MATERIALS SCIENCE AND TESTING

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TENSILE TEST

Theoretical review

The first tensile test was made by Leonardo da Vinci around 1495. He investigated the strength of ropes. A bucket was hung up with a rope and Leonardo poured sand into the bucket. The sand’s mass was measured as the rope broke. The rope’s strength was proportional with the mass of the sand. He discovered that if the length of the rope was increased its strength decreased. This discovery is well-known nowadays, because the longer the rope is the more possible it is that there are more defects in the material.

The aim of the tensile test is to determine material properties. This data is indispensable in designing. Several standards exist for the tensile test, which depends on the temperature, the material of the specimen, etc.

Our specimen in our test is cylindrical with diameter S0, and measures length L0. Force and elongation will be measured. In tensile test, the specimen has only one axis tensile stress. There are several types of standard specimens, because you may only have plate material, or the machine, which is used for the test, has only limited space. Table 1 shows some examples for different standard specimens.

Test machines has 3 types: (electro) mechanical, (electro) hydraulic and electro - dynamic. In mechanical machines the rotation of ball screw spindles creates the displacement. In hydraulic machines the oil pressure creates the displacement, while in the electro - dynamic the displacement is created by electricity with linear motors. It is worth knowing that these machines can also be used for compression and bending.

The force is measured with load cell, and the elongation is measured with the machine’s displacement register.

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Table 1. Standard cylindrical and plate specimens

Type Shape Capture

Cylindrical specimen with mechanical capture

Cylindrical specimen with threaded capture

Cylindrical specimen with “hook” capture

Plate specimen with mechanical capture

Plate specimen with rivet capture

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Figure 1 shows a cylindrical specimen. There is a specific relationship between diameter and the measuring length in the case of a standardized specimen: L0=5d0

(L0=5,65√𝑆0) for short and, L0=10d0 (L0=11,3√𝑆0) for long specimen.

Figure 1 Cylindrical specimen with initial diameter (d0), and measuring length (L0)

During the tensile test (constant speed) the force is measured as a function of the

elongation. Figure 2 shows a typical mild steel’s tensile diagram, while Figure 3 depicts a typical tensile diagram of aluminum. Figure 4-6 show the specimen schematic shape for the specific phases (I.-III.), while Figure 7 depicts a real aluminum sample tensile test.

Figure 2 Mild steel tensile diagram

Figure 3 Aluminum tensile diagram

Fracture

Fracture

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Tensile test diagram has 3 phases in the case of mild steel: I. Elastic deformation (line 0-e)

The deformation is fully elastic; it means the specimen’s shape returns to its initial form after unloading (Fig. 4).

Figure 4 Deformed shape of the specimen in the phase of elastic deformation

II. Constant plastic deformation phase (line e-m) The specimen has equally distributed plastic deformation along its length (Fig. 5).

Figure 5 Deformed shape of the specimen in the phase of constant plastic deformation

III. Necking phase (line m-u) The plastic deformation is concentrated in a small area, while the rest of the specimen remains the same. Specimen fractures in the neck (Fig. 6).

Figure 6 Deformed shape of the specimen in the phase of necking

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Figure 7 Aluminum specimen tensile test: point e (a), point m (b), after point m, where the necking

is observable (c), before point u (d), point u, after the fracture (e).

Standardized and non-standardized measuring numbers can be defined (Fig. 8).

Figure 8 Standardized and non-standardized measuring numbers

Standardized measuring numbers

One of the most important numbers is the yield stress. It indicates the stress which is needed to create plastic deformation. There are different types of yield stresses, but the most widely spread is practically the conventional yield stress. This is the engineering stress which can be measured at 0,2% of the plastic deformation (Fig. 9). Conventional yield stress:

(MPa) (Fig. 9)

2

0

2.0

2.0mm

N

S

FR

p

p

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Nominal yield stress:

(MPa) (Fig. 10)

Conventional yield stress after unloading:

(MPa) (Fig. 11)

Upper yield stress (cannot be defined in certain cases):

(MPa) (Fig. 12)

Lower yield stress (cannot be defined in certain cases):

(MPa) (Fig. 12)

Figure 9 The definition of Fp0.2

Figure 10 The definition of Ft0.5

Figure 11 The definition of Fr0.2

Tensile strength:

(MPa) (Fig. 12)

2

0

5.05.0

mm

N

S

FR t

t

2

0

2.02.0

mm

N

S

FR r

r

2

0 mm

N

S

FR eH

eH

2

0 mm

N

S

FR eL

eL

l

F

1ll

F

2l l

F

3l

2

0 mm

N

S

FR m

m

Fp0.2

Ft0.5

Fr0.2

%5.00

2

l

l %2.0

0

3

l

l%2.0

0

1

l

l

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Figure 12 The definition of FeH and FeL

Relative contraction:

(%)

where S0 is the initial cross section of the specimen, while Su is the smallest cross section

after fracture.

Relative fracture length:

(%) if = 5 (𝐿0 = 5,65√𝑆0)

(%) if = 10 (𝐿0 = 11,3√𝑆0)

1000

080

L

LLA u (%) if = 80 mm

where L0 the initial measuring length of the specimen, and Lu is the measuring length

after fracture.

%1000

S

SSZ

u

%1000

0

L

LLA u

0L 0d

%1000

03.11

L

LLA u

0L 0d

0L

0

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Non-standardized numbers

These numbers can also be defined in the engineering system and the real system. In the engineering system the stresses are calculated with the initial cross section while in the real system with the current cross section.

System Engineering Real

Stress 0S

Fm (MPa) vagy S

Fv (MPa)

Deformation1,2,3 10

0

0

S

S

l

ll

S

S

l

l 0

0

lnln

1 Deformation calculated from the length change can only be used until necking! 2 Integration of dε=dL/L0 and dφ=dL/L 3 SI dimension of deformation: 1

In the equations l is the current length of the measuring length while l0 is the

initial length. S is the current cross section, and S0 is the initial cross section. The engineering and the real stress – strain diagram can be calculated from the tensile diagram (Fig. 13).

Figure 13 Stress – strain diagram in real system (σ-φ) and in engineering system (σm- ε) of an

aluminum specimen

In the real system the stress always increases until the fracture.

Measuring numbers which can be calculated from tensile test

The fracture energy can be calculated from the stress–strain diagram. The specific fracture energy (Wc) is the area under the stress–strain diagram (Fig. 14). It is important that the strain must be calculated from the cross section change after point m.

uu

ddW m

c

00

)()( (J/cm3)

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Figure 14 The definition of specific fracture energy in real and engineering system

Specific fracture energy can be estimated without integration (Fig. 15):

u

v

um

c

RW

2(J/cm3)

Figure 15 Estimation of specific fracture energy

References

W.D Calister: Materials Science and Engineering – An Introduction. 7th edition

John Wiley & Sons, 2006, 2007

Tisza Miklós: Anyagvizsgálat. Miskolci Egyetemi Kiadó, 2001

Prohászka János: Bevezetés az anyagtudományba. Nemzeti Tankönyvkiadó,

Budapest, 1997

Dr. Gillemot László: Anyagszerkezettan és anyagvizsgálat. Tankönyvkiadó, 1972