1

MPE Laboratory Sheet for Solid Mechanics

1.0 TITLE

Tensile Test

2.0 OBJECTIVES

(a) To plot the stress-strain graph from the tensile test conducted

(b) To determine the following mechanical properties of the material, taken from

the plotted stress-strain diagram: Young’s modulus, upper yield strength (𝑆𝑌,𝑈),

lower yield strength (𝑆𝑌,𝐿), Ultimate tensile strength (𝑆𝑈𝑇𝑆), Fracture stress (𝑆𝐹),

% of elongation, % of area reduction and Modulus of resilience,

(c) To discuss the following properties with relation to the material understudied:

stiffness, ductility and toughness

3.0 THEORY

3.1 Introduction

We learned from the Solid Mechanics class that the subject is about “determining stress

to avoid failure”. Here, we are talking about 2 important contrasting aspects: Load vs

Material aspect or Stress vs Strength of material. As we applied a load to a structure,

we have to ensure that the resulted stress does not cross over the limit of failure. This

limit is actually given by one of the material properties, depending on the failure that

we are considering. For example, if we are considering yield failure, the material

property that sets the limit is the yield strength, 𝑆𝑌, Some of the important material

properties can be determined from the tensile test such as the stiffness, yield strength,

ultimate tensile strength, toughness and the ductility.

3.2 Tensile Test

Tensile test is the most important test that has to be conducted when a new material is

designed. From the tensile test, we know the important quality of the new material as

compared to the available ones. Tensile test is conducted usually on a dog-bone

specimen (see Figure 1(a)) using the Universal Testing Machine. From the dog-bone

specimen, the initial length or gauge length, 𝑙𝑜 and the initial diameter, 𝑑𝑜 are firstly

measured. The specimen is given incremental tensile loads and deformations are

measured at each stage. Being tabulated such as in Figure 1(b), loads are converted to

stress, 𝜎 while deformations are converted to strain, 𝜀 using the following formula.

2

𝜎 =𝑃

𝐴𝑜 (1)

𝜀 =∆𝑙

𝑙𝑜 (2)

where 𝑃 is load, 𝐴𝑜 is the original cross-sectional area and ∆𝑙 is the elongation.

Figure 1: (a) The dog-bone specimen (b) Tabulated 𝜎 − 𝜀 data

Elastic region

The typical plot for the mild steel specimen is as shown in Figure 2. It shows the linear

stress-strain relationship at the beginning of loading until the proportional limit stress,

𝜎𝑝𝑙 is reached. Within this region, the stiffness of the material is indicated by the slope

of the linear curve. This stiffness value is better known as the Young’s modulus. The

relationship between stress and strain here is known as the Hooke’s law.

𝜎 = 𝐸𝜀 (3)

Given further loading, the stress will reach yield stress, 𝜎𝑌 that shows the end of elastic

region or the beginning of plastic region. Elastic region is where specimen returns to its

original position when the load is released. For low carbon steel, we have the upper

yield stress, 𝜎𝑌,𝑈 and lower yield stress, 𝜎𝑌,𝐿.

Figure 2: The 𝜎 − 𝜀 curve for low carbon steel

Load, P(kN)

Deformation,

l (mm)Stress,

(MPa)Strain,

0.2 0.1 1.51 0.0020.4 0.2 3.02 0.0040.6 0.3 4.52 0.0060.8 0.4 6.03 0.008…. ….. ….. …..

3

Plastic region

Following the elastic region is the plastic region where entering this region, material

will have permanent deformation. Permanent deformation is considered a failure of

material and thus the value of the yield stress (𝜎𝑌) is also called the yield strength, 𝑆𝑌.

Given further loading after yielding, the material will go through strain hardening

process until it reaches maximum stress that is called the ultimate tensile stress, 𝜎𝑢𝑡𝑠.

The presence of the 𝜎𝑢𝑡𝑠 indicated the beginning of necking or fracture of the specimen

which means the breakage or collapse failure has occurred. As such the property 𝜎𝑢𝑡𝑠

is also called the ultimate strength, 𝑆𝑢𝑡𝑠. Furthering the load, the specimen will fracture

at a lower fracture stress value of 𝜎𝑓.

Ductility

Material that has big plastic region before breaking is called ductile material while

material having no or small plastic region is called brittle material. Low carbon steel

and cast iron are examples of ductile and brittle material, respectively. The ductility of

a material is measured using the following 2 properties:

% of elongation = 𝑙𝑓−𝑙𝑜

𝑙𝑜𝑥 100% (4)

% of area reduction = 𝐴𝑜−𝐴𝑓

𝐴𝑜𝑥 100% (5)

Toughness

Toughness is the amount of energy a material can absorbed before failure occurs. In

tensile test, energy absorbed comes from the work done by the applied tensile load.

This energy is the potential energy similar to potential energy absorbed by a spring

when it is loaded. For solid material, this potential energy is called strain energy, 𝑈.

From Applied Solid Mechanic subject we learned that 𝑈 is area under the force, F vs

deformation curve while the strain energy density, 𝑢 is area under the 𝜎 − 𝜀 curve. Two

important properties with regard to toughness of a material, see Figure 3 are: the

Modulus of resilience, 𝑢𝑟 which is the amount of 𝑢 a material absorbs before yielding

and the Modulus of toughness, 𝑢𝑡 which is the amount of 𝑢 a material absorbs before it

fractures.

Figure 3: (a) Modulus of resilience, 𝑢𝑟 (b) Modulus of toughness, 𝑢𝑡

4

4.0 GENERAL EQUIPMENT DESCRIPTION

The equipment set used in this experiment, shown in Figure 4 is as the following:

Name: Shimadzu Universal Testing Machine

Model: UH-X/Xh 200kN ~ 1000kN

Manufacturer: Shimadzu Cooporation

Year: 2011

The Shimadzu universal testing machine consist of 3 major parts: Load frame,

measurement controller and computer (not shown). The components of each part and

their roles are given in Table 1.

Figure 4: The Shimadzu Universal Testing Machine

2

1

5

Measurement Controller Load Frame

3

4

5

2

1

3

4

3

6

5

Table 1: Components of the Shimadzu Universal Testing Machine and their roles

No Name Remark

LOAD FRAME

Upper Crosshead Can be adjusted according to specimen length

Grip open-close

handle

Close: Turn it clockwise

Open: Turn it counter clockwise

Elevation motor To elevate upper and lower cross-head

Lower Crosshead Moving it up and down to adjust test interval

Table -

Ram Under the table

MEASUREMENT CONTROLLER

Analog force

indicator

The measured test-force is represented as a

needle position

Peak hold indication

The highest test-force value ever taken is held

and shown here

Scale graduation

indication

A five equally divided points of the full scale

(as for 300 kN model at six equally divided

point), digital test-force values are shown

Digital force

indicator

The current test-force is indicated as a digital

value.

Operation Unit

The LCD display of the operation unit not

only displays information such as the test

conditions, but also allows the test conditions

to be input on the touch panel installed on

screen surfaces

Safety reminder

1. To avoid finger pinch, do not put hands inside the crossheads when opening and

closing the grips.

2. To avoid injury by fractured specimen pieces, keep away from loading unit when

the test is doing.

1

2

3

4

5

6

1

2

3

4

5

6

3. At the end of each test, be sure to set the load control knob to the “RETURN”

position and lower the ram to its lowest position.

5.0 EQUIPMENT OPERATING PROCEDURE

The following is the manual test operating procedure that consists of operation flow

and tensile test.

Operational Flow

Warm-up operation

Adjusting Hold position

of load control knob

Calibration the test-

force amplifier

Repositioned the Upper

Crosshead

Select and attached the

grip jaws or the platen

Set the range of the

Analog Force Indicator

Set the external analog

voltage output

Start the test

Adjustment is needed only when the hold position does not

match the position indicated on the LCD display (Refer to

Manual 3.3.3).

Calibrate once per day after starting the testing machine

(Refer to Manual 4.2).

Adjust the position of the upper crosshead according to

the length of the test specimen (Refer to Manual 3.7).

For the tensile test, select the grip jaws that fit the type

(rod or plate) and size of the specimen and attached it in

the grip jaw holder (Refer to Manual 3.8).

Select the range depending on tests (Refer to Manual 4.3).

Set the external analog voltage output, if an analog

recorder is connected (Refer to Manual 3.4.12).

.

Start the test in Manual mode.

(Refer to Manual 4.1)

7

Tensile Test

1. Return the ram to its initial position by operating the load control knob. When the

ram is set in the initial positon, “READY” is shown in the operating status display

of the LCD display.

2. Grasp the test specimen with the upper grip jaw.

3. Adjust the test force zero point (needed only when the zero point setting is incorrect)

4. Reset the stroke to “0”. Touch the ZERO key above the position indication on the

LCD display.

5. Move the lower crosshead to a proper position, then press the lower GRIP switch

to have the lower grip jaw to grasp the test specimen.

6. Press the [START] key on the operation keypad.

7. Change to the manual mode, and turn the load control knob gradually toward

“OPEN” to apply load.

8. Turn the load control knob further toward “OPEN” to increase the load until the

specimen comes to a break.

9. When the specimen comes to a break, return the load control knob to the “HOLD”

position.

10. Press the lower OPEN switch. The lower gripper opens to release the specimen.

11. Press the upper OPEN switch. The upper gripper opens to release the broken

specimen.

12. With the load control knob kept in the “HOLD” position, press the RETURN key.

The ram returns to its initial position with “READY” shown in the operating status

display. After confirming that “READY” is shown, change to the Manual mode.

13. Read the maximum test-force value on the peak test-force value display.

14. If desired, continue the test by following Attach the specimen and later in the

Operational Flow.

6.0 EXPERIMENT

Design the experiments in order to meet the given objectives.

7.0 RESULTS AND DISCUSSION

Show the results appropriately in the form of table, graph or others. Conduct the

appropriate analysis and discuss the finding.

Data taken from the experiment need to be stamped by lab officer.

8

8.0 REPORT

Submit the FORMAL REPORT within 7 days from this experiment. Report must be

typed. Similarity test will be conducted using Turnitin where similarity index of 20%

is considered passing mark. Formal report must contain the following standard content:

1. Title

2. Objective

3. Introduction and Theory

4. Apparatus

5. Procedures

6. Data and results

7. Analysis and discussion

8. Conclusion

9. References

Refer to the provided front cover for the distribution of marks.