Showing papers on "Hydrostatic stress published in 2010"

The physics of chemical strengthening of glass: Room for a new view

Abstract: Glasses strengthen during an ion exchange experiment as a result of the high surface compression that develops from the stuffing of the invading alkali ion into the smaller host alkali ion site and the non-relaxation of this compression. The kinetics are described in terms of a Nernst–Planck interdiffusion coefficient of the exchanging ions in a stack of mixed-alkali glass layers with varying ratios of the alkali. The interdiffusion coefficient is suppressed by compression and enhanced by tension. However, the measured surface compression is usually 2–4 times lower than that calculated using thermal stress analogy incorporating an elastic suppression of the molar volume difference of the as-melted mixed-alkali glasses. A new view of the physics of deformations and failure of stress to continue to buildup is presented in an effort to seek technology improvements. Reduced stresses are ascribed to network yield in two separate modes: yielding of the shape-conserving hydrostatic stress component which prevents elastic expansion of molar volume and yielding of the volume-conserving deviatoric (pure shear) stress which leads to measurable shape change. An anomalous subsurface tension is also explained in this view. By drawing analogy to microindentation, it is concluded that optimum network topology glasses should undergo the least plastic deformation and, hence, develop a higher surface compression.

An experimental investigation of fracture by cavitation of model elastomeric networks

Abstract: A new methodology to investigate the failure of elastomers in a confined geometry has been developed and applied to model end-linked polyurethane elastomers. The experimental in situ observations show that the elastomers fail by the growth of a single cavity nucleated in the region of maximum hydrostatic stress. Tests carried out at different temperatures for the same elastomer show that the critical stress at which this crack grows is not proportional to the Young's modulus E but depends mainly on the ratio between the mode I fracture energy G IC and E. A reasonable fit of the data can be obtained with a model of cavity expansion by irreversible fracture calculating the energy release rate by finite elements with a strain hardening constitutive equation. Comparison between different elastomers shows that the material containing both entanglements and crosslinks is both tougher in mode I and more resistant to cavitation relative to its elastic modulus.

Probabilistic multiscale models and measurements of self-heating under multiaxial high cycle fatigue

Abstract: Different approaches have been proposed to link high cycle fatigue properties to thermal measurements under cyclic loadings, usually referred to as “self-heating tests.” This paper focuses on two models whose parameters are tuned by resorting to self-heating tests and then used to predict high cycle fatigue properties. The first model is based upon a yield surface approach to account for stress multiaxiality at a microscopic scale, whereas the second one relies on a probabilistic modelling of microplasticity at the scale of slip-planes. Both model identifications are cost effective, relying mainly on quickly-obtained temperature data in self-heating tests. They both describe the influence of the stress heterogeneity, the volume effect and the hydrostatic stress on fatigue limits. The thermal effects and mean fatigue limit predictions are in good agreement with experimental results for in and out-of phase tension-torsion loadings. In the case of fatigue under non-proportional loading paths, the mean fatigue limit prediction error of the critical shear stress approach is three times less than with the yield surface approach.

Simple Shearing of Incompressible and Slightly Compressible Isotropic Nonlinearly Elastic Materials

Abstract: The classical problem of simple shear in nonlinear elasticity has played an important role as a basic pilot problem involving a homogeneous deformation that is rich enough to illustrate several key features of the nonlinear theory, most notably the presence of normal stress effects. Here our focus is on certain ambiguities in the formulation of simple shear arising from the determination of the arbitrary hydrostatic pressure term in the normal stresses for the case of an incompressible isotropic hyperelastic material. A new formulation in terms of the principal stretches is given. An alternative approach to the determination of the hydrostatic pressure is proposed here: it will be required that the stress distribution for a perfectly incompressible material be the same as that for a slightly compressible counterpart. The form of slight compressibility adopted here is that usually assumed in the finite element simulation of rubbers. For the particular case of a neo-Hookean material, the different stress distributions are compared and contrasted.

Coupled Analysis of Hydrogen Transport using ABAQUS

Abstract: This paper describes two user subroutines developed within ABAQUS to simulate coupled hydrogen transport equations. Developed user subroutines incorporate two key features in coupled hydrogen transport equations, such as the hydrostatic stress and plastic strain effects on hydrogen transport, and hydrogen-induced dilatational deformation rate. To validate developed subroutines, present simulation results are compared with published results, showing good agreements for all cases considered.

Analysis of the Influence of Hydrostatic Stress on the Behaviour of an Adhesive in a Bonded Assembly

Abstract: Generally, adhesives are viscoelastic–plastic materials, for which the development of viscosity and plasticity varies depending on the type of adhesive and the stress state. Various models exist to represent the yield surface, or the so-called elastic limit, taking into account the two stress invariants, hydrostatic stress and von Mises equivalent stress. Moreover, to develop precise pressure-dependent constitutive models, it is necessary to have a large experimental database in order to accurately represent the adhesive strains which are strongly dependent on the tensile-shear loading combination. Under quasi-static loadings, for a given strain rate range viscous effects can be neglected, but only a few experimental results are available to model the behaviour of the adhesive in a bonded assembly accurately under realistic loadings. Moreover, edge effects often have a large influence on the mechanical response. This paper presents the possibility of combining the use of an experimental device, which stro...

Modelling the effect of hydrogen on ductile tearing resistance of steels

Abstract: The effect of hydrogen on the mechanical behaviour of steels is twofold: it affects the local yield strength and it accelerates material damage. On the other hand, the diffusion behaviour is influenced by the hydrostatic stress, the plastic deformation and the strain rate. This requires a coupled model of deformation, damage, hydrogen sorption and diffusion. The deformation behaviour is described by von Mises plasticity with isotropic hardening, and crack extension is simulated by a cohesive zone model. The local hydrogen concentration, which is obtained from the sorption and diffusion analysis, causes a reduction in the yield strength and the cohesive strength. Crack extension in a C(T) specimen of a ferritic steel under hydrogen charging is simulated by fully coupled finite element analyses of hydrogen kinetics and mechanical behaviour. The simulation results are compared with test results.

Triaxial deformation behavior of bituminous mixes

Abstract: The triaxial compressive response of bituminous mixes with volume fractions of aggregate in the range 52 to 85% was investigated over a wide range stresses and strain rates. The types of loadings considered include triaxial monotonic constant stress and constant applied strain rate, as well as creep recovery, continuous cyclic, and stress pulse train loadings. The mixes with a "fully dense" aggregate skeleton were found to dilate under all loading conditions and the creep response of the mixes was dependent on both the deviatoric and hydrostatic stresses. By contrast, recovery was found to occur under zero applied deviatoric stresses with the recovery rate only dependent on the "recoverable strain" and independent of any superimposed hydrostatic stress. Continuous and pulse loading cyclic stress-controlled tests showed that the response of the mixes was governed by the mean applied deviatoric stress in the continuous cyclic tests while strain recovery was important in the pulse loading tests. A phenomenological constitutive model was proposed to fit the measured triaxial response of the bituminous mixes and shown to capture the measurements over all the triaxial stress states and loading time histories investigated here. Furthermore, the model was extended to capture the temperature dependence of the mixtures which is governed by the temperature dependence of the bitumen binder.

Unified solutions for stresses and displacements around circular tunnels using the Unified Strength Theory

Abstract: The unified solutions are presented for stresses and displacements around a circular tunnel subjected to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic and governed by the Unified Strength Theory. The displacements are obtained accounting for three different definitions for elastic strains and different Young’s modulus in the plastic zone. The unified solutions obtained in this paper are especially versatile in reflecting the intermediate principal stress effect to different extents for different materials. The conventional solutions, based on the Mohr-Coulomb failure criterion and the Generalized Twin Shear Stress yield criterion, are special cases of the present unified solutions. The new unified solutions can compare with those computed by the latest generalized Hoek-Brown failure criterion. The results obtained demonstrate the importance of the intermediate principal stress influence for the stresses and displacements analysis. The effects of different definitions for elastic strains and different Young’s modulus in the plastic zone on the displacements are significant.

Modeling of electromigration of the through silicon via interconnects

Abstract: A finite element model which includes electromigration, thermomigration, stress migration and concentration diffusion is established to study the mass diffusion phenomenon. Numerical experiment is carried out to obtain the electrical, thermal, stress and atomic concentration fields of the sweat and through silicon via (TSV) structure under high current density load. The effectiveness of the electromigration FEM model is confirmed by the simulation of the sweat structure. The results from the simulation are consistent with the observation of the experiment conducted by Dallleau, D. et al. The current crowding, temperature distribution, von Mises and hydrostatic stress distribution and atomic concentration fields of the TSV structure is obtained from the numerical calculation. The current crowding occurs at the corner of the copper pad. The maximum compressive hydrostatic stress happens in the center of the copper via and the center of copper pads are under tensile hydrostatic stress which has important role in the migration of copper atoms. The probable location where the void and hillock may be generated is identified through the atomic distribution after 10000-second electromigration simulation. The migration failure mechanism which is critical for design and application of TSV technology in the 3D package is investigated.

Mechanical behaviour of transversely isotropic porous neo-hookean solids

Abstract: In this paper, the mechanical responses of a recently developed hyperelastic model for the neo-Hookean solids with aligned continuous cylindrical pores under finite homogeneous deformation that can capture the anisotropic compressibility as well as the coupling between the volumetric and deviatoric behaviours are examined. To this end, the strain energy function of this hyperelastic compressible transversely isotropic model contains terms for the coupling of volumetric and deviatoric behaviours. It is shown that, the asymptotic response of this anisotropic compressible model under extreme loading situations is considerably different from that of incompressible models. The unstable behaviour of the porous solid under hydrostatic stress/strain loadings is discussed in detail. When a general simple 2D shear deformation is applied to this porous solid in i1 – i2 plane, the normal stress in the third axial direction (i3) is nonzero. The loss of monotonicity of the stress tensor under off-axis simple 2D shear loading is demonstrated as well.

On Formulas for the Velocity of Rayleigh Waves in Prestrained Incompressible Elastic Solids

Abstract: In the present paper, formulas for the velocity of Rayleigh waves in incompressible isotropic solids subject to a general pure homogeneous prestrain are derived using the theory of cubic equation. They have simple algebraic form and hold for a general strainenergy function. The formulas are concretized for some specific forms of strain-energy function. They then become totally explicit in terms of parameters characterizing the material and the prestrains. These formulas recover the (exact) value of the dimensionless speed of Rayleigh wave in incompressible isotropic elastic materials (without prestrain). Interestingly that, for the case of hydrostatic stress, the formula for the Rayleigh wave velocity does not depend on the type of strain-energy function. © 2010 by ASME. Author Keywords: Incompressible; Prestrains; Prestresses; Rayleigh wave velocity; Rayleigh waves Index Keywords: Cubic equations; Elastic materials; Elastic solids; Hydrostatic stress; Isotropic solids; Parameters characterizing; Pre-strain; Prestrains; Prestresses; Rayleigh wave velocity; Strain energy functions; Acoustic wave velocity; Strain energy; Wave propagation; Rayleigh waves

Experimental Characterization of Damage Processes in Aluminum AA2024-O

Abstract: Much of the damage mechanics literature has focused on void growth due to tensile hydrostatic stress. To clarify the effect of combined shear stress and hydrostatic stress on the development of damage, specimens of various geometries were employed in an experimental program to cover a wide range of triaxiality and shear stress. Digital image correlation (DIC) is utilized to measure the fracture strain of the 2D specimens. Experiments are paired with simulations utilizing J 2 plasticity theory to complement the experiments and relate the fracture strain with combined hydrostatic and shear stresses. The results display accelerated damage for cases dominated by shear at low triaxiality. Crystal plasticity simulations were carried out using boundary conditions based on the DIC displacement field. These simulations indicate that tensile hydrostatic stress develops due to grain-to-grain interaction.

Magneto-elastic stress induced by an electric current in an infinite thin plate with an elliptical hole

Abstract: Two-dimensional magnetic field and stress analyses have been presented for soft ferromagnetic, paramagnetic, and diamagnetic materials of an infinite thin plate with an elliptical hole under steady electric current. The magnetic stress has been analyzed in the Maxwell Stress Model. Except for the approximation of the plane stress state since the plate is the thin plate, any assumption is not made for the stress analysis, though the Maxwell stress components are expressed by nonlinear terms. The boundary condition expressed by Maxwell’s stress is completely satisfied without any linear assumptions on the boundary. Two ways for the boundary condition are stated. The analysis of σz in the direction of the plate thickness is also carried out. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived, and the magnitude of the stress intensity factor for the magnetic stress and thermal stress due to the Joule heat caused by the electric current is discussed.

Modelling of the inertia welding of Inconel 718

Abstract: In this study, the inertia welding process was studied by both an FEM model and three analytical models. The thermal analysis shows that there is a steep temperature gradient near the mating surface, which is the cause for the existence of a band of high hydrostatic stress near the weld line. The holding effect of this high static stress is the reason for the presence of the very soft material at the welding interface. The models were used to predict the displacement of the weld line (upset) with a lambda model to describe the constitutive relation of IN718 at high temperature. The results from the different models are in broad agreement. The shear stress induced by friction at the interface is found to enlarge the upset value; its effect must be taken into account if the upset is to be predicted accurately. The extrusion of the burr during the last second of the welding is a direct result of the quick stop of the rotating part due to the balance of the momentum, which is clearly explained by the analytical mechanical model put forward in this work.

Numerical analysis of vacancy transport by residual stress in electromigration on LSI interconnects

Abstract: The Li multiplication method for the driving force induced particle migration equation was proposed to solve numerically the stress and electric fields induced vacancy migration equation. On the basis of this method, vacancy migration behaviors were found to be predicted under the competitive relationship between stress and electric field. When a residual stress is dominant, vacancies concentrate around the maximum hydrostatic stress region, such as elastic–plastic boundary. On the other hand, when the electric field is dominant, vacancies do not concentrate around the maximum hydrostatic stress region, but move from the cathode end to the anode end. An in situ observation of electromigration on AlCuSi interconnect was conducted to verify the simulation results. A void nucleated and grew at the tip of a notch on an AlCuSi line without passivation film, while many voids appeared and grew in cathode side in a line with passivation film. Greater hydrostatic stress gradient is considered to occur in the line without passivation film, owing to a small scale of yielding, and this leads to concentrate void formation at the tip of the notch. These results indicate that numerical analysis of electromigration is valid to represent the experimental result. Based on results mentioned above, various failure modes in interconnects cased by electromigration are predictable by the proposed Li multiplication method.

Optimal lower bounds on the local stress inside random thermoelastic composites

Abstract: A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on the maximum local stress. Explicit formulae for the optimal lower bounds are found that are expressed in terms of the applied macroscopic thermal and mechanical loading, coefficients of thermal expansion, elastic properties, and volume fractions. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to the applied loads and the thermal stresses inside each phase. These bounds are shown to be the best possible in that they are attained by the Hashin-Shtrikman coated sphere assemblage.

Macroscopic stress from dynamic, rotating granular media

Abstract: In this brief study, the stress is averaged over a two-dimensional rigid particle (disk) that is in contact with other objects via localized (point) contacts. In contrast to previous studies, the rotation dynamics of the particles is also taken into account here The stress contains four terms, (i) the static stress due to forces, (ii) the dynamic stress due to translational velocity fluctuations, (iii) the dynamic stress due to rotational velocity fluctuations, and (iv) the stress due to changes of angular velocities due to torques.

Influences of lubricant pocket geometry and working conditions upon micro-lubrication mechanisms in upsetting and strip drawing

Abstract: Micro-lubricant pockets located in the surface of plastically deforming workpieces are recognised to improve the performance of fluid lubrication in a metal-forming process. This work investigates the joint influence of pocket geometry and process working conditions on micro-lubrication mechanisms, during upsetting and strip drawing, by means of a rigid-viscoplastic finite-element formulation. Special emphasis is placed on the effect of pocket geometry on the build-up of hydrostatic pressure, which is responsible for the onset of micro-lubrication mechanisms. A good agreement is found between the numerically predicted and the experimentally measured distributions of hydrostatic stress.

Modelling Limit States Within the Framework of Hypoplasticity

Abstract: The focus of this paper is on modelling limit stress states or so‐called critical states in which a cohesionless granular body can be deformed continuously at a constant stress and a constant volume. The constitutive equations are based on the framework of hypoplasticity, which is an alternative concept to elasto‐plasticity. The requirements for modelling limit stress states are studied for both a standard and a micro‐polar hypoplastic model. As in a micro‐polar description the stress tensor is usually non‐symmetric, the question arises as to whether the result for the limit stress ratio based on the symmetric Cauchy stress tensor in the standard continuum is the same as the one obtained from the micro‐polar continuum description. To this end the limit stress state is analysed under plane shearing of a lateral infinite granular strip located between parallel rough platens under a constant normal stress. It is shown that the stress ratio in the limit state obtained from the micro‐polar hypoplastic model ca...

Quasicontinuum simulation of crack propagation in nanocrystalline Ni

Abstract: The propagation process of crack in the nanocrystalline Ni is simulated via the quasicontinuum method. The results show that the stress near the crack tip could prompt the disassociation of grain boundaries, and the formation of stacking faults and deformation twins. Farther front the crack tip, fewer deformation twins can be found. There are more stacking faults than deformation twins in the grains, which approximately have the same distance to the crack tip. The effect on deformation twins front the variation of local stress and generalized planar fault energies is manifested by these results. The distribution of hydrostatic stress on atomic-level around the crack tip is also calculated. It is shown that nanovoids can be easily created in grain boundaries in front of the crack tip. There exists an intense tensile stress state in the grain boundary regions around these nanovoids. As a result of the stress accumulation, the crack propagates along the grain boundaries. Our simulated results qualitatively uncover the propagation process of crack in nanocrystalline Ni, which agrees well with the relevant experimental results.