Theory of Cleavage Fracture:-

Introduction:-

•In metals or alloys the process of cleavage fracture has been attributed to the nucleation of a micro crack followed by its propagation into the surrounding matrix.

•How the critical cleavage fracture stress is influenced by the microstructural parameters like grain size, carbide diameters etc. and the energetic parameters like effective surface energies for particle-matrix (γpm) and matrix-matrix boundaries (γmm) is the subject of interest for theoretical models of cleavage fracture initiation.

• Three theories of cleavage fracture have been proposed: Stroh’s theory. Cottrell’s theory. Smith’s theory.

Stroh’s Theory:-Dislocations in a pile up are squeezed together to produce a crack nucleus.

From energy balance (considering γ constant):

• After nucleation of the crack, any increase in length lead to decrease in total energy of the system.

• So cleavage fracture is nucleation controlled.

Limitations:-

• It cannot explain why cleavage fracture predominates at lower temperatures where tensile yield strength is high but τeff is little different from its room temperature value.

• Also it cannot explain why tensile stress is important in notched-bar fracture.

• Reduction in dislocation energy so, crack nucleation easier.• Fracture will be propagation controlled.

Cottrell’s Theory:-• BCC metals: Ferritic steel.

Advantages: -• predicts a tensile stress controlled cleavage fracture• explains effect of grain size and yielding parameters.Limitation:-• It neglects the influence of microstructural variables other than the grain size.

Smith’s Theory:-Smith’s Theory:-A grain boundary carbide particle of thickness C0 is cracked by an impinging dislocation pile-upThe microcrack so formed subsequently propagates as a Griffith defect under combined influence of the pile up and the applied stress.

• As per Stroh’s theory the carbide will be cracked by the pile-up if:

• And the matrix will be cracked if :

• If τeff is in between above values, the change in energy due to crack extension is analyzed by Cottrell’s model i.e. growth controlled failure.

From energy balance:

Reference:-

• Knott, J. F.: ”Fundamentals of Fracture Mechanics”, Butterworths, London, 1973.