Frictional Interfaces: Stick, Slip and Load Transfer

The Coulomb Friction Model

The Coulomb friction model states that the tangential friction force Ff is proportional to the normal force N, with the proportionality constant μ being the coefficient of friction. For static friction (no sliding), Ff ≤ μs·N. For kinetic friction (sliding), Ff ≈ μk·N. The model is a simplified engineering approximation, not a fundamental physical law. The coefficient of friction is not a material property — it is a system property that depends on the complete interface condition.

  Coulomb friction model:

  Static (no sliding):   Ff ≤ μs · N
  Kinetic (sliding):     Ff ≈ μk · N

  where  Ff = friction force (tangential)
         N  = normal force
         μs = static coefficient of friction
         μk = kinetic coefficient of friction

  Typically:  μs > μk

The coefficient of friction is a model input for a particular interface condition — not an immutable material constant. It depends on surface condition, contact pressure, temperature, sliding speed and lubrication.

Stick, Slip and Partial Slip

When a tangential load is applied to a contact, the edge of the contact patch slips first — the local tangential force exceeds the local friction capacity (μ times the local normal pressure, which is near zero at the edge). The centre, with high normal pressure, sticks. The result is partial slip: the centre sticks, the edge slips, and the interface is globally stuck but locally sliding. As the tangential load increases, the slip zone grows inward. When the tangential load reaches μN, the entire contact slides — gross sliding. Partial slip produces surface damage at the stick-slip boundary, where the strain gradient is highest — this is where fretting cracks initiate.

An interface can be globally stuck while experiencing local microslip near the edge of contact. The centre sticks — high normal pressure provides high friction capacity. The edge slips — low normal pressure means low friction capacity.

Frictional Load Transfer

In a bolted joint, the shear load can be transferred by friction between the clamped members. If the preload is sufficient and the friction coefficient is high enough, the frictional load transfer capacity (μ × preload × number of interfaces) can exceed the applied shear, and the joint does not slip. This is the principle of friction-grip joints: the bolts provide the normal force (preload), and the friction between the clamped members provides the shear transfer. The bolts do not carry shear directly — they maintain the clamp force that enables the friction. The frictional load transfer is efficient (no bearing stress at the hole, no pin-bearing fatigue) but it depends on the preload being maintained and the friction coefficient being as assumed.

Uncertainty in Friction

Friction is one of the least certain modelling inputs. The coefficient of friction can vary by a factor of two or more for the same material pair under different conditions — dry vs lubricated, clean vs contaminated, room temperature vs elevated. The engineer who uses a single value of μ from a table without verifying the interface condition is introducing an unknown error. Good practice is to perform a sensitivity study: run the analysis with a range of μ values and assess the effect on the result. If the result is insensitive to μ, the model is robust. If the result is sensitive, the friction coefficient must be measured for the specific interface, or the design must be made insensitive to friction.

Friction can dominate joint behaviour while also being one of the least certain modelling inputs. The coefficient can vary by a factor of two or more under different conditions. Perform a sensitivity study — if the result is sensitive to μ, the design must be made insensitive to friction, or the friction must be measured.

Energy Dissipation and Damping

Friction dissipates energy. When two surfaces slide, the friction force times the sliding distance is the energy converted to heat. In a joint that experiences microslip under cyclic loading, each cycle dissipates a small amount of energy — this is a source of structural damping. Bolted joints, riveted joints and press-fit interfaces all dissipate energy through microslip, and this damping can be a significant fraction of the total structural damping. The energy dissipation also drives wear: each cycle of microslip removes a small amount of material, and over millions of cycles this produces measurable wear and fretting damage.

Fretting and Interface Degradation

Fretting is the surface damage caused by small-amplitude oscillatory relative movement between two contacting surfaces under normal pressure. It occurs at the stick-slip boundary of a partial-slip contact, where the strain gradient is highest. Fretting produces surface wear, oxidation debris and, critically, fatigue crack initiation. A fretted interface can have a fatigue strength less than half that of an unfretted interface. Fretting is a concern in bolted joints, spline teeth, bearing seats and blade attachments — any interface with high contact pressure and small oscillatory movement. Article 27 covers fretting in detail.

Friction in Nonlinear FEA

In contact FEA with friction, the Coulomb law is enforced at each contact element. The tangent stiffness resists sliding when sticking; it reduces when sliding. The friction coefficient is specified by the engineer, and it applies to every contact element in the pair. The stick-slip transition is resolved at the element level — elements where the tangential force is below the limit stick; elements where it exceeds the limit slide. The resolution depends on the mesh: a fine mesh resolves the stick-slip boundary accurately; a coarse mesh smears it. Friction adds another source of nonlinearity to the contact problem — the tangent stiffness changes between stick and slip, and this change can cause convergence difficulties similar to contact opening and closing.

Limitations of Simple Coulomb Assumptions

The Coulomb model assumes a constant μ, independent of pressure, speed, temperature and sliding distance. In reality, μ can vary with all of these. At very high pressure, the asperities deform plastically and the friction mechanism changes. At high sliding speed, the surface temperature rises and the friction may decrease (or increase, depending on the material). Over sliding distance, the surface condition changes — wear removes asperities, oxide films form and break, and the friction evolves. The Coulomb model is a first-order approximation that is adequate for most engineering analyses, but the engineer should be aware of its limitations and should consider whether a more sophisticated friction model is needed for the specific application.

The Coulomb model is a first-order approximation. It assumes constant μ, independent of pressure, speed, temperature and sliding distance. For most engineering analyses it is adequate — but for applications where friction is critical, consider whether a more sophisticated model is needed.

Key takeaways

• The coefficient of friction is a model input for a particular interface condition — not an immutable material constant. It depends on surface condition, contact pressure, temperature, speed and lubrication.
• An interface can be globally stuck while experiencing local microslip near the edge of contact. The centre sticks; the edge slips.
• Friction can dominate joint behaviour — frictional load transfer in a bolted joint can carry the entire shear load if the preload is sufficient — but friction is also one of the least certain model inputs.
• Partial slip produces surface damage at the stick-slip boundary, which is where fretting cracks initiate.