PSI - Issue 41

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

225

6

The damage (

) , Q z N accumulated over the first N cycles at the depth z is calculated by the formula:

m

( ) z

  

  

(

)

( ) z

max

, Q z N Nc =

,

(12)

Q

+

 

0

p

H

where ( ) 0 Q z is the initial damage at the depth z , which is assumed to depend only on the coordinate z . When the damage function reaches a critical value

* Q at some depth * z , the fracture of the material occurs, which

involves the separation from the surface layer thickness * z : ( ) * * *, Q z N Q = .

(13)

Here * N is the number of cycles until the first delamination occurs. The remaining part of the half-space

* z z  with

1 ( *) ( , *) Q z z Q z N − = for

* z z  comes into contact and becomes the initial damage *) 0 N N −  ) following the procedure, described

the accumulated damage

function for the next stage calculation of the accumulated damage ( (

above. Thus, the damage function significantly depends on the principal shear stress distribution under the ball. 4. Analysis of principal shear stress amplitude values in sliding and rolling contacts The stress state of elastic bodies in sliding contact is determined by the following parameters: the elastic characteristics of the material (the elastic modulus E , the Poisson ratio  ), the geometry of the contacting surfaces (the radius of the indenter R ) and the acting load P , linear sliding velocity V , as well as the sliding friction coefficient  . In addition in rolling contact, an important parameter that affects the stress state of the contacting bodies and the fatigue damage accumulation is the relative slippage (3), which is confirmed by the results of experimental studies (Guo et al. , 2016; Pal et al. , 2012; Zhang et al. , 2022; Zhou et al. , 2016). In this study, the elastic constants of materials, the geometry of the contacting bodies and the total load are considered fixed, so the following dimensionless parameters do not change in calculations:

0.00001

(14)

R P P E

,

0.3  = ,

= =

2

where P is the dimensionless load. For these parameters the dimensionless radius a of the contact region and the dimensionless maximum value of contact pressure H p have the following values:

0.008

0.024 a a R = = ,

H H p p E

(15)

= =

.

The dependences of the principal shear stresses amplitudes on depth for a sphere sliding over an elastic half-space with different sliding friction coefficients are presented in Fig. 2.