How does microcracking improve fracture toughness in a ceram

How does micro-cracking improve fracture toughness in a ceramic?

Solution

>> Fracture toughness is a property which describes the ability of a material containing a crack to resistfracture, and is one of the most important properties of any material for many design applications.

Consider a body with flaws (cracks) that is subject to some loading; the stability of the crack can be assessed as follows. We can assume for simplicity that the loading is of constant displacement or displacement controlled type (such as loading with a screw jack); we can also simplify the discussion by characterizing the crack by its area, A. If we consider an adjacent state of the body as being one with a broader crack (area A+dA), we can then assess strain energy in the two states and evaluate strain energy release rate.

The rate is reckoned with respect to the change in crack area, so if we use U for strain energy, the strain energy release rate is numerically dU/dA. It may be noted that for a body loaded in constant displacement mode, the displacement is applied and the force level is dictated by stiffness (or compliance) of the body. If the crack grows in size, the stiffness decreases, so the force level will decrease. This decrease in force level under the same displacement (strain) level indicates that the elastic strain energy stored in the body is decreasing—is being released. Hence the term strain energy release rate which is usually denoted with symbol G.

The strain energy release rate is higher for higher loads and broader cracks. If the strain energy so released exceeds a critical value G_c, then the crack will grow spontaneously. For brittle materials, G_c can be equated to the surface energy of the (two) new crack surfaces; in other words, in brittle materials, a crack will grow spontaneously if the strain energy released is equal to or more than the energy required to grow the crack surface(s). The stability condition can be written as

elastic energy released = surface energy created.

If the elastic energy released is less than the critical value, then the crack will not grow; equality signifies neutral stability and if the strain energy release rate exceeds the critical value, the crack will start growing in an unstable manner. Forductile materials, energy associated with plastic deformation has to be taken into account. When there is plastic deformation at the crack tip (as occurs most often in metals) the energy to propagate the crack may increase by several orders of magnitude as the work related to plastic deformation may be much larger than the surface energy. In such cases, the stability criterion has to be restated as

elastic energy released = surface energy + plastic deformation energy.