Incomplete Contacts Research Articles

The cohesive zone crack analogue for incomplete contacts under mild wear conditions

Fretting fatigue may appear in mechanical components that are in contact under vibrational loading, inducing oscillatory frictional stresses, often combined with alternating bulk stresses. Fretting fatigue cracking is important, with its initiation being difficult to estimate. This work extends a well-known fretting fatigue model, the crack analogue model that examines fretting fatigue induced by incomplete contacts of metallic surfaces. This is done by inserting a mode II type cohesive zone at the contact edges. In our previous work on fretting fatigue of complete contacts, we proposed mixed mode I and II cohesive zones because of the nature of the stress fields around the contact edges. The proposed cohesive zones address several issues related to the mechanics of friction and wear, by combining them in the case of mild wear where asperity plastic shakedown is the dominant inelastic mechanism. Thus, the micromechanical behaviour of the surface topology and its evolution are naturally introduced into the analysis. The surface roughness becomes an internal variable that evolves with the cyclic loading, establishing a steady state friction coefficient. Alternatively, friction evolution can be established pointwise by monitoring the accumulated micro-slip. The work of friction dissipates the mechanical work and at the same time becomes the precursor of large scale wear. A predictive methodology for fretting crack nucleation is proposed through the fatigue threshold stress intensity factor used in ordinary fatigue.

The cohesive zone crack analogue for fretting fatigue based on mild wear

Fretting fatigue is an important problem that plagues many mechanical components that are in contact under vibrational loading. Life assessment of fretting fatigue cracking is important, with the damage initiation being difficult to estimate. This work extends a well-known fretting fatigue model, the crack analogue model that examines fretting induced by complete contacts or by adhering incomplete contacts of metallic surfaces. This is done by introducing cohesive zones at the contact edges. These zones address several issues related to friction and wear, by combining them in the case of mild wear where asperity plastic shearing is the dominant inelastic mechanism. Thus, the micromechanical behaviour of the surface topology is naturally introduced into the analysis. The surface roughness becomes an internal variable that evolves with the cyclic loading. The work of friction dissipates the mechanical energy and at the same time becomes the precursor of large scale wear. A predictive methodology for fretting crack nucleation is proposed through a novel cohesive model that incorporates friction and mild wear, lifting much pathology encountered by simple friction models at high normal loads.

Analysing the accuracy of asymptotic approximations in incomplete contact problems

The error incurred in the representation of the contact pressure at the edges of incomplete contacts by first order asymptotes is treated, and the maximum value of the relative error found for a range of geometries, both symmetric and non-symmetric. For a symmetric power-law geometry, we identify when the first-order asymptote achieves maximum fidelity. Shear tractions are excited by both the application of a shear force and the application of bulk tension in one body. An asymptotic representation of the shear traction distribution under conditions of full stick is presented.

Asymptotic description of fretting wear and fretting fatigue for incomplete contacts

Looking at wear of incomplete contacts in partial slip we start from an asymptotic description of the contact tractions at the contact edges. We introduce distributed dislocations along the slip zone to account for the profile reduction due to wear and find the long-term time asymptote where the contact is wholly stuck. The resulting stress field is used to find the crack tip stress intensity factors for short contact edge cracks, which are useful in predicting the crack nucleation threshold.

On the fretting fatigue crack nucleation of complete, almost complete and incomplete contacts using an asymptotic method

In this work, the fretting crack nucleation of an aeronautical Ti-10V-2Fe-3Al titanium alloy is investigated. The main difficulty when designing complex industrial systems, especially helicopters rotor parts, lies in the prediction of the assembly interfaces behaviour. Those areas can be subjected to fretting loading characterized by a very confined multiaxial high stress gradient, leading to fatigue crack nucleation. This kind of failure reduces the parts potential lifetime and increases therefore the security margin that can be considered.The aim of this paper is to provide a criterion to prevent crack nucleation on industrial contacts configurations. To reach this objective, this study focuses on the geometrical conditions, loadings and material properties linked to crack initiation. Two dedicated fretting test campaigns are used to study crack initiation conditions with various contact shapes and loadings on the same material. The crack initiation conditions are compared with a contact mechanics representation based on asymptotic methods. This method allows the stress field evaluation at the hot spot location by using the problem’s eigenvalues.The combination of the asymptotic method with contact mechanics and the Goodman approach allows to represent the key parameters of the fretting fatigue crack initiation. They include the impacted material volume, the shear intensity and the bulk stress. A fretting fatigue crack initiation criterion is proposed. It is based on classical material properties and the bulk stress ratio Rσ0 only and is applicable to all sorts of contact shapes. The main interests of this prediction method are the absence of size effect parameters for industrial contacts and its efficiency, as it is only based on analytical formulations.

Stress intensity factor calibration for short cracks at the edge of semi-infinite contacts

An asymptotic representation of the sub surface stress field allows us to find crack tip stress intensity factors for cracks nucleating from the edge of incomplete contacts. For the asymptotic representation to be valid we require the cracks to be short compared to any other dimension characterising the contact. The general asymptotic formulation allows us to incorporate the results in different contact problems as long as the contact is incomplete. We show that, for the load cases considered, crack closure is not an issue as long as the mode I stress intensity factor is positive.

Explicit and asymptotic solutions for frictional incomplete half-plane contacts subject to general oscillatory loading in the steady-state

This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not only to approximate the size of the slip zones during the steady-state of a cyclic problem without knowledge of the geometry or contact law, but provides a solution when all known analytical solutions for incomplete contacts reach their limitations, that is, in the presence of a varying moment and a differential bulk tension large enough to reverse the direction of slip at one end of the contact. An insightful comparison between the mathematically explicit analytical solution and the asymptotic approach is drawn using the example geometry of a shallow wedge.

The minimum shear stress range criterion and its application to crack orientation prediction in incomplete contact fretting problems

A proper prediction of crack paths is required when assessing accurately the fatigue crack propagation life. Recently, some authors have pointed out that the criterion of minimum shear stress range leads to inconsistent results when predicting fretting crack paths under incomplete contacts. In this paper, different fretting experiments with cylinder-to-flat contact found in the literature are reviewed, and the corresponding crack path prediction using the extended finite element method and the minimum shear stress range crack orientation criterion is performed. Results show the applicability of the criterion to predict the crack orientation during stage II in incomplete contact fretting problems.

Magnetic-State Controlled Molecular Vibrational Dynamics at Buried Molecular–Metal Interfaces

Self-assembled molecular structures have been intensively used in molecular electronics and spintronics. However, detailed nature of the interfaces between molecular layers and extended metallic contacts used to bias the real devices remains unclear. Buried interfaces greatly restrict application of standard techniques such as Raman or scanning electron microscopies. Here we introduce low frequency noise spectroscopy as a tool to characterize buried molecular-metal interfaces. We take advantage of vibrational heating of the molecules with incomplete contacts to the interface. Electrons, being the main spin and charge carriers propagating through the interfaces involving self-assembled molecules, interact inelastically with charged atomic ions. Such interactions produce quantum molecular vibrations (phonons). Detailed investigation of both conductance and conductance fluctuations in magnetic tunnel junctions with few nm Perylenetetracarboxylic dianhydride (PTCDA) allows to map vibrational heating at specific biases taking place in 'hot spots' where self-assembled layers weaker contact the metallic electrodes. We follow this effect as a function of PTCDA thickness and find the best molecular-metal order for the lowest (3-5 monolayers) barriers. Moreover, we unveil interplay between spin and phonons at interface showing experimentally and by modelling spin-control over molecular vibrational heating. We find that vibrational heating related low frequency noise essentially depends on the relative alignment of the electrodes with noise changes well beyond expectations from fluctuation-dissipation theorem.

Incomplete contacts in partial slip subject to varying normal and shear loading, and their representation by asymptotes

We develop a method for the solution of partial slip contact problems suffering complex loading cycles where, generally, the normal load, shear force and, potentially, differential bulk tensions are all functions of time, using an edge-asymptote approach. The size of the slip zone and local shear traction distribution are revealed as functions of time. The results are then re-worked in asymptotic form, so that they do not hinge on inherent symmetry and anti-symmetry conditions for the contact overall, and are of general applicability. The multipliers on the local solutions (generalised stress intensity factors) are also appropriate as a means of taking laboratory tests quantifying fretting fatigue and employing them to wholly different prototypical problems.

A unified approach for representing fretting and damage at the edges of incomplete and receding contacts

This paper attempts to unify the analysis of fretting and damage at the edges of different classes of contact. Specifically edge asymptotes may be applied, in the same form, to both incomplete and to receding contacts. The benefit of this approach is that experiments carried out on incomplete contacts may be used to predict the life of a wide range of incomplete contact geometries, and also of receding contacts.

Partial slip incomplete contacts under constant normal load and subject to periodic loading

We present a general formulation for the stick slip behaviour of incomplete contact under oscillating loading, but with a constant normal load. An asymptotic description of the contact traction very close to the contact edges is used. The slip zones present in the steady state with cyclically varying bulk tension and shear force (with an arbitrary phase shift) are found. The range of the variation of the state of stress near both of the contact edges and the respective slip zone sizes are defined in terms of the loading parameters, including the phase angle. The quality of the approximations used by the asymptotic approach and the range of applicability of the method is also analysed in detail in this paper.

Correlation of fretting fatigue experimental results using an asymptotic approach

Small refinements are made to the bounded asymptotic forms recently developed to encapsulate the state of slip and stress at the edges of incomplete contacts. They are then used to re-analyse several sets of publicly available fretting fatigue data. Several different combinations of the asymptotes are used and it is shown that two are viable and give big improvements upon stress-based criteria. These procedures provide a practical method for both designing against fretting fatigue and quantifying nucleation times when fretting is unavoidable.

Comprehensive bounded asymptotic solutions for incomplete contacts in partial slip

Solutions for the traction distributions and corresponding sub-surface state of stress adjacent to the edge of an incomplete contact suffering partial slip are found. The effects of frictional shakedown and a synchronously varying in-plane tension on the solution are found in closed form. The value of the asymptote, and its characterisation by just three independent parameters is illustrated by applying it to the finite problem of a rigid, tilted punch pressed onto a half-plane, and suffering partial slip induced by the application of in-plane tension.

Bounded asymptotic solutions for incomplete contacts in partial slip

Asymptotic solutions for the contact pressure and shearing tractions present adjacent to the edge of an incomplete contact are derived, and for each a dimensional scaling factor (akin to a generalised stress intensity factor), is defined. These two quantities may therefore be used to define the complete local stress state, for which purpose the Muskhelishvili potentials are derived. The application of this technique to a comparison of the Hertz–Cattaneo contact, the flat and rounded contact and the tiled punch is described, and the extent of the domain of validity of the asymptote found.

Unsymmetrical shear loading and its influence on the frictional shakedown of incomplete contacts

Although incomplete contacts can never shake down to a completely adhered state, the self-development of residual frictional shearing tractions can reduce significantly the size of the slip zone. This phenomenon is demonstrated using the Hertz-Cattaneo contact.

Cyclic AMP modulates the rate of ‘constitutive’ exocytosis of apical membrane proteins in Madin-Darby canine kidney cells

Madin-Darby canine kidney and other epithelial cell lines (e.g. Caco-2, MCF-10A and MCF-7) develop intracellular vacuoles composed of apical membrane displaying microvilli (VACs) when impaired from forming normal cell-to-cell contacts. In a previous publication, we showed that VACs are rapidly exocytosed upon treatment with 8-Br-3',5'-cyclic adenosine monophosphate (8-Br-cAMP), a membrane-permeable analog of cAMP, and that this exocytosis correlates with variations in the cellular cAMP concentration in response to the cell-cell contacts. In the present work, we tested the hypothesis that cAMP may be a positive modulator of the 'constitutive' exocytic pathway. To mimic conditions in cells with incomplete intercellular contacts, the intracellular levels of cAMP were decreased by means of two independent approaches: (i) pores were induced in the plasma membrane with the polypeptidic antibiotic subtilin, thus allowing small molecules (including cAMP) to permeate and move out of the cytoplasm; and (ii) adenylate cyclase and protein kinase A were blocked with specific inhibitors. In all cases, the intracellular levels of cAMP were measured and, in porated cells, equilibrated to simulate the corresponding physiological intracellular concentrations. The decrease in cAMP within the physiological range resulted in a decreased rate of transport of an apical marker of the constitutive pathway (influenza virus hemagglutinin) from the trans-Golgi network to the apical plasma membrane. Likewise, the delivery of a number of cellular apical proteins to the plasma membrane was retarded at low cAMP concentrations. The inhibitors of adenylate cyclase failed to block basolateral delivery of vesicular stomatitis virus G protein. This differential modulatory effect may represent a differentiation-dependent control of the insertion of apical membrane in epithelial cells.

Exocytosis of vacuolar apical compartment (VAC): a cell-cell contact controlled mechanism for the establishment of the apical plasma membrane domain in epithelial cells.

The vacuolar apical compartment (VAC) is an organelle found in Madin-Darby canine kidney (MDCK) cells with incomplete intercellular contacts by incubation in 5 microM Ca++ and in cells without contacts (single cells in subconfluent culture); characteristically, it displays apical biochemical markers and microvilli and excludes basolateral markers (Vega-Salas, D. E., P. J. I. Salas, and E. Rodriguez-Boulan. 1987. J. Cell Biol. 104:1249-1259). The apical surface of cells kept under these culture conditions is immature, with reduced numbers of microvilli and decreased levels of an apical biochemical marker (184 kD), which is, however, still highly polarized (Vega-Salas, D. E., P. J. I. Salas, D. Gundersen, and E. Rodriguez-Boulan. 1987. J. Cell Biol. 104:905-916). We describe here the morphological stages of VAC exocytosis which ultimately lead to the establishment of a differentiated apical domain. Addition of 1.8 mM Ca++ to monolayers developed in 5 microM Ca++ causes the rapid (20-40 min) fusion of VACs with the plasma membrane and their accessibility to external antibodies, as demonstrated by immunofluorescence, immunoperoxidase EM, and RIA with antibodies against the 184-kD apical plasma membrane marker. Exocytosis occurs towards areas of cell-cell contact in the developing lateral surface where they form intercellular pockets; fusion images are always observed immediately adjacent to the incomplete junctional bands detected by the ZO-1 antibody (Stevenson, B. R., J. D. Siliciano, M. S. Mooseker, and D. A. Goodenough. 1986. J. Cell Biol. 103:755-766). Blocks of newly incorporated VAC microvilli and 184-kD protein progressively move from intercellular ("primitive" lateral) spaces towards the microvilli-poor free cell surface. The definitive lateral domain is sealed behind these blocks by the growing tight junctional fence. These results demonstrate a fundamental role of cell-cell contact-mediated VAC exocytosis in the establishment of epithelial surface polarity. Because isolated stages (intercellular pockets) of the stereotyped sequence of events triggered by the establishment of intercellular contacts in MDCK cells have been reported during normal differentiation of intestine epithelium (Colony, P. C., and M. R. Neutra. 1983. Dev. Biol. 97:349-363), we speculate that the mechanism we describe here plays an important role in the establishment of epithelial cell polarity in vivo.

LIMITATIONS OF THE REFLECTION SEISMIC METHOD; LESSONS FROM COMPUTER SIMULATIONS

Piece‐wise local linearity of the subsurface reflectors and uniqueness of primary reflection travel path between particular source‐receiver pairs are two of the fundamental assumptions of multiple ground coverage reflection seismic techniques as currently employed. Some recent developments in seismic exploration which spring from the progress made in velocity determination techniques violate these fundamental assumptions with potentially serious consequences such as spurious geometries after migration and unrealistic interval velocities. In this paper we apply analytic techniques and computer simulation to linear and nonlinear subsurface models in order to obtain better definitions of the limitations of the reflection seismic method. The resulting lessons are of immediate practical value in seismic interpretation and clarify a variety of commonly occurring but puzzling situations such as phantom faults, incomplete contacts and segmented reflectors at unconformities, and apparent reversal of dip. In its basic approach this work has much in common with the generation and study of synthetic seismograms. Examination of the groundwork of the seismic method provides a firm base for extending its use.

Limitations of Reflection-Seismic Method: Lessons from Computer Simulations: ABSTRACT

Multiple ground-coverage seismic techniques are based on a few key assumptions. Among the more important are the assumptions that subsurface reflectors locally are continuous and linear, and that the primary reflections between particular source-receiver pairs travel along unique paths. However, overenthusiasm concerning recent advances in the use of velocity spectra models has led to some violations of these important assumptions. The most common types of violations involve use of these models in (1) determining primary velocity, (2) computing interval velocities and dips, and (3) migrating depth sections. Although all three processes are industry-wide objectives which commonly are obtainable by other methods, their attainment through the use of the velocity spectra odels is beyond the limits of current theory. Therefore, those who use velocity spectra methods to predict subsurface conditions can be misled by the errors which result. The theory and limitations of the seismic methods currently employed can be clarified by examining linear End_Page 557------------------------------ and nonlinear computer-simulation models. Ideal time sections for some of these models illustrate phenomena such as dip reversal, loss of domal character, incomplete unconformity contacts, and creation of faults. Modeling also is becoming increasingly important in reflection-seismic processing and interpretation. However, true progress with models will not take place until we appreciate and understand the limitations of the method, the primary assumptions that are essential, and the consequences of violating these primary assumptions. End_of_Article - Last_Page 558------------