Let this regime be called Region III of fatigue, as indicated in Figure 1.6. View chapter Purchase book Read full chapter URL: Fatigue damage mechanisms R.
Fatigue Stress Equation Download As PDFFrom: Diesel Engine System Design, 2013 Related terms: Mechanical Fatigue Test Amplitudes High Cycle Fatigue Fatigue Failure S-N Curve Tensile Strength Endurance Limit Stress Amplitude View all Topics Download as PDF Set alert About this page A conceptual framework for studies of durability in composite materials R.![]()
Fatigue Stress Equation Full Chapter URLFatigue Stress Equation Crack Whose UnstableIf the metallic structure develops a crack whose unstable growth defines failure, then the fatigue threshold is expressed in terms of the range of the stress intensity factor, K. That threshold is the value of this quantity below which no crack growth is expected. Figure 1.5(b) schematically plots the crack growth rate (d a d N ) against K and indicates the fatigue threshold K 0. Figure 1.5. (a) A typical stresslife ( S N ) plot for metal fatigue, indicating fatigue limit S 0; and (b) a typical crack growth rate versus range of stress intensity factor, indicating the fatigue threshold ( K 0 ). Studies of metal fatigue have indicated that the fatigue limit is sensitive to the microstructure, for example, the grain size, and the mechanisms responsible for limiting fatigue have to do with creating microstructure barriers to the formation of cracks from cyclic slip within grains and, if a crack initiates, to block its advance by such barriers. In a composite undergoing Region II fatigue, the microstructure barriers are the fibers bridging the matrix cracks. These fibers provide resistance to crack growth by reducing the energy release rate (via reducing the crack surface displacement). The fibers ahead of the crack front provide obstacles to the crack growth. In spite of these mechanisms of crack growth retardation, it is likely that the failure condition is not avoided but is reached at very large numbers of load cycles. While in metals 10 6 cycles is viewed as a large number of cycles and is often used to define the fatigue limit, polymer-based composites are used in applications, such as wind turbine blades, where 10 7 or more cycles are expected in the design life. Since testing to such large numbers of cycles is time-consuming and costly, it is desirable that estimates for the fatigue limit can be made from considerations of the mechanisms. An attempt at this follows next. Figure 1.6 schematically depicts a scenario for arresting the fatigue crack growth in a composite. These cracks are assumed to form by the fatigue process in the matrix polymer under the applied cyclic load. Assuming the applied load level to be low enough that essentially no fibers fail, the matrix polymer surrounding the fibers undergoes cyclic stressing dictated by the cyclic deformation of the fibers. This cyclic deformation produces the same strain in the matrix as in the fibers (and the composite). In order for the matrix to form fatigue cracks, this cyclic strain must be equal to or greater than the fatigue limit of the matrix (measured in terms of strain). Thus, one estimate of the fatigue limit of the composite would be the fatigue limit of the matrix. Obviously, this estimate of the composite fatigue limit fl is an approximation, since the local strain in the matrix is assumed to be the same as that in the composite, neglecting any strain enhancement caused by fibers. Thus, the matrix fatigue limit m could be viewed as the lower bound to the composite fatigue limit, that is, fl m. On the other hand, because of the crack growth arrest by the fibers, depicted in Figure 1.6, the actual composite fatigue limit may be higher than the matrix fatigue limit, that is, fl m. Fundamental studies are needed to determine how the fiber architecture (e.g., straight fibers vs woven fabric), as well as the fiber volume fraction, affects the composite fatigue limit. For glass fiber-reinforced epoxy, data produced by Dharan (1975) suggested that the fatigue limit of epoxy, found to be at 0.6, was a good approximation to the UD composite fatigue limit at three different fiber volume fractions (0.16, 0.33, and 0.50). However, for composites with stiffer carbon fibers, the fatigue limit is usually higher than 0.6. Figure 1.6. Region III of the fatigue life diagram indicating the mechanism of matrix crack arrest by fibers. ![]() Let this regime be called Region III of fatigue, as indicated in Figure 1.6. View chapter Purchase book Read full chapter URL: Fatigue damage mechanisms R.
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