Virtual Materials Testing Karel Matous College of Engineering - PowerPoint PPT Presentation

Virtual Materials Testing ̌ Karel Matous College of Engineering Collegiate Associate Professor of Computational Mechanics Director of Center for Shock-Wave Processing of Advanced Reactive Materials

Shock W ave - processing of Advanced Reactive Materials Shock High Energy Ball Validation/UQ C-SWARM Milling (HEBM) Discovery Verification Prediction Truly multiscale in space, time, and constitutive equations Chemo-thermo-mechanical behavior Solid-solid state transformations ‣ Demonstration Ni/Al and Discovery c-BN systems 2 Department of Aerospace and Mechanical Engineering

Shock W ave - processing of Advanced Reactive Materials Macroscale Mesoscale Microscale Nanoscale ▪ Targeted ▪ Targeted ▪ Targeted ▪ Targeted Characteristics: Characteristics: Characteristics: Characteristics: – Layer Thickness – Crystal Size – Porosity – Particle Size – Layer Tortuosity – Crystal Shape – Pellet Size and – Particle Shape Shape – Reactant Surface – Crystal Orientation Area Contact Ni/Al demonstration system 3 Department of Aerospace and Mechanical Engineering

Image - based ( Data - Driven ) Modeling Hierarchical multiscale Macro-scale Meso-scale Micro-scale modeling concept Microstructure-Statistics- shock zone transition zone Property-Relations inert zone O(0.1 m) O(0.1 μ m) O(0.1 mm) Ensemble averaging Macro-continuum Micro-continuum Model reduction Real material Surrogate medium microscale/mesoscale statistical multiscale equivalence analysis macroscale 4 Department of Aerospace and Mechanical Engineering

Image - based ( Data - Driven ) Modeling Meso-scale Hierarchical multiscale Macro-scale Micro-scale modeling concept Microstructure-Statistics- Property-Relations O(0.1 m) O(0.1 μ m) Ensemble averaging Macro-continuum Micro-continuum O(0.1 mm) Model reduction Real material Surrogate medium microscale/mesoscale statistical multiscale equivalence analysis macroscale 4 Department of Aerospace and Mechanical Engineering

Image - based ( Data - Driven ) Modeling 0.5 N=500,000 S mm 9- bins S m4 0.4 2048 CPUs S m5 pack S m6 0.3 S rs S 55 0.2 cell 0.1 100 μ m 100 μ m 0 0 50 100 150 200 radius ( µ m) 0.25 voxel c p = 55.27% T pack scan - 19123 particles cell 0.2 cell - 1082 particles S c p = 54.20% Glass beads volume fraction 0.15 c p = 53.91% C µm scan - 1445x1288x798 0.1 µm cell - 400x400x400 0.05 Parallel Genetic Algorithm 0 0 10 20 30 40 50 60 70 80 diameter ( µ m) 5 Department of Aerospace and Mechanical Engineering

Polydisperse Systems 30 25 30 25 20 20 pdf 15 15 10 10 5 3.2928 2.7211 0 5 0.6046 2.1494 0.4585 1.5777 0.3124 0.1662 D (mm) d 1.006 0 0.0201 e ε Resolution 69.4 µm Rice & Mustard - cp=0.667 6 Department of Aerospace and Mechanical Engineering

Image - based ( Data - Driven ) Modeling raw data, processed data Resolution ~5 nm FIB/SEM (ND) Nano-tomography (Argonne) FIB/SEM - 5 nm Nano-tomography - 11.8 nm Ni-Al HEBM compact (blue=Ni) 7 Department of Aerospace and Mechanical Engineering

Image - based ( Data - Driven ) Modeling 25 Count [10 10 ] Effective 15 Stress 5 0 1 µ m 0 660 2000 3300 Thickness [nm] 2 Aluminum crystals mean 45.68 nm, variance: 0.66 nm 2 1 Nickel crystals mean 61.40 nm, variance: 6.36 nm 2 0 8 Department of Aerospace and Mechanical Engineering

Impact Simulations in Heterogeneous Materials fixed ‣ Aluminum powder periodic ‣ Voce-Kocks hardening Ne = 6,690,165 80 ellipsoids 1.0 mm Dofs = 3,431,023 60% volume fraction v = 100 m/s Δ t = 0.1 ns 1.0 mm 1.0 mm Hardening || σ || 10 +3 315 10 +1 280 10 -3 240 10 0 210 [MPa] [MPa] ‣ LANL Mustang, 4800 cores 9 Department of Aerospace and Mechanical Engineering

Image - based ( Data - Driven ) Modeling Third-order statistics q = 0° 4 d 19 3 d TPA-WR tetrahedra r 2 2 d 16 TPA-WR hexahedra d tetrahedra TPA-WR octahedra 0 13 TPA-WR dodecahedra 4 d 3 d TPA-WR icosahedra k e / k m 10 r 2 2 d TPA-WR spheres d octahedra HS bound 0 7 4 d 3 d 4 r 2 2 d d 1 icosahedra 0 0.2 0.4 0.6 0 d 2 d 3 d 4 d r 1 c p ‣ Morphology is important ‣ LANL Mustang, 7200 cores 10 Department of Aerospace and Mechanical Engineering

Heterogeneous Layers Welds S. Xu, D. Dillard and J. Dillard From Internet 11 Department of Aerospace and Mechanical Engineering

Multiscale Modeling of Heterogeneous Layers • Cohesive modeling P t traction-separation law ⟦ u ⟧ P t t ? ⟦ u ⟧ ⟦ u ⟧ l RUC t ⟦ u ⟧ ‣ Cohesive law based on lower scale physics 12 Department of Aerospace and Mechanical Engineering

Multiscale Cohesive Model • Critical assumption: l c ≪ ℴ ( L ) Adherends ∈ Ω ± 0 ϕ ( X ) = X + 0 u ( X ) 0 � Ω ± 0 F = 1 + ⇥ X 0 u ( X ) 0 Macro Interface: Average Deformation Gradient � 0 ϕ ( X ) ⇥ = 0 ϕ + − 0 ϕ − � 0 u ( X ) ⇥ = on Γ 0 0 F = 1 + 1 q 0 u y � 0 u ( X ) ⇥ ⊗ 0 N on Γ 0 0 t l c Micro Interface 1 ϕ ( X , Y ) = 0 F ( X ) Y + 1 u ( Y ) ∈ Θ 0 F = 0 F + ⇤ Y 1 u ( Y ) = 1 + 1 � 0 u ( X ) ⇥ � 0 N + ⇤ Y 1 u ( Y ) ̌ ⇥ Θ 0 Matous et al., 2008 l c ̌ Mosby and Matous, 2014, 2015 13 Department of Aerospace and Mechanical Engineering

Strong and W eak Forms Macroscale Strong Form Boundary Conditions 0 P · N = t p on ∂ Ω t � Ω ± ⇥ X · 0 P + f = 0 0 0 p 0 u = 0 u on ∂ Ω u 0 P = ∂ 0 W 0 � Ω ± t + + t − = 0 0 ∂ 0 F on Γ 0 Macroscale Weak Form � � � � t p · δ 0 u dA + 0 R = 0 P : ⇥ X ( δ 0 u ) dV f · δ 0 u dV � 0 t · � δ 0 u ⇥ dA = 0 � Ω ± Ω ± ∂ Ω t Γ 0 0 0 0 Microscale Strong Form Hill-Mandel Lemma • Microscale weak form ⇥ Y · 1 P = 0 � Θ 0 1 P = ∂ 1 W • Yields closure on 0 t � Θ 0 ∂ F • Restrictions on BC F = 1 + 1 � 0 u ( X ) ⇥ � 0 N + ⇥ Y 1 u ( Y ) l c 14 Department of Aerospace and Mechanical Engineering

Hill - Mandel Lemma ⇤ l c 0 W ( � 0 u 1 W � 0 F ( � 0 u 1 u ⇥ ⇥ ⇥ inf ) = inf 0 F inf ) + � Y dV | Θ 0 | � 0 u ⇥ 1 u Θ 0 1 R = l c ⇤ 1 P = ∂ 1 W � 1 P : ⇥ Y ( δ 1 u ) dV = 0 � | Θ 0 | � ∂ F Θ 0 � F = 0 F + � Y 1 u ⇤ ⌅ � ⇥ 1 ⇤ 0 t = ∂ 0 W � 0 u ⇥ R = 0 N · 1 P dV � 0 t δ ( 0 u ) · = 0 | Θ 0 | ∂ � 0 u ⇥ Θ 0 1 � At microscale No a ssumption on form of 0 t 0 t = 0 N · 1 P dV equilibrium | Θ 0 | Θ 0 Microscale Boundary Condition Admissibility  1 u = 0 on ∂ Θ 1 1 � �  1 u dV = 1 u · N Θ dA = 0  1 u + = 1 u − || ¯ t + = − ¯ � Y t − on ∂ Θ | Θ 0 | | Θ 0 | ∂ Θ 0 Θ 0  ¯ on ∂ Θ t = 0  15 Department of Aerospace and Mechanical Engineering

Constitutive Response of Adhesive Layer • Isotropic damage law 1 W ( F , ω ) = (1 − ω ) 1 W ( F ) • Damage surface Y ) − χ t ≤ 0 g (¯ Y , χ t ) = G ( ¯ � ¯ ⇥ p 2 ⌅ H = ∂ G ( ¯ ⇤ Y ) Y − Y in G ( ¯ Y ) = 1 − exp , ∂ ¯ − p 1 Y in Y • Irreversible dissipative evolution equations � ⇥ ω = ˙ ˙ ω = µ ˙ φ ( g ) 1/µ ≈ 𝜐 [s] κ H → χ t = ˙ χ t = µ � ⇥ Epoxy 𝜐 - ℴ (10 -6 -10 -2 ) ˙ ˙ φ ( g ) κ H → ⇧ ⌅⇤ ⌃ viscous regularization ‣ Different constitutive laws can be used 16 Department of Aerospace and Mechanical Engineering

Image - Based Modeling, Heterogeneous Layers • Digital Cell - 1000x1000x200 𝜈 m 3 1 0.8 Np = 4774 S pp 0.6 1/2 l RUC S rs S pm 1 l RUC S mp 0.4 2 l RUC S mm 1/2 l RUC 0.2 l c = 200 𝜈 m 0 0 50 100 150 r [ 𝜈 m] • 10 % volume fraction 1/2 l RUC - 70x70x200 𝜈 m 3 • 20 micron particles l RUC - 140x140x200 𝜈 m 3 2 l RUC - 280x280x200 𝜈 m 3 1/2 l RUC - Np = 23 l RUC - Np = 93 2 l RUC - Np = 374 1/2 l RUC 2 l RUC l RUC 17 Department of Aerospace and Mechanical Engineering

Representative Unit Cell Study • Mixed mode loading ⟦ u n ⟧ = ⟦ u s1 ⟧ = ⟦ u s2 ⟧ =1/ √ 2 ⟦ u s ⟧ 72 � � ˙ � = 0 . 10 [s − 1 ] � 0 u � /l c � � � � � ˙ 54 � = 0 . 01 [s − 1 ] � 0 u � /l c � � � 0 t n [MPa] � � ˙ � = 1 . 00 [s − 1 ] � 0 u � /l c � � � 36 • Ne ≃ 12,317,628 l RUC 18 • Nn ≃ 2,103,957 0 • Dofs ≃ 6,280,495 0 5 10 15 � 0 u n � [ µ m] 2 l RUC • Ne ≃ 48,537,975 p J u s 1 K 2 + J u s 2 K 2 J u s K = • Nn ≃ 8,294,617 • Dofs ≃ 24,758,080 ‣ Mean element size 1.5 𝜈 m 18 Department of Aerospace and Mechanical Engineering

RUC Study 27 18 0 t n [MPa] 9 l cell ≈ 1 / 2 l stat l cell ≈ l stat l cell ≈ 2 l stat 1/2 l RUC l RUC 0 0 1 2 3 4 5 6 � 0 u n � [ µ m] 25 10 0 t n [MPa] Normal 24 9 Shear ω 2 l RUC 23 8 50 100 150 200 250 300 l cell [ µ m] 19 Department of Aerospace and Mechanical Engineering

Multiscale Cohesive Model - Mixed Mode Loading • 10 % volume fraction • 2 l RUC - Np = 374 || 𝝉 || 0.8 30.0 0.6 15.0 0.4 0.2 0.00 0.0 [MPa] • 20 micron particles ‣ 512 CPUs ‣ Isocontours of ω ≥ 0.999 20 Department of Aerospace and Mechanical Engineering

Particle Diameter E ff ect ‣ 10 % volume fraction 27 d = 5 µ m d = 10 µ m d = 20 µ m 18 0 t n [MPa] 5 𝜈 m 10 𝜈 m 9 0 0 2 4 6 � 0 u n � [ µ m] • Smaller particles - higher strength • Non-monotonic fracture toughness 20 𝜈 m ω Effect of constraint on G n versus G s H. Parvatareddy and D. Dillard, IJF 1999. 21 Department of Aerospace and Mechanical Engineering