HARDNESS TESTS: Basics and Macrohardnessengr.bd.psu.edu/rxm61/214/Supplemental MchT 214 handouts.pdf · HARDNESS TESTS: Basics and Macrohardness ... charts for converting hardness

Mch T 214 page 1 knowledge base - macrohardness 8/17/11

HARDNESS TESTS: Basics and Macrohardness

Basics: Resistance to permanent indentation/penetration (by a much harder body) Estimate of tensile or ultimate strength for metals Very common, easy, inexpensive test Measurement of surface properties only Related Properties: Scratch Resistance, Wear Rate HARDNESS (3 classes)

1) MACROHARDNESS a. REGULAR (“HARDNESS’) large area, deep penetration b. SUPERFICIAL large area, shallow penetration

2) MICROHARDNESS small area, shallow penetration 3) MISCELLANEOUS

a. MOHS SCALE actually scratch resistance Scale: 1 to 10, 1 = Talc, 10 = diamond

b. SCLEROSCOPE actually rebound hardness – energy absorption under impact load measured by rebound of dropped diamond-tipped hammer

c. DUROMETER for elastomer and non-rigid plastics only not permanent deformation; elastic penetration indication of modulus, not strength VARIABLES: 1) Indentor/Penetrator (size and shape) 2) Load (magnitude of force applied to penetrator) 3) Dwell Time (time of force applied to penetrator) There is NO UNIVERSALLY ACCEPTED MEASURE OF HARDNESS! For more information see manufacturing and materials books such as

Serope Kalpakjian and Steven R. Schmid, Manufacturing Engineering and Technology, 4th edition, Prentice Hall, Upper Saddle River, NJ, 2001, pages 68-73.


BRINELL (macrohardness: large area and deep penetration) INDENTOR: 10 mm diameter hardened steel or carbide ball (approx. 3/8” dia.) LOAD: 500, 1500, or 3000 kg (usually 3000 kg or 6600 lb for metals) DWELL TIME: 15 sec (ferrous: steels) 30 sec (soft, non ferrous) APPLICATIONS: Casting, Forgings, etc. SURFACE CONDITION: Not critical (as-cast sometimes adequate)

Leaves very noticeable dent in specimen (considered a semi-destructive test); may cause objectionable appearance. Specimen must be relatively thick to handle large indentation. Measurements must be taken away from specimen edges and from other indentations (distance > 2 indentation diameters).

NOT SUITED FOR:

1) VERY HARD MATERIALS (causes excessive ball deformation) 2) VERY THIN MATERIALS (penetration is too deep)

3) CASE HARDENEND MATERIALS (penetration is too deep) RESULT: BRINELL HARDNESS NUMBER (BHNXXX) BHN = L/A (A = area of indentation surface; hard to determine) (Note: This is compressive stress --- force/area)

22

2dDDD

LBHN

where: L = applied load (kg; 3000) D = diameter of ball indentor (mm; 10) d = diameter of indentation (mm) ULTIMATE TENSILE STRENGTH = 500 × BHN (units of psi) for steels = 3.5 × BHN (units of MPa) for steels

D

d

Load = 3000 kg

D = 10 mm


ROCKWELL (macrohardness, regular or superficial, depending on ‘scale’) INDENTOR: varies depending on ‘scale’ LOAD: varies depending on ‘scale’ DWELL TIME: 3 sec SURFACE CONDITION: Important (as-cast should be ground) INDENTATION LOCATION: >2-1/2 diam. away from edges and each other 15 Regular Hardness Scales Only 2 are commonly used (‘B’ and ‘C’) 15 Superficial Hardness Scales Only 4 are commonly used (‘30N’, ‘45N’, ‘30T’,

‘45T’)

‘B’ and ‘C’ leave much smaller indentation than Brinell hardness test, but still a noticeable dent in specimen.

Hardness number is an indication of penetrator depth; not penetration area. There is no mathematical relationship to tensile strength; charts for converting hardness

number to strength are readily available. If hardness is unknown, start with ‘C’ scale so as not to damage ‘B’ penetrator! ‘B’ hardness number should be between 20 and 80; if greater than 80 go to ‘C’ scale; if

less than 20 go to another Rockwell scale. ROCKWELL ‘B’ SCALE Macrohardness; regular “hardness” INDENTOR: 1/16” diameter ball LOAD: 100kg (10 kg preload)

APPLICATION: Unhardened steels, copper alloys, aluminum alloys, malleable iron, etc.

ROCKWELL ‘C’ SCALE Macrohardness; regular “hardness” INDENTOR: diamond ‘brale’ (rounded cone point) LOAD: 150 kg (10 kg preload) APPLICATION: hardened steels, cast iron, titanium, etc. RESULT: ROCKWELL HARDNESS NUMBER HRBXX or RBXX HRCXX or RCXX R = Rockwell B or C = Scale XX = Hardness Number Warning: When operating a Rockwell test machine, watch the needle on the display. When the load is applied the needle may drop below the set point. If it does but does not rise back above the set point when the load is removed the measured hardness value is less than the set point. This usually means that the reading is off-scale and so a different scale must be used.


SUPERFICIAL ROCKWELL ‘Scale’ includes a number which is load and a letter which indicates indentor. (Specification is not complete without letter and number.) Examples: 30NXX 30, 45 = load (kg) 45NXX N – diamond ‘brale’ (similar to ‘C’) 30TXX T – 1/16” diameter ball (similar to ‘B’) 45TXX XX – Hardness Number CYLINDRICAL CORRECTION FACTOR (for Rockwell ‘B’ and ‘C’) SEE AVAILABLE CHARTS FOR CORRECTION!

Same indentor, load, dwell time, and material will not yield the same hardness number on a cylindrical surface as on a flat surface due to geometric constraints of the material as it is trying to permanently deform.

HARDNESS CONVERSION

Approximate conversions between various hardness scales are available. Because there are many factors involved, the conversions are only approximate. The scales are limited so hardness measurements on most scales only cover a small range of possible materials and conditions. Most manufacturing and materials books contain some version of comparison between different hardness scales.

≠

Mch T 214 page 5 Exercise 1 macrohardness 8/20/12 Name _________________________

Worksheet on Macro Hardness The purpose of this exercise is to become familiar with basic macro hardness measurement. A few parts will be supplied for testing. Instructions for use of the hardness testing machine will be given verbally. 1. Measure the Rockwell hardness of the supplied specimens. (2 points) Specimen Rockwell Hardness

___________________________ _______________

___________________________ _______________

___________________________ _______________

___________________________ _______________

___________________________ _______________

2. Examine the steel part with the Brinell hardness indentations already present. a. What is the likely load used to make these indentations?

b. Measure the diameter of one of the indentations.

c. Compute the hardness indicated.

(1 point) 3. Could you successfully Brinell hardness test a 6mm diameter bolt? Why or why not? (1/2 point) 4. If a hardness test is performed on a one inch thick plate, is the value obtained correct

for the entire volume of material, all the way through the thickness? Explain why or why not. (1/2 point)

Mch T 214 page 6 Exercise 1 macrohardness 8/20/12 Name _________________________ 5. Write a set of instructions for the use of the Rockwell hardness tester. Concentrate on

how to perform the test, specifically the order in which the handles are moved, where the pointer is to be set, etc. (Make good instructions so you can do this in two months from the instructions you write here.) (1 point)

Mch T 214 page 7 knowledge base - microhardness 8/17/11

MICROHARDNESS small area, shallow penetration

creates an indentation so small a microscope is needed to see it Microhardness Purposes: Case Hardened Materials Measure properties in the thin, hardened region.

Case Hardening Purposes: 1) improve surface wear/abrasion properties (primary) 2) improve fatigue properties (cyclic loading) (secondary)

Not for improved strength! Case Hardening Applications:

1) Splines (rotating shafts transmitting torque; axial slip) 2) Gear Teeth 3) Sheaves/Pulleys 4) Casters/Wheels/some large rolling element bearings

Minor Phases Grain Boundary constituents Plated Surfaces Diffusion Zones Properties Determined by Microhardness:

1) Case Hardness Only at specimen surface 2) Case Depth Important if wear rate is known Destructive section is required Test location – move specimen with micrometers (x & y)

CASE DEPTH (2 definitions)

1) Effective Case Depth – perpendicular distance from surface to deepest point that a specified hardness is maintained. RC50 equivalent unless otherwise specified Conversion to Rockwell is by chart or automatic by test machine readout Easily measured 2) Total Case Depth – perpendicular distance from surface to a point where chemical differences are indistinguishable; often 0.04% in carbon content.

Difficult and expensive to measure Microhardness Conditions:

1) Surface finish is critical; must be polished and etched. Specimen is generally mounted in (cast into) plastic before grinding/polishing/etching.

2) Specimen surface must be perpendicular to indentor 2 General Types of Microhardness VICKERS KNOOP

Many materials are not really homogeneous. Microhardness permits investigation of differences between regions that are nearby but not identical.


VICKERS (2 types) ENGLISH VICKERS - Macrohardness: similar to Brinell Rarely used Result: DPHXXX VICKERS - Microhardness (assume this when you hear ‘Vickers’ unless ‘English Vickers’ is specifically stated) INDENTOR: Square-based pyramid with prescribed angles

LOAD: Not standard; must be specified (25 to 1000 g; usually 500 g) DWELL TIME: Not standard; must be specified (usually 10 sec or 15 sec) RESULT: VHN = 1.8544 L/d2 L = load in kg d = average diagonal in mm KNOOP may be referred to as ‘Tukon’ erroneously (Tukon = brand/model of test machine) INDENTOR: diamond-based pyramid with prescribed angles

LOAD: Not standard; must be specified (25 to 1000 g; usually 500g) DWELL TIME: Not standard; must be specified (usually 10 sec or 15 sec) RESULT: KHN = L/0.07028l2 L = load in kg l = long diagonal length in mm

dy

dx

≈ d/7

d = (dx + dy)/2

l

≈ l/30


Example of Microhardness Data:

Notice that the measured data does not describe a smooth curve. It seems unlikely that hardening of a metal part could result in ‘stair steps’ of hardness, so the curve has been manually smoothed. If more traverses are done adjacent to this one, it can reasonably be expected that there will be some average at each depth, and some scatter at each depth. Hardening and Surface Hardening: Hardening of steel is accomplished by heating the material significantly above the critical temperature where the phase change to austenite occurs (always greater than 738°C, 1360°F), holding it at this elevated temperature until the phase change is complete, and then quenching the part to quickly lock-in a martensitic structure. If the carbon content is high enough and the quench fast enough the resulting material will be quite hard and brittle. Hard means that the material is strong but brittle is not a good thing usually. Usually the hardened material is tempered, allowing the martensite to convert to a softer mix of ferrite with cementite (Fe3C) particles. Tempering is performed be raising the part to a moderate temperature, a few hundred degrees, and allowing the structure time to arrive at a softer condition. In some cases, such as gears or large bearings, it is desirable to have a very hard surface but not to have the remainder of the part hardened. Another situation where a hard surface may be useful is for a part that sees wear on the surface, whether erosion or abrasion. Since a gear experiences very high contact stress and somewhat lesser bending stresses, it is an ideal candidate for surface hardening. A surface hardened gear is more resistant to surface cracking because it is hard/strong at the surface and yet it is not brittle since the body of the gear is not so hard. Surface hardening may be accomplished by two general methods. The first method works on a material that is hardenable, but only the surface is hardened. The second method changes the surface chemistry of otherwise unhardenable material.

Flame and Induction hardening To obtain a really hard structure in steel requires a carbon content of at least .4%. If the surface of a part can be raised above the transition temperature and then quenched, the

traverse 1 approx. smooth curve


surface will be quite hard. A flame applied directly to a part can be used for local heating, or alternately electrical induction heating may be used to locally heat a part. Whatever the source of heat, the heated material must be quickly cooled and then reheated to a lesser temperature and allowed to cool. One way to accomplish this is by heating the part, spraying water on the part to cool the surface, and then allowing the heat deeper in the part to temper the quenched surface. Typically the hardened layer is limited to .030inch or so.

Carburizing and Nitriding It is not really possible to get much hardening in steel with a low carbon content no matter how agressively it is quenched. But if the steel is heated in an environment of gaseous carbon or nitrogen, either of these elements can diffuse/dissolve into the steel. They won’t penetrate very deeply into the steel, but the chemical composition of the surface can be changed enough that they may now be quenched and significant surface hardness result. Carburizing can develop surface hardness equal to that developed by flame hardening, and nitriding can develop harder surfaces, sometimes higher than RC 70.

A part that is very soft often is not easy to machine because it acts like it is ‘gummy’. Likewise, a part that is hardened very much will also be difficult to machine. Typical hardness conditions might be: RC < 20 medium material as received from supplier RC = 30 considered hard for many industrial applications RC = 40 hard enough to be difficult to machine RC ≥ 60 typical case hardened surface or fully hardened high alloy material

Mch T 214 page 11 Exercise 2 microhardness 8/20/12 Name _________________________

Worksheet on Micro Hardness The purpose of this exercise is to become familiar with one test for micro hardness measurement and to see the effect of case hardening. 1. Briefly describe why Brinell and Rockwell hardness tests are not well suited for case

hardened parts or materials. (1 point)

2. If a 500 g load is used in Knoop hardness test and the measured length of the

indentation is .1146 mm, what is the KHN? What is the equivalent HRC? (1 point)

Due next laboratory period: (2 points) 3. A case hardened specimen will be measured during the laboratory period:

Measure Knoop hardness as a function of distance from outside surface of the part, every .005 inch from surface to core.

Record KHN and Rc values displayed by the machine.

a. Plot the Knoop hardness as a function of distance from the surface of the part. b. Plot equivalent Rockwell C hardness as a function of distance from the surface of the

part. c. Curve fit the points on your graphs (with a French curve if necessary to obtain smooth

curves). d. Determine and label the location of the limit of effective case depth at location(s)

tested.

Mch T 214 page 12 Exercise 2 microhardness 8/20/12 Name _________________________

Optional Activity #1: Another Macro Hardness Exercise Background: A pair of parts has been butt welded. The parts are known to be medium quality alloy steel that should be heat-treatable, so the heating and cooling from welding probably have affected the hardness of the parts. The heat treated region from welding is called a ‘heat-affected zone’, and may be harder or softer than the parts were before welding. As the parts are welded and allowed to cool, the cooling rate will not be the same for the entire length of the parts. Quite possibly, there will be areas that have cooled slowly enough that the material will act like it has been annealed. At other locations it may have cooled fast enough to be quite brittle. Hardness is really a measure of ultimate tensile strength; the changes in hardness are a change in tensile strength of the parts. You all need to be aware of material property changes from welding and it is likely that at least some of you will need to design welded parts and specify processes to prevent difficulty from heat effects. Purpose: To measure the effect of welding on the hardness of a part. Procedure: Mark the specimen at increments of 1/8 inch so that hardness tests may be performed at known distances from the weld. Perform Rockwell C tests at each location as far as the hardness is changing, but not less than every 1/4 inch along the entire length of the sample. Reporting: (1 point) Plot the Rockwell hardness as a function of distance from the center of the weld. Curve fit the points (with a French curve if necessary to obtain a smooth curve). Optional Activity #2: Laboratory Report Discussion Examples of sections of laboratory reports will be written, read, and the strong and weak features of each determined and discussed.

Not likely that we will do this

You should expect to do this:

Mch T 214 page 13 knowledge base - Tensile Test 1/6/12

The Tensile Test The tensile test supplies most of the basic information regarding a material for purposes of design. The test is also commonly performed by a material supplier or user to demonstrate that a batch of material meets the specifications for a particular design. An example of an idealized stress-strain curve is shown in Figure 1.

0

10

20

30

40

50

60

Strain, in/in

Str

ess,

ksi

Figure 1: Idealized stress-strain curve for steel 1. Basics of the Test In its simplest form, a tensile test consists of pulling a specimen apart while recording the specimen elongation and the force causing that elongation. Most commonly, the change in length due to each applied load is recorded. The strengths which are desired are the force divided by the cross-sectional area of the specimen. Several different material properties may be found from a single tensile test. The specimen used for tensile testing is usually flat or solid round. A section at each end is of larger diameter if round or larger width if flat (Figure 2) so that the specimen may be attached to the test machine where the specimen is not likely to break. A large transition radius is usually used so that the radius will not be a weak spot. Often the size of the specimen in the section with the smallest cross-sectional area is selected so that a convenient area is obtained. Figure 2: Typical tensile specimen Since the test is to be tension only and it is desired to have no bending on the specimen, tensile test machines have a variety of attachments for the specimen but most incorporate

(Strain axis is not linear in this

Proportional limit

Elastic limit

Yield point

Ultimate strength


some flexibility so that the load applied to the specimen is straight along the length of the specimen. Some common attachment methods are threaded ends which screw into attachments on the machine or a tapered holder and clamp fixture with jaws that grip harder as the specimen is pulled. Specimens with upset ends or so-called button ends are also used in some machines. The Tinius Olsen bench-top test machines at Behrend use the tapered holder and clamp fixture style of grips; see Figure 3 for a typical tensile test setup.

Figure 3: Typical Tensile Test Setup 2. Data from Tension Tests The specimen must be measured before the test is begun since for engineering work the desired results of the test are not specific to a given specimen size. The desired strength (stress) values are force divided by original cross-sectional area. The elongation data is reported in terms of change in length divided by original length which is called strain. Strain has units of inches per inch or millimeters per millimeter. To facilitate length measurements, a standard gauge length of 2 inches is often used, and if available a gauge length marking device may be used to make indentations into the specimen at the proper length. Changes in length are usually measured by an extensometer while the elongation is small, and are then may be measured by use of calipers and a steel scale after the elongation is greater than the capacity of the extensometer.

Upper

Extensomet

Lower

Handwheel for closing


Early in a test, the ratio of change in force to change in length will be nearly constant; the elongation is proportional to the force. In the proportional region the extensometer can almost always be used. This is the elastic region of the material, and the region of the test where accuracy is most important. The Tinius Olsen bench-top test machines at Behrend are able to record forces and change in length measured by the extensometers until significantly beyond the elastic range. The extensometer must be removed before the specimen breaks or the recorder runs out of paper, to protect the extensometer. After the extensometer is removed it is possible to measure changes in length with spring calipers and a steel scale if the test can be run slowly enough.

Figure 4: Extensometer The extensometers available at Behrend are set for a two inch gage length between the knife edges when installed on a specimen. Finger grip plates on the back of the extensometer open it up to allow it to be installed or removed from the specimen easily. When using this extensometer, the data collected is change in length over the two inch gage length and hence strain must be computed from this original length and the measured changes in that length. Forces are displayed on the control panel of the test machine and are recorded along with the associated changes in length. The machines are not configured to apply specific forces and measure the changes in length caused by the forces. Rather the machines apply whatever force is necessary to obtain change in length at the rate set on the control panel. The force is then plotted as a function of the change in length or strain when the extensometer is used. Traditionally this is what has been done and tensile test data is almost always presented as stress as a function of strain. Note that forces are not recorded after the extensometer is removed from the specimen, so it is essential to keep a close watch on the force display to capture the maximum force carried by the specimen for ultimate strength computation.

Upper knife edge (moving)

Lower knife edge (fixed position)

Roller for back side of specimen

Zero knob – puts knife edge to starting length


3. Measurements After Fracture After the specimen has broken, it should be removed from the grips. Note that in some cases the fracture surface may be examined by electron microscopy or other sophisticated methods. If one of these methods is planned, it is imperative that the broken ends be protected from contact of any kind. Since that is not the case in this course, the contact surfaces are to be fitted back together so that the specimen dimensions at the fracture zone and the final gauge length may be measured. Following the measurements, the ends of the specimen are placed beside each other and taped together. The specimen must be suitably identified since other tests may be later required on the broken specimen. 4. Data Reduction and Calculations Values of forces and elongations are recorded, stress and strain are calculated for each data point measured, and these items are then graphed on a stress-strain curve. The modulus of elasticity should be calculated and the yield and ultimate stresses determined from the graph. The modulus of elasticity is the slope of the stress-strain curve in the initial linear region. The best stress and strain values for calculation of modulus of elasticity are the difference between the values for two widely separated points in the linear region. The ultimate strength is the maximum stress recorded in the test. The yield strength is generally taken as the stress at which the stress and strain are no longer proportional, or at the appropriate offset strain value. For ductile steel samples, the yielding phenomenon may be seen as an increase in strain without any change in stress. For calculation of tensile stresses and strains, some general formulas are necessary:

a. Tensile Stress A

P

P = applied force A = cross-sectional area

b. Tensile Strain oL

L

ΔL = change in length Lo = original gage length

c. Percent Elongation %100

o

of

L

LL

Lo = original gauge length Lf = final gauge length (after break)

d. Percent Reduction of Area %100

o

fo

A

AA

Ao = original cross-sectional area Af = final cross-sectional area (after break)

e. Modulus of Elasticity 12

12

E

σ2-σ1 = difference in tensile stress between points 1 and 2 ε2-ε1 = difference in tensile strain between points 1 and 2

valid only in the straight line region of


Note well: the stresses and their associated strains used for computation of modulus of elasticity should be about as far apart a possible and still remain in the linear region of the stress-strain curve. The reason for this is that each individual data point may have some random variation from the straight line, and you should be capturing the slope of the line, not the variations of a couple of close-together points. 5. Operating Steps for Tinius Olsen 10 kip Bench Top Machines

Measure & record specimen cross-section size Check, set, & record force units on machine base (pounds or Newtons) Check, set, & record extension units on machine base (inches or mm) Install grips Mark gage length on specimen (2 inches for Behrend extensometers) Set to ‘Tension’ on machine controls Load specimen: square to grips and fully inserted into grips Zero the force reading on machine control Turn extensometer knob to zero Plug in the extensometer Install extensometer on specimen Turn extensometer zero knob off of ‘Zero’ position Zero the extension reading on machine control Set & record machine speed (typically ≤ .1 in/min) Load paper into plotter Load pen in plotter Turn plotter to ‘pen-up’ Set & record force scale on recorder (typically 100% for steel, 50% for

aluminum) Select strain range at signal conditioner Record force and strain axis information on plotter paper Zero the strain signal conditioner Adjust pen to zero in X and Y directions on plotter Turn plotter to ‘pen down’ on plotter Push ‘load Up’ button on machine control Watch the plotter! – turn plotter to ‘pen up’ when curve complete Stop machine loading Remove extensometer from specimen Resume loading, recording force and gage length every gauge length change of

.05 inch Continue loading & recording until fracture of specimen Stop travel of machine Remove specimen from grips Measure & record specimen final gauge length and cross-section size Remove paper from plotter Return machine to start position


6. Capacity and Operating Settings for Tinius Olsen 10 kip machines Capacities: Tension 10 kip Compression 5 kip Flexure (bending) 1 kip Plotter scales: Normal paper uses 7 inch by 10 inch plotting area Strain, when using extensometer (horizontal movement of pen) 1:1 10″ = .2 in/in strain .1″ = .002 in/in strain 2:1 10″ = .1 in/in strain .1″ = .001 in/in strain 4:1 10″ = .05 in/in strain .1″ = .0005 in/in strain 10:1 10″ = .02 in/in strain .1″ = .0002 in/in strain

(These strain values are total strain in the gauge length. Therefore an indicated strain of .1 in/in is an extension of .2 inches since the extensometer measures over a 2 inch gauge length.)

Elongation, when using crosshead motion scales 50″, 25″, 5″, 2.5″, .5″

These lengths are the maximum that can be displayed on the meter, or they are the full 10 inches of the plotter paper when the crosshead motion is recorded.

Force scales (vertical movement of pen) 100% 7″ = 10,000 pounds 50% 7″ = 5000 pounds 20% 7″ = 2000 pounds 10% 7″ = 1000 pounds 5% 7″ = 500 pounds

(These force values are the fraction of machine maximum capacity. For example, 20% of 10,000 pound capacity is 2000 pounds full scale. This 2000 pounds will be displayed as the full scale of the plotter when the machine is set to 20%.)


7. Comments on Tensile Testing & Data Reduction:

A. There is a big difference between force and stress. The force must be divided by the original area to be a stress. Big part breaks with big force, small part breaks with small force, but if same material the stress should be the same. Example: It might be easy to see from a graph that the material yielded at a

force of 1234 Newtons. This is useless information for a different sized part, so data must be reported as stress values. If the part is 3mm thick and 12 mm

wide, the yield strength is MPamm

N

mmmm

NS y 3.343.34

123

12342

.

B. Both stress data and strain data are required to determine elastic modulus (also

called modulus of elasticity or Young’s modulus). Elastic modulus is the change in stress divided by the change in strain, in the elastic region of the data. Units are the same as stress.

Example:

C. When making computations of things such as elastic modulus or percent reduction of area, the calculations are usually performed by pencil and paper with a calculator, not by a spread sheet. Unless a very large number of tests are to be made, generation and verification of a computer program would not be undertaken.


D. When a stress-strain curve is desired, a computer program or spreadsheet would usually be appropriate to convert force data and original area into stresses, and change in length data and original length into strains. A written hand calculation of one data point is required to verify that the spreadsheet works correctly. Name, date, specimen identity, and type of test are the minimum information that should be included on each page of the computer printed information. Graphing of stress as a function of strain can be done from the spreadsheet if desired.

E. When you put your laboratory report, memo, or other communication instrument together, make sure the bottom of all graphs is either the bottom of the page or the right hand edge of the page.

F. When reporting data from material testing, it is common to report yield strength and ultimate strength. When these values are measured, it is the strength of the material. When part of a structure is analyzed with some load applied, the stress is computed and most of the time it is hoped that the applied stress will be less than the strength of the material.

Mch T 214 page 21 Exercise 3 – first tensile 1/2/13

First Tensile Test At the completion of this exercise you should be familiar with the tensile testing process. 1. Review the meaning of terms: (Entire class activity)gage length

a. cross-sectional area b. stress (in contrast with force) c. strength d. yield strength

e. ultimate strength f. elastic modulus g. percent elongation h. percent reduction of area

2. Perform a tensile test We will then perform a tensile test of each specimen, attempting to capture length data from the extensometer and by means of spring calipers after the extensometer capacity is reached. Note that the graph drawn by the test machine plotter is change in length in inches, over the gage length in inches, versus force. Record:

a. sample description b. material description c. original gage length d. original width and thickness e. final gage length f. final width at fracture zone g. final thickness at fracture zone

Compute:

a. original area b. percent elongation c. final area d. percent reduction of area

Measure: Rockwell hardness of each specimen

3. Develop stress-strain curves Extract force and elongation values from the graph produced by the test machine. Convert forces as read from the display to stress values, and lengths measured with the calipers to strain data. Produce two plots/curves:

a. First from zero load to a bit beyond yield. b. Second of all stress and strain data on a single graph on the same axes.

From graph and areas computed above, determine:

a. yield stress (Sy) b. ultimate stress (Su) c. elastic modulus (E)

Grading: Possible Initials/dates/description of test on each page 1/2 Original data (plotter info, measured lengths, etc) 1/2 Percent elongation, percent reduction of area 1/2 Yield strength, ultimate strength 1 Rockwell hardness 1/2 Elastic modulus 1/2 Stress-strain curve, low strain region 1 Stress-strain curve, whole test 1/2

Mch T 214 page 22 Exercise 3 – first tensile 1/2/13

5. Optional Activity #1: A strain gage may be installed by the instructor in the gage length of the specimen. This allows the instructor to demonstrate the installation process in class. Likewise, the strain gage may be used to measure strain during the early portion of the tensile test, permitting another set of data to be captured. This data may or may not agree with the extensometer data since the single strain gage will measure bending of the specimen as well as tension. 6. Optional Activity #2: Data is listed below for a tensile test of a specimen with original diameter of .505 inch and original gage length of 2 inches.

a. Compute the stresses and strains, and plot the stress-strain diagram using a spreadsheet program.

b. Plot the elastic region and a bit more of the curve by hand, on graph paper, and determine the Modulus of Elasticity (E), proportional limit, and offset yield point.

c. Determine the ultimate strength (Su) and rupture stress (Sr).

Load (kips)

Elongation (inches)

0.0 0.0000 1.5 0.0005 4.6 0.0015 8.0 0.0025 11.0 0.0035 11.8 0.0050 11.8 0.0080 12.0 0.0200 16.6 0.0400 20.0 0.1000 21.5 0.2800 19.5 0.4000 18.5 0.4600

Mch T 214 page 23 Exercise 4 second tensile 1/4/12

LABORATORY REPORTS Why does anyone bother to write a report on laboratory testing? There are two or three general reasons. Assume something has failed in service or broken unexpectedly. Everyone wants to know why there was a failure, what went wrong, who is at fault. So everything about the failed thing will be tested, reports written about the results of the tests, and the reports will go to the attorneys and will be evidence in court. Imagine “The load came loose when the chains on the trailer broke. The manufacturer’s rated safe working load rating on this chain is 3 tons. Our laboratory test of a sample of this chain showed that it broke at 21 tons.” (And the chain manufacturer wipes off the worried look because the chain did more than what he promised.) Or assume you are to design a part for a bridge, and you choose steel with a published strength of 700MPa. To be sure that the steel that is used is equal to what you specified in the design, a sample is taken from the steel during construction of the bridge, the strength measured in a laboratory test. The company building the bridge will save the test report forever so that if anything ever happens they can prove that they did what was in your design. You design bridge, bridge fall down, no partial credit. Laboratory reports convey information to people who were not present in the laboratory, typically to management. In general, a laboratory report must accomplish several functions: Who did the test, when, what was tested, and what are the results? The laboratory report is also the long term memory of the results, so completeness is important, and the original data must be included so that calculations may be done over again if there is ever a question. The general arrangement of information in a technical report varies from organization to organization; there are even differences within companies. But in almost all situations you will find that when you write a technical report on the job there is a particular form that must be followed. The following arrangement WILL be used for Mch T 214 Lab reports: TITLE PAGE (Cover Sheet)

The title page must include report title, author's name, date, course, and section. Function: Tells who/what/when at a glance.

INTRODUCTION

This section should state the purpose or objective of the testing, a simple statement of what was done, and what the report includes. This information should tell the reader(s) whether there is anything in the report that concerns their interests or responsibilities.


Function: This section is read by other people to see if they need to read the entire report.

SUMMARY

This portion of the report should summarize the results, conclusions and recommendations. It should refer to pertinent diagrams, tables or charts. [Tables, Graphs or Drawings/Figures are usually placed at the back of the report in a separate section.] Do not include a "grocery list" of the complete results of the test in the summary. This section of the report should provide the reader(s) with sufficient information to determine whether action needs to be taken and/or whether the report needs to be completely read. Function: This section tells the boss the answer to the question that he/she sent you to answer. Be sure to clearly give the most important result; what the boss paid you to find. Alternative format: Sometimes the functions of the introduction and the summary are combined into what is called an Abstract.

PROCEDURE

A procedure will not be required for standard testing performed in MchT 214. For example, the procedure for a Rockwell hardness test is quite standard and is of no particular interest to most readers. Do not include a procedure section unless you developed the procedure (a test which you invented), or you are directed to do so. Function: A procedure allows another experimenter to follow the steps you performed to try to duplicate/verify your work.

DISCUSSION

State in general terms the results of the particular test and note the salient facts discovered. Describe the behavior of the material tested. Discuss critically the results and the test procedure. Draw indicated conclusions about the material and its performance. Provide the supporting arguments for your conclusions and/or recommendations. Discuss thoroughly any questions listed in the instructions for the test. Integrate the answers to the questions into the text of the DISCUSSION, not as a separate listing of answers. The questions must be answered in paragraph form and in a way that indicates to the reader what is being discussed. Do not leave the reader wondering "I see the answer, but what was the question?" Function: This is the heart of a report, where you explain why you arrived at particular conclusions, and back up your statements with reference to


charts/graphs/data sheets. This is what convinces the reader that you have evidence to prove what you say.

FIGURES/TABLES/GRAPHS If tables, figures and graphs have not been integrated with the text they should be included here. Be certain that the date and type of test and appropriate units are included on each.

Function: Presents data in an organized fashion.

APPENDICES

Function: This stuff is proof of what you really did and measured; it is the evidence necessary to support what you concluded from the testing. Original data sheets, sample computations, spreadsheets, or any material necessary to support the report but not included elsewhere. Initials or signature, date the work was performed, and type of test must be included on each page of data, sample calculations, etc. Note clearly that a copy of signed/dated, original data sheets is required.

Note that spelling and grammar will be corrected and will be included in the grade for each report. It is expected that these items will be 10 percent of the grade for the report. Also note that laboratory reports should be written using the passive voice. For example "The sample was placed in the furnace" is preferable to "We placed the sample in the furnace". One source of confusion in style is the use of abbreviations. Some very standard abbreviations may be used without any explanation. In text, the use of "12.3 psi" in place of "12.3 pounds per square inch" would be acceptable since psi is a standard abbreviation in strength of materials work. In general, do not abbreviate in titles or headings. Where abbreviation is desired but not extremely obvious, the phrase should be spelled out completely the first time used and the abbreviation shown in parentheses behind the phrase. This defines the abbreviation for subsequent uses. For example, SEM is not obvious when used without explanation, but Scanning Electron Microscope (SEM) defines the meaning of the abbreviation for further uses. (In the Angel version of this document a sample laboratory exercise and two reports on that exercise follow in the next several pages. The first is poorly done and the second is acceptable. Each one has many notations drawing attention to good or bad features.) The following page is the grading rubric for tension test and torsion test laboratory reports in this section of MchT 214.


Laboratory Report Grading Possible Score Typing, Spelling, Grammar

4 errors is 1/2 point Title Page 1 ______

Title Name, date, course, section Spacing on page

Introduction 1 ______

purpose or objective what was done stuff included in report

Summary 1 ______

brief summary of results, or one or two most significant results conclusions or recommendations (if any of either) where to find complete results

Discussion 1 ______

results discussion of results and behavior of material tested supporting facts how they lead to conclusion discussion questions

Figures/Tables/Graphs/ Appendices 1 ______

quality of graphs & axis scales page labels (initials, date, type of test) and units on each page original data sheets sample computations

Correct computations based on data collected 5 ______

stresses, strains, elastic modulus, percent elongation, reduction of area, and so on!!!!!

Total 10 ______


Second Tensile Test At the completion of this exercise you should be able to:

1. Perform a tensile test using a 10kip UTM in room 118. 2. Produce stress-strain curves from the data collected during tensile testing of metal

specimens. 3. Determine yield strength, ultimate strength, tensile elastic modulus, percent reduction

of area, and percent elongation. 4. Write a brief report conveying the results of your testing to a knowledgeable reader.

This exercise is to be performed by groups of three or four students. All testing and data collection is to be performed as a group; data reduction and calculations, and report writing is to be an individual effort. The only major part of the reports that should be identical is the graphs produced by the testing process. Photocopies of graphs are acceptable. You are to exercise good data collection habits by writing on the graph produced during testing.

Before you begin the test, write on the graph paper the date of the test and the type of specimen being tested.

During the test, with some load applied to the specimen, note the force on the display and confirm that you understand the force value on the graph. Mark the force graduations on the graph while it is still on the plotter. Do the same for what you understand to be the graduations of elongation, something like the following:

Testing and data analysis:

Perform a tensile test of each of the supplied specimens: measure force and elongation, from initial condition through fracture Compute for each specimen: yield strength ultimate tensile strength modulus of elasticity percent elongation percent reduction of area Draw stress-strain curves for each specimen: stress-strain curve from zero stress to a bit beyond yield stress strain curve from zero stress to fracture

Specimens:

1. Hot rolled low-carbon steel, 1018/1020, flat tensile specimen. 2. Cold rolled low-carbon steel, 1018/1020, flat tensile specimen. 3. Heat treated aluminum alloy, 6061-T6, flat tensile specimen. 4. Unknown condition and alloy aluminum, flat tensile specimen. (Maybe one of these)

XXX pounds

.Y inch


Three specimens are known material, the fourth is not known presently. For known materials, the test results are to be compared to published values. For the unknown material, the testing results are to be compared to published values to try to determine what the specific material is, but more importantly to provide data that may be used for design with that material.

Apparatus: Tinius Olsen 10kip capacity bench-top universal test machine Extensometer and signal conditioner Pen plotter Dimensional measuring tools Procedure:

Perform tensile tests according to the previously handed out instructions. Note carefully the definitions for force and strain scales and settings on the last sheet. [Be sure that the graph paper used in the plotter is the correct one for English units of force. The correct paper has 20 major divisions in 7 inches on the vertical (force) axis.]

Report:

A formal laboratory report of the style described in the laboratory report handout is required. The various material properties should be discussed and example computations included in the appendices. Compare the results to textbook values for the materials that are identified.

Discussion Questions: (answers must be discussed in the report discussion text) 1. Based on your observations, were the failures brittle or ductile? (For example, if you

were to hammer a glass rod [brittle] or a copper wire [ductile], what would you expect? Are your observations in this tensile test consistent with what you know of ductile materials or of brittle materials? What did the specimens do? How did they deform and fail?)

2. From the testing done here, is it possible to determine the elastic limit of each of the specimens tested? Is it possible to determine the proportional limit? (Check the definitions of these terms before finalizing your answer!)

3. Do the two steel specimens have similar elastic moduli according to your testing? 4. What alloy and heat treat does the unknown aluminum most closely resemble,

comparing your test data to textbook data? Grading: See the Knowledge base - Laboratory Report pages.

Mch T 214 Page 29 knowledge base - Torsion Test 8/18/12

The Torsion Test The purpose of the standard torsion test is to measure the torque-twist properties of the specimen and if possible to determine the modulus of rigidity (shearing modulus of elasticity), shearing yield strength, ultimate strength and breaking strength of the specimen. In some cases the behavior of the specimen, such as instability in a thin wall tube, is also to be observed, or observed instead of measuring the various strengths.

1. Basics of the Test Specimens for torsion testing are of two varieties. The standard specimen for determination of material properties is round and of (usually) constant diameter. The specimen may also be tubular. A second type of torsion specimen is a complete machine component such as a drive shaft which is to be tested for torsional load carrying capacity of the assembly. We will only deal with standard specimens in this course. In its simplest form, the torsion test consists of twisting the specimen until it fails, while recording the angle of twist and the torque causing that twist. The modified Tinius Olsen Lo-Torq bench type torsion testing machine available in the laboratory has a variable speed motor and gearing capable of applying torque up to 10,000 pound-inches, and applying that torque to specimens up to about 28 inches long. The machine in the Behrend lab has a plotter attached, permitting the torque and angle of twist to be recorded as the test is conducted.

2. Data from Torsion Tests Due to the nature of torsional stress on a member, the stress is not uniform through the entire diameter of the specimen. The stress is maximum at the outside surface and approximately zero at the center. Therefore it may not be possible to observe the exact yield point nor the ultimate shearing stress particularly on a solid bar during a torsion test. It is possible to calculate the stress and strain at the outside surface, or at any other radius for a solid bar as long as the outside surface has not begun to yield. The yield stress will be reached for the outermost radius before the stress is that high on the material just inside of that radius. As the torque is increased, the material just below the surface starts to yield, while the outer surface is already beyond yield. In contrast, shearing strain is proportional to radius and may be computed correctly both before and after yield.

For a thin wall tube, the stress is approximately uniform through the tube wall thickness. Therefore, the test results should more reliably permit the determination of the shearing yield and ultimate stresses. For both the solid and tubular specimens, the angles of twist which are

max shear stress on outside surface; stress

ti l t

max shear stress on outside surface; stress not

ti l t


below the yield point are small. Therefore it is essential that the data for this test be taken with care in the first ten degrees of twist. Prior to starting the test, make a prediction of the torque at which the shearing yield point is likely to be found so that this important data is not passed by. After the yield point has been reached, the number of data points taken may be decreased and the data taken as fast as it can be recorded.

The Tinius Olsen machine is equipped with a chart recorder which may be used to record the torque and angle of twist on the specimen to the limit of the troptometer.

3. Measurement of Angle of Twist A torsion specimen is clamped in chuck jaws at each end of the specimen. On the Tinius Olsen Lo-Torq machine in the Behrend lab, the left chuck measures the torque but does not rotate, and the right jaw rotates. If closely observed, it will be noticed that the specimen is not held perfectly rigidly in the chuck jaws, but rather does some slipping. Measurement of the angle of twist between the jaws includes this slipping. Therefore, it is essential that the measurement of angle of twist used for shearing strain computation be measured on the specimen only. This is accomplished by use of a torsional device that acts like an extensometer for tensions testing. This device is called a troptometer, and measures the angle of twist in the region between the attachments. 4. Data Reduction and Calculations For calculation of shear stresses and strains, some general torsional stress formulas are necessary:

Polar Moment of Inertia J = )(32

44 IDOD

OD = outside diameter (do these before putting ID = inside diameter specimen into chucks)

Shearing Stress at OD (Max) J

cT (valid only up to yield stress)

T = applied torque c = outside radius

Shearing strain (radians) L

c

θ = angle of twist (radians) L = length twisted

5. Operating Procedure Steps


It takes some serious fiddling to get the test machine and setup ready before a test. Do not turn on the test machine motor to twist the specimen until the test setup has been approved by the instructor. Plug in the torsion machine. Turn on the strain indicator, power supply, and plotter.

Let them warm up/stabilize for 1/2 hour for best results.

Zero the drive chuck Remove any specimen present Set the twist rate control to 5° per minute Toggle the direction switch to Forward Press Start (the green button) to start the motor

If headed toward zero, let it run May turn up the speed if desired

Press Stop (the red button) when chuck ‘zero’ aligned with indicator Measure the specimen length, and diameters (ID and OD) For tubular specimens, insert the proper plugs in the ends of the tube Strain Indicator: Press button to show Full bridge connection. (black turns yellow on this button)

Press Amp Zero button. Note black line from printed words ‘Amp Zero’ to the adjustment knob. Adjust amp zero knob to obtain 0000 reading on display.

Press Set button. Adjust ‘Gage Factor’ coarse knob to .50-1.8 position. Adjust Fine knob to obtain .887 reading on display.

Press Run button. Adjust ‘Excitation’ to 10 volts. Adjust ‘Coarse’ and ‘Fine’ Balance knobs to obtain 0000 reading on display.

Check: Gently twist the left (torque cell equipped) chuck clockwise (when facing the chuck). The strain indicator display should show a negative reading. The reading is the torque in pound-inches, and is valid to 10,000 pound inches.

On back panel of indicator case – Adjust Analog Level (gain) knob to setting of 682. This causes output of .500 volts for an indicator display of 1000µε, or 1000 pound-inches torque is .500 volts

Power Supply: Power supply for the troptometer is a little black box. Turn it to ‘ON’.

Plotter: Y channel (right side of front controls). Adjust the Y channel ‘zero’ knob to place the

pen near the bottom of the Y channel travel. Set attenuator knob to 100 (this is 100 mV/inch1V/10 inches. Y channel is now

1.00 volt for 10 inches, meaning 2000 pound-inches in 10 inches of plotter travel.

Check: Gently twist the left (torque cell equipped) chuck counterclockwise. The plotter should move higher on the page.

Check: Adjust the ‘Coarse’ knob on the strain indicator one click to the right. Strain display should be around 1200µε, and the plotter should move about 6 inches up the page.


Turn the ‘Coarse’ knob back to zero.

Specimen: Draw a line along the entire length of the specimen with a permanent marker. This is

so the twisting of the specimen will be easily visible. Install specimen into torque cell (left) chuck. Keep specimen 1/8 inch from bottoming

in the chuck. Run the motor and powered chuck forward or reverse as needed to obtain a desirable

starting point for rotation. Slide the left chuck, torque cell, and support assembly to the right and guide the

specimen into the powered (right) chuck. Tighten the chuck jaws. Measure exposed length between the chuck jaws.

Plotter and Troptometer: X channel (left side of front controls).

Switches: Multiplier switch to ‘x1’.

Units switch to ‘IN’. Sweep switch to ‘RESET’. Turn Attenuator knob to ‘2K’ position for 2 volts per inch of X travel. Turn Cal/Var knob to ‘MV’ setting on upper half of switch rotation.

Check: Gently rotate the troptometer, one end relative to the other. X channel of plotter should move one inch for a 20 degree rotation (2 volts).

Adjust X channel ‘Zero’ knob to place the pen near the center of the X channel travel. Manually rotate the troptometer to approximately a mechanically centered position.

Specimen: Install troptometer on specimen. Clamp the end frames to the specimen. Measure the distance between the end frames after they are clamped to the specimen.

Plotter and Troptometer:

Loosen the thumb screw on the shaft of the angle measurement sensor. Rotate the shaft to show the range of the angle measurement on the X channel. Rotate as necessary to obtain the center of travel and the plotter moving toward the right as the sensor shaft is rotated counterclockwise. Snug the thumb screws.

Reduce the X channel Attenuator knob voltage setting one position and adjust the ‘Zero’ knob on the X channel to center the pen in the X travel range.

Sequentially repeat the above step until the X channel is set to 200mV/inch. Settings and ranges are as follows: (for standard 11 by 17 plotter graph paper)

50mV/inch .5°rotation/inch of paper 8° for width of sheet 100mV/inch 1°rotation/inch of paper 16° for width of sheet


200mV/inch 2°rotation/inch of paper 32° for width of sheet (a good setting for a 1/2 inch steel bar, 12 inch gage length) 500mV/inch 5°rotation/inch of paper 80° for width of sheet There is sufficient clearance for the troptometer to rotate 32° from the

horizontal position to a final position. There is neither sufficient clearance nor sufficient range of the sensor to go from horizontal to 80° of rotation. If it is desired to use the maximum range of the system, it is necessary to attach the troptometer as shown in the following picture.

Plotter: Adjust both X and Y channel ‘Zero’ knobs to the desired location for the pen to start

for test recording. Install the pen, turn recorder to ‘Pen Down’.

Obtain instructor approval of the test setup at this point.

Test: Run the drive system in ‘Reverse’ mode. A speed of 30 degrees per minute is reasonable while plotting. When test has driven to right edge of plotter:

Turn plotter to ‘Pen Up’ Turn the X channel Attenuator knob back to ‘2k’ position. Remove the troptometer from the specimen.

Turn drive back on and record rotation and torque readings out to failure.

Turn off plotter, power supply, and strain indicator. Unplug the torsion machine. 6. Data Reduction & Reporting Plot as output from the plotter:

Troptometer on powered chuck end, starting position for maximum forward rotation angle. (CCW motion of powered chuck when facing powered h k)

starting

motion of powered chuck end of troptometer

ending position

torq

ue,

a point; you must d th l t t

approximate ‘knee’ of


Adjust your frame of reference so that you start at the point of zero twist and torque. From the twist/torque plot, multiple points must be selected from the start of the test up to the knee of the curve. It makes sense to select points in some repeatable fashion, like every 1 degree of twist or something like that. For each of those points you must read the twist and torque value off of the plot. Beyond the knee of the plot, select points much further apart since after the knee the part is yielding and less of interest is happening. After the plotter was shut off, you collected the points directly, angle of twist and torque, but remember that a different length applies beyond the knee. OK. So now you have a long list of points, each with a value for twist and torque. Even though stress values are not valid beyond the yield stress, determine the shear stress and strain and make a graph out as far as your plotter data will take stress and strain. Probably you will enter the angle and torque data into a spreadsheet, make a third column which is twist angle in radians, a fourth column which is shear strain and a fifth column that is shear stress. Now you have all the stuff to draw/plot a stress-strain diagram. Unfortunately, the shear stress equation is not applicable beyond the shearing yield stress, so a stress-strain curve will be partially invalid when carried beyond yield. Make a second plot of torque and twist data all the way to failure. This data is clearly not stress as a function of strain, but is unique to the particular specimen tested.

Mch T 214 page 35 Exercise 5 torsion 8/20/12

Torsion Test At the completion of this exercise you should be able to:

5. Produce stress-strain curves from the data collected during torsion testing of cylindrical specimens.

6. Determine shearing yield strength, shearing elastic modulus, and total strain at failure. 7. Write a brief report conveying the results of your testing to a knowledgeable reader.

This exercise is to be performed by groups of three or four students. All testing and data collection is to be performed as a group; data reduction and calculations, and report writing is to be an individual effort. The only major part of the reports that should be identical is the graphs produced by the testing machine. Photocopies of graphs are acceptable. You are to exercise good data collection habits by writing on the graph produced during testing.

Before you begin the test, write on the graph paper the date of the test and the type of specimen being tested.

During the test, with some torque applied to the specimen, note the torque on the display and confirm that you understand the torque value on the graph. Mark the torque graduations on the graph while it is still on the plotter. Do the same for what you understand about the graduations for twist, something like the following:

Specimens:

5. Hot rolled low-carbon steel, 1018/1020, solid round bar. For this specimen, compare the test results to published values.

6. EMT conduit, 1/2 inch nominal size. This is welded, galvanized (zinc electroplated), steel tubing.

Testing and data analysis:

Perform a torsion test of each of the supplied specimens: measure torque and angle of twist, from initial condition through specimen failure Compute for each specimen: shearing yield strength shearing modulus of elasticity, and shearing stress-strain curve for two specimens. angle of twist at specimen failure strain at specimen failure Draw curves for each specimen: shearing stress-strain from zero torque to a bit beyond shearing yield torque vs angle of twist from zero torque through specimen failure

Apparatus: Tinius Olsen Lo-Torq 10kip-in capacity bench-top torsion test machine

X lb-in

.Y degr.

Mch T 214 page 36 Exercise 5 torsion 8/20/12

Troptometer Pen plotter Dimensional measuring tools Procedure:

Perform torsion tests according to the instruction hand-out as a guide to operation of the machine, collection of data, and computations necessary for reduction of data.

Report:

A formal laboratory report of the style described in the laboratory report handout is required. The various material properties should be discussed and example computations included in the appendices. Compare the results to textbook values for the hot rolled bar. Include a plot of stress/strain to somewhere beyond yield but with sufficient resolution to clearly determine shearing elastic modulus from the graph. Include a plot of twist angle vs. torque all the way to failure.

Discussion Questions: (answers must be discussed in the report body text) 5. Were the failures brittle or ductile? Be clear to base your answer on what you

observed during the failure, and compare the observation to data collected if possible. 6. Discuss the potential uncertainty of measuring the twist angle from rotation of the

chucks rather than from the twist measurement system (troptometer) used here. 7. Draw two sketches of the stress present in a cross section of the solid bar tested. One

sketch of the stress prior to the bar reaching the yield point, and a second sketch after the bar has been twisted significantly beyond the yield point. (You may need to consult the textbook to get an idea of how this is usually sketched.) After the bar has been twisted beyond the yield point, can the stress on the outside surface of the bar be computed easily? Explain why or why not.

Grading: See the Knowledge base - Laboratory Report pages.

Mch T 214 page 37 Exercise 07 failure modes 1/5/12

Strain Gage Installation, Beam Stress and Strain, Poisson’s Ratio At the completion of this exercise you should be able to:

1. Do very basic installation and wiring of a strain gage. 2. Compute Poisson’s ratio

Each person in the class is to install a gage; this will be a group effort of two people to put two gages on the same member. The goal of this testing is to determine Poisson’s ratio for a steel specimen in bending. This is a 2-period exercise. Strain gages will be installed early in the semester; testing of the members will be performed later. Specimen:

3/16 thick by 1-1/4 wide by 10 inch long steel bar. Apparatus:

Strain gages and installation tools and supplies Tinius Olsen 10 kip bench-top universal test machine Flexure attachment for test machine Two strain indicators

Procedure:

1. Install two strain gages in the middle 4 inches of the specimen. Install one gage along the length of the bar (longitudinal), the other across the bar (transverse). Copies of the Student Manual for Strain Gage Installation will be available. Follow the procedure in that manual for installing gages on steel using M-Bond 200 adhesive.

Wires to the gages are to be soldered to the larger pads at the end of the gage. The red wire soldered to one pad, black and white together to the other pad. After soldering is complete, use a multimeter to test the electrical function of the soldering. Measure the resistance from the red wire to either the black or white wire, ~120Ω is to be expected for these gages. Resistance from white to black should be near zero, and resistance from any wire to the steel bar itself should be too high to detect. If these values are obtained, then clean the installation and apply the protective coating, label your beam with your name and date and store away for later in the semester.

longitudinal transverse

Grading: (exercise 6) Possible Made valid attempt to install strain gage 5


2. Compute the expected stress at the location of the gages, and the longitudinal strain that is expected to be produced by that stress. Be sure to draw shear and moment diagrams and show that the exact position of the strain gages is not significant; anywhere in the middle region is acceptable for this loading condition. Loading is to be as shown:

3. Connect strain gages to strain indicators.

a. Wiring to the strain indicators should be red wire to red terminal, white wire to white terminal, and black wire to D120 terminal.

b. Steps to operating the strain indicator are not too hard. Push left button – amp zero. Follow the line to amp zero knob; adjust knob until display is ±zero. Push second button – gage factor. Line to gage factor knobs; set left knob to range containing gage factor for gages you used, adjust right/fine knob until exact gage factor is displayed. Adjust excitation voltage thumbwheel to 5V excitation. Be sure last button shows black; 1/4 bridge wiring of indicator. Push third button – run. Adjust coarse balance knob and fine balance knob until display reads zero.

c. Now you should be ready to apply load and read strains. Display is directly in microstrain; a display of 1με is 1×10-6 in/in strain.

Apply the loading shown in #2 above (using a total of 300 pounds) with the flexure setup on the Tinius Olsen universal test machine. Measure longitudinal and transverse strains.

4. Compute Poisson’s ratio. 5. Compare measured longitudinal strain to that predicted in step 2. 6. Compare computed Poisson’s ratio to published value. A comment on Poisson’s Ratio: Poisson’s ratio is a fundamental property of the material,

and is defined as (the negative of) the ratio of the transverse to longitudinal strains in a uniaxial stress situation. What direction is the stress in this laboratory situation? Is there only one direction of stress? If so, then the definition of Poisson’s ratio applies and we may reliably compute the ratio. But in some other situation where there is stress in more than one direction, a stress in direction P still causes a strain in a perpendicular direction Q, but the computations are not so easy as the definition seems to indicate.

Report:

Submit your calculations and the results of your testing on a sheet of engineering paper.

6 inches 150 lbs 150 lbs

8 inches

Grading: (exercise 12) Possible Initials/date/description of test on each page 1/2 Shear/moment diag., comp. of stress/strains 1-1/2 Measured strains 1 Computed value of Poisson’s ratio 1 Comparisons of measured/computed to expected 1


MODES OF FAILURE – A Summary Concept:

A chain will break at its weakest link. Yet before a chain breaks, force flows through all the links, all parts having a stress. Application:

A structure or machine is not often made of supposedly identical links, rather from a variety of parts that must all work together and carry the loads. A single failed part usually causes the entire system to quit working. Some parts may carry the entire load, and other parts will carry only a part of the load.

An example is a jib crane, as shown in the following figure. The entire load that is lifted must be carried by the hook. The lift cable is reeved through a double block on the hook (that is, the cable runs through a pair of wire-rope pulley wheels) so that the lifted load is shared among four lengths of the cable. There are lots of parts in the hoist mechanism; we will ignore it for now. The hoist mechanism hangs from the jib beam, so the entire lifted load is carried by the beam. The cable carries the load in tension, where the beam is bent by the load, yet the same load is carried though it affects different parts differently.

Figure 5.1 Jib crane in Burke REDC room 127 Look more closely at the diagonal brace on the jib crane. Actual dimensions and

equilibrium computations using the principles of statics are required to determine the forces in the crane boom, however the free body diagram is much as shown in figure 5.2 below.

Figure 5.2 Jib crane free-body-diagram

tension in rod

load being lifted

reactions at wall


The load in the tension rod must go through some bolts, then a bracket, then a single bolt, then a different bracket, then through a large nut and finally into the tension

Figure 5.3 Jib crane tension rod connection

Example: Analysis of the bracket, and bolts into the crane beam, are somewhat complex because

of the angle of the tension rod and its force. But the big bolt through the bracket is not so hard. Assume for the sake of example that the force in the tension rod is 50 kN and the large bolt is 40mm diameter. What is the shear stress in the bolt?

Figure 5.4 Jib crane tension rod connection, top and side views If the bolt shears through on both sides, the shear stress is

19.9MPa

mm

N19.9

mm404

πplaces2

N50,000

A

Pτ

22

The angled, U-shaped bracket is a more interesting part. What stresses are in this part at the same time as the shear stress in the bolt? There are several that we will consider.

40 mm dia bolt

shear plane

forces in bolts

50 kN tension force in rod


Figure 5.5 Jib crane U-bracket

MPamm

N

mmmmplaces

N

DtNAreaBearingAwhereA

Fboltsofdiamthicknessboltsb

bbearing

5.625.6240102

000,502

Figure 5.6 Bearing stress in U-bracket side plates The bearing area is the projected area of the fastener, the diameter of the fastener and

the thickness of the plate. Bearing stress can sometimes be quite high, even causing some plastic deformation without there being any safety danger.

Tear-out stress, figure 5.7, will be low if the fasteners are far from the edge of the material. But if the fasteners are near to the edge tear-out can easily be the weak link in the structure.

Figure 5.7 Tear-out stress in U-bracket side plates

top view

rotated side view

force from bolt onto bracket

(2 places)

bearing stress – causes material to ‘mush out’ and/or hole to

elongate

assume 10 mm thickness of plates

tear-out stress – rips bolt through

the plates


assume 55 mm to edge of bracket


MPamm

N

mmmmplaces

N

AreaOutTearTotalAwhereA

Fto

toto

5.455.4555102

000,502

Figure 5.8 Net tensile stress in U-bracket side plates

125MPamm

N125

10mm2plates40mm160mm

50,000N

tDNwAreaTensileNetAwhereA

Fσ

2

Htt

t

Net tensile stress is the stress through the material that remains after the holes have

been drilled or punched, and in the line of the holes. If there is a line of 4 holes in a row, the net area remaining would be along that line. In contrast, gross tension is the tensile stress is the part some distance away from the fastener holes. In this bracket the gross tensile area would be the 60mm bracket height multiplied by the 10mm plate thickness times two locations.

A stress we are not going to compute, because at this stage you are not ready to compute it, is the bending stress present in any part. If bending is significant, as it is in the jib crane beam, bending computation is essential along with any other stresses that are present. An example of the effects of bending are shown in figure 5.9.

Figure 5.9 Exaggerated bending of U-bracket And at the same time, there is a tension stress in the rod and all the other stresses in all

the other parts in the complete crane. Which one is the weakest link? We cannot be certain

assume 60 mm height of bracket

net tensile stress tears part through

the smallest section



unless we load the crane heavier and heavier until something finally fails. What a mess that would be; let us hope the designer did a good job and there is never a failure.

Another example of stress computations: (This is how to report the data)


Assignment/Quiz: Your day will come to design and/or analyze a complex structure. Today the task is to

practice computation of the stresses present in a single fastened joint. The sketches below are the basis on which the quiz questions are built. The quiz is on Angel.

Questions 3 through 8:

Questions 9 through 15: Assume that the bolts are evenly spaced, and whatever ‘width’ is not used up by three

bolt spaces (three spaces, each one equal to ‘spacing’) is the edge distance.

spacing

width

edge distance in direction of load

thickness

bolt body diameter

Force

Force

Top view

Front edgeview

thickness

480 kN

480 kN

Top view

Front edgeview

60 mm

20 mm 12 mm

30 mm40 mm

24 mm bolts


Joints and Modes of Failure Test

At the completion of this exercise you should be able to: 1. Describe the appearance of some different possible modes of failure for a joint. 2. Compute the stress present at different locations in a joint. 3. Understand that at a single load there are different stresses at different locations in a

part. This exercise is to be performed by groups of three or four students. Dimensional measurement, testing, and data collection may be performed as a group. Each individual is responsible for individually performing all stress analysis. Specimens: See the attached pages for the sketches from which the specimens were manufactured. Be sure to check the actual thickness of the parts.

Apparatus:

Tinius Olsen 10 kip capacity bench-top Universal Test Machine Dimensional measuring tools

Procedure: Parts are to be tested in tension. Unlike the tensile tests performed previously, the goal of this testing is to record maximum force capacity for the pieces tested. A speed of .1 inch per minute should be a good starting point, but it may be useful to speed up some tests where there is significant elongation observed. Record the maximum force. (Use ‘peak hold’ capability of the UTM.) Draw sketches of the broken parts to show major locations of deformation. Record the actual failure mode. Compute the stress present, due to the maximum measured force, at each possible

failure region, whether the part failed at that location or not. For each specimen, calculate how it compares to a strip of material without a joint.

For example, a joint with a single rivet might fail at a force of 30% of the load of a new strip of that material.

Report:

A formal report is not required for this exercise. The primary purpose of this exercise is to do calculations of stresses present. Figures and computations are 80% of the total effort of this exercise. Make nice figures of the specimens as part of your original data sheets. Do the computations neatly. Compute every stress appropriate to every specimen, whether that stress caused failure or not. Indicate the actual mode of failure and actual force at failure. Show the ratio of joint failure force to failure force of a flat strip.


An example of a joint with computations is included in the Knowledge Base - modes of failure document. See a Strength of Materials book for additional information on computation of stresses and modes of failure.

Figure 1: Common joint failure modes

1. Shear Stress in Fastener:

4

2DNAreaShearTotalAwhere

A

F SS

S

2. Bearing Stress:

DNAreaBearingAwhereA

Fbb

bb t

3. Tear Out Stress:

AreaOutTearTotalAwhereA

Fto

toto

4. Net Tensile Stress:

tDNwAreaTensileNetAwhereA

FHt

tt

Rivet shear

Bearing failure – crushing of material

Tear-out

Net Tensile failure


Joint & Fastener test specimens:


stress analysis locations

fail

ure

mod

e gr

oss

tens

ion

net t

ensi

on

dire

ct s

hear

bear

ing

tear

-out

fail

ure

forc

e as

pe

rcen

t of

re

fere

nce

reference part N/A N/A one rivet 3-rivet, 1/8 to edge 3-rivet, 1/4 to edge 6 rivet braze N/A N/A 2 spot welds N/A

Grading: Possible Score Initials/dates/description of test on each page 1/2 ____ sketch of each failed part 1/2 ____ Each mode of failure identified 1/2 ____ Compute each stress existing in joint 3-1/2 ____ Total: 5 ____

Mch T 214 page 49 Exercise 08 flexure 1/5/12

Shear and Moment diagrams J. Student

sheet 1

V

M

Flexure Test – Bending and Horizontal Shear At the completion of this exercise you should be able to:

1. Compute bending stresses and horizontal shear stresses for members. 2. Describe the failure modes of members loaded in bending.

At least three specimens, more if available, are to be tested in 3-point bending. Only a very small amount of data is required; the majority of this exercise is computation of stresses for beams. A formal laboratory report is not required. A few sheets of engineering paper should be sufficient for all data, work, and reporting for this exercise. Specimens:

1. Rectangular cross section wood member 2. Thin web wood I beam 3. Thick web wood I beam 4. Other specimens if available

Apparatus:

Tinius Olsen 10 kip capacity bench-top Universal Test Machine Dimensional measuring tools

Computations prior to testing:

Draw shear (V) and moment (M) diagrams for one of these members with supports at 8 inches and a single load at the center. You may base the diagrams on a 1 pound load; when the actual failure load has been measured, the actual shear will be that load multiplied by whatever is shown on your shear diagram.

On each of the following sheets of paper, sketch and dimension the members to be tested, one member to a page.

Compute the second moment of area (I; also called the moment of inertia) for each specimen, on the specimen page. Compute c (distance from centroid to outermost fiber), web thickness, and Q for shear stress computations at the centroid surface (the centerline elevation).

Testing procedure and data collection:

Load each member to failure in 3-point bending. Record the force required to cause the failure. Describe the

Flexure Test Solid member

I = bh3/12 = ….. c = ….. Q = ….. .... type of failure @ force = …

Stresses at failure: σbending = ….. τweb shear = ….. Factor of safety at fracture: N bending = ….. N shear = ….

J. Studentsheet 2

Mch T 214 page 50 Exercise 08 flexure 1/5/12

fracture location and appearance of fracture surface for each specimen. Indicate whether you think the fracture was a result of shear stresses or bending (normal) stresses.

Computations following testing:

From the load at fracture, calculate the maximum shear and bending (normal) stresses for each specimen.

For each member, determine the factor of safety for each (shear and normal) type of stress. Assume the wood is southern pine, with an allowable bending stress of 1000 psi and an allowable shear stress of 70 psi. Factor of safety is the actual failure stress divided by the allowable stress.

Grading: Possible

Initials/date/description of test on each page 1/2 Shear and moment diagram 1/2 Correct units in every computation 1/2 I for each member 1/2 Q for each member 1/2 σfailure for each member 1/2 τfailure for each member 1/2 factor of safety on bending stress 1/2 factor of safety on shear stress 1/2 type of failure 1/2

MCH T 214 page 51 Exercise 9 flexure modulus 8/20/12

Shear & Moment J. StudentDiagrams sheet 1

V

M

Wood rectangle J. StudentComputations sheet 2

I = bh3/12 = …… σmax = Mc/I = …… Loadmax = ……

deflection load ……… …..

E = …… percent error = ….. spring rate k = …..

Deflection and Flexural Modulus of Elasticity At the completion of this exercise you should be able to:

1. Determine the flexural modulus of elasticity from bending deformation data. 2. Compute spring rate.

Multiple specimens are to be tested. All data and computations are to be done on engineering paper. You may be able to do this entire laboratory exercise on 6 sheets of paper. Each individual is responsible for all computations; do not submit a single set of work for a group. Specimens: maximum stress

1. Rectangular steel member 30 ksi 2. Rectangular aluminum member 15 ksi 3. Rectangular wood members 2 ksi

SPF (spruce-pine-fir, from a 2×4 structural member) Oak (from an oak floor board) Maple (from a very old/dead piano)

4. Plastic tubing 800 psi 5. Hockey stick 5 ksi

Apparatus:

Tinius Olsen 10 kip capacity bench-top Universal Test Machine Set up for 3-point bend testing Dimensional measurement tools

Procedure: On engineering paper, no more than two members to a page:

On your first sheet of engineering paper, draw shear and moment diagrams for an 8 inch long beam center loaded by a force of 100 pounds.

Sketch and dimension the members to be tested. Compute the second moment of area (I; also called the

moment of inertia) of the specimen. Compute the maximum load that may be applied to the

specimen while keeping the bending stress below the limit listed for each.

Load the specimen in bending, at a rate not to exceed .1 inch per minute. Record force data at every .01 inch of machine travel, until the computed maximum force or a maximum of .08 inches of deflection is reached. The plotter may be used to make this record if the horizontal

MCH T 214 page 52 Exercise 9 flexure modulus 8/20/12

Load vs. J. Student Deflection sheet 6

Deflection, inches

For

ce, p

ound

s

wood ….. steel ---- aluminum

kwood = …. kaluminum = …ksteel = ….. kplastic = …..

axis of the plotter is connected to indicate crosshead motion. The standard deflection formula for a simply-supported beam in flexure is

Re-arrange this equation algebraically and use it to compute E for each of these materials. Compute the percentage difference between your measured E and typical values of E. (about 29×106 psi for steel, 10×106 psi for aluminum, 1.3×106 psi for wood, and .4×106 psi for polymers, and maybe 5×106 psi for the composite hockey stick. Note that the values given here for wood and polymers are educated guesses and are expected to be significantly different from what is measured.)

Determine the spring rate (k) for each beam, pounds per inch of deflection.

On the last sheet of engineering paper, plot load vs. deflection for all of the specimens.

EI

FL

48

3

Grading: 10 items, 1/2 point each name, date, type of test on each page V & M diagrams I for each member Fmax for each member data for force vs deflection for each member computed E for each material correct units shown in computations percentage difference between computed E and guess of E listed above spring rate for each member graph of load vs. deflection for all members tested

Mch T 214 page 53 Knowledge base - impact 10/25/11

Absorbed Energy At the completion of this reading you should be able to:

1) Discuss the uses and validity of typical impact test data. 2) Explain the use of a Charpy and Izod impact test machine. 3) Explain how absorbed energy is determined for specimens in drop weight tests.

Background:

Impact test machine specimens are usually of one of three styles; Charpy, Izod, and drop weight. Charpy and Izod are well-defined, standard sized specimens. Drop weight machines may be set up for a specific specimen such as flat sheets, or may be used for penetration of materials, bending stiffness, helmet strength/penetration, or other somewhat imaginative testing. The general idea of impact tests is that the loading is quite rapid, to cause a very high strain rate, in contrast to much other testing which is quasi static. Both Charpy and Izod are bending tests, figure 1 and 2. The specimen is loaded into the machine and a pendulum with the appropriate striker is allowed to swing down and impact the specimen. Usually the specimen will break on contact. The swinging hammer is of known mass and starts from a known height, so its internal energy is known when it contacts the specimen. The hammer swings on past the impact point until it rises high enough to convert all its kinetic energy into potential energy. The amount of energy required to break the specimen is indicated by the difference between the original height and the final height of the hammer. A mechanical dial is usually used to show how high the hammer swings after impact, and the absorbed energy may be read from that dial. The pendulum of the machine we will use has kinetic energy of 300 ft·lb at the point of impact. (A comment on units is appropriate here. In statics, a moment is defined as force times distance, so the correct units are lb·ft. Both of the materials books in my collection use units of ft·lb for impact energy. I do not know if this is common, or an oddity of the authors.)

Figure 1: Charpy impact top view (a) after impact (b) just prior to impact

motion of pendulum point

notch

10×10×55 mm specimen

40 mm

support anvil


Figure 2: Izod impact side view just prior to impact The other general type of impact test is the drop-weight test. A known weight is raised to a known height above the specimen, the desired striker attached to the bottom of the weight, and the weight allowed to drop and impact the specimen. For example, the specimen may be a beam impacted in bending somewhat like a Charpy test, or the specimen a flat plate and the striker a round-nosed spike. Because it is a straight vertical drop, the weight will not find its own rest position after the impact. The impact energy absorbed by the specimen is determined by high-speed data collection equipment which records force and motion of the striker during the impact event. Absorbed energy is then computed from the physics definition of work, force times distance moved. (There is one of these machines in the PLET materials test area.) A relatively famous case of an impact failure is the breaking in half at dockside of a Liberty Ship during World War II. (Tanker SS Schenectady, Jan. 16, 1943) In testing of the material from which the ship was fabricated, it was discovered that for a high strain rate the material had essentially no ductility but only if cooled below a certain temperature. This property is evident in a variety of materials such as carbon steel, with the nil-ductility transition temperature varying with the chemistry of the material. Austenitic stainless steels (face-centered cubic crystal lattice, such as AISI 304 which is used for cookware among other applications) do not have this transition and are almost as resistant to sudden fracture at cryogenic temperatures as at room temperature. Most cryogenic storage containers are stainless steel, and their impact resistance is one reason.

Figure 3: General effect of temperature on impact properties. [from W. F. Smith, Materials Science and Engineering, McGraw-Hill, 1990]

motion of pendulum point 10×10×75 mm

specimen

22 mmclamping vise


Unfortunately, impact results are very sensitive to size of specimen and type of test. Even the same size of specimens cut from exactly the same block of steel will perform differently with different types of tests. The primary value in impact testing is comparative. If I use steel X, it transitions from ductile to brittle at this particular temperature. If I use steel Y, it transitions at a different temperature. Test results are so specific to geometry and type of test that the results are not able to be used in design from a quantitative standpoint. The test results do not allow computation of the effect of a particular impact force on a completed object. Rather, test data allows just the qualitative comparison that one material probably will be better than another, or that a material will probably transition to brittle at too high a temperature to be safe.

Figure 4: Comparison of impact performance and transition temperatures for some alloy steels, all at HRC40. [N.E. Dowling; harvested from UNM.edu website. Dowling, Mechanical Behavior of Materials, Pearson PrenticeHall, 2007. Attributed to H.J. French, 1956. “Some Aspects of Hardenable Alloy Steels”, Journal of Metals; Trans. AIME, vol.206, pp.770-782.]

The criterion used to determine the Nil-Ductility Transition temperature (NDT temperature), also called the Brittle-Ductile Transition Temperature (BDTT), is usually taken as the temperature below which the absorbed energy in a Charpy or Izod test is less than 15 ft·lb.

Procedure for impact testing:

If searching for transition temperature, each specimen will be heated or cooled to attain the desired metal temperature. Each one should be maintained at the desired temperature for at least 5 minutes so that there is some certainty that the metal has stabilized at the recorded temperature, and then it is essential that they be tested quickly so that the mass of the machine does not add or remove much heat from the specimen. The temperature range should extend from above the temperature of boiling water to liquid nitrogen at the low end. A sufficient number of different temperature conditions should be tested to


accurately find NDT, and this likely will require testing every 20°F in the ‘interesting’ range. The specimen is removed from the temperature bath with a special pair of tongs that orient the specimen. The specimen is moved with the tongs to the supports of the impact machine, and positioned so that the bar on the back side of the tongs just fits between the supports. The tongs are removed from the specimen and the machine, and the hammer released. Read the absorbed energy quickly when the hammer is in motion since it is desired to stop the hammer almost immediately and the brake will affect the needle position. Pick up the pieces and label them for specimen type and temperature.

Data to determine Nil-Ductility Transition temperature:

Record temperature and absorbed energy for each specimen tested. Plot the absorbed energy as a function of the specimen test temperature. For each specimen, record the appearance of the fracture surface. A ductile fracture should have observable deformation and a brittle fracture will not have much visible deformation.

Additional information:

Read “Dynamic Properties” section 2.3 through the end of Impact Test in Materials and Processes in Manufacturing by DeGarmo, Black, Kohser (the IET 101 textbook).

o Starts at the middle of page 42, ends at the middle of page 44 in 10th Edition o Starts at the top of page 40, ends in middle of page 41 in 9th Edition

Read “Temperature Effects” in DeGarmo o Starts at the middle of page 47, ends at the middle of page 49 in 10th Edition o Starts at the middle of page 44, ends in middle of page 46 in 9th Edition

Go back and re-read DeGarmo subsection on Toughness in the tensile testing section. o Starts at the bottom of page 34, ends at the top of page 35 in 10th Edition o Starts at the bottom of page 32, ends at the top of page 33 in 9th Edition

Mch T 214 page 57 Knowledge base - data acquisition operation 8/20/12

Data Acquisition Operation Getting UTM ready for the test: Turn on the 10 kip Universal Test Machine Run the machine up at least 1 inch, then down at least 1 inch Install the 3-point bending fixtures Set Force range to 5%

(This has meaning to the machine that a force of 500 pounds will cause a 1 volt output, or more generally an output of .002 volt per pound.)

Set Extension range to .5 inches (This has meaning to the machine that a motion of .5 inch will cause a 1 volt output, or .002 volt is equal to .001 inch motion.)

Capturing Data: Log into the computer adjacent to the UTM. StartAll ProgramsWINDAQDATAQ Instruments Hardware Manager When the hardware manager opens up, wait for a few seconds and a model DI-158-U should appear. (If not, the network cable may need to be wiggled. Don’t ask why I know this.) Click on Start Windaq. DI-158 Acquisition should start. Two channels of data are displayed. If not: view/format screen/2 waveforms edit/channels check 1,2 uncheck 3,4 In the left edge of the display, the range for both channels should be +1.25 volts to -1.25 volts. If not: edit/channel settings ch1 gain=8 ch 2 gain=8 We are not going to take an immense amount of data for pink foam beams, so: edit/sample rate 2/sec (1/sec per channel) Install the specimen into the machine and adjust the crosshead to bring the loading point close to the specimen. FileRecord Give the file a name that will remind you of the contents, and tell the machine to store it somewhere on your P drive where you will be able to find it easily. The program will tell you how many hours of recording time you have before your file is full. Just a hint – you won’t need nearly that much time. Start the test, watch the force (channel 1) and crosshead motion (channel 2) as the testing progresses.

Mch T 214 page 58 Knowledge base - data acquisition operation 8/20/12

When the test is complete (specimen fails): FileStop, FileClose, FileExit, OK. Export the file to Excel: StartAll ProgramsWINDAQWindaq Waveform Browser; go find your file to open. Open the file you saved above. Across the bottom of the display is a line labeled ‘DATA’ in the lower left. Place the cursor in that line, at the beginning of the interesting data, click once to get vertical line. Options… Enable Time Marker. (If don’t get 00sec in that bottom line, toggle Enable Time Marker again.) Move cursor to end of interesting data, click once to get vertical line. Should show number of seconds between first and second time markers. File…Save…file name.csv (comma separated variable format for export to Excel) File…Close Open Excel, import as .csv the file saved above. Data are all voltage as a function of time. Data points are taken sequentially, at the sample rate shown in the beginning of the data. Do whatever you need to do to the data.

Mch T 214 page 59 Exercise 10 impact 1/2/13

Computing area under a curve Example – force and movement as if from a tensile test Recorded data one region out of data Area of region = width * average height =(.2 inch-.1 inch) * ((78 lb+55 lb)/2) Total area under curve = total of all such regions If we assume data was taken every .1 inch, then the total runs from zero position to about .87 inches. There would be 8 regions with width of .1 inch, and the final region of width .07 inch. A short-hand version of what is done would be as a mathematical summation. The summation includes n areas, starting at number 1 and progressing to number n.

)2 1

i

n

1ii

i1-i

i1i1i

n

1ii

x)(xff

(

2

forceforce)distance(distanceArea

In the example above, xi is .2 inch, x i-1 is .1 inch, f i-1 is 55 lb and f i is 78 lb. It is more than likely that in many sets of laboratory data that i is time, so data from time i will be a force and a distance reading, and the time itself is of no particular value except to keep the data sorted in order.

.2 .4 .6 .80 0

20

40

60

80

100

position - inches

For

ce -

pou

nds

78 lb

55 lb

.1 in .2 in


If the distance spacing is made smaller and smaller, eventually there will be no real difference between the trapezoids and the curve. If the spacing is infinitely small, the difference between fi-1 and f i is negligible, and the result is an integral, but that only works if the function is known.

???

0

n

1ix1ii

n

1ix f(x)dxΔxfxxfArea


Impact and Energy Absorbed Determine Transition Temperature by Charpy Impact:

Practice quickly inserting the specimen against the Charpy anvils of the machine so that the temperature of the specimen is not much altered in the testing process. For the specific material for which transition temperature is desired, perform standard Charpy Impact test on at least 2 specimens at every 20 degrees at least from -100°F to +100°F. Record energy absorbed for each specimen. Plot absorbed energy as a function of temperature for the entire range. It should be expected that transition temperature effect will be clear from the graph.

Alternate exercise:

Break a couple of Charpy specimens to get the idea of how the machine operates and how to use the tongs to load a specimen into the machine without affecting the temperature of the specimen too remarkably. And then quit. Instead of a large number of impact tests, do a low speed bending test of a 1-1/8 wide by 1 inch thick piece of foam insulation. Loading rate of .4 inch per minute may be an OK starting point. Record force and deflection every 1 second, from zero load out to failure load. The data acquisition system will be utilized to record this data. Absorbed energy then is to be computed for the specimen, the sum of the force times distance. This is not impact energy, rather it is called the modulus of toughness, and is still a measure of energy absorbed. This is exactly what a drop-weight tester does, only the drop weight machine is much faster. From the foam insulation data:

plot force as a function of deflection compute area under the curve (absorbed energy)

-----it does make sense to do this in the spreadsheet----- prepare a hand calculation of one data point to verify that your spreadsheet does

the computations that you think it is doing stress at yield elastic modulus (yes, you will have to use the deflection formula for this like last

week.) stress at failure


Note about data sheets:

It is expected that the data recorded for any experimentation is carefully and maintained where it can be reviewed as needed. If the data is taken by hand, or captured by a plotter, it is usually expected that the original data will be included in any laboratory report, and certainly will be in the file where test results are stored. Where data is collected by computer, it is not usually printed out and stored on paper, rather the electronic file is archived by some means. Whether on paper or electronic, archiving of data is extremely important. From the standpoint of a report of laboratory testing, if data was collected electronically, there must be some mention of that fact, and a note detailing where the original data is archived.

Some impact data:

Because we are only capturing a limited number of impact tests, it may be useful to see the variation in the impact results for some different dates. The following is data taken from specimens in this course, and the dates of that data.

hot rolled steel specimens, batch prepared summer 2010, all were room temperature tests: spring 2011: 40 lb·ft, 30 lb·ft, 25 lb·ft, 35 lb·ft fall 2011: 40 lb·ft, 40 lb·ft 3/21/12 42 lb·ft, 32 lb·ft 10/31/12 42 lb·ft, 39 lb·ft 11/2/12 31 lb·ft, 31 lb·ft, 39 lb·ft, 40 lb·ft

Grading: Possible Initials/date/description of test on every page 1/2 Note stating data collected by DAQ; where archived. Force vs deflection graph 1 Absorbed energy 1 Hand computation to verify spreadsheet 1/2 Stress at yield 1/2 Elastic modulus 1 Stress at Failure 1/2

Mch T 214 page 63 Knowledge base - columns 11/1/11

Column Failure and Slenderness Ratio

Introduction: Compression members can fail in one of at least two different ways. Very short compression members fail by compressive yielding. Very long compression members fail by elastic buckling. Generally, compression members are somewhere between very long and very short, and predicting the failure mode and failure force or stress is of course important to the survival of the member. Compression members holding up buildings are almost always called columns, and compression members much longer than they are wide are usually called columns in other places as well. Whether called a column or not, a member in compression must be analyzed as a column most of the time. Compressive failure from yielding is more or less obvious. For short columns, the limiting stress is approximately the yield strength of the material. Buckling is less intuitive, for the column may bend or bow at a load well below the yield strength of the material. For a long column, the load capacity is a function only of the modulus of elasticity and the cross-sectional geometry of the column. This is shown schematically in the figure below. Long Columns: For a long column, buckling is usually predicted by the Euler (pronounced ‘Oiler’) formula for critical stress:

2

2

)/( rKL

Ecr

σcr = critical stress (the stress at which elastic buckling is predicted) = P/A E = modulus of elasticity of the material KL/r = slenderness ratio of the column K = end condition or fixity (see paragraph and figure below) L = column length

r = least radius of gyration of the column= AI /

Slenderness Ratio KL/r

Str

ess Failure by elastic buckling is predicted for

any stress greater than or equal to the critical stress according to the Euler

equation model

Failure by yielding is predicted for any stress greater than or

equal to the yield stress

Transition from yield to elastic buckling


Because elastic buckling of a compression member is a bending process, the moment of inertia as computed for bending is a component of the radius of gyration applied to columns here. End Fixity: The attachment of a compression member at its ends affects the performance of the member when load is applied. If the member is attached so that the ends may rotate freely, the failure force will be much less than if the ends are fixed so that rotation is not possible. End condition or fixity conditions have the effect of making the member act as if it is longer or shorter than the actual length of the member. To compute the Euler critical stress, the equivalent length is required, and so end condition fixity must be determined. End conditions are approximately as shown in the following figure.

Theoretical K value 1.0 .5 1.0 .7 2.0 Realistic value of K for design (AISC values)

1.0 .65 1.2 .8 2.1

End conditions Fixed end… rotation fixed and translation fixed

Pinned end…rotation free and translation fixed

Free end… rotation free and translation free

Guided end… rotation fixed and translation free

Le = L Le=.5L

Le=.7L

Le = L Le = 2L


Intermediate Columns: The difficulty with columns is what happens when the column is neither really long nor really short. The specimens in this exercise should span the transition from yielding to elastic failure, with some number of the specimens failing due to inelastic buckling in addition to the long columns failing elastically and the short members failing by yielding (plastically). For purposes of design, a variety of equations have been invented to match the measured behavior of intermediate columns, and to then apply a factor of safety. Various empirical equations are given in most strength of materials books. One of the more enduring versions is the J. B. Johnson formula. This equation approximates column behavior from KL/r of near zero up to KL/r equal to the transition slenderness ratio, or column constant Cc.

y

c S

EC

22

For columns with slenderness ratio (KL/r) longer than Cc, the Euler equation usually does an adequate job of predicting performance. For steel columns with slenderness ratio shorter than Cc, the performance usually is better predicted by the J. B. Johnson formula:

E

rKLSS y

ycr 2

2

4

/1

Summary: Short columns should be expected to fail when the applied compression stress is greater than the yield strength of the material. Intermediate columns, neither short nor particularly long, may fail in a mode that can neither be described as yielding nor as buckling. Intermediate columns are those where slenderness ratio for the column KL/r is less than or equal to Cc. Long columns should be expected to fail in an elastic buckling mode, defined by Euler buckling and the elastic modulus instead of material strength. Textbook Sections: Hibbeler chapter 13, sections 1 through 3.


1 in

2 in

Practice Problems: 1. Compute the both strong axis and weak axis slenderness ratios

for a member 2 inches wide, 1 inch thick, 36 inches long, and fixed both ends. partial answer: 31.2 about 1 axis

2. Assume the column in problem 1 is material with yield strength of 10 ksi. If a compressive force equal to 21 kips is applied to the member, is it likely to yield? partial answer: σ = 10.5 ksi

3. Assume the column in problem 1 is material with an elastic modulus of 10,000 ksi. If a compressive equal to 21 kips is applied to the member, does the Euler formula for critical stress predict that it will buckle? partial answer: σcr = 25.38ksi

4. A piece of 5 inch by 3 inch rectangular tubing is made from .06 inch thick sheet steel. Determine the maximum compressive force that may be applied in the long direction without either yielding or elastic buckling, assuming that the ends are pinned. Yield strength is 50 ksi, and elastic modulus is 30×103 ksi. partial answer: σcr = 33.39ksi

3 in5 in

120 in

.06 in

Mch T 214 page 67 Exercise 11 - columns 1/2/13

Column Failure and Slenderness Ratio At the completion of this exercise you should be able to:

1. determine slenderness ratio for a column. 2. describe the failure mode of short columns and failure mode of long columns.

Specimens:

1/2 inch EMT by 8 inches (flat ends) 1/4 dia by 3 inch 1/4 dia by 4 inch 1/4 dia by 5 inch 1/4 dia by 6 inch 1/4 dia by 8 inch 1/4 dia by 10 inch 1/8 dia. by 6 inch 1/8 dia. by 8 inch

Apparatus:

Tinius Olsen 10 kip capacity bench-top Universal Test Machine, set up for compression Dimensional measurement tools

Testing Data and Procedure:

Measure the cross-sectional properties of each specimen. Load each to failure in compression. Be sure to stop the machine as soon as initial

buckling is observed. Note the type of failure: straight compressive yielding, inelastic buckling (from local

compressive yielding), or elastic buckling. Computations: For each of the members tested, compute:

Compute the observed (actual) stress at failure (σfailure) the moment of inertia (I) the radius of gyration (r) slenderness ratio (KL/r) Euler critical stress (σcr)

all with hemispherical ends

Mch T 214 page 68 Exercise 11 - columns 1/2/13

Report: Prepare a (brief) formal report to discuss and convey your results to the reader. Plot on a single page: (Basically, build the graph on page 1 of the ‘knowledge base’ pages, but with real numbers.)

o Euler critical stress as a function of the slenderness ratio from KL/r = 300 down to wherever the critical stress is 80ksi. Critical stress every 10 of slenderness ratio… 300, 290, 280, 270, etc. until σcr > 80 ksi.

o A line at a constant stress of 58 ksi, which approximates the yield stress of the steel samples tested.

o Critical stress from KL/r = 0 to Cc using the J.B. Johnson equation. Critical stress in steps of every 10 slenderness ratio… 0, 10, 20, 30, etc. up to Cc .

o Observed failure stress data. (Your data points added as dots which of course will not fall exactly on any of the lines.)

It is suggested that you invent a spreadsheet to perform the calculations for this exercise.

Column Laboratory Report Grading Possible Score Typing, Spelling, Grammar

4 errors is 1/2 point Title Page 1 ______

Title Name, date, course, section Spacing on page

Introduction 1 ______

purpose or objective what was done stuff included in report

Summary 1 ______

brief summary of results, or one or two most significant results conclusions or recommendations (if any of either) where to find complete results

Discussion 1 ______

results discussion of results and behavior of material tested supporting facts how they lead to conclusion discussion questions

Figures/Tables/Graphs/ Appendices 1 ______

quality of graphs & axis scales initials, date, type of test, units original data sheets

Computations and correct results 5 ______ sample computations to validate spreadsheet computations Euler critical stress line J B Johnson line Yield line KL/r and stress for each data point

Total 10 ______

Mch T 214 page 69 Exercise 13 fatigue 4/9/12

Worksheet on Fatigue Testing At the completion of this exercise you should be able to:

1. Describe some standard test methods for measuring the fatigue properties of metals.

2. Use logarithmic graphing scales. Background:

When does failure occur? Certainly when a part breaks in two pieces, the part has failed. If a machine is grossly overloaded, causing some part to break, usually we would say the machine, or at least the part, has failed. If a load is applied to a machine and it causes visible deformation to the machine or parts of the machine, we would usually say there has been a failure. Equally, if a load on a machine causes a deformation that is not visible but yet makes the machine not work right, we would probably call that a failure as well. These failures can be caused by a single application of a load, quite possibly a static load. In design, we attempt to prevent these failures by selecting parts of sufficient size that the stress will be below the yield point and have small enough deflections that the machine will continue to function at full load. There is another class of failures that must be considered in the design and analysis of machines that are loaded more than once. Fatigue failure occurs from a stress below the yield point, but which is applied many times. Most mechanical failures are caused by repeated or ‘dynamic’ loading, even though neither yield strength nor ultimate strength were ever approached. For design, fatigue may be handled in at least two ways. The first is to estimate the endurance limit of the material and to be sure that the operating stresses in the parts are never higher than the endurance limit. The endurance limit, or endurance strength, is a stress that may be applied a very large number of times without causing a failure. For ferrous metals (steel) it is usually expected that there exists a stress that the part can survive an infinite number of times, and that if the part can be loaded more than a million cycles at some stress it will probably last an infinite number of cycles. Aluminum has no limit, and so the stress that an aluminum part can withstand without failure for 108 cycles is less that what it will carry for 106 cycles. The second method of handling design of parts for fatigue is to do regular inspections of the parts looking for cracks. The calculations must assume some crack size, and show that a part with the largest crack that was missed in this inspection will not grow to cause failure prior to the next inspection. This is the study of fracture mechanics. For design using fracture mechanics, fatigue data including crack growth rates from cyclic loading must be measured for the materials. Also the inspection process must be carefully tested to determine the minimum crack size that can be detected. The inspection frequency must be set from these design parameters.


Apparatus:

In the Behrend mechanical testing laboratory we have two fatigue machines available: a Sonntag reciprocating machine and an R.R. Moore style rotating bending machine. We also have an MTS universal test machine able to do tension-tension fatigue testing as well as general tension/compression tests.

Comparison of Fatigue Testing Machines in this laboratory: Sonntag Machine Notes R. R. Moore Machine Reciprocating beam Rotating beam Cantilever beam Simply-supported beam Stress-controlled test 1 Stress-controlled test Fatigue philosophy: infinite life 2 Fatigue philosophy: infinite life V ≠ 0, τ ≠ 0 V = 0, τ = 0 M = variable with length M = constant over length σ = constant over length 3 σ = variable with size & length Frequency = constant (30 Hz) Frequency = variable (up to 165 Hz) mean stress = variable (-1<r<1) mean stress = 0 (r = -1, “fully reversed”)lends itself to sheet-type stock lends itself to bar-type stock

Notes as applicable to the above machines:

1. Stress-controlled tests as opposed to strain-controlled tests. 2. Infinite life as opposed to “damage tolerant” fracture mechanics approach. 3. Stress is determined by Moment and specimen dimensions.

Specific exercise:

We do not have sufficient time to load a number of specimens and allow them each to cycle until failure, so we will use data collected some time ago.

1. Compute the bending stress, in the tapered region of the specimen below, which

would be caused by a 10-pound load at the loading point on the specimen. Be sure to draw the shear and moment diagrams in the spaces provided and show your determination of moment of inertia. .060 inch thick sheet metal.

Each student should compute the bending stress at a different location in the tapered region of the specimen, and then compare answer with the remainder of the class.

2. A set of data was collected some time ago for .060 thick sheet steel in bending, where the specimen was as shown above. Determine the stress level in the tapered region of the specimens for each of the loads listed below. Plot the data points and draw an S-N curve on the supplied log-log coordinates.


Workspace for computation of bending stress:

V

M

.060 in. thick

assume 3” length

Grading: Possible Initials/date/type of test on each page 1/2 Correct shear & moment diagrams 1/2 Stress in tapered section correct 1 Correct log-log graph of data 2-1/2 Correct axis labels/units on graph 1/2


Series1

specimen load, pounds Life, cycles ×103 Stress in tapered region 1 5 10,037 2 5.5 2,354 3 5.7 1,325 4 5.9 885 5 6 565 6 7 161 7 8 49 8 9 23 9 10 14 10 15 2

Documents

HARDNESS TESTS: Basics and Macrohardnessengr.bd.psu.edu/rxm61/214/Supplemental MchT 214 handouts.pdf · HARDNESS TESTS: Basics and Macrohardness ... charts for converting hardness