XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> Estimating Material Cyclic Properties From UTS & E
Laboratory Testing
The cyclic material properties required to define the cyclic stress-strain curve and the strain-life curve are usually determined by carrying out tests, under strain control, on a series of smooth highly-polished hourglass specimens. Typically, about 15 tests need to be performed at differing strain amplitudes. The properties can then be calculated by regression analysis on the following curves:
K' and n' : from a log stress vs. log plastic strain regression
sf' and b : from a log elastic strain vs. log 2Nf regression
ef' and c : from a log plastic strain vs. log 2Nf regression
Estimation of Material Cyclic Properties
It is often difficult to gain access to measured cyclic properties. For this reason, a lot of effort has been put into finding ways of relating monotonic properties, of which there are an abundant supply, to cyclic properties. The approaches have all been empirical but have provided some approximations which are useful.
The first method of approximating the strain-life relationship from monotonic properties was proposed by Manson and later modified by Muralidharan. The procedure is usually referred to as the method of universal slopes and it has been suggested that this method can be applied to
any metal. See
Table 15‑13.
More recently, Baumel Jr. and Seeger have compiled an alternative approach based on the results of more than 1500 fatigue tests. Currently, the approach is limited to plain carbon and low to medium alloy steels, aluminium, and titanium alloys.
The ductility factor
is calculated from:
= 1.0 for values of Rm / E <= 3 x 10-3
= (1.375 - 125 Rm / E) for Rm / E > 3 x 10-3
Table 15‑13 Parameter | Universal Slopes (Manson) | Modified Universal Slopes (Muralidharan) |
sf' b ef' c K' n' | 1.9 Rm -0.12 0.76 εf0.6 -0.6 sf' / (ef')0.2 0.2 | 0.623 Rm0.823 E0.168 -0.09 0.0196 εf0.155 (Rm / E)-0.53 -0.56 sf' / (ef')0.2 0.2 |
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Rm | | the ultimate tensile strength |
εf | | the true fracture strain calculated from ln (1 / (1 - RA)) and |
RA | | the reduction in area. |
Parameter | Uniform Material Law
plain and low alloy steels
(Baumel Jr & Seeger) | Uniform Material Law
Aluminium and Titanium alloys (Baumel Jr & Seeger) |
sf' | 1.5 Rm | 1.67 Rm |
b | -0.087 | -0.095 |
ef' | 0.59 α | 0.35 |
c | -0.58 | -0.69 |
K' | 1.65 Rm | 1.61 Rm |
n' | 0.15 | 0.11 |
a | | 1 for Rm/E ð 3E10–3 |
a | | 1.375 - (125 x Rm/E) for Rm/E > 3E10-3 |
Estimation of S-N Curve Data
S-N curves can be constructed purely on the basis of the ultimate tensile strength (UTS). The curve is constructed by fixing the stress axis intercept (one cycle) at the value of fracture stress, fixing the stress at 1000 cycles and the endurance limit according to the fraction of UTS detailed in the table below.
Life (cycles) | Stress (ksi) | Stress (MPa) |
Ferrous |
1.0 x 10e6 1.0 x 10e6 1.0 | 0.357 x UTS 0.357 x UTS Sf, (50.0 + UTS) | 0.357 x UTS 0.357 x UTS Sf, (345 + UTS) |
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Titanium |
1.0 x 10e6 1.0 x 10e6 1.0 | 0.307 x UTS 0.8 x UTS Sf, UTS | 0.307 x UTS 0.8 x UTS Sf, UTS |
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Aluminium |
5.0 x 10e8 1.0 x 10e3 1.0 | 0.258 x UTS 0.7 x UTS Sf, UTS | 0.307 x UTS 0.8 x UTS Sf, UTS |
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Other |
1.0 x 10e8 1.0 x 10e3 1.0 | 0.274 x UTS 0.8 x UTS Sf, UTS | 0.274 x UTS 0.8 x UTS Sf, UTS |
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Calculation of Kf’ (Kf at 1000 cycles) from Kf:
The effect of notches on the S-N curve are taken into account by calculating the values of Kf and Kf’ and dividing the stress at the endurance limit and 100 cycles by these values respectively.
Kf’ can be calculated from Kf by using the following table - in the UTS columns first values are in ksi, the second values (in parenthesis) are in MPa.
(Kf’ - 1)/(Kf - 1) | UTS | UTS | UTS |
0 0.2 0.4 0.6 0.8 | 48 (335) 98 (685) 158 (1104) 233 (1628) 343 (2396) | 16 (112) 33 (231) 53 (370) 78 (545) 114 (796) | 11 (77) 22 (154) 35 (244) 51 (356) 75 (524) |
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