Material Systems

metal
Ti7 Deterministic
metal
Ti7 Uncertainty Quantification
metal
Ti64 Deterministic

Overview

Introduction

The concept of parametric upscaling in constitutive models has been introduced by the Ghosh group in [1-10] to: (i) bridge length-scales through the explicit representation of lower-scale (microstructural) descriptors in higher-scale constitutive models, and (ii) overcome high computational costs incurred by many homogenization methods through an efficient computational platform.

The physics-based Parametrically-Upscaled Constitutive Models or PUCMs differ from conventional phenomenological models in their unambiguous depiction of constitutive parameters and their dependencies. PUCMs, incorporate a parametric representation of lower-scale microstructural descriptors in higher-scale constitutive coefficients. These PUCM coefficients are expressed as functions of Representative Aggregated Microstructural Parameters or RAMPs, representing lower-scale descriptors of microstructural morphology and crystallography, e.g., texture and orientation distribution, grain, and reinforcement size, etc. General forms of PUCM equations are a-priori selected to reflect the fundamental deformation characteristics of aggregated micromechanics response of microstructural statistically equivalent representative volume elements or (SERVEs). The first law of thermodynamics, governing the mathematical theory of homogenization, is used to bridge length scales and express constitutive coefficients as functions of lower-scale RAMPs. Machine learning (ML) tools, e.g., symbolic regression and artificial neural networks (ANN) are essential for generating PUCM constitutive coefficients as functions of the RAMPs, using data-sets generated from micromechanical simulations. The PUCM framework provides a window for the ML tools to create meaningful physics-informed constitutive coefficients as functions of lower-scale descriptors. The PUCMs are readily incorporated in FE codes like ABAQUS through user-defined material modeling windows such as UMAT. A significantly reduced number of solution variables in the PUCM simulations, compared to micromechanical models, make them several orders of magnitude more efficient, but with comparable accuracy.

Steps in Developing the PUCMs

  • Module 1 acquires data from microstructural characterization and mechanical testing for model calibration and validation.
  • Module II first establishes microstructure-based statistically equivalent RVEs or SERVEs. Following this, image-based micromechanical models are calibrated, and micromechanical simulations of the SERVE are performed for validation with experiments.
  • Module III begins with the creation of a database of evolving state variables from micromechanical simulations of the SERVEs with various microstructure and load combinations. Subsequently, the RAMPs of morphological and crystallographic descriptors, such as grain size, shape, orientation and misorientation distributions, are identified from detailed sensitivity analysis, e.g., Sobol analysis. Key RAMPs that affect the homogenized material response are identified.
  • Module IV generates functional forms of PUCM constitutive coefficients as functions of RAMPs using machine learning tools, operating on an extensive database of RAMPs and corresponding homogenized state variables resulting from micromechanical simulations of the SERVEs. The PUCMs are incorporated in commercial FE software like ABAQUS and ANSYS through user-defined material modeling interfaces, for microstructure-sensitive structural response predictions. Finally, uncertainty quantification is built into the PUCM framework following a Bayesian inference formulation [3,6,7] to derive probabilistic microstructure-dependent constitutive laws of the macroscopic response.
Module I
Experimental Data & Characterization		 Module II
Image-based Micromechanical Models		 Module III
Microstructural RAMP Identification		 Module IV
PUCM Calibration and Validation
Acquire data on microstructures from EBSD/SEM maps Generate statistically equivalent RVEs of microstructures Create a range of virtual microstructures with various parameters Database of homogenized micro-mechanical variables
Conduct mechanical tests for deformation and damage data Calibrate micro-mechanical constitutive models Identify critical distributions of micro-structural descriptors Machine Learning for functional forms of RAMPs in PUCMs
Generate statistical functions of micro-structural descriptors Validate image-based micromechanical models Establish RAMPs for PUCM coefficients using Sobol analysis Implement in macroscopic FE codes for validation
Uncertainty quantification
Table 1: Steps in the development of the Parametrically-Upscaled Constitutive Models (PUCMs)

Contact

Please email cmrl-codes@jhu.edu with questions, comments, or concerns.

References

  1. Kotha, S., Ozturk, D., Ghosh, S. Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations, Part I: Sensitivity analysis and parameter identification for Titanium alloys, Int. J. Plast., 120, 296-319, 2019.
  2. Kotha, S., Ozturk, D., Ghosh, S. Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations: Part II: Thermo-elasto- plastic model with experimental validation for titanium alloys, Int. J. Plast., 120, 320-339, 2019.
  3. Kotha, S., Ozturk, D., Smarslok, B., Ghosh, S. Uncertainty Quantified Parametrically Homogenized Constitutive Models for Microstructure-Integrated Structural Simulations, Integ. Mater. Manuf. Innov., 9(4), 322-338, 2020.
  4. Ozturk, D., Kotha, S., Pilchak, A., Ghosh, S. Two-way multi-scaling for predicting fatigue crack nucleation in titanium alloys using parametrically homogenized constitutive models, J. Mech. Phys. Solids, 128, 181-207, 2019.
  5. Ozturk, D., Kotha, S., Pilchak, A., Ghosh, S. Parametrically homogenized constitutive models (PHCMs) for multi-scale predictions of fatigue crack nucleation in Titanium alloys, JOM: J. Miner. Met. Mater. Soc., 71(8), 2564-2566, 2019.
  6. Kotha, S., Ozturk, D., Ghosh, S. Uncertainty-quantified parametrically homogenized constitutive models (UQ-PHCMs) for dual-phase α/β titanium alloys, npj Comp. Mater., 6(1), 1-20, 2020.
  7. Ozturk, D., Kotha, S., Pilchak, A., Ghosh, S. An uncertainty quantification framework for multiscale parametrically homogenized constitutive models (PHCMs) of polycrystalline Ti Alloys, J. Mech. Phys. Solids, 148, 104294, 2021.
  8. Zhang, X., Gao, J., O'Brien, D. J., Chen, W. and Ghosh, S., Parametrically homogenized continuum damage mechanics model for multiscale damage evolution in single-edge notched bending experiments of glass-epoxy composites, Compos. Part B, 09409 , 2021.
  9. Zhang, X. and Ghosh, S., Parametrically homogenized continuum damage mechanics (PHCDM) Models for unidirectional composites with nonuniform microstructural distributions, J. Comp. Physics, 435,110268, 2021.
  10. Zhang, X., O'Brien, D. J. and Ghosh, S., Parametrically homogenized continuum damage mechanics (PHCDM) models for composites from micromechanical analysis, Comp. Meth. App. Mech. Engin., 346(1), 456-485, 2019.