Dear All,
The cleavage initiators such as carbides/inclusion i.e. in general inhomogeneity in matrix phase generate micro-crack when a critical max. principal stress is realized by the inhomogeneity at a critical distance from crack tip (RKR).
However, when this criteria is not met the strain increases continuously and the same carbide may debond resulting in a void followed by growth and coalescence.
The question is
would this local phenomena of void nucleation at inhomogeneity (assuming it to be much smaller than grain size) result in stress amplification at neighbouring carbides?
For 'n' being number of inhomogeneity homogeneously distributed what fraction would change to trigger ductile damage? would it be a function of plastic strain?
What would be the effect of triaxiality on 'n0' being fraction of 'n' which result in micro-crack generation?
Thanks in advance.
I've done a great deal of quantitative fractography with a great deal of success. The outcome of measurements of this kind is that your observations can be checked with numbers and self consistency being introduced to replace qualitative arguments. It's often tempting to follow the various things that the fracture toughness mavens would have you believe but there's just no way to know whether or not such knowledge applies to your problem. It's possible to have a 1:1 correspondence between a mechanical measurement and a fracture surface measurement. Of course you've still must put things together nothing can be gotten for free.
Dann Passoja
In the normal case bonding between carbides and matrix is strong. After fracture of the sample, the carbides are hidden on the base of the dimple. As result, the carbides are difficult to see. After introducing a rather little amount of hydrogen the cohesion is weakened. Now the carbides are visible as the individual centre of rather shallow dimples as it occurs with normal inclusions. Under strong charging with hydrogen the matrix reacts brittle. The cracked interface of carbides acts as storage room for further intruding hydrogen. Mini-fish-eyes are formed with the carbides as centres.
Thus, diameter and distribution of carbides can easily be determined.
See:
Thank you all for your responses.
My question was to basically model the change in participation of inhomogeneities to micro-crack generation with change in matrix ductility.
Assuming there are 'n' number of inhomogeneities of same size and shape and the initial condition of loading corresponds to lower constraint in DBT region, such that all 'n' inhomogeneities debond and generate voids.
Now as the loading proceeds for some reason (not related to loading ) the triaxiality increases, would it cause the number of imhomogeneities taking part in void nucleation to decrease, i.e. the number of inhomogeneities turning into voids = 'n1', where n1 < n.
According to literature the void nucleation depends on plastic strain, however, Beremin, Argon and few others have given a temperature independent critical stress 'sigma(c)' for debonding of inclusions where
sigma(c) = sigma(m) + (Mises - YS)*k
from above equation, I can reformulate sigma(c) as
sigma(c) = Mises *[ q + k*(1-YS/Mises)]
which means for higher triaxiality sigma(c) will be achieved quickly.
but what if the matrix ductility is decreases by constraint increment i.e. the plastic strain is not sufficient to cause debonding ??
In that case would the number of inhomogeneities taking part in micro-crack generation to initiate cleavage will increase?
Carbides belong to the class of precipitations.
When steel cools down, the lattice structure changes from face cubic centered to body cubic centered. The solubility for carbon is strongly reduced resulting in the the precipitation of carbides. Therefore the cohesion between particles and matrix is very strong. Separation tooks place at the final stadium of fracture.
In opposition, inclusions are formed from unwanted trace-elements as sulfur and oxygen. These parts are excluded during solidification. Their bonding to the matrix is zero. They form holes.
For deeper knowledge see:
F. Zok and J. D. Embury: On the analysis of delamination fractures in high-strength steels. Metallurgical Transactions 21 A, Sept. 1990 p. 2565-2575
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