Fatigue In Engineering Materials

[Music] a piece of wire when bent once does not break but repeated bending back and forth will eventually produce failure failure under repeated loading is called fatigue in the case of the wire the fatigue life is short only a few cycles of load repetitions are required to break it because large plastic deformations are involved structural and mechanical components such as this automobile crankshaft are usually designed to carry all loads within the elastic range but as can be seen even these fail eventually although millions of load Cycles are required to cause such failures the crankshaft was subjected to repeated bending by the up and down movement of Pistons this Wing attachment from an aircraft has been repeatedly Bent by wind gusts to determine the life expectancy of various materials under fatigue loading special testing machines are needed in a rotating bending machine a bending moment is applied to the specimen by adding weights to the weighing pan this produces tensil stresses on the bottom surface and compression on top instead of bending the specimen in the opposite direction by pushing upward it is turned around and hence the bending stresses are reversed now the previously extended surface is compressed the specon is tapered to produce a break at the center where the stress amplitude is a maximum the machine rotates at a high speed and produces alternating tension and compression at every point on the specimen a counter determines the number of Cycles to failure this machine applies alternating bending to a flat specimen through the use of a variable eccentric cam the specimen is again tapered here the deflection of the Cal levered specimen has a constant amplitude a strain gauge attached to the specimen shows that the strain and the stress vary cidate in each cycle from Maximum tension to maximum compression if the tensil and compressive Peaks are equal in magnitude the mean stress is said to be zero on the other hand by moving the fixed end of the specimen upward the tensil peak becomes larger than the compressive trough and hence a positive mean strain and mean stress are applied the ratio of minimum to maximum stress is the stress ratio r r equal minus1 signifies complete reversal while r equal 0 means that the stress on one side of the specimen varies from zero to a maximum tensil stress this testing machine can apply tensil and compressive axial loads through a combination of eccentrics and fluid pressure the load is monitored by a load cell and its amplitude is kept constant by a Servo mechanism both mean stress and stress amplitude can be changed the number of Applied Cycles is again counted a Servo Hydra testing machine in which load is applied by High Press fluids can be used as a fatigue machine a smooth specimen will be tested the amplitude of the load or the amplitude of the strain can be controlled in this machine the load and hence the stress is monitored by a load cell while strain is measured by an extensometer both may be plotted automatically as functions of time the machine can also plot stress versus strain on load repetition the pen retraces the dynamic stress strain diagram in this test stresses are in the elastic range and hence there is no hysteresis Loop during a fatigue test the shape of the stress strain diagram changes if the load amplitude and hence the nominal stress amplitude is kept constant the height of the diagram is always the same but when large plastic deformations are present as is the case for this aluminum specimen The Strain increases in each cycle in such a case the Dynamic stress strain diagrams move forward eventually they become unstable and elongated within a few Cycles the specimen starts necking and finally fails such conditions usually lead to low cycle that is short life fatigue to prevent the onset of this plastic instability strain control may be used that is the strain amplitude is kept constant when a constant plastic strain amplitude is applied to our aluminum specimen necking does not take place and the test remains stable let us perform a constant load amplitude fatigue test on a mild steel specimen under axial load with a stress ratio of zero the maximum stress amplitude is set at 40,000 PSI this stress does not produce a large amount of plasticity the machine is started and will automatically stop when the specimen fails the number of Cycles to failure is plotted on a chart at the maximum applied stress amplitude a logarithmic scale is used for the number of Cycles when tests are repeated at the same stress amplitude different numbers of Cycles to failure are recorded and plotted on our chart typically fatigue data has a large statistical dispersion a higher stress amplitude will result in shorter lives while a lower stress produces longer fatigue lives the test results can be averaged at each stress level and a line may be drawn through these average values the line is called the average or mean SN diagram to show the statistical dispersion of the test results more SN diagrams may be drawn which indicate the fraction of specimens whose fatigue lives fall within the band for some Ferris Alloys the SN curve approaches a horizontal ASM toote this so-called fatigue limit is a stress level below which fatigue lives are infinitely long the SN curve is often divided into three regions low cycle fatigue below a th000 Cycles intermediate between 1,000 and 1 million cycles and high cycle fatigue above a million Cycles different SN curves are obtained when the stress ratio is changed so far our specimens were essentially smooth a notched specimen having the same root Dimension as as our smooth specimen when subjected to the same load amplitude has an identical nominal stress at the root of the notch however we have observed in another film that such discontinuities in shape produce stress concentrations and that the stress at the notch is higher than the nominal value when tested the fatigue life of the notch specimen will be shorter than that of a smooth specimen repeated tests result in an SN curve for Notch specimens which lies below the smooth specimen SN diagram the ratio of the stress amplitudes of smooth and notched specimens at a fixed number of Cycles is called the fatigue Notch Factor KF which is larger than Unity because of this sensitivity to notches discontinuities or even surface scratches the crankshaft broke at the fillet the crack in the aircraft Wing attachment initiated at a bolt hole fatigue failures can usually be traced to such stress razors let us examine next the propagation of a fatigue crack and Edge notched aluminum specimen will be tested under a constant load amplitude for several thousand Cycles there is no visible crack on the specimen this period is called the crack initiation stage submicroscopic damage is in progress however and eventually a small crack will form at the notch rout under additional load repetitions the crack propagates into the material first slowly but eventually at an increasing speed finally when the remaining cross-section is too small to carry the next applied load the specimen breaks after the crack has been initiated the rate of crack propagation is a function of the material properties the stress amplitude and the stress ratio higher alternating stresses usually produce faster crack propagation an examination of the fracture surfaces of some typical fatigue specimens shows two different regions the smooth shiny portion is the fatigue damaged region through which the fatigue crack propagated the rougher darker surface indicates the cross-section that broke under the last load cycle and is similar to fracture surfaces obtained in a simple tension test up to this point our tests were conducted either under a constant load amplitude or under a constant strain amplitude structures and machines in actual service are usually subjected to fluctuating loads that vary as irregular functions of time such random loads can be programmed and appli to specimens in this testing machine the load program has been taped in advance and is played back into the machine which through its Servo control system applies it to the specimen a typical portion of the load time curve is plotted here after an initiation time a crack forms again and propagates through the specimen until it fails typically such fracture surfaces exhibit the fatigued region and the section broken by the last load the surface shows curved lines so-called shell or Beach markings but in contrast to specimens broken under constant amplitude loads the surface exhibits Hills and Valley these markings show that a fatigue crack under random loads moves in spurts each curved line indicates that a crack has stopped there and advanced again when a sufficiently high load has occurred such markings are definite indicators of random loads a re-examination of our structural failures reveals shell marking on the aircraft Wing attachment which was buffeted by random wind gusts the head of this bolt also shows some influence of variable loading fatigue tests in the laboratory are performed in order to predict the safe life and strength of such structural components so that catastrophic failures in service will not take [Music] place I [Music]