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The Science and Engineering of Materials, 4th edDonald R. Askeland – Pradeep P. Phulé

Chapter 6 – Mechanical Properties and Behavior

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Objectives of Chapter 6

Introduce the basic concepts associated with mechanical

properties of materials.

Evaluate factors that affect the mechanical properties of

materials.

Review some of the basic testing procedures that

engineers use to evaluate many of these properties.

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Chapter 6 Outline 6.1 Technological Significance

6.2 Terminology for Mechanical Properties

6.3 The Tensile Test: Use of the Stress-Strain Diagram

6.4 Properties Obtained from the Tensile Test

6.5 True Stress and True Strain

6.6 Hardness of Materials

6.7 Strain Rate Effects and Impact Behavior

6.8 Properties Obtained from the Impact Test

6.9 Fatigue

6.10 Creep

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Section 6.1

Technological Significance

The materials used in sports equipment must be

lightweight, stiff, tough, and impact resistant.

Aircraft, such as the one shown here,

makes use of aluminum alloys and

carbon-fiber-reinforced composites.

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Section 6.2

Terminology for Mechanical Properties

Load - The force applied to a material during testing.

Stress - Force or load per unit area of cross-section over which the force or

load is acting.

Strain - Elongation change in dimension per unit length.

Viscosity ( ) - Measure of resistance to flow, defined as the ratio of shear

stress to shear strain rate (Pa-s).

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(a) Tensile, compressive, and shear stresses. F is the applied force. (b) Illustration showing

how Young’s modulus is defined for elastic material. (c) For nonlinear materials, we use

the slope of a tangent as a variable quantity that replaces the Young’s modulus constant.

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Section 6.3

The Tensile Test: Use of the Stress-Strain Diagram

Young’s modulus (Modulus of elasticity or elastic modulus) - The slope of

the linear part of the stress-strain curve in the elastic region (E).

Stiffness - A measure of a material’s resistance to elastic deformation.

Stiffness is the slope of a load-displacement curve and is proportional to the

elastic modulus. It depends on the geometry of the component under

consideration, whereas the elastic modulus is a materials property. The

inverse of stiffness is known as compliance.

Shear modulus (G) - The slope of the linear part of the shear stress-shear

strain curve.

Engineering stress - The applied load, or force, divided by the original

cross-sectional area of the material.

Engineering strain - The amount that a material deforms per unit length in a

tensile test.

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A unidirectional force is applied to a specimen in the tensile test by means of the

moveable crosshead. The cross-head movement can be performed using screws or a

hydraulic mechanism.

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Tensile stress-strain curves for different materials. Note that these are qualitative.

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Section 6.4

Properties Obtained from the Tensile Test

Elastic limit - The magnitude of stress at which plastic deformation

commences.

Yield strength - The level of stress above which a material begins to show

permanent deformation.

Tensile strength - The stress that corresponds to the maximum load in a

tensile test.

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Necking - Local deformation causing a reduction in the cross-sectional area

of a tensile specimen. Many ductile materials show this behavior. The

engineering stress begins to decrease at the onset of necking.

Hooke’s law - The linear-relationship between stress and strain in the elastic

portion of the stress-strain curve.

Poisson’s ratio - The negative of the ratio between the lateral and

longitudinal strains in the elastic region.

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Modulus of resilience (Er) - The maximum elastic energy absorbed by a

material when a load is applied.

Tensile toughness - The area under the true stress–true strain tensile test

curve. It is a measure of the energy required to cause fracture under tensile

test conditions.

Ductility - The ability of a material to be permanently deformed without

breaking when a force is applied.

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(a) Determining the 0.2% offset yield strength in gray cast ion, and

(b) upper and lower yield point behavior in a low-carbon steel.

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Localized deformation of a ductile material during a tensile test produces a necked

region. The micrograph shows necked region in a fractured sample.

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Typical yield strength values for different engineered materials.

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Comparison of the elastic behavior

of steel and aluminum. For a given

stress, aluminum deforms elastically

three times as much as does steel.

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Range of elastic moduli for different engineered materials.

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The effect of temperance (a) on the stress-strain curve and (b) on the tensile properties of

an aluminum alloy.

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Section 6.5

True Stress and True Strain

True stress - The load divided by the actual cross-sectional area of the

specimen at that load.

True strain - The strain calculated using actual and not original dimensions.

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(a) The relation between the true stress–true strain diagram and engineering stress-

engineering strain diagram. The curves are nominally identical to the yield point. The true

stress corresponding to the ultimate tensile strength (UTS) is indicated. (b) Typically true

stress–strain curves must be truncated at the true stress corresponding to the ultimate

tensile strength, since the cross-sectional area at the neck is unknown.

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Section 6.6

Hardness of Materials

Hardness test - Measures the resistance of a material to penetration by a

sharp object.

Macrohardness - Overall bulk hardness of materials measured using loads

more than 2 N.

Microhardness Hardness of materials typically measured using loads less

than 2 N using such test as Knoop (HK).

Nano-hardness - Hardness of materials measured at 1–10 nm length scale

using extremely small (~100 µN) forces.

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Indentors for the Brinell and Rockwell hardness tests

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Section 6.7

Strain Rate Effects and Impact Behavior

Impact test - Measures the ability of a material to absorb the sudden

application of a load without breaking.

Impact loading - Application of stress at a very high strain rate (~ > 100 s-1).

Impact energy - The energy required to fracture a standard specimen when

the load is applied suddenly.

Impact toughness - Energy absorbed by a material, usually notched, during

fracture, under the conditions of impact test.

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The impact test: (a) The Charpy and Izod tests, and (b) dimensions of typical specimens.

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Section 6.9

Fatigue

Fatigue - The lowering of strength or failure of a material due to repetitive

stress which may be above or below the yield strength.

Beach or clamshell marks - Patterns often seen on a component subjected to

fatigue.

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Fatigue fracture surface. (a) At low magnifications, the beach mark pattern indicates

fatigue as the fracture mechanism. The arrows show the direction of growth of the crack

front, whose origin is at the bottom of the photograph. (b) At very high magnifications,

closely spaced striations formed during fatigue are observed (x 1000).

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Schematic representation of a fatigue fracture surface in a steel shaft, showing the

initiation region, the propagation of fatigue crack (with beach markings), and catastrophic

rupture when the crack length exceeds a critical value at the applied stress.

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Rotating cantilever beam test - An older test for fatigue testing.

M: the bending moment

D: the specimen diameter

L: the distance between the bending force location and the support

F: the load

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Example 6.1 Fatigue Failure Analysis of a Crankshaft

A crankshaft in a diesel engine fails. Examination of the crankshaft reveals no

plastic deformation. The fracture surface is smooth. In addition, several other

cracks appear at other locations in the crankshaft. What type of failure

mechanism would you expect?

Example 6.1 SOLUTION

Since the crankshaft is a rotating part, the surface experiences cyclical loading.

We should immediately suspect fatigue. The absence of plastic deformation

supports our suspicion. Furthermore, the presence of other cracks is consistent

with fatigue; the other cracks didn’t have time to grow to the size that produced

catastrophic failure. Examination of the fracture surface will probably reveal

beach marks or fatigue striations.

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The stress-number of cycles to failure (S-N) curves for a tool steel and an aluminum alloy.

S-N curve (also known as the Wöhler curve) - A graph showing stress as a

function of number of cycles in fatigue.

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Section 6.10

Creep

Creep - A time dependent, permanent deformation at high temperatures,

occurring at constant load or constant stress.

Creep rate - The rate at which a material deforms when a stress is applied at

a high temperature.

Creep test - Measures the resistance of a material to deformation and failure

when subjected to a static load below the yield strength at an elevated

temperature.