PH8151 Engineering Physics Chapter 1

(achs6699) #1
8 CHAPTER 1. PROPERTIES OF MATTER

The slope of the linear segment in Figure1.6corresponds to the modulus of elasticity
E. This modulus may be thought of as stiness, or a material’s resistance to elastic
deformation. The greater the modulus, the stier the material, or the smaller the elastic
strain that results from the application of a given stress.

Most materials follow Hooke’s law only at small strains (typically less than 1%). Metals obey Hooke’s
law with fully elastic behaviour only for very small strains (typically <0.2%). In this region, the extension
is usually both linear and recoverable. At larger strains, extension is non-linear and nonrecoverable.

Elastic Limit:The elastic limit (the point 2 in Figure1.6) is the limit beyond which
the material will no longer go back to its original shape when the load is removed.
The stress corresponding to this point is the maximum stress that may be developed
such that there is no permanent deformation when the load is entirely removed.

Elastic Range: The region in stress-strain diagram from 1 to 2 in figure1.6is called
the elastic range. The stress is linearly proportional to the strain in this region and
Hooke’s law (‡Ã‘) is obeyed.

Yield Point: As the material is deformed beyond the elastic limit (the point 2 Figure
1.6), the stress is no longer proportional to strain (Hooke’s law,‡=E‘ceases to
be valid), and permanent, nonrecoverable, or plastic deformation occurs. This is
called the thephenomenon of yielding. Yield strength is indicative of the stress at
which plastic deformation begins. The position of the point separating plastic and
elastic regions is dicult to measure precisely. As a consequence, a convention has
been established wherein a straight line is constructed parallel to the elastic portion
of the stress–strain curve at some specified strain oset, usually 0.002 as shown in
Figure1.7. The stress corresponding to the intersection (the point 3 Figure1.6)of
this line and the stress–strain curve as it bends over in the plastic region is defined
as the yield strength‡y.

intended. It is therefore desirable to know the stress level at which plastic defor-
mation begins, or where the phenomenon of yieldingoccurs. For metals that expe-
rience this gradual elastic–plastic transition, the point of yielding may be determined
as the initial departure from linearity of the stress–strain curve; this is sometimes
called the proportional limit,as indicated by point Pin Figure 6.10a,and represents
the onset of plastic deformation on a microscopic level. The position of this point
Pis difficult to measure precisely. As a consequence, a convention has been estab-
lished wherein a straight line is constructed parallel to the elastic portion of the
stress–strain curve at some specified strain offset, usually 0.002. The stress
corresponding to the intersection of this line and the stress–strain curve as it bends
over in the plastic region is defined as the yield strength.^8 This is demonstrated
in Figure 6.10a.Of course,the units of yield strength are MPa or psi.^9
For those materials having a nonlinear elastic region (Figure 6.6), use of the
strain offset method is not possible, and the usual practice is to define the yield
strength as the stress required to produce some amount of strain (e.g.,!! 0.005).
Some steels and other materials exhibit the tensile stress–strain behavior shown
in Figure 6.10b.The elastic–plastic transition is very well defined and occurs abruptly
in what is termed a yield point phenomenon.At the upper yield point,plastic de-
formation is initiated with an apparent decrease in engineering stress. Continued
deformation fluctuates slightly about some constant stress value, termed the lower
yield point; stress subsequently rises with increasing strain. For metals that display
this effect, the yield strength is taken as the average stress that is associated with
the lower yield point, because it is well defined and relatively insensitive to the

sy

6.6 Tensile Properties • 163

Stress

!y

!y

Stress

Strain Strain

ElasticPlastic

0.

P

Upper yield
point

Lower yield
point

(a) (b)

Figure 6.
(a) Typical stress–
strain behavior for
a metal showing
elastic and plastic
deformations, the
proportional limit P,
and the yield strength
as determined
using the 0.
strain offset method.
(b) Representative
stress–strain
behavior found for
some steels
demonstrating the
yield point
phenomenon.

sy,

(^8) Strengthis used in lieu of stressbecause strength is a property of the metal, whereas
stress is related to the magnitude of the applied load.
(^9) For customary U.S. units, the unit of kilopounds per square inch (ksi) is sometimes used
for the sake of convenience, where
1 ksi !1000 psi
yielding
proportional limit
yield strength
JWCL187_ch06_150-196.qxd 11/5/09 9:36 AM Page 163
Figure 1.7: Representative stress–strain behaviour for steels demonstrating the conven-
tion of determining yield stress.(Picture courtesy :[ 1 ])
8

Free download pdf