Showing papers on "Hydrostatic stress published in 2000"

Isotropic constitutive models for metallic foams

Abstract: The yield behaviour of two aluminium alloy foams (Alporas and Duocel) has been investigated for a range of axisymmetric compressive stress states. The initial yield surface has been measured, and the evolution of the yield surface has been explored for uniaxial and hydrostatic stress paths. It is found that the hydrostatic yield strength is of similar magnitude to the uniaxial yield strength. The yield surfaces are of quadratic shape in the stress space of mean stress versus effective stress, and evolve without corner formation. Two phenomenological isotropic constitutive models for the plastic behaviour are proposed. The first is based on a geometrically self-similar yield surface while the second is more complex and allows for a change in shape of the yield surface due to differential hardening along the hydrostatic and deviatoric axes. Good agreement is observed between the experimentally measured stress versus strain responses and the predictions of the models.

Long-life torsion fatigue with normal mean stresses

Abstract: Relatively simple fatigue tests have been performed on two common engineering materials, cast ductile iron and low-carbon steel, using two stress states, cyclic torsion and cyclic torsion with static axial and hoop stresses. Tests were designed to discriminate between normal stress and hydrostatic stress as the most suitable mean stress correction term for high cycle fatigue analysis. Microscopy shows that cracks in low-carbon steel nucleate and grow on maximum shear planes, while for cast iron pre-existing flaws grow on maximum normal stress planes. The data illustrate that tensile normal stress acting on a shear plane significantly reduced fatigue life and is an appropriate input for fatigue analysis of ductile materials. Static normal stresses did not significantly affect the fatigue life for the cast iron because the net mean stress on the maximum normal stress plane was zero. Mean torsion significantly reduced the fatigue strength of the cast iron. A critical plane long-life parameter for nodular iron which accounts for both stress state and mean stress is proposed, and is found to accurately correlate experimental data.

Ductile fracture criteria and its prediction in axisymmetric drawing

Abstract: Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. The ductile fracture criteria (P.F. Thomason, Ductile Fracture of Metals, Pergamon, 1990; S. Dhar et al., A continuum damage mechanics model for void growth and micro-crack initiation, Engineering Fracture Mechanics 53 (1996) 917) developed based on the microscopic phenomena of void nucleation, growth and coalescence along with a simple criterion (N.V. Reddy et al., Central bursting and optimal die profile for axisymmetric extrusion, ASME Journal of Manufacturing Science and Engineering 118 (1996) 579) based on the concept of the hydrostatic stress component at a point in the deformation zone falling to zero and compressive elsewhere are used to predict the fracture initiation in drawing (i.e. central bursting). Even though the first two criteria are based on microscopic description, the material parameters required are available for a few steels only and their determination involves difficult metallurgical experimentation. The above criteria used along with the results of Eulerian Rigid-Plastic and Elasto-Plastic formulations are presented in this paper. Finite element formulations for obtaining the generalized strain distribution and for obtaining the damage distribution by using the critical damage criteria are also presented. The present study shows that predictions based on the simple criterion are in good agreement with the experimental as well as numerical results published earlier and are, in general, conservative. Further, comparison of the predictions of the three criteria shows that the hydrostatic stress criterion is highly conservative and hence safe for die design.

Fracture and yield behavior of adhesively bonded joints under triaxial stress conditions

Abstract: Most of adhesively bonded joints are under complicatedly distributed triaxial stress in the adhesive layer. For the estimating of the strength of adhesively bonded joints, it is crucial to clarify behavior of yield and failure of the adhesives layer under triaxial stress conditions. Two types of the adhesively bonded joints were used in this study: One is the scarf joint which is under considerably uniform normal and shear stresses in the adhesive layer, where their combination ratio can be varied with scarf angle. The other is the butt joint with thin wall tube in which considerably uniform pure shear can be realized in the adhesive layer under torsional load conditions. These joints can cover the stress triaxiality in adhesive layers of most joints in industrial application. The effect of stress triaxiality on the yield and fracture stresses in the adhesive layer were investigated using the joints bonded by three kinds of adhesives in heterogeneous and homogeneous systems. The results showed that both the yield and failure criterion depend on the stress triaxiality and that the fracture mechanism of the homogeneous adhesive is different from that of the heterogeneous one. From these experimental results, a method of estimating the yield and failure stresses was proposed in terms of a stress triaxiality parameter.

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

Abstract: Spatially resolved photo-luminescence (PL) line-scans were performed in a specific optical micro-probe to determine the soldering-induced local stresses in GaAs/GaAlAs laser diode arrays 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 associated with band-to-band transitions in the GaAs substrate. The sensitivity (minimal equivalent hydrostatic stress that can be detected) is better than 10 MPa. The spatial resolution of the micro-PL technique (of the order of 1 micrometer), together with the short acquisition times, allows for detailed investigations of the stress profiles along the whole laser bars with a large number of data points. Different aspects of the mechanical stress distribution at the various steps of the process could thus be revealed. Finally, correlations between solder-induced stress distribution and estimated lifetimes were established. In particular, > defects, which are known as a failure mechanism on this type of devices, were observed only on the laser bars for which the micro-PL indicates the strongest compressive stress. This leads to consider the micro-PL approach proposed here as a cost- effective screening technique for the high-power GaAs/GaAlAs laser diode arrays.

Interfacial Stresses and Void Nucleation in Discontinuously Reinforced Composites

Abstract: This paper presents the theoretical predictions of the stress state at the inclusion-matrix interface in discontinuous metal matrix composites by the generalized inclusion method. In the author's previous works, this method had been extended to the elastoplastic deformation in the matrix material. The present analysis of the ellipsoidal inclusion problem indicates that the regions at the pole and the equator of the particle/matrix interface essentially remain elastic regardless of the level of deformation, although the size of the elastic region keeps decreasing as deformation becomes larger. It was also found that, when the composite is undergoing a relatively large plastic deformation (strain), the maximum interfacial normal stress is approximately linearly dependent upon the von Mises stress and the hydrostatic stress. Based on the stress criterion for void nucleation, the author determined the void nucleation loci and nucleation strain for a composite subjected to an axisymmetric macroscopic stress state. The influences of interfacial bonding strength, inclusion shape, and volume fraction on the occurrence of void nucleation have been determined. The interfacial bonding strength in a SiC-aluminum system was re-evaluated by using existing experimental evidence.

Effect of Edges and Corners on Stresses in Thermally Grown Alumina Scales

Abstract: Residual stress near edges and corners of thermally grown alumina scaleswere investigated. In this study, an edge is the intersection of twoorthogonal flat surfaces and a corner is the intersection of three suchsurfaces. Microfluorescence measurements, performed on alloys withcomposition Fe–28Al–5Cr (at.%, bal. Fe) oxidized at 900°C,showed a large (>50%) reduction in hydrostatic stress in the vicinity ofedges and corners. Surprisingly, significant stress reduction persists outto distances twenty to fifty times the scale thickness from theedge. Finite-element analysis calculations confirm the experimental resultsand provide a considerably more detailed picture of the stress distributionand its components and show that much of the observed stress reduction nearan edge, is due to plastic deformation of the underlying metal.

Internal stress effect on grain-boundary diffusion in submicrocrystalline metals

Abstract: Grain-boundary diffusion in the regime affected by internal stresses of triple-line disclinations is analysed. The concentration profiles in a stressed solid averaged over a distribution of hydrostatic stress gradients are calculated. It is shown that the stresses from triple-line disclinations in as-prepared submicrocrystalline metals can significantly increase the effective grain-boundary diffusion coefficient, which is obtained by fitting the concentration profiles to the solution of a diffusion equation for an unstressed polycrystal.

Atomistic studies of stress effects on self-interstitial diffusion in α-titanium*

Abstract: The diffusion anisotropy of intrinsic point defects is an important factor governing the behavior of the HCP metals bombarded by energetic particles. The effects of stress on the diffusion and its anisotropy, although known to be important, have not been well understood. In this paper, we use a combination of molecular dynamics and molecular statics methods to investigate energy states of a self-interstitial in α-titanium, a typical HCP metal. Our calculation shows that the most stable configuration of the self-interstitial is the basal-split dumbbell configuration on the basal plane. Compression along the [0001] or the [1¯100] directions leads to an insignificant change in the migration energies, while compression along the [11¯20] direction leads to a larger migration energy. A significant change of the diffusion anisotropy is observed when a uni-axial compressive stress of 200 MPa is applied along the [11¯20] direction. Similar stress along the other two directions does not produce substantial changes of the anisotropy. We also show that an applied hydrostatic stress can significantly change the diffusion anisotropy of HCP metals and alloys. Thus, under irradiation, a hydrostatic stress can produce a significant creep-like deformation (i.e., with a deviatoric strain rate) through a stress-dependent change of the growth rate.

A Dilatational Plasticity Theory for Aluminum Sheets

Abstract: The nucleation, growth and coalescence of micro-voids are important failure mechanisms in ductile materials. Gurson (1977) has developed a dilatation plasticity theory to quantitatively characterize the state of deformation and damage associated with micro-voids in isotropic materials. This theory, however, is not applicable to aluminum sheets because they are highly anisotropic. A dilatational plasticity theory for anisotropic ductile materials is developed in this study. The constitutive law is established for aluminum sheets that contain micro-voids, where the matrix material of aluminum is characterized by an anisotropic constitutive model developed by Barlat et al. (1991). Based on the numerical analysis, an approximate yield function is given in the closed form for anisotropic sheets. It shows that the mean hydrostatic stress plays an important role in the plastic behavior of anisotropic micro-voided aluminum sheets.

Application of the Weibull Methodology to a Shallow-Flaw Cruciform Bend Specimen Tested Under Biaxial Loading Conditions

Abstract: This paper describes the application of the Weibull methodology to the analysis of a shallow-flaw cruciform bend specimen tested under biaxial loading conditions. The cruciform bend fracture mechanics specimen was developed at Oak Ridge National Laboratory (ORNL) to introduce a far-field, out-of-plane biaxial bending stress component in the test section that approximates the nonlinear stresses resulting from pressurized-thermal-shock or pressure-temperature loading of a nuclear reactor pressure vessel (RPV). Tests with the cruciform specimen demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower transition temperature region for an RPV material. High-constraint deep-flaw compact tension C(T) and low-constraint shallow-flaw cruciform fracture toughness data were used to assess the ability of the Weibull methodology to predict the observed effects of biaxial loading on shallow-flaw fracture toughness. A new hydrostatic stress criterion along with five equivalent-stress criteria from the literature were selected to serve as candidate kernels in the integral formulation of the Weibull stress. Among these candidates, the hydrostatic stress criterion, derived from the first invariant of the Cauchy stress tensor, was determined to have the required sensitivity to multiaxial-loading states. In addition, a new calibration technique developed by researchers at the University of Illinois for determining the necessary Weibull parameters is applied to the C(T) and cruciform data. A three-parameter Weibull model based on the hydrostatic stress criterion is shown to predict the experimentally observed biaxial effect on cleavage fracture toughness by providing a scaling mechanism between uniaxial and biaxial loading states. In summary, the conclusions that can be drawn from this study are as follows: (1) With respect to its effect on fracture toughness, the biaxial effect is a constraint effect. (2) A Weibull statistical fracture model has been successfully calibrated with uniaxial toughness data obtained from a conventional high-constraint C(T) specimen and a uniaxially loaded shallow-flaw cruciform that is effectively equivalent to a conventional shallow-flaw SE(B) specimen. (3) The calibrated fracture model was able to successfully predict the intermediate constraint-loss effects associated with two levels of biaxial loading. (4) These preliminary results at a single test temperature offer encouragement that complex multiaxial loading effects on transition region fracture toughness can be predicted with statistical fracture models developed using data obtained from conventional specimens. (5) Future work is required to investigate these effects at other temperatures within the transition region.

Analysis of Damage and Stress Fields of a Mode I Creep Crack in Steady-State Growth.

Abstract: Elaboration of the asymptotic stress and damage fields of a mode I creep crack in steady-state growth are analyzed by employing the continuum damage mechanics and semi-inverse method. The damage evolution equation are expressed as a power function of the equivalent stress, the maximum principal stress and the hydrostatic stress. Analytical relations among the exponent p of the stress singularity of the asymptotic stress field and the exponents n, m and q of the power creep constitutive law and the power creep damage law are obtained for plane strain state. Based on the results of the analysis, the conditions for the damage evolution equation required to obtain a non-singular crack -tip stress were discussed. For Kachanov-type damage evolution law, more precise numerical results are derived for both the plane stress and plane strain states. The effects fo the shape of damage distribution on the stress singularity are also discussed.

Analytical determination of cyclic hydrostatic stress-strain relations for a composite sphere with a soft inclusion and a hard bilinear, isotropically hardening matrix

Abstract: This paper deals with the analytical determination of cyclic hydrostatic stress-strain relations for an inclusion-matrix concentric sphere. Both phases are taken to be elastically isotropic, and the inclusion is taken as elastically softer than the matrix. The matrix is taken to be bilinear, and isotropic hardening is assumed. Yielding is assumed to occur in the matrix by the von Mises' criterion. Using Hill's [1] approach as a starting point, the exact solution is first determined for the first five sequences of loading (i.e., alternate tensile and compressive loadings). Based on the developed equations for the first five sequences and an inductive approach, the analytical relation for the overall hydrostatic stress and strain for the Nth loading sequence issuggested. With the developed equations the Bauschinger effect for the composite sphere is studied. Interestingly, it is seen that irrespective of the inclusion volume fraction, the relative stiffness of the soft inclusion/hard matrix or the work-hardening nature of the matrix, the composite response is initially governed by isotropic hardening, whereas an asymptotic response is approached where both kinematic and isotropic mechanisms play equally important roles. Such an evolution in the composite response is attributed to the evolution in internal stresses of the composite sphere.

Deformation mechanism in the forcefill process

Abstract: Forcefill is a method used in metallization of ICs to fill via holes with metal. At elevated temperature and under applied pressure the metal flows into the via hole. The method is applicable to aluminum as well as to copper. In this article the mechanism of the process is discussed based on measurements of the kinetics and on finite element calculations of the shear and hydrostatic stress in the film covering the via hole. It is demonstrated that naive use of deformation maps constructed by Frost and Ashby for the description of the forcefill process easily leads to highly inconsistent results. The calculated stress distribution shows that the relevant shear stress is more than one order of magnitude lower that the applied pressure. Since no deformation map was available for the grain size appropriate for the forcefill experiment a map for 1 μm grains was constructed. This map indicates that for the forcefill process diffusional flow is the dominant deformation mechanism. It is shown that under these conditions the diffusional flow process described by Frost and Ashby is in essence identical to our previously reported stress-induced diffusion model.

Interface crack propagation between a porous-ductile material and a rigid substrate

Abstract: Along the interfaces between ductile and brittle materials a slow, stable crack growth is often observed before the crack propagates into one of the two materials. In the present work, a numerical asymptotic solution is provided for the stress and velocity fields near the tip of an interface crack, steadily propagating between a porous elastic-plastic material and a rigid substrate, under plane strain conditions. The Gurson model with constant and uniform porosity distribution and isotropic hardening is assumed for the constitutive description of the ductile material. This model may accurately describe the behavior of incompletely sintered porous metals and particulate-reinforced metal matrix composites. In analogy with the problem of interface crack growth in fully dense elastic- plastic materials, two distinct kinds of solution can be found in variable-separable form, corresponding to predominantly tensile or shear mixed mode. These solutions exist only if the hardening coefficient is lower than a critical value. For higher values the solution may display a complex stress singularity, as for the problem of an interface crack between linear elastic materials. In any case, if the ductile material is elastically incompressible then the Dugdale parameter vanishes and variable-separable crack-tip fields can be found for every set of the material parameters. Due to the higher hydrostatic stress state, the porosity influences only the stress fields of the tensile mode significantly. In particular, for high porosities the maximum of the hoop stress deviates from the interface line ahead of the crack-tip towards the porous ductile material, causing possible kinking of the fracture, so that the toughness of the interface crack may increase significantly. Therefore, the performed analysis of debonding process of this kind of interface results to be essential for the determination of the overall strength, toughness and reliability of many advanced composite materials.

Investigation of ultra low indentation loading at elevated temperatures based on the hydrostatic stress-induced mass flow model

Abstract: A mechanism of hydrostatic stress-induced mass flow is proposed to describe a medium under an action of ultra low load indentation at elevated temperatures. Two types of indenters of conical and spherical shapes and two loading conditions of constant indentation speed and constant load were used in the investigation. For both shapes of indenters, the maximum hydrostatic stress is located in the vicinity of the indentation tip. The maximum hydrostatic stress is proportional to the indentation speed and applied load, but inversely proportional to the atomic mobility. Comparing the loading conditions, the maximum hydrostatic stress is linearly proportional to the indentation area at constant indentation speed, but inversely proportional to the indentation area at constant applied load.