1. S-N curve
The endurance of materials is studied in laboratory by subjecting to failure test bars cut in the material to be studied to stress of amplitude (or deformations), generally sinusoidal with zero mean.
Following the work of Wohler carried out on axes of trucks subjected to rotary bending stress, one notes, for each test bar, depending on a, the number N of cycles to failure 北京外语培训(endurance of the part 宗教笑话or fatigue life). The curve obtained while plotting CT against N is termed the S-N curve (stress number of cycles) or Wohler 's curve or 盘发化妆endurance curve. The endurance is thus the aptitude of a machine part to resist fatigue.
Taking into account the great variations of N with σ, it is usual to plot log N (decimal logarithm in general) on abscissas. Logarithmic scales on abscissas and on ordinates are also sometimes ud.
Figure 1.1. Main zones of the S-N curve
This curve (Figure 1.1): is generally compod of three zones:
- zone AB, corresponding to low cycle fatigue, which corresponds to the largest stress, higher than the yield stress of material, where N varies from a quarter of cycle with appro
ximately 104 to 105 cycles (for mild steels). In this zone, one very quickly obrves significant plastic deformation followed by failure of the test bar.
- zone BC, which is often clo to a straight line on log-lin scales (or sometimes on log-log scales), in which the fracture certainly appears under a stress lower than previously, without appearance of measurable plastic deformation. There are very many relationships propod between σ and N to reprent the phenomenon in this domain where N increas and when σ decreas. This zone, known as zone of limited endurance, is included between approximately 104 cycles and 106the end of the world to 107 cycles,
- zone CD, where D is a point which, for ferrous metals, is ad infinitum. The SN curve in general prents a significant variation of slope around 106 to 107 cycles, followed in a way more or less marked and quickly by a zone (CD) where the curve tends towards a limit parallel with the N axis. On this side of this limit the value of σ, noted σD, there is never failure by fatigue whatever the number of cycles applied.
σDsomeone like you 歌词 is called fatigue limit. σD is thus the stress with zero mean of greater amplitude for which one does not obrve failure by fatigue after an infinite number of cycles. This stress limit cannot exist or can be badly defined for certain materials (high-strength steels, non-ferrous metals).
For sufficiently resistant metals for which it is not possible to evaluate the number of cycles which the test bar would support without damage (too large test duration) and to take account of the scatter of the results, the concept of conventional fatigue limit or endurance limit is introduced. It is about the greatest amplitude of stress σ for which 50% of failures after N cycles of stress is obrved.
It is noted, for σm = 0, σD (N). N can vary between 10paparazzi6 and 108 cycles. For steels, N = 107 and σD(107)= σD. The notation σD阿里巴巴欺诈门 is in this ca ud.
Brittle materials do not have a well defined fatigue limit
For extra hardened tempered steels, certainly for titanium, copper or aluminium alloys, or
when there is corrosion, this limit remains theoretical and without interest since the fatigue life is never infinite.
When the mean stress m is different from zero, it is important to associate σm with the amplitude of the alternating stress. The fatigue limit can be written σa or σaD in this ca.
Figure 1.2. Sinusoidal stress with zero (a) and non zero mean (b)
周末愉快英文The endurance ratio is the ratio of the fatigue limit σD (normally at 107aabc cycles) to the ultimate tensile strength Rm of material:
NOTE. - The S-N curve is sometimes plotted on reduced scales in axes σ/Rm, N), in order to be able to proceed more easily to comparisons between different materials.
Figure 1.3. butyS-N curve on reduced axes
1.2. Analytical reprentations of S-N curve
Various expressions have been propod to describe the S-N curve reprentative of the fatigue strength of a material, often in the limited endurance domain (the definition of this curve having besides evolved over the years from a deterministic curve to a curve of statistical character).
Wohler relation (1870)
This relation does not describe the totality of the curve since a does not tend towards a limit σD when N -> ∞. It reprents only the part BC (Fig 1.1.). It can be also written in the form:
Basquin relation (1910)
The relation suggested by Basquin in 1910 is of the form
or
while tting:
and
The parameter b is sometimes named index of the fatigue curve
Figure 1.4. Significance of the parameter b of Basquin's relation
