<s>
In	O
engineering	O
and	O
materials	O
science	O
,	O
a	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
for	O
a	O
material	O
gives	O
the	O
relationship	O
between	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
.	O
</s>
<s>
It	O
is	O
obtained	O
by	O
gradually	O
applying	O
load	O
to	O
a	O
test	O
coupon	O
and	O
measuring	O
the	O
deformation	O
,	O
from	O
which	O
the	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
can	O
be	O
determined	O
(	O
see	O
tensile	O
testing	O
)	O
.	O
</s>
<s>
Generally	O
speaking	O
,	O
curves	O
representing	O
the	O
relationship	O
between	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
in	O
any	O
form	O
of	O
deformation	O
can	O
be	O
regarded	O
as	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curves	I-Algorithm
.	O
</s>
<s>
The	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
can	O
be	O
normal	O
,	O
shear	O
,	O
or	O
mixture	O
,	O
and	O
can	O
also	O
can	O
be	O
uniaxial	O
,	O
biaxial	O
,	O
or	O
multiaxial	O
,	O
even	O
change	O
with	O
time	O
.	O
</s>
<s>
If	O
not	O
mentioned	O
otherwise	O
,	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
refers	O
to	O
the	O
relationship	O
between	O
axial	O
normal	O
stress	O
and	O
axial	O
normal	O
strain	O
of	O
materials	O
measured	O
in	O
a	O
tension	O
test	O
.	O
</s>
<s>
Consider	O
a	O
bar	O
of	O
original	O
cross	B-Application
sectional	I-Application
area	I-Application
being	O
subjected	O
to	O
equal	O
and	O
opposite	O
forces	O
pulling	O
at	O
the	O
ends	O
so	O
the	O
bar	O
is	O
under	O
tension	O
.	O
</s>
<s>
The	O
material	O
is	O
experiencing	O
a	O
stress	O
defined	O
to	O
be	O
the	O
ratio	O
of	O
the	O
force	O
to	O
the	O
cross	B-Application
sectional	I-Application
area	I-Application
of	O
the	O
bar	O
,	O
as	O
well	O
as	O
an	O
axial	O
elongation	O
:	O
</s>
<s>
The	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
for	O
this	O
material	O
is	O
plotted	O
by	O
elongating	O
the	O
sample	O
and	O
recording	O
the	O
stress	O
variation	O
with	O
strain	O
until	O
the	O
sample	O
fractures	B-Application
.	O
</s>
<s>
Note	O
that	O
for	O
engineering	O
purposes	O
we	O
often	O
assume	O
the	O
cross-section	B-Application
area	O
of	O
the	O
material	O
does	O
not	O
change	O
during	O
the	O
whole	O
deformation	O
process	O
.	O
</s>
<s>
The	O
curve	O
based	O
on	O
the	O
original	O
cross-section	B-Application
and	O
gauge	O
length	O
is	O
called	O
the	O
engineering	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
,	O
while	O
the	O
curve	O
based	O
on	O
the	O
instantaneous	O
cross-section	B-Application
area	O
and	O
length	O
is	O
called	O
the	O
true	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
Due	O
to	O
the	O
shrinking	O
of	O
section	O
area	O
and	O
the	O
ignored	O
effect	O
of	O
developed	O
elongation	O
to	O
further	O
elongation	O
,	O
true	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
are	O
different	O
from	O
engineering	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
.	O
</s>
<s>
The	O
true	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
can	O
be	O
expressed	O
by	O
engineering	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
.	O
</s>
<s>
Thus	O
,	O
a	O
point	O
defining	O
true	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
is	O
displaced	O
upwards	O
and	O
to	O
the	O
left	O
to	O
define	O
the	O
equivalent	O
engineering	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
As	O
for	O
the	O
tensile	O
strength	O
point	O
,	O
it	O
is	O
the	O
maximal	O
point	O
in	O
engineering	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
but	O
is	O
not	O
a	O
special	O
point	O
in	O
true	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
The	O
stress	B-Algorithm
and	I-Algorithm
strain	I-Algorithm
at	O
the	O
necking	O
can	O
be	O
expressed	O
as	O
:	O
</s>
<s>
A	O
schematic	O
diagram	O
for	O
the	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
of	O
low	O
carbon	O
steel	O
at	O
room	O
temperature	O
is	O
shown	O
in	O
figure	O
1	O
.	O
</s>
<s>
Beyond	O
tensile	O
strength	O
,	O
a	O
necking	O
forms	O
where	O
the	O
local	O
cross-sectional	B-Application
area	I-Application
becomes	O
significantly	O
smaller	O
than	O
the	O
average	O
.	O
</s>
<s>
Such	O
positive	O
feedback	O
leads	O
to	O
quick	O
development	O
of	O
necking	O
and	O
leads	O
to	O
fracture	B-Application
.	O
</s>
<s>
This	O
region	O
ends	O
up	O
with	O
the	O
fracture	B-Application
.	O
</s>
<s>
After	O
fracture	B-Application
,	O
percent	O
elongation	O
and	O
reduction	O
in	O
section	O
area	O
can	O
be	O
calculated	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
distinguish	O
some	O
common	O
characteristics	O
among	O
the	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curves	I-Algorithm
of	O
various	O
groups	O
of	O
materials	O
and	O
,	O
on	O
this	O
basis	O
,	O
to	O
divide	O
materials	O
into	O
two	O
broad	O
categories	O
;	O
namely	O
,	O
the	O
ductile	O
materials	O
and	O
the	O
brittle	O
materials	O
.	O
</s>
<s>
During	O
this	O
stage	O
,	O
the	O
cross-sectional	B-Application
area	I-Application
decreases	O
uniformly	O
along	O
the	O
gauge	O
length	O
,	O
due	O
to	O
the	O
incompressibility	O
of	O
plastic	O
flow	O
(	O
not	O
because	O
of	O
the	O
Poisson	O
effect	O
,	O
which	O
is	O
an	O
elastic	O
phenomenon	O
)	O
.	O
</s>
<s>
Then	O
a	O
process	O
of	O
necking	O
begins	O
,	O
which	O
ends	O
in	O
a	O
'	O
cup	O
and	O
cone	O
 '	O
fracture	B-Application
characteristic	O
of	O
ductile	O
materials	O
.	O
</s>
<s>
Due	O
to	O
the	O
natural	O
inhomogeneity	O
of	O
the	O
material	O
,	O
it	O
is	O
common	O
to	O
find	O
some	O
regions	O
with	O
small	O
inclusions	O
or	O
porosity	O
,	O
within	O
the	O
material	O
or	O
on	O
its	O
surface	O
,	O
where	O
strain	O
will	O
concentrate	O
,	O
leading	O
to	O
a	O
local	O
reduction	O
in	O
cross-sectional	B-Application
area	I-Application
.	O
</s>
<s>
However	O
,	O
beyond	O
this	O
,	O
the	O
work	O
hardening	O
rate	O
will	O
decrease	O
,	O
such	O
that	O
a	O
region	O
with	O
smaller	O
area	O
is	O
weaker	O
than	O
nearby	O
regions	O
,	O
therefore	O
reduction	O
in	O
area	O
will	O
concentrate	O
in	O
this	O
region	O
and	O
the	O
neck	O
will	O
become	O
more	O
and	O
more	O
pronounced	O
until	O
fracture	B-Application
.	O
</s>
<s>
The	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
for	O
a	O
ductile	O
material	O
can	O
be	O
approximated	O
using	O
the	O
Ramberg	O
–	O
Osgood	O
equation	O
.	O
</s>
<s>
Brittle	O
materials	O
,	O
which	O
include	O
cast	O
iron	O
,	O
glass	O
,	O
and	O
stone	O
,	O
are	O
characterized	O
by	O
the	O
fact	O
that	O
rupture	O
occurs	O
without	O
any	O
noticeable	O
prior	O
change	O
in	O
the	O
rate	O
of	O
elongation	O
,	O
sometimes	O
they	O
fracture	B-Application
before	O
yielding	O
.	O
</s>
<s>
A	O
typical	O
stress	B-Algorithm
–	I-Algorithm
strain	I-Algorithm
curve	I-Algorithm
for	O
a	O
brittle	O
material	O
will	O
be	O
linear	O
.	O
</s>
