Exploring Tensile Strength of Materials using Chalk as a Case Study

Shane Clarkson, Beth Rieken, Dr. Mark Schar, Dr. Sheri Sheppard

Often, we like to think of engineering as providing us with the “exact answer” to a given problem, when in reality, engineering analysis helps us to better approximate solutions to complex, real-world questions. My work this summer centered on designing a lab for introductory engineering students to explore the tensile strength of standard, white Crayola blackboard chalk (see Figure 1) by measuring the force required to break the chalk under different loading configurations. Student data will be added to a running data set that approximates the true tensile strength of the chalk.

•  Begin the lab by watching the instructor break a piece of chalk on the Vernier Structures and Materials Tester (VSMT), a force measurement machine (see Figure 5)

•  Break into lab groups and use the tube scales and fishing leader (Figure 6 above) to record the amount of force required to break the chalk under a centered 3-point load (see Figure 7)

•  Data set and relevant statistics for chalk fracture

•  Lab Steps sheet detailing the flow of the lab

•  Student worksheet to fill out during lab, including bending moment equations, free body diagrams, and percent errors

•  SolidWorks file for a chalk holding apparatus (see Figure 12)

Through experimentation and calculation, students will: •  Connect concepts of fracture force and material strength •  Translate this understanding into shear and bending

moment diagrams •  Acquire hands-on experience with data variability •  Analyze data and consider implications of variability

Load Type Tests (n) Average Measured

Fracture Force

Theoretical Fracture

Force

Difference Average Measured Fracture σ

Theoretical Fracture σ

Difference

3-point center

24 11.74 N Base -- 2.33 MPa Base --

3-point offset

20 11.87 N 13.21 N +1.34 N 2.10 MPa 2.33 MPa +0.23 MPa

4-point 22 15.17 N 17.63 N +2.46 N 2.02 MPa 2.33 MPa +0.31 MPa

Introduction

Learning Objectives

Lab Procedure

Lab Setup Students will break the chalk using 20 N capacity tube scales along with sturdy loops of fishing leader. Using the provided chalk holding apparatus, students will break the chalk using a centered 3-point load, an offset 3-point load, and a 4-point load (see Figures 2-4).

Testing Results

Outcomes

•  Repeat for an offset 3-point load (1 cm offset from center)

•  Repeat for a 4-point load (evenly spaced at 2-cm intervals, see Figure 8)

•  Calculate the chalk’s tensile strength for each case (using the equation shown below)

•  Compare results both to fellow lab groups and to previously recorded results.

•  In addition to tensile strength calculations, students derive bending moment equations, sketch free body diagrams, and utilize engineering insight to answer questions during the lab

The table below summarizes the data obtained through experimentation and calculation with the VSMT. Two boxes of chalk were used for each load type, corresponding to 24 pieces of chalk. Some samples were excluded due to preexisting faults, among other reasons. Results from the 3-point center loading were extrapolated to calculate theoretical values of fracture force and tensile strength. We see some variability, but reasonable agreement between measured and theoretical values, as noted by the minimal differences.

Acknowledgments Thank you to the SURI program for the opportunity to pursue this work, to Dr. Sheri Sheppard and the entire Designing Education Lab for directing my research, and to Dr. Mark Schar for continued guidance in bringing everything together!

Figure 1: Crayola chalk

Figure 2: Center 3-point load

Figure 4: 4-point load

Figure 3: Offset 3-point load

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σ =MmaxyI

Figure 5: VSMT overview Figure 6: Tube scale

Figure 7: Sketch of testing setup for centered 3-point load

Figure 8: 4-point on the VSMT

Figure 12: Chalk testing apparatus

Free Body Diagrams

Figure 9: Center 3-point load FBD

Figure 10: Offset 3-point load FBD

Figure 11: 4-point load FBD

Figures 9-11 below depict free body diagrams for the loading configurations.