PSI - Issue 30

S.P. Yakovleva et al. / Procedia Structural Integrity 30 (2020) 193–200 Yakovleva S. P. et al. / Structural Integrity Procedia 00 (2020) 000–000

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4

phenomena in the metal during spring operation. At the same time, even at the stage of elastic deformation under the influence of long-time stresses that do not exceed the yield strength, some microdamage always occurs in metals, which is considered in particular by Botvina (2008) and Dodds (1991). During operation in the elastic area, the achievement of a certain level of microdamage development transfers the metal to the plastic deformation area, which is accompanied by the common phenomena of deformation hardening and softening. Depending on the stage of damage development, samples of groups I, II, and III should differ in the amounts of strain-hardened and strain softened crystallites, as well as discontinuities in the form of pores.

а

b

Fig. 2. The fracture surface piece (a) and the microstructure of the spring metal

The k coefficient suggested by Zorin (2013) characterizes the relative increase in the microscale damage density of the material in use as

* m 

*

* i i a n N a n N   i i

*

i

1



k

,



i

m 

i

1



i

  1 8 1 1 1 . i m 

 1 8 .

1

1







where . The calculated values of the coefficient k are presented in Table 1, and the average microhardness values and porosity characteristics are also presented there. According to the results of the article by Yakovleva et al. (2017), the metal in the spring center (zone III) goes through a hardening phase, the metal in zone I is considerably softened by the microscale damages; that was why the zones were arranged by the ascending degree of the damage as zone II, zone III and zone I. It follows from table 1 that the maximum value of the coefficient k does not correspond to zone I. This discrepancy can be explained as follows. It is known that the microhardness reflects the metal resistance to the indenter forcing-in, dependent on the strain hardening (or softening) degree that characterizes the damage. If we consider the porosity parameters, we see that an intensive generation of the new pores is observed in pre-fracture zone I (for the comparison, the volume fraction of the pores in zone III near the fixing center increases mainly due to their increasing dimensions). It is obvious that the multiple fine pores as well as the substructural softening, contribute to the accumulation of the fatigue damage, causing systemic loosening of the steel and changing the structural state of zone I. This manifests itself in the change of the distribution of the microhardness parameter. Verification of a statistical hypothesis of the normal distribution by the chi-squared test for the empirical distribution of the array Н 100 in this zone yielded  2 = 121 at the critical value calculated as  2 cr = 16, i.e.,  2 >  2 cr . Therefore, the hypothesis of normal distribution for the metal microhardness in the pre-failure state is rejected. Existence of the multiple pores also makes it more difficult to evaluate the coefficient k correctly in the pre-fracture stage. If we compare the data for the most loaded zones I and III of the spring leaf, we see that at the lower values of the coefficient k and volume fraction of the total porosity V total the failure occurred in the zone characterized by the lower value of the microhardness due to the softening; a deviation of the law of the microhardness distribution from the Gaussian law; significant prevalence of the fine pores (by ≈ 47%); and the much smaller quantity of the coarse pores (by ≈ 45%). i    for 2 i m  ; 1    1 i a m i m  for 2 i m  a