PSI - Issue 39

N.A. Makhutov et al. / Procedia Structural Integrity 39 (2022) 247–255 Author name / Structural Integrity Procedia 00 (2019) 000–000

250

4

Makhutov, 2008):

In the elastic range = ∙ In the elastoplastic range = ( / for ≤ .

(5)

) for ≥ and = / ,

(6)

where E is the modulus of elasticity, m is the strain hardening exponent in the plastic region.

Fig. 3. Stress-strain curves in absolute (a) and normalized (b) coordinates.

In what follows, the diagram (b) is used instead of diagram (a) (Fig. 3). Then expressions (5) and (6) can be rewritten in the form: � = / ; ̅ = / ; � = ̅ . (7) For the region of elastic strains: m = 1 and � = ̅ . The value of the exponent m for metallic structural materials (steels and alloys) is determined by experiments. If we assume that expression (7) is valid for the entire range of strains (0 ≤ ̅ ≤ ̅ ) и and stresses (0 ≤ � ≤ ̅ ) at the fracture point C = ℓ ̅ / ℓ ̅ , (8) ̅ is true fracture strain at the specimen neck; ̅ – fracture resistance ̅ = ℓ [1/(1 − )]/ , ̅ = [ (1 + 1 )]/ , (9) where is the relative narrowing of the cross-sectional area in the neck at fracture; is the ultimate strength corresponding to the end of the process of uniform deformation and the formation of a neck. Taking into account the power-law stress-strain dependence according to equation (7) one can get: = ℓ [1/(1 − )] . (10)