Showing papers on "Hydrostatic stress published in 1990"

An analysis of tensile decohesion along an interface

Abstract: A COHESIVE zone type interface model, taking full account of finite geometry changes, is used to study the decohesion of a viscoplastic block from a rigid substrate. Dimensional considerations introduce a characteristic length into the formulation. The specific boundary value problem analysed is one of plane strain tension with a superposed hydrostatic stress. For a perfect interface, if the maximum traction that the viscoplastic block can support is greater than the interfacial strength, decohesion takes place in a primarily tensile mode. If this maximum traction is lower than the interfacial strength, a shear dominated decohesion initiates at the block edge. Imperfections in the form of a non-bonded portion of the interface are considered. The effects of imposed stress triaxiality, size scale, loading rate and interfacial properties on the course of defect dominated decohesion are illustrated. The characterization of decohesion initiation and propagation in terms of rice's (J. appl. Mech. 35, 379, 1968) J-integral is investigated for a variety of interface descriptions and values of the superposed hydrostatic stress.

Experimental study on propagation of liquid-filled crack in gelatin: Shape and velocity in hydrostatic stress condition

Abstract: The three-dimensional shape and velocity of propagating cracks in the hydrostatic stress condition were studied by using gelatin, the physical properties of which were controlled to be constant. Various liquids (with various densities, viscosities, and volumes as the governed parameters) were injected in gelatin to form liquid-filled cracks. The directions of the crack growth and the propagation of an isolated crack are governed by the density difference between injected liquid and gelatin (Δρ), that is, a buoyancy. The propagation of a crack has two critical values: the first is the transition value to brittle fracture; the second is the value where segmentation begins to occur. The condition of a stable isolated crack formation is discussed. The crack shape of an isolated crack in the direction perpendicular to the crack plane is different from that of a growing crack with a fat tear drop form: the former has an elliptical top and a nearly flat bottom. The upper termination of an isolated crack in the vertical cross section has an elliptical shape, and the lower termination has a cusped shape. The lower part of the crack occupies the preexiting fracture which has formed by fracturing at the crack top. The crack thickness (w)/crack height (h) ratio is proportional to Δρ A, if the elastic moduli are constant. The crack length l/h ratio increase with h in the primary fracture, while the l/h ratio decreases with h in the preexisting fracture except for air-filled cracks. The ascending velocity of an isolated crack is proportional to Δρ3 h4, that is, Δρ w2, if the other physical properties are constant. The height and length of a growing penny-shaped crack are approximately proportional to A 3d1/3t4/9, so that the growth rate of height is in proportion to A3d3t−5/9 (A3d is constant injection rale). Some comparisons with the two-dimensional crack theory and applications for magma-filled cracks are discussed on the basis of these results.

Plane-Strain Crack-Tip Fields for Pressure-Sensitive Dilatant Materials

Abstract: Abstraet--In this paper we present plane-stress crack-tip stress and strain fields for pressure-sensitive dilatant materials. A hydrostatic stress-dependent yield criterion and the normality flow rule are used to account for pressure-sensitive yielding and plastic dilatancy. The material hardening response is specified by a power-law relation. The plane-stress mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, J. Mech. Phys. Solids 16, 13-31 and 337-347, 1968; Rice and Rosengren, J. Mech. Phys. Solids 16, l-12, 1968). ‘Ihe angular variations of the fields depend on the material hardening exponent and the pressure sensitivity parameter. Our low-hardening solutions for d&rent degrees of pressure sensitivity agree well with the corresponding perfectly plastic solutions. An important aspect of the eRecta of pressure.-sensitive yielding and plastic dilatancy on crack-tip fields is the lowering of the opening stress and the hydrostatic stress directly ahead of the crack tip. This effect, similar to that under plane-strain conditions (Li and Pan, to appear in J. Appl. Mech. 1989), has implications in the material toughening observed in some ceramic and polymeric composites.

Analysis of void closure in open-die forging

Abstract: Void closure studies have been conducted numerically and experimentally for open-die forging processes. The plane-strain FEM analysis was compared with bite forging experiments in order to determine how well the plane-strain approximation predicted the material flow in open-die forging. In addition physical modeling with plasticine was used to compare the measured and calculated deformation of the internal defect. The FEM analysis was in good agreement with the experimental results. Correlations for the computed effective strain and hydrostatic stress to the void closure were then calculated. Simulations of a solid cylinder side pressed with flat dies, V-shaped dies, and FML dies were done to determine the effectiveness of these dies at consolidating internal porosity based on the calculated strain and hydrostatic stress at the center of the billet. The V-shaped dies were found to be the most effective among those investigated. However, the press load for the V-shaped dies was also the highest.

Mechanical stability of shallow magma chambers

Abstract: The mechanical stability of the wall of a magma chamber depends on the value of the stresses likely to be developed in the immediate vicinity of this boundary in relation to the conditions for failure to occur. Various structural and physical factors contributing to these stresses are systematically analyzed. Models of volcanic systems having an axial symmetry around a vertical axis with an isolated reservoir, filled with magma under pressure, in a homogeneous elastic medium are investigated. Spheroidal magma chambers of different aspect ratios (0.7–2) and approximately the same volume (13.5–14 km3), with tops at 3.5–4.5 km depth, are considered. Stress distributions including the effect of gravity, free surface of the Earth, and remote stresses increasing with depth are calculated by using a numerical finite element method. The development of tensile tangential stresses greater than 10 MPa in the elements adjacent to the wall of the chamber is assumed to be a sufficient condition for its instability. The standard state of stress assumed for the crust (i.e., the boundary conditions imposed at large horizontal distance from the chamber) is varied in a continuous range having as lower limit a state of uniaxial strain in the vertical direction and as upper limit a state of hydrostatic stress. Calculations are first performed by making the assumption that the magma pressure P acting at the top of a chamber equals the lithostatic pressure of the overlying rocks. Alternatively, the upper limit of the values of P (critical pressure Pc) for which the initial shape of a chamber may be stable, according to the assumed necessary conditions for stability, is determined. For boundary conditions corresponding to uniaxial strain and Poisson's ratio v = 0.25, Pc turns out to be approximately half of the lithostatic pressure of the overlying rocks. A simple criterion is proposed to estimate if a chamber may evolve toward a new stable shape when P > Pc. This is highly improbable if P equals the lithostatic pressure of the overburden. Larger values of Poisson's ratio (0.30–0.35) favor stability, yielding critical pressures exceeding the lithostatic pressure. Stability is extremely sensitive to the standard state of stress assumed for the crust. Boundary conditions progressively approaching a hydrostatic state of remote stresses yield increasingly higher critical pressures. It turns out that the density contrast between magma and host rocks is not crucial for stability (for Δρ/ρ < 11%). For the rather large spheroidal chambers investigated, the shape is not a critical factor either. The effect of topographical details (e.g., a volcanic edifice, 1.5 km high and 6 km in radius) is practically irrelevant.

Finite element analysis of void growth in elastic-plastic materials

Abstract: Three-dimensional finite element computations have been carried out for the growth of initially spherical voids in periodic cubic arrays and for initially spherical voids ahead of a blunting mode I plane strain crack tip. The numerical method is based on finite strain theory and the computations are three-dimensional. The void cubic arrays are subjected to macroscopically uniform fields of uniaxial tension, pure shear and high triaxial stress. The macroscopic stress—strain behavior and the change in void volume were obtained for two initial void volume fractions. The calculations show that void shape, void interaction and loss of load carrying capacity depend strongly on the triaxiality of the stress field. The results of the finite element computation were compared with several dilatant plasticity continuum models for porous materials. None of the models agrees completely with the finite element calculations. Agreement of the finite element results with any particular constitutive model depended on the level of macroscopic strain and the triaxiality of the remote uniform stress field. For the problem of the initial spherical voids directly ahead of a blunting mode I plane strain crack tip, conditions of small scale yielding were assumed. The near tip stress and deformation fields were obtained for different void-size-to-spacing ratios for perfectly plastic materials. The calculations show that the holes spread towards the crack tip and towards each other at a faster rate than they elongate in the tensile direction. The computed void growth rates are compared with previous models for void growth.

Thermodynamic Theory of Single-Crystal Lead Titanate with Consideration of Elastic Boundary Conditions

Abstract: A phenomenological free-energy function including the effects of elastic boundary conditions was presented and used to investigate the single-domain, single-crystal properties of the ferroelectric perovskite, PbTiO3. In particular, the effects of tensile and compressive hydrostatic stress on the spontaneous polarization, Curie point, dielectric susceptibility, and piezoelectric property coefficients were examined. The calculated shift of the Curie point with hydrostatic stress, along with the entropy and enthalpy of the ferroelectric-paraelectric phase transition, was found to be in good agreement with experimental measurements. The isothermal variation of the relative dielectric susceptibility and piezoelectric coefficients with hydrostatic stress exhibited the expected behavior near the ferroelectric-paraelectric phase transition.

Front tracking thermomechanical model for hypoelastic-viscoplastic behavior in a solidifying body

Abstract: In assessing the quality of castings, a major consideration is the formation of cracks due to the induced thermal stress field. A means for understanding the casting process is the development and numerical implementation of mathematical models which account for all the heat transfer and deformation phenomena occurring in a solidifying body. In this paper a front tracking finite element method is used for the calculation of temperature and stress field development in a solidifying pure metal. The solid/liquid interface position and its velocity are considered as primary variables of the heat transfer analysis. A rate form of the virtual work principle and a rate dependent viscoplastic-hypoelastic constitutive model are employed to solve the equilibrium equations and to account for the hydrostatic stress state on the freezing interface and the fact that the material is in a state of residual stress immediately after solidification. Examples of the applicability of the technique are given with the analysis of the solidification of pure aluminium under realistic cooling rates and material representation. The effects of melt pressure, cooling conditions and geometry of a continuously cast metal strand on the residual stress pattern are examined and reported.

The yield and post-yield behavior of high-density polyethylene

Abstract: An experimental and analytical evaluation was made of the yield and post-yield behavior of high-density polyethylene, a semi-crystalline thermoplastic. Polyethylene was selected for study because it is very inexpensive and readily available in the form of thin-walled tubes. Thin-walled tubular specimens were subjected to axial loads and internal pressures, such that the specimens were subjected to a known biaxial loading. A constant octahederal shear stress rate was imposed during all tests. The measured yield and post-yield behavior was compared with predictions based on both isotropic and anisotropic models. Of particular interest was whether inelastic behavior was sensitive to the hydrostatic stress level. The major achievements and conclusions reached are discussed.

Equilibrium of a solute in an elastic continuum —A statistical approach

Abstract: A theory of stress-assisted diffusion has been previously derived using continuum mechanics by E. C. Aifantis [1]. This theory has subsequently served as the basis for a model of material degradation by Unger and Aifantis [2]. In this model, an equilibrium solution of Aifantis' stress-assisted diffusion equation was used to determine the distribution of a solute in an elastic continuum. However, as continuum mechanics gives no direct correlation between material coefficients and other physical characteristics such as temperature, these models relied solely on experimental data to determine the phenomenological coefficients of the theory. This process naturally limits the predictive capabilities of the model. In this paper we rederive the equilbrium distribution of a solute in an elastic stress field. We show that the use of a statistical approach can provide additional information about the various coefficients appearing in the equilibrium solution of the phenomenological theory. An equilibrium distribution for a dilute gas in an ideal gas thermostat is derived using statistical mechanics. It takes the form of the equilibrium solution of Aifantis' stress-assisted diffusion theory in terms of the hydrostatic stress and diffusion coefficients. However, as a result of the statistical approach, additional information is gained for the coefficients in terms of the temperature and number of atoms in the thermostat.

A model for the deformation behavior of amorphous alloys with application to the wear loading of the film-on-substrate geometry

Abstract: One method of addressing practical wear problems is via the creation of wear resistant films on the exposed surface by various surface modification techniques. A class of materials produced by such techniques, amorphous metals, is known to exhibit mechanical properties consistent with good wear resistance. In this paper we present a model for the mechanical behavior of these materials that is mechanistic in nature, yet sufficiently simple to allow treatment of the film-on-substrate geometry. The Eyring rate theory is used as a basis to describe the deformation rate, and agreement with stress sensitivity and activation energy data is shown to support this approach. The local creation of excess volume and its relaxation are integral parts of the deformation process in these materials. The kinetics of relaxation is analyzed, and the physical attributes of that process are examined. The effects on deformation of a hydrostatic stress component in the wear loading mode are addressed. The relation of all these factors to strain localization in the film is also studied. The strength of an amorphous film produced by ion implantation is estimated and correlations with plastic flow depth are established. Methods of predicting the wear responses of particular materials in this geometry are presented and compared with published wear data.

An Anisotropic Creep Damage Model for Multiaxial Cyclic Loadings Histories

Abstract: The purpose of this study is the development of an anisotropic creep damage theory within the continuum damage mechanics, applicable to creep-dominated cyclic loading histories. A damage distribution is expressd in rate form as a symmetric tensor of rank necessary to match physically measured damage. A theoretical model which expresses general anisotropic creep damage phenomena with power law cavity growth is proposed. The coupling of damage with a bounding surface cyclic viscoplasticity theory is also accomplished. Comparison with experimental results are made for weakly anisotropically damaging materials, type 304 stainless steel at 593°C. Good correlation of rupture time, secondary creep, and tertiary creep has been obtained for proportional and nonproportional, isothermal, constant isochronous nominal stress loading histories. A modification of the isochronous stress (the set of stress state which have a same rupture time) for compressive hydrostatic stress state has been offered.

Crack Size Limit and its Effects on the Shape of Local Yielding Zone at the Crack Tip

Abstract: The validity range of one single parameter of K-characterisation for the entire crack-tip stress and deformation fields under small-scale yielding conditions is shown to be surprisingly small. As a vehicle for demonstration purposes, an inclined crack buried in an infinite plane plate subjected to biaxial remote loadings is analysed. The standard singular fields are found to be inadequate in characterising, to within some reasonable accuracy, such important parameters in controlling such fracture phenomena as the hydrostatic stress, the maximum shear stress and the Mises equivalent stress or the size of the plastic zone at a crack tip. they also fail to describe, even roughly, the experimentally observed shape changes of the plastic zone under both plane stress and plane strain conditions. If, however, the non-singular term in Williams' eigenfunction series expansion is retained instead of being omitted arbitrarily, it is then found that such shape changes can be predicted quite adequately. Comparison with previous results based on elasto-plastic FEM analysis and inelastic modelling is favourable. Influences of specimen geometry configuration on the plastic zone shape are illustrated. Related topics such as the crack initiation angle prediction and fatigue crack propagation description are also discussed.