3. Contact Mechanics and Interfacial Deformation

Introduction and Context

Tribological performance is determined not by the nominal dimensions of two contacting bodies alone, but by what happens at their interface. A bearing raceway, gear tooth, seal lip, cutting tool, or electrical contact may appear to touch over a substantial region; microscopically, however, contact occurs through a population of asperities. The local pressures, strains, temperatures, adhesion forces, and residual stresses at these small regions control friction, wear, fatigue, sealing, heat transfer, and electrical conductance.

Contact mechanics provides the mechanical foundation for analysing these phenomena. It relates geometry, material properties, load, deformation, and contact area. Classical Hertz theory is essential for non-conformal, frictionless elastic contacts, but practical tribological interfaces frequently depart from its assumptions. Plasticity, adhesion, friction, roughness, lubrication, thermal gradients, and surface coatings may all modify the solution. A sound analysis therefore begins with the simplest valid model and introduces additional physics only when its scale and influence justify doing so.

This chapter develops the principal models used for conformal and non-conformal contact, explains the transition from elastic to elastic–plastic response, and examines adhesion, residual stress, thermal contact, and rough-surface interactions. The emphasis is not merely on equations, but on interpretation: what a model predicts, when it is reliable, and how it should influence engineering decisions.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Distinguish conformal and non-conformal contacts and identify the assumptions of Hertzian theory.

2. Calculate principal contact dimensions, pressure, deformation, and subsurface stress for elastic point and line contacts.

3. Explain the limitations of Hertz theory in the presence of friction, plasticity, adhesion, roughness, and coatings.

4. Use elastic–plastic and adhesive contact concepts to interpret real contact area and load carrying capacity.

5. Explain how residual stress, thermal mismatch, and thermal contact resistance influence tribological interfaces.

6. Select appropriate rough-surface contact models and assess their engineering implications.

7. Apply contact-mechanics reasoning to component design, failure diagnosis, and experimental interpretation.

Contact Geometry and the Meaning of Contact Area

Two bodies are described as being in conformal contact when their radii of curvature are similar over a relatively large region. Journal bearings, thrust pads, and many seals approach this condition. Non-conformal contact occurs when the surfaces have substantially different curvature, as in a ball on a flat, a gear tooth pair, or a rolling-element bearing. The undeformed geometrical intersection in a non-conformal contact is usually a point or line; deformation creates a finite contact patch.

For two isotropic bodies with elastic moduli \(E_1,E_2\) and Poisson ratios \(\nu_1,\nu_2\), the reduced elastic modulus is

\[

\frac{1}{E^*}=\frac{1-\nu_1^2}{E_1}+\frac{1-\nu_2^2}{E_2}.

\]

The equivalent modulus incorporates deformation of both bodies. Similarly, for two principal relative radii \(R_1\) and \(R_2\), the equivalent radius in a spherical or locally circular contact is

\[

\frac{1}{R^*}=\frac{1}{R_1}+\frac{1}{R_2},

\]

with the sign of each radius selected according to whether the corresponding curvature is convex or concave. These reduced quantities are valuable because they allow a two-body problem to be represented as an equivalent elastic body contacting a rigid surface.

The nominal contact area is based on macroscopic geometry. The real contact area is the sum of the microscopic regions where opposing materials actually touch. In rough interfaces the real area may be a small fraction of the apparent area, and the mean pressure over the real area can be much greater than the nominal pressure. This distinction is central to friction, wear, electrical contact resistance, and heat transfer.

Hertzian Contact: The Classical Elastic Baseline

Hertz theory assumes smooth surfaces, homogeneous isotropic materials, frictionless contact, small deformation, no adhesion, and purely elastic response. It also assumes that the contact dimensions are small compared with the radii of curvature, so that the surfaces can be approximated locally by quadratic profiles. Although restrictive, these assumptions provide a highly useful reference solution.

Spherical or Point Contact

For a sphere of equivalent radius \(R^*\) pressed against a flat by a normal load \(W\), the contact radius is

\[

a=\left(\frac{3WR^}{4E^}\right)^{1/3}.

\]

The circular contact area is \(A=\pi a^2\). The pressure distribution is semi-elliptical:

\[

p(r)=p_0\left(1-\frac{r^2}{a^2}\right)^{1/2},

\]

where the maximum pressure at the centre is

\[

p_0=\frac{3W}{2\pi a^2}.

\]

The maximum elastic approach of the bodies is

\[

\delta=\frac{a^2}{R^*}.

\]

These expressions show important scaling relationships. Contact radius varies with load as \(W^{1/3}\), area as \(W^{2/3}\), and maximum pressure as \(W^{1/3}\). Consequently, increasing load raises pressure even though the contact area grows.

The maximum subsurface orthogonal and shear stresses do not occur at the surface. For a frictionless spherical contact, the maximum subsurface shear stress occurs below the centre, at a depth of approximately a fraction of the contact radius; the precise value depends on the stress definition and Poisson ratio. This explains why rolling-contact fatigue can initiate beneath an apparently undamaged surface.

Cylindrical or Line Contact

For two parallel cylinders, the ideal Hertz contact is a strip of half-width \(b\). If \(W'\) is the normal load per unit length,

\[

b=\left(\frac{4W'R^}{\pi E^}\right)^{1/2},

\]

and the pressure distribution across the width is

\[

p(x)=p_0\left(1-\frac{x^2}{b^2}\right)^{1/2},

\qquad

p_0=\frac{2W'}{\pi b}.

\]

Line-contact pressure increases with the square root of load, rather than the one-third power found in point contact. Misalignment, crowning, edge relief, and finite cylinder length can strongly alter the ideal distribution. In gears and rollers, profile modifications are often introduced specifically to avoid excessive edge pressure.

Elliptical Contacts

Real rolling contacts are frequently elliptical rather than circular. The principal curvatures in two perpendicular directions determine the ellipse axes and pressure distribution. Numerical evaluation or standard contact charts is commonly used. The governing idea remains the same: local geometry and reduced modulus determine the contact dimensions, while load determines the pressure scale.

From Hertzian Contact to Conformal Contact

Hertz theory is not generally appropriate when the contact extends over a large fraction of the apparent surface or when the undeformed bodies are already geometrically fitted. In a journal bearing, for example, the clearance, eccentricity, lubricant film, and shaft flexibility determine the pressure field. The elastic deformation of the surfaces may be coupled with hydrodynamic pressure, producing elastohydrodynamic or thermoelastohydrodynamic behaviour.

Conformal contacts distribute load over a larger region and therefore often produce lower nominal pressures. However, they can be more sensitive to alignment, clearance, thermal expansion, lubricant starvation, and manufacturing errors. A conformal contact may also become locally non-conformal at an edge, defect, or waviness feature. Thus, the classification is a modelling starting point rather than a permanent description of every local event.

For contacts with friction, tangential loading produces shear tractions. In partial slip, part of the contact sticks while an outer annulus slips. This occurs in rolling contacts subject to traction, fretting contacts, and bolted joints under cyclic tangential loading. The resulting stress field can accelerate crack initiation even when the normal Hertz pressure remains below the static yield strength.

Elastic–Plastic Contact and Permanent Deformation

The Hertz solution predicts elastic deformation indefinitely, but real materials yield when the combined stress state reaches a critical condition. A useful first screening parameter compares maximum contact pressure with hardness or yield strength. The exact onset depends on Poisson ratio, work hardening, residual stress, friction, surface defects, and the chosen yield criterion.

At low load, asperities deform elastically. With increasing load, the highest asperities yield first. The interface may then contain elastic, elastic–plastic, and fully plastic microcontacts simultaneously. For a fully plastic asperity, the mean contact pressure is often of the order of the material hardness, so the real contact area becomes approximately proportional to load:

\[

A_r\approx \frac{W}{H},

\]

where \(H\) is an appropriate hardness. This relation is not a universal law: it assumes a representative hardness, a population of load-bearing junctions, and negligible effects from adhesion and pile-up. Nevertheless, it explains why real area in rough metallic contacts can increase nearly linearly with load even though a single elastic Hertz contact follows a different scaling.

Plastic deformation can be beneficial or harmful. Controlled plasticity may smooth asperities during running-in and increase conformity. Excessive plasticity produces permanent dents, ratcheting, surface distress, debris, and altered residual stresses. In rolling bearings, a local indentation from contamination can become a stress concentrator that causes repeated-impact fatigue.

Contact plasticity is also influenced by the substrate in coated systems. A hard thin coating on a soft substrate may appear elastic under a low load but undergo substrate yield when the contact stress field penetrates beneath the coating. Coating thickness, adhesion, residual stress, and elastic mismatch must therefore be considered together.

Adhesive Contact and Interfacial Forces

At small scales, surfaces can attract one another through van der Waals forces, chemical bonding, capillary bridges, electrostatic forces, or solid-state junction formation. Adhesion modifies both contact area and the load required to separate surfaces. It is particularly important for smooth compliant materials, microelectromechanical systems, polymers, biological interfaces, and clean metallic contacts.

The Johnson–Kendall–Roberts (JKR) model is most suitable when adhesion is strong and deformation is relatively compliant. The Derjaguin–Muller–Toporov (DMT) model is more suitable for stiff materials, small contact areas, and relatively long-range adhesive forces. The Maugis framework provides an intermediate description through a parameter representing the range and strength of adhesion. These models demonstrate that no single adhesive theory is universally correct.

Adhesion can increase the contact area at zero external load and can produce a finite pull-off force. In engineering contacts, adhesion may be desirable in seals, tapes, and friction-enhancing interfaces, but undesirable in precision mechanisms through stiction, material transfer, or galling. Surface contamination, humidity, chemistry, roughness, and loading rate strongly influence measured adhesion.

Rough-Surface Contact and Real Contact Area

Engineering surfaces are rough across multiple length scales. A roughness profile is not fully characterised by one parameter such as arithmetic mean roughness \(R_a\). Root-mean-square roughness, skewness, kurtosis, wavelength content, asperity radius, lay direction, and surface correlation length may all affect contact behaviour.

The Greenwood–Williamson model represents a rough surface as asperities with a statistical distribution of heights and a common radius. Asperities above a separation level carry the load. At low load, the model predicts that only the highest asperities contact and that many of them may deform elastically. More advanced models, including fractal and spectral approaches, account for multiscale roughness and elastic interactions between asperities.

The separation between mean planes is not directly measurable from roughness alone. It depends on load, material compliance, surface statistics, contamination, and deformation history. In lubricated contacts, the ratio of lubricant film thickness to composite roughness is often used to classify the likelihood of asperity interaction. A low ratio indicates mixed or boundary lubrication, whereas a high ratio indicates stronger separation by the fluid film.

Surface roughness has competing effects. Increasing roughness can raise friction and wear by increasing asperity interaction, but a textured surface may also retain lubricant, provide debris accommodation, or reduce adhesive junction growth. Directional roughness can produce anisotropic friction and permeability. Therefore, the specification of a single low roughness value is not automatically an optimum design.

Residual Stress and Interfacial Deformation

Residual stresses remain in a component after manufacturing or previous loading without an external force being applied. They arise from machining, grinding, shot peening, welding, coating deposition, phase transformation, thermal cycling, and plastic deformation. Because contact stresses are spatially varying and cyclic, residual stress changes the effective margin against yielding and fatigue.

Compressive residual stress near the surface generally delays tensile crack opening and can improve rolling-contact fatigue resistance. However, excessive compression may cause distortion, delamination, or subsurface tensile balancing stresses. Grinding burns and poorly controlled thermal treatments can introduce tensile residual stress, increasing crack susceptibility. The influence of residual stress must be evaluated with its depth profile, not merely its surface value.

In coated contacts, residual stress also affects interface integrity. A coating under tensile stress may crack or delaminate; compressive stress may improve crack resistance but can produce buckling if adhesion is inadequate. Contact pressure, thermal mismatch, and repeated tangential loading can combine to drive interface failure.

Thermal Contact and Thermomechanical Coupling

Real contact area is also the route through which heat crosses an interface. In a nominally contacting rough surface, heat flows through discrete microcontacts while the surrounding gaps may contain air, lubricant, or vacuum. The resulting constriction resistance is often much larger than the bulk thermal resistance of either solid.

The thermal contact conductance depends on real contact area, asperity deformation, material thermal conductivity, surface roughness, contact pressure, temperature, and interstitial medium. Increasing load generally increases conductance by enlarging and multiplying microcontacts. Soft, highly conductive interstitial materials may fill valleys and reduce resistance, while oxidation or contamination may introduce a thermally resistive layer.

Frictional heating adds a second coupling. The heat generated at a sliding interface is commonly estimated from the frictional power \(\mu Wv\), although the partition of heat between the two bodies depends on thermal properties, speed, contact size, and time. Temperature changes alter modulus, yield strength, viscosity, thermal expansion, and adhesion. A contact can therefore move from elastic to plastic or from lubricated to boundary operation as it heats.

Thermal expansion can also change clearance and contact pressure. In seals, thermal distortion may increase leakage or contact force; in bearings, differential expansion may reduce internal clearance and cause overheating. Thermoelastic instability may concentrate frictional heating into local hot spots, creating a feedback between temperature and deformation.

Methods for Contact Analysis

The appropriate method depends on the purpose and scale of analysis. Closed-form Hertz, JKR, or line-contact equations are efficient for preliminary sizing and parametric studies. They are transparent and reveal scaling laws, but they cannot represent complex geometry, plasticity, coatings, or coupled thermal and tangential effects without modification.

Finite element analysis is useful for non-axisymmetric geometry, layered materials, plasticity, residual stress, friction, and transient thermal response. Contact algorithms require careful selection of normal enforcement, tangential law, mesh density, and convergence tolerances. A very fine mesh is required near contact edges and stress singularities. Results should be checked against an analytical limiting case before being used for design.

Boundary element methods are attractive when deformation is mainly elastic and surfaces are geometrically complex, because only the contacting surfaces need to be discretised. They are widely used for rough-contact simulation. Measurements such as optical interferometry, pressure-sensitive films, electrical contact resistance, ultrasonic methods, and thermal imaging provide complementary evidence, but each has calibration limits and may measure an effective rather than literal contact area.

A robust workflow is to: define geometry and loading; calculate reduced properties; select the simplest physically credible model; compare predicted pressure and deformation with yield, fatigue, and thermal limits; introduce roughness, adhesion, or friction if their characteristic scale is significant; and validate the result experimentally or against a trusted benchmark.

Applied Case: Premature Pitting in a Rolling-Element Bearing

Background

An illustrative industrial case concerns a hardened steel roller bearing supporting a gearbox shaft. The bearing was selected using nominal load capacity and appeared adequate from a basic Hertzian calculation. After several months of operation, repeated spalling developed on one raceway.

Situation and Analysis

Inspection showed that the spalls were distributed near a narrow axial region rather than uniformly across the raceway. The initial hypothesis was insufficient material hardness, but hardness measurements were within specification. A contact analysis using ideal centred geometry predicted an acceptable maximum pressure and an elliptical contact patch.

Further investigation identified shaft misalignment and a small amount of edge loading. The actual contact ellipse was truncated near the raceway shoulder, producing a local pressure concentration not captured by the centred Hertz model. In addition, assembly contamination had produced shallow dents. Each dent acted as a geometric discontinuity, increasing local impact stress during every pass of a roller. Residual compressive stress from the finishing operation improved resistance in the undamaged region but could not eliminate the stress concentration at the dents.

The bearing also operated with a low lubricant-film-to-roughness ratio during cold starts. Asperity interaction and sliding at the misaligned edge increased frictional heating, reducing lubricant viscosity and further lowering film thickness. Thus, the failure was not caused by one excessive nominal load; it resulted from the interaction of alignment, roughness, contamination, lubrication, and cyclic subsurface stress.

Approach and Outcome

The corrective programme included shaft alignment verification, improved filtration and assembly cleanliness, raceway edge relief, and a review of lubricant viscosity at the lowest operating temperature. A three-dimensional finite element model was used to evaluate edge pressure, while a rolling-contact fatigue calculation included the measured residual-stress profile. Subsequent endurance tests showed that the modified configuration avoided the former edge concentration and substantially reduced dent-related impact signals.

Learning Points

The case illustrates four principles. First, a Hertz calculation is a baseline, not a guarantee of service life. Second, contact geometry must include alignment and edge conditions. Third, roughness, dents, and residual stress alter local rather than nominal stress. Finally, tribological failure is often a coupled mechanical, thermal, and lubrication problem.

Challenges, Limitations, and Common Mistakes

A frequent mistake is to substitute nominal area for real area when estimating pressure, friction, or thermal conductance. Another is to use hardness as a complete description of plastic response while ignoring work hardening, residual stress, and strain rate. Hertz theory is also misapplied to large conformal areas, rough contacts, coated systems, or contacts with substantial tangential traction.

The assumption of smooth, homogeneous, isotropic material can be particularly misleading for additively manufactured surfaces, fibre-reinforced polymers, porous materials, and multilayer coatings. Numerical models can create false confidence when friction coefficients, residual stresses, roughness spectra, or thermal boundary conditions are guessed rather than measured. Stress singularities at sharp edges should not be interpreted as literal infinite stresses; the relevant material length scale, edge radius, plasticity, or fracture criterion must be considered.

Experimental contact measurements also require caution. A pressure film may alter the contact, optical methods may require transparency, and electrical resistance measures conducting pathways rather than all mechanical contacts. Model validation should therefore use multiple observables where the design consequence is significant.

Professional and Emerging Practice

Modern contact analysis increasingly combines analytical mechanics, finite element modelling, surface metrology, and data-driven monitoring. Three-dimensional optical profilometry can provide measured surface spectra for rough-contact simulations. Digital image correlation and in situ microscopy can reveal deformation and slip. Sensors that measure vibration, acoustic emission, temperature, or electrical resistance can identify changes in contact state before visible damage develops.

Machine-learning methods may classify contact faults from large condition-monitoring datasets, but they do not replace mechanics-based interpretation. Training data can be biased toward particular loads, materials, or failure modes. For safety-critical components, explainable physical models, traceable data, uncertainty quantification, and engineering verification remain essential.

Current research is also addressing contact in soft robotics, biological tissues, two-dimensional materials, textured surfaces, solid lubricants, and architected coatings. These systems challenge conventional assumptions because adhesion, viscoelasticity, anisotropy, rate dependence, and size effects can be as important as classical elasticity.

Best-Practice Design Guidance

A reliable contact assessment should:

• distinguish nominal, apparent, and real contact area;
• calculate reduced modulus and equivalent curvature consistently;
• check elastic, elastic–plastic, fatigue, adhesive, and thermal regimes;
• include alignment, edge geometry, surface texture, coating thickness, and residual stress;
• use Hertz theory as a reference solution and identify its violated assumptions;
• validate numerical predictions with analytical limits and suitable measurements;
• report uncertainty in material properties, roughness, load, temperature, and friction;
• connect local contact predictions with component-level life, lubrication, heat removal, and maintenance decisions.

Professional practice also requires traceability. The analyst should record the source and condition of material properties, the surface measurement method, the assumed load spectrum, and the reason for selecting a particular contact model. This is especially important when contact analysis supports regulatory certification, product liability decisions, or failure investigations.

Chapter Summary

Contact mechanics describes how geometry, load, material properties, and interface physics determine deformation and stress. Hertz theory provides the fundamental elastic solution for smooth, frictionless, non-conformal contacts, including spherical, cylindrical, and elliptical geometries. Its scaling laws are useful, but its assumptions must be checked before application.

Real tribological contacts may be conformal, rough, adhesive, frictional, plastic, coated, thermally coupled, or residually stressed. Elastic–plastic asperity deformation changes the relation between load and real area; adhesion modifies contact and separation; residual stress alters yielding and fatigue; and thermal constriction and frictional heating couple temperature with mechanical response. Rough-surface models explain why real area differs from nominal area and why surface statistics matter.

Analytical equations, numerical methods, measurements, and condition-monitoring data are most effective when combined. The central engineering task is to identify the dominant physical mechanisms, select a model appropriate to their scale, validate its predictions, and translate local contact results into decisions about material, geometry, lubrication, manufacture, and service life.

Key Terms

Reduced elastic modulus: Combined elastic stiffness of two contacting bodies represented by an equivalent modulus.

Equivalent radius: Effective radius describing the combined local curvature of two surfaces.

Conformal contact: Contact in which mating surfaces have similar curvature and a relatively large apparent contact region.

Non-conformal contact: Contact in which surfaces meet initially over a point or line and form a finite patch through deformation.

Hertz contact: Frictionless elastic contact solution for smooth bodies with locally quadratic geometry.

Contact radius: Radius of the circular Hertzian contact patch.

Maximum contact pressure: Highest normal pressure in a contact patch, usually at its centre for an ideal Hertz contact.

Line contact: Contact extending substantially in one direction, such as between parallel cylinders.

Real contact area: Sum of microscopic regions where opposing surfaces physically touch.

Nominal contact area: Apparent macroscopic area assigned to an interface by its geometry.

Asperity: Local peak or micro-protrusion on a nominally rough surface.

Elastic–plastic contact: Contact containing deformation that is partly recoverable and partly permanent.

Hardness: Resistance of a material to local permanent indentation or plastic deformation.

Adhesive contact: Contact influenced by attractive interfacial forces in addition to externally applied load.

Partial slip: Tangential contact state containing both sticking and slipping regions.

Residual stress: Stress remaining in a body after external loading is removed.

Thermal contact resistance: Opposition to heat flow across an interface caused mainly by constriction and interstitial gaps.

Contact conductance: Reciprocal measure of thermal contact resistance per unit area or interface.

Roughness spectrum: Distribution of surface texture amplitudes across spatial wavelengths.

Thermoelastic instability: Localised thermal and mechanical feedback that concentrates heat and deformation in a contact.

Review Questions

Short Answer Questions

1. What is the physical meaning of the reduced elastic modulus in a two-body contact?

2. State the principal assumptions of classical Hertz theory.

3. Why is real contact area generally smaller than nominal contact area for rough surfaces?

4. What is meant by partial slip?

5. Why can residual compressive stress improve rolling-contact fatigue resistance?

Long Answer Questions

1. Derive and interpret the Hertzian relationships for a sphere contacting a flat, including the effects of load on contact radius, area, and maximum pressure.

2. Compare conformal and non-conformal contacts with reference to geometry, pressure distribution, deformation, and applications.

3. Explain the transition from elastic to elastic–plastic asperity contact and discuss the approximate relation between real area, load, and hardness.

4. Compare JKR and DMT adhesive contact descriptions and explain why neither is universally applicable.

5. Discuss the mechanical and thermal consequences of roughness, residual stress, and frictional heating in a rolling or sliding interface.

Analytical / Application Questions

1. A hardened steel ball is pressed against a flat steel specimen. Explain how you would determine whether a Hertzian elastic solution is valid before calculating contact life.

2. A bearing shows raceway pitting only near one shoulder. Develop a contact-mechanics investigation that distinguishes edge loading, contamination dents, residual stress, and lubrication effects.

3. A coated component operates at increasing temperature and load. Propose a coupled analysis procedure that evaluates coating integrity, substrate yielding, thermal contact resistance, and adhesive or frictional effects.

22. Multiple Choice Questions with Answers

Question 1

For a spherical Hertzian contact, if the normal load is increased by a factor of eight while all other quantities remain constant, how does the contact radius change?

A. It becomes twice as large

B. It becomes eight times as large

C. It becomes four times as large

D. It remains unchanged

Correct Answer: A. It becomes twice as large

Question 2

Which condition most directly violates the classical Hertz assumption of purely elastic response?

A. A smooth spherical surface

B. A homogeneous isotropic material

C. A contact pressure sufficient to cause local yielding

D. A frictionless normal load

Correct Answer: C. A contact pressure sufficient to cause local yielding

Question 3

In a rough metallic interface undergoing predominantly fully plastic asperity deformation, the real contact area is commonly approximated as proportional to:

A. The square of the load

B. Load divided by hardness

C. The cube root of load

D. The inverse of load

Correct Answer: B. Load divided by hardness

Question 4

Which contact model is generally associated with strong adhesion and relatively compliant materials?

A. JKR model

B. DMT model

C. Ideal Hertz model

D. Classical line-contact model

Correct Answer: A. JKR model

Question 5

Why can a Hertzian calculation predict acceptable pressure while a bearing still experiences edge-related pitting?

A. Hertz theory always overestimates edge pressure

B. The calculation may omit misalignment and local edge loading

C. Hertz theory includes residual stress automatically

D. Pitting is unrelated to contact stress

Correct Answer: B. The calculation may omit misalignment and local edge loading

Question 6

Which statement best describes thermal contact resistance in a rough interface?

A. Heat flows uniformly across the nominal area

B. It is caused only by the bulk conductivity of the solids

C. Heat is constricted through discrete microcontacts and gaps

D. It decreases when real contact area decreases

Correct Answer: C. Heat is constricted through discrete microcontacts and gaps

Question 7

What is a likely effect of compressive residual stress near a rolling-contact surface?

A. It generally delays tensile crack opening

B. It guarantees immunity from plastic deformation

C. It always causes coating delamination

D. It eliminates subsurface shear stress

Correct Answer: A. It generally delays tensile crack opening

Question 8

In a Hertzian point contact, the ideal pressure distribution is:

A. Uniform across the contact patch

B. Maximum at the edge and zero at the centre

C. Semi-elliptical, with maximum pressure at the centre

D. Linearly increasing from centre to edge

Correct Answer: C. Semi-elliptical, with maximum pressure at the centre

Question 9

Which factor can cause a conformal contact to behave locally as a severe non-conformal contact?

A. Perfect alignment and uniform curvature

B. An edge, defect, or local waviness feature

C. A reduction in material modulus of both bodies equally

D. A decrease in nominal area with no geometric change

Correct Answer: B. An edge, defect, or local waviness feature

Question 10

A low lubricant-film-to-composite-roughness ratio most strongly indicates:

A. Complete separation by a thick fluid film

B. A negligible possibility of asperity interaction

C. Mixed or boundary lubrication with likely asperity interaction

D. A purely adhesive contact without mechanical loading

Correct Answer: C. Mixed or boundary lubrication with likely asperity interaction