Report

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