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Fracture mechanics 
Nguyen Vinh Phu, PhD 
nvinhphu@gmail.com 
Researcher at Division of Computational Mechanics 
Ton Duc T...
Textbooks 
• Anderson, T.L. (1995) Fracture Mechanics: Fundamentals 
and Applications, 2nd Edition, CRC Press, USA. 
• Gdo...
Outline 
• Brief recall on mechanics of materials 
- stress/strain curves of metals, concrete 
• Introduction 
• Linear El...
Outline (cont.) 
Fatigue 
- Paris law 
- Overload and crack retardation 
Fracture of concrete 
Computational fracture mech...
Stress-strain curves 
Engineering stress and strain 
0 
0 
Young’s modulus 
ductile metals 
strain hardening (tai ben) 
Te...
Stress/strain curve 
Wikipedia 
fracture 
necking=decrease of cross-sectional 
area due to plastic deformation 
1: ultimat...
Stress-strain curves 
True stress and true (logarithmic) strain: 
(extension ratio) 
!t = 
P 
A 
, d✏t = 
dL 
L 
! ✏t = 
Z...
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Fracture mechanics

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Lecture notes for the master course on "Engineering Fracture Mechanics".

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  • Refreshed my memory, Good Lecture:)
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  • Very good!
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Fracture mechanics

  1. 1. Fracture mechanics Nguyen Vinh Phu, PhD nvinhphu@gmail.com Researcher at Division of Computational Mechanics Ton Duc Thang University Program “Master of Science, Civil Engineering, Nguyen Vinh Phu 2012, Ton Duc Thang University” 1 Sunday, September 30, 1
  2. 2. Textbooks • Anderson, T.L. (1995) Fracture Mechanics: Fundamentals and Applications, 2nd Edition, CRC Press, USA. • Gdoutos E.E (2005) Fracture Mechanics: an introduction, 2nd Edition, Springer. • Zehnder, T.A. (2007) Lecture Notes on Fracture Mechanics, Cornel University, Ithaca, New York • imechanica.org • wikipedia 2 Sunday, September 30, 2
  3. 3. Outline • Brief recall on mechanics of materials - stress/strain curves of metals, concrete • Introduction • Linear Elastic Fracture Mechanics (LEFM) - Energy approach (Griffith, 1921, Orowan and Irwin 1948) - Stress intensity factors (Irwin, 1960s) • LEFM with small crack tip plasticity - Irwin’s model (1960) and strip yield model - Plastic zone size and shape • Elastic-Plastic Fracture Mechanics - Crack tip opening displacement (CTOD), Wells 1963 - J-integral (Rice, 1958) • Mixed-mode crack propagation 3 Sunday, September 30, 3
  4. 4. Outline (cont.) Fatigue - Paris law - Overload and crack retardation Fracture of concrete Computational fracture mechanics - FEM, BEM, MMs - XFEM - cohesive crack model (Hillerborg, 1976) - Continuum Damage Mechanics - size effect (Bazant) 4 Sunday, September 30, 4
  5. 5. Stress-strain curves Engineering stress and strain 0 0 Young’s modulus ductile metals strain hardening (tai ben) Tension test elastic unloading !e = P A0 , ✏e = # L0 E !e = E✏e 5 Sunday, September 30, 5
  6. 6. Stress/strain curve Wikipedia fracture necking=decrease of cross-sectional area due to plastic deformation 1: ultimate tensile strength6 Sunday, September 30, 6
  7. 7. Stress-strain curves True stress and true (logarithmic) strain: (extension ratio) !t = P A , d✏t = dL L ! ✏t = Z L L0 1 L dL = ln L L0

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