27-301 Lab. 2 November 27, 2007

1

DEPARTMENT OF MATERIALS SCIENCE

AND ENGINEERING

CARNEGIE MELLON UNIVERSITY

27-301

Microstructure & Properties

September-November 2007

LABORATORY MANUAL

Experiment No. 2B:

Microstructure-Sensitive

Mechanical Properties in Wood

revised: ADR: Aug. ‘07

27-301 Lab. 2 November 27, 2007

2

Abstract

The main objective of this Lab is to stimulate students to learn how to optimize materials

properties in situations where multiple properties must be considered. By choosing a

pair of mechanical properties, toughness (Charpy) and strength (microhardness, verified by tensile testing), the students will also learn practical skills in testing of materials

properties. The various groups of students will work on different types of materials and

share their results. The objective of property optimization is both a useful exercise in the

integration of theoretical with practical knowledge and a useful preparation for the

Capstone Course with its Design component. Mechanical properties have chosen for this exercise because they are the basis for

many practical engineering applications. As an example to be described for Charpy

Impact testing, the lifetime of nuclear reactors is dependent in a critical and very direct

fashion on the toughness measured on pressure vessel steels as it changes with time (and irradiation). At a more detailed level, the microstructure of many materials can be

drastically changed through simple heat treatment and so steels (Fe-C alloys) have been

chosen to illustrate these variations in experiment 2A. Experiment 2B, described here,

addresses composite (and bio-)materials, and a much ignored material is wood. Its

properties are strongly anisotropic (sensitive to direction): it is almost intuitive that wood is stronger along the grain than perpendicular to it. Moreover, its strength is extremely

sensitive to the environment, especially the humidity level, which is again almost intuitive

but interesting to quantify. In this respect, wood is representative of many biomaterials in

its dependence on water content.

1. Introduction 1.1 Reading There is an enormous literature on this subject. The course text by Porter & Easterling gives a large amount of useful information. Also the text by Tom Courtney, Mechanical Behavior of Materials, is very helpful. 1.2 Objective of the Experiment The objective of the experiment is to show you, the student, how to manipulate microstructures in a given material, and how strong an effect on the properties this can have. This demonstration relies on a traditional structural material – wood. You as a materials engineer will be expected to understand and control the properties of materials such as wood. Your ability to do this depends on your grasp of the microstructure-

27-301 Lab. 2 November 27, 2007

3

properties relationships in this and any other system that you deal with. This experiment will illustrate some of the key aspects of mechanical behavior of composite materials and biomaterials. 1.3 Desired Educational Outcomes This set of experiments addresses several of the MSE Outcomes for the Undergraduate Program. Outcome D, “An ability to design and conduct experiments with an emphasis on relating properties and processing to structure” is most directly addressed by requiring students to perform experiments and analyze their own data. Outcome F, “An ability to function responsibly and ethically in a professional, multidisciplinary environment and as an individual or as a member of a team” is addressed by requiring students to perform the experiments in teams (3 per group) and share the workload of analysis and reporting. Outcome G, “An ability to employ the techniques, skills and tools of modern materials engineering practice” is addressed through hands-on training on instrumentation. Outcome C, “An ability to communicate effectively” is addressed by requiring the students to communicate their results with their own analysis through either presentations (for this second Lab) or written reports. Finally Outcome B, “An ability to apply core concepts in materials science (structure, properties, processing and performance) to materials engineering problems” is addressed through requiring students to relate their findings back to the basic principles discussed in the lecture part of the course (27-301). 1.4 This Document This document contains several sections with general information on mechanical behavior in metallic systems. Mr. H. Greenberg (former Industrial Internship Coordinator in MSE) is acknowledged for assembling the text. It has been retained in order to provide a basic introduction to the relevant materials science for this experiment. Students should, however, expect to read additional material. 1.5 Planning the Experimental Work Before performing experiments, you will be required to learn how to use the equipment safely and accurately. You will also be required to do some background reading, mainly focused on the properties of wood, its anisotropy and its sensitivity to moisture content. Then you must devise a plan for how you are proposing to proceed (see Outcome D above!) and what your expected results may be. Only after one of the Course Assistants and the Instructor have approved your plan will you be permitted to perform experiments. 1.6 Preparation Before the Laboratory Sessions The wood experiments and the tensile testing experiments do not require any pre-Lab work. Note however, that it is important to perform the wood testing on two days that are reasonably close together in order to be able to dry some specimens (for low moisture content) and soak others (for high moisture content). 1.7 Distribution of Experiments, Samples Optimization of mechanical properties. In Fall 2007 there are 9 groups. Of these x will perform the property optimization exercise with steel samples and 9-x will perform them with wood samples (x TBD). The wood properties will be strength and modulus with moisture content as the major variable. Since moisture content is not exactly a microstructural parameter, evaluation of the anisotropy of the properties with compression tests will be required in addition in

27-301 Lab. 2 November 27, 2007

4

order to quantify the effect of microstructure. For the experiments with wood, the objective is to maximize the product of strength (measured in MPa) and toughness (measured in Joules). Lastly, you are encouraged to perform the supplemental experiments on cork to find out why its Poisson’s ratio is so interesting (e.g. for bottle stoppers).

27-301 Lab. 2 November 27, 2007

5

2. INTRODUCTION 2.1 Purpose

The purpose of this manual is to help the student become proficient in experimental skills and to provide him/her with some practical applications of material discussed in lecture courses. In this volume you will find instructions for the experiments to be performed this term as well as some background material both for working in the laboratory and for the experiments. In this laboratory course considerable emphasis is placed on the formal technical report. Details for the format and content of the various sections of a report are presented in the Course Syllabus; please review them each time you write a report for this course. 1.2 Experimental Planning The following comments are extracted from Holman†. They are considered significant enough to be reproduced here. “The key to success in experimental work is to ask continually:

1. What am I looking for? 2. Why am I measuring this? 3. Does the measurement really answer any of my questions? 4. What does the measurement tell me?

These questions may seem rather elementary, but they should be asked frequently throughout the progress of any experimental program. Some particular questions which should be asked in the initial phases of experiment planning are:

1. What primary variables shall be investigated?

2. What control must be exerted on the experiment?

3. What ranges of the primary variables will be necessary to describe the phenomena under study?

4. How many data points should be taken in the various ranges of operation to ensure good sampling of data, considering instrument accuracy and other factors?

5. What instrument accuracy is required for each measurement?

† J.P. HOLMAN, EXPERIMENTAL METHOD FOR ENGINEERS, 2nd edition, McGraw Hill Book Go., New York, 1971.

27-301 Lab. 2 November 27, 2007

6

6. What safety precautions are necessary if some kind of hazardous material or operation is involved in the experiment?

7. What provisions have been made for recording the data?”

2.3 Basic Concepts Materials science can conveniently be thought of as involving four inter-related concepts: structure properties performance processing Remember that the purpose of this course is to make connections between structure (microstructure) and properties.

2.3.1 Structure

Structure can be at several levels starting with the discrete electron energy levels within individual atoms,

or the energy bands associated with an aggregate of atoms (solid, crystalline or not, or liquid but not a gas

at normal pressures - the atoms/molecules are too far apart). Crystal structure is important and results

from a balance between packing of atoms or molecules, (sometimes of different sizes) and directionality

(anisotropy) associated with certain types of bonding (usually covalent).

Defects in the structure such as vacancies, dislocations, grain boundaries and inclusions are important on

a scale generally bigger than atomic dimensions. Some of these defects also influence transformations by

changing rates (such as diffusion) or by offering preferred sites for nucleation of a new phase.

On an even larger scale, cracks or holes sometimes big enough to be visible to the naked eye can also be

present. These are important in that they can lead to premature failure.

2.3.2 Properties There are many properties that can be of interest depending on the application we have in mind. It is convenient to make a distinction between those which are: a) structure-sensitive - e.g. the yield strength of a material depends on such factors as the dislocation density, crystal structure, or grain size and b) structure-insensitive - e.g. the modulus, or density are (to a very good approximation) independent of imperfections in a given crystal structure. They do depend however on crystal structure, e.g. whether iron is present as fcc or bcc. Moreover, most structure-insensitive properties are anisotropic, as discussed in 201 (Perfect Crystals) and 301 (this course), which means that the arrangement of crystals in a material (texture) controls the degree of directionality of a property.

27-301 Lab. 2 November 27, 2007

7

In general, we will be interested in properties of the following types:

mechanical electrical magnetic chemical optical

2.3.3 Performance It is usually fairly simple to select a material that will meet the obvious initial requirements of a service application. For example, if we are designing a bridge, we need to consider:

1. What loads will be applied - by the weight of the bridge itself and the maximum traffic expected? This leads us to a design with materials of specified dimensions, yield stress, and fracture toughness.

2. What will be the corrosive conditions that might reduce cross-sections of certain

important structural members? 3. Can the materials being considered be effectively joined by welding or other

techniques without causing dangerous conditions e.g. cracks or stress concentrations?

4. Service frequently involves intermittent loading by the nature of traffic and thus

we must consider fatigue strength. This is much more difficult - it is hard to identify cyclic stresses accurately and thus we necessarily must be conservative resulting in a bridge heavier and more expensive than really needed.

5. We need to consider which aspects of structure and properties will give us the

most confidence in providing satisfactory performance over the expected life of the product, especially in situations where time of exposure causes changes to the structure (e.g. fatigue) or dimensions (e.g. corrosion).

2.3.4 Processing

There are many practical (and some rather impractical!) ways of obtaining a

particular structure at an acceptable cost. These can include: 1. solidification (I →s) 2. vapor deposition (g →s) 3. mechanical deformation (introducing dislocations, changing grain shape,

changing orientation textures) 4. heat treatment (changing phases present, often not at equilibrium; recovery,

recrystallization and grain growth in homophase solids). Occasionally, some of these are used simultaneously e.g. one can be deforming a material immediately before, or during, phase changes occurring during heat treatment.

27-301 Lab. 2 November 27, 2007

8

Often structure, properties, processing and performance are displayed as a tetrahedron to indicate that each can influence or be influenced by all of the others.

2.4 Recording Data

It would seem obvious that very careful provisions should be made to record the data and all ideas and observations concerned with the experiment. Unfortunately, many experimenters record data and important sketches on pieces of scratch paper or in such a disorganized manner that they may be lost or thrown away. In some experiments the readout instrument is a recording type so that a record is automatically obtained and there is little chance of loss. For many experiments, however, visual observations must be made and values recorded on an appropriate data sheet. This data sheet should be very carefully planned so that it may subsequently be used, if desired, for data reduction. Frequently, much time may be saved in the reduction process by eliminating unnecessary transferral of data from one sheet to another. A bound notebook must be maintained to record sketches and significant observations of an unusual character which may occur during both the planning and the execution stages of the experiment. The notebook is also used for recording thoughts and observations of a theoretical nature. Upon completion of the experimental program, the well-kept notebook forms a clear and sequential record of the experimental planning, observations during the experiment, and where applicable, correspondence of important observations with theoretical predictions. Every experimenter should get into the habit of keeping a good notebook; it will be graded twice during the course. It is not critical that the entries in your notebook be in extremely tidy form. However, they should be legible and permanent, i.e. pencil is not satisfactory because it can be erased. Use a pen, and if you make mistakes, cross them out neatly and firmly and do the portion again. Don't be afraid to make sketches even if your artistic talents are marginal - pictures are often better than words to convey results. Start each page (or experiment) with the date and the purpose of your exercise as you understand it. This can be done before you attempt any work, and it may help you to be sure you do understand what you are about to do. Follow this with sufficient detail of what you did so that someone reading it could reproduce it. e.g. “We weighed out 201.8 g of Al shot on a scale and added 9.7 g of copper powder to it in a crucible made of ceramic. The crucible was placed in a closed furnace whose temperature was 850±10°C. After the crucible contents were molten (17 minutes), we stirred the liquid and ...”

27-301 Lab. 2 November 27, 2007

9

Note the important details are underlined. You do not need to do this but the items illustrate the sorts of things it is important to include - mass, temperature, times, pieces of equipment, methods, etc. At the next stage, if there is one, you may do other things to your specimen. Write these down as above. Eventually you will have a result (or results). This can be recorded as numbers, if appropriate - perhaps as a table - or as a sketch or as a photograph. Remember you are trying to convey as much information as you can to a later reader (who may be you). Let us use a tensile test as an example. Record the initial width, thickness, and gauge length of the specimen. After pulling the specimen, perhaps to fracture, remeasure these dimensions. You will also need to note some important values from the chart printed out from the testing machine which should be pasted in your notebook along with the parameters of the test such as crosshead speed, etc. You will need to calculate various standard strength and ductility characteristics from the chart readings. Be careful not to mix units. We should all be using SI units but US units are still with us. Whichever you use, be consistent, i.e. do not end up with Kg/inch2. If you have data from enough samples, it is always a good idea to calculate statistical data such as averages and standard deviations. If you do not calculate values in lab class, but plan to do so at some later time, leave enough space in your notebook to enter the calculations before starting to write on the next topic in lab so the data for one experiment are not intermixed with data from another. At this stage, you need to consider what you have learned. Do the results make sense, or is there an obvious error? A number may not fall in a regular progression. Did you make a mistake in writing it down (happens a lot!) or is there some less obvious explanation? Do you understand what your results mean? Were they more or less what you expected - or were led to expect by the instructor? After studying the results, write down your comments, being careful to distinguish between things you feel sure about and those where you are speculating. Speculation, hypothesis, and “what-if” thinking are an important part of science and engineering because they suggest experiments which you might try to get a better understanding of the subject at hand. It is important that you and other readers know when you are speculating, so be sure to make it clear. Finally, look over the whole experiment and see if you could have done something differently or better. Maybe the plan suggested in the handout could be improved, or the equipment was not working well. It is rare that things are so perfect that they can not be

27-301 Lab. 2 November 27, 2007

10

improved - even at CMU! In any case, write down your thoughts on deficiencies in the experiment.

27-301 Lab. 2 November 27, 2007

11

3. LABORATORY POLICIES AND SAFETY 3.1 Policies 1. No alterations of the equipment may be made without the consent of the instructor.

Suggestions for improving the operation of equipment are always welcome. 2. Any necessary equipment (glassware, thermometers, etc.) and tools, if not already

available, must be obtained from an instructor, teaching assistant or laboratory technician.

3. At the end of each laboratory period, groups are responsible for making sure that

water, air, electricity, etc., are shut off and benches and sink tops are clean. 4. All glassware, tools, stopwatches, etc., must be returned to the proper cabinets and

locked up at the end of each laboratory period. Such items have a remarkably high vapor pressure, and will evaporate completely if left standing in the open. Each group member is responsible for all equipment charged out to the group. Failure to return equipment will result in financial assessment.

5. Do not “borrow” any tools or equipment from other laboratories. Report to an

instructor if anyone not in your section “borrows” tools or equipment belonging to the MSE Lab.

6. Students are expected to be familiar with the operation of all experimental

equipment. 7. Make sure that you understand the functions of all pieces of equipment before

beginning an experiment. If there are any questions at all about the operation of equipment, ask an instructor.

8. Feel free to ask questions or the advice of the instructor or professor in charge, and

if you wish, come in and inspect the equipment ahead of time. 9. All data are to be recorded in bound laboratory notebooks. You may be required to

produce this notebook at any time. It must be kept well organized and neat. The use of paper towels or other slips of paper for data recording will not be tolerated.

27-301 Lab. 2 November 27, 2007

12

10. Please notify an instructor when the supply of an expendable material runs low, or when something is broken. Irresponsible usage of equipment or of supplies (films, etc.) will result in financial assessment to the group.

11. All reports assigned must be submitted to complete the requirements of the course.

An incomplete report will not be averaged with other reports to give a passing grade. 3.2 General Background for Safety A prime requisite for all laboratory operation is conscious application of safe practices at all times.

Toleration of unsafe practices is not consistent with professional standards. The following rules are

applicable:

1. Pennsylvania law requires that safety glasses be worn at all times in the laboratory when there is an

eye hazard possibility. You should acquire your own pair. 2. No smoking is permitted in the laboratory. 3. No physical "horseplay" will be tolerated. 4. No experimental work can be performed unless an instructor is present in the laboratory or

permission is otherwise granted. 5. Familiarize yourself with the location and operation of fire extinguishers and other safety devices. 6. Watch your step in the laboratory. There are numerous irregularities in the grating and pipes across

the floor. Wet floors are very slippery. 7. Clean up all spills immediately. 8. No food or drink is permitted in the laboratory. 9. Prepare and mix all chemicals in the fume hoods. 10. In order to protect your clothing, lab coats should be worn in the laboratory.

3.3 Safety Practices and Procedures This is a summary of Safety Practices and Procedures. You are encouraged to review the Carnegie Mellon University Safety Manual in the MSE Office for additional information. The responsible faculty member or technician must be consulted prior to the performance of laboratory work of any kind. Many of the hazards in metallurgical laboratories are similar to those found in chemistry, electrical or mechanical laboratories. Solids or liquids at very high temperatures, for example, require special awareness. The safety practices concerning the handling of laboratory glassware and chemicals, the use of safety glasses, and respiratory and fire hazards as discussed in the American

27-301 Lab. 2 November 27, 2007

13

Chemical Society publication, “Safety in Academic Chemistry Laboratories”, are applicable to the MSE Laboratories and are a part of this manual. Also, the new second edition of “CRC Handbook of Laboratory Safety” is available in DH A320. To see either of these, contact Tom Gambal on ext. 8-2690. Upon entering a laboratory, a student should familiarize himself/herself with the safety features available in case of emergency, e.g.:

1. The location of fire extinguishers, their type, and method of operation; fire escape

routes, etc. 2. The location of emergency eye-wash fountains and safety showers. 3. The location of the nearest telephone. To report a fire or obtain help in other

emergencies, call Security Services, ext. 8-2323.

The following practices should be observed.

1. All bottles and containers should be properly labeled. 2. Keep all chemicals away from heat and sunlight. 3. Keep insoluble materials out of sinks and drain lines. 4. Keep the area clean and neat.

Working in a laboratory alone is hazardous. When working unusual hours, arrange with an associate to check on each other from time to time, or arrange for periodic checks by Security Services, ext. 8-2323. 3.4 Machines and Equipment

1. Machines or equipment should not be operated by anyone who is not completely familiar with the proper operating procedures.

2. Do not use equipment without the permission of the person responsible for the

laboratory. 3. When working around moving machinery, secure loose clothing - ties, sleeves,

etc. 4. When working with saws, rolling mills, etc. never push material directly with the

hands; use a wooden push stick to manipulate the workpiece. 5. Never use tongs with finger loops near rolling mills. Use straight-handled tongs to

move material from a furnace to the rolling mill work table. 6. Wear a face mask and/or goggles when a hazard exists.

27-301 Lab. 2 November 27, 2007

14

3.4.1 Cutting Equipment

1. Wear a face mask or goggles to protect your eyes from flying particles, or a piece

from a broken wheel. 2. When using a cutoff wheel, securely damp the piece being cut. 3. Give particular attention when placing a specimen on the polishing wheel or belt

sander. It may be wrenched from your hand. With small pieces use a vise, vise grips or pliers to protect fingers and hands.

4. Do not try to retrieve a loose specimen from a polishing wheel while it is running.

3.4.2 X-Ray Operating Procedure 1. Only authorized persons may operate X-ray equipment. Obtain authorization from

the technician in charge of X-ray equipment (Jason Wolf), or from the faculty member responsible for X-ray laboratories.

2. Persons using X-ray equipment must be completely familiar with the operational

instruction manual for the X-ray unit used. They must know and understand all the information on X-ray radiation warnings, which is given in the instruction manuals.

3. Any person wishing to use an X-ray machine must inform the laboratory

supervisor or X-ray technician as to the type of unit and target needed. He/she must sign the log book established for the instrument prior to each use of it.

4. Each operator who sets up the X-ray cameras and other equipment must place

lead shielding around the cameras, set timers for automatic shutoff and leave the area until exposure is completed. All switches, including the mains, must then be turned off. It is strongly recommended that safety glasses be worn during the alignment and adjustment of the X-ray cameras and tracks.

5. A survey meter is available for checking the alignment of the X-ray cameras and

for determining the presence of scattered radiation. 6. No other work is to be performed in areas where X-ray units are in operation.

This restriction does not apply to the diffractometer, where an operator may have to be present continuously.

7. Warning lights have been installed inside and outside each room and must be lit

when and X-ray unit is in use. 8. Because of the danger of electrical shock, equipment is not to be disassembled,

or tubes removed or replaced, without the technician or the responsible faculty member being present.

9. In the case of prolonged research, wear film badges to detect your exposure level

and to assure that your protection is adequate.

3.4.3 Hydrogen Hazards

27-301 Lab. 2 November 27, 2007

15

Hydrogen is particularly dangerous. Its presence cannot be easily sensed. It accumulates easily in amounts that can cause a violent explosion. In explosive mixtures it ignites readily.

1. All users of hydrogen must know where to turn off the hydrogen supply to their equipment. The valve must be located where it can be easily and safely reached during emergencies.

2. Never use pressures higher than those approved by the supplier. 3. Do not expose lines to mechanical damage or to high temperatures. 4. All hydrogen lines and hydrogen valves must be clearly identified with red tags.

3.5 - MSE Undergraduate Laboratory Facilities MSE undergraduate laboratories are housed in DH A300, DH A311 and DH A320. Mr. Tom Gambal (Office: DH A320) is responsible for the upkeep of this laboratory facility, including all experiments, chemicals, etc. Every student must become familiar with the location and operation of all equipment used in a given experiment prior to performing any experimental work. Expendable supplies are furnished free-of-charge to the students; however, some of them are relatively expensive and should be used judiciously. For example, make certain that samples are securely clamped in the vise of the cut-off machine so as not to break the abrasive wheel; abrasive discs and polishing cloths can be used for more than one sample; also, be certain that your sample is well polished and etched before photographing it.

27-301 Lab. 2 November 27, 2007

16

4. MECHANICAL PROPERTIES H. Greenberg

Mechanical properties are the characteristic responses of a material to applied stresses. Selection of mechanical tests for a particular application is based primarily on experience that many lots of a particular grade of material having properties falling within a certain range have performed satisfactorily in service. It can then be anticipated that new lots of this same material having the same mechanical properties will also perform satisfactorily in the same application. 4.1 Definitions

1. Strength - ability of a material to resist applied forces. 2. Ductility - ability of a material to undergo permanent shape change (plastic

deformation) without rupturing. 3 Toughness - ability of a material to absorb energy. 4. Tension test - simultaneously measures strength and ductility. There are several

types of tensile machines and test specimens. 5. Modulus of elasticity (Young's modulus) - the proportionality constant between

stress and strain - the slope of a plot of stress vs. strain within the elastic range – 90 GPa for steel.

6. Yield Strength - 0.2% offset is normally specified for a tensile test since it is too difficult to accurately measure the elastic limit. Speed of loading affects yield strength but not tensile strength.

7. Yield point - the stress in a material at which a marked increase in strain occurs without an increase in stress.

8. % elongation in 1" or 2" is usually determined by fitting the fractured specimen back together and measuring the distance between scribe marks - % elongation increases with shorter gage lengths.

9. % reduction of area (RA) is the ratio of the minimum cross-section of a tensile specimen after fracture to its original cross-section.

10. Shear stress is approximately half of the ultimate tensile strength for steel. 11. Hardness - resistance to deformation or penetration by a much harder indenter.

4.2 Mechanical Property Testing The tests most commonly used in evaluating the quality of metal products include the tension, hardness, notched-bar impact, creep, and fatigue tests. Other types of tests (e.g. bend, cupping, KIc, etc.) may be used depending on the particular product or its intended application.

27-301 Lab. 2 November 27, 2007

17

One of the primary purposes, in making mechanical property tests of metal products, is to determine conformance or non-conformance with specifications. The data may thus serve as an index to the quality of a product in comparison with similar products obtained previously. Since variations in the methods used in preparing test specimens may have a significant effect on the test data, it is essential that careful and uniform procedures be followed in machining and finishing test specimens. Procedures should be used that will not cause temperature changes or distortions which, in turn, would affect appreciably the mechanical property values.

4.2.1 Hardness Tests (From R.A. Flinn and P.K. Trojan, Engineering Materials and Their Applications, 2nd Ed., Houghton Mifflin Co., 1981, p. 79-82). Hardness is usually defined as resistance to penetration. Let us review a few of the most common tests (see Figure 4.1) and see how closely they fit this definition.

FIGURE 3.1: Hardness Testing Methods

4.2.1.1 Brinell Hardness Number (BHN) This is one of the oldest hardness tests but is still the most common standard. In this test method, a specimen with a flat upper surface is placed on an anvil. A steel or tungsten carbide ball is pressed into the sample with a load of either 500 or 3,000 kg. The lighter load is used for the softer nonferrous metals such as copper and aluminum alloys, and the heavier load is used for cast iron, steel, and other hard alloys. The load is left in

27-301 Lab. 2 November 27, 2007

18

place for 15 sec. for steels or 30 sec. for softer materials, and then removed. The diameter of the impression in millimeters is then read with a low-power microscope with a Filar (measuring) eyepiece. Next the observer reads the Brinell hardness number (BHN) that corresponds to the impression's diameter from a table of values for the load used. The more difficult the penetration, the higher the BHN. The hardness conversion table has been developed such that the BHN is about the same whether the 500- or 3,000-kg load is used, although obviously the impression diameter is different. The lighter load is used for aluminum and copper alloys because in very soft materials the ball with a 3,000-kg. load will continue to penetrate until it is deeply sunk into the surface.

4.2.1.2 Vickers Hardness Number (VHN) or Diamond Pyramid Hardness (DPH); a.k.a. Microhardness This is an improvement on the Brinell test. Here, a diamond pyramid indented is pressed into the sample under loads much lighter than those used in the Brinell test. The diagonals of the square impression are read, and averaged, and the Vickers hardness number (VHN) is read from a chart for the specific load. As shown in Fig. 4.2, the VHN is close to the BHN from 250 to 600. The figure does not show that the VHN climbs steadily with hardness at higher values, whereas the BHN is not used above 600. The advantages of the Vickers test are in greater accuracy, capability of obtaining hardness measurements at high levels, and in measuring the hardness of a small region. On the other hand, the BHN gives a better averaging effect because of the larger impression. Finally, one significant advantage of the microhardness test is that by dividing the load (and multiplying the mass by the acceleration due to gravity to obtain force) by the area of the indent, a value with units of stress can be obtained. This can then be related to yield stress or ultimate strength measured in a tensile test.

27-301 Lab. 2 November 27, 2007

19

FIGURE 3.2: Conversion values for Brinell, Vickers, and Rockwell Tests

4.2.1.3 Rockwell Hardness Testing (RA, RB etc.) The chief advantage of the Rockwell test is that the hardness is read directly from a dial. The indenter for the RC test is a suitably supported diamond cone or "Brale". The observer first turns a handle which presses the diamond cone a slight standard amount into the sample. This is called the "preload". Next the standard RC load of 150 kg is released. This forces the diamond farther into the sample. The same lever is used to remove the load. At this point the observer reads the RC hardness from the dial and then unloads the specimen. The principle of this test is that the dial, through a lever system, records the depth of penetration between the preload and the 150-kg load and reads directly in RC. The RC is approximately 1/10 BHN. The RB scale is used for softer materials. It employs a 1/16 -in. diameter ball and a 100 kg load. It is also direct reading. The RA scale is similar to RC except a 60 Kg load is employed; likewise, the RF scale is similar to RB except a 60 Kg load is used. There are also Rockwell Superficial tests

27-301 Lab. 2 November 27, 2007

20

utilizing 15, 30, or 45 Kg loads and either a diamond (N scales) or a 1/16" steel ball (T scales) as the indenter. 4.2.2 Tension Tests (by M. Stevens) The tension test is the most common characterization method used for determining design information on the strength and ductility of metals as well as for acceptance determinations in quality assurance applications. In a tension (or tensile) test, a specimen is subjected to a continually increasing uniaxial tension force while simultaneous observations are made of the elongation of the specimen. This is physically accomplished by mounting a machined specimen of the material of interest into mechanical "grips" which are attached to a load frame. One of these grips is mounted to a moving crosshead which is operated by two vertical lead screws which are rotated in a suitable direction by a servo-motor. Electronic instrumentation provides control signals to the servo-motor in order to control crosshead speed, direction of test, etc.... An additional feature included in the load train is a highly sensitive electronic load weighing system with load cells that use strain gages for detecting tensile or compressive load on the specimen. Similar strain gages are used on extensometers which may be attached to the specimen during testing in order to accurately measure elongation (strain). The load, or stress, on the specimen is subsequently plotted as a function of elongation or strain to constitute a stress-strain curve. The shape and magnitude of the stress-strain curve of a metal will depend on its composition, prior thermomechanical processing, strain rate, temperature and state of stress. The important parameters which can be deduced from a stress-strain curve include the yield strength, tensile strength, and percent elongation. These are indicated on the representative stress-strain curve shown in Figure 4.3.

27-301 Lab. 2 November 27, 2007

21

FIGURE 4.3: Stress-strain curve, after Courtney

The initial part of the curve represents the elastic regime of the material. If the load is released, the strain of the specimen will return to zero and no permanent deformation occurs. The slope of this part of the curve is called Young's modulus or Modulus of Elasticity. Further imposed strain results in a bending over in the curve and this denotes the onset of permanent plastic deformation. The yield strength is a measure of the stress required for permanent plastic flow. The usual definition of this property is the offset yield strength determined by the stress corresponding to the intersection of the curve and a line parallel to the elastic part but offset by a specific strain (usually 0.2%). Beyond this point, the material work hardens until the ultimate tensile strength is attained. At this point, the incremental increases in stress due to decrease in cross-sectional area becomes greater than the increase in load carrying ability due to strain hardening. Starting at this point, all further strain is concentrated in the "necked"" portion of the specimen.

27-301 Lab. 2 November 27, 2007

22

As measures of ductility, the reduction of area at fracture and the elongation to fracture are used as percent reduction of the original area and percentage increase of the original gage length. The percentage reduction of area at fracture is only slightly affected by the shape of the tensile test specimen. As long as the ratio of the width to thickness does not exceed about 5:1, for a rectangular cross-section, the percent reduction of area remains the same as for circular cross-sections. Elongation to fracture is usually measured by fitting the broken specimen back together and measuring the distance between punch or scribe marks. Elongation may also be taken from an autographic record of the load-extension diagram; the two do not necessarily agree. Elongation is so much affected by the gauge length over which it is measured that the gauge length must always be specified when reporting data. Variations in ductility from specimen to specimen, and from point to point and with direction in the same specimen are often considerable and are almost always greater than variations in the other tensile properties. Tests taken transverse to the direction of greatest elongation in working are generally inferior in ductility, often considerably so. Some useful definitions: ENGINEERING STRESS σ = P/Ao where P = Load Ao = Original cross-sectional area

ENGINEERING STRAIN E = L-LoLo

where L is instantaneous length and Lo is original

length of specimen

4.2.3 Charpy Impact Testing The Charpy test is the most widely used evaluation technique for measuring the toughness of materials; it utilizes impact loading conditions. Standard-sized specimens (10 mm sq x 60 mm long) containing a sharp notch (2 mm deep with a .015 mm radius) to localize the stress, are hammer-impacted and the energy absorbed during this fracture process is measured. As the pendulum hammer has a fixed weight and drops the same distance each time (see Figure 4.4) its kinetic energy when it strikes the specimen is always the same. Part of this energy is consumed in breaking the specimen; the energy remaining in the hammer causes the pendulum to continue its upward swing. By measuring the difference in the height of the upward swing after the pendulum has fallen

27-301 Lab. 2 November 27, 2007

23

freely and after it has broken the sample, the energy absorbed in breaking the sample may be calculated. This energy is the impact strength of the material and can be read directly from a dial gauge on the machine.

FIGURE 4.4: Operation of a Charpy impact test (from Hayden et al. The Structure and Properties of Materials, Vol. 3, Mechanical Behavior, John Wiley and Sons, 1965)

"The types of data obtained are shown schematically in Figure 4.5. FCC metals show high impact values and no significant change with temperature; however, BCC metals, polymers, and ceramics show a transition temperature below which brittle behavior is found. It should be emphasized that the actual transition temperatures for different materials vary greatly. For metals and polymers it is generally between -200 and 200°F (-129 and 93°C), while for ceramics it is above 1000°F (538°C)."***

FIGURE 4.5: Effect of temperature on the impact strength of various materials (schematic). From H.W. Hayden, et al., The

Structure and Properties of Materials, Vol. 3: Mechanical Behavior, John Wiley & Sons, 1965

27-301 Lab. 2 November 27, 2007

24

"There is a distinct difference in the appearance of the fractures of low-carbon steels, depending on whether the specimen was tested and broken below or above the transition temperature. As indicated in Figure 4.6, the fracture appearance of Charpy V-notch specimens varies from ductile to brittle as the specimen temperature is reduced from 200 to -321°F (92 to -196°C). Careful observation shows that a shear type fracture, as shown by the presence of a shear lip, is characteristic of the specimens tested at higher temperatures, while shear is absent in the specimens tested at the lowest temperatures, i.e., the fracture appearance is 100% cleavage."***

FIGURE 4.6: (a) Charpy impact strength vs. temperature of a 3.5%Ni, 0.1% C steel, with the fraction cleavage fracture surface. (b) Charpy impact fracture surfaces for different temperatures relative to the ductile-to-brittle transition temperature

4.2.4 Fatigue Testing (Extracted from Introduction to Engineering Materials, V.B. John) "If a material is subjected to repeated, or cyclic, stressing, it may eventually fail even though the maximum stress in any one stress cycle is considerably less than the fracture stress of the material, as determined by a tensile test. This type of failure is termed fatigue failure." "Very many components are subjected to alternating or fluctuating loading cycles during service, and failure by fatigue is a fairly common occurrence. The mechanism of fatigue in metals has been thoroughly investigated. When a metal is tested to determine its fatigue characteristics, the test conditions usually involve the application of an alternating stress cycle with a mean stress value of zero. The results are plotted in the form of an S-N curve (Figure 4.7), where S is the maximum stress in the cycle, and N is the number of cycles to failure. Most steels show an S-N curve of type (i), with a very definite fatigue limit, or endurance strength. This means that if the maximum stress in the stress cycles

27-301 Lab. 2 November 27, 2007

25

is less than this fatigue limit, fatigue failure should never occur. Many non-ferrous material show S-N curves of type (ii) with no definite fatigue limit with these materials it is only possible to design for a limited life, and a limit of 106 or 107 cycles is often used."

FIGURE 4.7: S-N curves for (i) metal showing fatigue limit (steel), (ii) metal showing no fatigue limit (aluminum),

Hayden et al., The Structure & Properties of Matter. Although maximum stress under fatigue conditions is nominally below the elastic limit of the material, it has been established that some plastic deformation by slip takes place. During continued cyclic stressing, slip bands appear on the material; and, at these slip bands, there are some extrusive and intrusive effects (Figure 4.8(a)). These extrusions and intrusions formed by slip are extremely small, being of the order of one micron (1 µm) in size. Once an intrusion has formed, it can then act as the commencement of a fatigue crack. The intrusion, with a very small root radius, acts as a point of stress concentration and the crack slowly propagates through the material until, eventually, the remaining sound portion of the cross-section is too small to be able to sustain the maximum load. At this point, sudden fracture occurs."

27-301 Lab. 2 November 27, 2007

26

FIGURE 4.8: (a) Intrusion and extrusions formed in early stages of fatigue.

(b) Fatigue fracture surface showing both smooth and crystalline (conchoidal) fracture zones.

"A fatigue fracture surface is distinctive in appearance and consists of two portions, a smooth portion, often possessing conchoidal markings showing the growth of the fatigue crack up to the moment of final failure, and the cleavage or shear final fracture zone (Figure 4.8(b))." " The type of stressing cycle to which a material in service is subjected may be classed as alternating, repeating, or fluctuating. In an alternating stress cycle the value of the mean stress is zero. A repeating stress cycle is one in which the stress varies from zero to some maximum value, and a fluctuating stress cycle is one in which neither the minimum stress nor the mean stress value is zero. There are many factors that affect the fatigue strength of a material; these include surface condition, component design, and the nature of the environment. Specimens for fatigue testing are usually prepared with a highly polished surface, and this condition will give the best fatigue performance. The fatigue limit for highly polished steels is approximately one-half of the tensile strength. If the surface of the specimen contains a scratch or notch, or is ground rather than polished, the fatigue limit of the material will be reduced. The presence of scratches or notches act as small defects from which fatigue cracks can be initiated. Similarly, a sharp change in section with a small fillet radius can act as a stress raiser, and fatigue cracks can commence from such points. Keyways and oil holes in shafts are often points at which fatigue commences. The effect of a notch or scratch is not the same for all materials; a ductile metal is much less sensitive to the presence of surface flaws than is a brittle material. If conditions are such that corrosion can occur, not only is the fatigue limit very greatly reduced but also the rate of corrosion is increased. For some materials,

27-301 Lab. 2 November 27, 2007

27

including some steels, there is no fatigue limit in a corrosive environment, and failure will eventually occur, even when the stress levels are very low. " " Materials other than metals are also subject to failure by fatigue, but comparatively little work has been done in this area. For concrete and polymers, as with metals, the number of stress cycles necessary for failure is increased as the maximum stress in the loading cycles is decreased, but there does not appear to be a definite fatigue limit with these materials. There are difficulties in the fatigue testing of polymers, because of their low thermal conductivities and high damping capacities. Furthermore, there is an increase in the temperature of a polymer test-piece during a test." "Fatigue tests are carried out by cycling the material either in tension compression or in rotating bending (Figure 4.9). The stress, in general, varies sinusoidally with time, though modern servo-hydraulic testing machines allow complete control of the wave shape."

Types of stress cyclic: (a) alternating, (b) repeating, (c) fluctuating

FIGURE 4.9: Fatigue testing 4.2.5 Creep Testing (From J.F. Shackelford, Introduction to Materials Science for Engineers, Macmillan, 1985). The tensile test alone cannot predict the behavior of a structural material used at elevated temperatures. The strain induced in a typical metal bar loaded below its yield point at room temperature can be calculated from Hooke's law. This strain will not generally change with time under a fixed load (Figure 3.10). Repeating this experiment at a "high" temperature (T greater than one-third to one-half times the melting point on the Absolute temperature scale) produces dramatically different results. Figure 4.11 shows a typical test design, and Figure 4.12 shows a typical "creep" curve in which the strain, ε,

27-301 Lab. 2 November 27, 2007

28

gradually increases with time after the initial elastic loading. Creep can be defined as plastic (permanent) deformation occurring at high temperature under constant load over a long time period. After the initial elastic deformation at t = 0, Figure 4.12 shows three stages of creep deformation. The primary stage is characterized by a decreasing strain rate. The relatively rapid increase in length induced during this early time period is the direct result of enhanced deformation mechanisms. A specific example is dislocation climb as illustrated in Figure 4.13. This enhanced deformation comes from thermally activated atom mobility, giving dislocations additional slip planes in which to move. The secondary stage is characterized by straight-line, constant strain-rate data (Fig. 4.12). In this region the increased ease of slip due to high-temperature mobility is balanced by increasing resistance to slip due to the buildup of dislocations and other microstructural barriers. In the final (tertiary) stage, strain rate increases due to an increase in true stress resulting from cross-sectional area reduction due to necking or internal cracking. In some cases, fracture occurs in the secondary stage, eliminating this final stage.

27-301 Lab. 2 November 27, 2007

29

27-301 Lab. 2 November 27, 2007

30

27-301 Lab. 2 November 27, 2007

31

FIGURE 4.14: Variation of the creep curve with (a) stress, or , (b) temperature. Note how the steady-state creep rate (e•)

in the secondary stage rises sharply with temperature

Figure 4.14 shows how the characteristic creep curve varies with changes in applied stress or environmental temperature. The thermally activated nature of creep makes this process another example of Arrhenius behavior. A demonstration of this is an Arrhenius plot of the logarithm of the steady-state creep rate (e•) from the secondary stage against the inverse of Absolute temperature (Figure 4.15). As with other thermally activated processes, the slope of the Arrhenius plot is important in that it provides an activation energy for the creep mechanism. Another powerful aspect of the Arrhenius behavior is its predictive power. The dashed line in Figure 4.15 shows how high-temperature strain rate data, which can be gathered in short-time laboratory experiments, can be extrapolated to predict long-term creep behavior at lower, service temperatures. This extrapolation is valid as long as the same creep mechanism operates over the entire temperature range. Many elaborate semi-empirical plots have been developed, based on the principle, to guide design engineers in material selection.

27-301 Lab. 2 November 27, 2007

32

FIGURE 4.15: Arrhenius plot of e• versus 1/T, where e• is the secondary-stage creep rate and T is the Kelvin temperature.

The slope gives the activation energy for the creep mechanism. A shorthand characterization of creep behavior is given by the secondary stage strain rate (e•) and the time to creep rupture (t) as shown in Figure 4.16.

FIGURE 4.16: Simple characterization of creep behavior is obtained from the secondary-stage strain rate (e•)

and the time to creep rupture (t).

27-301 Lab. 2 November 27, 2007

33

5. Mechanical Properties as a Function of Microstructure 5.1 Design of Experiment: WOOD as an example of a Cellular Solid As stated in the Introduction, the purpose of this Lab is for you to find an optimum treatment of wood to maximize a combination of stress and toughness. You will design a set of experiments, write a plan and submit it by the date specified in the Course Schedule. The instructor will provide feedback on your plan. You must measure the toughness measurements using Charpy impact tests. You must measure the strength by performing compression tests (in the Instron machine with the compression sub-press). You will perform optical metallography on the various samples in order to document the variations in microstructure. You may perform scanning electron microscopy in addition (e.g. for characterization of fracture surfaces) but this must be arranged well in advance with the staff member in charge of electron microscopy, Mr. Tom Nuhfer (Roberts Hall). A critical issue is the amount of time available for your tests, so you must manage your time with care, sharing out tasks etc. Thus you will primarily learn (or be reminded of) how to use (i) the tensile testing machine (Instron) with the compression sub-press, and (ii) the Charpy V-notch impact tester. By this means, the students should gain an appreciation of the techniques and care required to obtain valid measurements of a few material properties and the wide range in properties possible in common structural materials.

27-301 Lab. 2 November 27, 2007

34

5. Experiment Description 5.1 Optimizing Properties of Wood as a Function of Moisture Content; Measurement of Anisotropy In this experiment you will perform tests on wood. The focus will be on (a) the variation

in mechanical properties between different types of wood; (b) the anisotropy of wood properties; (c) the effect of thermal treatment (drying) and soaking (to vary the moisture

content of the wood) on mechanical properties; and (d) the composite nature of wood.

Note that only the first of these requires testing all the available species of wood. The

other series of experiments may be performed on only one type. 5.2 Design of Experiment You will design a set of experiments, write a plan and submit it by the date specified in the Course Schedule. The instructor will provide feedback on your plan. You will measure the mechanical properties by performing compression tests in the Instron testing frame. You will also compare the strength in compression with the strength in tension by performing tensile tests. Since performing tensile test on a wood specimen is difficult because of the care needed to grip the specimen without crushing the material, you will only perform a few tensile tests for comparison with the compression tests (which will provide your primary measurement of strength). You will analyze the data from the tensile tests to produce a true stress-true strain curve. You will use the Charpy tester to measure toughness. You will use optical microscopy on the various samples in order to document the variations in microstructure. You may perform scanning electron microscopy in addition (e.g. for characterization of fracture surfaces) but this must be arranged well in advance with the staff member in charge of electron microscopy, Mr. Tom Nuhfer (Roberts Hall). A critical issue is the amount of time available for your tests, so you must manage your time with care, sharing out tasks etc. The mechanical properties of wood are dependent on the microstructure just as they are

for any other class of material. The main objective of the lab therefore is to illustrate this

point for a material class that is in widespread use but receives little attention in

conventional materials science. It also illustrates the complexity of the structure of wood, which you will explore to a limited extent. The mode of testing will be compression

instead of tension (or Charpy impact) in order to demonstrate an alternative method and

because gripping wood specimens in a tensile test is not as straightforward as for metal

or polymer specimens. Nevertheless, you will be provided with your own tension

27-301 Lab. 2 November 27, 2007

35

samples and test them to compare tensile properties and failure modes with

compression testing. Lastly, although wood is itself a natural composite, it is highly

anisotropic as you should observe in the test results. Therefore it is often used in a man-made, macroscopic composite form i.e. plywood. You will test a common form of

plywood to compare its properties with those of regular wood.

Although you will be working in a group of two or three students for each experiment,

each student must submit an individual report which encompasses Experiments 1 a, b and c. Raw data sheets may be common, i.e. Xeroxed, to the reports of each member of

the group, but graphs and tables of data must be individually prepared. Record the

initials of the individual responsible for each data point.

5.3 Types of Wood to be tested: 1) White Pine: a standard softwood much used for building frames and simple cabinetry 2) Oak: a tough hardwood with a relatively open grain, much used for sailing ships in

former times and still used extensively in furniture and cabinetry.

3) Cork: technically this is the bark of a type of oak. This is provided in case you have

time to measure its Poissons ratio.

Some specimens may also be available for these wood types (in limited numbers): 4) Plywood: you will test interior grade plywood laminated from softwoods.

5.4 Experimental Procedure Compression Testing: this will be the main type of test to be carried out. One of the

frames will have a subpress which is a cage constructed to hold the specimen and, in effect, reverse the action of the testing apparatus. You will need to arrive at a collective

plan for performing the tests in order to ensure that all the test parameters have been

covered. When you consider the anisotropy of wood, recall its microstructure and be

aware that all three directions have different properties (which point group describes the

symmetry of the properties?!). As a natural material, wood is very sensitive to its environment: in order to demonstrate this, you will test samples in the as-received

condition and artificially dried (by baking samples in an oven) and after soaking in water

for an extended period (at least overnight). You must also use lubrication on the faces

that contact the platens of the subpress. A soft graphite pencil rubbed on the contacting faces should suffice to lubricate your specimens.

27-301 Lab. 2 November 27, 2007

36

Special Test 1: One of the mechanical properties of materials that is important in certain

applications is the Poisson’s Ratio (see text for definition). For many structural materials

its value is the range 0.25-0.35. Certain materials have values very different from this, however, with interesting and useful consequences. Cork is considered to be a cellular

material and, as such, it has a Poisson’s Ratio close to zero. You will attempt to

determine the ratio for cork and for one of your test woods by measuring the initial

dimensions (as you should do in any case), placing the specimen in the test frame,

loading to a substantial fraction of the yield stress (or in the case of cork, a displacement that will yield approximately 10% longitudinal strain) and measuring the lateral

dimensions. If this proves too awkward in the subpress used for compression testing,

you may use a vice (or equivalent device) to apply compressive loads since load

measurement is not required. Special Test 2: You will be provided with tensile specimens (two per group) in pine and

in plywood. Test the tensile properties following the standard protocol. Compare your

results with handbook values. Discuss whether you encountered any special problems

with the testing such as the accuracy of the specimens relative to the design, gripping of the specimens (to transmit the load) etc.

Special considerations in testing wood: Compliance Correction: Although compliance correction is generally a necessity when performing tensile tests on high-modulus materials such as metals, wood has a low modulus, especially across the grain. If your measured modulus (from the elastic portion of the stress-strain curve) is within the range for the type of wood being tested, then there is little point in trying to apply a compliance correction. If it turns out thus, note in your report that you evaluated the elastic modulus and did not find any need to apply a compliance correction. Special considerations in testing wood: true stress, true strain: Plastic (irreversible) deformation of metals to large strains occurs without volume or density change. Thus the cross-sectional area of a metal specimen increases during a compression test as the specimen height is reduced. This typically leads to an engineering stress-strain curve that appears to “accelerate” with strain. Wood is a cellular material, however, so it responds to compression across the grain mainly by collapse of the pores. You should check what your specimens actually do (i.e. try to measure the change in cross-sectional area during a compression test), but the area may well remain approximately constant. This, if true, is convenient because it means that the true stress is equal to the engineering stress. Strain can be measured as the change in specimen height, divided by the original height (or the logarithm of this ratio, to obtain log strain).

5.5 Report Parameters:

27-301 Lab. 2 November 27, 2007

37

A) Type of wood B) Direction of testing (parallel to grain/parallel to radial direction/ parallel to the circumferential direction) C) Condition of the wood (As received/ Oven dried/ Water saturated) D) Testing Direction relative to the grain 5.5.1 Observations: i) Elastic modulus ii) Yield Stress (you may have to use back extrapolation to determine a yield) iii) Maximum Stress (this may depend on the failure mode) iv) Failure mode (buckling? fracture? along the grain? plywood: do the laminations remain intact?) v) Dimensions and weight of each sample (including before and after treatment to vary moisture content) 5.5.2 Analysis: a) Mechanical Property values (compare to handbook values): elastic modulus, yield stress, maximum stress b) Stress-Strain Curves (mark essential features such as yield, failure etc.) c) Anisotropy of Modulus, Strength. Report the elastic anisotropy tensor for stiffness in the matrix notation (Cij). Note which values you were able to measure, and which ones your experiments could not address d) Document the appearance of the specimen after testing: how did it fail? e) Optical microscopy of the fracture surfaces f) Density – attempt to calculate the moisture content 5.5.3 Questions for discussion about the results: 1) How important is the anisotropy of wood (be quantitative)? 2) Do you expect wood to be tough or brittle? Could its toughness vary with circumstances? 3) How useful is wood as an engineering material? Why? 4) How significant is its sensitivity to environmental conditions? How does wood compare with other materials? 5) How do the specific properties of wood (modulus/density, strength/density) compare with other materials? Useful ref: http://www.fpl.fs.fed.us/documnts/FPLGTR/fplgtr113/fplgtr113.htm 5.5.4 Typical Values: Compression tests on 1cm cubes: Area = .01*.01 m2 = 1.10-4 m2. Oak/Northern Red/ green: compression along grain = 23,700 kPa = 23.7 MPa Load at "strength" = 23.7.106*1.10-4 = 23.7e2N = 2,370 N Oak/Northern Red/ green: compression across grain = 4,200 kPa = 4.2 MPa Load at "strength" = 4.2.106*1.10-4 = 4.2e2N = 420 N Oak/Northern Red/ 12%: compression along grain = 23,700 kPa = 23.7 MPa Load at "strength" = 46.6.106*1.10-4 = 46.0e2N = 4,600 N Oak/Northern Red/ 12%: compression across grain = 7,000 kPa = 7.0 MPa Load at "strength" = 7.0.106*1.10-4 = 7.0e2N = 700 N White Pine/ green: compression along grain = 16,800 kPa

27-301 Lab. 2 November 27, 2007

38

Load at "strength" = 1,680 N White Pine/ green: compression across grain = 1,300 kPa Load at "strength" = 130 N White Pine/ 12%: compression along grain = 34,700 kPa Load at "strength" = 3,470 N White Pine/ 12%: compression across grain = 3,200 kPa Load at "strength" = 320 N Poplar/ green: compression along grain = 18,300 kPa Load at "strength" = 1,830 N Poplar/ green: compression across grain = 1,900 kPa Load at "strength" = 190 N Poplar/ 12%: compression along grain = 38,200 kPa Load at "strength" = 3,820 N Poplar/ 12%: compression across grain = 3,400 kPa Load at "strength" = 340 N 5.6 Tensile Tests Objective: To become familiar with tensile testing equipment and procedures and to develop an understanding of the range in mechanical properties of various structural materials. In particular, since tensile testing has been performed in other Labs, to become familiar with analysis of stress-strain data on a computer. The following points must be addressed: 1. Correct your data for machine compliance. 2. Produce both engineering stress-engineering strain plots, and, 3. Produce true stress-true strain plots. 4. Analyze the true-stress true-strain curves (necking analysis does not apply to woods). N.B. Tensile testing is a time-consuming operation, so only one group will be able to use the instrument on any given day. Consult the Lab Groups document for which group will be performing tensile tests. 5.6.1 Reporting Tensile Test Results C1. Include raw data and sample calculations of TS, YS, % elongation, and % RA in an appendix. C2. Include a computer plot of at least one stress-strain curve obtained through the computer interface for the Instron. Explain what you did to convert a load-displacement curve to a stress-strain curve. From the same data set, calculate both an engineering stress-strain curve, and a true stress-strain curve. Find the point on the true stress-strain curve at which the hardening rate has decreased to the point of being equal to the true stress; compare the strain at this point with the strain on the engineering stress-strain

27-301 Lab. 2 November 27, 2007

39

curve that corresponds to the maximum (ultimate) tensile stress. The suggested steps for analyzing the load-displacement curves are as follows.

• Convert the load-displacement data to engineering stress (σeng) - engineering strain (εeng). • Correct the strains for the machine compliance. To do this, compare the measured elastic slope against the handbook value for the (Young’s) modulus. For each data point, subtract a strain that corresponds to the difference between the apparent elastic strain and the true elastic strain. Note that the amount that you subtract depends on the load, not on the strain! This also means that the correction changes most rapidly at small strains, and least rapidly at large strains (where the load and therefore the elastic strain is changing rather slowly). The procedure is illustrated in the figure below.

• Subtract the elastic strain from the total strain in order to obtain the plastic strain. The elastic strain is a small fraction of the total strain once yield has occurred. • At this point, you have engineering stress versus engineering strain and can plot a curve. • We now convert the plot of engineering stress versus engineering strain to a plot of true stress versus true (logarithmic) strain. • First we note that;

A(ε) L(ε) = A0 L0 for all points on the curve.

27-301 Lab. 2 November 27, 2007

40

From this, we obtain the true stress in terms of the engineering stress:

!

" true =F

A=F

A0

#A0

A=" eng.

A0

A

$log. =%l

l1

+%l

l2

+K =%l

lii

&

Taking the limit of infinitesimally small changes in length, the latter becomes the logarithmic strain (also called true strain). Therefore we can write:

!

"# ="l

l.

Then integrating both sides (i.e. taking the limit of ∆L → 0) yields:

!

" = d"l0

l

# =dl

l= d ln l( )

l0

l

#l0

l

#

"true $ "log = lnl

l0

%

& '

(

) *

"log = ln 1+ "e( )

This gives us a method to calculate the logarithmic strain from the engineering strain at every point. Finally, we re-write the true stress in terms of the engineering stress and the engineering strain.

!

" true =F

A=F 1+ #e( )

A0

=" eng 1+ #e( )

C3. Incorporate and discuss the data in the report (presentation) for Experiment 2. Be sure to compare the different characteristics of the various materials. Remember to address the four questions listed above.

Useful notes on recording the data from tensile test on the Instron in the undergraduate Laboratory [based on an email from an Instron service engineer]:

If you are using Series IX version 8, in the method editor under Main--Global Parameters there is a field called ASCII Test Data. Enabling this will create a file with all the data points with each test/replay in the Instron\s9\output directory. If you are using a previous version of Series IX, you can export an ASCII file of the data as follows. Click on “Utilities” in the Main Window and select “Display Raw Data” (under the “Raw Data” menu item). Under the File Menu, select “Create ASCII file”. Answer the prompts at the bottom of the screen. Note: The

27-301 Lab. 2 November 27, 2007

41

default setting of "Header" will not give the actual data points. "Raw Data" or "Header and Raw Data" must be selected (F2 will pop up a menu with these 3 choices). This will create a file (F10 will do this) of the same name as the MRD file in the same directory as the MRD file. The new file will have an “.MAD” extension. Note: to open an MAD file in Excel97, the extension must be changed, e.g. to “.TXT”. As of October 2004, there are two computers, one for each Instron frame. The older machine (left) has a version of the Utilities that will make the conversion as described above; the newer machine (right) will display raw data but the window does not allow a conversion to ASCII. One can copy a data file to the older machine and perform the conversion there. Notes from October 2004: There are two Instron frames in the Laboratory. One is newer than the other and each has its own computer that you can (and should) use to control the tests and acquire data (in the form of load+displacement data points). The software is the same on the two computers. However, when choosing the units for plotting, the new frame (on the right) will function with either British or SI units: the older frame (on the left) will only function with British units.

27-301 Lab. 2 November 27, 2007

42

6. Report Requirements Experiment 2 will be reported through a presentation. The presentations will take place in the regular classroom for 27-301 during the lecture times noted in the Course Schedule posted on Blackboard. Each presentation will last a maximum of 20 minutes, not including questions. See the posted schedule for when each individual Group will present. Your presentation must be made with PowerPoint. You are free to select the format of your slides, but make sure that you select a font size that will be readable from the back of the room. Also, use color sparingly, to highlight things of importance, but don’t turn your slides into multi-color “artworks”. Think of color in a text as having the same impact as using italic or bold fonts. Each group should bring a portable computer from which the Powerpoint file will be projected. Make sure that the file actually works on that computer! If you want to do a dry-run, to make sure that the projection works correctly, contact me via email and we’ll set up a time during the week before the presentations to try things out. 6.1 General Requirements for the Presentation (Please review before preparing your slides)

1. Title Page -- The title page, should include a title identifying the report, its author, and the names of the group members. The title itself should be concise, yet descriptive and include key words that identify the experiments and convey the message of the report.

2. Introduction -- The introduction should be a maximum of three slides. Explain the motivation for the experiment and any required background that will help the audience understand the experiment.

3. Experimental Procedure -- The test procedure should be described concisely and should include any operational features that were discovered during the course of the experiment. For instance, time to reach steady state, length of an individual experiment and techniques used in sampling are important. The testing equipment and materials used in the project should be described in this section in sufficient detail so that they could be duplicated by the reader. Common items (balances, graduated cylinders, etc.) need not be named. You must address how your experimental plan guided your work in terms of the design of the experiment (and how you might improve the planning process).

4. Results -- This is the most important part of the report, for it represents your interpretation of the results of the experiment. Even though the results may be most effectively presented in tabular or graphical form, they must be preceded by text describing them. If appropriate, an estimate of precision of the data in terms of a relative uncertainty or confidence limit should be included. References should be made in the text to figures, graphs, tables, and equations, which are inserted in the report immediately following reference to them or as the next page. An analysis of the data should be included. Sample calculations should be included and are best presented as an Appendix.

6. Discussion --In this section, compare your results with theory or previous work. Discuss points of similarity or divergence and, if possible, give sources of these discrepancies. It

27-301 Lab. 2 November 27, 2007

43

is quite proper to include another author's curves on your plots, but not his individual data points. Evaluate trends in the results and any conclusions that can be drawn. Development of conclusions must begin in this section where they can be supported by logical argument, even though they will be dealt with exclusively in the next section. In the event of poor results, explain how the experiment should be modified to obtain satisfactory ones. This important section demonstrates your thinking and understanding of what was intended. In this section, you must discuss how you optimized the combination of toughness and strength as measured by the product of the two quantities (units to be discussed).

7A. Conclusions -- This section should be a numbered listing of the more important test results and major conclusions reached in the discussion. Conclusions are single sentences and typically 5 to 8 of them should be sufficient.

7B. Summary -- This section is a recapitulation of major points made in the Discussion in bulletized form and is intended to leave your audience with a clear idea of what you accomplished.

8. References -- This is a list of references in alphabetical order by author.

1. Use journal abbreviations as follows (article titles need not be included): Example: Author, Journal, Year, Vol. No., pp. R. M. Horn and R.O. Ritchie, Met.Trans., 1978, vol. 9A, pp. 1039-1053.

2. References to books should include the title and pages within the book. Example: Author, Book, edition, vol., pages, publisher, place, date.

George E. Dieter, Mechanical Metallurgy, 2nd ed., pp. 160-165, McGraw-Hill Book Co., New York, 1976.

9. Appendices (Supplemental Slides) -- Detailed technical information for which there is not space in the actual presentation should be included in these sections. An appendix contains information that would enable a reader to go into depth and completely check and reproduce the results. Included should be at least one complete set of sample calculations from original data to final results, copies of original data sheets, computer programs, etc. Appendices should not contain information vital to the report such as graphs or tables of data that properly belong in the Test Results section.

6.2 Report Grading

Make sure that each team member gets to talk for about the same amount of time. Your presentation grade will depend on the following items: • 25 points for Content: was the content correct? Was it complete? Were figures and tables properly cited? • 25 points on Slides: were the slides readable and informative? Were they prepared with care or just slapped together at the last minute? • 25 points on the Oral presentation: did you have a fluent speaking style? Was the presentation rehearsed or was this the first time you talked out loud about this topic? (Note that this component of the grade will be different for each student; the other items are common to all the students of a particular group). • 25 points on the Question and Answer session: how well (and professionally) were questions answered after the presentations? Questions will be asked by the faculty present, the TAs, and also by students from the 4 groups that do not have their presentation that day. Final copies of your slides (which constitute the written report) must be submitted by 5pm on the submission date noted in the Course Schedule.

27-301 Lab. 2 November 27, 2007

44

Grading for reports submitted late will be reduced 20% for the first week and an additional 20% for each succeeding week. Note the following chart of guidelines for how to differentiate between high quality and low quality presentations.

Students are referred to the University Policy About Cheating and Plagiarism (Organization Announcement No. 297, 6116/80). It shall be the policy in this course to discourage cheating to the extent possible, rather than to try to trap and to punish. On the other hand, in fairness to all concerned, cheating and plagiarism will be treated severely.

"Cheating includes but is not necessarily limited to: 1.Plagiarism, explained below.

2.Submission of work that is not the student's own for reports or quizzes.

3.Submission or use of falsified data.

Plagiarism includes (but is not limited to) failure to indicate the source with quotation marks or footnotes, where appropriate, if any of the following are reproduced in the work submitted by a student: 1. A graph or table of data.

2. Specific language.

3. Exact wording taken from the work, published or unpublished, of another person.

27-301 Lab. 2 November 27, 2007

45

Appendix I - The Properties of Wood I.1 Abstract Wood is a natural material that has been used as a structural material since ancient times. Its properties may be defined in a similar manner to other materials in order to perform quantitative design of structures. The properties of wood - and the degradation processes that limit its useful life - can be very well described in terms of its structure. Such descriptions must include, however, not only the basic structural unit, i.e. the cellulose molecule, but also some description of the spatial arrangements within the material. All this is perfectly satisfactory from an engineering point of view but tends to leave the materials scientist with the dissatisfying conclusion that the very fact of wood's natural origin precludes manipulation of the material in order to optimize its properties - the essence of materials science and engineering. This is from being the case, however, as many man-designed forms of wood product are now available from plywood to "glu-lam" beams. These products depend critically on composite design and on the adhesives used to assemble the materials. I.2 Memory Card • Wood is a cellular composite, whose mechanical properties are largely dependent on density. The cell walls of different species have similar mechanical properties, although their chemistry varies significantly. Eaxial ∝ Ecell (ρ ρcell) Etransverse ∝ Ecell (ρ ρcell)2 • The properties of wood are highly dependent on the humidity of its local environment which is a result of the chemical nature of its constituents and its porosity. • Wood is a natural material but is used both in its natural state, and in man-made (macro-)composite forms (e.g. plywood). • The lifetime of wood components is limited by both mechanical properties (creep) and by biological decay processes. I.3 Useful Books, Handbooks • The Wood Handbook at

http://www.fpl.fs.fed.us/documnts/FPLGTR/fplgtr113/fplgtr113.htm. • Cellular Solids: Structure & Properties, Gibson, Lorna J. , Cambridge Univ. Press,

1988. • Materials for Engineering, L. H. Van Vlack, Addison Wesley. the basic book; largely qualitative description. • Engineering Materials (2), M. F. Ashby and D. R. H. Jones, Pergamon. more explanation of mechanical properties. • Timber - its Nature and Behavior, J. M. Dinwoodie, Van Nostrand Reinhold. useful descriptions of properties in terms of microstructure.

27-301 Lab. 2 November 27, 2007

46

• Mechanics of Wood and Wood Composites, J. Bodig and B. A. Jayne, Van Nostrand Reinhold.

detailed textbook, emphasis on mechanics. • The New Science of Strong Materials, J. E. Gordon, Princeton. pleasant, qualitative account of the development of a wide range of materials, with

reference to aeroplanes, ships .... I.4 Structure It is important to understand wood as a cellular, composite structure. It is one, however, that has several different length scales from that of the cellulose molecule to the macrostructure of lumber as we accustomed to looking at it at the visual scale. The summary viewgraph illustrates the hierarchy of length scales that are pertinent to wood from the atomic structure of cellulose to the structure of a tree trunk. The basic building block of wood is the polymer of glucose known as cellulose, which occurs as a (mostly) crystalline fiber. The other critical component of wood is lignin, which is a complex, amorphous material containing phenyl groups. Lignin sets wood apart from other plants; its occurrence as outer and inner linings of the cell walls is critical for both structural properties and for wood’s (relative) insensitivity to environment. I.5 Mechanical Properties The most useful way to develop an understanding of the mechanical properties of wood is to relate the variation in modulus, strength etc. to the density. For this we follow the analysis of cellular structures in order to relate the macroscopic modulus to the modulus of the cell wall material. I.5.1 Basic Equations: Modulus

Eaxial ∝ Ecell (ρ ρcell) (1)

Etransverse ∝ Ecell (ρ ρcell)2 (2) The first equation simply quantifies the idea that the tensile modulus of wood parallel to the grain is just the volume average of the area fraction occupied by cell wall. The second equation is more subtle and states that the elastic modulus transverse to the grain varies more rapidly - with the square of the density - than the axial modulus. The reason for this can be understood very simply in terms of the cellular structure. When wood is loaded across the grain, the cell walls bend like miniature beams. This response can be quantified by use of beam theory to arrive at the functional dependence of equation 2. The mechanical behavior can be modeled by a framework of beams (see the last page of figures in this handout). The deflection, � , of a beam of length l and thickness t, under a load F, is given by standard beam theory as Fl3/EcellI, where Ecell is the Youngs modulus of the beam material (i.e. cell wall) and I is the bending moment which is proportional to t4. The force is stress multiplied by area, i.e. F=σl2. The strain, ε, is the displacement, δ, divided by the cell length, ε=δ/l. Thus we can obtain Eq. 2 as the ratio of stress to strain:

Etransverse = σ/ε =σ { Fl3 /EcellIl}-1 =σ { σl2l3 /EcellIl}-1 = C {EcellI/l4} = C’ {Ecell t4/l4} But we also relate the density to the cell dimensions by writing ρ ∝ (t/l)2 and obtain Eq. 2,

27-301 Lab. 2 November 27, 2007

47

Etransverse = C” Ecell ρ 2.

Note that this derivation is a general one for open-celled foams and happens to be a simple, easy-to-understand approach. Woods have more complex structures than the open cell model, which helps to explain the scatter in the data.

I.5.2 Basic Equations: Strength σaxial ∝ σcell (ρ ρcell) σtransverse ∝ σcell (ρ ρcell)2 Here, the story is very similar to that of modulus. The axial modulus is determined by the area fraction of cell wall material, hence the linear dependence on density. The transverse strength, however, is limited by bending and plastic hinge behavior of the cellular structure, hence the quadratic dependence on density. The difference between axial and transverse properties is so great for both modulus and most other mechanical properties that it is always necessary to be aware of the anisotropy of wood, i.e. that the properties vary markedly with direction. Another topic, which we will not treat quantitatively here, is that of variability in properties. Wood of a particular species exhibits a wide range of strength, modulus and toughness because of the variation in the growth conditions such as rainfall, humidity, temperature etc. The measured variability must be accounted for in design in a manner that guarantees a minimum level of confidence in any structure. I.5.3 Basic Equations: Toughness KIC� axial ∝ KICcell (ρ ρcell)3/2 KICtransverse ∝ KICcell (ρ ρcell)3/2 KICtransverse » KIC� axial

27-301 Lab. 2 November 27, 2007

48

For fracture toughness, the result is given without proof that the cellular structure leads to a 3/2 exponent in the density dependence. The crucial point is that propagating a crack parallel to the grain is much easier than transverse. More than one microstructural feature contributes to the high transverse toughness, including fiber pull-out, propagation of secondary cracks perpendicular to the primary crack, and elongation of the polymer chains in the cell walls. Again, there are many different directions and planes for crack propagation in this anisotropic material which further increases the variability of the toughness. I.6 Time Dependent Properties Although it is straightforward to perform mechanical tests on wood, many of the basic mechanical properties are time dependent. For modulus, this simply means that there is a frequency dependence with significantly higher effective moduli at high frequencies. For strength, the phenomenon of creep means that the allowable values of strength for design must be derated (decreased) when sustained stress is encountered. For current values of accepted design allowables, the appropriate handbook should be consulted: the data suggest that a derating of 50% is sufficient to account for time-dependent deformation. Again, the effect of moisture is so large that realistic lifetimes for wood must account for expected moisture-temperature cycles in the particular service location. I.7 Effect of Moisture The primary modifier of mechanical properties of wood is the moisture content. The higher the moisture content, the lower the strength until one reaches the fiber saturation point; this is, ideally, the moisture content above which the cell walls can not absorb any more water, and the further uptake of water is as free water in the interior of the cells. As before, it is useful to think of this discontinuity in the response of the material as being a characteristic of its cellular microstructure. Simply knowing the chemistry of the material (i.e. that the majority component is cellulose) is insufficient to explain the properties of the material. It is important to realize that, as is so often the case with materials, there is no free lunch. In more precise terms, as the strength goes up (with decreasing moisture content) the toughness goes down. This reciprocal relationship between strength and toughness is well known in metal alloys. I.8 Degradation of Wood The lifetime of wood is limited by its vulnerability to biological decay. This can take both microscopic and macroscopic forms. At the microscopic level, there are many species of fungus that consume one or more of the constituents of wood. Brown Rots attack the cellulose and the hemicellulose. White Rots are more omnivorous and find the lignin edible too. The probability of attack by rot varies considerably by timber species because of the variation in extractives present. Teak, for example, is extremely durable whereas Balsa is highly perishable. In any case, a minimum moisture content of ~20% is required for fungal attack to occur, which is much higher than for non-lignified plants. This is another illustration of the importance of lignin in the properties of wood! At the macroscopic level, many insects enjoy feasting on wood. Termites are notorious for their depradations, partly because they have the habit of tunneling through beams and posts in order to stay out of the light (and in moist conditions). By the time

27-301 Lab. 2 November 27, 2007

49

that termite damage is evident on the exterior of a piece of wood, all structural integrity has been lost. In colder climates, several wood boring beetles leave their characteristic calling card of fine (~1mm diameter) holes on the surface. The processing of wood now includes a variety of impregnation procedures which impart greater resistance to decay. The use of wood ties for railroad track prompted the development of creosote impregnation methods. This is a good example of lifecycle costs being considered more important than cost of purchase, since the enhanced lifetime of treated ties more than pays for the increased cost per tie. Note, however, that impregnation is only routine for softwoods. Also, the design of wooden structures now places considerable emphasis on avoiding contact between wooden members and the ground. I.9 Processing of Wood Lest you think that wood is limited to its naturally occurring forms, it is very important to be aware of the wide variety of man-made forms of wood products. Most of these forms are motivated by cost as well as engineering design considerations. Plywood, for example, uses a significantly larger fraction of the available volume of a log because the individual sheets from which it is made are shaved off a log as a continuous strip. Not only can knot-holes be filled but the anisotropy of wood is much reduced in plywood. “Glu-lams” are wood beams made from relatively thick lamellae that, again, permit more efficient use of available lumber and offer increased dimensional stability. Conventional wooden floor joists can only take advantage of the shape of rectangles (in cross section), as compared, for example, to the more efficient shape of steel I-beams. Recently, more elaborate composites are being manufactured for joists that approximate I-beams in shape and offer very good resistance to sound transmission. I.10 Joining of Wood As with many composites, a major difficulty with the application of wood is joining. In ancient times, great care was used to avoid tension joints; where these were unavoidable, mechanical pinning was used with subtlety that the pins (“pegs”) needed to be drier than the beams so that, in time, the structural members would shrink onto the pins and hold them. Ship construction resulted in the need to seal the joints between the planks used to sheath the hull which was done with, amongst other materials, tar or pitch. The phrase “devil to pay” is actually a contraction of the frustrated shipbuilder’s remark that there was “the devil to pay and only half a bucket of pitch left”; in this context, the “devil” was a particular seam that was prone to leak. Modern glues based on caesin (milk products) and on epoxies have greatly improved the prospects of wood, especially the man-made composites based on wood. I.11 Cork Cellular Solids, Lorna Gibson & Michael Ashby, Pergamon detailed description of the properties and structure of cellular solids. Cork in its natural form is simply the bark of the cork oak, Quercus Suber, which happens to grow as an unusually thick layer of the cork cambium layer in the bark. Unlike regular wood, where there is considerable heterogeneity in the structure, cork is nearly a homogeneous structure of (approximately) hexagonal cells, whose prism axis is parallel to the radial direction in the tree trunk. The exception to this concerns the

27-301 Lab. 2 November 27, 2007

50

lenticels which are planar channels in the cork whose plane normal is in the tangential direction. The cell walls themselves have corrugations which are very important in controlling the mechanical properties of the honeycomb. They also are covered in suberin (an unsaturated fatty acid) and waxes, with the result that cork is highly resistant to chemical and biological attack. The mechanical properties of cork can be predicted based on its microstructure. The key feature of the prediction is the incorporation of the corrugated nature of the cell walls, because it allows one to predict the zero value of the Poisson ratio(s) for compression on the prism axis (radial direction), for example. The values shown for the predictions are based on measured values of cell wall density of 1150 kg/M3, and modulus of 9 GPa. Note that the agreement is surprisingly good except for the in-plane Poisson ratio, for which the variation is probably due to the heterogeneities in the structure.

Table of Mechanical Properties of Cork

Calculated Measured Moduli

Etransverse (MPa) 15 13 ±5 Eprism (MPa) 20 20 ±7

Gin-plane (MPa) 4 4.3 ±1.5 Gout-of-plane (MPa) - 2.5 ±1 Poisson ratioin-plane 1.0 0.5 ±0.05

Poisson ratioout-of-plane 0 0 ±0.05

Collapse Stresscompr. in-plane (MPa) 1.5 0.7 ±0.2

out-of-plane (MPa) 1.5 0.8 ±0.2 Perhaps the best known application of cork is for wine bottle corks (also for gaskets in general, e.g. in internal combustion engines). The chemical resistance of cork is ideal for long-term use, but the elastic properties are also crucial to this application. Although the low Young's modulus is useful, note that the bulk modulus is also low, unlike other solid polymers above their glass transition temperature. Better yet, when cork is compressed along its prism axis, there is no change in lateral dimension. One might imagine that cutting corks along the radial direction would be ideal. The lenticels mentioned above, however, render this impracticable because they offer a leak path across the cork. The solution is materials engineering, such that a practical cork has two layers cut with the prism axis along the bung axis, topped with a cork composite made from bonding cork particles. This then is another example of manipulation of natural materials for particular applications.

27-301 Lab. 2 November 27, 2007

51

27-301 Lab. 2 November 27, 2007

52

27-301 Lab. 2 November 27, 2007

53

27-301 Lab. 2 November 27, 2007

54

27-301 Lab. 2 November 27, 2007

55

27-301 Lab. 2 November 27, 2007

56

27-301 Lab. 2 November 27, 2007

57

27-301 Lab. 2 November 27, 2007

58