Mechanical Properties of

Materials

Terminology• Stress

– Force acting on the unit are over which is force is applied

– Unit : psi (pounds per square inch) or Pa (Pascal)

– Symbol : σ

• Strain– The change in dimension per unit length– Unit : No dimension – in/in or cm/cm– Symbol : τ

• Stress – cause / Strain - effect

• Deformation– Elastic deformation

• Nonpermanent• When applied load is released, the piece

returns to its original shape• Linear & Non-linear elastic

4

Elastic means reversible!

Elastic Deformation1. Initial 2. Small load 3. Unload

F

bonds stretch

return to initial

F

Linear- elastic

Non-Linear-elastic

5

Plastic means permanent!

Plastic Deformation (Metals)

F

linear elastic

linear elastic

plastic

1. Initial 2. Small load 3. Unload

p lanes

still

sheared

F

elastic + plastic

bonds

stretch

& planes

shear

plastic

•In materials, elastic stress and elastic strain are linearly related• The slope of tensile stress-strain curve in the linear regime defines

•The Young’s modulus or modulus of elasticity, E

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Stress-Strain Testing• Typical tensile test machine

Adapted from Fig. 6.3, Callister 7e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)

specimenextensometer

• Typical tensile specimen

Adapted from Fig. 6.2,Callister 7e.

gauge length

• One of the most common mechanical stress-strain tests is performed in tension.

• Tension test can be used to ascertain several mechanical properties of materials that are important in design.

• A specimen is deformed, usually to fracture, with a gradually increasing tensile load that is applied uniaxially along the long axis of a specimen.

• Normally, the cross section is circular, but rectangular specimens are also used.

• This "dogbone" specimen configuration was chosen so that, during testing, deformation is confined to the narrow center region (which has a uniform cross section along its length), and, also, to reduce the likelihood of fracture at the ends of the specimen.

• The standard diameter : 12.8 mm (0.5 in.), whereas the reduced section length (should be at least four times this diameter) : 60 mm (2 ¼ in.)

• The specimen is mounted by its ends into the holding grips of the testing apparatus

• The tensile testing machine is designed to elongate the specimen at a constant rate, and to continuously and simultaneously measure the instantaneous applied load (with a load cell) and the resulting elongations (using an extensometer).

• A stress-strain test typically takes several minutes to perform and is destructive; that is, the test specimen is permanently deformed and usually fractured.

10

Stress has units:

N/m2 or lbf/in2

Engineering Stress• Shear stress, :

Area, A

Ft

Ft

Fs

F

F

Fs

= Fs

A o

• Tensile stress, :

original area before loading

Area, A

Ft

Ft

=Ft

A o2f

2m

Nor

in

lb=

Engineering Strain

• Engineering strain є is defined

є = li – lo = Δ l

-------- ------

lo lo

• in which lo is the original length before any load is applied, and li is the instantaneous length. Sometimes the quantity li

- lo is denoted as Δ l , and is the deformation elongation or change in length at some instant, as referenced to the original length

• Engineering strain (subsequently called just strain) is unitless, but meters per meter or inches per inch are often used; the value of strain is obviously independent of the unit system.

• Sometimes strain is also expressed as a percentage, in which the strain value is multiplied by 100.

Tensile Test•Table 6-1 shows the effect of the load on the changes in length of an aluminum alloy test bar.

•These data are then subsequently converted ioto stress and strain.

•The stress-strain curve is analyzed further to the extract properties of materials (e.g. Young’s modulus, yield strength, etc.)

Unit• Many different units are used to report the results of the tensile test.• The most common units for stress are pounds per square inch (psi) and

Megapascals (Mpa).• The units for strain include inch/inch, centimeter/centimeter, and

meter/meter. • The conversion factors for stress are summarized below. Because strain is

dimension-less, no conversion factors are required to change the system of units.

1 pound (lb) :4.448 Newtons (N)

1 psi : pounds per square inch

1 MPa : MegaPascal : MegaNewtons per square meter (MN/m2)

: Newtons per square millimeter (N/mm2) : 106 Pa

I GPa : 1000 MPa : Gigapascal

1 ksi : 1000 psi : 6.895 MPa

1 psi : 0.006895 MPa

1 M Pa : O. 145 ksi : 145 psi

Properties obtained from Tensile Test

• The critical stress value needed to initiate plastic deformation is defined as the elastic limit of the material. – In metallic materials, this is usually the stress

required for dislocation motion, or slip to be initiated.

– In polymeric materials, this stress will correspond to disentanglement of polymer molecule chains or sliding of chains past each other.

• The proportional limit is defined as the level of stress above which the relationship between stress and strain is not linear.

• In most materials the elastic limit and proportional limit are quite close (not determine precisely)

• Define them at an offset strain value (typically, but not always, 0.002 or 0.2%)

• We then draw a line starting with this offset value of strain and draw a line parallel to the linear portion of the engineering stress-strain curve.

• The stress value corresponding to the intersection of this line and the engineering stress-strain curve is defined as the offset yield strength, also often stated as the yield strength.

• The 0.2% offset yield strength for gray cast iron is 40,000 psi as shown in Figure 6-8(a).

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Tensile Strength, TS

• Metals: occurs when noticeable necking starts.• Polymers: occurs when polymer backbone chains are aligned and about to break.

Adapted from Fig. 6.11, Callister 7e.

y

strain

Typical response of a metal

F = fracture or

ultimate

strength

Neck – acts as stress concentrator

eng

inee

ring

TS s

tres

s

engineering strain

• Maximum stress on engineering stress-strain curve.

• Tensile Strength : The stress obtained at the highest applied force is the tensile strength (σts), which is the maximum stress on the engineering stress-strain curve.

• In many ductile materials, deformation does not remain uniform. At some point, one region deforms more than others and a large local decrease in the cross-sectional area occurs. This locally deformed region is called a "neck." This phenomenon is known as necking.

• Because the cross-sectional area becomes smaller at this point, a lower force is required to continue its deformation, and the engineering stress, calculated from the original area Ao, decreases.

• The tensile strength is the stress at which necking begins in ductile materials.

• Many ductile metals and polymers show the phenomenon of necking.• In compression testing, the materials will bulge, thus necking is seen

only in a tensile test.

Elastic Properties• The modulus of elasticity, or Young's

modulus (E), is the slope of the stress-strain curve in the elastic region.

• This relationship is Hooke’s Law:E = σ / ε

• Young's' modulus is a measure of the stiffness of a component.

• A stiff component with a high modulus of elasticity, will show much smaller changes in dimensions if the applied stress is relatively small and, therefore, causes only elastic deformation.

Ductility• measures the amount of deformation that a

material can withstand without breaking. • We can measure the distance between the

gauge marks on our specimen before and after the test.

• The percent elongation describes the permanent plastic deformation before failure (i.e., the elastic deformation recovered after fracture is not included).

• Note that the strain after failure is smaller thaq the strain at the breaking point.%Elongation = lf – lo

--------------- x 100

lo

True Stress and True Strain

• The decrease in engineering stress beyond the tensile strength point on an engineering stress-strain curve is related to the definition of engineering stress.

• We used the original area A0 in our calculations, but this is not precise because the area continually changes.

• We define true stress and true strain by the following equations:

Hardness• The hardness test measures the resistance to

penetration of the surface of a material by a hard object.

• Hardness as a term is not defined precisely. Hardness, depending upon the context, can represent resistance to scratching or indentation and a qualitative measure of the strength of the material.

• In general, in macrohardness measurements the load applied is -2N.

• A variety of hardness tests have been devised, but the most commonly used are the Rockwell test and the Brinell test. Different indentors used in these tests.

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Hardness: MeasurementTable 6.5

Brinell hardness test• In the Brinell hardness test, a hard steel

sphere (usually 10mm in diameter) is forced into the surface of the material.

• The diameter of the impression, typically 2 to 6mm, is measured and the Brinell hardness number (abbreviated as HB or BHN) is calculated from the following equation:

where F is the applied load in kilograms, D is the diameter of the indentor in millimeters, and Di is the diameter of the impression in millimeters. The Brinell hardness has the units of stress (e.g., kg/mm2).

Rockwell hardness• The Rockwell hardness test uses a small-diameter steel

ball for soft materials and a diamond cone, or Brale, for harder materials.

• The depth of penetration of the indentor is automatically measured by the testing machine and converted to a Rockwell hardness number (HR).

• Since an optical measurement of the indention dimensions is not needed, the Rockwell test tends to be more popular than the Brinell test.

• Several variations of the Rockwell test are used, including:– A Rockwell C (HRC) test is used for hard steels, whereas a

Rockweil f (HRF) test might be selected for aluminum.

• Rockwell tests provide a hardness number that has no units.

Knoop hardness• The Knoop hardness (HK) test is a microhardness test,

forming such small indentations that a microscope is required to obtain the measurement.

• In these tests, the load applied is less than 2N. • The Vickers test, which uses a diamond pyramid

indentor, can be conducted either as a macro and microhardness test.

• Microhardness tests are suitable for materials that may have a surface that has a higher hardness than the bulk materials in which different areas show different levels of hardness, or on samples that are not macroscopically flat.

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