About fracture mechanics

In materials science fracture mechanics applies the physics of stress and strain, in particular the theories of elasticity and plasticity, to the microscopic crystallographic defects found in real materials in order to predict the macroscopic mechanical failure of bodies.

In modern materials science, it is an important tool in improving the mechanical performance of materials and components.

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New update of Wikipedia's Fracture Mechanics page provided by John West, August 2005

Fracture Mechanics

Arising from the manufacturing process, interior and surface flaws are found in all metal structures. Not all such flaws are unstable under service conditions. Fracture mechanics is the analysis of flaws to discover those that are safe (that is, do not grow) and those that are liable to propagate as cracks and so cause failure of the flawed structure.

Internal and external flaws act as stress raisers, 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 50-200 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

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 facture propagates across the whole structure. The 'fatigue life' of a component is the time it takes for critically 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.

Stress-Corrosion Cracking (SCC)

This phenomenon is the unexpected sudden failure of normally ductile metals subjected to a constant tensile stress in a corrosive environment. Certain 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     SCC environment	 K_Iscc
                     MN/m^3/2                      MN/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.

References

  1. Knott, Fundamentals of Fracture Mechanics (1973). I am afraid, now being retired, I have mislaid many of my books and the more up-to-date booklist that went with them. You will have to provide one or more suitable texts.
  2. Foroulis (ed.), Environmentally-Sensitive Fracture of Engineering Materials (1979).
  3. West JM, Basic Corrosion & Oxidation (Horwood 1986, 2nd edn), chap.12. I am sure there are more up-to-date books but I have been retired for over 20 years!