Depends on the nature of the precipitate: if a soft gummy protein, it will interfere in a major way by absorbing the force of the crack, like a shock absorber. If a granular crystal, it might deflect or might amplify the force, but directionality would suffer.

Dear Kristine,

Thank you very much for your response.

I have a nickle sample in which the matrix has higher shear modulus compared to gamma prime and gamma double prime precipitates. But the

elongation is seen when the precipitates are not present.

Supriya

I think there are several aspects to consider when you talk about fracture in composites-- I am assuming you are talking about composites as there are precipitates involved. Also based on your response to Kristine, I believe you are working on Ni based super alloys which have a gamma prime and gamma double prime precipitate.

Before answering your doubt on the role of shear modulus, you have to first acknowledge that crack propagation and deformation mechanisms are very different for materials containing incoherent and coherent precipitates. Once you recognize the strength and coherency of the interface, you can break the problem down into two parts.

Coherency is related to the structural compatibility of precipitates and the matrix; the atomic planes of each phase follow a specific orientation relationship or have a similar inter-planar spacing (Lattice parameter is also important). There can be some semi-coherency as well depending on the size of the precipitate. Coherent and semi-coherent precipitates usually share a very strongly bonded, low energy interface.

An incoherent precipitate has no lattice match with the matrix, which implies that they will share a weakly bonded interface.

Now, we can tackle your question regarding the shear modulus of the interface. In this answer, I will consider the case of a crack propagating through a metallic solid with an embedded precipitate. The precipitate is also within the plastic zone envelope of the crack tip.

Coherent and semi-coherent Precipitates : A crack is like an electron travelling in a metal conductor, i.e. it chooses the path with least resistance. Owing to the precipitate's coherency with the matrix, the stress fields of the crack will interact with the stress fields associated with the precipitates. The relative tendency of the crack to deflect towards or away from the precipitate is governed by the classical dundurs parameter. The dundurs parameter considers the effect of shear modulus and can quantitatively predict crack deflection. It would be a good idea to read some papers on this.

Typically, if the shear modulus of the precipitate is lower than that of the matrix, the crack attempts to go through the precipitate and in the process gets arrested as local plastic deformation of the precipitate will absorb all the crack driving force. This in turn increases the fracture toughness of the material. Conversely, if the shear modulus of the precipitate is higher, it can still toughen the material by deflecting the crack from its original propagation path. For instance, a crack propagating under mode I loading conditions can become inclined to the loading axis due to some precipitate-induced deflection. Thereafter, it may require a higher driving force to propagate as it is locally oriented to propagate under mode II loading conditions.

Incoherent precipitates: Although the precipitates do not experience the elasto-plastic stress fields of the crack tip, the interface will have a lower shear modulus. This is good enough for attracting the cracks towards the precipitates. Once the crack encounters the interface, it can do various things depending on the nature of the precipitate. Brittle precipitates sometimes fracture and advance the crack but the crack could also propagate along the interface in certain cases. Interfacial crack propagation may also happen along the coherent precipitate boundary if local conditions permit it. Note that since the interface has the lowest shear modulus of the three, it may appear that the crack would always move along the interface. However, remember that for the crack to do so, it would have to deflect at angles that are not compatible with the globally enforced loading mode. Overall, one has to be clever to trace back the possible mechanisms after conducting a fracture test.

For more detailed discussions, one should also go through the papers by C. Fong Shih. Overall, the phenomenon i quite intuitive. Note that the shear modulus of precipitates also influence the dynamics of dislocation pinning and Orowan bowing in metals. However, fracture and dislocation motion are not completely analogous.