PSI - Issue 81

Serhiy Fedak et al. / Procedia Structural Integrity 81 (2026) 305–309

308

i , М P а

Е ’

1.1 . 10 4 1.05 . 10 4 1 . 10 4 0.95 . 10 4 0.9 . 10 4

235 255

275

295

315

325

345

 p (  i ) , М P а

Fig. 4. Dependence of the proportionality coefficient on the magnitude of the fracture stress of inclusions  p(  i ).

This trend is accompanied by growing deformation  е і just before the next instantaneous deformation increment. The relationship between the coefficient і Е  and the inclusion fracture stress  p (  i ) is expressed by the following formula:     i р i р i K L E        ( ) ' (2) Here, K =1.26 . 10 4 ; L =-9.1. When the AMg6 alloy is subjected to controlled uniaxial tension, its total deformation includes the elastic component  el , plastic deformation  pl before the stress of jump-like deformation begins  st , as well as instantaneous  (  i ) and linear  е і strain increments that appear on the stepped section of the diagram under mild loading. In the intervals between the jumps, the deformation increases Δεе i according to formula (1), provided the dependence (2) of the proportionality coefficient   ( ) ' i р i E   is taken into account:

  

і 

(3)

е   

  i р

і

K L

 

Hooke's law effectively describes the dependence of elastic strain on the yield strength to the value  02 :



    

(4)

el

E

Within the elastic-plastic deformation region extending up to  st , the growth of plastic deformation is adequately modelled by a power law:     е n pl С 02        (5) Once the stress exceeds the  st threshold, instantaneous jump-like deformation increments  (  i ) are observed. These increments can be quantified using machine learning methods as it is shown by Smola and Vishwanathan (2010), Hastie et al. (2009), specifically based on their dependence on  i which is described by Yasniy et al. (2020), Didych et al. (2022), Yasniy et al. (2019). Based on the conducted research, the total deformation can be found as the sum of deformations: in the elastic region it is described by formula (4), in the plastic regions it is expressed by formula (5), of deformations of instantaneous increments  (  i ), and deformations in the strengthening regions between jumps. Table 1 below presents the characteristics and constants used in formulas (1) – (5) for the AMg6 alloyat a temperature of =293 K.

Table 1. Characteristics and constants used for calculation of tensile strain of AMg6 alloy

 st , МPа

C, 

n e

K

L

 02 , МPа

E, МPа

 e n МPа 

0.74 . 10 5

175

235

2.9 . 10 -12

4.2 1.26 . 10 4

-9.1