Showing papers on "Hydrostatic stress published in 1995"

Predicting stress-induced velocity anisotropy in rocks

Abstract: A simple transformation, using measured isotropic V P and V S versus hydrostatic pressure, is presented for predicting stress-induced seismic velocity anisotropy in rocks. The compliant, crack-like portions of the pore space are characterized by generalized compressional and shear compliances that are estimated from the isotropic V P and V S . The physical assumption that the compliant porosity is crack-like means that the pressure dependence of the generalized compliances is governed primarily by normal tractions resolved across cracks and defects. This allows the measured pressure dependence to be mapped from the hydrostatic stress state to any applied nonhydrostatic stress. Predicted P- and S-wave velocities agree reasonably well with uniaxial stress data for Barre Granite and Massillon Sandstone. While it is mechanically similar to methods based on idealized ellipsoidal cracks, the approach is relatively independent of any assumed crack geometry and is not limited to small crack densities.

The influence of mobility of dissolved hydrogen on the elastic response of a metal

Abstract: The general principles of the mechanics of materials are used to describe the effect of interstitial mobile hydrogen on the linear elastic behavior of metals and alloys. The linear field equations reveal that during transient hydrogen diffusion the Laplacian of the hydrostatic stress is related to the Laplacian of the hydrogen concentration in the lattice, and it is not zero, as has often been assumed in calculations involving stress-driven diffusion of hydrogen under plane strain conditions. When the hydrogen reaches equilibrium with the local stress and diffusion terminates, the linear elastic constitutive response of the solid accounting for the hydrogen effect can be described by the standard Hooke's law of infinitesimal elasticity in which the stiffness moduli are termed moduli at fixed solute chemical potential and are calculated in terms of the moduli at fixed solute composition, the nominal hydrogen concentration, and the material parameters of the system. These moduli at fixed solute chemical potential can be viewed as the counterparts of those characterizing the drained deformation at constant pressure of fluid-infiltrated porous geomaterials, or the adiabatic deformation of thermoelastic materials. Next the linear transient field equations are solved in the case of a dislocation and a line force in an infinite medium under plane strain conditions by using analytic function theory. The range of validity of the solution to the linear field equations for an isolated edge dislocation is investigated for specific materials. Lastly, the implications of the constitutive behavior of the hydrogen-metal binary system on the fracture and dislocation behavior are discussed when the hydrogen is in equilibrium with local stress.

Hypoplastic constitutive equation with internal variables

Abstract: A new version of a hypoplastic constitutive equation is presented which is characterized by the introduction of a stress-like internal parameter called back stress. The back stress is a function of the void ratio and of the hydrostatic stress. Using a unique set of material constants, the new constitutive equation describes many aspects of the behaviour of cohesionless soils including the influence of density and stress level. This is demonstrated by a series of verification tests. The determination of the material constants from laboratory tests is described analytically.

Two-dimensional sections of the yield locus of a Ti6%Al4%V alloy with a strong transverse-type crystallographic α-texture

Abstract: Results obtained from mechanical tests on a Ti6%Al4%V sheet alloy were used to obtain the biaxial normal stress and the in-plane simple shear flow stress sections of its yield locus The critical resolved shear stress (CRSS) of the different activated slip systems is derived from these experimental results of mechanical tests combined with microstructural observations A strong asymmetry of the CRSS and some influence on it of the hydrostatic stress state was found for pyramidal 〈 c + a 〉 systems, ie a deviation from the Schmid law Owing to the high sharpness of the texture in this alloy, a quasi-single-crystal approximation of the plastic anisotropy on the rolling plane (RP) and of the yield locus sections measured was made The good agreement between the simulated and the experimental results encourages the use of the proposed CRSS values for a simulation of polycrystalline texture development and yield locus derivation

Vickers indentations in glass—II. Comparison of finite element analysis and experiments

Abstract: This paper presents a comparison of a three-dimensional finite element numerical analysis of Vickers indentation with an experimentally observed indentation load—depth ( P—h ) relation on soda-lime glass. Several mechanical properties, such as yielding stress, strain hardening and elastic modulus, are then estimated from the analysis of the experimental P—h curve. This paper also compares the experimentally-measured residual stress field around a Vickers indentation at the surface of glass with an FEM numerical calculation. The FEM calculation uses Mises elastoplasticity to describe the residual stress state at the unloading. The comparison shows a very good agreement between the numerical calculation and the experimental results for the P—h relation, the Mises stress and the hydrostatic stress. The results further confirm that the residual stress field close to the indentation is a non-equal bi-axial stress field, which is not circular in shape but reflects the shape of the indentation impression. The formation of radial cracks also causes significant modification of the stress field. The FEM analysis shows that the P—h relation can provide much useful information on mechanical properties using the analysis developed here.

Residual Stresses in Alumina/Ceria‐Stabilized Zirconia Composites

Abstract: Measurements of the residual stresses in Al2O3/Ce-TZP (12 mol% CeO2) sintered composites, containing 10, 20, and 40 vol% zirconia, obtained by neutron diffraction and by piezospectroscopy using optical fluorescence and Raman are compared. The techniques give essentially the same values for the spatial average of the hydrostatic residual stresses in the two phases despite the difference in the parameters measured in the two techniques. The measured stresses are also in accord with those predicted from a stochastic stress analysis for materials cooling from a stressfree temperature of ∼1180°C. Over the range of volume fraction investigated the hydrostatic stress in the alumina phase varies linearly with zirconia content, corresponding most closely to the upper Hashin bound.

Critical stress criteria for interfacial cavitation in MMCs

Abstract: Density measurements and microstructural examinations have been used to follow the formation, growth and coalescence of cavities during tensile loading of metal matrix composites (MMCs). Finite element modelling has been used to predict the stress states around reinforcements of various shapes. The positions of peak hydrostatic and normal stress components at the interface have been compared with the microstructural sites where voids were found to form experimentally in aluminium reinforced with alumina particles or fibres. It is concluded that cavities form when a critical hydrostatic stress is reached.

Investigation of deformation field and hydrogen partition around crack tip in fcc single crystal

Abstract: In situ fracture experiments and measurements of the hydrogen distribution in the immediate vicinity of the crack tip were used to investigate the effects of hydrogen on a face-centered cubic (fcc) single-crystal fracture process. The techniques used were scanning electron microscopy (SEM), a scribed-grid method with a computer-controlled data acquisition system, and ion microprobe mass analysis (IMMA). It was observed that the general features of plastic deformation are similar in both charged and uncharged hydrogen samples under mixed-mode loading conditions, and in both cases the strain field ahead of the crack tip is best expressed by an exponential equation. There are also differences. Hydrogen easily enlarges the crack tip opening displacement (CTOD) under a lower threshold stress-intensity factor, inhomogeneously increases the localized plastic deformation, and markedly enhances the steepness of strain curve near the crack tip. Internal hydrogen increases plasticity in the immediate vicinity of the crack tip but its effective range is smaller when compared with external hydrogen effects. The results show that two peaks of hydrogen concentration appear ahead of the crack tip: one peak is in the immediate vicinity of the crack tip and another peak is located some distance from the crack tip. It is concluded that the distribution of dissolved hydrogen with two peaks around the crack tip corresponds to the distribution of strain and stress fields, respectively, due to the interaction of hydrogen with dislocation and hydrostatic stress.

Plastic constraint of large aspect ratio solder joints

Abstract: The aspect ratio (joint area/joint thickness) of thin (0.001-0.006 in.) surface mount solder (60S-40Pb) joints plays an important role in determining the mechanical properties and fracture behavior of the joints. This study demon-strates that plastic constraint of a large aspect ratio 60Sn-40Pb solder joint can develop triaxial (hydrostatic) stresses several times greater than the average tensile strength of the bulk solder material. A four to sixfold increase in average joint stress and up to a tenfold increase in peak stress was measured on joints with aspect ratios ranging from 400 to 1000. Although a direct relationship of the aspect ratio to the average tensile stress is shown, as the Friction Hill model predicts, the observed stress increase is not nearly as high but proportional to the classical prediction. This is attributed to the existence of internal defects (oxide particles and micro-voids) and transverse grain boundaries which fail producing internal free surfaces. Thus, the actual aspect ratio is thickness/d2, where d equals the distance between internal surfaces. The fracture of these constrained joints was brittle, with the separation occurring between a tin-rich copper tin intermetallic at the interface and the solder matrix. Voids within the solder joint are shown to relieve the plastic constraint and lower the average tensile stress of the joint. The Friction Hill model may play an important role in explaining the small percentage of atypical solder joint failures which sometimes occur on electronic assemblies. In particular, the sudden failure of a thin joint in a strain controlled environment may be attributed to the development of a large hydrostatic stress component. Therefore, a flaw free, plastically constrained joint which develops a high stress state will be a high risk candidate for failure.

Microstructural modelling of grain-boundary stresses in Alloy 600

Abstract: The stress distribution in a random polycrystalline material (Alloy 600) was studied using a topologically correct microstructural model. The distributions of von Mises and hydrostatic stresses, which could be important factors when studying the intergranular stress corrosion cracking, at the grain vertices were analysed as a function of microstructure, grain orientations and loading conditions. The grain size, shape, and orientation had a more pronounced effect on stress distribution than the loading conditions. The stress concentration factor was higher for hydrostatic stress (1.7) than for von Mises stress (1.5). Hydrostatic stress showed more pronounced dependence on the disorientation angle than von Mises stress. The observed stress concentration is high enough to cause localized plastic microdeformation, even when the polycrystalline aggregate is in the macroscopic elastic regime. The modelling of stresses and strains in polycrystalline materials can identify the microstructures (grain-size distributions, texture) intrinsically susceptible to stress/strain concentrations and justify the correctness of applied stress state during the stress corrosion cracking tests.

Deformation and fracture of particulate epoxy in adhesive bonds

Abstract: The effect of bond thickness, t, on the mode I, mode II and mode III fracture energies of two epoxy adhesives toughened by a wide range of particle size, distribution and hardness was evaluated using DCB type test specimens. A high-magnification video recording and scanning electron microscopy were used to study the damage evolution and the post-fracture morphology in the bond. The stress-strain behavior in shear was determined for a limited number of bond thicknesses using the napkin ring test specimen. Similarly to previous findings on homogeneous polymeric adhesives, GIIC and GIIIC coincided irrespective of t. Moreover, all three fracture energies converged to a single value when t was decreased to the micrometer range. New trends were found, however, when t approached the size of the reinforcement. A predominant feature of the crack propagation in this case was coalescence of voids that originated from particles ahead of the crack tip. The relief of hydrostatic stress caused by this damage is believed to be responsible for the alteration of the mode I fracture behavior as compared to homogeneous adhesives. The stiffness of the reinforcement particles played an important role in the fracture in shear.

A study of constitutive behaviour of powder assembly by particulate modeling

Abstract: We have been investigating in the past the compaction behaviour of powder by particulate modeling in two-dimensions and three-dimensions. This model incorporates plastic deformation of particles at contact besides inter-particle friction, viscous force and gravity. An attempt is made in this study to perform simulation of three-dimensional compaction of powder, where powder is compressed with arbitrary strain rate ratios, and to examine its constitutive behavior, i.e. yield surface and the normality of strain rate vector to the surface. The simulated results show that the shape of the yield surface in principal stress space is a part of an ellipsoid whose axis coincides with hydrostatic stress axis; this qualitatively agree with experimental observations. The normality rule, on the other hand, does not necessarily hold, in particular in a stress state near uni-axial strain compaction.

Backward can extrusion of steels: Effects of punch design on flow mode and void volume fraction

Abstract: Finite element analyses of backward can extrusion are performed with two punch dimensions to enhance the sliding or the sticking of workpiece material at the punch nose contact surface. The punch geometry effect on the effective plastic strain and hydrostatic stress distributions are discussed and the evolution of microvoid volume fraction during the whole extrusion is predicted.

Asymptotic analysis of growing crack stress/deformation fields in porous ductile metals and implications for stable crack growth

Abstract: Asymptotic stress and deformation fields near a quasi-statically growing plane strain tensile crack tip in porous elastic-ideally plastic material, characterized by the Gurson-Tvergaard yield condition and associated flow rule, are derived for small uniform porosity levels throughout the range 0 to 4.54 percent. The solution configuration resembles that for crack growth in fully dense, elastically compressible, elastic-ideally plastic Huber-Mises material for this porosity range, except that the angular extents and border locations of near-tip solution sectors vary with porosity level, as do the stress and deformation fields within sectors. Increasing porosity is found to result in a dramatic reduction in maximum hydrostatic stress level, greater than that for a stationary crack; it also causes a significant angular redistribution of stresses, particularly for a range of angles ahead of the crack and adjacent to the crack flank. The near-tip deformation fields derived are employed to generalize a previously-developed, successful ductile crack growth criterion. Our model predicts that for materials having the same initial slopes of their crack growth resistance curves, but different levels of uniform porosity, higher porosity results in a substantially greater propensity for stable crack growth.

The stress jump of a semirigid macromolecule after shear: Comparison of the elastic stress to the birefringence

Abstract: In this work it is shown that the amount of stress retained at the instant of shear cessation, denoted as the elastic stress by Doi, and not the total shear stress is proportional to the shear equivalent of the optic birefringence even in the nonlinear shear stress–shear rate region. The system studied was xanthan gum in a viscous solvent, fructose dissolved in water, and may be considered as a system with rigid constraints. Coaxiality of the elastic stress and refractive index ellipsoids has been predicted theoretically for these systems; however, previous studies have only compared the total stress to the birefringence which generally leads to invalidation of the stress‐optic relation. The results of this work have three consequences; it reinforces the fact that stress jumps are present, the stress‐optic relation is only true when the elastic and not the total stress is used, and two unique types of stress constitute the total stress as predicted by theory for systems with rigid constraints.

Constraint effects on ductile crack growth in cladded components subjected to uniaxial loading

Abstract: A two-parameter approach based on the J-integral and the parameter h, the ratio of the hydrostatic stress to the effective stress, was examined for ductile crack growth in cladded specimens. A series of cracked specimen configurations were tested and analysed by FEM to study the crack-tip constraint in different geometries. The test program consisted of homogeneous SEN specimens of a base material (A533-B steel), homogeneous SEN specimens of a cladding material (stainless steel weldment) and cladded specimens containing surface cracks through the cladding. Some issues concerning the cladding/base interface were also discussed from the basis of metallographical and fractographical examinations. While the crack growth initiation of the investigated materials appeared to be insensitive to the crack-tip constraints, the propagation of ductile crack growth was significantly influenced by crack-tip constraints. The crack-tip constraints in different specimen configurations could successfully be characterized by the parameter h. Prediction of crack growth along the crack fronts in two cladded specimens using the developed resistance laws accounting for constraint effects gave promising results.

Analysis of shear localization in porous materials based on a lower bound approach

Abstract: The conditions for shear localization in porous materials are examined based on the lower bound approach proposed by the present authors. The influence of void nucleation and material inhomogeneity on the critical strain to localization is investigated and an improved plastic strain controlled nucleation criterion is proposed which makes it possible to include the influence of hydrostatic stress and avoid the ambiguity caused by the non-normality flow rule. The constitutive behavior of porous materials (including the yield loci, the void growth rate and the stress-strain curve) is also examined and comparison is made between the theoretical result and the experiment. Finally the instability and fracture of sintered CP Ti alloy and AISI4340 steels is analyzed and results are compared with the experiment.

Hot triaxial compaction

Abstract: The present invention pertains to an apparatus to hot triaxially compact powder. The apparatus includes a device for hydrostatically stressing the powder. The apparatus also includes a device for applying a shear stress to the powder simultaneously with the hydrostatic stress. Additionally, there is a device for heating the powder while the powder is hydrostatically in shear stress. The presence of the shear stress during the compaction of the powder has three primary effects. It can increase the final density and the densification rate of the compacted powder. It can cause microstructural changes in the compacted powder, and it can disrupt heterogeneities.

Mechanics of hot isostatic pressing of a densified unidirectional SiC/Ti composite

Abstract: The effect of standard and modified hot isostatic pressing programs on local residual stresses is investigated with an axisymmetric micromechanical model of a unidirectional SCS6/Ti-15-3 composite, made of an elastic fiber and a thermo-viscoplastic matrix. The processing parameters studied include the cooling rate under sustained pressure, the magnitude of the hydrostatic stress, and the ratios of the axial/transverse components. Local stresses in the fiber and in the matrix at their interface are evaluated after cooling from 980°C to room temperature, and during reheating to 500 and 980°C. As in our previous studies, the results indicate that inelastic deformation of the matrix along the cooling path, promoted here by slow cooling rates at sustained pressure, is responsible for reduction of the residual stresses in the fibrous composite. The magnitudes of the local residual stresses at room temperature are nearly linear functions of the logarithm of the cooling rate. Higher processing pressures also contribute to residual stress reduction, and especially so when the transverse pressure component is much higher than the axial.

超大形軸材の鍛造における内部空げき圧着に関する研究 : 第1報,空げき閉鎖特性評価式の導出

Abstract: Open-die forging experiments using different die geometries under hot isothermal conditions and three-dimensional simulations using rigid-plastic finite-element method were performed to formulate a void-closing behavior using only two factors : the integral of hydrostatic stress and the equivalent strain. First, upsetting, side-upsetting and V-shape die cogging of several cylinders with a spherical void at the center are carried out and the information on the void volume reduction is obtained. Seconds, the same forgings, but without voids is treated numerically and the development of stress and strain at the location of voids is investigated. Then, by combining these results, and using regression analysis, it is found that the void volume reduction is expressed as a polynomial function of the two factors. When the polynomial function is used, various forging methods can be evaluated quantitatively in terms of void-closing behavior. Therefore it is beneficial to optimize the forging process for a large rotor shaft.

Birefringence measurement under hydrostatic pressure in twisted highly birefringent fibers

Abstract: A new method of birefringence measurement in highly birefringent fibers influenced by hydrostatic pressure conditions up to 100 MPa is presented. The birefringence measurement method is based on twist-induced effects and has never been applied before in a high-pressure environment. The experiments were conducted using a specially designed pressure facility, which made it possible to simultaneously generate several mechanical perturbations, including twist and hydrostatic stress, and to investigate their effects on mode transmission in optical fibers. The results indicate that in the case of HB single-mode bow-tie fibers, hydrostatic pressure up to 100 MPa increased birefringence with a mean coefficient of (1//spl Delta/B/sub 0/)(/spl Delta//spl beta/)/dp=0.2%/MPa which is in very close agreement with our previous measurement based on Rayleigh scattering. >

Analysis of Observed Initial Stress by the Isotropic Spherical Shell Theory and Considerations.

Abstract: A general theory of isotropic elastic spherical shell has been presented to evaluate the initial stress field. Extending the original theory of isotropic elastic spherical shell presented by McCutchen, the thermal stress has been analyzed and the influence of the temperature gradient near the surface and the thermal stress has been discussed. The theoretical solution shows that the fundamental relationships realized near the surface are as follows. Namely, the vertical normal stress coincides with the overburden pressure and the horizontal strain is determined by the ratio of the surface subsidence to the radius of the earth. Then, in the general model, the average horizontal stress at a certain depth is given by a function of the elastic constants with stress dependency.To make clear the profile of the average horizontal stress and to investigate the applicability of the general theory, the ratio of the average horizontal stress to the vertical stress has been analyzed and compared to the measurements by means of the stress relieving method in the world. Showing the close agreement between the measurement and the calculation, it has been concluded that the vertical distribution of the Young's modulus, which is deeply depending on the mean normal stress, plays an important role in determining the magnitude of the average horizontal stress. Finally, the expansion of the theory to the anisotropic field has been pointed out to be a future work.

Effects of Fiber Morphology in Short Fiber Reinforced Composites

Abstract: The upper and lower bounds of fiber/fiber interaction effects induced by the different fiber morphologies in a short fiber reinforced composite were studied using an axisymmetric finite element (FE) model that employs a periodic hexagonal array of elastic short fibers embedded in an elastoplastic matrix. An equivalent representative volume element (RVE) was modeled to maintain vertical and horizontal constrained boundary conditions for the reduction of modeling efforts. The internal stress fields were evaluated for the ideally aligned single fiber model and compared to a staggered model. It was found that both fiber and matrix stresses in a staggered fiber model are significantly altered from those of the perfectly aligned case. Finally, the hydrostatic stresses in the matrix along the fiber/matrix interface and the evolution of matrix plasticity for each model were illustrated.

Estimate of the stress field in Kilauea's South Flank, Hawaii

Abstract: SUMMARY We estimated stress and seismic strain tensors for the Kilauea volcano's south flank. The stress orientation inversion and the seismic strain calculation were performed using fault-plane solutions. The principal stress and seismic strain directions are approximately uniformly distributed in space and time during the interval covered by the data. However, the 01,03 plane is approximately orthogonal to the plane. Therefore, a weak layer may exist beneath the south flank. o1 has a plunge of 59" and an azimuth of 152", with a 10" 95 per cent confidence range. We also developed a stress magnitude inversion to estimate magnitudes of boundary and interior stresses. In this inversion, the principal stress directions were taken as constraints in the seismic volume, and surface geodetic observations were used as data. The maximum magmatic pressure in Kilauea's rift zone is about 160 MPa. The direction of o1 can be interpreted as the superposition of hydrostatic stress (pgh) and magmatic pressure. Without the constraint imposed by the direction of ol, the estimated pressure is only 60 MPa. The distribution of magmatic pressure may be similar to that of pgh. In contrast, the upper rift zone may be in tension. The shear stress in the rift zone is about one order of magnitude smaller than the maximum compressive stress, supporting the interpretation of magmatic flow as fluid in dikes or channels. The combination of stress orientation inversion, seismic strain calculation, and stress magnitude inversion performed in this study provides a means by which to estimate the stress state in seismic areas.

Analysis of the strengthening mechanism based on stress-strain hysteresis loop in short fiber reinforced metal matrix composites

Abstract: The strengthening mechanism of short fiber or whisker reinforced metal matrix composites has been studied by a continuum mechanics treatment utilizing finite element analysis (FEA). To assess the tensile and compressive constitutive responses, a constraint-unconstraint comparative study based on stress-strain hysteresis loop has been performed. For analysis procedures, the aligned axisymmetric single fiber model and the stress grouping technique have been implemented to evaluate the domain-based field quantities. Results indicate that the development of significant triaxial stresses within the matrix both for the tensile and compressive loading, due to the constraint imposed by reinforcements, provide an significant contribution to strengthening. It was also found that fiber stresses are not only sensitive to the fiber/fiber interaction effects but also substantially contribute to the composite strengthening both for the tensile and compressive loading.