Fracture toughness

From Wikipedia, the free encyclopedia

This article or section may require cleanup to meet Wikipedia's quality standards.
Please help improve this article or replace this tag with a more specific message. This article has been tagged since March 2006. (help, talk)

In materials science, fracture toughness is a property which describes the ability of a material containing a crack to resist fracture, and is one of the most important properties of any material for virtually all design applications. It is denoted K_Ic and has the units of $MPa\sqrt{m}$ . Fracture toughness is a quantitative way of expressing a material's resistance to brittle fracture when a crack is present. If a material has a large value of fracture toughness it will probably undergo ductile fracture. Brittle fracture is very characteristic of materials with a low fracture toughness value.

1 Table of values
2 Sources
3 Conjoint Action
4 Stress-Corrosion Cracking (SCC)
5 See also
6 References

[edit] Table of values

Here are some typical values of fracture toughness for various materials:

Material	K_Ic ( $MPa\sqrt{m}$ )
Metals
Aluminum alloy	36
Steel alloy	50
Titanium alloy	44-66
Aluminum	14-28
Ceramics
Aluminum oxide	3-5
Silicon carbide	3-5
Soda-lime-glass	0.7-0.8
Concrete	0.2-1.4
Polymers
Polymethyl methacrylate	1
Polystyrene	0.8-1.1

[edit] Sources

Internal and external flaws act as stress risers, raising the effective stress normal to the crack plane. More important for the purpose of predicting instability, we can estimate the elastic stress field in the neighbourhood of a crack tip and thereby determine the elastic strain energy that would be released if the crack were to grow. In order for the crack to propagate spontaneously this energy must exceed the surface energy of the (two) new crack surfaces. 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. This total energy release rate is given the symbol G_Ic, where the Roman number I (II or III) indicates the way the crack opens (e.g. whether there is a twisting component or not) and c denotes criticality — the crack will only propagate when G_Ic exceeds some critical value. In short, when

elastic energy released = surface energy created

For ductile metals G_Ic is around 50 to 200 kJ/m², for brittle metals it is usually 1-5 and for glasses and brittle polymers it is almost always less than 0.5.

More significant adjustments to this kind of calculation take account of the shape of the flaw and its relationship to the shape and size of the structure. This has led to the concept of a stress intensity factor. Analogously to G_Ic, at criticality this is given the symbol K_Ic. Typical values are 150 MN/m^3/2 for ductile (very tough) metals, 25 for brittle ones and 1-10 for glasses and brittle polymers. Notice the different units used by G_Ic and K_Ic. Engineers tend to use the latter as an indication of toughness. Where there is extensive plastic deformation this treatment has to be modified because the plastic zone at the tip of the crack consumes the major part of the work of fracture and modifies the elastic strain field in the crack tip region:

elastic energy released = surface energy + plastic deformation energy

[edit] Conjoint Action

There are 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. 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.

[edit] Stress-Corrosion Cracking (SCC)

Main article: Stress corrosion cracking

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 present 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.e. small surface flaws propagate (usually smoothly) under conditions where fracture mechanics predicts that failure should not occur. That is, in the presence of a corrodent, cracks develop and propagate well below K_Ic. In fact, the subcritical value of the stress intensity, designated as K_Iscc, may be less than 1% of K_Ic, as the following table shows:

Alloy	K_Ic ( $M N / m 3 / 2$ )	SCC environment	K_Iscc ( $M N / m 3 / 2$ )
13Cr steel	60	3% NaCl	12
18Cr-8Ni	200	42% MgCl₂	10
Cu-30Zn	200	NH₄OH, pH7	1
Al-3Mg-7Zn	25	Aqueous halides	5
Ti-6Al-1V	60	0.6M KCl	20

The subcritical nature of propagation may be attributed to the chemical energy released as the crack propagates. That is,

elastic energy released + chemical energy = surface energy + deformation energy

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 length appears in the calculation of stress intensity). Finally it reaches K_Ic , whereupon fast 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.e. effectively inert. Very often one finds a single crack has propagated while the rest of the metal surface stays apparently unaffected.

[edit] See also

[edit] References

Anderson TL, Fracture Mechanics: Fundamentals and Applications (CRC Press, Boston 1995).
Lawn B, Fracture of Brittle Solids (Cambridge University Press 1993, 2nd edition).
Knott, Fundamentals of Fracture Mechanics (1973).
Foroulis (ed.), Environmentally-Sensitive Fracture of Engineering Materials (1979).
Suresh S, Fatigue of Materials (Cambridge University Press 1998, 2nd edition).
West JM, Basic Corrosion & Oxidation (Horwood 1986, 2nd edn), chap.12.
http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/exper/gordon/www/fractough.html