5. Plasticity and Fracture Prediction Under Nonlinear Loading

Wing Kam Liu, Walter P. Murphy Professor, Northwestern UniversityPresident of the International Association for Computational Mechanics

Past Chair of National Committee on Theoretical & Applied Mechanics of US National Academies

Member of the Board of International Scientific Organizations of US National Academies

Member of Center for Hierarchical Materials Design (CHiMaD)

Member of Northwestern Initiative on Manufacturing Science and Innovation (NIMSI)

http://www.tam.northwestern.edu/wkl/liu.html, w-liu@northwestern.edu

Project PIs: Wing Kam Liua, Greg Wagnera, Jian Caoa, Brad Kinseyb, Marko Knezevicb, Amine Benzergac

aNorthwestern UniversitybUniversity of New Hampshire

cTexas A&M

Executive Summary:

• Objective/Industrial Need: The capability of quickly predicting macroscale properties based on microstructure evolution

• Approach: Data-driven multiscale modeling using reduced order Self-consistent Clustering Analysis (SCA) [1000x faster in 3D sim.]

• Deliverable: Experimentally-validated simulation tools

• Budget and Timeline: $500K for 3 years; supports 3 RAs (micro/meso-scale modeling, meso/macro-scale modeling, experimental characterization)

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5. Plasticity and Fracture Prediction

• Plasticity and fracture lead to failure of metallic material during processing and service

• High-fidelity simulation tools can:

– Predict part’s behavior under nonlinear loading

– Improve understanding of material’s properties

– Reduce number of experiments and cost

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Industrial Needs and Relevance:

Malhotra, R., Xue, L., Belytschko, T. and Cao, J., 2012, “Mechanics of Fracture in Single Point Incremental Forming”, Journal of Materials Processing Technology, Vol. 212 (1), pp. 1573-1590.

Double-side Incremental Forming Simulation

Industrial Needs and Relevance:

Save development time and less iteration in product and process design

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Plasticity and Fracture Prediction Under Nonlinear Deformation Paths

(a) Strain reversal in a punching process(b) Edge crack of Advanced High-

Strength Steel sheets(c) Forming to crash simulation in car

bodies

(b) (c)(a)

Project Objectives:

• Develop data compression and data analysis methods to accelerate computations

• Combine data processing techniques and multiscale simulation methods to establish a data-driven multiscale simulation framework

• Use such framework to reduce computational cost while keeping accuracy in modeling

• Extend this framework to plasticity and fracture prediction

• Under this common goal, the project objectives include, but are not limited to:

1. Simulate different metal forming processes

2. Predict macroscale properties based on microstructure evolution

3. Increase computational efficiency by data-driven multiscale modeling

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CP SCA picture

Plastic Strain

Vernerey, Liu and Moran, Multiscale Micromorphic Theory for Hierarchical Materials, JMPS, 2007

Vernerey, Liu, et al., A Micromorphic Model for the Multiple Scale Failure of Heterogeneous Materials, JMPS, 2008.

McVeigh & Liu, Multiresolution modeling of ductile reinforced brittle composites. JMPS, 2009.Tian & Liu et al., A Multiresolution Continuum Simulation of the Ductile Fracture Process, JMPS, 2010.

Approach/Methodologies:

The group has many technologies ready to use or in development stage. Selected technologies are listed below:

a) Multiresolution Continuum Theory (MCT)

b) Self-consistent Clustering Analysis (SCA)

c) Experiments for fracture calibration

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Multi-resolution Continuum Theory

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Slide 7

Too expensive to model microstructure explicitly

Captures size effects

Mesh independent

Low computational cost

Captures multiple scales of localization

Captures size effects

Mesh independent

Low computational cost

Captures only one scale

Cannot capture size effects

Mesh dependent

Reduce Order Modeling by SCA

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Offline or training stage (SCA)

1) Domain decomposition (k-means

clustering): find material clusters.

Reduced order model

2) Compute the interaction tensors

based on Green’s function

3D- 16 clusters

2D- 16 clusters

•Strain concentration tensor is used for characterizing the responses.

Computational time drastically reduced

16 clusters: 1 s

256 clusters：20 s

600 × 600 FEM

1420 s

2-Dimension

80 × 80 × 80 FEM

3-Dimension

25.7 hours

on 24 CPUs

16 clusters: 2 s

256 clusters：50 sO. Goury, D. Amsallem, SP. Bordas, WK. Liu, P. Kerfriden, “Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization,” Comput Mech (2016) 213–234Z. Liu, MA. Bessa, WK. Liu, “Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials,” Comput. Methods Appl. Mech. Engrg. (2016) 319–341.Z. Liu, JA Moore, WK Liu, “An Extended Micromechanics Method for Probing Interphase Properties in Polymer Nanocomposites,” Journal of the Mechanics and Physics of Solids, 2016,

Online or predictive stage (SCA) Self-consistent clustering analysis

based on Lippman-Schwinger equation.

Numerical modeling of ductile fracture mechanisms

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• Remeshing algorithm• Large plastic strain• Ductile matrix

• Composite with brittle particles• Cracks modeled with Level-Sets & remeshing• Plastic localization and void coalescence

Void growth & coalescence Particle debonding & fragmentation

Loading condition: Forming

Shakoor, M. "Three-dimensional numerical modeling of ductile fracture mechanisms at the microscale". PhD thesis, Mines ParisTech, 2016.

Concurrent Simulation Based On SCA

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• Same microscale SCA database is used for materials with hard and soft inclusions

• The SCA reduced order module is implemented as a VUMAT in ABAQUS under 2D plane strain condition.

Microscale model (SCA)

Evolution of The Macroscale Effective Plastic Strain Field

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Damage Parameter Comparison: 1-step vs. 3-step homogenization

One-step homogenization

Three-step homogenization

elastoplastic material without damage

SCA Concurrent simulation: Damage evolutions (Hard Inclusions)

Point 1: Damage field

Point 1: Mises stress field Point 2: Mises stress field

Point 2: Damage field

• Hard inclusions help to carry theload and increase the overallstiffness. The damage initiationis sensitive to the shear loading.

• Numerical models developed here can be used as numerical experiments to simulate loading paths that are impossible or hard to obtain in physical tests

• Provide more realistic deformation mechanisms at the microstructure level

• Use microstructure and fracture data already generated from A/SP projects as a starting point to build up and validate the multi-scale model

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Relation to A/SP Projects

– Microstructure characterization– Tests for determining fracture models– In-situ damage evolution using ANL facilities

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Proposed testing efforts under monotonic and multiaxial loadings

Most tests can be done in one universal testing machine.

Experimental Characterization

5. Plasticity and Fracture Prediction Under Nonlinear Loading

Deliverables:

• An experimentally-verified computational platform for evaluating fracture and material damage of advanced materials while incorporating micromechanical effects with macrostructural models.

• A multiscale software interface and integration tool for fracture prediction in existing commercial CAE tools (e.g., ABAQUS, LS-DYNA), with documentation

• Training and consulting services for new software interface.

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5. Plasticity and Fracture Prediction Under Nonlinear Deformation Paths

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Budget and Timeline:

Estimated cost of the project is $500K for three years, including 3RAs and experimentation cost.

Task / MilestoneYear 1 Year 2 Year 3

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

Material characterization

Multi-scale theory

Tool integration

Model validation and Doc

5. Plasticity and Fracture Prediction Under Nonlinear Loading

Discussions:– Are the industrial need and relevance accurately captured?

– Are the objectives realistic and complete?

– Are the approaches technically sound and appropriate?

– Are there alternative implementation paths or better approaches?

– Are the deliverables impactful to industrial partners?

– Are the budget and timeline reasonable?

– Are there conflicts with intellectual property or trade secrets?

– List additional project specific questions are appropriate.

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