ME 207 – Material Science I

Chapter 4

Properties in Bending and Shear

Automotive EngineeringAdana Science and Technology University

Dr. İbrahim H. Yılmazhttp://web.adanabtu.edu.tr/iyilmaz

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 under

the conditions that simulate the actual service loading.

Static bending and shear properties of materials are not of the same interest

as static tension and compression properties. Such properties might be

determined 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 its

yield strength in tension: Ssy Sy / 2).

The preparation and adequate testing of tension test specimens might be

difficult, 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 as

a beam with a primary function of resisting this loading.

In bending, both tensile and compressive stresses

are induced over a cross section of the beam. Thus,

bending tests are less severe than tensile tests, but

more severe than compressive tests.

In fact, bending test does not provide extra information

on mechanical behaviour of a material unless bending

causes special failure. Its value is defined as a direct

means of evaluating behaviour of beams under loading

to determine strength and ductility.

Since the loads required to cause failure are relatively

small and easily applied, bending tests can be made

with simple and cheap apparatus. Test specimens are

simple and easy to prepare. Gripping problems are

eliminated and deflection data are easily obtained.

3

Bending Tests

1 2

3

P/2 P/2

L aaL

a a

4

beam

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 method

is often used due to its

simplicity.

On the contrary, 4-point

bending (pure-bending)

method provides better

material characteristics

due to the constant

bending moment which

occurs between inner

load points.

4

Bending Tests

Bending tests are intended for brittle materials when scope of test is to determine

the bending strength of material.

Thus, such tests are notably employed for cast iron (based on ASTM A48) as well as

concrete, wood and certain plastics (according to ASTM D790-66, BS 2782 and DIN

53452) using circular or rectangular specimens.

To determine bending strength, beam must be proportioned so that it will not fail in

shear or by lateral deflection before reaching its ultimate flexural limit. Usually, long

specimens 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

5

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 L

I w h2

M : bending moment

I : area moment of inertia

c : distance from neutral axis

F : load at span center

L : distance between supports

w : width of specimen

h : thickness of specimen

Mc

N. A.

Bending strength of brittle materials obtained

from bending tests would be greater than that

from tensile tests. As approaching failure, neutral

axis shifts toward compression face (by distance

of c), which tends to strengthen the beam.

For a rectangular part in 3-point bending test,

bending strength is the highest stress at moment

of 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 by

load-deflection diagram (Fig. 2).

Load-deflection measurements are carried out using

3-point bending test, and hence “elastic modulus

in bending” is defined from straight portion of curve.

Figure 2

deflection

load

d

F

max

48 4 bend

F L F Ld E

E I w h d

3 3

3

F : load at the straight portion of curve

d : deflection corresponding to load

L : distance between outer supports

w : width of specimen

h : thickness of specimen

F

d

Deflection is dependent upon not only

the material but also the configuration of

cross-section and unsupported length.

Hence, stiffness in bending for identical

specimens to be tested under identical

conditions can be compared.

6

7

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 cracking

occurs on the outer surface. The aim is to determine the angle ( ) at which cracking

starts (Fig. 3a). If no cracks produced while specimen is bent around the pin, testing

is continued by compressing the specimen on itself between the compression platens

referred as “folding” (Fig. 3b).

h

Figure 3

( a ) ( b )

Such tests are used for testing special parts:

structural steels (ASTM A36-74), boiler rivet

steels and rivets (ASTM A141), pressure

vessel plates (ASTM A285-72).

For ductile materials, cold-bend and folding tests

are applied to determine whether they can be bent

sharply without cracking. The scope is to check

ductility for a particular type of service or to detect

loss of ductility under certain types of treatment.

8

Cold-Bend Tests

Minimum ductility that must be possessed by a material is defined by

“Tetmajer’s bending limit (Bg)”. Pin diameters and the corresponding

bending limits are given in table below:

D

D+3h

Figure 4

50Bg h rh : thickness of specimen

r : folding radius (Fig. 3a)

D 0 0.5h 1.0h 1.5h 2.0h 2.5h 3.0h

Bg 100 67 50 40 33 28 25

3-point bending test of ductile flat specimens (30-50 mm wide) is covered in

DIN 1605. Bending load is applied slowly and steadily, and the ductility is

defined as angle ( ) until which specimen can be bent without cracking on

the tension side (Fig. 4).

The inner distance between

supports should be D+3h, and

the supports must have a radius

of 25 mm (for h < 12 mm) and

50 mm (for h > 12 mm).

9

Special Bend Tests

1. 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 through

about a right angle (using Monsanto Tensometer in Fig. 5) can also be

employed as “toughness index number” that is expressed as product of

force applied by the nose and the distance through which it moves.

Figure 5

10

Special Bend Tests

2. 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 on

the tension side or the specimen is bent to extreme limit in the fixture (in

such 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 welds

according to ASTM E16-64 and DIN 50121, respectively.

Figure 6a Figure 6b

11

Special Bend Tests

3. Fiber-Strain Measurements: made in connection with weld tests. Tension

side of specimen is marked over a distance and “percent elongation” of

outer 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 to

determine suitability of material to hot-working. This test is also employed

for welded joints to test “blue brittleness”. Plain carbon steels experience

discontinuous yielding within 230-370 °C (known as “blue brittle region”)

as steel heated in this range shows a lower tensile ductility and higher notch

sensitivity. Hot-bend test of welded joints is important if the weld seam is

going 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