Class Example: Cumulative Fatigue Damage

1.A solid circular link made of 4340 steel as the following fatigue characteristics:

Stress amplitude / N (cycles)
1158 / 100
1103 / 1350
1034 / 3500
965 / 7100
896 / 14200
827 / 28000
758 / 55500
689 / 110000
620 / 216000
552 / 440000
483 / 1198000
469 / 

The link is to be subjected to a spectrum of axial directed load during each duty cycle, the subjected loads are as follows:

Pa = 98 KNfor 1200 cycles,

Pb = 53 KNfor 7000 cycles, and

Pc = 29 KNfor 50000 cycles.

The duty cycle is to be repeated 3 times during the life of the link.

Question:Estimate the required cross-section area of the link using

(a) MINER-PALMGREN RULE

(b) CORTEN-DOLAN RULE

of accumulated damage.

Fatigue Failure (Estimation of Crosssectional Area of Component)

1.An alloy steel tension member for an aircraft application is fabricated from a material whose completely reversed fatigue properties, based on experiment, are given in the chart below.

______

Stress amplitude, S (MPa) Cycles to failure, N

______

758

724

690

655

620

586

552

517

503

490

483

476

472

469

6,600

9,500

13,500

19,200

27,500

39,000

55,000

87,000

116,000

170,000

220,000

315,000

400,000

______

In service, the tension member is to be subjected to the following spectrum of completely reversed axial loads during each duty cycle

PA = ± 49kN for 1000 cycles

PB = ± 37kN for 4000 cycles

PC = ± 29kN for 50,000 cycles.

This study cycle is to be repeated three times during the life of the member. Estimate the required cross-sectional area of the member, using the Miner and Corten-Dolan damage theories.

2.The critical point in the main rotor shaft of a new VSTOL aircraft of the ducted-fan type has been instrumented, and during a "typical" mission the equivalent completely reversed stress spectrum was found to be

± 345 MPa for 15 cycles

± 207 MPa for 100 cycles

± 414 MPa for 3 cycles

± 70 MPa for 10,000 cycles

Ten missions of this spectrum have been run. It is desired to overload the shaft to 10% above this "typical" loading spectrum. Using Miner linear cumulative damage law, estimate (a) the number of additional "overloaded" missions that can be run without failure and (b) how many additional runs could have been made under normal loading conditions.

The fatigue properties of the shaft material are given in Figure Q2.

3.A special instrument package in an experimental aircraft weighs 270N. It is supported by three small cables, each cable attached to one end of a cantilever beam spring, as shown in Figure Q3(a).

The beams are symmetrically placed and equally loaded by the package. The system is damped so that it does not vibrate, but during various maneuvers the instrument is subjected to various levels of vertical acceleration. Thus, the total effective tension force on the three cables ranges from 0 to 7 kN during the mission. The mission loading spectrum for one "typical" mission is found to be

0 to 5400N for 100 cycles

1000N to 7000N for 10,000 cycles

1200N to 5970N for 50,000 cycles

The cantilever beam has the dimensions shown in Figure 2(b) and the relevant fatigue properties of the beam material are presented in Figure Q3(c).

Estimate the total number of missions that can be flown before failure of a cantilever spring would be expected, using Miner's cumulative damage law.

4.An annealed 1040 steel alloy has completely reversed fatigue properties given in Figure Q4. A solid cylindrical bar of 25mm diameter is made of this material and subjected to the following schedule of completely reversed axial loads:

± 150 kN for 5000 cycles

± 110 kN for 3 x 105 cycles

± 80 kN for 2 x 106 cycles