Unit 1 Engineering Physics

10 CHAPTER 1. PROPERTIES OF MATTER

Displacement
Time

Stress

Strain

True

Corrected

Engineering

M

M’

Figure 1.8: A comparison of typical tensile engineering stress–strain and true

stress–strain behaviours. Necking begins at point M on the engineering curve, which corre-

sponds to M on the true curve. The “corrected” true stress–strain curve takes into account

the complex stress state within the neck region.(Picture courtesy :[ 1 ])

design purposes, the yield strength is used. This is because by the time a stress cor-

responding to the tensile strength has been applied, often a structure has experienced

so much plastic deformation that it is useless. Furthermore, fracture strengths are not

normally specified for engineering design purposes.

There will always be uncertainties in characterizing the magnitude of applied loads

and their associated stress levels for in-service applications; ordinarily load calculations

are only approximate. Furthermore, all engineering materials exhibit a variability in their

measured mechanical properties, have imperfections that were introduced during manu-

facture, and, in some instances, will have sustained damage during service. Consequently,

design approaches must be employed to protect against unanticipated failure. Therefore,

a safe stress or working stress,‡w, is used. This safe stress is based on the yield strength

of the material and is defined as the yield strength divided by a factor of safety (N),

where:

‡w=‡y/N (1.2)

The choice of an appropriate value ofN is necessary. IfNis too large, then component

over-design will result; that is, either too much material or an alloy having a higher-than-

necessary strength will be used. Safety factor values normally range between 1.2 and

4.0. Selection ofN will depend on a number of factors, including economics, previous

experience, the accuracy with which mechanical forces and material properties may be

determined, and, most important, the consequences of failure in terms of loss of life and/or

property damage.

1.3.3 Uses of Stress-Strain Diagrams

• To concisely and pictorially represent the elastic properties materials (elastic mod-
  ulus, yield strength, ultimate tensile strength etc)


• To estimate safety factor and to select materials suitable for a given application.

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