ruby fluorescence measurements and finite element simulations are used to examine residual thermal stresses and strains that result when the convoluted scales are cooled to room temperature. Unlike a flat scale that is in biaxial compression, a convoluted scale contains significant gradients, with tensile stress components along the outside and near the interface of the convoluted peaks. The experimental results are in good agreement with model calculations and provide much needed verification of the model assumptions. Because the ruby fluorescence technique provides only the hydrostatic stress averaged over an excited volume that includes the entire alumina scale thickness, modeling provides detail and insight to the experimental measurements.

Microphotoluminescence mapping of packaging-induced stress distribution in high-power AlGaAs laser diodes

Abstract: Spatially resolved photoluminescence line scans were performed to determine the local stresses in AlGaAs laser diodes designed for high-power operation at 808 nm. In this approach, the sign and magnitude of the local stress are deduced from the spectral shift of the peak associated with band-to-band transitions in the n-type GaAs substrate. The sensitivity of the technique (minimal equivalent hydrostatic stress that can be detected) can reach 10 MPa or better. Correlations between solder-induced stress distribution in the devices and estimated lifetimes are demonstrated.

Atomistic simulations of structures and mechanical properties of polycrystalline diamond : symmetrical (001) tilt grain boundaries

Abstract: Atomic structures and energies of symmetrical {l_angle}001{r_angle} tilt grain boundaries (GB{close_quote}s) in diamond have been calculated over a wide range of misorientation angle using a many-body analytic potential, and for some selected short-period grain boundaries with tight-binding and first-principles density-functional methods. The grain boundary energies from the tight-binding and first-principles methods are about 75{percent} of those calculated with the analytic bond-order potential. The energy rankings of the GB{close_quote}s calculated with the empirical potential, however, are similar to that calculated from the tight-binding and the density functional approaches. Atomic-level energy and stress distributions calculated with the bond-order potential reveal relations between local interface reconstruction and the extent and value of hydrostatic and shear stresses. From the calculated local volume strain and hydrostatic stress fields, the atomic bulk moduli are evaluated, and zones of different elastic behavior in the vicinity of the interface are defined. {copyright} {ital 1999} {ital The American Physical Society}

Finite-element method simulation of effects of microstructure, stress state, and interface strength on flow localization and constraint development in Nb/Cr2Nb in situ composites

Abstract: The effects of volume fraction of particles, stress state, and interface strength on the yield strength, flow localization, plastic constraint, and damage development in Nb/Cr2Nb in situ composites were investigated by the finite-element method (FEM). The microstructure of the in situ composite was represented in terms of a unit rectangular or square cell containing Cr2Nb particles embedded within a solid-solution-alloy matrix. The hard particles were considered to be elastic and isotropic, while the matrix was elastic-plastic, obeying the Ramberg-Osgood constitutive relation. The FEM model was utilized to compute the composite strength, local hydrostatic stress, and plastic strain distributions as functions of volume fraction of particles, stress state, and interface strength. The results were used to elucidate the influence of volume fracture of particles, stress state, and interface property on the development of plastic constraint and damage in Nb/Cr2Nb composites.

Fracture modelling of WC-Co hardmetals using crystal plasticity theory and the Gurson model

Abstract: The behaviour of edge cracks under Mode I loading in the WC-Co material system is studied using the finite element method (FEM). This work focuses on ductile failure mechanisms in the Co binder. A micromechanical approach is taken whereby Co layers are modelled explicitly. An embedding technique is employed. Crystal plasticity theory and J 2 flow theory are used to represent plastic deformation in Co ligaments. Areas of high hydrostatic stress, triaxiality and accumulated slip or effective plastic strain are identified within the binder material. The Gurson model is used to model crack growth in the Co ligaments. Fracture resistance curves are obtained giving a relationship between macroscopic material behaviour and microscopic failure mechanisms. Factors effecting the crack growth in single and multiple ligaments are identified.

Crystal plasticity analysis of the effect of dispersed β-phase on deformation and fracture of lamellar γ+α2 titanium aluminide

Abstract: A finite element analysis based on the crystal plasticity theory was carried out to investigate the deformation and fracture behavior of polycrystalline lamellar γ -TiAl+ α 2 -Ti 3 Al material containing 10 vol.% of b.c.c. β -phase precipitates. The effects of both the stable β -phase precipitates which deform by slip and the metastable β -phase precipitates which deform by a combination of stress-induced martensitic transformation and slip are studied. To model the cracking along the grain boundaries and the matrix–precipitate interfaces, the grain boundaries and interfaces were modelled using a cohesive zone approach. All the calculations were carried out using the commercial finite element code ABAQUS. The results obtained suggest that incompatibilities in the plastic flow between the adjacent grains give rise to a large build-up in hydrostatic stress in the region surrounding certain three-grain junctions which, in turn, leads to the nucleation of grain boundary cracks and ultimate failure. The stable β -phase precipitates located at the three-grain junctions help accommodate the incompatibilities in plastic flow doubling the strain to failure. The lattice expansion, which accompanies martensitic transformation in the metastable β -phase precipitates, further delays nucleation of the grain boundary–interface cracks giving rise to an additional increase in the fracture strain.

Strain Directed Assembly of Nanoparticle Arrays Within a Semiconductor

Abstract: The use of strain to direct the assembly of nanoparticle arrays in a semiconductor is investigated experimentally and theoretically. The process uses crystal strain produced by a surface structure and variations in layer composition to guide the formation of arsenic precipitates in a GaAs-based structure grown at low temperature by molecular beam epitaxy. Remarkable patterning effects, including the formation of single and double one-dimensional arrays with completely clear fields are achieved for particles in the 10-nm size regime at a depth of about 50-nm from the semiconductor surface. Experimental results on the time dependence of the strain patterning indicates that strain controls the late stage of the coarsening process, rather than the precipitate nucleation. Comparison of the observed particle distributions with theoretical calculations of the stress and strain distributions reveals that the precipitates form in regions of maximum strain energy, rather than near extremum points of hydrostatic stress or dilatation strain. It is therefore concluded that the patterning results from modulus differences between the particle and matrix materials rather than from other strain related effects. The results presented here should be useful for extending strain directed assembly to other materials systems and to other configurations of particles.

Cross-sectional observation on the indentation of [001] silicon

Abstract: A transmission electron microscope (TEM) micrograph of cross-sectionally viewed Vickers indentation made on the surface of (001) silicon at ambient temperature was obtained. The picture clearly reveals a triangle area, pointing downward and having nondiffraction-contrast, left after unloading, which further confirms the amorphized range induced by indentation in silicon. Analysis of the picture directly manifests a significant recovery of indentation depth. Surface shape and range of the amorphous silicon region do not coincide with that of the indenter and the corresponding distribution pattern of hydrostatic stress beneath indentation predicted by elastoplastic theory, respectively. It seems that the amorphization could not be attributed to the result of hydrostatic stress alone.

Mechanical strains and stresses in aluminum and copper interconnect lines for 0.18 μm logic technologies

Abstract: The mechanical stress state of conventional Al, damascene Al and damascene Cu lines of a 0.18 μm logic technology flow has been determined using a novel X-Ray diffraction method that permits measurement of stress on an array of critical-dimension lines on the product die. The mechanical stress levels in narrow RIE Al lines are small when the lines are unpassivated, but quite large (Hydrostatic stress of 537 MPa) when an inter-level dielectric (ILD) is deposited onto the lines. The large stress level is an important reliability concern for the IC industry. The damascene fabrication methodology changes the magnitude and distribution of stress in the Al interconnect lines. Unpassivated, damascene Al lines have a purely hydrostatic stress. Even though the deposition temperature of the metal and ILD are the same for RIE and damascene. Al lines, the hydrostatic stress of passivated, damascene Al lines (411 MPa) and the maximum shear stress in the lines are sharply reduced. Comparing damascene Al and Cu lines, it is found that the stresses are much smaller in Cu than Al (Hydrostatic stress of 286 MPa), suggesting that stress-induced voiding may be less of a reliability concern for Cu.

Shallow Flaws Under Biaxial Loading Conditions, Part II: Application of a Weibull Stress Analysis of the Cruciform Bend Specimen Using a Hydrostatic Stress Criterion

Abstract: Cruciform beam fracture mechanics specimensl have been developed in the Heavy Section Steel Technology (HSST) Program at Oak Ridge National Laboratory (ORNL) to introduce a prototypic, far- field, out-of-plane biaxird bending stress component in the test section that approximates the nonlinear biaxial stresses resulting from pressurized-thernxd-shock or pressure-temperature loading of a nuclear reactor pressure vessel (RPV). Matrices of cruciform beam tests were developed to investigate and quantify the effects of temperature, biaxial loading, and specimen size on fracture initiation toughness of two-dimensional (constant depth), shtdlow, surface flaws. Tests were conducted under biaxial load ratios ranging from uniaxial to equibiaxial. These tests demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower transition temperature region for RPV materials. Two and three- parameter Weibull models have been calibrated using a new scheme (developed at the University of Illinois) that maps toughness data from test specimens with distinctly different levels of crack-tip constraint to a small scale yielding (SSY) Weibull stress space. These models, using the new hydrostatic stress criterion in place of the more commonly used maximum principal stress in the kernel of the OW integral definition, have been shown to correlate the experimentally observed biaxiaI effect in cruciform specimens, thereby providing a scaling mechanism between uniaxial and biaxial loading states.

Method for predicting molding defect in spinning machining

Abstract: PROBLEM TO BE SOLVED: To develop a spinning-machined product in a short development period at small development cost by calculating and predicting molding defects in spinning molding. SOLUTION: Meshes for FEM analysis representing a base material shape and a metal mold shape are prepared (11) and used, molding conditions are set, and drawing simulation of spinning machining by the FEM analysis by a dynamic explicit solution method is performed (13); and hydrostatic stress, equivalent stress, and equivalent strain for every unit time in a molding process are found (14), the value I of a decision parameter is found from the found hydrostatic stress, equivalent stress, and equivalent strain for every unit time by using an Oyane's theoretical crack decision expression (15), and on the basis of the found theoretical crack decision parameter value I, the occurrence of a molding defect is predicted.

Project PAJ2, Report No. 7, An evaluation of yield criteria for adhesives for finite element analysis.

Abstract: Tensile and shear tests on bulk specimens of adhesives and tensile tests on butt-joint specimens have been employed to obtain stress/strain data for use with elastic-plastic models in finite element analyses of bonded joints. The adhesives investigated were a toughened epoxy and a toughened acrylic. The tests were carried out in an Instron machine at different crosshead speeds chosen to give the same effective plastic strain-rate for each mode of deformation. The results of the tensile and shear tests reveal that the von Mises yield criterion is not applicable to these materials except possibly at small plastic strains. The test results were therefore used to derive parameters for the linear Drucker-Prager and the exponent Drucker-Prager materials models. These models were then used in finite element analyses to predict force-extension curves for the butt-joint specimens. It was observed that the exponent Drucker-Prager model appeared to accurately describe the deformation behaviour of the epoxy whilst the linear Drucker-Prager model was more appropriate for the acrylic. These are believed to be chance observations, and a more detailed analysis of results has indicated that none of these models are suitable for toughened adhesives under all stress states. It is concluded that the von Mises criterion, possibly modified to include a small dependence on hydrostatic stress, is suitable for stress states and magnitudes in which the hydrostatic tensile stress is insufficient to initiate cavitation in the rubber or crazing in the matrix polymer. When the stress state and magnitude induce cavitation or crazing in the adhesive, then an alternative or modified model must be used to describe the influence of these mechanisms on deformation behaviour. The basis for the development of a new model is briefly discussed.

Numerical simulation of the large elastic±plastic deformation behavior of hydrostatic stress-sensitive solids $

Abstract: The present paper deals with the numerical simulation of the large elastic±plastic deformation and localization behavior of metals which are plastically dilatant and sensitive to hydrostatic stresses. The model is based on a generalized macroscopic theory taking into account macroscopic as well as microscopic experimental data obtained from tests with iron based metals. It shows that hydrostatic components may have a signi®cant e€ect on the onset of localization and the associated deformation modes, and that they generally lead to a notable decrease in ductility. The continuum formulation relies on the mixed-variant metric transformation tensor which leads to the de®nition of an appropriate logarithmic strain measure. Its rate is additively decomposed into elastic and plastic as well as isochoric and volumetric strain rate tensors. Particular attention is focused on the formulation of a generalized I1yJ2 yield

On the Dynamic Growth of a Spherical Inclusion With Dilatational Transformation Strain in Infinite Elastic Domain

Abstract: _tran~formation region expands at a constant speed, the strain field inside the t_ncluswn ts ttme-mdependent and uniform for uniform eigenstrain. Following the basic tdeas of crac:k propagation problems in dynamic fracture mechanics, the reduction rate of ~he m~chantcal part of the free energy accompanying the growth of the transformation mcluswn ~as derived as the driving force for the move of the interface. Then the equation to determme the propagatwn speed was established. It is found that there exists a steady SP_eed for the gro_wth of the transformation inclusion when time is approaching infinity. Fmally the relatwn between the steady speed and the applied hydrostatic stress was derived explicitly.

Strain and Stress Measurements with a Two-Dimensional Detector

Abstract: A new strain and stress measurement method is developed for Siemens General Area Detector Diffraction System (GADDS). The conventional “ sin 2 ψ ” method has been commonly used for stress measurement with point detectors or one-dimensional position-sensitive detectors. However, the conventional method can only use a small fraction of the diffraction data collected by a 2D (two-dimensional) detector. In the new method, a direct relationship between the stress tensor and the diffraction conic section distortion is given. The new theory, which combines the elasticity theory and the Bragg law into one equation, provides a basis for strain and stress measurements with 2D detectors. All the diffraction data collected by the two-dimensional detector, including data with different lattice plane indices can be used simultaneously to solve the stress tensor. By introducing a pseudo hydrostatic stress component, the stress tensor for the biaxial stress state can be calculated with an approximate value of the unstressed d-spacing. Since it is possible to measure stress without sample rotation during the whole procedure, the incident beam coverage on the sample is fixed. This allows the method to be used for complex sample surface, microdiffraction, and residual stress mapping over the sample surface area. An experimental comparison between the conventional method and the new method shows that the new method can measure residual stress with higher accuracy from the same set of 2D detector data.

Hydrostatic Stress Effects in Metal Plasticity

Abstract: Since the 1940s, the theory of plasticity has assumed that hydrostatic stress does not affect the yield or postyield behavior of metals. This assumption is based on the early work of Bridgman. Bridgman found that hydrostatic pressure (compressive stress) does not affect yield behavior until a substantial amount of pressure (greater than 100 ksi) is present. The objective of this study was to determine the effect of hydrostatic tension on yield behavior. Two different specimen geometries were examined: an equal-arm bend specimen and a double edge notch specimen. The presence of a notch is sufficient to develop high enough hydrostatic tensile stresses to affect yield. The von Mises yield function, which does not have a hydrostatic component, and the Drucker-Prager yield function, which includes a hydrostatic component, were used in finite element analyses of the two specimen geometries. The analyses were compared to test data from IN 100 specimens. For both geometries, the analyses using the Drucker-Prager yield function more closely simulated the test data. The von Mises yield function lead to 5-10% overprediction of the force-displacement or force-strain response of the test specimens.