Tech.info, Tensile Testing

8/13/2019 Tech.info, Tensile Testing

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Technical Information:

Stress and Strain Tension Testing

Engineering Stress

Engineering stress, , is force, F, divided by original area, A0:

!=

F

A0

(1)

Tension positive.

[=] N/m2= Pa (usually MPa) or [=] lb/in2= psi (usually ksi)

1 MPa !145 ksi

Engineering Strain

Engineering strain is the change in length divided by the original length:

! =

l" l0

l0

=

#l

l0

(2)

True Stress

True stress, T, is force divided by the actual area:

!T =

F

A (3)

For uniform deformation:

!T=!1+"( ) (4)

True Strain

True strain is:

d!T =dl

l (5)

For uniform deformation:

!T =ln l

l0

# $

&'=ln 1+!{ } (6)

Once necking begins:

!T =ln A0

Aneck

"#$

%&'

=ln( d0( )

2

( dneck( )2

#)

$)&)

')=2 ln

d0

dneck

*

+,

-

./ (7)

Shear Stress and Shear Strain

Plastic deformation conserves volume. Plastic deformation is by shear. Plasticdeformation may produce surface markings and localized heating.

Linear Elastic Loading

The initial part of the stress-strain curve is linear, with slope:

E =!

"

(8)

E is Youngs Modulus or the elastic modulus. E [=] Pa. E is the slope of themodulus line in Figure 1. E is valid for uniaxial tension.


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For small strains, deformation is reversible; the specimen exhibits linear elasticity.


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General Characteristics of an Engineering StressStrain Curve

Plastic Yielding

A stress-strain line that changes slope gradually, as seen in Fig. 1 and Fig. 2, indicates

homogeneous plastic deformation throughout the specimen.

The yield strength, !Y, is taken as the start of significant plastic yielding. A practical

measure of the yield strength is the stress where a line of slope E drawn through

! =0.002intersects the stress-strain curve (Fig. 1). If plastic flow begins at one point and then propagates along the specimen, the result is

a yield point (Fig. 3). On the stress-strain diagram, this shows up as a peak (the Upper

Yield Point, UYP), a load drop, a small irregular strain, and a point (the Lower YieldPoint, LYP) where the normal curve continues. In this case the yield strength is taken as

the stress at the LYP.

Uniform Deformation and Strain HardeningAfter yielding, uniform plastic deformation leads to a nonlinear increase in the

engineering stress referred to as strain hardening.

Tensile StrengthThe tensile strength, TS(or ultimate tensile strength, UTS), is the maximum engineering

stress in a tension test. (Fig. 2 and Fig. 3)

Figure 1. Initial portion of the stress-strain curve for annealedpolycrystalline copper. The 0.2% offset yield strength is indicated. Ifthe specimen were unloaded to the yield strength and then unloaded,it would suffer a permanent strain of 0.002.

!


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Figure 2. Complete engineering stress-strain curve for annealedpolycrystalline copper. The 0.2% offset yield strength (taken fromFigure 1), tensile strength, and percent elongation at fracture areindicated"

Figure 3. Complete engineering stress-strain curve for a mild

steel (1018 hot-rolled steel). The upper and lower yield points(UYP and LYP), tensile strength, percent elongation at fracture,and Lders strain are indicated.#


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General Characteristics of a True StressStrain Curve

Low-Strain Portion

The low-strain portion of a true stresstrue strain curve is virtually identical to the low-

strain portion of an engineering stressengineering strain curve. Therefore, Young'smodulus and the yield strength can be evaluated from either.

Strain Hardening

Strain hardening is the slope of the true stresstrue plastic strain curve at any point priorto the onset of necking. The primary cause of strain hardening is an increase in

dislocation density. Dislocations are generated during plastic flow and dislocation motion

during slip is impeded because of the increasing dislocation density.

True stress true strain data often can be fitted the empirical expression:

!T,plastic =K "T,plastic( )n

(11)

or:

ln !T

{ }=ln K{ }+ n ln "T

{ }

if K(the strength coefficient) and n(the strain-hardening exponent) are constant. The

greater the value of n, the greater is the strain hardening. For metals, nranges from close

to zero up to slightly greater than 0.5.

Necking (Plastic Instability)

After the onset of necking, all further plastic deformation occurs in the neck region. The

hydrostatic stress component and the developing voids make it impossible to calculate the

true stress in the neck.

Reduction of Area After Fracture

The reduction in area at fracture (% basis), which is one measure of ductility, is uniquelyrelated to the true strain at fracture.

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