Teraflop Crack Growth Simulation Need: Hydraulic Fracturing

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Finite Element Methods and Crack Growth
Simulations
Materials Simulations Physics 681, Spring 1999
David (Chuin-Shan) Chen Postdoc, Cornell Fracture
Group david_at_lager.cfg.cornell.edu www.cfg.cornell.
edu
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Tentative Syllabus

• Part I Finite Element Analysis and Crack Growth
  Simulation
• Introduction to Crack Growth Analysis
• Demo Crack Propagation in Spiral-bevel Gear
• Introduction to Finite Element Method
• Stress Analysis A Simple Cube
• Crack Growth Analysis A Simple Cube with A Crack
• Part II Finite Element Fundamentals
• Basic Concepts of Finite Element Method
• Case Study I A 10-noded Tetrahedron Element
• Case Study II A 4-noded Tetrahedron Element

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Motivation Why we are interested in
Computational Fracture Mechanics

• Cracking Is a Worldwide-Scale Problem
• gt 200B per year cost to U.S. national economy
• Energy, Defense and Life Safety Issues
• Simulation of Crack Growth Is Complicated and
  Computationally Expensive
• An evolutionary geometry problem
• Complex discretization problem
• Many solutions of mega-DOF finite element
  problems
• We Were at An Impasse
• Needed better physics--required larger problems
• Larger problems impossible/impractical

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Crack Propagation in Gear

• Simulation Based on Fracture Mechanics

• Determine Crack Shape Evolution
• crack growth direction from SIFs
• user specified maximum crack growth
• increment

Compute Fracture Parameters (e.g., Stress
Intensity Factors) from Finite Element
Displacements
Initial Crack
Final Crack Configuration (29 Propagation Steps)
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Crack Growth Simulation Need Life Prediction in
Transmission Gears
Project NASA Lewis NAG3-1993
Allison 250-C30R Engine
U.S. Army OH-51 Kiowa
Fatigue Cracks in Spiral Bevel Power Transmission
Gear
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Crack Growth Simulation Need
A LIFE-SAFETY ISSUE
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A NATIONAL DEFENSE ISSUE
Crack Growth Simulation Need
The combined age of the 3 frontline aircraft
shown here is over 85 years. Defense budget
projections do not permit the replacement of
some types for another 20 or more years.
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Projects NASA NLPN 98-1215, NASA NAG 1-2069,
AFOSR F49620-98-1
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KC-135 Blow-out!
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Finite Element Method

• A numerical (approximate) method for the analysis
  of continuum problems by
• reducing a mathematical model to a discrete
  idealization (meshing the domain)
• assigning proper behavior to elements in the
  discrete system (finite element formulation)
• solving a set of linear algebra equations (linear
  system solver)
• used extensively for the analysis of solids and
  structures and for heat and fluid transfer

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Finite Element Concept
Differential Equations L u F
y
W
x
General Technique find an approximate solution
that is a linear combination of known (trial)
functions
Variational techniques can be used to reduce the
this problem to the following linear algebra
problems
Solve the system K c f
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3D tetrahedron element
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Crack Propagation on Teraflop ComputersSoftware
Framework Serial Test Bed 1
Solid Model
FRANC3D
Boundary Conditions
Crack Propagation
Life Prediction
Introduce Flaw(s)
Fracture Analysis
Volume Mesh
Finite Element Formulation
Iterative Solution