# Need Help-MSE 250 HW 4 Reading: Callister Ch. 7 and Ch. 8

Need Help-MSE 250  HW 4 Reading: Callister Ch. 7 and Ch. 8

MSE 250  HW 4

Reading: Callister Ch. 7 and Ch. 8.

Academic Integrity:  Students are encouraged to study with a partner or small group, but each student should complete their homework by themselves (no copying allowed). The data table and plots referred to are given at the end of the homework.

Please write clearly, show all work in an organized fashion, and circle answers.

1)  Using the data shown in Figures 6.14 (at 25oC) and 6.21, combine both curves onto one plot, being careful to correctly plot the modulus, yield strength, tensile (ultimate) strength, and ductility.  Discuss how the modulus, yield strength, and ductility compare for pure iron (figure 6.14) vs. the alloy steel.

2)  The equation for the effect of grain size on yield strength is given by:

sy = sI +kD-0.5

where sy is the yield stress, sI is the intrinsic resistance of the lattice to dislocation motion, k is the “blocking parameter” which measures the effectiveness of grain boundaries in blocking dislocation motion, and D is the grain diameter.

Use this equation to determine the change in yield strength of a typical steel when the grain size is increased from 10micron to 50 micron (1 micron = 10-6 m), due to grain growth.  .  sI = 150 MN/m2 and k = 0.70 MN/m1.5 .

3)  Using the data shown in Callister Figure 7.19, draw an approximate stress-strain curve for the 1040 steel at 0% cold work and at 30% cold work, clearly indicating the yield strength, ductility, and tensile strength of the steel before and after cold-working (Young’s modulus of steel E = 250 MPa).

4)  A fatigue test is carried out on a steel having an ultimate strength of 289 MPa.  The number of cycles required to break the specimen at different stresses are given below:

Stress Amplitude                  Fatigue Life

(MPa)                                     (cycles)

223                                         4.5 x 104

209                                         2.4 x 105

192                                         8.0 x 105

178                                         1.5 x 106

175                                         2.7 x 106

168                                         7.8 x 106

168                                         >1.0 x 107 (did not break)

165                                         >2.6 x 107

162                                         >2.2 x 107

1. a) Plot the data on linear-log scale, preferably with a computerized figure-plotting program.
2. b) Determine the average fatigue strength at 106 cycles (hint: use curve-fitting software to fit the line).
3. c) What is the ratio of the fatigue strength at 106 cycles to the ultimate strength?
4. e) If you plan to use this material for 108 cycles, what is the maximum fatigue strength you would recommend (assuming 20% fluctuations in stress amplitude).

Callister Homework Problems:  7.22, 8.4, 8.12 (see next page)

Need Help-MSE 250  HW 4 Reading: Callister Ch. 7 and Ch. 8

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