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
Following all of this, the load is changes to ± 130 kN, completely reversed loading.
How many cycles can the bar withstand at this final stress before failure occurs? Use the Miner cumulative damage law.