PSI - Issue 39

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

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For the most common structural steels 0.05≤ m ≤0.30. 3. The effect of temperatures and strain rates Power-law functions can describe the effect of temperatures 0 C and strain rates ̇ = de/d τ on the mechanical properties of steels: yield strength σ Y and ultimate strength σ u (Makhutov, 1981; Makhutov, 2008). � , � = � , �ехр �� , � 1 − 1 0 ��� , (11) � ̇ , ̇ � = � , � ( ̇ / ̇ 0 ) � , � , (12) where σ y , σ u - characteristics of mechanical properties at room temperature ° and standard strain rate ̇ 0 ( ̇ 0 ≈ 2 ∙ 10 −3 1/ ); β y , β u , α y , α u - characteristics of steel, determined experimentally; T = t + 273. In the absence of these data, it can be assumed that if σ y is in the range from 350 to 700 MPa, the value of β y decreases almost linearly from 100 to 50, and the value of α y decreases from 0.065 to 0.02. Parameter β u depends on S c , σ y and σ u : = ℓ ( / ) ℓ � / � ; ≈ 0,67 . (13) Plasticity is determined by the following equation: , ̇ = [1 − � ̇ − − � ] 2 . (14) 4. The effect of stress triaxiality on mechanical properties The stress triaxiality at the crack tip with different components of the principal stresses σ 1 ≥σ 2 ≥σ 3 affects (Makhutov, 1981; Makhutov, Reznikov, 2020) the resistance to the initiation of plastic deformations. Under the action of normalized tensile principal stresses � 1 = 1 / 1 = 1, � 2 = 2 / 1 , � 3 = 3 / 1 the von Mises equivalent yield stress increases: = � 2/[(1 − � 2 ) 2 + ( � 2 − � 3 ) 2 + ( � 3 − 1) 2 ] = , (15) where is the factor of the increase of the resistance to plastic deformation due to stress triaxiality. In this case, the limit plasticity decreases, it depends on the ratio of the von Mises equivalent stress to the sum of the principal stresses = с ∙ � 3 � = � ( 1+ � 2 ⁄3+ � 3 ⁄3 ) = ∙ / = ∙ . (16) 5. Stress states at the crack tip In the general case, a three dimensional stress state arises at the crack tip with the local normal and tangential components determined by the equations of linear fracture mechanics: � , , , , , � = √2 { , }, (17) where F { θ , r } is the coordinate function of the current point A (Fig. 4).