Fracture Mechanics of Ceramics: Volume 8: Microstructure, Methods, Design, and Fatigue

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This, however, is not the trend for other material classes. As a first example, consider the polymer foams and porous ceramics. In direct contrast to alloys, the trend in this material class is to have an upward slope. Explicitly, when the strength of these materials is increased we can expect to see an accompanied increase in fracture Yitoughness. Indeed, in the subgroup of balsa and ash we observe a close to one order of magnitude increase in both properties.

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Porous ceramics have been shown to behave exactly like this under both compression stress and tensile stress, however, the fracture toughness values are ten times lower under tension. This behavior can most easily be grasped by considering the porosity of these materials, where these voids can be modeled as preexisting cracks, which increase the nucleation energy of cracks under stress and impede the propagation of these cracks.

Note that the engineering ceramics also show the same sloping trend as the porous ceramics, however, the slope is much greater, which makes it less noticeable in the log-scale. In general, materials that are on the upper-leftmost part of the diagram are used to design a system's failure against flow, because these materials yield before they are fractured. While materials on the lower rightmost part of the diagram are used to design a system's failure against fracture, because these materials fracture before yielding.

Consider a body with flaws cracks that is subject to a load; 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. 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.

Fracture toughness

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. 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. For ductile 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. The problem can also be formulated in terms of stress instead of energy, leading to the terms stress intensity factor K or K I for mode I and critical stress intensity factor K c and K Ic.

These K c and K Ic etc. Notice the different units used by G Ic and K Ic. Engineers tend to use the latter as an indication of toughness. There are a number of instances where this picture of a critical crack is modified by corrosion. Thus, fretting corrosion occurs when a corrosive medium is present at the interface between two rubbing surfaces. Fretting in the absence of corrosion results from the disruption of very small areas that bond and break as the surfaces undergo friction , often under vibrating conditions.

The bonding contact areas deform under the localised pressure and the two surfaces gradually wear away. Fracture mechanics dictates that each minute localised fracture has to satisfy the general rule that the elastic energy released as the bond fractures has to exceed the work done in plastically deforming it and in creating the very tiny fracture surfaces.

Fracture toughness

This process is enhanced when corrosion is present, not least because the corrosion products act as an abrasive between the rubbing surfaces. Fatigue is another instance where cyclical stressing, this time of a bulk lump of metal, causes small flaws to develop. Ultimately one such flaw exceeds the critical condition and fracture propagates across the whole structure. The fatigue life of a component is the time it takes for criticality to be reached, for a given regime of cyclical stress. Corrosion fatigue is what happens when a cyclically stressed structure is subjected to a corrosive environment at the same time.

This not only serves to initiate surface cracks but see below actually modifies the crack growth process. As a result, the fatigue life is shortened, often considerably.

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This phenomenon is the unexpected sudden failure of normally ductile metals subjected to a constant tensile stress in a corrosive environment. Certain austenitic stainless steels and aluminium alloys crack in the presence of chlorides , mild steel cracks in the presence of alkali boiler cracking and copper alloys crack in ammoniacal solutions season cracking. Worse still, high-tensile structural steels crack in an unexpectedly brittle manner in a whole variety of aqueous environments, especially chloride.

With the possible exception of the latter, which is a special example of hydrogen cracking , all the others display the phenomenon of subcritical crack growth; i. That is, in the presence of a corrodent, cracks develop and propagate well below K Ic. The subcritical nature of propagation may be attributed to the chemical energy released as the crack propagates. That is,. The crack initiates at K Iscc and thereafter propagates at a rate governed by the slowest process, which most of the time is the rate at which corrosive ions can diffuse to the crack tip. As the crack advances so K rises because crack size appears in the calculation of stress intensity.

Finally it reaches K Ic , whereupon swift fracture ensues and the component fails.

One of the practical difficulties with SCC is its unexpected nature. Stainless steels , for example, are employed because under most conditions they are passive; i. Very often one finds a single crack has propagated whiles the left metal surface stays apparently unaffected. Intrinsic toughening mechanisms are processes which act ahead of the crack tip to increase the material's toughness. These will tend to be related to the structure and bonding of the base material, as well as microstructural features and additives to it.

Examples of mechanisms include crack deflection by secondary phases, crack bifurcation due to fine grain structure and modification to the grain boundaries, and crack meandering by pores in the material.

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Any alteration to the base material which increases its ductility can also be thought of as intrinsic toughening. Extrinsic toughening mechanisms are processes which act behind the crack tip to resist its further opening. This transformation is triggered by a change in the stress state of the material, such as an increase in tensile stress, and acts in opposition to the applied stress. Thus when the material is locally put under tension, for example at the tip of a growing crack, it can undergo a phase transformation which increases its volume, lowering the local tensile stress and hindering the crack's progression through the material.

This mechanism is exploited to increase the toughness of ceramic materials, most notably in Yttria-stabilized zirconia for applications such as ceramic knives and thermal barrier coatings on jet engine turbine blades. This martensitic transformation occurs as a result of stress and parallels elastic transformation, it is also quite similar to the transformation that occurs within TRIP steels, but that martensitic transformation is a result of plastic strain. The two phases that exist within pure Zirconia are the tetragonal form at high temperature, and the monoclinic form at low temperature.


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The transformation in pure Zirconia contains significant shear ca. Thermal cracking and even loss of key structural principles can result from these strains if cooling occurs rapidly.


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  • Additionally, cooling induces this transformation sluggishly as only a small fraction of the tetragonal form actually transforms. For specific PSZ compositions, the transformation transition temperature falls below room temperature with stress assistance. Figure 1 illustrates the transformation induced via a crack and its corresponding stress field.

    If tetragonal particles lie within one radius r c of the crack fracture plane, certain particles transform into the monoclinic phase, and the material toughness increases as a result of the work invested into the transformation process. The toughness contributed from transformation toughness is quite analogous to that from crack toughening, and the equations involved will be quite similar. Key parameters include the stress, which induces the transformation, the transformational strain, and the composition within one r c of the crack.

    This distance is dependent upon the fracture toughness of the matrix along with the inducing stress. Furthermore, the phenomena within transformation toughening also parallel those within microcrack toughening.

    The grain-size effect of microcrack toughness is quite analogous to the particle-size effect prevalent within transformation toughening. This causes the stress required to initiate martensitic transformation to decrease with increasing tetragonal particle size due to the fact that larger particles result in a lower constraint from the cubic matrix on the transformation. For particularly large particle sizes, the transformation can spontaneously occur while cooling, yet again similar to the spontaneous crack formation in microcrack toughness.