Running Head: Material failure


          This paper seeks to explore the crack growth fracture mechanics with a focus on the factors that influence the fatigue crack growth rate and how the Paris-Erdogan equation can be used to predict fatigue crack growth as well as in the calculation of crack growth rate.  The paper also presents research on modes of mechanical failure.

Crack Growth Fracture Mechanics

           According to Hancock, G. J. (2003, p.125), fracture mechanics is used to predict the effect of cracks on the durability and integrity of structures and components. It helps in detecting cracks in structure before a crack grows to significant length as a result of sustained stress cycles. During fatigue, crack growth rate can be calculated by the Paris-Erdogan equation given by da/dn = C (?k)n  where a represents the crack length, n represents the number of fatigue cycles, ?k represents the applied stress intensity factor range while c and m are considered to be constants of a material.  ?k increases with time as a load is applied due to the growth of the crack. For a crack of length a, the rate of crack growth given by da/dn  per cycle varies with ?k. Where c and m are constant with m between 2 and 4. The upper limit of a crack growth rate curve represents the fracture toughness of the material while the lower limit is the threshold. There is characterization of sub-critical crack growth using linear plastic fracture mechanics parameters and acoustic emission data to predict crack propagation rates. This determines the number of cycles required for an existing crack to attain a substantial size. (Reuter, W. G, Robert, S. P. 2002, p.458)Acoustic emissions are elastic stress waves generated by a rapid release of energy from a localized source within a stressed material. Fatigue crack growth rate is influenced by many factors some of which include: notch radius where research indicates presence of higher fatigue crack growth rate in a blunt notch. This is because of accumulation of fatigue damage at the tip of the notch initiating the crack a head of the notch. Material strength, initial crack tip condition, mean stress, overload as well as non-proportional load determine the crack growth rate. Research has also shown that ferroelectric ceramics experience cracking and mechanical degradation when subjected to large alternating electric fields. (Anderson, T.L., 2005, p.455)

Mechanical Failure Mode

               Mechanical failures in machine have been found to occur in a number of ways. Depending on the nature of their use, machines may fail as a result of being subjected to a given load. This loading may be regular or irregular with different weights and sizes involved. When loads are used on a machine especially repeated use, the machine experience pressure on its movable and immovable parts hence resulting in failure or reduction in performance which may include loosing shape. Due to repeated machine use, most researchers attribute majority of mechanical failures to fatigue, due to its routine nature this failure can go unnoticed until the machine is grounded. The other mode is the environment. These encompass the temperature and corrosion factors which are found in the surrounding of the machine. According to Anderson, I.S, Fuchs, O. H, Fatemi A. (2001, p.126), machines operate in surroundings with different temperatures ranging from too low to too high. These affect the component parts of a machine depending on the materials used as well as technical specification. For instance, some radios can not function in an extremely cold and misty surrounding. The machine environment can also influence the rate of machine rusting; salty environments like areas near the Indian Ocean accelerate the rate of rusting hence this can cause machine failure in the absence of proper maintenance. A machine that is used for a long period of time is most likely to experience failure compare to one used for a short period of time. Long time usage involves tear and wear which affect machine performance. (Anderson, I.S, Fuchs, O. H, Fatemi A., 2001, 125).

               The other failure mode is excess deformation which is based on the maximum shear stress criterion. This excess deformation can both be plastic and elastic.  Plastic deformation causes ductile fracture through ductile dimpling when exposed to high energy absorption. The reason for low-energy absorption and very high crack growth velocity during fracture is due to the fact that brittle fractures contain little macro or micro plasticity. (Hancock, G. J., 2003, p.125).  The machine design and make up can result in stress concentration as a failure mode. It may be designed in a way that allows for regions of sharp stress concentrations, residual tensile stresses, multiaxial stress state, and low fracture toughness. Such a machine experience undue strain through dynamic loading hence failure due to reduced tensile toughness.  When metallic parts of a machine are subjected to elevated temperatures, the machine experience creep and relaxation failures. An overheated metal expand and when it’s subjected to very cold temperatures can easily break or undergo deformation. This expansion and contraction of metals is responsible for crack nucleation and crack growth behaviors.   Wear and tear has also contributed to machine failure by the degeneration of the moving parts and surfaces which are compressing against other surfaces.  Buckling failure can be induced by external loading or thermal conditions. Apart from environmental factors, corrosion can be as a result of interaction with applied and/or residual stresses resulting in pitting and crack nucleation. This stress corrosion cracking has a degrading effect on the surface of metals like steel hence resulting in aesthetic failure. (Gdoutos, E. E. 1990, p.276)


From the paper it is clear that Paris-Erdogan equation can be use to calculate as well as predict the crack growth rate in a number of engineering works. Mechanical failures can also occur through a number of modes including temperature, environment, loading, excess deformation, wear, creep and relaxation as well as fatigue from machine usage.


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Hancock, G. J. (2003). Advances in structure. New York: Taylor and Francis. P. 125

 Anderson, T.L. (2005). Fracture Mechanics. New York: CRC press, p.455

Anderson, I.S, Fuchs, O. H, Fatemi A. (2001). Metal fatigue in engineering. NY:

                         Wiley.p.125, 126

Reuter, W. G, Robert, S. P. (2002). Fatigue and fracture mechanics, 33rd vol. New York:

                          ASTM international. P.458.

Gdoutos, E. E. (1990). Fracture mechanics criteria and application. New York: Springer. P.276.



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