PSI - Issue 28

NikolayA. Makhutov et al. / Procedia Structural Integrity 28 (2020) 1347–1359 N.Makhutov, D.Reznikov/ Structural Integrity Procedia 00 (2019) 000–000

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The approach presented in this paper allows accounting for the dependence of the stress and strain concentration factors on the level of nominal stresses, strain rates and temperatures, thereby making it possible to assess the stress strain response and ultimate states in the notch zone under conditions of high-speed low-temperature deformation. A flat smooth bar under elastic (Fig. 2a), elastoplastic (Fig. 2b) loading and a bar with a one-sided sharp notch called the Charpy specimen (Fig. 2c) are analyzed.

Fig. 2: Loading scheme (a) loading of a flat specimen in the elastic region; (b) loading of a flat specimen in the elastoplastic region; (c) loading of the specimen with a V shaped notch with a radius of curvature at the notch vertex ϱ. 2. Constitutive equations in wide ranges of strains, strain rates and operating temperatures In the practice of analytical and numerical studies (Makhutov, 1981) of the processes of high-speed loading of the structural components and machine parts under various temperature conditions, different phenomenological models are used. The constitutive equations in these models are written as relationships between equivalent (effective) stresses σ eq and strains e eq , strain rates eq e  and temperatures t : A simplified multiplicative form of the function ( , , ) eq eq f e e t  is usually used in engineering design in which the effects of strain rate hardening as well as temperature softening or hardening (in the case of elevated or low temperatures, respectively) are considered independently and represented by separate functionals: (2) When carrying out calculations, it is often convenient to make a transition from the absolute coordinates e     to the normalized coordinates e     (Fig. 1b) in which expression (2) takes the form: 1 eq eq f e f e f t    2 3 ( ) ( ) ( ) eq   . ( , , ) eq eq f e e t  eq   . (1)

1 eq eq f e f e f t    2 3 ( ) ( ) ( )

eq  