PSI - Issue 42

D.I. Fedorenkov et al. / Procedia Structural Integrity 42 (2022) 537–544 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Ohno (1980), Tvergaard and Needleman (1984), De Souza Neto et al. (2008), Azinpour (2018). The most popular are the phenomenological models of plastic isotropic damage accumulation proposed by Lemaitre (1985) and Chaboche (1988). Lemaitre postulated a law in which the damage parameter is determined by reducing the elastic modulus in the perfectly isotropic case. This theory was extended by Chaboche (1988), and materials aging effects were later incorporated into Marquis (1988). Later, the original model was extended by Lemaitre (2000) taking into account the damage anisotropy. During cyclic deformation, the yield surface position is shifted in the space of the principal stresses. If the yield surface changes in size, then it’s an isotropic hardening. The yield surface radius is described by the hardening function, which relates true strains and stresses: bilinear approximation, exponential Voce law, Ramberg-Osgood power law and others. If the yield surface size doesn’t change, but its position changes, then it’s kinematic hardening. The displacement distance of the yield surface center is called back stresses. The material hardening and softening processes observed under cyclic loading can be described by the kinematic hardening law. A typical manifestation of this hardening is the Bauschinger effect, which describes the phenomenon of reduction of the elastic limit when the loading sign (compression) changes, if a small plastic strain took place before. During cyclic deformation, materials are mainly characterized by a combination of isotropic and kinematic hardening. In the description of kinematic hardening, early works such authors as Ishlinskii (1954) and Prager (1956) mainly used linear functions. Linear kinematic hardening is the simplest type of kinematic hardening and is able to represent the Bauschinger effect, but isn’t able to cause plastic strain accumulation in the presence of mean stress. A nonlinear law of kinematic hardening was developed by Frederick and Armstrong (2007), which is based on the Prager law taking into account back stresses. Depending on the material properties and the temperature during a single test, certain cyclic loading stages may be accompanied by a decrease, increase and constancy of the elastic-plastic strain strength. The model by Chaboche (1991) allows the superposition of several independent back-stress tensors and makes it possible to combine different kinematic hardening laws to describe various stages of cyclic deformation. However, its applicability is accompanied by an increase in the number of identifiable constants. One of the main advantages of nonlinear kinematic models is taking into account ratcheting and shakedown under asymmetric stress controlled, as well as mean stress relaxation under asymmetric strain controlled. The correct identification of hardening parameters is a very topical issue under consideration by Eslami and Mahbadi (2001), Mahmoudi et al. (2011), Coppieters and Kuwabara (2014), Peroni and Solomos (2019), Wójcik and Skrzat (2021). Nevertheless, a number of papers based on similar formulations of damage and hardening practically don’t focus on the identification algorithm of constants and parameters, referring to the same articles in numerical studies, in which the identification method is described ambiguously. Other papers describe a variety of non-standard and difficult to implement tests. This article implements an algorithm based on a set of solving equations and combines the exponential isotropic hardening, the Armstrong-Frederic kinematic hardening and the Lemaitre damage model. This algorithm has been implemented in the ANSYS user material subroutine. The structure of the algorithm solving equations includes constants that are the material characteristics for predetermined loading conditions. The aim of this work was to verify the method for identifying the parameters used in the isotropic hardening law, kinematic hardening law and the Lemaitre damage model, based on two standard uniaxial tension and low-cycle fatigue tests.

Nomenclature

e pl  e pl  R 

von-Mises equivalent plastic strain; total equivalent plastic strain rate;

yield stress;

0  e  u  R 

von-Mises equivalent stress;

pl

plastic fracture strain;

ultimate stress; fracture stress;

pl   plastic strain range;

pl ε

plastic strain tensor rate;

true fracture stress; maximum cyclic stress; asymptotic fatigue limit;

k S

pl

max 

plastic strain corresponding to the ultimate stress;

u  



f 

plastic multiplier;