final report (2)

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1.0 Project Background 1.1 Sample description In this engineering material project our group was given three specimen with two lines marked at the narrow center region of the specimens as shown in Figure 1.1. The specimen is a dog bone shaped polymers. We can see that our specimen has the following characteristics: Figure 1.1: Sample I. Physical Appearance : Three pieces of specimen which are in dog bone shape, at which the specimen is narrow at the center region. It is white in colour, and light in weight. II. Size and specification Table 1: Specimen Dimension Specimen A B C Width overall (mm) 18.68 18.40 18.50 Width of narrow section (mm) 12.80 12.80 12.80 Length overall (mm) 162 162 162 Gage length (mm) 50 50 50 Thickness (mm) 3 3 3 1

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Page 1: Final Report (2)

1.0 Project Background

1.1 Sample description

In this engineering material project our group was given three specimen with two lines marked at the narrow center region of the specimens as shown in Figure 1.1. The specimen is a dog bone shaped polymers. We can see that our specimen has the following characteristics:

Figure 1.1: Sample

I. Physical Appearance : Three pieces of specimen which are in dog bone shape, at which the specimen is narrow at the center region. It is white in colour, and light in weight.

II. Size and specification Table 1: Specimen Dimension

Specimen A B CWidth overall (mm) 18.68 18.40 18.50Width of narrow section (mm) 12.80 12.80 12.80Length overall (mm) 162 162 162Gage length (mm) 50 50 50Thickness (mm) 3 3 3

III. Mechanical properties The specimen surface is smooth. It is bendable and ductile.

IV. Chemical properties

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The specimen surface is clean. No oxidation or corrosion sign can be observed from the specimen.

V. Optical properties The specimen is opaque.

1.2 Problem Statement

In engineering application, it is important and critical to identify the properties of materials. This is due to the difference of applications that required different and specific material properties in order to achieve the desire design. Failure to do so can lead to a serious problem that can affect human, environment and engineering application.

Therefore, it is vital to ensure that the properties and characteristics of the materials that are discovered through testing are suitable and practicable for its corresponding application. Thus by selecting appropriate materials with suitable properties for a given application, catastrophes can be avoided.

The purpose of the project is to determine two mechanical properties of the given sample specimen. Tests that are relevant and practicable with the sample specimen should be identified and conducted in order to determine its mechanical properties. The tests can either be destructive or non-destructive depending on the characteristic of the sample specimen.

1.3 Objectives and Scopes

The objectives of this research are as follows:

1. To identify and analyse the two mechanical properties of specimens (polymer).2. To determine the suitable testing and testing standard based on the mechanical

properties chosen.3. To justify the test conducted and the mechanical properties that have been identified.4. To determine the material of the specimens.

The scopes of this research are as follows:

1. Identify and analyse the mechanical properties of the polymer.2. Perform tests in compliance with ASTM standards.3. Perform tensile tests to identify tensile strength and formability of the samples.4. Analyse the results of the experiments.

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2.0 Literature review

2.1 Polymer

According to American Chemistry Council (2014), polymer is defined as a chemical which is composed of many repeating units. It can be a three dimensional or two-dimensional network or a one-dimensional network. Polymers are often known as macromolecules because they are large in size. (Callister & Rethwisch, 2008). A repeating unit in polymer is the “-mer”. The word “poly-mer” means many repeating units whereas “monomer” means small unit that can be synthesized into a polymer. Repeating units are usually consist of carbon and hydrogen, sometimes oxygen, nitrogen, sulphur, chlorine, fluorine, phosphorous, and silicon. The polymer chain is formed by sequential addition and polymerization of many “-mers” (Mitchell, 2004).

There is two type of polymer which are natural polymer such as proteins or enzymes and synthetic polymer such as nylon or polyethylene. Since most of the polymers are organic or synthesized from organic molecules, they are made of hydrocarbons which are compounds of carbon and hydrogen. These polymers are specifically made of carbon atoms bonded together, forming long chains known as backbone of the polymer (Callister & Rethwisch, 2008).

Properties of a polymer is affected by the attractive force between the polymer chains. Dipoles in the monomer units affects the intermolecular forces in polymers Ionic or hydrogen bonding which have stronger force can be formed between polymer chains. Polymers that consist of amide or carbonyl groups can form hydrogen bonds between adjacent chains. The partially positively charged hydrogen atoms in N-H groups of one chain and partially negatively charged oxygen atoms in C=O groups on another are strongly attracted to each other. These strong hydrogen bonds usually result in the high tensile strength and melting point of polymers (K. S. Kumar, K. Rahman, G. M. Varma & K. Krishna, 2012).

2.2 Mechanical Properties of Polymer

Mechanical property is the characteristic shown by a material when it is subjected to a force. It is measured by performing several tests, usually destructive test, on a specimen of the given material (K. G. Budinski & M. K. Budinski , 2010). Mechanical property is used to determine whether a material is suitable for a specific mechanical application where the material need to withstand force or deformation. The mechanical properties studied help in material selection for product and application, so as to prevent any failure. Strength, formability, stiffness, toughness and durability are the five properties under mechanical properties.

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Generally, mechanical properties of polymer are different from metal and ceramic. Polymers have lower stiffness and lower strength at room temperature as compared to metal and ceramics. Many polymers are ductile (Callister & Rethwisch, 2008). Different type of polymers have different mechanical properties. Mechanical properties of polymers depend on several parameters such as nature of monomer unit, molecular weight, cross-linking, degree of crystallinity and etc. (S.L. Kakani& A. Kakani, 2004). For example, the greater the molecular weight of the polymer, the higher is its melting temperature.

In order to determine the mechanical properties of the specimen, tests are performed on the specimen. This paper will focus on the strength and formability of the given polymer specimens, which can be determined by performing tensile test. Tensile testing will be discussed in next section before proceeding to strength and formability properties.

2.2.1 Tensile Testing

Tensile testing is a method of determining how specimen will react when it is subjected to a force in tension. It give the tensile property data for the specification of plastic materials. The standard tensile specimens are usually in “dogbone” shape so that the deformation is within the narrow center region Dimension for the specimen must conform to ASTM Standard D638. Load applied uniaxially along the long axis of the specimen are increased slowly, pulling and deforming the specimen until it fracture (Callister & Rethwisch, 2008). Data on property of material of a component or product can be obtained by measuring loads required to elongate a materials up to fracture point. These data will ensure manufacturers that their products are suitable for their application (Mecmesin Limited, 2010). Properties that can be directly obtained from tensile test are ultimate tensile strength, maximum elongation and reduction area of the specimen. The universal testing machine is the most common testing machine used in tensile testing experiment (as shown in Figure 2.1).

Figure 2.1

According to ASTM Standard D683 (2010), tensile properties may change with the way specimen is prepared and with speed and environment of testing. Therefore, in order to get accurate and precise results, these factors must be controlled carefully. The samples needed to be prepared in exactly same way when comparative tests of materials are required. Significant data can be obtained from the tensile properties for plastics engineering design purposes. These data cannot be considered valid for application which load-time scales and environments are greatly different from those of tensile testing. This is because plastic are highly sensitive to rate of straining and environmental conditions, the result obtained are not reliable.

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From the tensile test alone, we can detect important parameters such as yield strength, ultimate tensile strength, fracture point and ductility of the interested materials that is in our case, a polymer shape of a dog bone. When a specimen is subjected to a tensile loading, the specimen will undergo elastic and plastic deformation. Initially, the specimen will elastically deform giving a linear relationship of stress and strain relationship. These two parameters are then used for the calculation of the engineering stress and strain to give a relationship. Engineering stress is defined as the ratio of the applied load, P, to the original cross-sectional area, A0 of the specimen (Callister & Rethwisch, 2008).

Engineering strain is expressed as the change in length ΔL per unit of the original length L of

the material. It is expressed as the ratio of total deformation to the initial dimension of the

material body in which the forces are being applied (Callister & Rethwisch, 2008).

Engineering stress- engineering strain curve is plotted based on the stress and strain values calculated.

2.2.2 Strength

Strength is the ability of a material to withstand stress. It is the limiting stress a material can withstand under different types of loading. Its definition varies according to the material type, applied load and application (K. G. Budinski & M. K. Budinski, 2010). This paper will focus on yield strength and ultimate tensile strength.

2.2.2.1 Ultimate Tensile Strength (UTS)

Ultimate tensile strength or sometimes known as tensile strength is the maximum tensile stress that a material withstand during tension test (ASTM Standard D638, 2010). It is the maximum stress on the stress-strain curve. The specimen will break if this stress is maintained. 

5

….………… Equation Number (2.1)

….………… Equation Number (2.2)

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After yielding, stress will reach the maximum point in the stress-strain curve with the continuously applied load. The corresponding stress at this point is known as ultimate tensile strength (UTS). Generally, the stress at fracture is taken as tensile strength for plastic polymer (Callister & Rethwisch, 2008). Tensile strength is very important in applications that depends on a polymer's physical strength. Design stress must be less than the tensile strength to prevent fracture of the structure.

2.2.3 Formability

Formability is the ability of a workpiece to undergo plastic deformation without being damaged. Ductility is a measure of the degree of plastic deformation that has been sustained at fracture. Ductility is a solid material's ability to deform under tensile stress. This is often characterized by the material's ability to be stretched into a wire. Tensile ductility of the specimen can be represented as percent elongation or percent reduction in area expressed in the equations given below. Knowledge of ductility of materials is important because it indicates to a designer the degree to which a structure will deform plastically before fracture and it specifies the degree of allowable deformation during fabrication operations (Hosford, 2005).

2.2.3.1 Percent Elongation

Percent Elongation is the percentage of change in gage length relative to the original gage length. It is calculated by using Extension Indicator which determine the distance between two designated points within the gage length of the test specimen as the specimen is pulled and extended. Percent Elongation is usually determined at the yield point and at fracture point (ASTM Standard D638).

%EL= (l−lο)lο

Io – initial length of specimenl – length of specimen at fracture

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….………… Equation Number (2.3)

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3.0 Methodology

3.1 Test Methodology

After observing and analysing completely the dimensions and shape of our sample which is polymer, our group has decided to perform the tension test. According to ASTM D368-10, we found that tension test is a suitable method to test for the strength and formability of polymers in the form of standard dumbbell-shaped. The dimensions of our test specimen conform to the dimensions of the Type I molded polymer.

3.1.1 Experiment Verifications

1. The distance between the ends of the gripping surfaces when using flat specimens shall be 115mm.

2. Do not tighten the grips to the point where the specimen would be crushed.3. Speed is set to a proper rate of 50 mm/min.

3.1.2 Apparatus and materials:

Computerized tensile testing machine as shown in Figure 3.1 Extension indicator 3 specimens

Figure 3.1: Computerized tensile testing machine

3.1.3 Procedure

1. The specimen is placed in the grips of the testing machine. 2. The grips are tighten evenly and firmly to prevent slippage of the specimen during the

test.

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3. The extension indicator is attached. 4. The speed of testing is set and the machine is started. 5. The load-extension curve of the specimen is recorded. 6. The load and extension at the yield point and the load and extension at the moment of

rupture is recorded. 7. The work piece is replaced with another one and the steps from 1 to 6 is repeated

respectively.

3.2 Project Activities

3.2.1 Tasks Assignment

Eileen Wong Wee Chin Tasks assignment, key milestones, Gantt chart, conclusion and compilation

Mohd Zaid Bin Rozilan Project background, result

Muhammad Khairy Bin Jamaluddin Literature review, result

Wong Lee Hong Testing Methodology and tools required, discussion

Soon Zhen Sheng Minutes of meeting, discussion

3.2.2 Scheduling

Date Agenda11/06/2014 Lab Briefing Sessions / 1st Meeting18/06/2014 2nd Meeting24/06/2014 3rd Meeting09/07/2014 Compiling Progress Report10/07/2014 Progress Report Submission10/07/2014 Progress Report Viva21/07/2014 Testing / 4th Meeting04/08/2014 5th Meeting06/08/2014 Compiling Final Report08/08/2014 Final Report Submission

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3.2.3 Minutes of Meeting

MINUTES OF MEETING (1)

MCB 3023 Engineering MaterialsLaboratory Group 11

Date: 11 JUNE 2014 Venue: 17-00-04Time: 10.30am – 11.00am Day: WednesdayAttendance:

Group Leader : Eileen Wong Wee ChinGroup Member :

1. Wong Lee Hong2. Soon Zhen Sheng3. Muhammad Khairy bin Jamaluddin4. Mohd Zaid bin Rozilan

Prepared by:

Soon………....…………………….

(SOON ZHEN SHENG)Secretary,

Approved by:Eileen

………....…………………….(EILEEN WONG WEE CHIN)

Leader

No. Agenda ACTION1 Lab Briefing

- Rules and Regulations- Safety- Lab booking procedure

Lab Technician

2 Ice Breaking Session with members- Introduce ourselves

All

MINUTES OF MEETING (2)

MCB 3023 Engineering Materials Laboratory Group 11

Date: 18 JUNE 2014 Venue: 17-00-04Time: 10.30am – 11.00am Day: WednesdayAttendance:

Group Leader : Eileen Wong Wee ChinGroup Member :

1. Wong Lee Hong2. Soon Zhen Sheng

Prepared by:

Soon………....…………………….

(SOON ZHEN SHENG)Secretary,

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3. Muhammad Khairy bin Jamaluddin4. Mohd Zaid bin Rozilan Approved by:

Eileen………....…………………….

(EILEEN WONG WEE CHIN)Leader

No Agenda ACTION1 Receive specimen from lab technician Eileen

2 Discussion with lab technician(s)- Material of specimen- Appropriate test for the specimen

All

3 Examining and measuring the specimens All

MINUTES OF MEETING (3)

MCB 3023 Engineering Materials Laboratory Group 11

Date: 24 JUNE 2014 Venue: Pocket C (Café)Time: 3.50pm – 4.10pm Day: TuesdayAttendance:

Group Leader : Eileen Wong Wee ChinGroup Member :

1. Wong Lee Hong2. Soon Zhen Sheng3. Muhammad Khairy bin Jamaluddin4. Mohd Zaid bin Rozilan

Prepared by:

Soon………....…………………….

(SOON ZHEN SHENG)Secretary,

Approved by:Eileen

………....…………………….(EILEEN WONG WEE CHIN)

Leader

No. Agenda ACTION1 Introduction

- Discussion of suitable mechanical properties for specimen

- Test selected: Tensile test- Mechanical properties: Strength, Formability

Eileen

2 Tasks Distribution

1. Project background2. Literature review3. Testing Methodology & tool required4. Minutes of Meeting5. Tasks Assignment, Scheduling & Gantt Chart

Eileen

ZaidKhairy

Lee HongSoonEileen

3 Meeting Adjourned Eileen

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MINUTES OF MEETING (4)

MCB 3023 Engineering Materials Laboratory Group 11

Date: 21 JULY 2014 Venue: Block 17Time: 12.00pm – 2.00pm Day: MondayAttendance:

Group Leader : Eileen Wong Wee ChinGroup Member :

1. Wong Lee Hong2. Soon Zhen Sheng3. Muhammad Khairy bin Jamaluddin4. Mohd Zaid bin Rozilan

Prepared by:

Soon………....…………………….

(SOON ZHEN SHENG)Secretary,

Approved by:Eileen

………....…………………….(EILEEN WONG WEE CHIN)

Leader

No. Agenda ACTION1 Conducting Tensile Test All

2 Analysis and discussion of result All3 Task Assignment

1. Result2. Discussion3. Conclusion

Zaid & KhairyLee Hong & Soon

Eileen

MINUTES OF MEETING (5)

MCB 3023 Engineering Materials Laboratory Group 11

Date: 4 August 2014 Venue: Pocket C (Café)Time: 11.00pm – 12.00pm Day: TuesdayAttendance:

Group Leader : Eileen Wong Wee ChinGroup Member :

1. Wong Lee Hong2. Soon Zhen Sheng3. Muhammad Khairy bin Jamaluddin4. Mohd Zaid bin Rozilan

Prepared by:

Soon………....…………………….

(SOON ZHEN SHENG)Secretary,

Approved by:Eileen

………....…………………….

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(EILEEN WONG WEE CHIN)Leader

No. Agenda ACTION1 Compilation of final report All

2 Error Checking and Correction All

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3.3 Gantt Chart

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4.0 Result and Discussion

Material : Polymer

Test method: ASTM D638

Test speed: 50.000 mm/min

Table 4.1: Test Specimen Initial DimensionTest specimen 1 2 3Width overall (mm) 18.68 18.40 18.50Width of narrow section (mm) 12.708 12.728 12.710Length overall (mm) 162 162 162Gage length (mm) 50 50 50Thickness (mm) 3.128 3.104 3.028

4.1 Tensile Test 1

Table 4.2: Result of Mechanical Properties of Specimen1

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Figure 4.1: Engineering Stress versus Engineering Strain Curve for Specimen 1

4.2 Tensile Test 2

Table 4.3: Result of Mechanical Properties of Specimen 2

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Figure 4.2: Engineering Stress versus Engineering Strain Curve for Specimen 2

4.3 Tensile test 3

Table 4.3: Result of Mechanical Properties of Specimen 3

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Figure 4.3: Engineering Stress versus Engineering Strain diagram for Specimen 3

Figure 4.4: Engineering Stress versus Engineering Strain curve for Specimen 1, Specimen 2 and Specimen 3

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4.4 Calculations

Only Test number 1 and 3 are considered because the specimen break inside the marked gage length but in test number 2, the specimen break outside the marked gage length thus can affect the average value and result in inaccurate final result. Below is the sample calculation. The engineering stress and engineering strain are calculated by using computer software.

Tensile Test 1: at time 7.09s

Area = 39.751 mm2

Engineering Stress= 105.397×9.8139.751×10−6 =26.011MPa

Engineering Strain = 2.04450

=0.0409

Tensile Test 3: at time 7.10s

Area = 38.486 mm2

Engineering Stress= 103.940×9.8138.486×10−6

=26.494MPa

Engineering Strain= 1.84350

=0.0369

Average percentage of elongation at fracture based on test number 1 and 3:

Percentage of elongation at fracture =78.5+115.117

2=96.81%

Average tensile strength based on test number 1 and 3:

Tensile strength = 26.231+27.033

2=26.632 N

mm−2=26.632MPa

4.5 Discussion

The tensile test is conducted to study the mechanical properties, which is the strength and formability of the material. The experiment is repeated three times to obtain the average tensile strength and average percentage elongation. However, only the results of specimen 1 and 3 are considered. The result of specimen 2 is disregarded because specimen 2 breaks outside of the marked narrow cross-sectional section of length 57mm. Speed is set to 50 mm/min instead of 5 mm/min to speed up the test and save time instead of spending hours as suggested by our technician.

Both specimen 1 and 3 exhibits consistent behaviour. From the tensile test graphs of specimen 1 and 3, both the specimens first elongate uniformly and deform elastically until they reach the point of yielding where the curve depart from linearity of the stress-strain curve. After yielding, the

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specimens continue plastic deformation and the stress increases to a maximum point which is the ultimate tensile strength. After the maximum point, the specimens do not break immediately. The specimens continue to elongate and necking occurs. The engineering stress corresponding to the deformation decreases to fracture point where the specimens break. There is a considerable amount elongation up to the fracture point.

The ultimate tensile strength for all the specimens varies little. This shows the repeatability of the ultimate tensile strength of the specimens is good. The average ultimate tensile strength of the specimen is 26.632 MPa, which is considerably lower as compared to metal and ceramic based on the tensile strength value in reference book (Callister & Rethwisch, 2008). This proves that the specimen is non-metal and has low strength. The percentage elongation is the indicator of the ductility of a material. The percentages of elongation at break values of the specimens obtained are highly variable because of the inconsistencies in necking center section of the specimens. The average percentage elongation of the specimen is 96.81% at fracture, which is considered large. Hence, we can conclude that the specimens are ductile.

Since only tensile strength and percentage of elongation are studied in this report, based on these two mechanical properties, the values of tensile strength and percentage elongation at fracture of the specimens fulfil all the characteristics of the material polymer. The values of tensile strength and percentage elongation at fracture of the specimens are closest to the values of the high density polyethylene based on the tensile strength (22.1 – 31.0 MPa) and percent of elongation (10% – 1200%) of the tested material from book Fundamentals of Materials Science and Engineering (refer to Appendix). Thus it is concluded that the specimen is high density polyethylene (HDPE).

There are some deviation of the actual result of the tensile strength and percentage of elongation value compared to the tested material value from reference book. This is due to the difference in condition of testing of the specimen. Tensile strength and percentage of elongation vary with specimen preparation and testing speed and environment. The properties given in the book do not specify the speed and environment of testing, hence the condition during tensile testing most probably differs from the condition of the tested specimen from book. Besides, mechanical properties of polymers are sensitive to temperature changes near room temperature, thus difference in temperature during testing also affect the mechanical properties of the specimen, resulting in different value obtained compared to the book. Other than that, the method preparation of the three given specimens is not known. All the specimens have to be prepared in the exactly same way for comparison of the result. The non-uniformity in preparation, treatment and handling of the three specimens causes the result to vary from the tested material in reference book.

There are few errors that lead to discrepancy of the results. Poor adjustment of damping mechanism and or worn knife edges of the extensometer can cause extensometer slippage which will lead to inaccuracy of results. Regular inspectionshould be done on the extensometer to ensure better performance. Specimen slippage due to worn or dirty grip faces can cause the results to be inaccurate It is advised that inspection on the grip faces should be done regularly to ensure better performance. Offsets in alignment of the grips and the specimen will affect the readings by creating bending stress. It may even cause the specimen to fracture outside the gage length. The specimens should to be properly aligned when they are clamped. Besides that, at least five specimens should be used for the tensile testing according to the ASTM D638 standard. However, due to limited number of specimen given, only three tests can be conducted. Furthermore, one of the specimen broke outside of the marked narrow cross-sectional test section and had to be discarded, leaving

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only two useful test result, cause the final result to be less accurate. Therefore, more number of test specimens, at least 5 specimens, should be used for the testing to obtain more accurate result.

5.0 Conclusion

In conclusion, three polymer specimens were given to identify two mechanical properties of the specimens. The mechanical properties chosen to be analysed are strength and formability which are important properties in selection of suitable material for engineering application. Tensile test was being conducted to find the two mechanical properties because the specimens are dog-bone shaped. Through the testing, the tensile strength and percentage of elongation of the specimens were identified, with average of 26.632MPa of ultimate tensile strength and 96.81% of elongation at fracture. The polymer specimen given is concluded to have low strength based on the value ultimate tensile strength and is ductile based on the value of percentage of elongation at fracture. With reference to the book Fundamentals of Materials Science and Engineering, the specimen is concluded to be High Density Polyethylene (HDPE) based on the mechanical properties determined.

Due to the low strength of the material, the material cannot be used in application where it has to withstand large load as it will deform easily and fail. The high percentage of elongation of the material suggests it can be used in application of that require the material to be formed into various shapes, such as bottles, toys or packaging film.

Several methods can be done to improve the result of the testing. More number of specimens should be given, at least five specimens, to get more accurate results. The specimens should be conducted under the same conditions as the referred standard tested materials, such as speed, temperature of testing and treatment of specimens. More care should be given when handling the specimens like avoiding excessive bending of the specimens. The testing equipment should be inspected regularly to ensure it is under good condition during testing.

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6.0 Reference

American Chemistry Council (2014). The Basics: Polymer Definition and Properties. Retrieved on 2014, July 4, 8:00pm from http://plastics.americanchemistry.com/Education-Resources/Plastics-101/The-Basics-Polymer-Definition-and-Properties.html.

ASTM Standard D638, 2010, "Standard Test Method for Tensile Properties of Plastics," ASTM International, West Conshohocken, PA, 2010, DOI: 10.1520/C0033-03, www.astm.org.

Budinski, K. G. & Budinski, M. K. (2010). Engineering Materials Properties and Selection (9th ed.). NY, USA: Prentice-Hall.

Callister, W. D. & Rethwisch, D.G. (2008). Fundamentals of Material Science and Engineering (3rd ed.). United States: John Wiley & Sons, Inc.

Engineer’s Handbook. Engineering Materials - Mechanical Material Properties. Retrieved on 2014, July 4, 8:00pm from http://www.engineershandbook.com/Materials/mechanical.htm.

Hosford, W. F. (2005). Mechanical Behavior of Materials. New York., NY:Cambridge University Press.

Kakani, S. L. & Kakani, A. (2004). Material Science. New Delhi: New Age International (P) Ltd., Publishers.

Kumar, K. S., Rahman, K., Varma, G. M. & Krishna K. (2012). Characterization of Bio-Degradable Polymers and its Properties–An overview. International Journal of Pharmaceutical and Chemical Sciences, 1 (3), 951 - 961.

Mecmesin Limited. (2013, Jun 11). Tensile Testing - Theory, Applications and Systems from Mecmesin. Retrieved on 2014, July 4, 8.00pm from http://www.azom.com/article.aspx?ArticleID=5551.

Mitchell, B. S. (2004). An Introduction to Materials Engineering and Science for Chemical and Materials Engineers. New Jersey, NJ: John Wiley & Sons, Inc.

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7.0 Appendix

Source: Fundamentals of Material Science and Engineering (3rd ed.). John Wiley & Sons, Inc.

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