Gradient plasticity in isotropic solids

We discuss a framework for the description of gradient plasticity in isotropic solids based on the Riemannian curvature derived from a metric induced by plastic deformation. This culminates in a flow rule in the form of a fourth-order partial differential equation for the plastic strain rate, in contrast to the second-order flow rules that have been proposed in alternative treatments of gradient plasticity in isotropic solids.

An Experimental and Numerical Study of Quenching-Induced Residual Stresses under the Effect of DSA in an IN718 Superalloy Disc

The effects of Dynamic Strain Ageing (DSA) on residual stresses generated in Ni-base superalloys during heat treatments are not well understood. In this work, the residual stress field induced by water quenching an IN718 disc while undergoing DSA is studied using coupled thermo-mechanical finite element analyses in conjunction with neutron diffraction (ND) measurements. A visco-plastic constitutive model which incorporates the effect of DSA is proposed to describe the experimentally observed negative strain rate sensitivity and abnormal temperature dependence phenomena in the stress-strain response of solid solution treated IN718. The predicted quenching residual stresses in the disc agree well with the ND measurements. Due to the DSA, a propagating high plastic strain rate region can be identified in the disc during the early stages of the quenching process. Due to the negative strain rate sensitivity and abnormal temperature dependence effects caused by DSA, the predicted residual stresses are approximately 10% greater than when those two effects are not accounted for. The effects of different convection heat transfer conditions in the FE model are examined and discussed. It is found that the convection heat transfer coefficients have a great influence both on the disc residual stresses and DSA-related plastic strain rate field predictions.

Evolution of Strain Gradient Formulation in Capturing Localization Phenomena in Granular Materials

This paper highlights the use of incorporating strain gradient into flow stress to study localization behavior in materials. Pioneered by Zbib and Aifantis in the late 1980s, the formulation enabled incorporation of length scales into continuum formulations naturally. The formulation has also evolved into being able to study the effects of microstructure and heterogeneity on localization in granular materials. A multi-slip Mohr-Coulomb type plasticity model with the flow stress in the constitutive equation modified with a higher order gradient term of the effective plastic strain is used for this purpose. The possibility of abrupt changes of mobilized friction caused by intense shearing rate often leads to particle breakage. Its effects on localization is accounted for by modifying the material properties such as mobilized friction using a scaling parameter averaged over a representative elementary area. The change of shearing rate in the integration points was monitored through quasi-statistically measure parameter called inertia number. The inertia number was set to be all the time to consider quasi static less than l.0E-3. The formulation was implemented into a finite element code and used to simulate plane strain compression tests on dry sand. The model highlights effects of confining pressure, anisotropic microstructure, the non-coaxial angle between the direction of principal stress and principal plastic strain rate directions on shear band characteristics.

Slip-free multiplication and complexity of dislocation networks in FCC metals

During plastic deformation of crystalline solids, intricate networks of dislocation lines form and evolve. To capture dislocation density evolution, prominent theories of crystal plasticity assume that 1) multiplication is driven by slip in active slip systems and 2) pair-wise slip system interactions dominate network evolution. In this work, we analyze a massive database of over 100 discrete dislocation dynamics simulations (with cross-slip suppressed), and our findings bring both of these assumptions into question. We demonstrate that dislocation multiplication is commonly observed on slip systems with no applied stress and no plastic strain rate, a phenomenon we refer to as slip-free multiplication. We show that while the formation of glissile junctions provides one mechanism for slip-free multiplication, additional mechanisms which account for the influence of coplanar interactions are needed to fully explain the observations. Unlike glissile junction formation which results from a binary reaction between a pair of slip systems, these new multiplication mechanisms require higher order reactions that lead to complex network configurations. While these complex configurations have not been given much attention previously, they account for about 50% of the line intersections in our database.

Examination of Dynamic Strain Ageing Effects during Rapid Quenching of Inconel 718 Superalloy Disc

In this work, an experimental measurement, contour method, is implemented for an after quenching IN718 forging specimen to obtain the distribution of residual stress field. A sequentially coupled thermal mechanical finite element model is developed with the similar 3D geometry of the experimental specimen and implemented the same heat transfer boundary of the rapid quenching with the experimental condition. A thermal mechanical rate dependent continuum plasticity model for IN718 alloy, with the dynamic strain ageing (DSA) effect incorporated, is developed to study the impact of DAS effect on the evolution of residual stress during rapid quenching. The modelling predictions of residual stress are in good agreement with the contour method measurements. The impact of DSA effect is further quantified, indicating that an annular high plastic strain rate region in the core part of the disc is captured during the simulation of the quenching process.

A note about hardening-free viscoelastic models in Maxwellian-type rheologies at large strains

Maxwellian-type rheological models of inelastic effects of creep type at large strains are revisited in relation to inelastic strain gradient theories. In particular, we observe that a dependence of the stored energy density on inelastic strain gradients may lead to spurious hardening effects, preventing the model from accommodating large inelastic slips. The main result of this paper is an alternative inelastic model of creep type, where a higher-order energy contribution is provided by the gradients of the elastic strain and of the plastic strain rate, thus preventing the onset of spurious hardening under large slips. The combination of Kelvin–Voigt damping and Maxwellian creep results in a Jeffreys-type rheological model. The existence of weak solutions is proved by way of a Faedo–Galerkin approximation.

Low Cycle Fatigue of an Ultrafine Grained AA5083 Aluminum Alloy Composite Produced by Cryomilling

Low cycle fatigue (LCF) properties were investigated for a novel cryomilled AA5083 aluminum composite with duplex coarse and ultrafine grain sizes and reinforced with boron carbide particulates, referred to as trimodal material. Fully reversed cyclic tests were conducted under plastic strain control at plastic strain amplitudes from 0.15 to 0.6 pct using a constant plastic strain rate in a servo-hydraulic testing system. A nonlinear elastic modulus was used to calculate the elastic contribution to the measured total strain. The LCF performance of this trimodal material is compared to previous results for unreinforced AA5083 aluminum alloy with bimodal grain size (85/15 pct CM/UM) and its coarse-grained wrought counterpart, AA5083-H131. Stress response curves for the trimodal material revealed slow hardening until failure associated with the presence of particulate reinforcements. The very small asymmetry between tension and compression stresses reflects a lack of strain localization beyond the initial cycles. The trimodal and 85/15 pct CM/UM alloys have similar and superior low cycle fatigue strength compared to AA5083-H131. From the Coffin-Manson plot, the trimodal material has a shorter fatigue life than 85/15 pct CM/UM alloy and AA5083-H131 for high plastic strain amplitudes, but nearly identical life at low amplitudes. Microcracks were observed near the dominant crack on trimodal specimen surfaces at failure. Back-scattered images revealed that particulates altered the crack propagation direction; cracks nearly always propagated around particulates.

MODELING OF THE FATIGUE DURABILITY OF STRUCTURAL ALLOYS UNDER TWO-FREQUENCY LOADING

The processes of fatigue life of polycrystalline structural alloys under the combined action of low- and high-cycle fatigue mechanisms are considered. From the standpoint of damaged medium mechanics (DMM), a mathematical model has been developed that describes the processes of plastic deformation and the accumulation of fatigue damage. The DMM model consists of three interrelated parts: relations that determine the cyclic elastoplastic behavior of the material, taking into account the dependence on the fracture process; equations describing the kinetics of fatigue damage accumulation; criterion for the strength of the damaged material. Variant of the constitutive relations for elastoplasticity is based on the concept of a microplastic loading surface in the von Mises form and the principle of the gradient of the plastic strain rate vector to the surface at the loading point. This version of the equations of state reflects the main effects of the process of cyclic plastic deformation of the material for arbitrary complex loading trajectories. A variant of the kinetic equations for the accumulation of fatigue damage is based on the introduction of a scalar damage parameter, is based on energy principles and takes into account the main effects of the formation, growth and fusion of microdefects under arbitrary complex loading conditions. A unified form of the evolutionary equation for the accumulation of fatigue damages for low-cycle and high-cycle fatigue is proposed. As a criterion for the strength of the damaged material, the condition for reaching the critical value of the damage is used. To assess the reliability and determine the limits of applicability of the constitutive relations of the DMM, numerical studies of the processes of accumulation of fatigue damage by cyclic inelastic deformation and fatigue failure of steel 20 and 08Х18Н12Т were carried out under single-frequency loading of the upper frequency and two-frequency loading with different amplitude ratios. And the comparison of the obtained numerical results with the data of field experiments is carried out. The results of comparing the calculated and experimental data showed that the developed model of the damaged environment reliably describes the durability of structures under the action of low- and high-cycle fatigue mechanisms.