NATURE OF PLASTIC DEFORMATION

NATURE OF PLASTIC DEFORMATION

The change of any dimension or shape of an object under the action of external forces is generally considered as a deformation.

When external forces are applied on an object, then the deformation along the direction of the applied force is called longitudinal deformation where as any deformation along its transverse directions are called as lateral deformations.

When external forces are applied in an object, the object will be deformed first. Due to this deformation crystal structure is also deformed and thus creating an unbalanced internal resisting force, which neutralizes the external force and a condition of equilibrium is achieved as deformation stopped.

When the deformation per unit length is small, the material shows a remarkable ability to recover its original shape and size as the external forces are removed.

Hence, as the external force is withdrawn, the deformation will be vanished.

This type of deformation is called elastic deformation and this property of the material is known as Elasticity.

During the elastic phase of deformation, no permanent change in crystal structure happens, but as the magnitude of the applied force increases, resistance due to the change or distortion of the crystal structure becomes insufficient and as a result crystal dislocation occurs.

Plastic deformation is the deformation which is permanent and beyond the elastic range of the material. Very often, metals are worked by plastic deformation because of the beneficial effect that is imparted to the mechanical properties by it.

The necessary deformation in a metal can be achieved by application of large amount of mechanical force only or by heating the metal and then applying a small force.

The deformation of metals which is caused by the displacement of the atoms is achieved by one or both of the processes called slip and twinning. These two are the prominent  mechanisms  of  plastic  deformation,  namely  slip  and  twinning.

SLIP AND TWINNING

Slip is the prominent mechanism of plastic  deformation in metals. It involves sliding of blocks of crystal over one other along definite  crystallographic planes, called slip planes.

It is analogous to a deck of cards when it is pushed from one end. Slip occurs when shear stress  applied exceeds a critical value. 

During  slip  each  atom  usually  moves  same  integral  number  of  atomic  distances  along  the  slip  plane  producing a  step  but  the  orientation  of  the  crystal remains the same.

 Generally  slip  plane  is  the  plane  of  greatest  atomic  density, and  the  slip  direction  is  the   close  packed  direction  within  the  slip  plane.

Twining : Portion  of  crystal  takes  up  an  orientation  that  is  related  to  the  orientation  of  the  rest  of  the  untwined  lattice  in  a  definite, symmetrical  way.

The  twinned  portion  of  the  crystal  is  a  mirror  image  of  the  parent  crystal.

The plane of symmetry is called twinning plane.

The  important role of twinning in plastic deformation is that it causes changes in plane orientation so that further slip can occur.

On the macroscopic scale when plastic deformation occurs, the metal appears to flow in the solid state along specific directions which are dependent on the type of processing and the direction of applied force.

The crystals or grains of the metal get elongated in the direction of metal flow. This flow of metal can be seen under microscope after polishing and suitable etching of the metal surface. These visible lines are called as “fibre flow lines".

Since the grains are elongated in the direction of flow, they would be able to offer more resistance to stresses acting across them. As a result, the mechanically worked metals called wrought products would be able to achieve better mechanical strength in specific orientation, that of the flow direction.

Since it is possible to control these flow lines in any specific direction by careful manipulation of the applied fibres. It is possible to achieve optimum mechanical properties.

The metal of course, would be weak along the flow lines. The wastage of material in metal working processes is either negligible or very small and the production rate is in general very high. These two factors give rise to the economy in production.

HOT WORKING AND COLD WORKING

The metal working processes are traditionally divided into hot working and cold working processes.

The division is on the basis of the amount of heating applied to the metal before applying the mechanical force. Those processes, working above the recrystallisation temperature, are termed as hot working processes whereas those below are termed as cold working processes.

Under the action of heat and the force, when the atoms reach a certain higher energy level, the new crystals start forming which is termed as recrystallisation.

Recrystallisation destroys the old grain structure deformed by the mechanical working, and entirely new crystals which are strain free are formed.

The grains in fact start nucleating at the points of severest deformation.

Recrystallisation temperature as defined by American Society of Metals is "the approximate minimum temperature at which complete recrystallisation of a cold worked metal occurs within a specified time".

The recrystallisation temperature is generally between one-third to half the melting point of most of the metals. The recrystallisation temperature also depends on the amount of cold work a material has already received. Higher the cold work, lower would be the recrystallisation temperature as shown in Fig. given below.

Though cold work affects the recrystallisation temperature to a great extent, there are other variables which also affect the recrystallisation temperature

In hot working, the process may be carried above the recrystallisation temperature with or without actual heating.

For example, for lead and tin the recrystallisation temperature is below the room temperature and hence working of these metals at room temperature is always hot working. Similarly for steels, the recrystallisation temperature is of the order of 1000^oC, and therefore working below that temperature is still cold working only.

In hot working, the temperature at which the working is completed is important since any extra heat left after working will aid in the grain growth, thus giving poor mechanical properties.

The effect of temperature of completion of hot working is profound. A simple heating where the grain start growing after the metal crosses the recrystallisation temperature. But, if it is cooled without any hot working, the final grain size would be larger than the grain size in the initial stage of heating.

Again, after heating, if the metal is worked before cooling the result is the reduction in size. It is due to the process of recrystallisation, that new grain will be started to form and the final grain size is reduced. This phenomena rises due to working of metal at recrystallisation, that gives rise to a large number of nucleation sites for the new crystals to form.

But if the hot working is completed much above the recrystallisation temperature the grain size start increasing and finally may end up with coarse grain size.

This increase the size of the grains occurs by a process of coalescence of adjoining grains and is a function of time and temperature.

This is not generally desirable. If the hot working is completed just above the recrystallisation temperature, then the resultant grain size would be fine. The same is schematically shown for hot rolling operation.

METAL FORMING PROCESS

METAL FORMING PROCESSES

Have you ever wonder how does a car door or a Saucepan or most of the kitchen utensils are manufactured? All of them are produced by a group of similar manufacturing processes governed by the same physical laws where large forces are applied to deform sheets of metal into a desired shapes and sizes and we classify them as Metal forming processes.

Metal forming is a general term for a large group of processes, that includes a wide variety of manufacturing processes.

Forming is the process in which the desired size and shape are obtained through the plastic deformation of a materials, i.e., when a metal is plastically or permanently deformed under the action of a strong applied force, it is in general classified as a metal forming process.

There are different types of metal forming processes, although in each case the basic principle remains same i.e. permanent deformation also known as plastic deformation of metal by the application of large force. Therefore, we can define forming , or metal forming, as the metalworking process of fashioning metal parts and objects through mechanical deformation. In this process the workpiece is reshaped without adding or removing material, and its mass remains unchanged. Forming operates on the materials science principle of plastic deformation, where the physical shape of a material is permanently deformed.

The characteristic of metal forming process is that the metal being processed is plastically deformed to shape it into a desired geometry. In order to plastically deform a metal, a force must be applied that will exceed the yield strength of the material.

When low amounts of stress are applied to a metal it will change its geometry slightly, in correspondence to the force that is exerted. Basically it will compress, stretch, and/ or bend a small amount.

The magnitude of the amount will be directly proportional to the force applied. Also the material will return to its original geometry once the force is released.

Just think of stretching a rubber band, then releasing it, and having it go back to its original shape. This is called elastic deformation. Once the stress on a metal increases past a certain point, it no longer deforms elastically, but starts to undergo plastic deformation.
In plastic deformation, the geometric change in the material is no longer directly proportional to stress and geometric changes remain after the stress is released; meaning that the material does not recover its shape.

The actual level of stress applied to a metal where elastic deformation turns to plastic deformation is called the proportional limit, and is often difficult to determine exactly.

The .002 offset convention is usually used to determine the yield point, which is taken for practical purposes as the stress level where plastic deformation, (yielding), begins to occur.

Stress and Strain Curve

It can be seen by the stress-strain graph that once the yield point of a metal is reached and it is deforming plastically, higher levels of stress are needed to continue its deformation. The metal actually gets stronger, the more it is deformed plastically. This is called strain hardening or work hardening.

As may be expected, strain hardening is a very important factor in metal forming processes. Strain hardening is often a problem that must be overcome, but many times strain hardening, when used correctly, is a vital part of the manufacturing process in the production of stronger parts.
Compared to other metalworking processes like cutting and joining metal forming tends to have more uniform characteristics across its different sub processes.

Characteristics of Metal Forming Processes

Metal forming processes are characterized by:

Very high required loads and stresses, between 50 MPa and 2500 MPa

Large, heavy, and expensive machinery in order to accommodate such high stresses and loads

Production runs with many parts, to maximize the economy of production and compensate for the expense of the machine tools.

THE CONCEPT OF FLOW STRESS

During a metal forming operation, it is important to know the force and power that will be needed to accomplish the necessary deformation. The stress- strain graph shows us that the more a work piece is deformed plastically, the more stress is needed.
The flow stress is the instantaneous value of the force necessary to continue the yielding and flow of the work material at any point during the process.
Flow stress can be considered as a function of strain. The flow stress value can be used to analyze what is going on at any particular point in the metal forming process.
The maximum flow stress may be a critical measurement in some metal forming operations, since it will specify the maximum force and power requirements for the machinery to perform the process.
The force needed at the maximum strain of the material would have to be calculated in order to determine maximum flow stress.
For different types of metal forming processes, the flow stress analysis may be different. For a process like forging, the maximum flow stress value would be very important. However, for a process like extrusion, where the metal is continuously being deformed and the different stages of the metal's deformation are occurring simultaneously, it is of interest to analyze the mean flow stress value.

THE CONCEPT OF STRAIN RATE

The strain rate for any particular manufacturing metal forming process is directly related to the speed at which deformation is occurring. A greater rate of deformation of the work piece will mean a higher strain rate. The specific process and the physical action of the equipment being used has a lot to do with strain rate. Strain rate will affect the amount of flow stress. The effect strain rate has on flow stress is dependent upon the metal and the temperature at which the metal is formed.

EFFECT OF TEMPERATURE ON METAL FORMING

Properties of a metal change with an increase in temperature. Therefore, the metal will react differently to the same manufacturing operation if it is performed under different temperatures and the manufactured part may posses different properties. For these reasons, it is very important to understand the materials that we use in our manufacturing process.

This involves knowing their behavior at various temperature ranges. In industrial metal forming manufacture, there are three basic temperature ranges at which a metal is mechanically worked or formed (which is known as metal forming process), the metal forming processes can be classified as,

COLD FORMING

HOT FORMING

WARM OR SEMI HOT FORMING

COLD FORMING / COLD WORKING OF METAL

Cold working, (or cold forming), is a metal forming process that is carried out at room temperature or a little above it.

In cold working, plastic deformation of the work causes strain hardening as discussed earlier. The yield point of a metal is also higher at the lower temperature range of cold forming. Hence, the force required to shape a part is greater in cold working than for warm working or hot working.

At cold working temperatures, the ductility of a metal is limited, and only a certain amount of shape change may be produced. Surface preparation is important in cold forming. Fracture of the material can be a problem, limiting the amount of deformation possible.

In fact, some metals will fracture from a small amount of cold forming and must be hot formed. One main disadvantage of this type of process is a decrease in the ductility of the part's material, but there are many advantages. The part will be stronger and harder due to strain hardening.

Cold forming causes directional grain orientation, which can be controlled to produce desired directional strength properties. Also, work manufactured by cold forming can be created with more accurate geometric tolerances and a better surface finish. Since low temperature metal forming processes do not require the heating of the material, a large amount of energy can be saved and faster production is possible. Despite the higher force requirements, the total amount of energy expended is much lower in cold working than in hot working.

WARM FORMING/ WORKING

Warm working, (or warm forming), is a metal forming process carried out above the temperature range of cold working, but below the recrystallization temperature of the metal. Warm working may be preferred over cold forming because it will reduce the force required to perform the operation. Also, the amount of annealing of the material that may have been necessary for the cold formed part may be less for warm working.

HOT FORMING OR HOT WORKING OF METAL

Hot working, (or hot forming), is a metal forming process that is carried out at a temperature range that is higher than the recrystallization temperature of the metal being formed.

The behavior of the metal is significantly altered, due to the fact that it is above its recrystallization temperature. Utilization of different qualities of the metal at this temperature is the characteristic of hot working.

Although many of these qualities continue to increase with increasing temperature, there are limiting factors that make overly high temperatures undesirable.

During most metal forming processes the die is often cold or slightly heated. However, the metal stock for hot working will usually be at a higher temperature relative to the die.

In the design of metal forming process, it is critical to consider the flow of metal during the forming of the work. Specific metal flow, for different forming processes, is discussed in latter sections under each specific process. For metal forming manufacturing, in general, the temperature gradient between the die and the work has a large effect on metal flow during the process.

The metal nearer to the die surfaces will be cooler than the metal closer to the inside of the part, and cooler metal does not flow as easily. High temperature gradients, within the work, will cause greater differences in flow characteristics of different sections of the metal, these could be problematic. For example, metal flowing significantly faster at the center of the work compared to cooler metal near the die surfaces that is flowing slower, can cause part defects. Higher temperatures are harder to maintain throughout the metal forming process. Work cooling during the process can also result in more metal flow variations.

Another consideration with hot forming manufacture, with regard to the temperature at which to form the part, is that the higher the temperature the more reactive the metal is likely to be. Also if a part for a hot working process is too hot then friction, caused during the process, may further increase heat to certain areas causing melting, (not good), in localized sections of the work. In an industrial hot metal working operation, the optimum temperature should be determined according to the material and the specific manufacturing process. When above its recrystallization temperature a metal has a reduced yield strength, also no strain hardening will occur as the material is plastically deformed.

Shaping a metal at the hot working temperature range requires much less force and power than in cold working. Above its recrystallization temperature, a metal also possesses far greater ductility than at its cold worked temperature. The much greater ductility allows for massive shape changes that would not be possible in cold worked parts. The ability to perform these massive shape changes is a very important characteristic of these high temperature metal forming processes.

The work metal will recrystallize, after the process, as the part cools. In general, hot metal forming will close up vacancies and porosity in the metal, break up inclusions and eliminate them by distributing their material throughout the work piece, destroy old weaker cast grain structures and produce a wrought isotropic grain structure in the part.

These high temperature forming processes do not strain harden or reduce the ductility of the formed material. Strain hardening of a part may or may not be wanted, depending upon the application. Qualities of hot forming that are considered disadvantageous are poorer surface finish, increased scale and oxides, decarburization, (steels), lower dimensional accuracy, and the need to heat parts. The heating of parts reduces tool life, results in a lower productivity, and a higher energy requirement than in cold working.

Selection Of Temperature Range For A Metal Forming Operation

Production at each of these temperature ranges has a different set of advantages and disadvantages. Sometimes, qualities that may be undesirable to one process may be desirable to another. Also, many times work will go through several processes. The goal is to design the manufacture of a part in such a way as to best utilize the different qualities to meet or enhance the specifications of the part. To produce a strong part with excellent surface finish, then a cold forming process could be a good choice. However, to produce a part with a high ductility a hot forming process may be best. Sometimes the advantages of both hot forming and cold forming are utilized when a part is manufactured by a series of processes. For example, hot working operations may first be performed on a work piece to achieve large amounts of shape change that would not be possible with cold forming due to strain hardening and limited ductility. Then the last process that completes the manufacture of the part is a cold working operation. This process does not require a significant shape change, since most of the deformation was accomplished by the hot forming process. Having a cold forming process last will finish the shape change, while strengthening the part, giving a good surface finish and highly accurate tolerances.

UNIQUE CLASSES; JINDAL NAGAR

There is a popular belief that there are two types of study techniques, where as one is for quick and vague learning basically to score easily in the examination. This process is also known as vomiting techniques. Here, before examination students study basically notes and Question answer seried like Quantum books of UP.
The other process is the process of concept building and it needs attentive study with high concentration. It is difficult but it is the process which helps to clear various entrance examinations and qualifying examinations of various PSU jobs as well as jobs in the private sectors
Personally, I was never a believer of the Cramming Process, although I know language problems often force a student to take the help of Cramming. But, to get rid of this tandency, we wanted to establish a learning center near the place where students reside. Partially it will reduce their travelling time and get more time to study.
As per our requirement Jindal Nagar becomes the choice of our place. When we enquired about a suitable place, then we came to contact with UNIQUE CLASSES in JINDAL NAGAR. We liked the place and overtaken the UNIQUE CLASSES and merged our venture CRACKGATE EDUCATION. The new entity will be named as UNIQUE CLASSES and it will be run by us.

UNIQUE CLASSES : JINDAL NAGAR

Address: SHYAM HOSTEL; JINDAL NAGAR
NEAR PUNJAB & NATIONAL BANK

Call at 7500113349; 9555921800

THE COURSES OFFERED BY US
COACHING FOR GATE 2015 in MECHANICAL ENGINEERING.

Complete syllabus will be covered

@Rs. 2000 per month

Introducing BACK PAPERS coaching for sure pass in (@Rs.1300 per subject)

Engineering Mechanics

Applied Thermodynamics

Mathematics

Sensors and instrumentation

Physics

Regular Classes for 1st, 3rd and 5th Mechanical Engineering Subjects,

Engineering Mechanics (1st Sem)

Engineering Mathematics (1st Sem)

Thermodynamics(3rd Sem)

Fluid Mechanics(3rd Sem)

Strength Of Materials (3rd Sem)

I C Engines & Comptessors (5th Sem)

Heat and Mass Transfer (5th Sem)

Subhankar Karmakar

SAMPLE SHEET: GATE 2015; STRENGTH OF MATERIALS (MECHANICAL ENGINEERING)

CRACKGATE EDUCATION

House No: 237; Sector – 5; Chiranjeev Vihar, Ghaziabad

                     Contact No : #9555921800

PRACTICE WORKSHEET GATE-2015

MECHANICAL ENGINEERING

TOPIC: STRENGTH OF MATERIALS

Difficulty Level: 1

SET ONE: Each question has several entries, choose the most appropriate one

01)  The intensity of stress which causes unit strain is called

            a) unit stress                                                     b) bulk modulus

            c) modulus of elasticity                                               d) principal stress

02)  Which of the following materials has poisson’s ratio more than unity

            a) steel                                                                         b) copper

            c) cast iron                                                       d) none of these

03) The change in the unit volume of a material under tension with increase in its Poisson’s ratio will

            a) increase                                                       b) decrease

            c) increase initially and then decrease              d) remain same

04) In a tensile test, near the elastic zone, the tensile strain

            a) increases more quickly                                b) decreases more quickly

            c) increases in proportion to the stress                         d) increases more slowly

05) The stress necessary to initiate yielding is

            a) considerably greater than that necessary to continue it

            b) considerably lesser than that necessary to continue it

            c) remain same to continue it

            d) can’t be predicted

06) Flow stress corresponds to

            a) fluids in motion                                           b) breaking point

            c) plastic deformation of solids                                   d) rupture stress

07) The maximum strain energy that can be stored in a body is known as

            a) impact energy                                              b) resilience

            c) proof resilience                                            d) modulus of resilience

08) Thermal stress is always

            a) tensile                                                          b) compressive

            c) tensile or compressive                                 d) none of these

09) The loss of strength in compression due to overloading is known as

            a) hysteresis                                                     b) relaxation

            c) creep                                                            d) Bouschinger effect

10) If a material expands freely due to heating, it will develop

            a) thermal stress                                               b) lateral stress

            c) creep stress                                                  d) no stress

SAMPLE SHEET: GATE 2015; FLUID MECHANICS (MECHANICAL ENGINEERING)

CRACKGATE EDUCATION

House No: 237; Sector – 5; Chiranjeev Vihar, Ghaziabad

                     Contact No : 09678534833; 09555921800

PRACTICE WORKSHEET GATE-2015

MECHANICAL ENGINEERING

TOPIC: FLUID MECHANICS

Difficulty Level: 1

SET ONE: Each question has several entries, choose the most appropriate one

01) If no resistance is encountered due to displacement then such a substance is called

            a) fluid               b) real gas                 c) ideal fluid          d) visco-elastic fluid

02) The volumetric change of a fluid due to a resistance is called as

            a) volumetric strain,                             b) volumetric index

            c) compressibility                                d) cohesion

03) Mercury does not wet glass due to a property of liquids known as

            a) adhesion                                          b) cohesion

            c) viscosity                                          d) surface tension

04) The surface tension of Mercury at normal temperature compared to that of water is

            a) more                                                          b) less

            c) depends upon the glass tube                        d) equal

05) Kinematic viscosity is dependent upon

            a) pressure       b) distance       c) density         d) flow

06) Alcohol is used in manometers because

            a) it is clearly visible                            b) it provides suitable meniscus

            c) it can provide longer column due to its low density

            d) it has low surface tension

07) The buoyancy depends upon

            a) mass of liquid displaced                  b) viscosity of the liquid

            c) pressure of the displaced liquid       d) none of the above

08) The centre of gravity of the volume of the liquid displaced by an immersed body is called

            a) meta-centre                                      b) centre of gravity

            c) centre of pressure                            d) centre of buoyancy

09) Surface energy per unit area of a surface is numerically equal to

            a) atmospheric pressure                                   b) surface tension

            c) force of cohesion                                         d)  viscosity

10) Flow occurring in a pipeline when a valve is being opened is

            a) steady flow                                                 b) unsteady flow

            c) laminar flow                                                d) vortex flow

For answers contact at 09555921800

SAMPLE SHEET: GATE 2015; THERMODYNAMICS (MECHANICAL ENGINEERING)

CRACKGATE EDUCATION

House No: 237; Sector – 5; Chiranjeev Vihar, Ghaziabad

                     Contact No : #9555921800

PRACTICE WORKSHEET GATE-2015

MECHANICAL ENGINEERING

TOPIC: BASIC THERMODYNAMICS

Difficulty Level: 1

SET ONE: Each question has several entries, choose the most appropriate one

01) Gas laws are applicable to

            a) Gases as well as vapours     b) Gases alone and not applicable to vapours

            c) Gases and Steam                  d) Gases and Superheated vapours

02) An ideal gas compared to a real gas at very high pressures occupies

            a) more volume           b) less volume            

c) same volume           d) can’t be predicted

03) Temperature of a gas is produced due to

            a) its heating value                   b) kinetic energy of the molecules

            c) molecular vibration              d) inter-molecular attractions

04)  According to kinetic theory of gases, the absolute zero temperature is attained when

            a) volume of the gas is zero                             b) pressure of the gas is zero

            c) kinetic energy of the molecule is zero                     d)  specific heat is zero 

05)  The quantity δQ – δW; where δQ is elemental heat transfer and δW is the elemental work    

transfer is

            a) path function                       b) point function

            c) cyclic function                     d) in-exact differential

06)  The workdone in an adiabatic process between a given pair of end states depends on

            a) the values of the endstates only,      b) the end states and specific heat ratio  γ

            c) the end states and polytropic index n,          d) none of the above.

07)  If the value of polytropic index n is high, then the compressor work between given pressure limits will be

            a) less                                      b) more

            c) no effect                              d) zero

08)  A perfect gas at 27^oC is heated at constant pressure till its volume becomes double. The final temperature will be

            a) 54^oC                                    b) 327^oC

            c) 108^oC                                  d) 600^oC

09)  Mixing of ice and water at 0^oC at atmospheric pressure is an example of

            a) reversible process                b) irreversible process

            c) quasi-static process              d) isentropic process

10)  Change in enthalpy in a closed system is equal to heat transferred if the reversible process takes place at constant

            a) pressure                               b) temperature

            c) volume                                d) entropy

GATE 2015: MECHANICAL ENGINEERING COACHING IN CHIRANJEEV VIHAR AND GOVINDPURAM GHAZIABAD

GATE 2015

MECHANICAL ENGINEERING COACHING IN

CHIRANJEEV VIHAR AND GOVINDPURAM

THE SALIENT POINTS OF THE COURSE:

• THE COURSE HAS BEEN DESIGNED TO HELP THOSE STUDENTS WHO HAVE DIFFICULTIES IN THE BASIC CONCEPTS.
• AT FIRST THE BASIC CONCEPTS WOULD BE TAUGHT AND THEN ADVANCED CONCEPTS WILL BE INTRODUCED.
• WHILE TEACHING A CONCEPT, SIMULTANEOUSLY MULTIPLE CHOICES QUESTIONS WILL BE SHOWN FROM THAT CONCEPT.
• MORE THAN 2500 MULTIPLE CHOICES QUESTIONS WILL BE DISCUSSED WITH SOLUTIONS.
• PROBLEM SOLVING TECHNIQUES WOULD BE TAUGHT WITH THE HELP OF MASTER CHARTS.
• TWO HOURS PER DAY SIX DAYS PER WEEK CLASSES.
• CLASSES ON IMPROVING LEARNING ABILITIES, INCREASING CONCENTRATION AND THE SCIENTIFIC STUDYING TECHNIQUES WILL BE TAKEN.
• CONCEPTS WOULD BE TAUGHT USING ANIMATIONS, GRAPHS, PICTOGRAMS, MNEMONICS AND OTHER LEARNING ENHANCEMENT TOOLS.
• ONLY 20 STUDENTS PER BATCH TO FOCUS MORE ON THE INDIVIDUAL NEEDS OF THE STUDENTS.
• ASSISTANCES FOR INDIVIDUAL PSU (LIKE ONGC, IOC etc.)
• TRIAL CLASSES ARE THERE TO BE AWARE OF THE PERFORMANCES OF THE CLASSES.
• HIGH TECH STUDY MATERIALS AT AFFORDABLE PRICE.
• COURSE DURATION IS SIX MONTHS.
• INTRODUCTORY PRICES ARE AS LOW AS @₨ 2500 PER MONTH
• CLASSES WILL BE STARTED FROM 25^th JULY; 2014
• CALL AT # +91-9458042791; +91-9555921800; +91-9678534833

CRACKGATE EDUCATION

House No: 237; Sector – 5; Chiranjeev Vihar, Ghaziabad

                     Contact No : +91-9458042791; +91-9555921800; +91-9678534833