Calculation Of Stress Field Research Articles

Continuum mechanics of crack blunting on the atomic scale: elastic solutions

In order to improve upon continuum models for understanding the origins of ductile versus brittle response in materials, an accurate assessment of the stress fields near a crack tip must be developed. Existing continuum models have considered the crack tip to be perfectly sharp in order to use convenient analytical solutions for the stress fields around the crack tip. Numerous experimental observations have indicated that an atomically sharp crack is very rare and that crack tip blunting can precede or accompany crack propagation. A two-dimensional finite element model has been developed to evaluate the stress fields at a blunted crack tip subjected to loading. Stress fields have been calculated for mode I loading as well as for the self-stress due to the presence of a dislocation near a crack tip. These calculated stress fields have been compared with analytical solutions for appropriate limiting cases.

Enhanced plasticity in metal matrix composites during thermal cycling under load

The deformation behaviour of a SiC particle reinforced 2009 Aluminium alloy is studied during thermal cycling between 305 and 443 K superimposed on a tensile load of 150 MPa. After several cycles, the strain rate observed under these conditions is found constant and higher than the strain rate observed under pure creep conditions. An Arrhenius law and a power law are found for dependencies of the strain rate on the upper temperature of the cycles and the mechanical applied stress, respectively. Calculations of stress fields during thermal cycling based on Eshelby theory show that the enhanced deformation is likely to be due to emission and punching out of dislocations from the matrix-particle interface in relation with the relaxation of the thermal local stress fields arising on the cooling of the sample.

An Axisymmetric Method of Elastic-Plastic Analysis Capable of Predicting Residual Stress Field

Linear elastic solution of an axisymmetric boundary value problem is used as a basis to generate its inelastic solution. This method treats the material parameters as field variables. Their distribution is obtained as a part of solution in an iterative manner. Two schemes of updating material parameters are discussed and compared. A procedure for calculation of residual stress field is presented. Application of the method to autofrettage is presented. Residual stress calculation based on actual material curve, isotropic and kinematic hardening models, and variable Bauschinger effect factor (BEF) is carried out. It is concluded that consideration of dependency of BEF on plastic strain makes significant changes to residual hoop stress near the bore for low-level autofrettage. However, this dependency is insignificant for high-level autofrettage. Results obtained here are shown to be in good agreement with experimental and finite element results.

Fe calculations of stress fields from cracks located at the fusion line of weldments

This paper investigates the stress fields for a crack located at the fusion line of a weldment. The strength mis-matching and the size of the HAZ were varied, and the corresponding distribution of the maximum principal stress was examined. The weld metal strength was globally overmatched with respect to the base material, but locally over- and undermatched with respect to the heat affected zone. Three cases of mis-match were compared, and it was found that reducing the strength of the HAZ lowered the maximum principal stresses.

An Analysis of the Plane-Strain Compression of Viscoplastic Materials

A theoretical analysis for the plane-strain compression of viscoplastic materials with a Tresca wall boundary condition is described. The analysis is based upon the incorporation of a viscoplastic associated flow rule into the cycloidal solution originally developed for rigid-perfectly plastic materials. The evolution of the calculated stress field suggests that the influence of strain rate hardening is similar to that reported previously for strain hardening. The calculated strain fields are elliptical in form and are consistent with those measured for a viscoplastic paste. Previous analyses of the compression of viscoplastic materials have employed the lubrication approximation for fluid flows with a resulting kinematic inconsistency in the predicted velocity fields.

Oscillatory shear of a confined fiber suspension

Starting from a nonlocal description of the stress in a slender, rigid fiber suspension [Schiek and Shaqfeh (1995)], we calculate the dynamic properties of a free-fiber suspension under oscillatory shear in a very narrow gap. For a fiber suspension, three field quantities including the fluid velocity, the fiber concentration, and the fiber configuration strongly affect the suspension’s behavior. When the width of the gap confining the suspension is of the same scale as a suspended fiber’s length, then all three of the important field quantities change rapidly on that scale. The nonlocal stress equation is coupled to the momentum conservation equation for the fluid velocity and a Fokker–Plank equation for the fiber’s probability density function resulting in a closed set of nonlinear, integrodifferential equations. These equations were solved in the limit of a small Péclet number, where Brownian motion dominates, for arbitrary gap widths and oscillation frequencies. From the calculated stress fields, we obtained the real and imaginary viscosities that one would measure in flow experiments. The dependence of all four dynamic properties on gap width was investigated and we find that below a critical gap width (equivalent to one full fiber length) all dynamic properties undergo dramatic changes. Additionally, as the gap width shrinks, the relaxation time of the suspension was found to decrease, approaching the relaxation time of the pure Newtonian solvent in the limit of zero gap width. Scalings for the relaxation time as a function of small gap width are also presented.

Thermoelastic stresses in a bonded layer due to repetitively pulsed laser radiation

A method is presented for the calculation of thermoelastic stress and displacement fields in a bonded layer that absorbs thermal energy from a repetitively pulsed laser in its surface plane. A function with three adjustable parameters is used to simulate the temporal variation of each pulse while the radial intensity distribution (or mode structure) of each pulse follows a Gaussian profile. The pulse duration is of the order of the characteristic time for heat to diffuse across the layer thickness, and hence axial heat conduction cannot be neglected. Stress and displacement components due to heat absorption from three successive pulses are calculated and examined specifically at the free surface, at selected points within the layer, and at the bonded interface. The stress components at the bonded interface are also examined over a range of layer thicknesses to illustrate key differences between the thermoelastic responses of thin and thick layers.

Calculation of stress—strain curves by using 2 dimensional dislocation dynamics

A method is presented to derive stress-strain curves by using 2 dimensional dislocation dynamics. The simulation treats plastic deformation of single grains, in which one or more slip systems are active. The involved dislocations are regarded as infinite straight line defects which are embedded in an otherwise isotropic linear elastic medium. As the model is two dimensional only edge dislocations are incorporated. The calculation of the local stressfield considers the long range elastic stress contribution of all dislocations within the grain, of the externally imposed stressfields and of the short range stressfield imposed by large angle grain boundaries. Due to the net local value of the stressfield the dislocations may either glide or climb. Dislocation multiplication, annihilation and reactions are taken into account. Thermal activation is considered. The simulations allow to compute the evolution of the dislocation distribution, the stressfield and the plastic strain during a simulated deformation experiment. The latter quantities are used for the calculation of stress-strain curves.

Topographic perturbations of regional stresses and consequent bedrock fracturing

Stresses at Earth's surface are profoundly influenced by topography. Simple models indicate that gravitational and regional stresses are concentrated, attenuated, even reversed within landforms. Such topographically induced stresses are potentially manifest as bedrock fractures. Fractures reduce rock mass strength, decrease erosional resistance, and create conduits for water. By creating fractures, topographically induced stresses can alter processes of mass wasting, bedrock incision, and groundwater flow. We use Savage et al.'s [1985] solution for stresses in symmetric ridges and valleys on an elastic half‐space in plane strain to assess topographic effects on regional and gravity‐induced stresses. We have extended their solution to include lateral loads that vary with depth, which better approximates states of stress found in Earth's crust and allows us to examine a greater range of stress regimes. We examine the calculated stress fields to assess, in a classic Mohr‐Coulomb context, the potential for consequent fracture. This model indicates that topographic relief can cause stresses of sufficient magnitude to break rock, creating fracture sets having a spatial distribution and orientation governed by landform shape and the regional state of stress. We find that in extensional tectonic regimes, topographically induced stresses favor surface‐parallel fractures through ridges and steeply dipping fractures through valleys. Conversely, in compressional regimes, topographically induced stresses favor steeply dipping fractures through ridges and surface‐parallel fractures through valleys. Such topographic interactions with regional stresses pose consequences for interpretations of fracture orientation, for assessments of slope stability, and for processes of landscape development.

Brittle intergranular failure in 2D microstructures: Experiments and computer simulations

Brittle intergranular fracture (BIF) is a common mode of failure for monolithic ceramics and intermetallics, as well as for some refractory metals and metals exposed to environmental corrosion, stress corrosion cracking or high temperature creep. As interest in applications for these materials grows, research programs have been developed to characterize and predict their fracture behavior. In order to experimentally quantify the effects of microstructure on local BIF, systems which have a minimum number of variables which influence fracture must be used. Evaluation of materials with two dimensional (2D) microstructures can considerably reduce the complexity of the system. In addition, providing a biaxial stress state in the 2D microstructure ensures that all boundaries experience exclusively Mode I loading prior to failure. Biaxial elastic loading of this simplified microstructure allows the calculation of (a) local stress and strain fields (and their concentrations) prior to failure, as well as (b) prediction of grain boundary strength criteria, and (c) prediction of intergranular crack paths. This can be achieved by conducting computer simulations of the experimentally observed fracture phenomena in polycrystalline specimens having a given texture and microgeometry. These simulations use high resolution finite-difference grids below the crystal scale, and involve the derivation of a spring-network model for arbitrary in-plane crystal anisotropy. Since the grain boundary strength criterion is easily controllable in such simulations, it can be inferred by a comparison with actual experimental results. The latter is complemented by results on fracture of materials with very weak grain boundaries, thus providing a clear perspective on evolution of the failure process for varying degrees of embrittlement.

Induced stresses and fault potential in eastern Canada due to a realistic load: a preliminary analysis

SUMMARY In order to understand the causal relation between postglacial rebound and earthquakes, a simple disc load model is used to: (1) calculate stresses induced in the lithosphere and mantle by glacial loading, melting and postglacial rebound; and (2) evaluate the effect of glacial loading/rebound on the failure potential for earthquakes in the upper crust. The dependence of the failure potential and the actual mode of failure on the coefficient of friction, the ambient tectonic stress magnitude/direction, the stress due to the overlying rocks, and lithospheric thickness are investigated. Prominent features of this paper are the inclusion of: (1) a viscoelastic mantle and thus the migration of stress; and (2) the ambient tectonic stress and overburden stress contributions in the calculation of the total stress field. It is assumed that, throughout the Earth, there are optimally oriented pre-existing virtual faults that are initially close to but not at failure; thus, a time-dependent quantity called dFSM (related to the Coulomb-Mohr failure criterion) can be defined such that a negative value of dFSM would advocate faulting or earthquake activities whereas a positive value of dFSM would promote stability. The results indicate that, under all combinations of tectonic stress magnitude and overburden stress, crustal loading promotes fault stability directly underneath the load. Upon the removal of the load, thrust faulting is predicted within the ice margin if the horizontal stress (S,) induced by the overburden is greater than or equal to the vertical component (S,) of the overburden stress (121, where (=SJS,). Under this condition, theory predicts that faulting or earthquake activity should have reached a maximum immediately after deglaciation. If the horizontal stress induced by the overburden is less than the vertical component of the overburden stress (1 < l), then theory predicts fault stability within the ice margin. The theory predicts fault instability both north and south of the ice margin. The mode of failure, however, is completely determined by the value of i. The trade-off between the tectonic stress magnitude and the overburden stress parameter (1) is also investigated. It is shown that a larger tectonic stress magnitude can be used to compensate a smaller value of 1. The results of this analysis show that variations in the coefficient of friction, lithospheric thickness and a ductile zone below the upper crust do not significantly affect the above conclusions.

Numerical study of twin‐screw extruders by three‐dimensional flow analysis—development of analysis technique and evaluation of mixing performance for full flight screws

AbstractWe have developed a method for predicting the three‐dimensional flow field in the melt conveying zone in counter‐rotating and co‐rotating twin‐screw extruders. We applied this technique to the full flight screws with thin flight width and open C‐shaped channels in both rotating type extruders having the same screw configurations. We compared the details of velocity and stress fields, the flow rates of transportation, and various kinds of leakage flows for both rotating type extruders. Also, we obtained the spatial distribution of tracer particles and residence time distribution using a numerical tracer experiment. The flow rate in the transport direction in the co‐rotating twin‐screw was larger than that in the counter‐rotating twin‐screw, and this suggested that the latter has higher transport performance when the screws have thin flight width and open C‐shaped channels as used in this study. As for the distributive mixing, it was found that the co‐rotating twin‐screw excels in the area of fluid rearrangement between the two screws and distribution in the rotational direction, while the counter‐rotating twin‐screw has the desirable characteristic of wide distribution in the axial direction. With regard to dispersive mixing, there was no considerable difference between calculated stress fields in both rotating type extruders.

Induced Stresses and Fault Potential In Eastern Canada Due to A Disc Load: A Preliminary Analysis

In order to understand the causal relation between postglacial rebound and earthquakes, a simple disc load model is used to: (1) calculate stresses induced in the lithosphere and mantle by glacial loading, melting and postglacial rebound; and (2) evaluate the effect of glacial loading/rebound on the failure potential for earthquakes in the upper crust. the dependence of the failure potential and the actual mode of failure on the coefficient of friction, the ambient tectonic stress magnitude/direction, the stress due to the overlying rocks, and lithospheric thickness are investigated. Prominent features of this paper are the inclusion of: (1) a viscoelastic mantle and thus the migration of stress; and (2) the ambient tectonic stress and overburden stress contributions in the calculation of the total stress field. It is assumed that, throughout the Earth, there are optimally oriented pre-existing virtual faults that are initially close to but not at failure; thus, a time-dependent quantity called dFSM (related to the Coulomb-Mohr failure criterion) can be defined such that a negative value of dFSM would advocate faulting or earthquake activities whereas a positive value of dFSM would promote stability. The results indicate that, under all combinations of tectonic stress magnitude and overburden stress, crustal loading promotes fault stability directly underneath the load. Upon the removal of the load, thrust faulting is predicted within the ice margin if the horizontal stress (Sh) induced by the overburden is greater than or equal to the vertical component (Sv) of the overburden stress (1, where=Sh/Sv). Under this condition, theory predicts that faulting or earthquake activity should have reached a maximum immediately after deglaciation. If the horizontal stress induced by the overburden is less than the vertical component of the overburden stress (>1), then theory predicts fault stability within the ice margin. The theory predicts fault instability both north and south of the ice margin. the mode of failure, however, is completely determined by the value of The trade-off between the tectonic stress magnitude and the overburden stress parameter () is also investigated. It is shown that a larger tectonic stress magnitude can be used to compensate a smaller value of the results of this analysis show that variations in the coefficient of friction, lithospheric thickness and a ductile zone below the upper crust do not significantly affect the above conclusions.

Calculation of stress fields near inclusions by use of the fracture mechanics weight function

The weight function method normally applied to fracture mechanics problems is applied to problems without cracks. A procedure is described which allows the stresses in the surrounding of inclusions to be computed. The method is applied to compute stresses near inclusions and phase-transformation zones in infinite bodies. The results are in good agreement with analytical and FE solutions.

Computation of transient hygroscopic stresses in laminated composite plates

This paper deals with the calculation of transient and non-uniform stress fields which are induced by transient moisture concentration distributions in laminated composite plates. It is shown that the heterogeneity and anisotropy of such plates generally result in transient stress distributions which are very different from the equilibrium stress distributions. Some stacking sequences exhibit important stresses within the plies. These stresses have to be taken into account for the design of composite structures submitted to a moist environment.

Effect of Slide-to-Roll Ratio on Interior Stresses Around a Dent in EHL Contacts

The present, study extends the transient EHL point contact model and subsurface stress field calculation model to examine the influence of a surface dent on interior stresses in an EHL point contact under various slide-to-roll conditions. Results revealed that under the pure rolling condition the effect of a surface dent on the stresses is quite negligible. The presence of a shallow surface dent is unlikely to reduce the contact fatigue, life so long as pure rolling motion and good lubrication conditions are maintained. Unfortunately, the same cannot be said of the contact if it is operating in the boundary lubrication regime. When sliding was introduced, the surface indentation generated significantly high pressure spikes with a strong directional preference. These high-pressure spikes cause severe stress concentrations either below the trailing edge of the dent, if it moves faster than the opposing surface, or below the leading edge of the dent, if it moves slower than the opposing surface. The maximum ...

Superconductor superlattice model for small-angle grain boundaries in Y-Ba-Cu-O.

The measured critical current ratios of small-angle Y-Ba-Cu-O grain boundaries fabricated by Dimos {ital et} {ital al}., are calculated from a superconducting superlattice model where the periodicity is given by the Read-Shockley formula. The layers` thicknesses are estimated from stress-field calculations of a periodic edge-dislocations array model. The measured critical current dependence on the misalignment angle and the temperature are reproduced with a single fitting parameter. This parameter is related to the stress field in proximity to an edge dislocation. The model`s validity and comparison with other attempts at the same data are discussed.

Damage mechanics approach for predicting high-temperature crack growth under mixed-mode loading conditions

Recent studies of the factors that control high-temperature crack growth under mixed-mode loading conditions are reviewed. In particular, measurements of crack growth direction and crack growth rate in specially designed specimens under mode I, mode II and mixed-mode loading conditions are discussed. Attempts have been made with the aid of finite element results to determine how both the crack path and the crack growth rate are influenced by the nature of loading. Discrepancies as to the ability of the von Mises equivalent stress in correlating the experimental data have been observed. A damage mechanics approach is proposed that brings mixed-mode crack growth data into better agreement when plotted against an effective value of C ∗ . This approach is also shown to correlate mixed-mode stress field calculations with reported observations of crack growth direction. The results demonstrate the importance of addressing damage mechanics ahead of the crack tip for accurate predictions of high-temperature crack growth under mixed-mode loading conditions.

δ' nucleation and growth on low-angle dislocation boundaries in Al-Li

A transmission electron microscopy (TEM) investigation indicates that, at small undercooling, δ' (Al 3 Li) precipitates are restricted almost entirely within the strain fiield of dislocations in the early stages of aging and preferentially nucleate on edge dislocations and low-angle dislocation boundaries. The study is conducted on binary Al-Li alloys which are cold rolled to a 50% reduction in area. Two types of dislocation boundaries, i.e. simple tilt boundaries and a planar network of dislocations, are characterized by two-beam analysis. The role of the simple tilt boundaries on competitive growth kinetics of δ' precipitates is quantitatively examined. The experimental results support the related theoretical prediction on the effect of the simple tilt boundary stress field on solute diffusion. Concerning the dislocation network, δ' nucleates on dislocation node configurations where the reacted dislocation has a large edge component and at the site of the network plane where the dilatation stress is compressive. This is confirmed by calculation of the dilatation stress field of the dislocation nodes which also further clarifies and is consistent with the experimental observations

Demagnetization due to inverse magnetostriction effects in longitudinal thin film media

Unpredictable mechanical stresses that occur during the operation of hard disk drives can degrade the recorded signal. On the basis of a micromagnetic analysis and the calculated stress field during head-disk impact, inverse magnetostriction effects in longitudinal recording thin film media are considered and demagnetization due to head-disk impact is simulated numerically. Thin film media are modeled as planar hexagonal arrays of hexagonally shaped grains. The computation uses the conjugate gradient algorithm to minimize the variation of the total energy. In particular, the effect of the stress on the relaxation process is investigated. Also the change in the remanent magnetization due to repetitive head-disk impacts is calculated. We obtained results indicating that the effect of the impact stress during dynamic loading is not so significant as to cause data loss during operation for the longitudinal thin film media. >