ME 215 – Engineering Materials I

Dr. A. Tolga Bozdanawww.gantep.edu.tr/~bozdana

Mechanical EngineeringUniversity of Gaziantep

Chapter 4

Properties in Bending and Shear (Part I)

1

Introduction Many machine and structural parts are often subjected to bending and

shear stresses. In most cases, it is highly desirable to test such parts underthe conditions that simulate the actual service loading.

Static bending and shear properties of materials are not of the same interestas static tension and compression properties. Such properties might bedetermined directly, or some insight may be gained from tensile test data(e.g., shear yield strength of a material is approximately equal to half of itsyield strength in tension: Ssy Sy / 2).

The preparation and adequate testing of tension test specimens might bedifficult, hence simpler shear and bending tests are often employed.

Behaviour of Materials in Bending

2

M

M

When a member is subjected to bending load, it acts asa beam with a primary function of resisting this loading.

In bending, both tensile and compressive stressesare induced over a cross section of the beam. Thus,bending tests are less severe than tensile tests, butmore severe than compressive tests.

In fact, bending test does not provide extra informationon mechanical behaviour of a material unless bendingcauses special failure. Its value is defined as a directmeans of evaluating behaviour of beams under loadingto determine strength and ductility.

Since the loads required to cause failure are relativelysmall and easily applied, bending tests can be madewith simple and cheap apparatus. Test specimens aresimple and easy to prepare. Gripping problems areeliminated and deflection data are easily obtained.

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Bending Tests

1 2

3

P/2 P/2

L aaL

a a

4beam

Figure 1b

3

1 2

P

L

L

beam

Figure 1a

There are two common types of bending tests:

a) 3-point bending (Fig. 1a): applying a concentrated load at the span centre.

b) 4-point bending (Fig. 1b): applying half-loads equally distant from supports.

3-point bending methodis often used due to itssimplicity.

On the contrary, 4-pointbending (pure-bending)method provides bettermaterial characteristicsdue to the constantbending moment whichoccurs between innerload points.

4

Bending Tests Bending tests are intended for brittle materials when scope of test is to determinethe bending strength of material.

Thus, such tests are notably employed for cast iron (based on ASTM A48) as well asconcrete, wood and certain plastics (according to ASTM D790-66, BS 2782 and DIN53452) using circular or rectangular specimens.

To determine bending strength, beam must be proportioned so that it will not fail inshear or by lateral deflection before reaching its ultimate flexural limit. Usually, longspecimens of high length-to-depth ratio (L/h > 10) are used. Shorter beams (L/h < 6)are intended for shear failure testing in bending.

3-point bending test 4-point bending test

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Bending Strength “Bending strength” is also known as: flexural strength, cross-breaking strength,transverse strength, modulus of rupture, and coefficient of bending strength.

3 2 max

M c F LσI w h

2

M : bending momentI : area moment of inertia

c : distance from neutral axis F : load at span centerL : distance between supports

w : width of specimenh : thickness of specimen

McN. A.

Bending strength of brittle materials obtainedfrom bending tests would be greater than thatfrom tensile tests. As approaching failure, neutralaxis shifts toward compression face (by distanceof c), which tends to strengthen the beam.

For a rectangular part in 3-point bending test,bending strength is the highest stress at momentof rupture:

Stiffness in Bending “Stiffness in bending” is the resistance to deformation in bending within elastic

range. A measure of this property is “modulus of elasticity in bending” defined byload-deflection diagram (Fig. 2).

Load-deflection measurements are carried out using3-point bending test, and hence “elastic modulusin bending” is defined from straight portion of curve.

Figure 2

deflection

load

d

F

max

48 4 bendF L F Ld EE I w h d

3 3

3

F : load at the straight portion of curved : deflection corresponding to loadL : distance between outer supports

w : width of specimenh : thickness of specimen

F

d

Deflection is dependent upon not onlythe material but also the configuration ofcross-section and unsupported length.Hence, stiffness in bending for identicalspecimens to be tested under identicalconditions can be compared.

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Cold-Bend Tests Bending tests cannot be employed to determine bending strength of ductile materials

as they can be fully bent without rupture.

The test involves sharp bending of a bar through a large angle and noting if crackingoccurs on the outer surface. The aim is to determine the angle (θ) at which crackingstarts (Fig. 3a). If no cracks produced while specimen is bent around the pin, testingis continued by compressing the specimen on itself between the compression platensreferred as “folding” (Fig. 3b).

h θ

Figure 3

( a ) ( b )

Such tests are used for testing special parts:structural steels (ASTM A36-74), boiler rivetsteels and rivets (ASTM A141), pressurevessel plates (ASTM A285-72).

For ductile materials, cold-bend and folding testsare applied to determine whether they can be bentsharply without cracking. The scope is to checkductility for a particular type of service or to detectloss of ductility under certain types of treatment.

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Cold-Bend Tests Minimum ductility that must be possessed by a material is defined by

“Tetmajer’s bending limit (Bg)”. Pin diameters and the correspondingbending limits are given in table below:

DD+3h

Figure 4

50Bg h r h : thickness of specimenr : folding radius (Fig. 3a)

D 0 0.5h 1.0h 1.5h 2.0h 2.5h 3.0hBg 100 67 50 40 33 28 25

3-point bending test of ductile flat specimens (30-50 mm wide) is covered inDIN 1605. Bending load is applied slowly and steadily, and the ductility isdefined as angle () until which specimen can be bent without cracking onthe tension side (Fig. 4).

The inner distance betweensupports should be D+3h, andthe supports must have a radiusof 25 mm (for h < 12 mm) and50 mm (for h > 12 mm).

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Special Bend Tests1. Notched-Bar Test: Used to specify the resistance of a material against

shock and its ability to withstand stress concentration.

Similar to tension test, the work done in bending the specimen throughabout a right angle (using Monsanto Tensometer in Fig. 5) can also beemployed as “toughness index number” that is expressed as product offorce applied by the nose and the distance through which it moves.

Figure 5

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Special Bend Tests2. Weld Test: Similar in concept to 3-point bending test, weld test is carried

out by subjecting a butt-welded specimen to transverse loading in a fixture.The load is applied slowly and steadily until either cracks are produced onthe tension side or the specimen is bent to extreme limit in the fixture (insuch case, specimen is removed and testing is continued as in folding test).

Fig. 6a & 6b show the free-bend test fixtures for testing the ductility of weldsaccording to ASTM E16-64 and DIN 50121, respectively.

Figure 6a Figure 6b

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Special Bend Tests3. Fiber-Strain Measurements: made in connection with weld tests. Tension

side of specimen is marked over a distance and “percent elongation” ofouter fiber is specified through the use of flexible tape. Hence, original (L0)and final (Lf) lengths are used to calculate ductility (R):

4. Hot-Bend Test: made with specimens heated to “red-hot” temperature todetermine suitability of material to hot-working. This test is also employedfor welded joints to test “blue brittleness”. Plain carbon steels experiencediscontinuous yielding within 230-370 °C (known as “blue brittle region”)as steel heated in this range shows a lower tensile ductility and higher notchsensitivity. Hot-bend test of welded joints is important if the weld seam isgoing to be subjected to forming operation.

5. Quenched-Bend Test: used in connection with the plates used for boilers.The specimen is heated to 650 °C and held at this temp. about half an hour.Then quenched in warm water around 28 °C, and subjected to bend test.Aim is to detect traces of nitrogen present in metal, indicated by fracture.

10000 LLLR f