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A Simple Experiment To Demonstrate the Effects of Cracks on Materials Strength Frederick C. Sauls* Department of Chemistry and Physics, King’s College, Wilkes-Barre, Pennsylvania 18711, United States ABSTRACT: A simple in-class experiment was designed to expose students to an aspect of materials science dealing with defects. Students break a series of paper strips to gauge the breaking strength. A precut transverse “crack” weakens the paper strip by a surprising amount. Adding a precut “crack stopper” greatly reduces the effect of the original “crack”. The observations are explained by the stress lines in the paper strips. KEYWORDS: First-Year Undergraduate/General, High School/Introductory Chemistry, Upper-Division Undergraduate, Chemical Engineering, Interdisciplinary/Multidisciplinary, Hands-On Learning/Manipulatives, Materials Science, Physical Properties
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he chemistry of materials is taught at many institutions and at all levels of sophistication, from high school, college liberal arts science requirements, general chemistry, advanced undergraduate and graduate courses, through Ph.D. programs. These courses must address the problem that observed strengths of materials are far less than those predicted from their bonding and structures.1 The principal reason is that real materials do not have the perfect structures that theory assumes and that defects profoundly influence the properties of the materials. Griffith2 recognized the effects of cracks on glass strength and his insights are the basis for modern treatments of materials strengths.1,3 Gordon has written a delightful and highly accessible discussion,4 as has Eberhart.5 However, there do not seem to be any simple experiments to demonstrate the effects of cracks to assist students in translating this intellectual knowledge into a more visceral understanding.
strength. Repeating this action on strip B will lead the students to conclude that strip B is roughly twice as strong as strip A and that the breaking strength is approximately proportional to the width. The students then examine strip C with the transverse crack extending half way across the width of the paper. The students may then be led to predict that strip C should have the same strength as strip A. Their looks of astonishment when they pull this strip indicate the demonstration’s success. Strip C has virtually no tensile strength and practically falls apart. Several repetitions with new strip C’s are often required before the students are convinced of the reality of this observation. Finally the students examine strip D and note both the transverse and vertical cracks. Again students make predictions as to the strength needed when they pull the strip. When the students pull strip D, they feel it partially break, then the strip becomes much stronger, approximately equal to A. This result demonstrates that cracks may have beneficial as well as harmful effects: another counterintuitive conclusion.
’ EXPERIMENT To demonstrate the profound effects of cracks on the strength of materials, a series of paper strips are cut as shown in Figure 1. Cuts should be made with a sharp blade, not scissors. The small lateral tear that the scissors may leave at the end of the cut defeats the experiment. The paper strips should be prepared before class. This experiment can be done in the classroom with any number of students. The experiment and discussion typically take 30-45 min. Students grip strip A by the ends (at the points indicated by circles) and pull with gradually increasing force until the paper breaks. It is important that the pull be even across the width of the strip, not concentrated along one edge. This action is repeated several times until the students have a sense of the breaking Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
’ HAZARDS The only hazard associated with this experiment is the possible paper cuts. ’ DISCUSSION These effects occur because cracks deflect the lines of stress. The stress lines in strip B align with the direction of the pull Published: March 18, 2011 607
dx.doi.org/10.1021/ed1007298 | J. Chem. Educ. 2011, 88, 607–608
Journal of Chemical Education
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defects). The resulting observations lead readily into a qualitative discussion of the effects of cracks, crack stoppers, and fiber reinforcements, as well as more quantitative treatments. Students enjoyed this simple experiment and gained a deeper understanding of cracks and defects in materials.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
Figure 1. Paper strips demonstrating of the effect of cracking. The gray lines are the premade cuts. The students grip the strips by the ends (at the points indicated by circles) and pull in the direction indicated by the arrows.
’ ACKNOWLEDGMENT Jeannine Eddleton of the Department of Chemistry in the College of Science at Virginia Polytechnic Institute and State University (Virginia Tech) is thanked for checking this experiment. ’ REFERENCES (1) Tilley, R. Understanding Solids: The Structure of Materials; Wiley: Chichester, U.K., 2004; p 547. (2) Griffith, A. A. Trans. R. Soc. 1921, 221, 163–198. (3) Gersten, J. I.; Smith, F. W. The Physics and Chemistry of Materials; Wiley: New York, 2001; p 348. (4) Gordon, J. E. The New Science of Strong Materials; Princeton University Press: Princeton, NJ, 1976. (5) Eberhart, M. E. Why Things Break: Understanding the World by the Way It Comes Apart; Three Rivers Press: New York, 2003.
Figure 2. Stress concentration by cracks: stress lines are shown by the dotted lines and the cuts by the gray lines.
(Figure 2B). The transverse crack in strip C concentrates the stress lines at the end of the crack as shown in Figure 2C. The effective stress near the end of the crack in strip C is far greater than the average value in strip A. Longer cracks are more effective at stress concentration; thus, there is a critical “Griffith crack length” for any applied stress. Under this stress, such cracks will grow rapidly, causing catastrophic failure. More quantitative approaches compare the available stress energy at the crack tip with that required to form new surface area.1,3 With the understanding gained from strip C, the behavior of strip D makes sense. The stress is concentrated at the crack tip (Figure 2D) and failure occurs until the preexisting vertical crack is reached (Figure 2D0 ). Further progress of the transverse crack is thus diverted at right angles, but there is no stress in this direction, so the breakage stops. The right angle cut is a “crack stopper”. These concepts are important in both engineering practice and in everyday life. Designs of aircraft, bridges, and so forth incorporate crack stoppers. Periodic inspections place great emphasis on detecting and repairing cracks before they grow to Griffith length. On an everyday level, the ends of, for example, potato chip packages are serrated, providing stress concentrating cracks to ease opening. It is virtually impossible to open these packages by tearing across the smooth side.
’ CONCLUSION This simple experiment helps students gain a physical understanding of the strength of materials and the effect of cracks (or 608
dx.doi.org/10.1021/ed1007298 |J. Chem. Educ. 2011, 88, 607–608
