Critical issues in predictive discrete to continuum multiscale modeling of materials are the stochasticity nature of discrete simulation methods and the presence of uncertainties due to loos of information during scale-up. To make the multiscale models truly predictive, one needs to account for such variabilities in high-resolution models along with the uncertainties due to model inadequacy. This contribution is centered around developing a physics-based machine learning method to integrate continuum-scale strain gradient plasticity model with discrete dislocation dynamics simulations of the size effect in plastic deformation of metallic micro-pillars. Dislocation dynamics simulations are performed on geometries similar to micro-scale testing techniques, including micro-pillar compression. The DDD simulations show that, in contrast to the classical plasticity theories, the onset of plasticity is stochastic in small volumes. Such stochasticity is due to the statistical variation of the initial dislocation density as well as the initial spatial distribution of dislocations. Additionally, the numerical results exhibit a strong dependency of the plastic deformation (yield stress and hardening) to the specimen geometry size. The upscaled model of the size effect in plastic deformation of small-volume materials is provided by a strain gradient plasticity model in continuum scale. Possessing two length parameters (so-called energetic and dissipative length scales), the thermodynamically consistent strain gradient plasticity model accounts for size-dependent yield stress and kinematic hardening. The coupled partial differential equations that arise from both macroscopic and microscopic forces balances are solved using finite element methods. The continuum model, however, is inadequate to address the materials’ initial dislocation content. To developed a predictive hierarchical discrete-to-continuum multiscale model, we proposed a physics-based machine learning framework. The machine-learning methods enable training the continuum model against the synthetic data furnished by the discrete dislocation dynamics simulations. Based on Bayesian inference, the framework also allows for quantifying uncertainties due to the inadequacy of the strain gradient plasticity model along with the intrinsic stochasticity of the dislocation dynamics simulations. Markov chain Monte Carlo (MCMC) methods are employed to solve the statistical inverse problem and to determine the probability distribution of the parameters of the continuum model. The simulation results indicate that the strain gradient plasticity is capable of addressing some plasticity features observed in dislocation dynamics simulations. With the aid of the uncertainty quantification method embedded in the proposed physics-based machine learning framework, we further assess the reliability of the multiscale model in the prediction of the size effect in the plastic deformation of micropillars.

 

 

 

 

 

 

 


A Predictive Multiscale Modeling of Microscale Plasticity: Discrete Dislocation Dynamics to Strain Gradient Plasticity

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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