Lab Manual Mechanic of Materials SEM 2 20132014

DEPARTMENT OF MECHANICAL ENGINEERING COLLEGE OF ENGINEERING UNIVERSITY TENAGA NASIONAL

Mechanics and Materials Lab Manual MEMB221

Semester 2 2013/2014

TABLE OF CONTENTS ITEMS

PAGES

Laboratory & Reports: An Overview

3

Guidelines for Informal Laboratory Report

4

Guidelines for Formal Laboratory Report

6

Basic Laboratory Safety Rules

8

Experiment 1

Tensile Test

9

Experiment 2

Torsion Test

14

Experiment 3

Bending Test

20

Experiment 4

Buckling Test

23

Experiment 5

Hardness Test

34

Experiment 6

Thin Cylinder

37

Experiment 7

Impact Test

51

Experiment 8

Microstructure Analysis

57

References Lab Schedule

61

2

Laboratory & Reports: An Overview Preparations and procedures

: The experiment is conducted by groups of students under the guidance of instructor.

Pre Lab and Quiz, Informal Reports and Formal Reports

: Pre Lab and Quiz - Each student must answer the pre lab/quiz at the beginning of each session in group. These practices to ensure each student are fully prepared to conduct the experiment as stated in course schedule. Informal Reports - The informal report needs to be submitted at the end of each session. The informal report must have following criteria: date of experiment; title of experiment; objective(s); data and observation; analysis; results and discussion; and conclusion. Formal Reports - vital part of good engineering practice. They permit the organisation, condensation, analysis, interpretation, and transmission of meaningful result. Two (2) Individual Formal Reports and one (1) Group Formal report must be submitted once identified by instructor. The reports are to be handed in at the beginning of the next period unless otherwise directed by the instructor. No late reports will be accepted. Late submission will be subjected to mark deduction penalty. 20 marks will be deducted for one day late, 40 marks for 2 days, 60 marks for 3 days and no report will be accepted after that.

Grading

: In order to obtain credit for each laboratory period, a student must: a. answer the pre lab quizzes b. work effectively as part of a team to obtain accurate data c. submit an acceptable reports These requirements imply that each student must come to the lab meeting on time and fully prepared. Students who are tardy, who do not do their best in being efficient and careful in conducting the experiment will receive a zero, failing, or incomplete grade for that experiment. There will be no opportunity to makeup work, which has been missed because of an unexcused absence or tardiness. Exceptions will be made in cases where acceptable excuses are received in writing. If conditions develop which may cause a student to miss any laboratory work, the student must inform their lab instructor as soon as possible in advance of the scheduled laboratory.

Plagiarism

: Student must not adopt or reproduce idea words or statements of another person without an appropriate acknowledgement. Copying someone else‟s work or facilitating academic dishonesty constitutes plagiarism. Plagiarism will be heavily penalized and the student will receive zero marks for that report. Students must submit their formal report (individual and group formal report) in Microsoft Word format to http://turnitin.com/ for similarity checking. Class details (class section/ID and enrolment password) will be given later by respective instructor. The similarity checking must not exceed 70%. Special highlight will be given to summary, discussion and conclusion.

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Guidelines for Informal Laboratory Report General Instructions: Informal Report has to be prepared individually and manually. No Items Description 1. Cover page 1. Author‟s name and SID no. 2. Title of experiment 3. Day and date of experiment 4. Course and course code 5. Semester and Academic Year (e.g. Sem 1 2013/14) 6. Section and group number 2.

Statement of Purpose / Introduction / Objective (1%) Data (2%) and Observations (1%) Analysis and Results (8%)

This should be a brief description of what the experiment is demonstrating. Be specific. It should be consistent with the statement of the experiment instructions.

5.

Discussions (4%)

This section should tie the results of the experiments to the purpose. Sources or error, deviations and uncertainty should be discussed and how they might affect the results. Any points that are specifically asked for in experiment instructions should be discussed in this section.

6.

Conclusions (3%)

This section summarizes the lab report. Any conclusions drawn from the results should be given in this section. Express the implication of the results. Examine the outcome in the light of the stated objectives.

7.

References (1%)

A list of all references used in writing the report should be included in this section. Use the following format: 1. Book :

3.

4.

The data and observations obtained in the experiments should be presented in an orderly form – in a data table if possible. The data obtained will be analysed with a view towards fulfilling the purpose stated at the beginning of the report. If there is an accepted or expected value for a quantity that is to be obtained by the experiment, the percentage difference between the expected and experimental value should be calculated. In many cases, complete with graph, which is often a very helpful way of showing the relationship between two quantities. The graph must have a title, each exist will show scale, units, and a label. All data points must have a marking to show that it is an observed data point and all data points must be connected showing the trend of the data.

4

(Note: Books and Journals are highly recommended)

a. Author (s). Year. Title. Edition. Place: Publisher. Page number. (example: L.H. van Vlack. 1989. Elements of Materials Science and Engineering. 6th Ed. Reading :Addison-Wesely Publ. pp100-105.) b. Title. Year. Book Title. Edition. Place: Publisher. Page number. (Example: Materials Science Handbook. 1986. 20th Ed. Ohio: C.R.C. Press. pp. 1986) 2. Journals : Author (s), Year, Article Title; Journal Title, Volume, Page number. (Example: Brandt, A. 1977. Multtilevel adaptive solution to boundary value problems. Math of Computation. 31: 333-390) 3. Internet : Title. Year. URL. (Example: Selected encyclopedias and major reference works in polymer science and technology at Stanford University. 1998. http://wwwsul.stanford.edu/depts/swain/polymer/encys.html

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Guidelines for Formal Laboratory Report General Instructions: 1. Formal Lab Report has to be prepared individually or in group and must be printed properly. 2. Softcopy has to be submitted to http://turnitin.com/ with similarity checking not exceed 70%. No 1.

Items Title page (3%)

Description This page must include: 1. Title of experiment 2. Course and course code 3. Semester and Academic Year (e.g. Sem 2 2012/13) 4. Day and date experiment was performed and due date 5. (a)* Individual reports: Author‟s name and matrix no; and Names and matrix no(s) of group member (b)* Group Reports: Names and matrix no(s) of group member * Either (a) or (b) 6. Section and group number 7. Name of the lab instructor

2.

Table of content (2%)

This should be placed following the title page (for reports more than 10 pages). It should list up each section of the report and corresponding page number.

3.

Summary / Abstract (10%)

This should encapsulate the major portion of the report and provides a concise overview of the work. The length should be no more than 200-300 words or 2-3 paragraphs. It should highlight the objectives, results and conclusions of the experiment.

4.

Statement of Purpose / Introduction / Objective (5%)

This should be a brief description of what the experiment is demonstrating. Be specific. It should be consistent with the statement of the experiment instructions. Some experiments have one or more parts and each part demonstrates a different aspect. Be sure to include all objectives of the experiment in this section.

5.

Theory (5%)

Any theory related to the experiment should be included. The theory must be clearly explained and complete with diagrams where necessary. The relevant equations should be introduced. Each figure should be labelled and numbered.

6.

Equipment / Description of Experimental Apparatus (5%) Procedure (10%)

A list of equipment and specimen used should be included. This may be the same as the list on the experiment instructions. Sketch of the equipment should also be included where necessary.

7.

This is a step-by-step explanation of what was done in the lab and why each step was performed. The procedure listed in the experiment instructions may be used as a guide. The description does not have to be very lengthy, but should enough detail so that a reader knowledgeable in the field would understand

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what was done. Sufficient information should be provided to allow the reader to repeat the experiment in an identical manner. 8.

Data (10%) and Observations (5%)

The data and observations obtained in the experiments should be presented in an orderly form – in a data table if possible. A spreadsheet would be ideal, especially if there are many repetitive calculations in the analysis of the data. Each table, figure and graph should be labelled and numbered.

9.

Analysis and Results (15%)

The data obtained will be analysed with a view towards fulfilling the purpose stated at the beginning of the report. When possible, part of the analysis may be combined with the data table in a spreadsheet. If there is an accepted or expected value for a quantity that is to be obtained by the experiment, the percentage difference between the expected and experimental value should be calculated. In many cases, another part of the analysis will be the construction of the graph, which is often a very helpful way of showing the relationship between two quantities. The graph must have a title, each exist will show scale, units, and a label. All data points must have a marking to show that it is an observed data point and all data points must be connected showing the trend of the data. If the student is using a computer software package to generate graphs, then this package must convey the same information as would a hand generated graph.

10.

Discussions (15%)

This section should tie the results of the experiments to the purpose. Sources or error, deviations and uncertainty should be discussed and how they might affect the results. Any points that are specifically asked for in experiment instructions should be discussed in this section.

11.

Conclusions (10%)

12.

References (5%)

This section summarizes the lab report. Any conclusions drawn from the results should be given in this section. Express the implication of the results. Examine the outcome in the light of the stated objectives. A list of all references used in writing the report should be included in this section. Use the following format: Book : 1. Author (s). Year. Title. Edition. Place: Publisher. Page number. (example: L.H. van Vlack. 1989. Elements of Materials Science and Engineering. 6th Ed. Reading :Addison-Wesely Publ. pp100-105.) 2. Title. Year. Book Title. Edition. Place: Publisher. Page number. (Example: Materials Science Handbook. 1986. 20th Ed. Ohio: C.R.C. Press. pp. 1986) Journals : Author (s), Year, Article Title; Journal Title, Volume, Page number. (Example: Brandt, A. 1977. Multtilevel adaptive solution to boundary value problems. Math of Computation. 31: 333-390) Internet : Title. Year. URL. (Example: Selected encyclopedias and major reference works in polymer science and technology at Stanford University. 1998. http://www-sul.stanford.edu/depts/swain/polymer/encys.html Note: Books and Journals are highly recommended

13.

Appendices

7

Basic Laboratory Safety Rules Each and every students taking MEMB221 (Mechanics and Material Laboratory) are expected to follow these requirements in order to ensure the safety throughout the semester: GENERAL GUIDELINES 1. Do not enter laboratory until you are instructed to do so. 2. Conduct yourself and your experiment in a responsible manner at all times in the laboratory. 3. When first entering laboratory do not touch any equipment, chemicals, or other materials in the laboratory area until you are instructed to do so. 4. All personal belonging, which you do not need during the experiments, must be placed in the cupboard. 5. Perform only those experiments authorized by your instructor. Unauthorized experiments are not allowed. 6. Follow all written and verbal instructions carefully. 7. Never work alone in the laboratory. No student may work in the laboratory without the presence of the instructor or technician. 8. Do not eat sweets, drink beverages, or chew gum in the laboratory. 9. Be prepared for your work in the laboratory. Read all procedures thoroughly before entering the laboratory – remember you have to answer pre lab questions before performing the experiments! 10. Never fool around in the laboratory. 11. Clean up all areas of the laboratory where you (and your group) worked. 12. Experiments must be monitored at all times. Do not wander around the room, distract other students, startle other students or interfere with the laboratory experiments of others. 13. Dress properly and decently during a laboratory activity. Shoes must completely cover the foot. No sandals and open toed shoes are allowed on lab days. ACCIDENTS AND INJURIES 14. Report any accident (spill, breakage, etc.) or injury (cut, burn, etc.) to the instructor or technician immediately. HANDLING CHEMICALS 15. Check the label on all chemical bottles twice before removing any of the contents. Take only as much chemical as you need. 16. Never return unused chemicals to their original container. 17. Place the used chemical in a labelled beaker inside the fume hood. Do not throw it into sink. 18. Never remove chemicals or other materials from the laboratory area.

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Experiment 1 Tensile Testing (Universal Tester) Objectives 1. To understand the principles of tensile testing. 2. To determine the stress-strain relationship for two types of material 3. To determine the values of: i. elongation at fracture ii. tensile strength (UTS) iii. yield strength (offset of 0.2%) iv. Modulus of Elasticity Theory If a load is static or changed relatively slowly with time and is applied uniformly over a cross section /surface of a member, the mechanical behaviour may be ascertained by a simple stressstrain test. These tests are most commonly conducted for metals at room temperature. There are three principal ways in which the load may be applied: tension, compression and shear. Tension is one of the most common mechanical stress-strain tests. The stress-strain diagram shows the different behaviour of the individual materials particularly clearly. Each material has a characteristic pattern of stress and strain. A standard specimen is deformed, usually to fracture with a gradually increasing tensile load that is applied uniaxially along the long axis of a specimen. Most of the tension tests for metals are conducted according to the ASTM Standard E 8 and E 8M, “Standard Test Methods for Tension Testing of Metallic Materials”. Technical Description of the Equipment The WP 300 material testing device is a robust unit designed specifically for technical instruction and is one of the classical materials testing device in materials science. The flexible design of the unit permits a wide range of different tests requiring tensile or compressive force. Thanks to its clear, sample layout, the unity is ideally suite for both students‟ experiments and for demonstrations. Its compact dimensions and relatively low weight permit mobile use and erection on all common laboratory benches.

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Basic In its basic form, the unit does not require any external connections. The test force is generated via a manually actuated hydraulic system and displayed via a large, easily legible display instrument with a trailing pointer. Elongation of the samples is recorded via a dial gauge. All accessories are screwed to the cross members. This means that the test unit can be quickly and easily refitted for various tests. The basic unit essentially consists of the following elements:  machine base (1) with handgrip (11)  support with cross-head (2)  load frame with upper (3) and lower crossmember (4)  hydraulic system consisting of a main cylinder (5) and a master cylinder with hand wheel (6)  force display (7)  elongation display via a dial gauge (8) gripping heads (9) with sample (10)

Machine Base The rigid machine base made of cast iron forms the foundation and ensures stability of the test unit in connection with 4 rubbers feat. The machine base supports the hydraulics and the frame.

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Support The posts (1) and cross-head (2) form fixed support of the test unit. The various fixed sample receptacles are fastened to the cross-head. The mobile load frame is also mounted on it lowfriction linear ball bearings. Load Frame The load frame consists of the upper (1) and lower crossmember (2) and the guide rod (3). The load frame transmits the test force from the hydraulic main cylinder to the relevant sample. The load frame is slide-mounted in the cross-head of the support. Tensile samples are clamped between the upper cross-member and the cross-head, whilst compressive samples are clamped between the lower cross-member and the cross-head.

Hydraulic system The test force is generated by hydraulic means. A piston in the master cylinder (2) actuated via the hand wheel (1) and the threaded spindle creates a hydrostatic pressure, which induces the test force in the main cylinder (3). The hydraulic transmission ration is 2.77:1, whilst the mechanical transmission ratio hand wheel / spindle is 503:1. Excluding friction losses, this would correspond to a manual force of 1 N per 1.3 kN test force. The full stroke of the main cylinder of 45 mm requires 83 revolutions of the hand wheel. Force display & elongation measurement

The force measuring device operates according to the manometer principle. It measures the hydrostatic pressure in the hydraulic system. The large display with a diameter of 160 mm facilitates precise reading. A maximum pointer stores the maximum force. The elongation is measured via an adjustably mounted dial gauge. The dial gauge indicates the relative displacement between the upper cross member and the cross-head.

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Gripping heads

The gripping heads are designed for tensile samples with an M10 threaded head. In addition, flat compression pads can easily be inserted in the crosshead and cross-member and are held by nut.

Tensile sample

Round samples with an M10 threaded head in accordance with DIN 50125 made of aluminium, copper, brass and steel are supplied with the machine. Tensile sample B6 x 30 DIN 50125 This is a short proportional test bar with a measuring length of 30 mm and a diameter of 6 mm.

Procedure The test device is set up as follows: 

 

Untwist the hand wheel on the master cylinder as far as it will go and move the load frame down to its lowest position. (if this has not been done, insert the gripping heads in the upper cross-member and crosshead). Screw down the gripping heads with the short bolt at the bottom and with pressure pad. Gripping head with the long bolt at the top

Insert the required tensile sample.    

Measure and note down the test length L O of the sample between two marks. Screw the sample by hand into the lower gripping head as far as the end stop. Screw the sample into the upper gripping head as far as the end stop, by rotating the gripping head itself. Tighten the nut on the upper gripping head by hand until he gripping head is seated without slack in the upper cross-member. 12

.    

          

Adjust the dial gauge Push the dial gauge upwards on the support bar until the tracer pin is touching the drive. Set the rotating scale on the dial gauge to zero. Set the maximum pointer on the force display to zero.

Slowly and constantly loaded by rotating the hand wheel. Application of the force should spread over a time interval of 5-10 minutes It is essential to avoid sudden, jerky force application. Observe the dial gauge and the sample. For the first 1 mm extension, record the force value for every 0.1 mm extension. Above 1 mm extension, record the force value for every 0.2 mm extension Monitor the sample and note when constriction begins. From now on, the force will be no longer increase, but instead, will tend to decrease. ATTENTION: don‟t be startled! Particularly with some material, fracture will occur with a loud bang. Remove the sample from the gripping heads Twist back the hand wheel on the master cylinder as far as it will go and move the load frame down. Repeat with the other specimen.

Question 1. Concrete is strong in compression but relatively very weak in tension. How to improve such mechanical properties in order to transmit better tensile force?

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Experiment 2 Torsion Test Objectives 1. To understand the principle of torsion test. 2. To determine the modulus of shear, G through measurement of the applied torque and angle of twist. Theory Torsion is a variation of pure shear wherein a structural member is twisted, torsional forces produce a rotating motion about the longitudinal axis of one end of the member relative to the other end. Torsion tests are normally performed on cylindrical solids shaft or tube. Most of these tests are performed according to ASTM Standard E 143, “Standard Test for Shear Modulus”. In each test, torque and twisting angle are measured to determine the shear modulus, G.

T G  J L

, J

r 4 2



d 4 32

Where; T = torque J = polar moment of inertia G = shear modulus  = angle after application of torque L = length d = diameter r = radius

Specimen made of various materials, with differing diameters and lengths may be investigated. The effective torque is recorded with the aid of a reference rod equipped with strain gauges. The torque is directly displayed on a digital display of a strain gauge measurement amplifier. This also incorporates important principles of electronic measurement of mechanical values into the experimental program. The unit is primarily intended for practical laboratory experiments. Technical description of the apparatus The apparatus consists mainly of:  1 – Loading device with scale and revolution counter for twisting angle measurement  2 – Torque measurement unit  3 – Calibration device  4 – Specimen (is mounted between the loading device and torque measurement unit into hexagon socket)  5 – Track base  6 – Digital torque meter

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Figure 2.1: Layout of the torsion apparatus

Technical data General data: Main dimension Weight

: 1400 x 350 x 300 mm : 25 kg

Loading device: Worm gear reduction ratio Revolution counter Output scale Input scale Indicator

: 62 : 5 digit, with reset : 360 : 360 : Adjustable

Torque Measurement unit: Range Display Temperature operating range Power supply

: 0 – 30 Nm : 6 digit, LED 14 mm : 0 - 50  C : 230 V, 50/60 Hz

Calibration device: Maximum load Load increment

: 30 Nm : 2.5 Nm

15

Loading Device The torsional loading is transmitted to the specimen by a worm gear (1) and a hand wheel (4). The twisting angle at the output and the input is read off by two 360 scales (2,3). At the input side of the gear there is in addition a 5-digit revolution counter (5) which shows the input revolutions 1:1. The worm gear has a reduction ratio of 62. The specimen‟s hexagon ends are set into an axial moveable socket (6) at the worm gear output end. Torque measurement unit In this testing the torque will be measured by a reference torsion rod and strain gauges. The specimen is mounted on one side to the loading device and on the other side to the torque measurement device. The load torque applied to the specimen produce shear stresses in the measurement torsion rod. These shear stresses are proportional to the load torque. Strain gauges are used for detecting the shear stresses. Because strain gauges can only measure strain but not twisting they must be applied in the direction of the maximum principal stress. In the case of pure torsion the maximum of principal stress will occur at a 45 to the axial axis of the torsion rod. Due to the arrangement of 4 strain gauges in form of a full bridge circuit the distortion influence of additional bending and direct stresses is minimized. The signal of the gauges is conditioned by a measuring amplifier with a digitally read out. The amplifier also delivers the supply voltage for the bridge circuit. The load torque will occur a slight deformation of the torsion rod. This will cause an error in determining the twisting angle of the specimen.

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To reject this error, the specimen holder of the torque measurement unit is turnable. The deformation can be compensated by a lever and a threaded spindle at the fixed side of the torsion rod. The compensation can be controlled by a dial gauge at the side of the specimen holder.

The output signal of the strain gauge bridge is conditioned in a measurement amplifier with a digital display. (Attention: strain gauge circuit and measurement amplifier is calibrated together at our works. They should not be changed, otherwise the accuracy will not be given any more.) Specimen

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Procedure a) Calibration For calibration of the torque measurement unit a defined load torque is used as reference. This reference load torque is generated by a calibration unit. The calibration unit mainly consists of a lever and a load weight. The weight of the lever is balanced by a certain counter weight. By that the load torque only depends on the load weight. A wide range of torque between 0 and 30 Nm can be set thanks a division into weight discs. The resolution is 2.5 Nm. The calibration unit must be clamped near by the specimen holder of the torque measurement unit. To connect both units use the 15 mm hexagon socket.

To calibrate the torque measurement unit:  Set the read out of the amplifier to zero.  Connect the torque measurement unit to the measurement amplifier  Switch on measurement amplifier at the back plane  To set the read outs to zero press and hold V button and press P. there should be no load torque.  Increase the load torque in steps by 5 Nm and notice the read out  After reload check the offset and set it to zero as necessary.

The read out values should be corresponding to the applied load torque. The noticed values of load torque and read out can be graphed in a diagram. The curve will show you nonlinearities, if exist. In this case, you can use it as calibration curve. Graph 2.1: Example for a calibration curve of the torque measurement unit.

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b) Performing the test 

Mounting the specimen

1. 2. 3. 4. 5.

In this test the short specimen is used. Mount the specimen between the loading device and the torque-measuring unit. Use the 19 mm hexagon socket. Make sure the shifting holder of the load device is in the mid position. Make sure that there is no preload on the specimen. If necessary turn the hand wheel at the input of the worm gear until the read out of the amplifier is zero. 6. Set both indicators at the input and at the output shaft of the worm gear to zero. 7. Set the dial gauge of the compensation unit to zero. Therefore turn the turnable scale. 8. Reset revolution counter. 

Loading the specimen

1. Turn the hand wheel at the input of the gear clockwise to load the specimen. Turn it only for a defined angle increment. 2. For the first rotation choose an increment of a quarter rotation (90), for the second and third rotation of a half-quarter (180) and for the 4th to 10th rotation of one rotation (360). 3. To calculate the twist angle at the specimen (output angle of the gear) divide the rotations at the input by the reduction ratio of 62. 4. Fracture will occur between 100 and 200 rotations. 5. Compensates the deformation of the measuring torsion rod after each angle increment. Doing this turn the hand wheel of the compensation unit until the dial gauge indicates zero. 6. Read the torque value from the display of the amplifier and note it together with the indicated twist angle. 7. Table the result. 8. Repeat the experiment with other test specimen Questions 1. Plot a graph of calibration curve of Amplifier Torque value (read-out at amplifier torque value) vs. the Applied Load Torque value. Observe and determine the trend of the curve. 2. The specimen torque value is measured by the amplifier (read-out at amplifier torque value). By using the equation from the calibration curve, determine the actual Load Torque value from the read-out amplifier torque value. Plot a graph of Load Torque vs. Revolution in radian at gear output. 3. Determine the experiment shear modulus, Gexp for each material. Compare the results with the theoretical value, G. 4. Based on your results, concluded the different between specimens tested. 5. What are the common mechanical parts that are subjected to torsion?

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Experiment 3 Bending test – tensile strength (OPEN-ENDED LAB) Objectives 1. To investigate the relationship between load, span, width, height and deflection of a beam, placed on two bear affected by a concentrated load at the center. 2. To ascertain the coefficient of elasticity for steel, brass, aluminum and wood. Theory The stress-strain behavior of brittle materials (e.g. ceramic, low toughness composite material) is not usually ascertained by tensile tests as outline in Exp. 1. A more suitable transverse bending test is most frequently employed, in which a rod specimen either a circular or rectangular cross section is bent until fracture using a three- or four-point loading technique. The assessments are conducted according to ASTM Standard C 1161, “Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature.” In this module, the apparatus has been design to enable students to carry out experiments on simply supported and cantilever beams in order to investigate:(a) the relationship between the deflections and the applied loads (b) the effect of variations in 1ength and cross sectional i.e. deflection per unit load.

Simply supported beam with central point load

For this arrangement, it can be shown that the deflection under the load i.e. maximum deflection

Wl 3  48 EI

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bd 3 where I  12

beam compliance

 l3  W 4Ebd 3

Determination of coefficient of elasticity

Calculations: Deflection formula for the load given above:

 

FL3 48 EI

E

FL3 48 I

A determination of the flexural stress yields: M L b  b M b  F  F1  Wb 4 Where:  = L = Mb = Wb = b =

Deflection (mm.) Span(mm.) Moment of Flexure (Nmm) Resistance to Flexure (mm3) Flexural Stress (N/mm2)

E = I = F1 = F =

Set of Apparatus Twist and Bend Test Machine MT 210.

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Coefficient of Elasticity Inertia Factor Load occasioned = by weight of load device =2.5N Load occasioned by additional weight (N)

Procedure Task 1: To investigate the relationship between load, span, width, height and deflection of a beam, placed on two bear affected by a concentrated load at the center. a): Investigate the relationship between load and deflection b): Investigate relationship between span and deflection c): Investigate the relationship between width and deflection of the test specimen. d): Investigate the relationship between the height and deflection of the test specimen. Task 2: To ascertain the coefficient of elasticity for steel, brass, aluminum and wood. When E is calculated, the initial load caused by the load device has no significance since the gauge has been set at zero with the device in place. However, when calculating flexural stress, F 1 is included. Questions Q. 1: Discuss the relationship observed for a, b, c & d and Q. 2: Compare the Coefficient of Elasticity obtained with the theoretical value for steel, brass, aluminum & wood. Discuss the result. Q. 3: Give two reasons why the tensile properties of most brittle materials are accessed by transverse bending tests and not ascertain by tensile tests.

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Experiment 4 Buckling Test Objectives 1. To determine critical buckling loads for columns with support. 2. To examination the Euler theory of buckling. 3. To investigate the influence of different material parameters. Introduction All relevant buckling problems can be demonstrated with the WP 120 test stand. Buckling, as opposed to simple strength problems such as drawing, pressure, bending and shearing, is primarily a stability problem. Buckling plays an important role in almost every field of technology. Examples of this are: -

Columns and supports in construction and steel engineering Stop rods for valve actuation and connecting rods in motor construction Piston rods for hydraulic cylinders and Lifting spindles in lifting gear

Theory

a) Applying the Buckling Theory If a rod is subjected to longitudinal forces, as implied in the sketch, it can fail in two ways. On the one hand, it can be plasticized and flattened if its admissible compressive strain is exceeded (see Fig. 3.8). On the other hand, it is possible that it will suddenly shift to one side and buckle before attaining the admissible compressive strain. This effect is called buckling. The shape of the rod is the factor determines which of the two cases of failure will occur. A slender, thin rod is more likely to buckle than a thick, stout rod.

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b) Euler Formula Buckling occurs suddenly and without warning when a certain limit load is attained. It is therefore an extremely dangerous type of failure, which must be avoided by all means. As soon as a rod begins to buckle, it will become deformed to the point of total destruction. This is typical unstable behavior. Buckling is a stability problem. The critical limit load Fkrit, above which buckling can occur is dependent on both the slenderness of the rod, i.e. influence of length and diameter, and the material used. In order to define slenderness the slenderness ratio  will be introduced here. l  k i In this case l k is the characteristic length of the rod. It takes both the actual length of the rod and the mounting conditions into consideration.

For example, clamping the ends of the odds causes rigidity. The buckling length decisive for slenderness is shorter than the actual length of the rod. Altogether, a differentiation is made between four types of mountings, each having a different buckling length. The influence of diameter in the slenderness ratio is expressed by the inertia radius i. It is calculated using the minimum geometrical moment of inertia ly and the cross-sectional area A.

i

ly A

The influence of material is taken into consideration by the longitudinal rigidity of the rod EA. Here, E is the modulus of elasticity of the respective material and A is the cross-sectional area. The influence of various factors on the critical load are summarized in the so-called “Euler formula":

Fcrit   2

EA

Fcrit   2

El y

or expressed in a different form:

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2 l2

c) Influencing Factors Below the influence of various characteristic values such as the E modulus, geometric moment of inertia, length and the type of mounting on buckling behavior will be examined using the Euler formula. E modulus The E modulus is a measure of the rigidity of a material. A stiff material is sensible for high resistance to buckling. Since strength has no influence on buckling, materials with as high an E modulus as possible should be used. For example, in the case of buckling strength a simple constructive steel St37 with a tensile strength of only 370 N/mm should be given preference over a high strength titanium allow TiAI6Zr5 with 1270 N/mm. Whereas the constructive steel has an E modulus of 210 kN/mm, the titanium alloy only features 105 kN/mm. Geometric moment of inertia The geometric moment of inertia indicates the resistance against deflection resulting from the cross-sectional shape of the rod. Since a rod buckles in the direction of least resistance, the minimum geometric moment of inertia is the decisive factor. The table contains the geometric moment of inertia for several cross-sectional shapes. Here, hollow sections with small wall thickness are more favorable at the same weight as solid cross sections. For example, the ratio of the geometric moment of inertia of a thin tube (dia. 52 x 2) to that if a solid rod (dia. 20 mm) with the same cross-sectional area is 12.5 to 1. In addition, double symmetrical cross-sections such as tubes or quadratic cross sections should be used since their geometric moment of inertia is the same in every direction. Buckling length The length of the rod as well as the type of mounting determines the buckling length 1k. The influence of the length is quadratic. At twice the length the admissible load is only one-fourth the original value. d) Tensions in Buckling Rod In order to determine whether a rod has failed due to exceeding the admissible compressive strain or by buckling, the normal compressive strain in the rod, which is part of the critical load, must be calculated.

k 

Fk  A

2

E

2

If this normal compressive strain is lower than the admissible compressive strain, the rod will fail

25

due to buckling. If the admissible compressive strain is used as the normal compressive strain, the critical slenderness ratio crit at which buckling occurs can be calculated.

crit   2

E

p

For constructive steel St37 with p =192 N/mm the crit = 104. Above crit buckling according to Euler can be expected. The buckling strain curve can be seen in Diagram 3.10.

e) Estimation of Buckling Force and Deformation It is expedient to calculate the expected buckling force prior to conducting the test. This is especially true with regard to rod specimens from other manufacturers with unknown behavior. The buckling force can be determined according to the foil wing formula (Euler formula). Fcrit   2

EI y l2

The modulus of elasticity E for steel is 210000 N/mm. T geometric moment of inertia I y is calculated as follows for a square cross section:

Iy 

bh 3 12

26

Technical Description of Unit a) Layout of Test Device The test device mainly consists of a basic frame, the guide columns and the load cross bar. The basic frame contains the bottom mounting for the rod specimen, consisting of a force-measuring device for measuring the testing force and an attachment socket which can hold different pressure pieces for realizing various storage conditions. The height of the load cross bar can be adjusted along the guide columns and it can be clamped in position. This allows rod specimens with different buckling lengths to be examined. The load cross bar features a load spindle for generating the test force. Using the load nut, the test force is applied to the rod specimen via guided thrust pieces. An axial mounting between the load nut and the thrust piece prevents torsional stresses from being applied to the rod specimen. Two different thrust pieces are available for different storage conditions. The device can be used both vertically as well as horizontally. The device is equipped with a base foot on one of the guide columns for horizontal set-up. The display instrument of the force measuring device can be turned 900 for easy readability. b) Force Measurement The measuring path is very small due to the hydraulic transmission (max. 0.3 mm). The display is well damped by a hydraulic throttle. Disturbing influences causes by friction are prevented by direct support of the rod specimen on the force measuring cell.

27

c) Specimen Holders

Bottom specimen holder Two different mounting options are available:

Two diffe 

For articulated mounting Thrust piece with V notch for knife-edge mounting  For clamped mounting A thrust piece, which is firmly connected to the rod specimen The thrust pieces are inserted in the attachment socket and are clamped firmly with a screw.

Two different

Top specimen holder Two different mounting options are available: 

For articulated mounting Long thrust piece with V notch for knife-edged mounting  For clamped mounting Short adapter and thrust piece firmly attached to the rod specimen. The thrust pieces are inserted into the guide bush of the load cross bar d) Deformation Measurement

The measuring gauge for measuring the lateral deflection of the rod specimen is fasted to a guide column with the supplied support.

e) Lateral Load Device T The lateral load device can only be used when the test stand is in vertical position. The lateral load device consists of a rope, a pulley, a bracket and a set of weights. The pulley is clamped to one of the guide columns. The bracket holds the rod specimen and is locked in place with a cotter pin. A lateral force of 0-20 N can be produced in 5 N increments.

28

f) Device Technical Data Dimensions Length: Width: Height: Weight:

620 mm 450 mm ll50 mm 35 kg

Max. test force: Max. lateral load: Max. lateral deflection: Max. rod specimen length: Max. load spindle stroke: Rod specimen hole:

2000 N 20 N 20 mm 700 mm l0 mm 20 mm dia.

Rod Specimens

The rod specimens contained in the standard set can be used to conduct tests on the influence of mountings, length and material. The influences of eccentric mounting and different cross sectional shapes can be studied with the WP120.01 accessories set. a) Standard Set WP120 No: S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11

Material Tool steel 1.2842 Tool steel 1.2842 Tool steel 1.2842 Tool steel 1.2842 Tool steel 1.2842 Tool steel 1.2842 Tool steel 1.2842 Alu. AlMgSiO.5 F22 Brass CuZn40Pb2 Copper E-Cu Fieberline

Diameter mm

Length mm

20 x 4 20 x 4 20 x 4 20 x 4 20 x 4 20 x 4 20 x 4 25 x 6 25 x 6 25 x 6 20 x 10

350 500 600 650 700 650 650 600 600 600 600

29

Mounting knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge clamped/knife-edge clamped/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge

b) Accessories Set WP 120.01 No. SZ1 SZ2 SZ3 SZ4 SZ5 SZ6 SZ7 SZ8 SZ9 SZ10

Material Alu. AlMgSiO.5 F22 Alu. AlMgSiO.5 F22 Alu. AlMgSiO.5 F22 Alu. AlMgSiO.5 F22 Fieberline PVC PVC Alu. AlMgSiO.5 F22 Alu. AlMgSiO.5 F22 Alu. AIMgSiO.5 F22

Diameter mm 25 x 6 25 x 6 25 x 6 40 x 6 25 x 10 1 6 x 2 20 x 1.5 20 x 10 x 2 1 5 x 2 1 4

Length mm 500 500 500 500 700 400 400 700 700 700

Mounting knife-edge/knife-edge (e=0 mm) Knife-edge/knife-edge (e=1 mm) Knife-edge/knife-edge (e=3mm) knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge knife-edge/knife-edge

Procedure 1) Introductory Test

In this test the operation of the WP 120 buckling test device and how to conduct a buckling test be demonstrated. A rod with articulated mounting at both ends cording to Euler case 1 is slowly subjected to an axial force. Above a certain load it will buckle laterally. In this case the buckling (deformation) of the rod specimen will be measured in the middle of the rod and recorded in a table along with the accompanying force. A force/deformation graph will be developed using these measured values. The results of the test should be compared with the buckling theory values. The S2 rod specimen made of flat steel, dimensions 20 mm x 4 mm x 500 mm should be used has shaped edges at both ends which sit in corresponding V notched of the testing machine thrust pieces to form an ideal articulated mounting.

30

b) Testing 1. Set up the test device in vertical or horizontal position. The force gauge can be turned 90o for this purpose

2. Insert thrust piece with V notch into attachment socket and fasten with clamping screw

3. Insert long thrust piece with V notch into the guide bush of the load cross-bar and hold it firmly

4. Insert the S2 rod specimen with edges in the V notch.

31

5. The load cross-bar must be clamped on the guide column in such a manner that there is still approx. 5 mm for the top thrust piece to move. 6. Align the rod specimen in such a manner that its buckling direction points in the direction of the lateral guide columns. Here, the edges must be perpendicular to the load cross-bar. 7.

Pretighten the rod specimen with low, non-measurable force.

8. Align the measuring gauge to the middle of the rod specimen using the support clamps. The measuring gauge must be set at a right angle to the direction of buckling. 9. Pretighten the measuring gauge to 10-mm deflection with the adjustable support.

10. Slowly subject the rod specimen load using the load nut. 11. Read the deflection from the measuring gauge. Read and record the deflection every 0.25-mm up to 1 mm. 12. Above 1-mm deflection, it suffices to record the deflection and force every 0.5-mm.

13. The test can be concluded when the force does not change, despite an increasing load (in the case of rod specimen S2 this as at approx. 4 mm). 14. Slowly remove the tension from the rod specimen. 15. Table the result 16. Repeat the experiment with two other specimens

32

Safety DANGER! 

The load cross arm can drop of the clamping screws are loosened!



A drop could damage parts of the testing machine located underneath the cross arm.



Carefully support the cross arm by hand when loosening the clamping screws!



Before removing a rod specimen make sure that the clamping screws are tightened securely! Pay attention to the top thrust piece when removing the rod specimen!



The hazards mentioned do not apply when the test device is set up horizontally.



Caution when working with brittle materials!



The rod specimen could break suddenly in this case. Pieces of specimen could fly around and cause injuries!



This hazard is not posed with original G.U.N.T. rod specimens, since they are made of ductile material.

CAUTION Do not overload device! The maximum testing force is 2000 N. Overloads can occur if attempts are made to force a loaded rod specimen in the direction opposite that of deflection. Never deflect more than max. 6 mm, since there is a risk or plastic deformation and damage to the rod specimen. Questions Q1. Plot a graph of Force vs. Deflection (mm) Q2. From the graph, identify the maximum experimental critical force. Q3. Identify the theoretical critical force for each material. Q4. Compare between Q2 and Q3. What are the different between one material and another? Q5. Identify one engineering example where buckling is highly concerned.

33

Experiment 5 BRINELL HARDNESS TESTING Objectives: 1. To study the hardness of different material. 2. To understand the principles of Brinell Testing method. Theory Brinell Fundamental principles Hardness refers to the resistance, which a body has to the penetration of another. Accordingly, in common hardness testing methods, a hard test body is pressed into the sample perpendicular to its surface. A three-dimensional stress forms in the sample beneath the penetrating test body. Lasting impressions can be achieved in very hard and brittle materials without resulting in cracks. This distinguishes hardness testing from tensile testing in which only a mono-axial stress is generated in the sample and no plastic deformation is possible with hard materials.

Fig 1: Hardness testing according to Brinell One advantageous aspect of hardness testing is that, in contrast to tensile testing, material properties can be determined without destroying the sample, apart from the relatively small impression made by the test body (incoming goods testing). One disadvantage of hardness testing is that it is only possible to give a number corresponding to strength, which depends on the test method used, but not the strength itself. For this reason, the test method used must always be specified. For hardness testing according to Brinell a ball made of hardened steel is used as the test body. The ball is pressed onto the sample with a defined test force, which depends on the diameter of the ball and the test material. After a certain time, the diameter of the remaining impression of the ball is measured.

34

Brinell Hardness Brinell hardness is calculated from the test force F and the surface area of the Impression AB caused by the ball. With the ball diameter D and the diameter of the impression d this then produces

HB 

0.102F 0.102F  AB 0.5D D  D 2  d 2





The factor 0.102 is an historical one and takes into account the conversion from kp/mm 2 to N/mm2. If the impression from the ball is not circular, the average from two vertically superimposed measurements should be used. To ensure that the hardness numbers for various materials, sample forms and ball diameters are comparable, certain rules must be observed. Ball diameter The ball diameters 10, 5, 2.5 and 1-mm are standardized. Application time The test force should be applied to the sample for at least 10 to 15 seconds and with creeping materials 30 seconds or more. The increase in the test force to its maximum should last at least 5 seconds. Load factor In order to obtain a legible, reproducible ball impression, the diameter of the impression should be between d = 0.2 and 0.7 D. In order to adhere to this for various hard materials, various pressures per unit of area are recommended, i.e. the force and the square of the ball diameter must be at a certain ratio to one another. This ratio is termed load factor x. x

0.102F D2

Here too, the factor 0.102 results from the conversion from kp to N. The following table lists the load factors for various materials.

35

Load Factor x  Load factor x 30 Measurable 67….400 hardness range HB Material Iron materials Steel Cast steel Cast iron

10 22…315 Light metals Copper Brass Gunmetal Nickel

0.102F depending on material D2 5 2.5 1.25 11…158 6...78 3...39

Pure aluminum Magnesium

Bearing Lead metals Tin Zinc CastSoft brass solder

0.5 1...15 Soft metals at higher temperatures

Technical description The WP300 materials testing device is a robust unit designed specifically for technical instruction and is one of the classical materials testing devices in materials science. The flexible design of the unit permits a wide range of different tests requiring tensile or compressive forces. Thanks to its clear, simple layout, the unit is ideally suited for both student experiments and for demonstrations. Its compact dimensions and relatively low weight permit mobile use and erection on all common laboratory benches. The device can easily be transported by two persons using the four handgrips. Basic unit

In its basic form, the unit does not require any external connections. The test force is generated via a manually actuated hydraulic system and displayed via a large, easily legible display instrument with a trailing pointer. All accessories are screwed to the cross-members. This means that the test unit can be quickly and easily refitted for various tests. The basic unit essentially consists of the following elements: - Machine base (1) with handgrip (11) - Support with cross-head (2) - Load frame with upper (3) and lower cross-member (4) - Hydraulic system consisting of a main cylinder (5) and a master cylinder with a hand wheel (6) - Force display (7) - Elongation display via a dial gauge (8) - Gripping heads (9) with sample (10) 36

Machine base

The rigid machine base made of cast iron forms the foundation and ensures stability of the test unit in connection with 4 rubber feet. The machine base supports the hydraulics and the frame.

Support The posts (1) and cross-head (2) form the fixed support of the test unit. The various fixed sample receptacles are fastened to the cross-head. The mobile load frame is also mounted on it in low-friction linear ball bearings.

Load frame The load frame consists of the upper (1) and lower crossmember (2) and the guide rods (3). The load frame transmits the test force from the hydraulic main cylinder to the relevant sample. The load frame is slide-mounted in the cross-head of the support. Tensile samples are clamped between the upper cross-member and the cross-head, whilst compressive samples are clamped between the lower cross-member and the cross-head. Load frame

37

Hydraulic system The test force is generated by hydraulic means. A piston in the master cylinder (2) actuated via the hand wheel (1) and the threaded spindle creates a hydrostatic pressure, which induces the test force in the main cylinder (3). The hydraulic transmission ratio is 2.77:1, whilst the mechanical transmission ratio hand wheel/spindle is 503 : 1. Excluding friction losses, this would correspond to a manual force of 1 N per 1.3 kN test force. The full stroke of the main cylinder of 45 mm requires 83 revolutions of the hand wheel.

Force display and elongation measurement. The forcemeasuring device operates according to the manometer principal. It measures the hydrostatic pressure in the hydraulic system. The large display with a diameter of 160 mm facilitates precise reading. A maximum pointer stores the maximum force. The elongation is measured via an adjustably mounted dial gauge. The dial gauge indicates the relative displacement between the upper cross-member and the cross-head.

38

Hardness test The basic unit includes a device for hardness testing according to Brinell. Hardness testing is performed with a hardened steel ball with a diameter of 10 mm. Metal plates 10 x 30 x 30 mm made of the materials aluminum, copper, brass and steel are used as samples.

The hardness testing device (1) is inserted in the compression zone of the test device between the cross-head (2) and the lower crossmember (3). The sample (4) is placed on the compression pad (5) of the lower cross-member.

Set up The hardness-testing device is mounted in the compression zone of the test unit. -

Insert the pressure plate in the lower cross-member

-

Mount the Brinell tester on the cross-head with the threaded rod and knurled nut. Hand-tighten the knurled nut

-

Unscrew the hand wheel on the master cylinder as far as it will go. A minimum distance of 15 mm between the test ball and the pressure plate should be observed

39

Procedure

Samples of 4 different materials are tested. For all materials, a load factor of 10 is selected. For the steel sample, a load factor of 30 is recommended in accordance with the table on page 38. However, the necessary test force of 29 kN cannot be applied with the WP3OO. As the Brinell hardness of the steel sample is undoubtedly less than HB 315, the load factor of 10 is still permissible. (Part A) - 1. Position the test piece on the lower pressure plate so that the center of the test ball is at least 20 mm from the edge. -

2. Carefully lower the test ball onto the sample by rotating the hand wheel.

-

3. Smoothly apply the test force of 10 kN with the hand wheel. Do not apply the force too quickly. The increase to the maximum level should take at least 5 seconds.

-

4. Hold the test force for around 10 - 15 sec and then release

-

5. Remove the sample and measure the diameter of the impression using a measuring magnifier; if necessary, form an average. Note the reading.

-

6. Repeat with other test pieces.

Questions 1. Calculate the Brinell hardness. 2. Discuss the different hardness results for different materials and explain the significance of the Vickers hardness measurement. 3. Compare the testing techniques in terms of indenter, load and equations for Rockwell, Brinell, Knoop and Vickers methods. 4. What are the important samples preparations need to be considered before conducting hardness test? 5. Give two examples regarding the importance of hardness test. 6. What is the advantage of hardness testing in contrast to tensile testing? 7. Discuss the hardness and softness of the materials.

40

Experiment 6 THIN CYLINDER Objective 1. Determination of circumferential stress under open condition, and analysis of combined and circumferential stress. Theory a) Complex Stress System The diagrams in Figure 4.1 represent (a) the stress and (b) the forces acting upon an element of material under the action of a two-dimensional stress system.

a) Stress diagram

b) Force Diagram Figure 6.1: Stress and force diagrams for two dimensional stress systems

41

Assuming (b) to be a 'wedge' of material of unit depth and the side AB to be of unit length: Resolving along  will give:

    y cos cos   x sin   sin    cos  sin    sin   cos     y cos2     x sin 2    2 sin  cos     y

cos 2  1   1  cos 2    sin 2 x

2

2 1 1     y   x    y   x cos 2   sin 2 2 2

(1)

Resolving along  will give:

    y cos sin    x sin   cos   sin  sin    cos  cos    y  

sin 2 sin 2  x   sin 2    cos2  2 2

1  y   x sin 2   cos2 2

(2)

From equation 2 it can be seen that there are values for e for which  is zero and the planes on which the shear component is zero are called 'Principal Planes'. For equation 2: 0

1  2

y

 c os 2   

1  2

y

  x sin 2   c os 2 1  2

y

  x sin 2

  x  tan 2

(3)

This will give two values of 2 differing by 1800 and, therefore, two values of  differing by 900. This shows that Principal Planes are two planes at right angles to each other.

Figure 6.2: Diagram representation of Equation 3

42

From the diagram: sin 2  



and

cos 2  



2

(4)

  x   4 2 2

y



y

x

(5)

  x   4 2 2

y

The stresses on the principal planes are normal to these planes and are called principal stresses. From equation 1 and substituting the above values:

 

1  y   x   1 2 2



  x   4 2 2

y

(6)

Principal stresses are the maximum and minimum values of normal stress in the system. The sign will denote the type of stress. i.e

Negative sign - Compressive Stress Positive sign - Tensile Stress

Figure 6.3: Force diagram for an element Assuming BC and AC are principal Planes, i.e. =0, and 1 and 2 are the principal stresses

 

1  2   1 sin 2 2

(7)

Now maximum shear stress  will be seen to occur when sin2 = 1, i.e. when =450.

43

Therefore the maximum shear stress occurs on planes at 450 to the principal planes, and

 

1  2   1  2

(8)

or (using equation 6)

 



  x   4 2 2

y

(9)

b) Two Dimensional Stress System

Figure 6.4: Diagram of principal stresses on an element Strain in direction of 1:

1  Strain in direction of 2:

2 

1 E

2 E



v 2 E

(10)



v 1 E

(11)

1 and 2 are the values of the principal strains. A negative quantity denotes compressive strain. A positive quantity denotes tensile strain. These strains can be used to construct a 'Mohr Strain Circle' in the same way as stresses.

44

Figure 6.5: Representation of strain on a Mohr circle In the usual manner, referring to Figure 4.5: OR is the maximum principal strain. OP is the minimum principal strain at right angles to maximum Q is the center of the strain circle. From the diagram :   1   2   1   2    cos2  2   2         m   2 1    1 2  cos2  2   2 

m  2  

(12)

and  1   2   1   2    cos2  2   2         n   2 1    2 1  cos2  2   2 

n  2  

45

(13)

Theory as Applied to the Thin Cylinder Because this is a thin cylinder, i.e. the ratio of wall thickness to internal diameter is less than about 1/20, the value of H and L may be assumed reasonably constant over the area, i.e. throughout the wall thickness, and in all subsequent theory the radial stress, which is small, will be ignored. I symmetry the two principal stresses will be circumferential (hoop) and longitudinal and these, from elementary theory, will be given by: -

H 

pd 2t

(14)

L 

pd 4t

(15)

and

As previously stated, there are two possible conditions of stress obtainable; 'open end' and 'closed ends'

Figure 6.6: Stresses in a thin walled cylinder a) Open Ends Condition The cylinder in this condition has no end constraint and therefore the longitudinal component of stress L will be zero, but there will be some strain in this direction due to the Poisson effect. Considering an element of material: H will cause strains of:-

H  1

and

L  1

H E

(16)

 v H E

(17)

46

and these are the two principal strains. As can be seen from equation 17, in this condition L will be negative quantity, i.e. the cylinder in the longitudinal direction will be in compression. b) Closed Ends Condition By constraining the ends, a longitudinal as well as circumferential stress will be imposed upon the cylinder. Considering an element of material: H will cause strains of:-

H 

H

and

L   1

L will cause strains of:-

L  and

(18)

E

v H E

(19)

L E

H  

(20)

v L E

(21)

The principal strains are a combination of these values i.e.

H  and

L 

1  H  v L  E

(22)

1  L  v H  E

(23)

The principal strains may be evaluated and a Mohr Strain Circle constructed for each test condition. From this circle the strain at any position relative to the principal axes may be determined. c) To determine a value for Poisson's Ratio Dividing equations 16 and 17 gives :-

L  v H

(24)

1

1

This equation is only applicable to the open ends condition.

47

Description of the apparatus

Figure 6.7: Thin cylinder SM1007 Figure 6.7 shows a thin walled cylinder of aluminum containing a freely supported piston. The piston can be moved in or out to alter end conditions by use of the adjustment screw. An operating range of 0-3.5 MN/m2 pressure gauge is fitted to the cylinder. Pressure is applied to the cylinder by closing the return valve, situated near the pump outlet, and operating the pump handle of the self-contained hand pump unit. To release pressure unscrew the return valve. Open and Closed Ends

Figure 6.8: Sectional plan of the thin cylinder The cylinder unit, which is resting on four dowels, is supported in a frame and located axially by

48

the locking screw and the hand wheel. The hand wheel sets the cylinder for open and closed ends conditions. When the hand wheel is screwed in, it forces the piston away from the end plate and the entire axial load is taken on the frame, thus relieving the cylinder of all longitudinal stress. This creates „open ends‟ experiments as shown in Figure 6.9. Pure axial load transmission from the cylinder to frame is ensured by the hardened steel rollers situated at the end of the locking screw and hand wheel.

Figure 6.9: Open Ends Conditions When the hand wheel is screwed out, the pressurized oil in the cylinder forces the piston against caps at the end of the cylinder and become „closed Ends‟ of the cylinder. The cylinder wall then takes the axial (longitudinal) stress as shown in Figure 6.10.

Figure 6.10: Closed Ends Conditions

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Strain Gauges

Figure 6.11; strain gauges positions Six active strain gauges are cemented onto the cylinder in the position shown in Figure 6.11; these are self-temperature compensation gauges and are selected to match the thermal characteristics of the thin cylinder. Each gauge forms one arm of a bridge, the other three arms consisting of close tolerance high stability resistors mounted on a p.c.b. Shunt resistors are used to bring the bridge close to balance in its unstressed condition (this is done on factory test). The effect on gauge factor of this balancing process is negligible. To give a direct reading of strain, the raeding from a strain gauge is multiplied by a constant called the gauge factor. This compensates for the slight difference in manufacture between each batch of gauges. The gauge factor usually varies between 1.8 and 2.2. The manufacturer set the gauge factor into the electronic circuit of the SM1007, thus allowances no need to be considered. The strain display on the front of the equipment shows the reading from each strain gauge in  (microstrain). The display shows only four reading at a time, use the scroll readings button to scroll up or down to see all six values. Negative reading is a compressive strain and positive reading is a tensile strain.

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Thin cylinder technical information

Items Dimensions Nett weight Electrical supply Fuse Maximum cylinder pressure Strain gauges Cylinder oil Total oil capacity Cylinder dimensions Cylinder material Young’s modulus (E) Poisson’s ratio

Details 370 mm high x 700 mm long x 380 mm front to back 30 kg 85 VAC to 264 VAC 50 Hz to 60Hz 20 mm 6.3 A Type F 3.5 MNm-2 Set by a pressure relief valve on the hand pump Electrical resistance self-temperature compensation type Shell Tellus 37 (or equivalent) Approximately 2 litres 80 mm internal diameter 3mm wall thickness 359 mm length Aged aluminium alloy 6063 69 GN/m2 0.33

Table 6.1 : Technical Details The pump is fitted with a pressure relief valve, adjacent to the pump handle pivot, which is set to operate at approximately 3.5 MN/m2. A bleed nipple is fitted to the right hand end of the cylinder. PROCEDURE a) General Switch on the power to the thin cylinder and leave it for at least five minutes before conduct the experiment. This allows the strain gauges to reach a stable temperature and give accurate readings. Two conditions of stress may be achieved in the cylinder during test: (i) (ii)

a purely circumferential stress system which is the 'open ends' condition a biaxial stress system which is the 'closed ends' condition.

To obtain the circumferential condition of stress; - (refer to Figure 6.9) Ensure that the return valve on the pump is fully unscrewed so that oil can return to the oil reservoir. Screw in the hand wheel until it reaches the stop. This moves the piston away from the left-hand end plate and thus the longitudinal load is transmitted onto the frame. When in this

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condition, the value of Young's Modulus for the cylinder material may be determined and also the value for Poisson's Ratio. To obtain the biaxial stress system: - (refer to Figure 6.10) Ensure that the return valve on the pump is fully unscrewed. Unscrew the hand wheel and push the crosspiece to the left until it contacts the frame end plate. Now close the return valve and operate the hand pump to pump oil into the cylinder and push the piston to the end of the cylinder. Thus, when the cylinder is pressurized, both longitudinal and circumferential stresses are set up in the cylinder. Before any test, and at zero pressure, each strain gauge channel should be brought to zero or the initial strain readings recorded as appropriate. This equipment is equipped with VDAS (Versatile Data Acquisition System), however, for teaching purposes, students are encouraged to conduct the experiment manually. Precaution: NEVER pump the oil pressure higher than 3.1 MN/m2 a) Experiment 1 – Open ends i. Open the pressure control and screw in the hand wheel to set up the Open Ends condition. ii. Close the Pressure control and use the „press & hold to zero‟ button to zero the strain gauge display readings. iii. Increase the pressure in 0.5 MN/m2 steps up to 3 MN/m2, at each step allowing a couple of seconds for the pressure and strain readings to stabilize. Note the reading. iv. Open the Pressure Control to relieve the pressure. b) Experiment 2 – Closed Ends i. Open the pressure control and carefully unscrew the hand wheel to set up the Closed Ends condition. ii. Open the Pressure Control to release the pressure. iii. Close the Pressure control and use the „press & hold to zero‟ button to zero the strain gauge display readings. All the strain gauge readings should now read 0  (+/-5), and the pressure meter should read 0 MN/m2 (+/- 0.05 MN/m2). iv. Increase the pressure in 0.5 MN/m2 steps up to 3 MN/m2, at each step allowing a couple of seconds for the pressure and strain readings to stabilize. Note the reading. v. Open the Pressure Control to relieve the pressure.

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Data

Reading

Pressure (MN.m-2)

Cylinder Condition: OPEN ENDS Direct Strain Hoop Gauge Gauge Gauge Gauge Stress 1 2 3 4 (MN.m-2)

Gauge 5

Gauge 6

Gauge 5

Gauge 6

1 2 3 4 5 6 7 Values from actual Mohr’s Circle (at 3 MN.m-2) Values from theorethical Mohr’s Circle (at 3 MN.m-2) Data Table 6.1: Open Ends Results

Reading

Pressure (MN.m-2)

Cylinder Condition: CLOSED ENDS Direct Strain Hoop Gauge Gauge Gauge Gauge Stress 1 2 3 4 (MN.m-2)

1 2 3 4 5 6 7 Values from actual Mohr’s Circle (at 3 MN.m-2) Values from theorethical Mohr’s Circle (at 3 MN.m-2) Data Table 6.2: Closed Ends Results

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Questions: Open Ends Conditions 1. Plot a graph of Hoop Stress against Hoop Strain. Find the Young‟s Modulus for the cylinder material. Compare your result. 2. Plot a Longitudinal Strain against Hoop Strain. Find the Poisson‟s ratio for the cylinder material. Compare your result. 3. Draw the Mohr‟s Circle at 3 MN/m2. Identify the Principles Strains for Open Ends Conditions. Compare the values with theoretical Mohr‟s Circle (Hint: to construct the theoretical Mohr‟s Circle, consider Poisson‟s Ratio and Young‟s Modulus given in technical details, use these values with the Principal Strain equations 16 and 17 to calculate theoretical principal strain with calculated Hoop Stress at 3 MN/m2 pressure). Closed Ends Conditions 1. Draw the Mohr‟s Circle at 3 MN/m2. Identify the Principles Strains for Closed Ends Conditions. 2. Compare the values with theoretical Mohr‟s Circle (Hint: to construct the theoretical Mohr‟s Circle, consider Poisson‟s Ratio and Young‟s Modulus given in technical details, use these values with the Principal Strain equations 22 and 23 to calculate theoretical principal strain with calculated Hoop Stress at 3 MN/m2 pressure).

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Experiment 7 IMPACT TEST Objective To investigate the impact strength of polymers Theory Impact testing For determination of both tensile strength and hardness testing, the test piece is loaded continuously and slowly. How a material reacts to a sudden tension due to a quick blow or impact is shown by means of an impact tester. The test is conducted according to D6110-06 Standard Test Method for Determining the Charpy Impact Resistance of Notched Specimens of Plastics.

Fig. 8:1. Impact tester. The test is completed using a drop hammer mounted as a pendulum; see fig. 8:1, which breaks a test piece. In Europe the test is completed by the Charpy method, which consists of placing the test piece between two supports, see fig. 8:2. In the USA the Izod method is used. This entails fixing the test-piece and allowing the pendulum to break off a piece of the test-piece. See fig. 8:3.

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Fig 8.2: Charpy method

Fig 8.3: Izod Method

Test pieces Charpy test-pieces see fig. 8:4 can have slightly different instruction as to how the test is conducted. Keyhole and U test-pieces give equally good results. The specific impact energy or impact unit KCU is measured in kj /m2. For U test-pieces the impact energy or impact strength kV, is measured in j (joules). There is no sure method of calculation of impact energy for test pieces, for tests carried out with different instructions on the test piece.

Fig. 8:4. Charpy test pieces.

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Impact Strength

LR = Reduced length of pendulum = distance to center of impact Fig.8.5: Pendulums potential To be able to calculate the impact strength KCU, the pendulum potential energy when released, is first calculated. K = F* LR (1 + sin (1 - 900)). The potential energy in the pendulum after is has broken the test piece is than calculated T=F* LR (1 –cos 2) The energy consumed when breaking the test piece is than E=K – T, neglecting friction and wind resistance losses. To calculate the impact strength KCU, the energy received is divided by the cross sectional area of the test piece. The impact test apparatus can be graduated directly in joules. DESCRIPTION OF APPARATUS Impact Tester MT 3076 Impact tester MT 3016 is intended for mounting on a bench, with fixing holes at the front and back of the baseplate. If the impact tester is mounted on a bench, the zero point must be set when installing. Read the chapter relating to this setting.

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The impact tester has maximum impact energy of 1 joule, each scale division being 0.1 joules. Test pieces suitable for the tester are 6 x 6 x 44 mm. The reduced length of the pendulum requires a test piece smaller then standard. The impact tester weights 30 kg and has dimensions of 195 x 315 x 590 mm. The weight of the pendulum is 2 kg.

Fig. 8.8: Impact Tester MT 3076.

Procedure a) Setting the zero point of the start point Because of friction and wind resistance, the pendulum will not have the same striking angle as the fall angle. This can be compensated for by inclining the impact tester slightly. The fall angle will then be larger and the striking angle less but the scale is fixed and a non-loaded blow of 15 joules should show a value of 15 joules.

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Method: 1.

Set the pointer to 1 5 joules (straight down).

2.

Raise the pendulum to the start point. Release the pendulum by means of the black knob. KEEP FINGERS AND HANDS CLEAR OF THE PENDULUM MOTION THUS AVOIDING JAMMING ACCIDENTS.

3.

Stop the pendulum using the friction brake. Take the reading of the pointer. The pointer should point to zero (0) if the impact tester is properly set.

4.

If the pointer shows more than zero, fixed impact testers should be angled slightly by inserting a spacer (washer) under the pendulum side. For the freestanding model, screw down the allen screw using an MOO allen key. If the pointer shows less than zero, i.e. the pointer is over the scale, then the spacer (washer), shall be placed under the back edge for fixed models end the allen screw in the free standing model, turned anti clockwise (upwards).

5.

Check the setting with an unloaded test. Complete further adjustment until exactly zero is registered.

Fig. 8.10 Direction of impact b) Testing Method: 1.

The test piece is placed on the supports so that the break indentation faces the direction of the pendulum swing and that the indent is exactly in the middle of the supports.

2.

Raise the pendulum to the start point.

3.

Set the pointer to 15 joules, i.e. straight down.

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4.

Release the pendulum by turning the black knob, top right. KEEP HANDS CLEAR. The test piece is broken off.

5.

Stop the pendulum by lifting the friction brake. Be sure that the pendulum is at standstill before removing the test pieces.

6.

The energy consumed when breaking the test piece can now be read directly from the scale, indicated by the pointer.

7.

Read and note the value of the impact energy. Calculate the fracture area and subsequently the impact strength.

Data Test

Fracture Area (cm2)

Impact Energy (joule)

Impact Strength (joule/cm2)

HDPE LDPE Questions 1. Calculate the impact strength for all test pieces and note in the table. 2. HDPE and LDPE have different polymeric chain. Explain how it affects the impact strength obtained. 3. What others information can be gathered through Izod & Charpy method? 4. Give one example of engineering application where impact is a real concern.

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Experiment 8 Microstructure Analysis Objective: 1. To be familiar with metallography techniques such as grinding, polishing and etching. 2. To be familiar with metallurgy microscope 3. To investigate the microstructure of metal and alloy. Theory Metallurgy is the study of microstructural features of materials. The structure studied by metallography are indicative of the properties and hence the performance of material in service. Typical application of metallography techniques in research centres and industry may include: a. To monitor metal alloy heat treatment b. To measure the thickness of coating c. To evaluate/examine the weld or braze d. To evaluate corrosion, etc. e. For failure analysis In this technique, planar surface is prepared by sectioning followed by mounting in a thermosetting resin prior to grinding and polishing to obtain a reflective surface. In order to delineate the microstructure chemical or other etching method is often employed prior to microscopy investigation. a) Sectioning and cutting The areas of interest forming the metallography specimens need to be sectioned for ease of handling. Depending on the type of material, the sectioning operation can be done by using abrasive cutter (for metal and metallic composite), diamond wafer cutter (ceramics, electronics, and minerals) or thin sectioning with a microtome (plastics). In order not to damage the specimen, proper cutting requires the correct selection of abrasive cutting wheel, proper cutting speed & cutting load and the use of coolant. b) Mounting The mounting operation accomplishes three important functions: 1. To protects the specimen edge and maintain the integrity of materials surface features. 2. Fill voids in porous materials. 3. Improves handling of irregular shaped samples.

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Samples for microstructure evaluation are typically encapsulated in a plastic mount for handling during sample preparation. Large sample or samples for macrostructure evaluation can be prepared without mounting. The metallography specimen mounting is done by encapsulating the specimen into: 1. A compression/hot mounting compound (thermosets – e.g. phenolics, epoxies or thermoplastics – e.g. acrylics) 2. A castable resin/cold mounting (e.g. acrylics resins, epoxy resins and polyester resins) c) Grinding Grinding is required to ensure the surface is flat & parallel and to reduce the damage created during sectioning. Grinding is accomplished by decreasing the abrasive grit size sequentially to obtain the required fine surface finish prior to polishing. It is important to note that the final appearance of the prepared surface is dependent on the machine parameters such as grinding/polishing pressure, relative velocity distribution and the direction of grinding/polishing. d) Polishing For microstructure examination a mirror/reflective finish is needed whereas a finely ground finish is adequate for macrostructure evaluation. Polishing can be divided into two main steps: 1. Rough polishing The purpose is to remove the damage produced during grinding. Proper polishing will maintain the specimen flatness and retain all inclusions or secondary phases by eliminating the previous damage and maintaining the specimen integrity. 2. Fine polishing The purpose is to remove only surface damage. e) Etching Etchans are specially formulated for the specific material and evaluation objectives. Etching alters the microstructural features based on composition; stress or crystal structure and it will develop the surface topology, which can be visible in the microscope. Typically, chemical etching involves immersing the polished surface in the prepared chemical solution for a specified time (usually seconds) followed by rinsing the etched specimen under running tap water and drying. f) Microscopic Analysis For microscopic analysis, a reflective surface is required. The analysis can be done by using a metallurgy microscope.

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g) Equipment, Apparatus and Sample 1. 2. 3. 4. 5. 6. 7.

Abrasive cutter machine Polisher Lubricant Ultra sonic cleanser Soapy water Nital solution (2% HNO3) Metallurgy microscope

8. Grinder 9. Silicon carbide paper (4 different mesh) 10. Diamond spray (6 micron and 1 micron) 11. Dryer 12. Cotton 13. Alcohol 14. Sample – mild steel

Procedure 1. Grinding is done using rotating discs covered with silicon carbide (SiC) paper and water. In this operation four different grade of paper is used. Starts with the smallest grit number; which represents coarse particles. 2. During grinding apply light pressure on the centre of the sample. Continue grinding until all the blemishes have been removed, the sample surface is flat, and all starches are directed in one direction. 3. Wash the sample in water and move to the next grit, orienting the starches from the previous grade normal to the rotation direction. 4. Repeat the grinding procedure until the final grinding operation. After that wash the sample thoroughly followed by cleaning using alcohol and dry the sample. 5. Polishing is done using rotating disc covered with soft cloth impregnated with diamond particles and lubricant. Begin the polishing operation with 6-micron grade and continue the process until the grinding starches have been removed. 6. Wash the sample under running tap water followed by cleaning with alcohol, immerse the sample in ultrasonic cleaner for one minute and then dry the sample. 7. Repeat the same procedure for final polishing stage using 1-micron lubricant. 8. Examine your sample by using metallurgy microscope. Note down your observation. 9. Immerse the polished sample in the etching solution for about 2 to 3 seconds. Wash the sample with water followed by alcohol. Dry the sample prior to microscopy examination. Precaution: While using the microscope be careful not to raise the stage too much which may result in contact between the objective lens and the specimen and cause damage. Never touch the optical surfaces with your fingers or any object.

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Questions 1. Label the microstructure obtained. 2. Discuss the difference between before- and after- etching process. 3. Discuss the effect of etching process. What will happen if the process is too long (more than 3 seconds)? 4. Other than metallurgy microscope, identify other methods applicable to study microstructure. 5. Give two real examples where microstructures study are real concern in engineering application.

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Lab Schedule Mechanics and Materials Laboratory Schedule (MEMB221) S1 (Thurs, 3-6 pm), S2 (Wed, 3-6 pm), S3 (Wed, 9 -12 pm), S4 (Mon, 9-12 am), S5 (Tue, 11 - 2 pm), S6 (Tues, 3-6 pm), S7 (Fri, 8-11 am), , S8 (Thu, 9 - 12 pm) and S9 (Tue, 8 -11 am) Semester 2 2013/2014

W2

W3

W4

W5

W6

W7

W8

W9

W10

W11

W12

W13

W14

W15

7-11 Oct 2013

14-18 Oct 2013

21-25 Oct 2013

28 Oct1 Nov 2013

4-8 Oct 2013

11-15 Nov 2013

18-22 Nov 2013

25-29 Nov 2013

2-6 Dec 2013

9-13 Dec 2013

16-20 Dec 2013

23-27 Dec 2013

30 Dec 3 Jan 2014

6-10 Jan 2014

13-17 September 2013

6

8

25 Dec Christmas Day

1 Jan New Year

2

3

4

7

G2

2

3

4

7

6

8

1/5

4

7

6

8

1/5

2

7

6

8

1/5

2

3

6

8

1/5

2

3

4

8

1/5

2

3

4

7

1/5

2

3

4

7

6

G3 G4 G5 G6 G7

3 4 7 6

Mid Sem Break

1/5

Introduction

G1

8

Study week

W1

G8

15 Oct Hari Raya Qurban

Note

Mid Semester Break

11 Dec Keputeraan Sultan Selangor

11&12 Convo

Exp No.: 1

Tensile test (Universal Tester)

4

Buckling Test

7

Impact test

2

Torsion Test

5

Hardness Test

8

Microstructure Analysis

3

Bending Test

6

Thin Cylinder