# Modes of Failure and Fos – Introduction to Mechanical Engineering Design – Machine Design 1

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from Ekeeda Hello friends in last video we have seen the basic principles that

are used in machine design in today’s session we are going to look at the

modes of failure and the factor of safety modes of failure of any machine

design part or any mechanical part or system this them many ways a machine can

fail you will say what why we are talking about the failure because we are

most concerned about the safety guys machine design is the only field where

you have to consider the failure first and after the success because we have to

avoid the failure you know in order to avoid the failure you must know what are

the ways of failure so in today’s session we are going to look at this

different important types of modes of failure of machines or machine parts so

let us begin as you can see the very first type is normal stresses normal

stresses are induced resistance given to the applied forces or these are the

intensities which are produced against the applied forces now there are two

ways your normal stresses will be induced either your stresses will be

induced in tensile manner or they will induce in compressive manner so friends

we know that tensile stresses are induced when the body is subjected to

full forces means body is subjected to elongation of that particular part right

and compressive stresses are induced when the body is being compressed means

the body is being contracted by the applied forces so it is the opposition

to the tension and it is a position to the compression which is nothing but

your tensile stresses and compressive stresses no body can fail in normal

manner so when the surface area on which the force is acting is pappan

to that particular force direction they will be called normal stresses like we

said first type is of stress our tensile stress second is of compressive stress

so in case of tensile stress if this material is not sufficient to carry

these the forces which are applied on it in whole manner then the body will fail

or it be for the material is not sufficient to carry the compressive

forces which are acting on them which are push forces in such cases I will

call or we will call that the materials fail in tension or the material is

failed in compression so this is the very first and basic mode of failure

which we consider almost everywhere almost in each and every part which is

subjected to loading as you can see the second type is shear stresses as we know

that shear happens when two successive planes try to slide against each other

in such a case when the separation happens between two successive planes

the failure is called shear failure and the stress which is responsible for this

or the stress which is generated while this shear happens is called shear

stress so second mode of failure is shear failure

the third type let us move to the third type that is called a rupture no rupture

happens when something is you know when a body subjected to loads in such a

manner that the body will be destroyed in uneven manner like if a hammer is a

hammer is objected on certain small object or the hammer is filled or a pile

on some small object the object will destroy in an uneven manner you can’t

decide whether it is failing in compression or whether it is tension

whether it is shear in such a case that the body or the bodies fail in the

rupture so that is a third mode of failure the fourth mode of failure you

can see is tearing airing we know we tear the page with

tear these thin sheets so in such a manner where the the particle or the

object or the thin sheet lamina which fails in two separate parts but

application of forces in parallel manner to the through the plane of failure

it’s called tearing the best example is steering of page we can demonstrate it

in simple manner a page which we have kept in this way there is a line along

which I want to tear it off I’ll apply the forces in parallel manner only to

this lines the only thing is the nature and the direction of forces will be

different can you see this object is failing along the line so this

particular phenomenon is called theory so this is just an another way of

failure of the object let’s move ahead a click so there is next type is buckling

and as we have already learned this topic in strength of materials buckling

of columns and struts so something or some part which is which have which has

its length larger than its lateral dimensions for example the length is

larger than its diameter there are chances that if axial forces are applied

on such object it will buckle buckling is nothing but bending of the

things in vertical manner generally we consider bending of beams but bending of

the things which have length in a y direction after application of axial

loads is called bugling so there is another way where things can buckle now

huge shafts which are vertical in manner can buckle right so that’s another way

of failure of next type is bending called obvious beams are the members

which which are subjected to bending after application of transverse loading

yes so this is the another way of failure where in bending not only

deflection will be larger but also the bending stresses will be induced

a last topic of the last type of failure is fatigue no fatigue is called the

deadliest failure nano because in case of sly cyclic loadings what are the

cyclic loadings when some object or the part is subjected to loadings which

continue for n number of cycles or which come back to the object after ‘s equal

in interval of time are called cyclic loading for example a wristwatch

there are many gears in the wristwatch when they work when they function they

perform some cyclic motion or the oscillating motion so they undergo

cyclic loading situations the parts the objects which undergoes such kind of

situation the cyclic loading they may fail in fatigue because during the

cyclic loading their plastic deformation keeps on happening the problem is due to

the machine is running we can’t identify we can’t trace this plastic deformations

so at certain point it fails in fatigue that means it fails without any prior

identification or without any prior information so all such kind of failures

are called fatigue failures guys in today’s session

we have seen so far are the modes of failure there are different modes of

failure so there are different ways in which the loadings that happen on the

product so guys remember forever whenever you go for the designing of a

machine element very first thing you have to look at is the mode of failure

of different objects in different manner once you have mode of failure is desired

decided for that particular topic or particular product you can decide the

design method for that particular product let us move ahead and let us

look at the last part of this topic that is factor of safety guys

factor of safety is something we can call as the margin let us say we have

purchased a bottle water bottle it has the real capacity of 5 kilo 5 litres

right but instruction if it is written that just pour in 1.4 liter or just pour

in 4 litres of water inside it so why that one litre margin is given guys Bo

the water is designed to carry 5 litres it is desired I mean according to the

manufacturer it is desired to pour in only 4 litres of water so that one liter

margin is nothing but your factor of safety yes guys the extra margin we must

give and why that margin is required this when we designed some product we

consider some boundary conditions we apply some constraint to that design we

assume that the product is going to sustain or the product is going to

experience these conditions but that is not always the case for example if you

design a product to carry the in cell stresses of course the loads are acting

in the normal manner in that case but somehow by any chance the loads at in

shear manner that means the load acting perpendicular manner in that case not

only the tensile stresses but also the shear stresses will be induced in that

product but a product is designed only to carry stencil services so that

inclusion of shear stresses may fail the product so in such cases where you have

even a slight idea whether apart from normal stresses shear stresses may also

come into picture you have to design it with certain margin so that the product

will not fail second example argue if you design a product to carry 10 Newton

of force but somehow by some means the load act on it is actually 15 Newton in

that case the product is going to fail so when you have even a slight idea

the force actually is going to act we’ll be having some slightly larger magnitude

than the design value in such case you have to design it in some / manner so

that even after 15 Newton of force is acted on it by mistake the product will

not fail yes so that was the basic idea of factor of safety let us look at it

properly that is the types of stresses of course we have we have already seen

the types of stresses one of the stress-strain curve I will draw like

this and the second one like this this is the stress so this is this trace and

this is this strain this crease and strain can you identify this one yes you

are right this is the stress-strain curve for the pile materials and this

one is for brittle materials of course we have learned this we know

these salient points also the important points also this curve of course is the

starting point this is the point of elastic limit this is a primal point

this is lower yield point this is ultimate point and this is breaking

point for any ductile material whereas in brittle material yes there is some

elastic point and beyond that you can’t have distinguishing points so what do

you have is ultimate point and the breaking point so I will call it

breaking BR point ultimate you point and this is elastic

point whereas here we have elastic point upper yield point lower yield point a

limit point and breaking point again BR point guys when the things are designed

this traces are taken into consideration to certain extent yes the yield points

and the ultimate points as you need to understand this thing very important see

whatever we design they actually undergo different forces when they undergo

forces stresses induced in them stress can be shear stress it can be a tensile

stress and can be a compressive stress similar stress-strain diagrams are used

for their analysis know when I say my object has reached its elastic point I

have the chances if I remove the lower which is acting right now in the product

it will trace the same line back to the origin and it will regain its original

shape because the section which lies up to this is called elastic section or

elastic region the region thereafter is called plastic region now what do we

mean by elastic region when your object is stretched or it is elongated or it is

compressed in the elastic region there are chances it will regain its original

shape and size but once it starts going ahead of it

it actually goes into its plastic deformation area what does it mean at

certain points after this elastic point if I start reducing the load on the body

it will not trace the exact go back to its original shape that means it will

come to certain shape like this so can I say this small amount of permanent

deformation is there yes it is called plastic deformation so we can conclude

that after elastic point there will be always some plastic deformation the

retain inside the body this plastic deformation goes on increasing as we

goes on increasing the force applied so one thing is very clear that after

elastic point or after yield point it is impossible for the material to regain

its original shape and size that is if we keep on adding this kind of forces

which introduce the stresses which are greater than a per yield point the body

is going to experience the permanent plastic deformation which in other way

going to help only failure failure of the product not other productive thing

we don’t want the failure of the product so that we should consider that the only

possible stresses are only up to this which is up to yield point guys when we

design a material we’ll consider that the material or the body or the

particular part will have only limitation that is Sigma of a per yield

point means we consider this as the extreme stress that the metal can handle

whereas it can handle up to the ultimate stress we’ll consider and this is the

extreme aim and we will design the product in this manner only that is

first thing but when we switch back to or brittle stresses it’s not that simple

brittle faces somewhat show the elastic point but thereafter they don’t give us

the significant points like a foil point lower yield point

directly give us the ultimate stresses and then breaking stress so in case of

brittle material I have to consider ultimate stress as the reference point

so I’ll consider that I can apply the forces on brittle material or a brittle

element to the extent of ultimate stress can you see the distinguishing thing yes

for ductile materials my maximum possible stress is upper yield stress

and for my brittle it is ultimate stress now when I consider these two stresses

what I’m supposed to do is guys we know that these two things these two things

are nothing but the extremities that are the maximum possible stresses a material

can handle so what is factor of safety factor of safety is a ratio ratio of ratio of ideal to the actual so that

ideal is the possible extreme and shall say extreme value divided by actual

value we know that extreme value is always greater than the actual value so

in such case factor of safety is always greater than one there is always

remember this thing this is very important thing your factor of safety is

always greater than one so factor of safety should be greater than one that

is one condition now we have seen that the extreme ends or extreme values for

ductile and the brittle metals are different that means the factor of

safety formula will be different for both of them so in case of the tail

material and in case of brittle material factor of safety is equal to extreme

value that we use in the pel material is its upper limit Sigma of per year that

means stress that is induced at the upper yield point divided by actual

value so I will call it working stress whereas

in case of brittle material FS will be defined by extreme value brittle which

is ultimate Sigma ultimate divided by actual value this value also I’ll called

working value that’s it factor of safety so these are the formula we use for

factor of safety but what do we find out in that case there are two ways you can

use this concept if you already know see guys we already know what is ultimate

tail point for a material and we already already know what is ultimate point or

ultimate stress point for a material we need to know this Sigma working that is

the maximum stress that can be induced in the part or in the object once we

know these two things we can find out factor of safety but guys the working

stress generally is experienced by the product it’s not a defined thing because

empirical formally sometimes fail in descending the actual stress that is

going to be induced so in such a case that you have to work with factor of

safety guys these are the things of experience and judgment through judgment

we can suggest the factor of safety required for that particular for the

particular product or for that particular element so as of now we have

the values with us of ultimate yield point or appeal point and factor of

safety now using this two ratios I can definitely find out Sigma working so

that I will define the extreme value the distress can be induced in the body so

that with the margin of factor of safety my body will be kept safe the same thing

we can apply here we already know Sigma ultimate for brittle we through

experience already know what is factor of safety for brittle material we can

find out the value of Sigma working using these two relations so what is my

purpose my purpose is to find out Sigma working first

and then design the product accordingly or if the product is already design

where I know Sigma working I can define factor of safety for example if my

machine is capable of carrying 100 Newton but when I specify the

specification of this particular product I’ll say maximum capacity is only 50

Newton in that case my F face becomes the maximum possible extreme which is

hundred divided by the maximum working which is specified which is 50 so in

this case it becomes 2 now guys you will say you are not talking about stresses

you are talking about forces as we know that stress is directly proportional

with the force and hence factor of safety can be defined in terms of forces

as well as of loads and stresses so FS can be specified as extreme force divided by working force or it can be

defined as extreme stress divided by working stress now the same thing is

applicable not only for Britain but also for ductile materials now there are some

specified factor of safety s which are predetermined by the agencies and the

air towed of course we are going to look at them at a time we are going to solve

the problems we are going to solve the numerical zuv machine design

so let me conclude this topic we looked at different types of failures they can

be failure in shear failure in normal and tensile stresses in compressive

stresses failure in buckling failure in bending the tearing failure the fatigue

failure etcetera we all or we also looked at the thing that the failure

modes are important while designing the products the next thing we looked at is

factor of safety we went to the definition of factor of safety we looked

at the expression of factor of safety and then we define the factor of safety

expressions not only for ductile but also for brittle materials now the same

concept we are going to use while solving numericals on machine design so

that was for this particular topic thank you so much for watching the video if

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