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Transcript of Small Scale Yielding Model for Fracture Mechanics · Small Scale Yielding Model for Fracture...
Small Scale Yielding Model for Fracture Mechanics
J. Thomas, J.S. Crompton, and K.C. Koppenhoefer
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Overview
• Motivation • Theory • Use of COMSOL Multiphysics • Results • Summary
2
Motivation
• Fracture mechanics – study of cracked structures • Structural failures often produced by
propagation of existing defects • Calculate safe life for structures containing
defects
3
S.S. Schenectady – 16 January 1943
Motivation • Determine the capabilities of COMSOL
Multiphysics for conducting computational fracture mechanics
• Compare results with well-established computational fracture mechanics software
4
Theory
5
• Early work – single parameter to describe crack tip stress/strain – K for linear elastic fracture mechanics – J for elastic-plastic fracture mechanics
• Computational fracture mechanics – calculate crack tip stress/strain – Calculate single parameter for complex structures – Determine effect of finite length scales on crack tip
stress/strain
Small Scale Yielding Model
• Plastic zone small compared with all length scales
• Used as a reference solution in computational fracture mechanics
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−+
=
+−
=
2cos21
2sin
22
2sin21
2cos
222
2
θκθπ
θκθπr
GKu
rGKu
yR
xR
Modeling Methodologies
• Linear elastic fracture mechanics (LEFM) – Elasticity dominates the solution – Singularity at crack tip defined by stress intensity
factor (K)
• Elastic plastic fracture mechanics (EPFM) – Ramberg-Osgood - – Small strain plasticity
• ε = 12𝛻𝛻𝐮𝐮 + (𝛻𝛻𝐮𝐮)𝐓𝐓
– Large strain plasticity • ε = 1/2 [𝛻𝛻𝐮𝐮 + (𝛻𝛻𝐮𝐮)𝐓𝐓+(𝛻𝛻𝐮𝐮)𝐓𝐓 𝛻𝛻𝐮𝐮]
7
n
+=
000 σσα
σσ
εε
Use of COMSOL Multiphysics
8
b0=10µm
Use of COMSOL Multiphysics – J-Integral
9
∫Γ
∂∂
−= dsxuTnWJ i
ixs
Results - LEFM
10
Normalized Stress
Normalized Distance ahead of crack tip
Results – EPFM (Small Strain)
11
Results – EPFM (Large Strain)
12
Summary
• COMSOL Multiphysics provides the capabilities needed for computational fracture mechanics
• Software accurately calculates the near tip strain/stress fields for – LEFM – EPFM (small and large strain)
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