Subsurface Stress Field Research Articles

Visualization of Geologic Stress Perturbations Using Mohr Diagrams

Huge salt formations, trapping large untapped oil and gas reservoirs, lie in the deepwater region of the Gulf of Mexico. Drilling in this region is high-risk and drilling failures have led to well abandonments, with each costing tens of millions of dollars. Salt tectonics plays a central role in these failures. To explore the geomechanical interactions between salt and the surrounding sand and shale formations, scientists have simulated the stresses in and around salt diapirs in the Gulf of Mexico using nonlinear finite element geomechanical modeling. In this paper, we describe novel techniques developed to visualize the simulated subsurface stress field. We present an adaptation of the Mohr diagram, a traditional paper-and-pencil graphical method long used by the material mechanics community for estimating coordinate transformations for stress tensors, as a new tensor glyph for dynamically exploring tensor variables within three-dimensional finite element models. This interactive glyph can be used as either a probe or a filter through brushing and linking.

Contact Fatigue Life Analysis Of Rough Surfaces

An analytical model to calculate the contact fatigue life of rough surfaces is presented in this paper. The effect of surface roughness can be calculated using this model. The computational method and the theoretical basis are also discussed. Contact stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions; the subsurface stress field is obtained using rectangular patch solutions. A mesoscopic multiaxial fatigue criterion which can yield satisfactory results for non-proportional loading is then applied to predict fatigue damage. A suitable counting method and damage rule were used to calculate the fatigue life of random loading caused by a rough surface. As a result of the analysis the relationship between the life and the roughness as well as the most probable depth of the crack initiation is calculated.

Evaluation of cyclic inelastic response in fretting based on unified Chaboche model

Fretting in high strength metalline materials is one of primary failure mechanics that reduces the structural integrity of engineering component. The cyclic deformation response in the region experiencing fretting plays a central role. A unified cyclic viscoplasticity Chaboche model at finite deformations that incorporates fully explicit contact analysis is used to investigate the plastic strain history in fretting process. The analyses are accompanied by finite element simulations using a non-linear kinematic hardening rule with isotropic cyclic hardening and the full details of contact behavior are solved for at all stages of the loading. Numerical evaluations have explored the nature of subsurface cyclic plasticity and interface contact stress fields for realistic fretting fatigue geometries for an applied bulk stress amplitude with a stress ratio of R=−1, two tangential loads, and two different values of coefficient of friction. The characteristics of the fretting fatigue, including local cyclic stress strain and cumulative plastic strain are all better described. Owing to the fact that the plastic anisotropy in the scale of grain size plays a significant role especially in the very local region near the contact edge, an analysis of plastic anisotropy is presented in fretting problem. In the case of fretting configuration considered here, the plastic history combines cyclic plasticity and plastic ratcheting when plastic anisotropy is considered, while the ratcheting plasticity dominates during the fretting process without consideration of plastic anisotropy.

Microstructural Effects in Multilayers with Large Moduli Contrast Loaded by Flat Punch

An efficient solution methodology is employed for the frictionless contact of half-planes built up with large number of layers to study the effect of microstructural refinement on the surface and subsurface stress fields. Half-planes with increasing numbers of alternating stiff and soft layer pairs spanning a fixed depth below the top surface are considered to determine the convergence behavior of the contact pressure and subsurface stresses relative to the corresponding quantities in fully or partially homogenized configurations with macroscopically equivalent properties. The results indicate that not all stress components converge to the corresponding values in the fully homogenized configuration with increasing microstructural refinement. This is only achieved by a partial homogenization wherein the layered half-plane is homogenized below a certain depth with the top surface layers retained. The number of retained surface layers required for an accurate stress field reproduction depends on the punch length and microstructural scale and depth of the alternating layers. The characteristic contact pressure profiles observed in the layered configurations suggest a basis for the development of a sensing technique for the microstructural architecture and property identification of the subsurface region.

Thermomechanical Analysis of Semi-infinite Solid in Sliding Contact With a Fractal Surface

A thermomechanical analysis is presented for a semi-infinite elastic solid sliding against a rigid, rough surface characterized by fractal geometry. A piecewise-linear distribution of the contact pressure was obtained by superposition of overlapping triangular pressure elements. The normal surface displacements due to the effects of contact pressure, shear traction, and thermoelastic distortion caused by frictional heating are incorporated in the influence coefficients of the matrix-inversion method. Results for a smooth, cylindrical surface sliding over a semi-infinite elastic solid demonstrate the accuracy of the analysis and provide reference for comparison with results obtained with the rough (fractal) surface. The effects of surface topography and interaction between neighboring asperity microcontacts on the surface and subsurface temperature rise and stress field of the elastic semi-infinite solid are discussed in the context of numerical results. The significance of frictional heating on the contact pressure, temperature rise, and stresses is interpreted in terms of the Peclet number and topography (fractal) parameters. The results provide insight into the likelihood for cracking and plastic flow at the surface due to the combined effects of mechanical and thermal surface tractions.

Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

The impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β⩽1), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β>1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β⩽1, and increases gradually for β>1. Based on finite element results for the subsurface stress, strain, and velocity fields, a simple theoretical model that yields approximate closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β⩽1), and its validity was confirmed by favorable comparisons with finite element results.

Atomic scale stresses and strains in Ge∕Si(001) nanopixels: An atomistic simulation study

Recent progress in the growth of nanostructures on nonplanar (patterned) substrates has brought to the forefront issues related to atomic-level surface and subsurface stress and strain field variations, as these govern the process of formation of such nanostructures and strongly affect their physical properties. In this work, we use atomistic simulations to study the atomically resolved displacements, stresses, strains, and the strain energy in laterally finite nanoscale Si(001) mesas, uncovered and covered with the lattice-mismatched Ge overlayers. The spatial variations of the stress are examined both across the surface profile of the mesas and in the direction down to the substrate. We find that the hydrostatic stress and strain at the Ge∕Si interface undergo rapid changes from tensile in the interior of the Si mesa to compressive in the Ge overlayer, with the transition taking place over distances of the order of Si lattice constant. Substantial relaxation of the hydrostatic stress and strain, in both the lateral and vertical directions, is observed in the Ge overlayer, in the Si(001) mesa interior, and in the substrate. Atomic displacement fields, computed in the Ge overlayer and in the Si(001) mesa interior, demonstrate considerable inhomogeneity due to both finite geometry effects and the lattice-mismatched Ge overlayer–induced stresses. The maximum magnitude of displacements is as large as 0.7Å, even in the case of uncovered Si(001) mesa. Moreover, we find nonzero displacements in the Si substrate as far deep as 100ML (monolayer) from the Ge∕Si interface, showing that a substantial degree of the misfit-induced stress accommodation occurs through relaxation in the Si(001) mesa interior and the substrate. The topology of the equal displacement contours, in regions adjacent to the mesa edges and corners, is close to semielliptical. To reveal the impact of stress accommodation in the mesa interior and in the substrate, we compute the strain energies of the Ge overlayer atoms as a function of both the Si(001) mesa height and the Ge overlayer thickness. We find that the normalized (per Ge atom) elastic energy of a fixed thickness overlayer decreases with increasing mesa depth. At a fixed mesa height, the Ge overlayer energy per Ge atom increases as a function of Ge overlayer thickness. In both cases, the dependencies are shown to be adequately fitted with exponential forms. The shear stresses in both bare and 16ML thick Ge overlayer covered mesa systems show dramatic variations in both lateral and vertical directions. These variations are responsible for nonlinear stress-strain behavior in the regions around the finite geometry features (i.e., edges and corners).

Analysis of rough line contacts operating under mixed elastohydrodynamic lubrication conditions

AbstractHeavily loaded machine elements, such as gears, usually operate in the mixed lubrication regime. Surface roughness has a significant effect on the pressure distribution, the subsurface stress field, and the friction coefficient. Based on the superposition of a dry rough and a fully flooded smooth contact, a mixed lubrication model has been developed. The roughness profile is assumed to be known. Surface deformation is calculated by taking into account the pressure distribution that is built up by asperity contacts, asperity interactions, and lubricant flow. Thermal and sliding effects are incorporated into the analysis. Non‐Newtonian lubricant behaviour is considered by using a power‐law rheological model. The pressure distribution, subsurface stress field, and friction coefficient were calculated from the model at several points along the contact path for an FZG type C gear pair. It was shown that a significant part of the load is carried by the contacting asperities. The position of the maximum shear stress is very close to the surface.

The Fatigue Crack Initiation Life Prediction Based on Several High-Cycle Fatigue Criteria under Spherical Rolling Contact

In this study, the simulation of rolling contact fatigue is conducted under spherical contact. To predict a crack initiation life accurately, it is necessary to calculate contact stress and subsurface stresses accurately. Contact stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and the subsurface stress field is obtained using rectangular patch, solutions. Based on these stress values, several multiaxial high-cycle fatigue criteria are used and the critical loads corresponding to fatigue limits are calculated. The criteria were classified into three categories, namely the critical plane approach, the stress invariant approach and the approach based on the mesoscopic scale. The simulation results show that the critical load is decreasing rapidly and the site of crack initiation also moves rapidly to the surface from the subsurface when the friction coefficient exceeds a specific value for all three fatigue criteria. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Cancun, Mexico October 27–30, 2002

Effects of Surface Micro-Geometry on the Pressures and Internal Stresses of Pure Rolling EHL Contacts

A fast approach for the calculation of 3-D pressures and subsurface stresses in pure rolling EHL contacts with real (measured) roughness is presented. For the calculation of pressures the model uses the analytical work of Greenwood and Morales-Espejel for transverse (to the rolling direction) moving sinusoidal waviness. The model is extended to handle longitudinal waviness as well. By using these two basic components the pressure distribution for real rough surfaces can now be calculated form the 3-D roughness map. From the surface pressures, the sub-surface stress field can then be calculated with a similar technique. The result is the total Stress State in a rolling rough EHL contact. In this paper the method for calculating the pressures and stress fields is first described. It is then applied to several types of surface finish. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Cancun, Mexico October 27–30, 2002

Subsurface stress field of a dry line contact

The calculation of the pressure distribution and the subsurface stress field developed at the dry line contact of two cylinders, can be carried out with sufficient accuracy, using the Hertzian theory assuming that both cylinders are smooth. However, for the investigation of surface failures, such as micro-pitting, Hertz’s solution cannot be applied, because the effect of roughness is significant. This paper presents a model for the determination of the asperity pressure distribution at the contact of two rough cylinders, assuming elastic–perfectly plastic deformation. Having determined the surface load, the subsurface stress field is then calculated. The effect of roughness on the stress field is investigated. For this investigation, numerically generated rough surfaces are used. The results show that the maximum shear stresses developed in small depths are significantly higher than those predicted by the Hertzian solution. This conclusion is in good agreement with the small depth of cracks observed on the flanks of gears that have suffered from micro-pitting.

Analyzing Elastic-Plastic Real Rough Surface Contact in Running-in

A numerical method is presented for evaluating the elastic-elastic contact of real rough surface contacts during running-in. For the surface contact, an elastic-plastic model based on the variational method is applied to analyze the pressure distribution and contact area of worn surfaces during running-in. In conjunction with the classical statistic model of Greenwood and Williamson, the numerical result showed that the plasticity index Ψ was decreased to one in the elastic range as running-in proceeded. In comparison with the Hertzian solution, the influence of the asperities is very significant on the pressure distribution, thereafter causing a higher peak value of contact pressure. For the subsurface, the interior stress from the von Mises criterion was calculated to evaluate the subsurface stress field subject to both normal and tangential forces. In the calculated of the interior stress, the total stress is decomposed into a fluctuating component and a smooth component. The fluctuating part is solved by using FFT from the concept of the convolution theorem while the smooth part is obtained directly by analytical solution. Calculations of contact area and subsurface stress on experimentally produced surfaces whose topography has been determined using an atomic force microscope and friction coefficient front sliding have been carried out. The results showed that asperities and friction coefficient gave rise to stress increase in the near-surface stress field and produced a high stress zone towards the surface. As a result, transverse asperity cracking was produced. The calculations and supporting experimental evidence clearly confirmed that the reduction of peak pressure during running-in decreased the plastic deformation of contact.

A Theoretical Study of Residual Stress Effects on Fatigue Life Prediction

Recently, the trend has been toward the use of the full subsurface stress field in rolling element bearing fatigue life prediction (stress field-based life models). By using the stress field-based bearing life models, more accurate assessments of such things as fitting practice and thermal treatments on the bearing performance are achieved. However, one aspect missing in most models has been the consideration of the changing residual stress during operation of the bearing. This study was conducted to investigate the time dependent residual stress on contact fatigue life predictions. This study concluded that the changes in residual stress during operation were most likely a fatigue reaction of the material to the pre-fatigue residual stress and cyclic contact stress fields. The materials fatigue response changes the instantaneous values of the material constants in most stress field-based life equations, thus making them in-calculable. As such, the pre-fatigue residual stress field should be used in the stress field-based models. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in San Francisco, CA October 21–24, 2001

Effect of friction on subsurface stresses in sliding line contact of multilayered elastic solids

A numerical integral scheme based on Fourier transformation approach is employed to investigate the effect of friction on subsurface stresses arising from the two-dimensional sliding contact of two multilayered elastic solids. The analysis incorporates bonded and unbonded interface boundary conditions between the coating layers. Two line contact problems are presented. The first one is the contact problem between a rigid cylinder and a two-layer half space and the second one is the indentation of a multilayered elastic half-space by a flat rigid punch. The effects of the surface coating on the contact pressure distribution and subsurface stress field are presented and discussed.

Numerical Analysis for the Elastic Contact of Real Rough Surfaces

The elastic contact of rough surfaces and the subsurface stresses caused by the contact have been analyzed by means of a numerical model based on fast Fourier transforms (FFT) and minimization of complementary energy. The elastic contact has been modeled mathematically as a linear complementarity problem and solved by a robust algorithm, Conjugate Gradient Method, while the force-displacement relation is determined through a FFT approach. After solving for the pressure distribution, the subsurface stress field is obtained by calculating the stresses due to the application of a point force, and then integrating over the contact region. In comparison with the matrix based method published in recent years, the numerical approach presented in this study is more efficient, more stable and requires less memory. It has great potential in application to problems with general contact geometry and three-dimensional surface roughness. The results show that high frequency roughness could lead to very sharp impulses and significant oscillations in pressure distribution. The amplitude and location of the maximum shear stress in the subsurface region are constantly changing when the contacting rough surfaces are in relative motion. Presented at the 53rd Annual Meeting in Detroit, Michigan May 17–21, 1998

Boundary element modelling of coated materials in static and sliding ball–flat elastic contact

Boundary element modelling of elastic ball–flat contact is presented. The loading of a homogeneous medium is considered and the validity of the half space assumption is shown to depend on the relative dimensions of the specimen; i.e. the ratio of the real dimensions over the contact radius. The subsurface stress field in a coating–substrate composite is analysed. It is influenced by the ratio of Young's moduli of the materials. As to the impact of relative specimen dimensions, the key parameter is the relative coating thickness. All the general tendencies of the subsurface stress field modifications are identical to those of plane strain (cylinder–flat) contact geometry. Friction is shown to mainly affect stresses in the coating close to the contact surface.

Experimental and Theoretical Investigation on Rolling Contact Fatigue of 52100 and M50 Steels Under EHL or Micro-EHL Conditions

The purpose of this investigation is to clarify the role of roughness on rolling contact fatigue. Tests have been carried out on a two-disk machine, for two rolling bearing steels (52100 and M50), two surface roughnesses corresponding to EHL and micro-EHL conditions (two different surface finishing), three normal loadings (1.5, 2.5 and 3.5 GPa), and under pure rolling or rolling plus sliding conditions. No surface damage has been observed up to 50 106 cycles for tests with smooth specimens. Tests with rough specimens have produced a typical surface damage, called here surface distress, made of a large population of asperity-scale micro-cracks and micro-spalls. The paper describes the surface distress observed, such as micro-cracks and micro-spalls. Surface damages obtained are different for tests under pure rolling conditions and tests under rolling plus sliding conditions. Therefore, the role of the friction direction is underlined. A link is made between our experimental observations and calculations that have been carried out using a transient EHL model. The influence of an indent in a line contact, simulating a micro-spall, is studied. Surface pressure and associated sub-surface stress field are analyzed versus the sliding direction.

Boundary element modelling of a coating–substrate composite under an elastic, Hertzian type pressure field: cylinder on flat contact geometry

The boundary element model (BEM) approach is established as a surface engineering tool on standard personal computers with reasonable computation times. Modelling of a cylinder–flat contact is presented. The effects of changing material and geometric parameters on stresses is analysed. For homogeneous materials the validity of the useful half space assumption (HSA) is shown to depend on the relative dimensions of the specimen; i.e. the ratio of real sizes over the Hertz contact half width. For coated systems the numerical results reveal the existence of two major local stress maxima whose exact locations depend on the geometry and the materials parameters. In addition, a step discontinuity in sub-surface stress is seen to exist at the coating–substrate interface. The details of the sub-surface stress field depend crucially on the ratio of coating and substrate Young's moduli as well as the relative coating thickness. Another key parameter is the difference between the Poisson ratios of the materials.

Three-Dimensional Finite Element Analysis of Subsurface Stress and Strain Fields Due to Sliding Contact on an Elastic-Plastic Layered Medium

A three-dimensional finite element analysis of a rigid sphere sliding on an elastic-plastic layered medium is presented. Results for the subsurface stress and strain fields are given for a perfectly adhering layer with an elastic modulus and yield stress both two and four times that of the substrate, and contact loads 100 and 200 times the initial yield load of the substrate material. Sliding is simulated to distances of approximately two to three times the initial contact radius. The sphere is modeled by contact elements, and the interface friction coefficient is assumed equal to 0.1 and 0.25. The effects of layer material properties, contact friction, and normal load on the sliding and residual stresses in the layer and the substrate are examined. The distributions of tensile stresses in the layered medium and shear stresses at the layer/substrate interface are presented and their significance for crack initiation and layer decohesion is discussed. Reyielding during unloading is also analyzed for different material properties and contact loads.

Three-Dimensional Finite Element Analysis of Subsurface Stresses and Shakedown Due to Repeated Sliding on a Layered Medium

Results of three-dimensional finite element simulations are presented for the subsurface stress and strain fields in a layered elastic-plastic half-space subjected to repeated sliding contact by a rigid sphere. A single perfectly adhering layer with an elastic modulus and yield strength both two and four times that of the substrate material is modeled. Applied sliding loads are equivalent to 100 and 200 times the initial yield load of the substrate material and sliding is performed to distances of approximately two times the contact radius. The effects of layer material properties and normal load on the loaded and residual stresses occurring from repeated load cycles are examined and compared with stresses produced during the first load cycle. Results for the maximum tensile stresses at the layer/substrate interface and the maximum principal stress in the substrate are presented and their significance for layer decohesion and crack initiation is discussed. Further yielding of substrate material during unloading is discussed, and the possibility of shakedown to an elastic or plastic loading cycle is analyzed for the different material properties and contact loads investigated.