Glass Fracture Lab

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Purdue University *

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23500

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Mechanical Engineering

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Jan 9, 2024

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1 MSE 235: Fracture Lab Instructions: This lab activity will meet in ARMS 2130. Portions of this lab activity are very hazardous (see Figure 1). You will need to wear proper safety attire and it recommended that you wear no accessories on your hands. You must also tie back any long hair. Instructions for your lab report begin on page 3 of this handout. Background Reading: Sections 8.1 through 8.6 in Chp 8: “Failure” from W. D. Callister, Jr. and David G. Rethwisch, Materials Science and Engineering: An Introduction , 8 th Edition, John Wiley & Sons, Inc., Hoboken, NJ (2010); B.L. Bramfitt and S.J. Lawrence. Objectives: By the end of the lab activity, the students will be able to: ➢ operate an optical microscope and take images of micron-scale features of a glass sample, ➢ describe the operation and outputs of a 3-point fracture test, and ➢ develop a better understanding of fracture mechanics of ceramic materials Materials and Equipment: Glass rods, load frame with 3-point bending fixtures, and optical stereomicroscopes. INTRODUCTION Toughness is defined as the energy per unit volume necessary to cause fracture in a particular material. While the engineering significance of this quantity is readily apparent, the particulars of a standard test for toughness are not obvious. Measurements of the work performed to fracture a sample may vary over a wide range and are dependent upon such variables as the geometry of the experimental apparatus, the geometry of the specimen to be tested, the velocity of the propagated crack, the surface condition of the specimen, and other factors. To permit the employment of toughness as a design criterion, measurements of this quantity must be: 1. Made in a uniform, repeatable fashion. 2. Sufficiently simple and inexpensive to allow widespread use. 3. Applicable to a wide variety of materials. 4. Considerate of the many variables that can alter the properties of materials, even those of otherwise identical composition and history. Two aspects of fracture behavior will be examined in this laboratory. Fracture statistics. Brittle materials typically display a large degree of scatter in their fracture strength because of the variability in the size of strength limiting flaws. Remember that the fracture stress, σ f , is related to the fracture toughness, K Ic , by the flaw size via: 𝜎 𝑓 = ? 𝐼𝑐 √𝜋𝑎 (Eq. 1)

2 Since K Ic for a given material is roughly a constant (like many material properties, K Ic depends on temperature and microstructure), a larger flaw size, a , results in a lower fracture strength. Fracture testing of brittle materials is often conducted using bend tests. You will measure the fracture stress of glass rods using a three-point bend test (see pages 485-487 in Callister). The fracture stress is given by: 𝜎 𝑓 = 𝐹 𝑓 ? 𝜋𝑅 3 (Eq. 2) where F f is the applied load at failure, L is the distance between the inner and outer loading points of the three- point bend fixture and R is the radius of the glass rod. We will use the collected data of the class to build a histogram of fracture strength values for glass, and then use Weibull statistics to calculate a “Weibull modulus”. Referring to Figure 6.4 in “Reporting Results”, you will notice that a higher value of “m” or Weibull modulus implies a narrower distribution of fracture strength values. A narrower distribution means a narrower range of possible fracture values thereby making the material more predictable (or more reliable). A material with a small Weibull modulus has a greater variability in fracture strength making it less predictable or less reliable. LAB TASKS 1. Your TA will demonstrate flexure testing using glass rods. The tests will be conducted in three-point bending configuration. Due to safety concerns, your TAs will allow you to operate the flexure testing once they have demonstrated safe operation. 2. Measure L and R as described above. 3. Record the load at fracture (do not forget to add the force applied by the top half of the three-point bend fixture) and use L and R to calculate the strength of the glass rod in MPa. 4. Record your data in the shared google sheet. You will work in pairs or groups of 3, and your small group should record at least 2-3 different glass rods. 5. You will use the entire class data (from the google sheet) to examine the distribution of strength values in a brittle material and calculate a Weibull modulus (see Figure 1). 6. Finally, use an optical stereological microscope to record images of the fracture surfaces of at least two specimens: one exhibiting a low fracture strength and another with a high fracture strength.

3 Figure 1: Example of glass rod fracture data (black square data points) with linear equation fit (red line); slope of the linear equation fit is the Weibull modulus. Lab Report (65 pts): Your lab report should be prepared using the template on Brightspace and submitted using the appropriate assignment link. Keep in mind the important tenets of technical writing, the best practices for figure design and data displays (e.g., all images should have scale bars), and the proper methods of finding and citing information from primary sources. This lab report is worth 65 total points, 5 of which will be used to score your overall technical writing abilities . You should prepare the following for your report: Introduction (10 pts): Write one or two paragraphs introducing the lab activity. You should begin by introducing why fracture properties of materials are important in engineering design. Then, introduce common experimental methods used to determine fracture properties of materials. Finally, you should include one sentence that briefly introduces the rest of the lab report. You must include at least four references (not including Callister and ay reference materials provided by the instructor) in the introduction section to obtain full credit. Experimental Methods (15 pts): Write one paragraph that fully describes the materials, machine(s), and methods you used/performed during the three-point bend testing. Results and Discussion (30 pts): ➢ Using the data of fracture strength values for glass rods from the entire class please complete the following: o A histogram (with a caption) showing the distribution of strength values collected by the class. (5 pts) 5.0 5.5 6.0 6.5 -3 -2 -1 0 1 Weibull Parameter Ln(Stress, MPa)

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4 o A plot of failure probability vs. applied stress similar to Fig. 15.3 in the “Weibull Statistics” reading posted on Brightspace. The failure probability (F) can be estimated by 𝑛 𝑁+1 where n is the ranking of a given sample (e.g., for 80 samples, sample 1 would be the sample with the lowest strength and sample 80 the highest strength) and N is the total number of samples in the data set. At first it might seem odd that the lowest strength value is assigned the lowest probability of failure. Think of it this way: If the stress is below the fracture stress of the weakest sample, the probability that a given sample will fail at such a low applied stress is essentially zero. The stress causing failure in the strongest sample will always result in failure (at least for that group of samples). Therefore, the probability of failure at an even larger applied stress is 1. (10 pts) o Make a plot of lnln[1/(1- F )] vs. ln σ (see Fig. 15.5 in the “Weibull Statistics” reading). The slope of the linear portion is m, the Weibull modulus. Determine the slope and provide the value of m along with your plot. (10 pts) ➢ A figure of the fracture surfaces of two specimens: one exhibiting a low fracture strength and another with a high fracture strength (10 pts) ➢ Write a short paragraph (less than 250 words) that reports/discusses the following: (15 pts) o Compare your Weibull modulus results to other ceramic materials o Compare the fracture surfaces of the low fracture strength to high fracture strength specimens. o Describe the appearance of the fracture surface and where the fracture initiated. References (5 pts): Be sure to include your references here using a consistent and appropriate format. Include at least four references.