PSI - Issue 5

Chmelko Vladimír et al. / Procedia Structural Integrity 5 (2017) 825–831 Chmelko, V., Margetin, M./ Structural Integrity P ocedia 00 (2017) 000 – 000

829 5

Therefore, it is necessary to define for cyclic time-depending non-uniform loading a new characteristic in the form

i ( t ) n pl( t ) i( t ) . 

E.

k









(7)

( t )

e( t )

where in an instant time the  e(t) , i.e.  pl(t) is elastic and plastic component of the strain for current magnitudes of nominal stress, n i(t), k i(t) are the variable parameters of non-linear relationship region for i -th amplitude of loading spectrum. The non-linear part of this characteristic depends on two parameters:  the length of the linear part of the dependency  -  for the cyclic loading  loading history (so called memory effect of material) The problem of the linear relationship between  and  is analysed in detail by Chmelko (2014), where the cyclic boundary of inelasticity is defined as a intersection of the elastic and the elastic-plastic region for cyclic loading. The effect of loading history on parameters of non-linear region was observed on measured hysteresis loops, which were the response of the material on created sequence of random loading amplitudes. This experimental research allowed to formulate the following principles of memory effect of the material behavior under the random cyclic loading:  hysteresis loops created by the random amplitude process are closed in the largest loop of the process  the hysteresis loop preceding the current shaping loop conditions its shape even if its peak is lower, and also if it is higher than the current forming peak of the loop  the overpassed hysteresis loop peak is not more involved on influencing the shape of the following loops The hierarchy of mutual interaction of hysteresis loops is therefore an evolving process that is constantly updated during the amplitude loading spectrum. The use of these procedures for a continuous chain of the time-depending random amplitude process, is possible to perform as a gradual step-by-step transformation. Nominal stresses that are given by the algebraic difference of two consecutive local peaks of the loading process (Fig. 4) are gradually entering into the calculation. The transformation always takes place in a coordinate system with the beginning at the peak of the last transformed peak of the stress in the loading process and the procedure of transformation can be described in following steps:  calculation of nominal stress i+1  n =   i+1 -  i  (8) 3. The Algorithm of computational transformation of the nominal loading into root of the notch

S by Eq.3 i.e. 6 in coordinate system [ 

i+1 ,  i+1 ] that means in local coordinate

iterative calculation of i+1 



system,

 transformation of the peak stress value into global coordinate system [  G ,  G ],

i 1 

i

G i 1 

G



  



(9)

S

S

 calculation of the subsequent nominal stress, i 1 i 2 i 2         n

(10)

 i+2 ,  i+2 ] and so on. Prior to the start of the transformation, it is necessary to input Young´s modulus of material, limit of inelasticity and during the transformation to observe the current hierarchy of the memory effect of hysteresis loops. iterative calculation of i+2  S by Eq. 3, i.e. 6 in rotated coordinate system [ 