PSI - Issue 28

Y. Matvienko et al. / Procedia Structural Integrity 28 (2020) 584–590 Author name / Structural Integrity Procedia 00 (2019) 000–000

588

5

employs calculations in the case of strain control loading, does not valid in the case of stress control loading of hardening aluminium alloys inherent in most of airplane structures. Monotone varying parameter must be introduced for quantitative description of damage accumulation. Number m N of loading cycles is precisely this parameter in the present case. Damage degree (damage parameter) D depends on number m N of loading cycle, stress ratio R and stress range   . Thus, there is a good reason to introduce into consideration damage accumulation function     , , D N R m m that describes a degree of damage proceeding from evolution of local stress-strain state. Variation of this function during low-cycle fatigue is described by kinetic equation (Lalanne (2014)):     , ) , ( , , , 1 i m i I m m m m N K R N dN dD N R       , (1) where  is damage accumulation rate. The effect of elastic-plastic deformation process on damage accumulation in argument of  -function (1) is expressed by means of SIF values , ) ( , 1 i m i I K R N   , which are related to different stages of low-cycle fatigue. These stages are characterized by discrete values of the stress ratio and stress range. Damage accumulation function can be derived by integration of equation (1):          F N i m m i I m m m N K R N dN D N R 0 1 , ) , ( , , ,   (2)



 i

  , , must obey the following equations:

i m m D N R

Boundary conditions of damage accumulation function

  0 0, ,    i i m m D N R  ,



 1

, , F m m D N N R 

  i i 

.

(3)

1  m D in relations (3) is defined as

F m N N  that corresponds to fracture of specimen.

Limiting case

4. Damage accumulation function in the case of stress ratio variation

  =333.3 MPa, explicit form of function  from equations (1) and (2) can

In the case of constant stress range be represented in the following form:

( ) i D K N N R S K R N    ( 0) ( , i ) 1 1 F I m I

 

,

(4)

where D S =1.36 is the constant that has been derived from the experimental data obtained for three sets of coupons with given geometrical parameters, which have been tested for different stress ratio i R ( 0.33 1   R , 0.66 2   R and 1.0 3   R ). The stress intensity factor ( , ) 1 i m I K R N represents a set of experimental SIF values obtained after m N cycles for different i R . The value of ( 0) 1  K N I is SIF for the first notch length increment in the specimen that has no cycle exposure. Number ( ) i F N R of cycles means number of cycles before fracture for different stress ratios i R . Substitution of function  (4) into relationship (2) and using summing up along the segments , 1 m m m N N N     at end points of which SIF values ( , ) 1 i m I K R N have been determined instead of integration, give the explicit form of damage accumulation function:

  K N N R S K R N N 1 1 ( ) ( 0) ( , )    i m I D

N N

   m F m 0

( , )

m D R N

m



,

(5)

N

I

F

i