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Fatigue of Materials

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Fatigue life is defined as the number of loading (stress) cycles of a specified character that a specimen sustains before failure of a specified nature occurs. The number of cycles is related to engine speed. It can be converted to equivalent durability hours. Fatigue life is affected by cyclic stresses, residual stresses, material properties, internal defects, grain size, temperature, design geometry, surface quality, oxidation, corrosion, etc. The fatigue life of a component under the following different fatigue mechanisms can be ranked from low to high as: thermal shock, high temperature LCF, low temperature LCF, and HCF. In the assessment of the risk of fatigue failure, it may be assumed that the component is safe for an infinite number of cycles if it does not show failures after more than ten million cycles. The total fatigue life is equal to the life of crack formation and crack propagation. Fatigue life is dependent on the cycle history of the loading magnitude since crack initiation requires a larger stress than crack propagation. The fatigue life of the component can be determined by the strain, stress, or energy approach. Fatigue is a very complex process affected by many factors

It is usually more effective to use a macro phenomenological method to model the effects of fatigue mechanisms on fatigue life rather than using a microscopic approach.

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Metal fatigue is caused by repeated cycling of the load. It is a progressive localized damage due to fluctuating stresses and strains on the material. Metal fatigue cracks initiate and propagate in regions where the strain is most severe. This cyclic loading and crack initiation is represented using S-N curves. The Fig 1.1 consists of constant cyclic stress amplitude(S) which is applied to a specimen and the number of loading cycles (N) until the specimen fails is determined. The process fatigue failure is consists of three main stages. The first stage consists of initial crack initiation

The second stage consists of progressive crack growth across the part and the third and final stage consists of sudden fracture of the remaining cross section. The fatigue strength is the stress at which failure occurs for a given number of cycles, whereas the fatigue life is the number of cycles required material to fail. The most important concept of the S-N diagram is shown in Fig 1.1. This figure consists of S-N curves for Steel and Aluminium. (By Shawn M. Kelly) http://www.efunda.com/formulae/solid_mechanics/fatigue/images/fatigue_SN_01.gif Figure 1.1 S-N curves for steel and aluminium. The subject of fatigue testing is extensive, and is complicated by the important factors like the surface conditions of the specimen, the type of the stress variation, and the influence of the shape of the specimen on the stress flow. As it is known as that the highly polished specimens withstand better fatigue than the normal fatigue ones. The most damaging type of stress variation is the complete reversal, which is between the limit ±Ïƒ for which the stress range is 2σ. Fluctuating stresses are less damaging, the standard case is between the limit 0 and +σ. For some materials such as aluminium, no endurance limit exists and therefore it should be planned lifetime of the structure to be less than the failure point. http://htmlimg1.scribdassets.com/izqlx4lamohzwzk/images/10-d0617ea942/000.jpg Figure 1.2 Fluctuating Stress Cycle. The above figure illustrates repeated stress cycle in which σmax (Rmax) is the maximum stress and σmin (Rmim) is the minimum stress and both are not equal. Here t is the time and σa is the stress amplitude and σm is the mean stress. In low fatigue cycle region (N<104 or 105 cycles), tests are conducted with controlled cycles of plastic and elastic strain instead of stress cycle. The basic procedure of determining an S-N curve is to test the first specimen at a high stress where failure is expected within a less number of cycles, e.g., at around two-thirds the static tensile strength of the material. The applied load/stress is decreased for each succeeding specimen until one or two specimens do not fail under the specified number of cycles, which is at least 107 cycles. The highest stress or load at which the specimen runout (non-failure) that point or limit is taken as a fatigue limit of the material. The materials without a fatigue limit the test is usually terminated for practical consideration at low stress at about 108 or 5x108 cycles. (www.key-to-metals.com.cn) In this experiment fatigue test for aluminium alloys of series 2000 have been conducted and described. S-N Curve Experiment for 6000 and 2000 Aluminium Alloys Series: The fatigue failure experiment is carried out for two different types of aluminium alloys i.e. 6082 and 2011 specimens. These experiments are carried in two different groups. A typical standard specimen is shown in Fig 1.3 as below. It is recommended to test at least 10 specimens of each type and they all must be cut from one length of the material. http://static.tecquipment.com/Products/RF1020_ALUMINIUM-FATIGUE-SPECIMEN.jpg Figure 1.3 Test Specimen. A set of bending stresses from 0.9 of the yield or proof stress to 0.4 of the ultimate strength is selected to match the number of the test specimens for the complete experiment. The setting up of the specimen on the machine is a reasonably simple operation which is done in proper methodology. The main object is to align the specimen and loading arm with the axis of rotation to eliminate stresses due to eccentric whirling of the specimen. Both in drive shaft and the loading arm chucks, loose collet grip is inserted. These inserts 9mm diameter ends of the test specimen are slid as shown in Fig. 1.4. http://www.twi.co.uk/twiimages/jk78f1.jpg Figure 1.4 Setting up of machine. ( by http://www.twi.co.uk/content/jk78.html) The collet is first tighten on the drive shaft chuck so that so that about 1 mm shoulder shows between the start of the neck and the face of the collet of the specimen. Then the loading arm is pushed on to the end of the specimen and adjusts the collet to give a sliding fit. The position of loading the loading arm is in such a way that the dimension of 109.5 mm is attained from the rear face of the bearing housing to the adjacent end of the neck of the specimen as shown in Fig 1.4 and finally tight the collet with the spanner. The specimen is rotated to check that the end of the cantilever run axially otherwise the specimen must get bend and can be discarded. Bearing Drive shaft and bearing Electric motor Chuck in which specimen is fitted. ON/OFF SwitchC:UsersasimDesktopall folderpicsmaterialsimagesattachments_16_12_2010DSC01501.JPG Figure 1.4 Rotating Fatigue Machine The counterbalance and load hangers should be ensured are in place. Switch motor ON and OFF to verify smooth running. The bending stress for the test is selected and required load or weight is applied on the load hanger. The revolution counter is set to zero before starting the machine and safety guard is used over the apparatus. The fracture time which might occur is estimated and noted.

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The works of (Lei, 2016a), (Lei, 2016b) and of (Wallin, 2010) are devoted to some statistical aspects of brittle fracture and fatigue strength in relation to microcrack and materials particle distributions, respectively

Finally, (Akbardoost et al, 2017), (Spagnoli et al, 2016) and (Yan et al, 2015) deal with size effect on the fracture resistance of quasi-brittle materials, like natural stones and concrete.

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To sum up, conventional practice is to minimize the risk of thermal fatigue by proper design and operation in order to minimize thermal stresses and thermal cycling

Such measures include: Designs that minimize stress concentration sites, blend grinding of weld profiles and requiring that transitions in thickness be gradual and smooth. Use of controlled rates of heating and cooling rates during start-up and shut-down. Minimizing the frequency of start-ups and shut-downs, particularly “trips.” Minimizing differential thermal expansion in dissimilar metal joints. Where possible, incorporate flexibility that will accommodate differential expansion.

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W.-S. Lei
Volume 39, Issue 5, May 2016, Pages 611–623

W.-S. Lei
Volume 39, Issue 11, November 2016, Pages 1337–1351

Statistical aspects of fatigue life and endurance limit
K. Wallin
Volume 33, Issue 6, June 2010, Pages 333–344

Andrea Spagnoli, Andrea Carpinteri, Daniele Ferretti, Sabrina Vantadori
Volume 39, Issue 8, August 2016, Pages 956–968

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