Transcript Teraflop Crack Growth Simulation Need: Hydraulic Fracturing

Finite Element Methods and Crack Growth Simulations
Materials Simulations
Physics 681, Spring 1999
David (Chuin-Shan) Chen
Postdoc, Cornell Fracture Group
[email protected]
www.cfg.cornell.edu
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
Motivation: Why we are interested in
Computational Fracture Mechanics
• Cracking Is a Worldwide-Scale Problem:
– > $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
Crack Propagation in Gear
• Simulation Based on Fracture Mechanics
Compute Fracture Parameters
(e.g., Stress Intensity Factors)
from Finite Element Displacements
Determine Crack Shape Evolution
• crack growth direction from SIFs
• user specified maximum crack growth
increment
Initial Crack
Final Crack Configuration
(29 Propagation Steps)
Crack Growth Simulation Need:
Life Prediction in Transmission Gears
Project: NASA Lewis NAG3-1993
U.S. Army OH-51 Kiowa
Fatigue Cracks in Spiral Bevel
Power Transmission Gear
Allison 250-C30R Engine
Crack Growth Simulation Need:
A LIFE-SAFETY ISSUE
The National Aging Aircraft Problem
April 28, 1988. Aloha Airlines Flight 243
levels off at 24,000 feet...
The Impetus
...T he plane, a B-737-200,
has flown 89,680 flights, an average of 13 per dayr ove
its 19 year
lifetime. A “ high me”
ti aircraft has flown 60,000 ghts.
fli
Crack Growth Simulation Need:
A NATIONAL DEFENSE ISSUE
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.
The KC-135 Fleet Will Be Operating for
More Than 70 Years
Corrosionand Fatigue Can Become aP roblem
T he Residual St rength of the St ruc
ture
with Bot h P resent Must be P redict able
Projects: NASA NLPN 98-1215, NASA NAG 1-2069, AFOSR F49620-98-1
KC-135 Blow-out!
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
Finite Element Concept
Differential Equations : L u = F
y
W
W
x
General Technique: find an approximate solution that is a linear
combination of known (trial) functions
n
u * ( x , y)   ci  i ( x , y)
i 1
Variational techniques can be used to reduce the this problem to
the following linear algebra problems:
Solve the system K c = f
K ij    i (L j ) dW
W
f i    i F dW
W
3D tetrahedron element
Crack Propagation on Teraflop Computers
Software Framework: Serial Test Bed 1
Solid
Model
FRANC3D
Life
Prediction
Crack
Propagation
Fracture
Analysis
Iterative
Solution
Finite Element
Formulation
Boundary
Conditions
Introduce
Flaw(s)
Volume
Mesh