PSI - Issue 41

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Irina Goryacheva et al. / Procedia Structural Integrity 41 (2022) 220–231 Author name / Struc ural Integrity Procedia 00 (2019) 000 – 0 0

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Nomenclature 

Poisson’s ratio Young's modulus linear velocity angular velocity contact region contact pressure load

E V ω P Ω

p

H p

maximum value of contact pressure

radius of contact region

a s τ µ ∆

slip velocity shear stress

sliding friction coefficient

relative slippage

σ 1 σ 3 Q Q 0 Q*

maximum of principal value of stress tensor minimum of principal value of stress tensor

accumulated damage initial accumulated damage

critical value of accumulated damage rate of damage accumulation

q

τ max

principal shear stress

∆τ max

principal shear stresses amplitude

number of cycles

N

strength parameter (coefficient) strength parameter (exponent)

c

m

P a

dimensionless load

dimensionless radius of contact region dimensionless maximum value of contact pressure

H p

2. Problem formulation The contact of an elastic spherical body (ball) sliding/rolling over an elastic half-space made of the same material in conditions of cyclic interaction is considered. The constant load P is applied to the ball. The movement of the ball with the constant linear velocity V is described as steady relative to the moving coordinate system Oxyz , which origin is located under the center of the ball. The contact scheme is presented in Fig. 1.

Fig. 1. Contact scheme of an elastic ball rolling over an elastic half-space