Mechanical Engineering Principles

TENSILE TESTING 21

(b) Ultimate tensile strength

=

maximum load

original cross-sectional area

=

120000

0. 0001767

= 679 × 106 Pa=679 MPa

(c) Stress at limit of proportionality

=

load at limit of proportionality

cross-sectional area

=

85000

0. 0001767

= 481 × 106 Pa=481 MPa

(d) Percentage elongation

=

increase in length

original length

× 100

=

( 55 − 40 )mm

40 mm

× 100 = 37 .5%

Now try the following exercise

Exercise 8 Further problems on tensile

testing

1. What is a tensile test? Make a sketch of
   a typical load/extension graph for a mild
   steel specimen to the point of fracture
   and mark on the sketch the following:
   (a) the limit of proportionality, (b) the
   elastic limit, (c) the yield point.


2. In a tensile test on a zinc specimen
   of gauge length 100 mm and diameter
   15 mm, a load of 100 kN produced an
   extension of 0.666 mm. Determine (a) the
   stress induced, (b) the strain, (c) Young’s
   modulus of elasticity.

[(a) 566 MPa (b) 0.00666 (c) 85 GPa]

3. The results of a tensile test are:
   Diameter of specimen 20 mm, gauge
   length 50 mm, load at limit of propor-
   tionality 80 kN, extension at limit of pro-
   portionality 0.075 mm, maximum load
   100 kN, and final length at point of frac-
   ture 60 mm.

Determine (a) Young’s modulus of elas-

ticity, (b) the ultimate tensile strength,

(c) the stress at the limit of proportion-

ality, (d) the percentage elongation.

[

(a) 169.8 GPa (b) 318.3 MPa

(c) 254.6 MPa (d) 20%

]

2.3 Further worked problems on

tensile testing

Problem 4. A rectangular zinc specimen is

subjected to a tensile test and the data from

the test is shown below. Width of specimen

40 mm; breadth of specimen 2.5 mm; gauge

length 120 mm.

Load (kN)

10 17 25 30 35 37.5 38.5 37 34 32

Extension (mm)

0.15 0.25 0.35 0.55 1.00 1.50 2.50 3.50 4.50 5.00

Fracture occurs when the extension is

5.0 mm and the maximum load recorded is

38.5 kN.

Plot the load/extension graph and hence

determine (a) the stress at the limit of

proportionality, (b) Young’s modulus of

elasticity, (c) the ultimate tensile strength,

(d) the percentage elongation, (e) the stress

at a strain of 0.01, (f) the extension at a

stress of 200 MPa.

A load/extension graph is shown in Figure 2.5.

(a) The limit of proportionality occurs at pointP

on the graph, where the initial gradient of the

graph starts to change. This point has a load

value of 26.5 kN.

Cross-sectional area of specimen

=40 mm× 2 .5mm=100 mm^2

= 100 × 10 −^6 m^2.

Stress at the limit of proportionality is given by:

σ=

force

area

=

26. 5 × 103 N

100 × 10 −^6 m^2

= 265 × 106 Pa=265 MPa