Energy Dissipation Mechanism Based Materials and Materials Systems Design

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1 Energy Dissipation Mechanism Based Materials and Materials Systems Design Wing Kam Liu Walter P. Murphy Professor of Mechanical and Civil Engineering President, International Association for Computational Mechanics Chair, US National Committee for Theoretical & Applied Mechanics Department of Mechanical Engineering, Northwestern University Jacob Smith, John A. Moore, Miguel Bessa Department of Mechanical Engineering, Northwestern University UCSD February 2015

Composite Materials Design Development of

Development of micro-mechanical model for

RVE Main objective: decrease dependence on

2 Composite Materials Design Development of nano-scale model for polymeric matrix; Development of micro-mechanical model for composite informed from the nano-scale model; Macro-scale constitutive law homogenization. RVE Main objective: decrease dependence on experimental testing Epoxy constitutive model Homogenization of nano-mechanical model 2

3 Vehicle Performance & Crash Worthiness Possible Failure Modes Input Anisotropic elastic property Stress-strain curve Strain rate Fiber orientation Fiber Content Ply layups Porosity Interface strength Output Failure prediction Crash Safety O. Faruque

4 Energy Dissipation in Car Crash Experiment

5 Nanoscale Modeling of Epoxy Matrix Crosslink GLASSY THERMOSETS MICROSTRUCTURE Amorphous Very high cross-link density (over 90%) Short chains interconnected by Polymer cross-links chain Cross-link density dramatically changes the mechanical behavior 5

6 Fully Atomistic Epoxy Model Fully atomistic model for Epon DDS Epoxy [1] Equilibrated structure Structure under large deformation a. b. Glass transition temperature c. Molecular structures of (a) DGEBA, (b) activated DGEBA, and (c) 33DDS. [1] C. Li and A. Strachan. Macromolecules 2011, 44, /25

7 Atomsitic Results for Epoxy Matrix Fully atomistic model for Epon DDS Epoxy [1] Energy evolution Tension Tension Temperatute dependence predictions Elas%c modulus E = 2.9 Gpa (T = 300K) The experimental elas/c modulus (Epon825-33DDS) = 3.0! 0.1Gpa; Yield stress = 2.0! 0.2 The experimental elas/c modulus (Epon862- Detda) = 2.5! 0.6Gpa Compression Tension Compression Compression [1] C. Li and A. Strachan. Macromolecules 2011, 44, /25

8 Woven Polymer Composite RVE Model 8

Material Models for Constituents Fiber Interface τ n σ ε Interface strength Linear elastic, transversely isotropic, and very brittle Cohesive law Matrix

9 Material Models for Constituents Fiber Interface τ n σ ε Interface strength Linear elastic, transversely isotropic, and very brittle Cohesive law Matrix Nonlinear behavior [1] δ cr Pure tension Pure shear Pure compression [1] Werner & Daniel (2013). Dynamic Behavior of Materials, Volume 1 (pp ). Springer New York. 9

10 Simplest approach: Homogenization: Nano to Micro 1. Use MD to calibrate the tension & compression curves of the continuum plasticity model; 2. Predict shear behavior in both models. Coarse-grained model Fully-atomistic model Predictions 10 10

11 RVE for Polymer Matrix Composite STEP 1: high-fidelity modeling by RVE Strain rate: 1E-4/s or DNS 1/s Damage value tension Damage value compression 11

Microvoid Softening and Ballistic Performance Challenge Statement: Establish microstructural design parameters for

shear bands to inform improved simulation of role of particle/ microvoid interaction in Microvoid Ballistic ballistic

Integrate Plugging Simulation effects of microvoid and thermal softening in efficient multiresolution continuum

Microvoid Reconstruction Microvoid TiC IN100 Quasistatic Carbides Shear Band Design Research Tools Consortium Contract No.

reconstruction demonstrates spatial distribution of microvoids at submicron grain refining carbides in modified 4330

12 Microvoid Softening and Ballistic Performance Challenge Statement: Establish microstructural design parameters for ballistic protection performance against shear plugging failure Approach: Reconstruct 3D microvoid distributions in steel shear bands to inform improved simulation of role of particle/ microvoid interaction in Microvoid Ballistic ballistic plugging. Integrate Plugging Simulation effects of microvoid and thermal softening in efficient multiresolution continuum constitutive model linked to microstructural parameters. Microvoid Reconstruction Microvoid TiC IN100 Quasistatic Carbides Shear Band Design Research Tools Consortium Contract No. N C-0241 Gurson Particle/Microvoid Microvoiding+ Thermal Softening Impact: High resolution tomographic reconstruction demonstrates spatial distribution of microvoids at submicron grain refining carbides in modified 4330 martensitic steel shear band. Simulations of particle/microvoid interactions provide constitutive Voiding Interaction model with improved representation of microvoid based ballistic plugging. Multiresolution continuum model combines microvoid +thermal softening with heat conduction, predicting shear band velocities under ballistic conditions.

13 Multiscale Multicomponent Materials Multiresolution theory Multiscale: Separable length scales Crystalline structure Quantum Chemistry Polycrystallinity GB Grain interface Modern Alloy ABC theory grain2 grain1 Space Lattice grain3 Tailoring chemistry/atomic content to form Secondary phases Multiple length scales When nested and separable à multiresolution When comparable scales à ABC ** Can be combined into ABC + Multiresolution Need a theory that defines MULTIPLE STRAINS per continuum point How many material laws at a continuum point? How many strains/constitutive equations at a point?

Image-based Microstructure Reconstruction Fracture test Tomography Fatigue crack tip

Submicron Carbides Microvoids crack Mod4330 crack tip specimen #1: Primary particles

$857 um Spacing: 16 um Volume fraction: 1.$ $117035 um Spacing: 2 um Volume fraction: 0.$

14 Image-based Microstructure Reconstruction Fracture test Tomography Fatigue crack tip Microstructures of Ultra High Strength Alloys Primary Inclusions Primary Voids Oxides Submicron Carbides Microvoids crack Mod4330 crack tip specimen #1: Primary particles (yellow) near crack tip Reconstruction area: 633x516x259 um 3 Averaged: um Spacing: 16 um Volume fraction: 1.756% Mod4330 specimen #1: Secondary particles (white dots) inside shear band Reconstruction area: 70x15x28um 3 Averaged: um Spacing: 2 um Volume fraction: % Microscopy 10 um Lath martensite Multiscale microstructures: within one grain we see primary particles, secondary particles, laths (too many to model explicitly)

$Volume frac/on: 1.$

15 Reconstruction Implementation in FEA Fracture test Tomography Fa/gue crack /p Mod4330 crack /p specimen #1: Primary par/cles (yellow) near crack /p Reconstruc/on area: 633x516x259 μm 3 Averaged: μm Spacing: 16 μm Volume frac/on: 1.756% Fracture Process Model to be Validated 3μm Degrees of Freedom: 30 million (132 par%cles) crack

16 Why Are We Interested in AM? Additive Manufacturing 1.Complex geometry 2.control microstructure 1. 3.Design material %Powder #1 %Powder #2 %Powder #3 1. Unique Powder Combination Powder Combination + Thermal History = Microstructure Microstructure = Final Product Performance 1. W Ge et al, The effect of scan pattern on microstructure evolution and mechanical properties in electron beam melting Ti47Al2Cr2Nb.2014.SFF Macroscopic Properties = Product design 16

17 Introduction to the Problem Process Modeling Mechanics Materials Science Process Optimization Final Product Characterization Simplifying Assumptions Residual Stress Distribution Anisotropic Elastic- Plastic Analysis Powder Composition Selection Key Parameter Set Determination Microstructure Characterization Heat Source Model Thermal analysis Cooling Rate Solidification & Melting Behavior A C Fatigue Life B Microstructurebased Fracture Toughness and Damage Materials design Phase Evolution Microvoid and Precipitate Distribution Key Parameter Set Optimization Porosity % Lack of fusion Gas Global Energy Density Surface Topology Characterization Non-destructive Microstructure Evaluation Strength and Fatigue Characterization

19 Acknowledgements Darpa/ONR D3D AFOSR: ABC Stochastic Resolution Theory for Micro-structure Based Predictive Materials Science: Application to Multiphase Polymer Systems Goodyear, DoE/Ford Composites Projects National Institute of Standards and Technology: Additive manufacturing US Dept. of Defense NDSEG Fellowship Program Collaborators at Northern Illinois University Collaborators at Quad City Manufacturing Laboratory

20 Thank You!

Analysis and design of composite structures

Analysis and design of composite structures Class notes 1 1. Introduction 2 Definition: composite means that different materials are combined to form a third material whose properties are superior to those