1. ENT 487 FRACTURE MECHANISMS IN METALS
DR. HAFTIRMAN
LECTURE 11
Thu, 24 SEPTEMBER 2008

2. Void Growth and Coalescence

3. Void Growth and Coalescence
A model originally developed by Gurson and later modified by Tvergaard analyzes the plastic flow in a pouros medium by assuming that the material behaves as continuum.
Voids appear in the model indirectly through their influence on the global flow behavior.
The effect of the voids is averaged through the material, which is assumed to be continuous and homogenous.

4. Void Growth and Coalescence
The limit-local model for void instability. Failure is assumed to occur when the next section stress between voids reaches a critical value.
Figure illustrates a two-dimensional case, where cylindrical voids are growing in a material subject to plane strain loading. If the in-plane dimensions of the voids are 2a and 2b and the spacing between voids is 2d, the row of voids illustrates is Figure is stable if where σ1 is the maximum priciple stress.
The void interactions leading to ductile failure are far too complex to a captured by a simple area reduction model.

5. Ductile Crack Growth Mechanism for ductile crack growth Initial state
Void growth at the crack tip
Coalescence of voids with the crack tip.

6. Ductile Crack Growth
Figure schematically illustrates microvoid initiation, growth and coalescence at the tip of a preexisting crack.
As the cracked structure ia loaded, local strains and stresses at the crack tip become sufficient to nucleated voids.
These voids grow as the crack blunts, they eventually link the main crack.
As this process continues, the crack grows.

7. Ductile Crack Growth

8. Ductile Crack Growth
Figure is a plot of stress and strain near crack tip of a blunted crack.
The strain exhibits a singularity near the crack tip, but the stress reaches a peak at approximately two times the crack-tip-opening displacement (CTOD).

9. Ductile growth of an edge crack
Ductile growth of an edge crack. The shear lips are produced by the same mechanism as the cup and cone in uniaxial tension

10. Ductile crack growth in a 45° zigzag pattern.

11. Ductile Crack Growth
The high-triaxiality crack growth at the center of a plate appears to be relatively flat, but closer examination reveals a more complex structure.
For a crack subject to plane strain Mode I loading, the maximum plastic strain occurs at 45° from the crack palne, illustrates in Figure a.
On the local level, this angle is the prefered path for void coalescence, but global constarins required that the crack propagation remain in its original plane.
One way to reconcile these competing requirements is for the crack to growth in a zigzag pattern (Figure b), such that the crack appears flat on a global scale, but oriented 45°, from the crack propagation direction when viewed at higher magnification.
The zigzag pattern is often observed in ductile materials.

12. Ductile Crack Growth
Figure shows a metallographic cross-section of a growing crack that exhibits the zigzag pattern behavior

13. Cleavage
SEM fractographs of cleavage in an A 508

14. Mechanisms of Cleavage Initiation
Formation of river patterns as a result of a cleavage crack crossing a twist boundary between grain.

15. Mechanisms of Cleavage Initiation
River patterns in an A 508 Class 3 steel.
Note the tearing (light areas) between paralel cleavage planes.

16. Mechanisms of Cleavage Initiation
SEM fractographs of cleavage initiation in an A 508.
Initiation at a grain boundary carbide.
Initiation at an inclusion near the center of a grain.

17. Mechanisms of Cleavage Initiation
Examples of unsuccessful cleavage events.
Arrest at particle/matrix interface.
Arrest at a grain boundary
Arrest due to a steep stress gradient.

18. Arrested cleavage cracks a head of a macroscopic crack in a spherodized 1008 steel.

19. Intergranular fracture
In most cases metals do not fail along grain boundaries.
Ductile metals usually fail by the coalescence of voids formed at inclusions and the second-phase particles, while brittle metals typically fail by transgranular cleavage.
Under special circumstances, however, cracks can form and propagate along grain boundaries.

20. Intergranular fracture
There is no single mechanism for intergranular fracture. Rather, there are a variety of situations that can lead to cracking on grain boundaries, including:
Precipitation of brittle phase on the grain boundary.
Environmental assisted cracking.
Intergranular corrosion.
Grain boundary cavitation and cracking at high temperatures.

21. Intergranular fracture

22. Intergranular fracture