3. Background to the experimental investigation

Tensile testing is one of the most important mechanical tests which can be conducted on an

engineering material. To compare and select materials for various applications one must

know the important properties of that material. For example, steel, one of the most important

engineering materials, is manufactured in different grades with different strengths,

toughness, ductility etc. For this reason, it is important to have an effective method of

determining these properties. Tensile testing can accurately measure many of the most

important engineering design properties.

Stress,o (MPa)

Utimate

Strength

Yield Point

Plastic

Deformation

• Young's modulus

• Yield point

• Ultimate tensile strength

• Ductility

• Toughness

• Resilience

Necking

Figure 1: Stress/strain curve showing yield point, ultimate tensile strength, fracture point and deformation regions.

In tension tests, a specimen is subjected to a continually increasing extension while

simultaneous observations are made of the uniaxial load on the specimen. An engineering

stress-strain curve is constructed from the load-elongation measurements. In the first part of

the practical session, you will see how the load versus elongation curve is obtained, and in

the later part of the session, you will use load and elongation results to draw a stress-strain

curve and calculate some of the most important materials properties parameters. This

procedure is expanded on below. Through this process, the following material properties can

be determined:

Strain,c (%)

It is important to note that not all mechanical properties can be determined through tensile

testing. Examples of important properties which must be obtained through other tests

include hardness, fatigue, and impact properties./n3.1. Stress-Strain Conversion

The load-elongation data must first be converted into stress-strain data for the determination

of material properties. Stress (a) can be found using (Eq 1) as the force (F) divided by the

original cross-sectional area (A). The strain (e) can be found using (Eq 2) as the change in

length (AZ) divided by the original gauge length (4). This data can then be used to produce a

stress-strain curve from which various material properties can be found.

0 = 7/10

==

3.2. Young's modulus

Young's modulus is the linear relationship between stress and strain of a material. At low

levels they are proportional to each other through the below (Eq 3) relations. Also known as

Hooke's law.

Eq. 1

a = Ee

Where o is the stress, E is the Young's modulus and is the strain.

Whilst the material exhibits this linear behaviour the materials deformation is reversible. The

Young's modulus is the first linear region of the stress/strain graph. See Figure 1.

3.3. Yield point

Eq. 2

I

The abrupt transition from elastic to plastic deformations is called the yield point. If no yield

point exists, the offset yield strength is calculated for a strain offset of 0.2%. This is where a

line is plotted on top of the stress/strain curve using Hooke's law, and then a parallel line is

D

Eq 3

drawn at 0.2% strain. The corresponding stress is known as the 0.2% offset yield strength. See

Figure 2.

Figure 2: Stress/strain curve showing 0.2% offline./n3.4. Ultimate tensile strength

Ultimate tensile strength (UTS) is the maximum stress the material can handle before failure.

Whilst this point may not represent the fracture point, it is the materials strength limit. See

figure 1.

3.5. Ductility

Ductility is a measure of the degree of plastic deformation at fracture. To calculate the

ductility of a material, the strain at fracture is required. It can be determined by Eq 4.

EL%=100

Eq. 4

Where EL% is the elongation, L, is the length at failure and L is the original length of the

material.

3.6. Toughness

Toughness is the ability of material to absorb energy and plastically deform before fracturing.

It is approximated by the area under the stress strain curve and determined by Eq 5.

24₂ = ¹o de

Where u, is the toughness, &, is the strain at failure and is the stress.

3.7. Resilience

Resilience is the capacity of a material to absorb elastic energy when it is deformed elastically,

and then upon unloading to have this energy recovered. To determine this, the area under

the linear region of curve is needed. This relationship can be simplified as shown in Eq 6.

Eq. 5

ur = fode = a₂²y

Eq. 6

Whereu, is the resilience, &, is the strain at yield, dy is the stress at yield and a is the stress.