PSI - Issue 40

19 3

Aleksey Antimonov et al. / Procedia Structural Integrity 40 (2022) 17–26 Aleksey Antimonov, Nadezhda Pushkareva / Structural Integrity Procedia 00 (2019) 000 – 000

Figure 1. Diagram of the breaking process.

Figure 2. Plastic 1 and elastic 2 components of the deformation  range.

The process is based on rolling breakage by alternating bending (Fig. 1). One end of the bars product 1 is fixed in the clamp 3. The other end is free and performs a circular motion with deviation from its axis under the action of applied load. While moving the sharp edge of tool 2 is introduced into the bar with the application of the stress concentrator 4 on its surface. The combination of alternating elastoplastic bending and notch action creates a high stress concentration with a pronounced fatigue effect. This leads to failure of the rolled product in the notch plane. The end of the bar breaks off at a certain number of load cycles. Such destruction in the theory of strength of

materials is called low-cycle fatigue by Moskvitin (1965). 4. Theoretical basis of low-cycle fatigue strength calculation

Under the low-cycle fatigue conditions, cyclic elastoplastic bending of the bar ends with a notch for stress concentration leads to its failure. The main problem of low-cycle fatigue calculations is to determine the number of cycles before material destruction. The theory of strength calculations is based on numerous experimental data on resistance and fracture of materials under cyclic elastoplastic deformations. Based on the results of processing a large amount of experimental data during tests on various materials, the following dependence was proposed by Manson (1974):

0,6



  

 

0,6

0,12

ln 1

3,5





N

N

     



B

,

(1)

p

e

1

E

 

where  =  max –  min is the deformation range,  max and  min – max and min loading cycle amplitudes, N – is the number of cycles before destruction,  – relative constriction at specimen rupture, B  and E – ultimate tensile strength and modulus of the material elasticity. The first term in this formula defines the plastic component of deformation  p and the second term - the elastic component  e . The calculations made by the formula (1) for mild steel with a of 0,2% carbon content at  = 0,55; B  =460 MPa; E = 1,9  10 5 MPa are presented in Fig. 2. It follows from the figure that the plastic component of the deformation amplitude has the main influence on fracture at a small number of cycles. Thus, at N= 100,  p /  e =11,3 and at N=1200,  p /  e =3,4. Experiments with several materials show that the effect of the elastic component becomes noticeable at N = (1  20)  10 3 . Considering that the expected number of cycles in the breaking process will be significantly lower, the elastic component can be neglected in the calculations. Then, the equation (1) for determination of the deformation range will be as follows: