Sensitivity of polycrystal plasticity to slip system kinematic hardening laws for Al 7075-T6

Abstract

The prediction of formation and early growth of microstructurally small fatigue cracks requires use of constitutive models that accurately estimate local states of stress, strain and cyclic plastic strain. However, little research has attempted to systematically consider the sensitivity of overall cyclic stressstrain hysteresis and higher order mean stress relaxation and plastic strain ratcheting responses introduced by the slip system back-stress formulation in crystal plasticity, even for face centered cubic (FCC) crystal systems. This paper explores the performance of two slip system level kinematic hardening models using a finite element crystal plasticity implementation [1]. The two kinematic hardening formulations aim to reproduce the cyclic deformation of polycrystalline Al 7075-T6 in terms of both macroscopic cyclic stress-strain hysteresis loop shape, as well as ratcheting and mean stress relaxation under strain-or stress-controlled loading with mean strain or stress, respectively. The first formulation is an Armstrong-Frederick type hardening-dynamic recovery law for evolution of the back stress [2]. This approach is capable of reproducing observed deformation under completely reversed uniaxial loading conditions, but overpredicts the rate of cyclic ratcheting and associated mean stress relaxation. The second formulation corresponds to a multiple back stress Ohno-Wang type hardening law [3] with nonlinear dynamic recovery. The adoption of this back stress evolution law greatly improves the capability to model experimental results for polycrystalline specimens subjected to cycling with mean stress or strain. The relation of such nonlinear dynamic recovery effects are related to slip system interactions with dislocation substructures.

Prediction of asymmetric cyclic‐plastic behaviour for cyclically stable non‐ferrous materials

“…The observed differences are postulated to originate from the nature of the materials having different deformation behaviour. The CS steels investigated in the previous report by using the same methodology typically exhibit predominantly bcc phase, while the non‐ferrous alloys examined in this study are reported to have close packed (fcc or hcp) crystal structure; it is well known that the deformation behaviour in these crystal structures are different.…”

“…In the current investigation, the contribution of the fourth backstress component for the non‐ferrous alloys is found to be significantly higher compared with that for ferrous alloys (Tables and Table ). It is postulated here that the deformation behaviour of primarily bcc crystal structures of ferrous alloys and that of the fcc or hcp crystal structures of non‐ferrous materials are resulting in the difference. This assumption is commensurate with the consideration that the combined hardening model used in the present study can phenomenologically capture the micromechanical aspects of material deformation, as discussed by Chaboche …”

“…The deformation behaviour is primarily responsible for the nature of ratcheting and evolution of the backstress components (as considered in the cyclic plastic models) in different materials . The macroscale features of the ratcheting phenomena are characterized by the progressive accumulation of plastic strain and are naturally dependent on the magnitude of loading, loading rate, loading axes, and loading history (spectra, directionality, non‐proportionality) .…”

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

“…These researchers simulated the first few cycles and then extrapolated their results to larger cycle numbers. More recently, Hennessey et al (2017) and Cruzado et al (2017) proposed to change the kinematic hardening law from an Frederick and Armstrong (2007) formulation to a modified Ohno and Wang (1993) (Cruzado et al, 2012;Azzouz et al, 2010;Mary and Fouvry, 2007) to extrapolate the constitutive response. Both groups focus on the macroscopic properties of the aggregate rather than on local stress and strain distributions.…”

Micromechanical Modelling of the Cyclic Deformation Behavior of Martensitic SAE 4150—A Comparison of Different Kinematic Hardening Models

“…For realistic simulations of the cyclic material behavior, the use of appropriate constitutive models is also important in addition to adequate RVEs. Cyclic loading conditions including mean stresses require kinematic hardening (KH) models which are not only able to capture first order stress-strain hysteresis behavior but also higher order phenomena such as mean stress relaxation behavior [17]. It has been widely noted in literature for J 2 plasticity that the Armstrong Frederick KH model failed to predict the mean stress evolution in cyclic loadings with non-zero mean stresses [18,19].…”