PSI - Issue 28

NikolayA. Makhutov et al. / Procedia Structural Integrity 28 (2020) 1347–1359 N.Makhutov, D.Reznikov / Structural Integrity Procedia 00 (2020) 000–000

1349

3

strains in the inelastic regions for specimens and structural components are carried out by approximate analytical, numerical and experimental methods (Makhutov, 1981; Makhutov, 2008; Makhutov, Matvienko, Romanov, 2018). Approximate analytical methods for the estimation of the state of stresses and strains in stress concentration zones establish relationships between the stress and strain concentration factors during elastic and inelastic material deformation in the stress concentration zone. Among these methods are the Neuber, Hardrath – Ohman, and Molski – Glinka methods which allow obtaining fairly precise estimation of the state of stress in the notch zone for limited elastoplastic strains ( e p ≤ 2.5%). In the case of the emergency loading conditions resulting in the development of severe plastic strains ( e p =50–70%) that can reach the values close to fracture strains ef and cause strain rates of the order of 10 4 s -1 , the accuracy of the methods decreases considerably. In this case, basically more complex problems appear, when the development of severe plastic strains induces a change in the geometric shapes, stress concentration zones, and boundary conditions, which requires the use of the constitutive equations written in true stresses and strains rather than in engineering local stresses and strains. These methods also do not allow accounting for the influence of strain rates and operating temperatures on the state of stresses and strains. The formation of fracture criteria for notched structural components subjected to high-speed loading under various temperature conditions should be considered as a separate and quite an urgent problem. The problem of concentration of stresses and strains has become especially relevant recently when assessment of strength, service life, and safety began to be carried out in a general nonlinear formulation with the transition from stress-based failure criteria expressed in terms of extreme local stresses σ max с to strain-based criteria written in extreme local strains e max с . Given the variety of structural forms, loading conditions, and mechanical behavior of materials, analytical solutions of nonlinear boundary value problems of stress and strain concentration in the most loaded and damaged zones have again gained their relevance. These solutions are based on a modified Neuber equation for the case of a nonlinear power-law approximation of the stress-strain diagram.

σ σ eq



1 2 3

4

σ Y 4

3

4

2

( ,e) Y

t  

1

( )

Y t 

1

σ Y

0

( , ) Y t e e  ( ) Y

t e

е e eq

e f4

e f

e y

( ,e) t 

( ) t

f e

f 

1

e

( b )

( а )

Fig. 1. Strain diagrams under various loading conditions

eq e

 

e   » and « eq

» ; ( b ) in normalized coordinates «

( a ) in absolute coordinates «

e   »

1 is uniaxial tension at room temperature and static loading 2 is single-axis tension under static loading at a low temperature t 1