Crystal plasticity modeling of the cyclic behavior of polycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses

Abstract

When a sample is cyclically loaded under a mean stress or strain, incremental strain ratcheting or mean stress relaxation phenomena are usually observed. Experiments show that for metallic materials there is generally no full mean stress relaxation as well as saturation of macroscopic strain ratcheting. In contrast, most macroscopic constitutive models produce both quantities in excess, and complex sets of additional internal variables must be introduced to improve the modeling. Little attention has been paid to model such phenomena using polycrystal aggregates especially going up to the regime of cyclic mechanical stability. In this work based on an elementary crystal plasticity model for FCC crystals and large scale finite element, it is be shown that the interaction between different grains is sufficient to cater for such complex phenomena. Light is shed on how different regions of the polycrystal accommodate each other and how the classical definition of constant rate strain ratcheting or a zero mean stress is nearly impossible to apply to a polycrystalline aggregate. In addition, it is shown that even if a macroscopic stable hysteresis stress strain loop is observed, ratcheting phenomena can still be observed at the local scale. The distributions of different constitutive quantities within a polycrystal are also analyzed which gives a new insight into what is happening inside a polycrystal in terms of stress and strain redistribution. In particular, the existence of evolving bimodal distributions of stress and accumulated plastic strain is evidenced and related to the occurrence of plastic shakedown and incomplete mean stress relaxation. Two numerical criteria to detect strain ratcheting are finally proposed and discussed. Kang et al., 2010). Mean stress in this article is defined as (Σ max + Σ min )/2 where Σ max and Σ min are the 15 maximum and minimum applied stresses in a cyclically loaded component. The stress amplitude is defined as Σ max −Σ min /2. With regards to asymetric strain controlled cyclic loadings, it is also known that under a given stress amplitude, increasing the mean stress, or increasing the applied mean stress under constant amplitude, both increase the rate of ratcheting (Goodman, 1984). On the other hand, experimental observations indicate levels of mean stress for which there is very low ratcheting and the mechanical state of the material converges 20 towards plastic shakedown (Pellissier-Tanon et al., 1982). Similarly, for asymmetric strain controlled loading conditions, a cyclic mean stress is observed, and several experimental studies (Wehner and Fatemi, 1991;Nikulin et al., 2019;Prithivirajan and Sangid, 2018) have deciphered the corresponding physical mechanisms. These observations show that for a given positive mean strain, and a low strain amplitude, the mean stress does not completely relax to zero. Also, increasing the strain amplitude leads to a nonlinear decrease of the 25

Identifying material parameters in crystal plasticity by Bayesian optimization

“…decrease for increasing number of cycles, see Farooq et al (2020) and Cruzado et al (2020) for recent discussions of ratcheting and the Bauschinger effect, respectively.…”

“…For modeling the response to cyclic loading accurately, the Bauschinger effect, which concerns a decrease of the resistance to plastic deformation also when a change in loading directions, for instance from tension to compression, takes place, needs to be accounted for Cruzado et al (2020). Also, the ratcheting behavior, i.e., the consistent accumulation of plastic slip under stress-driven cyclic loading conditions, is necessary to consider (Farooq et al 2020). Then, simulations for lifetime predictions may be set up (McDowell and Dunne 2010;, often based on kinematic hardening models (Gillner and Münstermann 2017), also considering thermal activation (Xie et al 2004), atmospheric conditions (Arnaudov et al 2020) or crack initiation (Anahid et al 2011) and crack growth (Dunne et al 2007).…”

Lagrange multiplier based vs micromorphic gradient-enhanced rate-(in)dependent crystal plasticity modelling and simulation

“…Another possible way to select the active slip systems is to use the rate-independent formulation proposed by Forest and Rubin (2016) and intensively used by Farooq et al (2020) (later referred to as RubiX formulation). It is characterized by a smooth elastic-plastic transition with no slip indeterminacy.…”

Cyclic response of electrodeposited copper films. Experiments and elastic–viscoplastic mean-field modeling

“…To quantify the mechanical fields in a polycrystal, crystal plasticity finite element calculations on aggregates (e.g. Farooq et al (2020)) or mean field approaches based on self-consistent scheme (see for instance…”