1. Basic principles of metallic fracture
Author: Miha Povšič
Mentor: izred. prof. dr. Leon Cizelj
Co-mentor: dr. Samir El Shawish
Ljubljana, January 2016

2. Introduction fracture mechanics is a science about cracks
rapid expansion after World War II
categories of fracture mechanics:
linear elastic fracture mechanics (LEFM)
elastic-plastic fracture mechanics (EPFM)
fracture analysis:
the energy criterion
the stress intensity approach

3. Microscopic view of material fracture
material fracture : applied stress is sufficient to break the bonds between the atoms
cohesive stress σC of the order of E/π

4. Microscopic view of material fracture
stress for global fracture several orders of magnitude lower
flaws in the material
flaws magnify the local stress and cause the global strength to decrease
propagation of breakings
failure stress σf

5. Stress concentration at crack tip
singularity in stress amplitude
stress field near the crack tip:
stress intensity factor K:
critical stress intensity factor KIc :

6. Modes of loading Mode I – Opening Mode II – In-Plane Shear
Mode III – Out-0f-Plane Shear

7. Critical stress intensity factor
defined by Irwin in 1957
measure for fracture toughness
higher value means tougher material
Material
KIc [MPam1/2]
Steel alloy (4340) 50
Aluminium
14-28
Soda lime glass
0,7-0,8
Concrete
0,2-1,4
Polystyrene
0,7-1,1
Silica aerogels
0,0008–0,0048

8. Energy criterion approach
Griffith, 1920
energy available for crack growth > resistance of the material
we define potential energy Π from strain energy U and work of internal forces F

9. Energy criterion approach – LEFM
energy release rate G:
critical energy release rate:
connection with critical stress intensity factor:

10. Energy criterion approach – EPFM
energy release rate J:
J is equal to:
connection with G:

11. Resistance curve - LEFM
crack growth stability
R; material resistance to crack extension
depend on crack length a
stability criterion
stable
unstable

12. Resistance curve - EPFM
similar to LEFM
R -> JR
includes plasticity
stability criterion
stable
unstable

13. Experimental methods – Charpy impact test
determines the amount of energy absorbed by the material during the fracture
absorbed energy is measure of material's notch toughness
widely applied in industry
easy, cheap, quick

14. Experimental methods – unloading compliance method
method for monitoring the crack growth behaviour
single-specimen test technique
measurements of a crack length during the loading
with this method we can calculate R curve

15. Simulation limitation of analytical calculation -> simulation
2D approximation of 3D
plane strain
plane stress
Abaqus FEA
finite element analysis

16. Simulation - preparation
homogeneous compact tension (CT) specimen
material: 18MnD5 ferritic steel
geometry:
mesh:

17. Simulation – stress distribution
elastic and elastic - plastic material under the same load
higher stress concentration at the crack tip for elastic material

18. Simulation - J - integral
J integral vs. load diagram
J contour integral
plane stress is more conservative approximation

19. Conclusion cracks are important in fracture mechanics
fracture toughness - crack initiation:
simple one-parametric approaches for describing fracture
critical stress intensity factor KIC, critical crack driving force GIC , critical J contour integral JIC
stability of crack growth:
R curve or JR curve

20. References
[1] T. L. Anderson, Fracture mechanics: Fundamentals and application, Third edition (CRC Press, 2005)
[2] Irwin, G.R., "Analysis of Stresses and Strains near the End of a Crack Traversing a Plate," Journal of Applied Mechanics, Vol. 24, pp , 1957.
[3]
[4] Griffith, A.A., "The Phenomena of Rupture and Flow in Solids," Philosophical Transactions, Series A, Vol. 221, pp , 1920
[5] I. Simonovski, O. Martin, G. Machina, WP4.2 K/J Value Estimation of different Specimen Designs Part 1: Homogeneous Specimens - Report on Round2 results, January 2015
[6]