sample copy. not for distribution.5 heat treatment of metals and alloys 88 classification, purpose...

Sample Copy. Not For Distribution.

i

Engineering Practical Book Vol -II


ii

Publishing-in-support-of,

EDUCREATION PUBLISHING

RZ 94, Sector - 6, Dwarka, New Delhi - 110075 Shubham Vihar, Mangla, Bilaspur, Chhattisgarh - 495001

Website: www.educreation.in _____________________________________________________________________________

© Copyright, Author

All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form by any means, electronic, mechanical, magnetic, optical, chemical, manual, photocopying, recording or otherwise, without the prior written consent of its writer.

ISBN: 978-1-61813-687-9

Price: ` 336.00

The opinions/ contents expressed in this book are solely of the author and do not represent the opinions/ standings/ thoughts of Educreation.

Printed in India


iii

Engineering Practical Book Vol -II

Basic Mechanics and Science of Materials

By

Farrukh Hafeez

Mohd Arif

EDUCREATION PUBLISHING (Since 2011)

www.educreation.in


iv


v

About Authors

Dr Farrukh Hafeez is PhD from Jamia Millia Islamia in materials. He has been in

teaching profession for the last 20 years and has experience of serving some of the

prestigious institutions of India and abroad. In the 20 years he has taught graduate and

post graduate courses of mechanical engineering in universities of India such as; Aligarh

Muslim University (a central Government University), Institute of Technology and

Management Gurgaon, IIT Delhi, Jamia Millia Islamia New Delhi , International

University of Shaqra in Saudi Arabia Presently he is serving as an Associate Professor in

Aligarh Muslim University. His experience in writing this book will be helpful for

engineering graduate and Diploma classes. The book will be extremely helpful as a text

and for establishing Strength of Materials and Materials science laboratories.

Mohd Arif is M.Tech in thermal materials engineering having an industrial experience of

about 20 years in handling, developing and testing of mechanical equipments and thermal

materials within and outside India. For the last eleven years he is working as an Assistant

Professor in Aligarh Muslim University and has been engaged in various teaching and

practical laboratories of Mechanical engineering.

*****


vi

Preface

The importance of practical training in engineering education, as emphasized by the

AICTE, has motivated the authors to compile the work of various engineering

laboratories into a systematic text and practical laboratory book. The manual is written in

a simple language and lucid style. It is hoped that students will understand the manual

without any difficulty and perform the experiments.

The first part of the book has been designed to cover the mechanics and testing of

Materials as per ASTM standards. It incorporates basics of mechanics required to handle

the latest testing equipments for testing of Materials. Later half of the book covers the

basic science and properties of materials along with the micro analysis of the materials.

Brief theory and basic fundamentals have been incorporated to understand the

experiments and for the preparation of lab report independently. Sample calculations

have been provided to help the students in tabulating the experimental and theoretical

results, comparing and interpreting them within technical frame. The book also covers the

general aspects for the preparation of a technical report and precautions to be taken in the

laboratories for accurate and save performance of experiments. In end of each

experiment questions related to each experiment have been provided to test the depth of

knowledge gained by the students.

The manual has been prepared as per the general requirements of strength of material

laboratory and Material science text laboratories for any graduate and Diploma level class

syllabus. Material mechanics, testing and their analysis is an important engineering

aspect and its knowledge is applied in almost all industries. We hope that manual would

be useful for establishing a new laboratory and for the students of all branches. Any

suggestions for further improvement of the manual will be welcome and incorporated in

the next edition.

Farrukh Hafeez

Mohd Arif

*****


vii

Content List

S. No. Contents Page

1 Material Mechanics : 1

Introduction, Mechanics of rigid bodies, Mechanics of deformable

bodies, types of external loadings, stresses, types of stresses,

deformation and strains, stress vs strain curves, Mechanical

characteristic of materials, ductile behavior ,brittle behavior,

Factor of safety, Poisons ratio, Residual strain, creep, stress

concentration, Fatigue, Types of loading conditions, deformation

in axially loaded members, statically indeterminate problems ,

Lateral strain due to direct stresses, thermal stresses, summary ,

modes of failure summary

2. Testing of Materials:-. 28

2.1 Study of Fracture Mechanics

2.2 Impact Test

2.3 Hardness Test

2.4 Cupping Test

2.5 Testing Test

2.6 Torsion Testing

2.7 Three Point Bending Test

3 Material Science 67

Classification of engineering materials; metals, alloys, ceramics,

organic polymers, composites. Mechanical properties of

engineering materials ; stiffness, toughness, resilience, proof

resilience, ductility, brittleness, malleability, hardness, creep.

electrical properties; conductivity, resistivity, dielectric strength.

Chemical properties; corrosion, oxidation, degradation, rusting.

Thermal properties; specific heat, coefficient of thermal

expansion, conductivity, magnetic properties., selection of

engineering materials, structure of metals and their relation with

their properties. Chemical bonding in solids, metallic bonding ,

structure of metals, crystal structure, grains and grain boundary,

influence of grain boundary on properties.

4 Metals and Alloys:- 77

Ferrous metals, non- ferrous metals, manufacturing of pig iron,

properties and applications, white cast Iron , malleable cast iron,


viii

nodular cast iron, mottled cast iron, effect of alloying elements on

the properties of cast iron, carbon steels, effect of carbon on the

properties of steel, difference between cast iron and steel, alloy

steels, effect of alloying elements on properties of steel,

classification of alloy steel, mechanism of corrosion resistance.

5 Heat Treatment of Metals and Alloys 88

Classification, purpose of heat treatment, micro structures of steel,

allotropic forms of iron ,phase rule, iron and carbon phase

(equilibrium ) diagrams, time temperature transformation diagram

(TTT) , problem, heat treatment processes; hardening, tempering,

some methods of hardening combined with tempering,

normalizing, annealing. spheroidization, carburizing, cyaniding,

nitriding, diffusion.

6 Non Ferrous Metals and Alloys 103

Common metals, properties and advantages, properties and

applications of aluminum, copper, zinc, lead, tin, copper alloys,

types of brasses and their properties, types of bronzes and their

properties, aluminum alloys, bearing metals and alloys,

classification, nickel, important nickel alloys, lead and tin based

alloys, solders, refractory materials, dielectric materials,

7 Plastic Ceramics and Composites 110

Plastics, classification of plastics, polymerization, thermosetting

plastics, properties, examples of thermoset materials, common

plastics and their typical uses, processing of plastics, injection

molding, compression moldings, extrusion molding, composites,

examples of large particle reinforced composites, dispersion

strength composites, structural composites, insulating materials;

dielectric materials ,ceramics, types and applications,

8 Analysis of Materials 118

8.1 Study of Various Crystal Structure

8.2 Study of Metallurgical Microscope and Specimen Polishing

Machine

8.3 Study of Heat treatment Furnace and Thermocouple Pyrometer

8.4 Study of Crystal defects and Imperfections

8.5 Micro structural Examination of Heat treated Specimen

8.6 Performance of heat treatment Process

8.7 Study of Chemical Corrosion and Its Prevention

8.8 Study of Creep mechanism of Materials

8.9 Study of Various Types of Plastics

8.10 Study of Thermosetting Plastics


ix

General Instructions

To make laboratory experiments safe and effective, each student is expected to follow the

given instructions.

Safety Instructions

1. High voltage source in the laboratory should be handled properly under the guidance

of lab assistant, as it may cause a serious accident.

2. All students shall wear aprons /avoid loose clothes, shirts should be properly tucked,

skirts with extra flares should be avoided, slippers are not allowed, shoes with rubber

soles are recommended for mechanical work laboratories.

3. There should be no over-crowding and only trained person should operate the

machine

4. Make sure that all power sources are off during set-up of machines.

5. Keep safe distance from moving parts of machines.

6. Follow the instruction given by the instructor

7. In case of operating furnace, don‟t touch the inside parts of furnace.

8. Failure to obey instructions may result in being expelled from the lab

9. Be careful not to damage any machine or instrument. Care must be taken in handling

all instrument

10. Do not start any machine or operate it without the permission from instructor.

11. Lubrication and water-cooling should be checked before starting an engine.

12. All the valves must be opened and close slowly.

13. The application or removal of the load should be gradual.

14. Any unusual behavior or noise of the machine must be reported immediately reported

to the instructor and investigated

Preparation of Lab Report

1. Before coming to the laboratory, each student must read and review appropriate

experiment to be conducted on the subsequent turn.

2. Record your experiment observations and sample calculations carefully.

3. Each student is required to write a neat and clean report for the experiment

conducted.

4. Every student should bring his own set of drawing instruments logbooks, slide rule

etc

5. Student should get the necessary apparatus issued against their names before starting

the experiment should carefully inspect the apparatus and returned it well to the lab in

charge after finishing the work


x

6. Reports are due one week after the completion of the experiment.

7. Each report shall be submitted with all necessary instructions, sample calculations,

graphs, and discussion over data and graph.

8. Observations should be recorded in tabular form and in a proper order

9. Sample calculations should be done on a set of most important data. The calculations

should be complete, leading from observed quantities to final results.

10. Results within the scope of the object should be given, with graphical representation

wherever possible.

11. Sources of error should be reported properly. It provides a limit for admissible

inaccuracy in the results.

12. Discussion over results should be analyzed properly and compared with the

manufacture‟s rating.

13. A brief criticism of the test procedure and apparatus used with concrete suggestions,

if any, for improvement should be explained. Any unusual occurrence observed

during the test should be reported.

14. Discussion should reflect the opinion of the writer. It should not be a collection of

merely the self-evident facts.

15. Questions give at the end of each experiment have to be answered appropriately with

in the space provided in the manual.

16. Students should remain prepare for the viva-voce on any turn.

How To Plot A Graph

1. Before drawing a graph between two observed variables it is necessary to know the

nature of expected theoretical graph.

2. Decide which parameter to be considered on X axis and which one on the Y-axis.(

parameter which is under the control of the student is generally kept over X axis)

3. Selection of appropriate scales for the two variables should be chosen such that it

appears as square graph.

4. The following procedure should be observed in drawing the graphs.

a. A curve should first be drawn freehand in pencil. It should then be faired,

preferably in black ink, with proper instruments.

b. Unless otherwise specified, the independent variables should be plotted on the

abscissa.

c. The axes should be well defined and bold.

d. The scales should be chosen for easy reading with due regard to the accuracy of

the observed quantities so that variations are neither concealed nor exaggerated.

Too large a scale should not be chosen simply to fill a curve sheet. Some times

the scale of abscissa may be taken larger than ordinate to make the curves clear.

e. The scale for the axes may or may not start from zero; but scale for the curves of

efficiency, economy rate, capacity, etc should always start from zero.

f. When several curve are drawn over the same abscissa, care must be taken in

choosing the ordinates of the scales such that the curves do not overlap

confusingly.

5. Different indent points should identify each curve separately.


xi

Points plotted should be joined such that it appears smooth and near to the theoretical

nature of the curve. It is not necessary to join all points on the graph. Average graph is

always advisable, instead of point to point plotting. Students shall be encouraged to use

professional software‟s for plotting the curves.

Grading Policy:

1. The following is the grading policy shall be adopted for the lab report ;

GRADES.

A+

= 10.0 A = 9.5 A

= 9.0

B+

= 8.5

B = 8.0

B

= 7.5

C+

= 7.5

C = 7.0

C

= 6.5

2. Make up Lab: Make up lab is only allowed in the case of valid excuse

3. The distribution is as follows.

Lab reports: 80%

Lab quiz: 10%

Attendance: 10%

*****


Engineering Practical Book Vol-II

1

CHAPTER - I ________________________________________________________________________

1. Introduction

Strength of materials mainly deals with the analysis and designing of various machines

and load bearing structures. Both the analysis and the design of a given structure involve

the determination of stresses and deformations. To fulfill this task, we apply both

theoretical (computational) and experimental approaches; the latter mainly for

verification of computed results. This subject owes much of its development to mostly

French mathematicians in the first half of the last century, of which the most outstanding

names are Poisson, Lamé, Navier, Poncelet, Saint-Venant, and Boussinesq. Being

mathematicians, they naturally considered their problem completely solved as soon as

they had a formula relating stress to loading, hence they gave a practical name “strength

of Material” to their subject.

The general mathematical problem of finding the stresses for given applied loads on a

body of arbitrary shape is extremely difficult. However, with certain assumption the

solutions for simplified bodies, such as beams, shafts, thin plates , slabs, and curved

shells having negligible thickness with respect to the other two dimensions are possible.

The simpler parts of the theory applied to the idealized structure is called as strength of

materials while the more complicated parts of the theory is named as theory of

elasticity. This can further be subdivided into two streams i.e mechanics of rigid body

and mechanics of deformable solids.

1.1 Mechanics of Rigid Bodies

The mechanics of rigid bodies is primarily concerned with the static and dynamic

behavior under external forces of engineering components and systems which are treated

as infinitely strong and un-deformable. Primarily it deals with the forces and motions

associated with particles and rigid bodies.

1.2 Mechanics of Deformable Solids

The mechanics of deformable solids is a branch of applied mechanics and is known by

several names i.e. strength of materials, mechanics of materials, solid mechanics etc. The


Farrukh Hafeez , Mohd Arif

2

mechanics of deformable solids is more concerned with the internal forces and associated

changes in the geometry of the components involved and to predict the type of failure

during in-service conditions. Therefore, the traditional content of a course in strength of

materials can be described as the '' statics of de formable elastic bodies" with the subject

focus over stresses and deflections or deformations in the beams, shafts, pipes, or other

structures as functions of the loads imposed upon them and of the dimensions of the

structure. As we shall see later, these stresses are usually independent of the material: a

steel beam and a wooden beam of the same dimensions under the same loads will have

the same stresses. The subject of mechanics of materials or strength of materials is

therefore central to the whole activity of engineering design i.e. for the analysis of

material to determine the stresses, strains, and deflections produced by loads. Moreover

besides theoretical analyses experimental results have equal roles in this field.

1.3 Types of External loads (forces)

1) Surface Forces: When the application of force is over the entire body surface it is

termed as surface force.

a) Point Load: Although they are distributed over a certain surface but as the surface

of application of load is very small in comparison with the whole surface they are

treated as point loads, e.g. concentrated loads on beams, forces in hangers, reactions

in supports, etc.

b) Distributed loads: They are distributed either over the whole active area of the

body surface, or over parts of it, e.g. pressure in a vessel, soil pressure, aerodynamic

forces, etc.; distributed load is given per a unit area.

2) Volume Forces: These are the forces which are generated by a field of force and

spreads over the whole body mass, e.g. the dead weight of a body, the force of inertia,

centrifugal force, etc.

1.3.1 Forces can be further be subdivided with respect to:

1. Force changing with time:

a) Static Loading: which is either constant or increases slowly from a certain value

(usually from zero) up to its nominal magnitude, and then remains unchanged. Slow force

application is necessary so that deformation time changes can be developed fully and the

forces of inertia can be neglected;

b) Dynamic Loading: A type of dynamic load when applied suddenly or instantaneously

with a certain loading acceleration is called as impact load, whereas the load which is

changing periodically and that leads to a body fatigue fracture is called as cyclic load.

2. Force site stability:

a) Fixed load: The load point does not change in time;

b) Travelling load: The load point changes in time, e.g. crane crab, bridges, etc.



3

1.4 Stress

When an external force is applied on a body it suffers a deformation and for a body to be

under equilibrium this action is opposed or reacted by internal forces which are set up

within the particles of material due to cohesion. These internal forces give rise to a

concept of stress. Therefore, stress is defined as an internal resistance to the deformation

against the externally applied load

Let us consider a rectangular bar of a given cross – sectional area and subjected to some

load or force (in Newtons )

Fig1.1

If the bar is assumed to be cut into two halves at section XX, then the equilibrium of each

section under the action of load P and the internal forces acting at the section XX can

been shown as in Fig1.2.

Fig1.2

and stress „ζ „can be obtained as the force intensity or force per unit area.

ζ =P/A (1.1)

where, P is the load and A is the uniform cross-sectional area.

However, if the force carried by a component is not uniformly distributed over its cross –

sectional area „A‟ then stress at any small area „ dA' bearing a small load „dP‟ of the total

force „P' can be obtained as;

ζ =δP/δA (1.2)



4

Table 1.1: The units of stress in S.I. system (International system)

Units Conversion Factor (Pa) or N/m2

GPa 109

MPa (N/mm2

) 106

KPa 103

1.4.1 TYPES OF STRESSES

The two basic type of stresses resulting due to externally applied load are classified as;

1. Normal stress

2. Shear stress.

However, these basic stresses give rise to several other form of stresses which are either

similar to these basic stresses or are a combination of these e.g. bending stress is a

combination of tensile, compressive and shear stresses. Torsional stress, as encountered

in twisting of a shaft is a shearing stress. The resultant stresses, either normal or shear or

combination of both, responsible for the failure of the member is called as principal

stresses.

1.4.2 Normal stresses: We have defined stress as force per unit area. If the stresses are

normal to the areas concerned, then these are termed as normal stresses. The normal

stresses are generally denoted by a Greek letter ( ζ ). As shown the Fig 1.3 if the stresses

on the member acts only in one direction then such state of stress is termed as a uniaxial

state of stress.

Fig 1.3

However, such a state rarely exists, therefore biaxial and tri-axial state of stresses are the

real state of stresses, where either the two or three mutually perpendicular normal stresses

acts simultaneously along different axis as shown in the Fig 1.4.



5

Fig 1.4

1.4.3 Tensile or compressive stress

The normal stresses can be either tensile or compressive depending upon the stresses

either acting out of the area or into the area. When one object presses against another and

direction of stress is into the plane then it is referred to a compressive stresses or bearing

stress. whereas when an object is pulled and the direction of the stress is out of the plane

then it is termed as tensile stress. Fig 1.5

Fig 1.5

1.4.4 Shear Stress

When the cross – sectional area of a block of material is subject to a distribution of forces

which are parallel, rather than normal, to the area concerned and results in the shearing

of the material, then such type of forces are the shear force, where as the resulting force

intensities is known as shear stresses. Fig 1.6

If „ P‟ is the total force and „A‟ is the area over which the shear force acts then shear

stress can be obtained as;

ζ =P/A (1.3)



6

Fig1.6

1.5 Deformation and Strains

After analyzing stresses in the earlier section another important aspect of the analysis and

design of structures is related to the deformations due to applied loads on the structure.

For safe design it is very important to avoid deformations that are large enough to prevent

the structure from fulfilling the purpose for which it was intended.

However, the analysis of deformations may also help us in the determination of stresses.

Sometimes it is not always possible to determine the forces in any structural members by

applying only the principles of statics. This is because statics is based on the assumption

of un-deformable rigid structures. However by considering the member as deformable

and analyzing the deformations in their various members, it is possible to compute the

forces which are statically indeterminate.

Let us consider a suspended rod, of original length „L0‟ and uniform cross-sectional area

„A0‟. as shown in the Fig 1.6. Apply a load „F‟ to its end, the rod assumed to be having

uniform stress along its length will elongate by „δL‟.

Fig 1.7



7

The resulting length of the rod becomes;

L = L0 +δL 1.4

Thus, the incremental length „ δL‟ represents the total deformation or elongation of the

structural member. The deformation per unit length i.e. the ratio of deformation to the

original length (on which the stress distribution remains same) is called as the Normal

Strain and denoted by a Greek letter epsilon;

ε = (L-Lo)/Lo 1.5

Strain is usually expressed in (m/m) or (mm/mm) , therefore it‟s a dimensionless

quantity. Total deformation is expressed in „mm‟ and can also be expressed as the

percentage of elongation.

1.6 Stress-strain curve

In a normal tensile test a standard specimen of steel having either flat or round cross-

section, Fig 1.8 or other material is fixed in between the grips of a universal testing

machine and is being pulled slowly.

As per the ASTM standards the load rate shall not exceed 700N/mm2/min or alternatively

a strain rate of (1-1.5)mm/min shall be maintained uniformly .

The ratio of gauge length „Lo‟ and area of cross-section „Ao‟ shall be maintained as

Lo/(Ao)1/2

=4.5.

As the axial load „F‟ is gradually increased in increments „δF‟, the total change in length

(elongation) „δL‟ , of the central portion of the specimen, over the gauge length of the

specimen is recorded automatically through computer software along with the each

increment of load and this is continued until fracture of the specimen takes place.

Fig 1.8

Flat tensile specimens of ductile metals often show shear failures if the ratio of width to

thickness is greater than 6:1.

A completely shear-type failure may terminate in a chisel edge, for a flat specimen, or a

point rupture for a round specimen. Separation failures occur in brittle materials, such as

certain cast irons. Combinations of both shear and separation failures are common on

round specimens of ductile metal. Failure often starts at the axis in a necked region and

produces a relatively flat area which grows until the material shears along a cone-shaped

surface at the outside of the specimen, resulting in a cup-and-cone fracture.

Knowing the original cross-sectional area ‘A0’ and the original gauge length ‘L0’ of the

test specimen, various normal stress and number of normal strain values may be obtained

as;

ζ 1, 2 ,3… = δF/Ao and ε 1,2,3.. = δL/L0 respectively



8

Theses numerous pairs of values of normal stress and normal strain when plotted over

ordinate and abscissa, respectively gives the engineering stress-strain diagram.

Similarly, while calculating stress values for each incremental load if we substitute the

instantaneous( time interval δt) cross-sectional area of the specimen, till fracture, a

different stress stain curve known as true stress strain curve is obtained.

Fig 1.9

The figure (1.9), showing engineering and true strain curve, illustrates in detail the

overall failure phenomenon of a ductile specimen, during a simple tension test. From the

above curves most of the important mechanical properties of the material can be

determined.

1.7 Mechanical Characteristic of Materials

1.7.1 Ductile Behavior

The stress-strain curve for steel shown in Fig.1.9, obtained after simple tension test, is

used to characterize several mechanical properties of a ductile material;

(i) The initial portion of the stress-strain curve „oa’, being a straight line with a steep

slope, is known as the proportional limit. This linear relationship between elongation

and the axial force causing it (these quantities differ from the strain and stress only by a

constant factor) was first noticed by Sir Robert Hooke in 1678 and is called Hooke's law.

Mathematically it may be represented as;

Stress is directly proportional to strain within the proportional limit i.e

ζ=Eε 1.7

where „E‟ termed as modulus of elasticity or Young’s Modulus, denotes the (steep)

slope of the straight-line portion of the curves in Fig.1.9.

Since the unit strain is a pure number (being a ratio of two lengths) therefore „E‟ has the

same units as that of stress, i.e., MPa. For many common engineering materials the

modulus of elasticity in compression is very nearly equal to that found in tension.



9

(ii) The ordinate point ‘b’ almost near to „a‟ is known as the elastic limit. The curve ‘ob’

shows that upto a certain maximum stress that there is no permanent or residual

deformation when the load is entirely removed. The area under the curve „ob‟ represents

the elastic range.

(iii) The ordinate point ‘c‟ represents a critical loading value called yield point and the

corresponding stress is the yield stress. The specimen loaded beyond the yield point

undergoes a large deformation with a relatively small increase in the applied load. This

mechanism of deformation is caused due to the collateral changes within the material,

called slippage of the material along oblique surfaces and is due, primarily to shearing

stresses. The area under the curve „c-f‟ represents the permanent deformation region or

plastic region.

(iv) It can be noted from the stress-strain diagrams of mild steel (Fig.1.9), the elongation

of the specimen after it has started to yield may be 200 times as large as its deformation

before yield.

(v) Now beyond a certain maximum value of the load called ultimate point ‘e’ or ultimate

load, the diameter of the portion of the specimen begins to decrease, due to local plastic

instability. This phenomenon is known as necking.

(vi) After necking has begun, further application of load keep the specimen elongating

until it ruptures or fracture point ‘f’ is achieved. Analysis of the specimen shows that the

rupture occurs along a cone-shaped surface which forming an angle of approximately 45°

with the original surface of the specimen. This further indicates that shear is primarily

responsible for the failure of ductile materials, and confirms the fact that, under an axial

load, shearing stresses are largest on surfaces forming an angle of 45º.

(vi) The stress corresponding to point „c‟ at which yield is initiated is called the yield

strength (ζy ) of the material, the stress corresponding to point „e‟ representing the

maximum load applied to the specimen is known as the ultimate strength (ζu ), and the

stress corresponding to rupture point „f‟ is called the breaking strength or fracture

limit (ζf ) .

(vii) If a specimen made of a ductile material is loaded in compression instead of tension,

the stress strain curve obtained would be essentially the same through its initial straight-

line portion and through the beginning of the portion corresponding to yield and strain

hardening, however there is no necking phenomenon during compression of the

specimen. It is noteworthy that for a given steel, the yield strength is same in both tension

and compression.

(viii) In the case of steel (Fig.1.9), the stress remains constant over a large range of values

of the strain after the yield has started. Later the stress increases to keep elongating the

specimen, until the maximum value (ζu) has been reached. This is due to a property of

the material known as strain-hardening.



10

(ix) For materials such as Aluminum and of many other ductile materials there is no clear

yield point and yield is not characterized by a horizontal portion of the stress-strain curve.

But the stresses continuously increases, though non- linearly, until the ultimate strength is

reached and finally the fracture of the specimen through the same necking mode of

failure.

(x) The Yield point of such ductile materials is determined using the offset method.

According to this method a line starting at strain ε= 0.2% is drawn parallel to the initial

linear stress- strain curves. The intersection at the non linear part of the curve locates the

yield strength at 0.2% offset.

As shown in Fig. 1.10

Fig 1.10

1.7.2 Brittle Behavior

(i) The characteristics curve of brittle materials Fig1.11(a & b), such as cast iron, glass,

and stone, for tension failure shows that the fracture occurs without any noticeable

change in the rate of elongation (Fig1.11) failure Thus, for brittle materials, there is no

difference between the ultimate strength ‘ζu’ and the fracture strength ‘ζf’

(ii) Further, the strain at the time of fracture is much smaller for brittle than for ductile

materials.

(iii)When a brittle material is loaded in tension, rupture occurs along a surface

perpendicular to the load; while in compression, the rupture occurs in a surface parallel to

the load.

(iv) Since, the brittle failure occurs without any necking of the specimen therefore it is

concluded that the normal stresses are primarily responsible for the failure of brittle

materials.

(v) For most brittle materials the ultimate strength in compression is much larger than that in tension. This is due to the presence of flaws, such as microscopic cracks or



11

Get Complete Book At Educreation Store

www.educreation.in


sample copy. not for distribution.5 heat treatment of metals and alloys 88 classification, purpose...

Documents