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					ME 215 – Engineering Materials I

            Chapter 3 – Properties in Tension
                 and Compression (PART II)




Mechanical Engineering                  Dr. A. Tolga Bozdana
University of Gaziantep                  Assistant Professor
                 Plastic Behaviour - Tensile Strength
Transition of mechanical behaviour from elastic to plastic depends upon
the material type and its condition as tested (hot-rolled, cold-rolled, heat
treated, etc.). This section presents material properties in plastic region.

“Tensile strength”, also called “ultimate strength”, is the capacity of a
material to resist tensile loads without fracture (kg/mm2 or psi).

1 kg/mm2 = 9.81 * 10-3 Pa = (9.81 * 0.145) * 10-6 psi = 9.81 * 10-8 bar

Though tensile strength is the most commonly                                                 x
                                                                                                               Figure 11
                                                                     90
employed design parameter, “compressive                                                      Glass in compression




                                                   Stress (kg/mm2)
                                                                                                                            x
strength” of a material may not necessarily                          60
                                                                                                     Gray CI in compression
be equal to its tensile strength. Fig. 11 shows
the tensile and compressive strengths of glass                       30
                                                                                 x Gray CI in tension
                                                                                                            x : fracture point
and gray cast iron. However, making a design                                  x Glass in tension

                                                                          0           0.01          0.02      0.03         0.04
based on the tensile strength is not incorrect                                                     Strain

since most materials are weaker in tension.
                                                                                                                                  1
                  Plastic Behaviour - Tensile Strength
In Fig. 12, for aluminum oxide and natural rubber, stresses corresponding
to the maximum tensile load and the rupture of specimens are coincident.
However, for low carbon steel, the stress for maximum tensile load is not
destructive and its value considerably differs than the stress for rupture.
The results of a failure due to                                               Nominal Strain * 100 ( % ) – scale for rubber

plastic deformation would not                                     25
                                                                       0           200             400             600               800
                                                                                                                                       1.5
                                                                       x                                                         x
be as severe as in the case of                                             Aluminum               Low carbon steel




                                                                                                                                             Nominal Stress ( kg/mm2 ) – scale for rubber
                                                                           Oxide
fracture. Hence, even though a                                    20
                                                                           (Al2O3)




                                      Nominal Stress ( kg/mm2 )
designer chooses the working                                                                 Plastic Deformation                 x     1.0
                                                                  15
stresses within the elastic limit,
tensile strength is a reference                                                  Elastic
                                                                  10
                                                                                 Deformation
point to define a suitable factor                                                                                                      0.5

of safety against overloading.                                    5                                             Cross-linked
                                                                                                                natural rubber


                                                                  0                                                                    0
                                                                       0          5           10          15             20          25
                                                                                         Nominal Strain * 100 ( % )
                                     Figure 12
                                                                                                                                                                                            2
                 Plastic Behaviour - Tensile Strength
Fig. 13 shows the strength of                                       Figure 13
various material groups and the
relative cost per unit weight.

The steels are for high strength
applications. Different types of
steels are available acoording to
application and cost demands.

Cast irons are noted for high
compressive strength though
malleable and nodular CI also
have good strengths in tension.

Nonferrous metals offer very little choice when high strength is the primary
design parameter. The exceptions are alloys of titanium, nickel and leaded
berylium copper, which can be precipitation hardened to increase strength
and high-temperature resistance.
                                                                                3
                  Plastic Behaviour - Tensile Strength
Due to their high melting points,                                 Figure 13
refractory metals promise to be
high-strength & high-temperature
metals of near future. However,
oxidation problem forces their
uses with protective coatings.

Ceramics are significant for their
high-temperature properties so
that they are preferred in specific
applications even though they
present some design problems
and are costly materials.

Polymers are far from being strong materials. On the other hand, composite
materials employing an assortment of reinforcements have improved the
tensile properties of polymers as they can compete with carbon steels.
                                                                              4
        Plastic Behaviour - Compressive Strength
“Compressive strength” is an important property when the element is
subjected primarily to compression. In principle, it is opposite of tensile
strength. The material first goes through the elastic strain range and then
deforms plastically.

For ductile materials, the specimen bulges as the load increases in plastic
range (Fig. 14a), and hence it is not possible to define ultimate and/or
freacture strength. In fact, compressive strength is the stress value at
which specimen has distorted to a degree regarded as effective failure.

Unlike ductile materials, a definite         P                             P

strength value can be obtained for                   Original specimen

brittle materials. Large lateral                    Shear fracture plane
                                                     Deformed specimen
deformations are not produced, but
failure occurs by shear and sliding    (a)   P         Figure 14           P   (b)

along an inclined plane (Fig. 14b).

                                                                                     5
         Plastic Behaviour - Compressive Strength
Obtaining stress-strain curves in compression is more difficult due to:
1. irregularites of alignment introducing bending stresses additionally
2. lateral straining caused by friction between specimen and platens.
3. possibility of a failure by buckling if the specimen is too long.

Moduli of elasticity and yield strengths for many metals and alloys are
approximately equal in tension and compression.

For polymers, always properties in tension are specified.

Brittle materials have big difference in tensile and compressive strengths.

Gray iron has compressive strength ranging from 63 to 130 kg/mm2, which
is 3-5 times greater than its tensile strength.

Ceramics and refractory hard metals (cermets) are also characterized by
their high compressive strength.
                                                                              6
        Plastic Behaviour - Ductility and Brittleness
Ductility and brittleness are the terms describing how much a material
could deform plastically. A ductile material (like steels) undergoes plastic
deformation before it breaks. A brittle material (e.g. certain types of brass,
cast iron and glass) does not deform plastically or exhibits negligible
amount of plastic deformation prior to fracture.

Ductility is measured by sometimes percentage elongation (δL) and
                                                          δ
sometimes percentage reduction in area (δA):
                                         δ
                                                  L0: original gauge length
        L f − L0                 A0 − A f         Lf: gauge length after fracture
 δL =              100 & δ A =              100
          L0                       A0             A0: original cross sectional area
                                                  Af: area of fractured cross section


The method of percentage elongation is commonly used due to ease of
measurement compared with reduction in area method.

                                                                                        7
        Plastic Behaviour - Ductility and Brittleness
When a ductile material is strained                                                     Necking




                                        Stress
beyond its ultimate strength, the
                                                 Ultimate Strength (St)                            Fracture
deformation is no longer uniform
over gauge length, but concentrated
                                                                                            x
in a region of weakness which is                                          Plastic
called “necking” as in Fig. 15.                                           Deformation


Necking is an indication of ductility                   Yield Strength (Sy)

and cup and cone type of fracture is
                                                             Elastic
obtained (Fig. 16). On the contrary,                         Deformation
brittle materials do not have necking                                             Figure 15        Strain

before fracture (Fig. 17).
                                        Figure 16                                                 Figure 17

Percentage elongation method may
not give reliable results in necking
region, and hence reduction in area
method shall be employed.
                                                                                                              8
       Plastic Behaviour - Ductility and Brittleness
A fully brittle material can be used if there is no danger of overloading and
all stress concentration could be eliminated. Conversely, if retaining of the
shape is unimportant, then localized plastic flow could be tolerated.

In metal forming operations, extent of forming depends upon ductility and
strain hardening properties. Strain hardening is the resistance of a metal
to further plastic deformation. The tendency of a metal to strain harden is
indicated by tangent moduli of the plastic curve (i.e. smaller slope refers
to less tendency).

The term “malleability” is used to describe this tendency. Malleable
material could undergo severe plastic deformation without excessive
strain hardening. Malleability is a desirable property in metal working
processes, but is of limited interest to designer unless combined with
some other useful property such as strength.

                                                                                9
                               Plastic Behaviour - Toughness
Toughness is the ability of a material to absorb energy in plastic range. It
is the area under the plastic curve including fracture point, which indicates
amount of work per unit volume which can be done without causing rupture.

Fig. 18 shows stress-strain curve of a high toughness steel. It is difficult to
measure the area under plastic curve, so “Toughness Index Number (T0)”
is employed to compare toughness of different materials. It is approximately
the area of the rectangle 1-2-3-4: T0 = St ∗ ε f

Equation states that                                            St
                               stress

                                         2                                   3
toughness comprises
both strength and                       Sy                                   Sf
ductility. It is a desirable
property in parts that                              toughness

are subjected to shock
or impact (axles, gears,                 1                                   4
automobile frames, etc.)       Figure 18           strain                   εf
                                                                                  10
        Plastic Behaviour - Hyperelastic Resilience
Hyperelastic resilience is the energy released when the plastic loading
upon the specimen is removed. When the load on a metal is released in
plastic region, the unloading curve follows a path that is almost parallel to
the elastic portion of stress-strain diagram (Fig. 19). The energy included
by triangle ABC or CDE is hyperelastic resilience.
Hyperelastic resilience is important in                         Figure 19




                                            stress
                                                                            D
metal forming operations representing                hyperelastic    A
“springback” from initial deformation.                resilience

Consider a bar to be bent into U shape.
Let the permanent strain for required
curvature is point C. Material has to be
strained to point D to achieve required
permanent strain. If the material is not
ductile enough, point D will be beyond
ultimate limit strain causing necking,
                                                O           B        C      E   strain
thus impossible to have desired shape.
                                                                                         11
           An Example for Understanding Terminology
  A tensile test was done on a steel specimen with cross-sectional area of 20 mm2 and a gauge
  length of 100 mm. Following results were recorded:
  Load at yield point: 500 kg               Gauge length at yield point: 100.1225 mm
  Maximum load: 800 kg                      Gauge length at fracture: 133.2mm
  Fracture load: 570 kg                     Diameter of fractured cross-section: 3.8 mm


1. The yield stress: S y = Fy A = 500 20 = 25 kg/mm 2


                                Sy     F ∗L   500 ∗ 100
2. Modulus of elasticity: E =        =      =            = 2.04 ∗ 10 4 kg/mm 2
                                ε      A ∗ δ 20 ∗ 0.1225
                                  2
                                 Sy   25 2
3. Modulus of resilience: U =   =                = 15.32 ∗ 10 −3 kg ⋅ mm/mm3
                              2E 2 ∗ 2.04 ∗ 10 4

4. Total energy absorbed: W = U ∗ A ∗ L = 15.32 ∗ 10 −3 ∗ 20 ∗ 100 = 30.64 kg ⋅ mm

                                                                                                12
           An Example for Understanding Terminology
5. The tensile strength: S ut = Fmax A = 800 20 = 40 kg/mm 2


6. The fracture stress: S f = F fracture A = 570 20 = 28.5 kg/mm 2


                                   L f − L0         133.2 − 100
7. Percentage elongation:   δL =              100 =             ∗ 100 = 33.2%
                                       L0              100
                                                                            2
                                            A0 − A f         20 − π ∗ (3.8 2 )
8. Percentage reduction in area: δ A   =               100 =                   ∗ 100 = 43.3%
                                              A0                    20

9. Toughness index number:    T0 = St ∗ ε f = St ∗ δ L = 40 ∗ 0.332 = 13.28 kg ⋅ mm/mm3




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