Linear regression

Consider the shaft with a shoulder fillet at the middle (x = L/2). The material is AL2024-T3. Use the loads
provided in item 5. The shaft is machined, with a 95 % reliability, subject to an operating temperature of 350◦F.
Assume residual stress effects are important and are taken into account using a factor of 0.7 (this is an added factor
to your k∞). An additional factor of safety of 1.25 is desired. For a d = 2.1500 and a proposed Aluminum (2024-T3)
built shaft, D = 1.25 d, do fatigue assessment at this location. The fillet has a radius of 0.125–in.
You are asked to determine if the substructure will be safe.

1. Write the material properties.
2. Find is Kt for all loading conditions.
3. Find is Kf for all loading conditions (axial, bending, torsion). Use traditional approach (assuming that plastic
   strain at notch can be avoided: Kf = Kfa = Kfm).
4. What would be the load factors for mean and alternate stress components?
   (a) Find endurance limit:
   i. Find is S
   0
   e
   .
   ii. Determine k∞.
   iii. Calculate Se.
   (b) Determine the stress for N = 100
   , 103
   (Sut and f Sut).
   (c) Staying nonconservative (using different curves for low and high cycles), plot the S–N Diagram. Also,
   the Fatigue Diagram. Do this by hand and compare with MATLAB code.
   (d) Find the curve constants for high cycle fatigue. In other words, determine the constants a and b in
   SN = a Nb
   (Use the Basquin Equation treatment as posted in Class lectures. Note that Equations 6–14 and 6–15
   only apply to materials with an endurance limit at 106
   .)
   Created in Master PDF Editor
   ME 4141 – Machine Design
   Fatigue
   Department of Mechanical Engineering
   Due Date Posted on See D2L
   Homework 7 Part 1: Ductile Materials
   Page 3 of 4
5. Use Distortional Energy find all stress values (should be in ksi).
   (a) The following is the three-loading sequence In a 30-second repetitive data the following sequence is know:
   i. LOAD CASE A: 5,000 cycles
   a) The moment load M is fully reversed at 20,000 in–lb.
   b) Torque T is fully reversed at 5,000 in–lb.
   ii. LOAD CASE B: 1,000 cycles
   a) The axial load P is fully reversed at 20,000 lb.
   b) The moment load M fluctuates in tension at 10,000 in–lb.
   c) Torque T fluctuates in tension at 15,000 in–lb.
   iii. LOAD CASE C: 2,000 cycles
   a) Axial load P is alternates from 5,000 to 20,000 lb.
   b) Torque is fully reversed at 5,000 in–lb.
   (b) For each load case, find the alternating and mean fatigue stresses (Sa, Sm). These are using the von Mises
   values from you alternating and mean state of stresses (not Goodman). (Lecture notes)
   (c) Check for static failure for maximum absolute value of the loads for each loading cycle. (Lecture notes)
   (d) Note that Ni
   is calculated using:
   Seq = a Nb → N =
   
   Seq
   a
   1/b
   where Seq is the Goodman stress, and a and b are calculated from the MATLAB code (provide hand
   calculations, as well)
6. How many duty cycles before failure? We need the part in service for 300 days a year. (Lecture notes)
   Bf
   
   n1
   N1
   +
   n2
   N2
   +
   n3
   N3
   
   ≤ D
   where Bf are duty cycles, ni the service cycles for the i
   th cycle loading conditions, Ni the life cycles for the i
   th
   cycle loading conditions, and D the damage parameter (D = 1, for this homework).

Example (not values from this homework):
Bf

n1
N1
+
n2
N2
+
n3
N3

≤ 1 → Bf ≤
1
n1
N1
+
n2
N2
+
n3
N3
Bf ≤
1
1.34761 × 10−5 → Bf ≤ 72705.7 duty cycles
Bf ≤ 72705.7 duty cycles
90 sec
1 duty 1 min
60 sec 1 hr
60 min 1 day
24 hr
= 75.74 days
If 300 days were required, the part for this mini-example would not meet the requirement. Resign is recommended.