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MECH4900

Final Assignment

T3-2022

The purpose of this assignment is to apply the knowledge learned in MECH4900 to understand problems that a practicing engineer might face in their career.  This will include:

1) Reading two assigned journal articles,

2) Completing a very short multiple choice (no calculations) Moodle quiz, and

3) Submitting an assignment of questions and calculations.

Quiz will be open Thursday 17 November 13:00 until Friday 18 November at 23:59. The quiz questions are meant to assess if you read the articles and case studies carefully enough to understand the concepts. The quiz is meant to be a relatively easy part of the final assignment.  

The assignment is to be typed and uploaded to Moodle by Friday 18 November at 23:59, links to Moodle are also available on MS Teams. When using mathematics software, please insert the relevant sections (screenshots, PDFs, etc.) in each problem or attach your code/notebook (with references to problem numbers) to your assignment.

Problem set 1: Statistics of Fatigue Lifetime Analysis

Download from Teams/Moodle and read the article:

· Yuhan Xue, Gangyin Luo, Xiang Liu, Yuan Xing, Bo Hu, Zhenglong Liu, “An Analysis on the Engineering Failure of the Wire Rope Used in Surgical Instruments,” (2022). Journal of Failure Analysis and Prevention, 22, 724-737. https://doi.org/10.1007/s11668-022-01356-2 

Textbook fatigue lifetime analysis problems are often quite simple where you insert values into an equation to determine the number of cycles for the fatigue life. Real engineers face serious uncertainties in the fatigue life of their designs, and they must rely on statistical analysis to determine an acceptable probability of fatigue failure. In this journal article, the authors conduct accelerated life testing (ALT) of wire rope used for surgical instruments and develop a fatigue life distribution model to help them predict the probability of fatigue failure as various stress levels.  However, I believe their approach falls short of the goal. We will take a critical look at this article.

Problem set 2: Understanding Effects of New Manufacturing Methods on Fracture Toughness

Download from Teams/Moodle and read the article:

· Moses J. Paul, Yokasundery Muniandy, Jamie J. Kruzic, Upadrasta Ramamurty, Bernd Gludovatz, “Effect of heat treatment on the strength and fracture resistance of a laser powder bed fusion-processed 18Ni-300 maraging steel,” (2022) Materials Science and Engineering A, 844, 143167. https://doi.org/10.1016/j.msea.2022.143167 

Recently industries around the world have begun adopting additive manufacturing processes for producing metal components.  One of the most popular methods for producing high quality metal parts is known as laser powder bed fusion (also known as selective laser melting).  With this process, the component is built up layer-by-layer by melting metal powders. This layer-by-layer processing can produce significant anisotropy in the mechanical properties, including the fracture toughness. In this journal article, your brave demonstrator, Moses, worked to understand the anisotropy in the material structure and fracture toughness for a maraging steel produced by laser powder bed fusion.  

Problem Set 1: Statistics of Fatigue Lifetime Analysis

Yuhan Xue, Gangyin Luo, Xiang Liu, Yuan Xing, Bo Hu, Zhenglong Liu, “An Analysis on the Engineering Failure of the Wire Rope Used in Surgical Instruments,” (2022). Journal of Failure Analysis and Prevention, 22, 724-737. https://doi.org/10.1007/s11668-022-01356-2 

1) On pages 726-727, the authors describe their method for accelerated life testing (ALT). How did they accelerate the fatigue tests compared to the actual service conditions?  Explain in your own words how this accelerated testing method might affect the ability of the test results to predict the actual fatigue lives for the service conditions?  

2) Figures 5 and 6 show how the scatter of the fatigue data increases with decreasing stress level. This is a very common trend for fatigue life data. Explain in your own words why this occurs.  

3) Let’s check the article results in Table 3.  Please substitute Eq. 1 into Eq. 3 and use the values in Table 2 to calculate N₅₀ and N_99.9 for each stress level. I expect you will need to use numerical software like MATLAB or Mathematica so please show your calculations/code clearly.  Note, for the left side of Eq. 3: P(N₅₀) = 0.5 and P(N_99.9) = 0.999.  To present your final results, create a table listing your 8 calculated values, the 8 calculated values from the article, and the difference between them in % of the article value.

4) Please comment on the % error difference for the N₅₀ and N_99.9 values.  Are your calculated  N₅₀ values close to the article values? Are your calculated N_99.9 values close to the article?  For each case (N₅₀ and N_99.9), explain in your own words the possible reasons for the differences.

5) Considering that the N_99.9 values are expected to predict when less than 1 in 1000 samples will fail at a stress level, give your opinion regarding the authors’ experimental methods to achieve accurate N_99.9 predictions.  Explain in your own words what you would change for a future study to get more accurate and more reliable predictions.

Problem Set 2: Understanding Effects of New Manufacturing Methods on Fracture Toughness

· Moses J. Paul, Yokasundery Muniandy, Jamie J. Kruzic, Upadrasta Ramamurty, Bernd Gludovatz, “Effect of heat treatment on the strength and fracture resistance of a laser powder bed fusion-processed 18Ni-300 maraging steel,” (2022) Materials Science and Engineering A, 844, 143167. https://doi.org/10.1016/j.msea.2022.143167 

6) Figure 1a shows the layer-by-layer laser scanning strategy for laser powder bed fusion (LPBF) used in this study, and Figure 2 shows the resulting as-built microstructures viewed from different directions.  

a) Explain in your own words the microstructure features that might introduce anisotropy in the mechanical properties in LPBF processing that would not exist in other manufacturing methods.

b) Moses compared the mechanical properties for loading in the X and Z directions. What about loading in the Y direction? Explain in your own words how the properties for loading in the Y direction might compare to the other directions, and why.  

7) Heat treatment affected the microstructure of the LPBF maraging steel as shown in Figure 3. Of all samples, the TCA samples showed the most anisotropy in the tensile and fracture properties.  Explain in your own words why the TCA samples specifically showed the most anisotropy in mechanical properties.  

8) According to the authors, the fracture toughness values obtained for the as-built samples are not sample size independent, i.e., a different result might be expected for larger sample dimensions.

a) Why did the authors come to such conclusion?

b) After publishing this article, Moses carried out an additional R-curve test on an as-built sample with 12 mm thickness. The obtained J-integral and crack extension values can be found in the “JIc Dataset” excel sheet. Construct the J-R-curves, calculate J_Q, and check the size-requirement qualification criteria for J_IC mentioned in Chapter 7.4 of the Anderson Textbook, 4^th edition*. Show your work clearly.  

c) The fracture surface of the 12 mm thickness sample is given below. Explain in your own words the key differences that you can find when you compare this image to the results provided in the journal article.

d) Compare the J_Q value that you calculated in part (b) to the values listed in Table 3 of the journal article. If the new value is significantly different from the article, explain in your own words what causes the new value to be higher or lower using fracture mechanics theory.  

*Important note:  Testing standards get updated over time. The 3^rd edition of the Anderson textbook has outdated criteria for J_IC qualification, and we used the old 3^rd edition criteria for the workshops. For this assignment, be sure to refer to the 4^th edition of the textbook for the correct criteria. The correct criteria can also be found in the current version of the ASTM Standard E1820 (Section A9.10) which we uploaded to Moodle for your reference.