Mechanical Engineering Principles

THE EFFECTS OF FORCES ON MATERIALS 11

by 0.8 mm when carrying a load of

200 kN. [(a) 27.5 mm (b) 68.2 GPa]

7. A metal rod of cross-sectional area
   100 mm^2 carries a maximum ten-
   sile load of 20 kN. The modulus of
   elasticity for the material of the rod
   is 200 GPa. Determine the percentage
   strain when the rod is carrying its max-
   imum load. [0.10%]


8. A metal tube 1.75 m long carries a ten-
   sile load and the maximum stress in the
   tube must not exceed 50 MPa. Deter-
   mine the extension of the tube when
   loaded if the modulus of elasticity for
   the material is 70 GPa. [1.25 mm]


9. A piece of aluminium wire is 5 m
   long and has a cross-sectional area of
   100 mm^2. It is subjected to increasing
   loads, the extension being recorded for
   each load applied. The results are:

Load (kN) 0 1.12 2.94 4.76 7.00 9.

Extension (mm) 0 0.8 2.1 3.4 5.0 6.

Draw the load/extension graph and

hence determine the modulus of elastic-

ity for the material of the wire.

[70 GPa]

10. In an experiment to determine the mod-
    ulus of elasticity of a sample of copper,
    a wire is loaded and the corresponding
    extension noted. The results are:

Load (N) 0 20 34 72 94 120

Extension (mm) 0 0.7 1.2 2.5 3.3 4.

Draw the load/extension graph and de-

termine the modulus of elasticity of the

sample if the mean diameter of the wire

is 1.23 mm and its length is 4.0 m.

[96 GPa]

1.9 Ductility, brittleness and

malleability

Ductilityis the ability of a material to be plastically
deformed by elongation, without fracture. This is
a property that enables a material to be drawn out
into wires. For ductile materials such as mild steel,
copper and gold, large extensions can result before

fracture occurs with increasing tensile force. Ductile

materials usually have a percentage elongation value

of about 15% or more.

Brittlenessis the property of a material manifested

by fracture without appreciable prior plastic defor-

mation. Brittleness is a lack of ductility, and brittle

materials such as cast iron, glass, concrete, brick and

ceramics, have virtually no plastic stage, the elastic

stage being followed by immediate fracture. Little or

no‘waist’ occurs before fracture in a brittle material

undergoing a tensile test.

Malleabilityis the property of a material whereby it

can be shaped when cold by hammering or rolling.

A malleable material is capable of undergoing plas-

tic deformation without fracture. Examples of mal-

leable materials include lead, gold, putty and mild

steel.

Problem 17. Sketch typical load/extension

curves for (a) an elastic non-metallic

material, (b) a brittle material and (c) a

ductile material. Give a typical example of

each type of material.

(a) A typical load/extension curve for an elas-

tic non-metallic material is shown in Fig-

ure 1.10(a), and an example of such a material

is polythene.

(b) A typical load/extension curve for a brittle

material is shown in Figure 1.10(b), and an

example of such a material is cast iron.

(c) A typical load/extension curve for a ductile

material is shown in Figure 1.10(c), and an

example of such a material is mild steel.

Extension

Load

(a)

Extension

Load

(b)

Extension

Load

(c)

Figure 1.