ControlArm.example - Heirarchical Multiscale Modeling: From...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Heirarchical Multiscale Modeling: From Atoms to Autos Mark Horstemeyer CAVS Chair Professor in Computational Solid Mechanics Mechanical Engineering Mississippi State University mfhorst@me.msstate.edu
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
D C B A E Where, how, when does this control arm fail? Can we reduce the weight of this control arm? Finite element analysis (D) Materials science analysis (B) GM Cadillac
Background image of page 2
Fem Analysis Idealized Geometry Realistic RVE Geometry Monotonic/Cyclic Loads Crystal Plasticity Experiment Fracture of Silicon Growth of Holes Experiment Uniaxial Monotonic Torsional Monotonic Notch Tensile Fatigue Crack Growth Cyclic Plasticity FEM Analysis Torsion Compression Tension Monotonic/Cyclic Loads Continuum Model Cyclic Plasticity Damage Structural Analysis Structural Analysis Steering Knuckle Upper Control Arm Experiments FEM Model Cohesive Energy Critical Stress Analysis Fracture Interface Debonding Atomistics Atomistics Experiment Fracture Interface Debonding ISV Model Void Nucleation FEM Analysis Idealized Geometry Realistic Geometry Micromechanics Mesomechanics Mesomechanics Macromechanics Macromechanics ISV Model Void Growth Void/Crack Nucleation Multiscale Methodology: Development of Microstructure-Based Internal State Variables
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
200-500 μ m μ m 50-100 σ σ mm 1-20 μ m 10-1000 A cm cm m m Schematic of important modeling aspects at each size scale .
Background image of page 4
Kinematics of Damage Framework F = F e F v F p F F F F p v e R 0 R 1 R 2 R 3 Multiplicative Decomposition of the deformation gradient Damage definition V 2 = V 0 + V v J = det F v = V 2 V 0 = 1 1 φ = V v V 2 F v = 1 1 ( 29 1 3 I ( 29 I D v - = 1 3 1 - = F F L
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Damage Descriptions Barbee et al. (1972), Davison et al. (1977), etc. Davison et al. (1977) Kolmogorov (1937), Avarami (1939), Johnson (1949) Gurson, Needleman, Tvergaard, LeBlond, McDowell, etc. D = dV v dV 2 = dV v dN dN dV 2 = v a η N - total number of nucleation site s V - void volume v v v D v D + = = 1 1 ; ( 29 2 2 2 1 ; 1 v v v D v v D + + = + = ( 29 ( 29 ( 29 v v v D v D - + = - - = exp ; exp 1 3 3 v n v D D D D D D + = + = 4 4 ;
Background image of page 6
Constraints on Damage Descriptions η≤ 1 v a v a 1 η Consider D1: multiplicative constraint , Consider D2: no constraint as D saturates at unity (binomial expansion) D 2 = η v a 1 + η v a ( 29 - 1 = η v a 1 v a + v a ( 29 2 - η v a ( 29 3 + ... D 1 = η v a Consider D3: no constraint as D saturates at unity (exponential expansion) D 3 = 1 - exp( v a ) = 1 - 1 v a + v a ( 29 2 2 - v a ( 29 6 3 + ... = η v a - v a ( 29 2 2 + ... 1 - v a v a 1 Consider D4: additive constraint , D 4 = η+ v a
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Trends for Different Damage Descriptions 0 0.5 1 1.5 2 0 0.5 1 1.5 2 nucleation growth damage1 damage2 damage3 damage4 damage triaxiality
Background image of page 8
Description of Damage η = N V 0 # voids/unit volume v v = 1 N v i i = 1 N average void volume V v V o v v total volume of voids updated volume at new state damage definition damage in terms of nucleation density and void volume damage with coalescence term φ= v v C 1 + η v v C V 0 v v V 0 + V 0 v v = v v 1 + v v V 2 = V 0 + V v state 2 state 0 V 0 V 2 φ = V v V 2
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Domain R increasing strain over domain R main constituent second phase void Domain R main constituent second phase void Domain R main constituent second phase void Evolution of Damage
Background image of page 10
(a) increasing void growth (b) increasing nucleation sites Types of Damage
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
natural coalescence void sheet mechanism increasing deformation Types of Coalescence
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 43

ControlArm.example - Heirarchical Multiscale Modeling: From...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online