Spatial strain correlations, machine learning, and deformation history in crystal plasticity.

Systems far from equilibrium respond to probes in a history-dependent manner. The prediction of the system response depends on either knowing the details of that history or being able to characterize all the current system properties. In crystal plasticity, various processing routes contribute to a history dependence that may manifest itself through complex microstructural deformation features with large strain gradients. However, the complete spatial strain correlations may provide further predictive information. In this paper, we demonstrate an explicit example where spatial strain correlations can be used in a statistical manner to infer and classify prior deformation history at various strain levels. The statistical inference is provided by machine-learning techniques. As source data, we consider uniaxially compressed crystalline thin films generated by two dimensional discrete dislocation plasticity simulations, after prior compression at various levels. Crystalline thin films at the nanoscale demonstrate yield-strength size effects with very noisy mechanical responses that produce a serious challenge to learning techniques. We discuss the influence of size effects and structural uncertainty to the ability of our approach to distinguish different plasticity regimes.

Morphology Dependent Flow Stress in Nickel-Based Superalloys in the Multi-Scale Crystal Plasticity Framework.

This paper develops a framework to obtain the flow stress of nickel-based superalloys as a function of γ-γ' morphology. The yield strength is a major factor in the design of these alloys. This work provides additional effects of γ' morphology in the design scope that has been adopted for the model developed by authors. In general, the two-phase γ-γ' morphology in nickel-based superalloys can be divided into three variables including γ' shape, γ' volume fraction and γ' size in the sub-grain microstructure. In order tfo obtain the flow stress, non-Schmid crystal plasticity constitutive models at two length scales are employed and bridged through a homogenized multi-scale framework. The multi-scale framework includes two sub-grain and homogenized grain scales. For the sub-grain scale, a size-dependent, dislocation-density-based finite element model (FEM) of the representative volume element (RVE) with explicit depiction of the γ-γ' morphology is developed as a building block for the homogenization. For the next scale, an activation-energy-based crystal plasticity model is developed for the homogenized single crystal of Ni-based superalloys. The constitutive models address the thermo-mechanical behavior of nickel-based superalloys for a large temperature range and include orientation dependencies and tension-compression asymmetry. This homogenized model is used to obtain the morphology dependence on the flow stress in nickel-based superalloys and can significantly expedite crystal plasticity FE simulations in polycrystalline microstructures, as well as higher scale FE models in order to cast and design superalloys.

Velocity fluctuations in a steadily sheared model foam.

Numerical simulations are conducted to calculate velocity fluctuations in a simple two-dimensional model of foam under steady shear. The width of the velocity distribution increases sublinearly with the shear rate, indicating that velocity fluctuations are large compared to the average flow at low shear rates (stick-slip flow) and small compared to the average flow at large shear rates. Several quantities reveal a crossover in behavior at a characteristic strain rate gamma(x), given by the yield strain divided by the duration of a bubble rearrangement event. For strain rates above gamma(x), the velocity correlations decay exponentially in space and time, and the velocity distribution is a Gaussian. For strain rates below gamma(x), the velocity correlations decay as stretched exponentials in space and time, and the velocity distribution is broader than a Gaussian.

Effective temperatures of a driven system near jamming.

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.

Random packings of frictionless particles.

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.