Effect of finite size of component The SIF derived earlier is for cracks in an infinite body. However the finite size, geometry of the component, loading conditions have effect on SIF. The shape or configuration effect is given by a factor Y such that SIF for some of the standard geometry are shown below

What is Fracture Toughness? Fracture toughness is a measure of the ability of a material to resist the growth of a pre-existing crack or flaw. The fracture toughness of a material is characterized by the energy per unit area which is required to create new crack surfaces, and thereby propagate a crack through the material. This value is known as the critical stress intensity factor. The critical SIF at plane stress condition is denoted by K C ( ) In practice we may attain K C by increasing either  or a. For a defect of fixed length a,  C  is the critical value of the applied stress for fracture. Alternatively, for a constant applied stress , a C is the critical defect size for fracture.Note that K C is a macroscopic criterion for failure. It makes no assumptions about the precise mechanism of fracture. K IC is the critical SIF at plane strain condition

Typical Values of Fracture Toughness K Ic pure ductile metals pressure vessel steel 170 high strength steel titanium alloys GFRP, fibreglass aluminium alloys cast iron reinforced concrete polystyrene 2 silicon nitride 4--5 magnesia 3 granite 3 wood 1 glass 0.5 ice 0.2 Units are.

Application of the Fracture Mechanics Approach The material is Al alloy 2024, which has a yield stress of 200 MPa. The value of the fracture toughness is. We assume that the Y parameter is 1.12, corresponding to an edge crack. We assume that a safety factor of one half is built in to the design; the nominal stress must then not exceed one half of, i.e. 100 MPa. What is the size of the critical flaw, ? From the data given we have We therefore conclude that a crack will propagate in an unstable fashion if the length exceeds 0.37 m. This is a reassuringly large magnitude. We conclude that the structure can tolerate small defects such as incipient cracks at rivet holes. Inspection of the wing is expected to allow cracks to be detected before they reach the critical size.

For civil airliners, the material is employed is commonly a high strength steel. The yield stress is 1200 MPa, MPa, i.e. a safety factor of 0.6 is employed. The fracture toughness is. Take Y=0.95 corresponding to a semi- elliptic crack. Therefore We therefore conclude that a crack of length greater than 2.4 mm will cause catastrophic brittle failure. As a consequence, we need to inspect after every heavy landing and non-destructive testing methods need to be used frequently, typically every week. It is essential to detect cracks of length 1 mm.

Imagine that this is fabricated from pressure vessel steel, which has. The yield stress is 300 MPa and a safety factor of 0.66 is taken. We take Y=1 and hence The failure of pressure vessels can be so catastrophic that special precautions are always undertaken. One concerns the need for the vessel to leak before breaking. Consider the above example in which a crit =115 mm. If the wall thickness is t = 250mm then a crit <t, i.e. if the crack remains undetected and grows by fatigue, explosion of the vessel by catastrophic brittle fracture will occur. Alternatively, by appropriate choice of steel toughness, stress and thickness, we can redesign. Now if an undetected crack undergoes slow growth, it must penetrate the wall thickness before it can achieve a size sufficient for unstable fracture. But penetration of the wall will cause leakage which leads to a loss of pressure which in turn reduces the stress and lowers the driving force for failure, i.e. the vessel leaks before it breaks.

A steel ship deck is 30 mm thick, 12 m wide and 20 m long and has a fracture toughness of K C = 28.3 MPa.m 1/2. If a 65 mm long central transverse crack is discovered, calculate the nominal tensile stress that will cause catastrophic failure. Compare the stress found to the yield strength of.

A plate of width 1.4 m and length 2.8 m is required to support a tensile load of 4 MN (in the long direction). Inspection procedures are capable of detecting through-thickness edge cracks larger than 2.7 mm. The two titanium alloys are being considered for this application. (Alloy (A) K IC = 115 MPa.m 1/2 and  y =910 MPa; alloy (B) K IC = 55 MPa.m 1/2 and  y =1035 MPa. For a factor of safety of 1.3 against yielding and fracture, which one of the two alloys will give the lightest weight solution?