APPLIED THERMAL ENGINEERING IMPORTANT QUESTIONS

1. P-V and T-s Diagrams of Diesel Cycle:

p-V Diagram	T-s Diagram

Otto cycle is a gas power cycle that is used in spark-ignition internal combustion engines (modern petrol engines). This cycle was introduced by Dr. Nikolaus August Otto, a German Engineer.

An Otto cycle consists of four processes:

1. Two isentropic (reversible adiabatic) processes
2. Two isochoric (constant volume) processes

These processes can be easily understood if we understand p-V (Pressure-Volume) and T-s (Temperature-Entropy) diagrams of Otto cycle.

2. P-V and T-s Diagrams of Otto Cycle:

p-V Diagram	T-s Diagram

Note:

In the above diagrams,

p → Pressure

V → Volume

T → Temperature

s → Entropy

Vc → Clearance Volume

Vs → Stroke Volume

3. DUAL Cycle:

The cycle is the equivalent air cycle for reciprocating high speed compression ignition engines. The P-V and T-s diagrams are shown in Figs.12 and 13. In the cycle, compression and expansion processes are isentropic; heat addition is partly at constant volume and partly at constant pressure while heat rejection is at constant volume as in the case of the Otto and Diesel cycles.

4. Baryton Cycle:

The Brayton cycle is a theoretical cycle for simple gas turbine. This cycle consists of two

isentropic and two constant pressure processes. Figure.4.10 shows the Brayton cycle

on p-v and T-s coordinates. The cycle is similar to the Diesel cycle in compression and

heat addition. The isentropic expansion of the Diesel cycle is further extended followed

by constant pressure heat rejection. The thermal efficiency is given by,

ηth = Heat added - Heat rejected / Heat added

THE IRON-CARBON PHASE DIAGRAM

The Iron-Carbon Phase Diagram

In their simplest form, steels are alloys of Iron (Fe) and Carbon (C). The study of the constitution and structure of iron and steel start with the iron-carbon phase diagram. It is also the basis understanding of the heat treatment of steels. The Iron Carbon diagram is shown in Fig. 1.

Fig 1 Iron Carbon phase diagram

The diagram shown in Fig 1 actually shows two diagrams i) the stable iron-graphite diagram (dashed lines) and the metastable Fe-Fe3C diagram. The stable condition usually takes a very long time to develop specially in the low temperature and low carbon range hence the metastable diagram is of more interest.
Many of the basic features of this irpn carbon system also influence the behavior of alloy steels. For example, the phases available in the simple binary Fe-C system are also available in the alloy steels, but it is essential to examine the effects of the alloying elements on the formation and properties of these phases. The iron-carbon diagram provides a solid base on which to build the knowledge of both plain carbon and alloy steels.
There are some important metallurgical phases and micro constituents in thr iron carbon system. At the low-carbon end is the ferrite (?-iron) and austenite (?-iron). Ferrite can at most dissolve 0.028 wt% C at 727 deg C and austenite (?-iron) can dissolve 2.11 wt% C at 1148 deg C. At the carbon-rich side there is cementite (Fe3C).
Between the single-phase fields are found regions with mixtures of two phases, such as ferrite & cementite, austenite & cementite, and ferrite & austenite. At the highest temperatures, the liquid phase field can be found and below this are the two phase fields liquid & austenite, liquid & cementite, and liquid & ferrite. In heat treating of steels, the liquid phase is always avoided. Some important boundaries at single-phase fields have been given special names that facilitate the understanding of the diagram.
Main micro-structures of iron and steels in equilibrium are
1. Austenite or ?-iron phase – Austenite is a high temperature phase and has a Face Centred Cubic (FCC) structure (which is a close packed structure). ?-iron is having good strength and toughness but it is unstable below 723 deg C.
2. Ferrite or ?-iron phase – It is relatively soft low temperature phase and is a stable equilibrium phase. Ferrite is a common constituent in steels and has a Body Centred Cubic (BCC) structure (which is less densely packed than FCC). ?-iron is soft , ductile and has low strength and good toughness.
3. Cementite – It is Fe3C or iron carbide. It is intermediate compound of Fe and C. It has a complex orthorhombic structure and is a metastable phase. It is hard, brittle and has low tensile strength, good compression strength and low toughness
4. Pearlite is the ferrite-cementite phase mixture. It has a characteristic appearance and can be treated as a micro structural entity or micro constituent. It is an aggregate of alternating ferrite and cementite lamellae that degenerates (“spheroidizes” or “coarsens”) into cementite particles dispersed with a ferrite matrix after extended holding below 723 deg C. It is a eutectoid and has BCC structure. It is a partially soluble solution of Fe and C. It has high strength and low toughness.
In case of non-equilibrium solidification of Fe-C system the following main micro structures may be formed.
• Bainite is a phase between pearlite and marten site. It is hard metastable micro constituent; non lamellar mixture of ferrite and cementite on an extremely fine scale. Upper bainite is formed at higher temperatures has a feathery appearance. Lower bainite is formed at lower temperatures has an acicular appearance. The hardness of bainite increases with decreasing temperature of formation. It is having good strength and toughness.
• Martensite is formed by rapid cooling and is hard and brittle. It is super saturated solution of C atoms in ferrite. It has a bct structure and a hard metastable phase. It has lath morphology when 1.0 wt% C and mixture of those in between. It is having high strength and hardness and low toughness.
• Sorbite / troostite
There are many temperatures and critical points in the Iron-C diagram which are important both from the basic and the practical point of view.
• The A1 temperature at which the eutectoid reaction occurs, which is 723 Deg. C in the diagram. A1 is called eutectoid temperature and is the minimum temperature for austenite.
• At the lower-temperature boundary of the austenite region at low carbon contents is the ?/? + ? boundary.
• Acm is the counterpart boundary for high carbon contents, that is, the ?/? + Fe3C boundary (Pearlite boundary). The carbon content at which the minimum austenite temperature is attained is called the eutectoid carbon content (0.77 wt% C).
• The A4 temperature at which austenite transforms to ?-iron, 1390 Deg. C in pure iron but this temperature is increased as carbon is added.
• The A2 temperature is the Curie point when iron changes from the ferro to the paramagnetic condition. This temperature is 769 Deg. C for pure iron, but no change in crystal structure is involved.
• Accm is the temperature when in hypereutectoid steel at which the solution of cementite in austenite is completed during heating.
• Ac1 is the temperature at which austenite begins to form during heating, with the c being derived from the French chauffant.
• Ac3 is the temperature at which transformation of ferrite to austenite is completed during heating.
• Aecm, Ae1, Ae3 are the temperatures of phase changes at equilibrium.
• Arcm is the temperature when in hypereutectoid steel, the temperature at which precipitation of cementite starts during cooling, with the r being derived from the French refroidissant.
• Ar1 is the temperature at which transformation of austenite to ferrite or to ferrite plus cementite is completed during cooling.
• Ar3 is the temperature at which austenite begins to transform to ferrite during cooling.
• Ar4 is the temperature at which delta ferrite transforms to austenite during cooling.
• Ms (or Ar”) is the temperature at which transformation of austenite to martensite starts during cooling.
• Mf is the temperature at which martensite formation finishes during cooling.
All of the changes, except the formation of martensite, occur at lower temperatures during cooling than during heating and depend on the rate of change of temperature.
The austenite- ferrite transformation

Under equilibrium conditions, pro-eutectoid ferrite will form in iron-carbon alloys containing up to 0.8 per cent carbon. The reaction occurs at 910 Deg. C in pure iron, but takes place between 910 Deg. C and 723 Deg. C in iron-carbon alloys.
However, by quenching from the austenitic state to temperatures below the eutectoid temperature Ae1, ferrite can be formed down to temperatures as low as 600 Deg. C. There are pronounced morphological changes as the transformation temperature is lowered, which it should be emphasized apply in general to hypo-and hyper-eutectoid phases, although in each case there will be variations due to the precise crystallography of the phases involved. For example, the same principles apply to the formation of cementite from austenite, but it is not difficult to distinguish ferrite from cementite morphologically.
The austenite-cementite transformation
The Dube classification applies equally well to the various morphologies of cementite formed at progressively lower transformation temperatures. The initial development of grain boundary allotriomorphs is very similar to that of ferrite, and the growth of side plates or Widmanstaten cementite follows the same pattern. The cementite plates are more rigorously crystallographic in form, despite the fact that the orientation relationship with austenite is a more complex one.
As in the case of ferrite, most of the side plates originate from grain boundary allotriomorphs, but in the cementite reaction more side plates nucleate at twin boundaries in austenite.
The austenite-pearlite reaction

Pearlite is the most familiar micro structural feature in the whole science of metallography. It was discovered by Sorby over a century ago, who correctly assumed it to be a lamellar mixture of iron and iron carbide.
Pearlite is a very common constituent of a wide variety of steels, where it provides a substantial contribution to strength. Lamellar eutectoid structures of this type are widespread in metallurgy, and frequently pearlite is used as a generic term to describe them.
These structures have much in common with the cellular precipitation reactions. Both types of reaction occur by nucleation and growth, and are, therefore, diffusion controlled. Pearlite nuclei occur on austenite grain boundaries, but it is clear that they can also be associated with both pro-eutectoid ferrite and cementite. In commercial steels, pearlite nodules can nucleate on inclusions.

It may be seen that the normal Iron carbon equilibrium diagram represents the metastable equilibrium between iron and iron carbide. Cementite is metastable as the true equilibrium is between iron and graphite. Although graphite occurs extensively in cast irons (2 to 4 wt per cent carbon), it is usually difficult to obtain this equilibrium phase in steels (0.03 to1.5 wt per cent carbon). Therefore, the metastable equilibrium between iron and iron carbide is normally considered, since it is relevant to the behavior of a variety of steels in practice.
On comparing austenite (?-iron) with ferrite (?-iron) it is noticed that solubility of carbon is more in austenite with a maximum value of just over 2 wt per cent at 1147 Deg. C. This high solubility of carbon in austenite is extremely important in heat treatment, when solution treatment in the austenite followed by rapid quenching to room temperature allows formation of a supersaturated solid solution of carbon in iron.
The ferrite phase is restricted with a maximum carbon solubility of 0.02 wt per cent at 723 Deg. C. Since the carbon range available in common steels is from 0.05 to 1.5 wt per cent, ferrite is normally associated with cementite in one or other form. Similarly, the ?-phase is very restricted and is in the temperature range between 1390 and 1534 Deg. C and disappears completely when the carbon content reaches 0.5 wt per cent.

Strain Hardening (Work Hardening)

Strain Hardening (Work Hardening)

Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the favorable properties of steel result from interstitial incorporation of carbon into the iron lattice. Brass, a binary alloy of copper and zinc, has superior mechanical properties compared to its constituent metals due to solution strengthening. Work hardening (such as beating a red-hot piece of metal on anvil) has also been used for centuries by blacksmiths to introduce dislocations into materials, increasing their yield strengths. The ability of a metal to plastically deform depends on the ability of dislocation to move.

Restricting or hindering dislocation motion renders a material harder and stronger.

Phenomenon where ductile metals become stronger and harder when they are deformed plastically is called strain hardening or work hardening. Increasing temperature lowers the rate of strain hardening. Hence materials are strain hardened at low temperatures, thus also called cold working. During plastic deformation, dislocation density increases.  And thus their interaction with each other, resulting in increase in yield stress.

Dislocation density (ρ) and shear stress (τ) are related as follows:

During strain hardening, in addition to mechanical properties physical properties also change:

-a small decrease in density

-an appreciable decrease in electrical conductivity

-small increase in thermal coefficient of expansion

-increased chemical reactivity (decrease in corrosion resistance).

Deleterious effects of cold work can be removed by heating the material to suitable temperatures–Annealing. It restores the original properties into material. It consists of three stages–recovery, re-crystallization and grain growth. In industry, alternate cycles of strain hardening and annealing are used to deform most metals to a very great extent

Precipitation & Dispersion hardening

Foreign particles can also obstruct movement of dislocations i.e. increases the strength of the material. Foreign particles can be introduced in two ways – precipitation and mixing -and- consolidation technique. Precipitation hardening is also called age hardening because strength increases with time.  Requisite for precipitation hardening is that second phase must  be soluble at an elevated temperature but precipitates up on quenching and aging at a lower temperature.

E.g.:Al-alloys ,Cu-Be alloys, Mg-Al alloys, Cu-Sn alloys

If aging occurs at room temperature–Natural aging; If material need to be heated during aging– Artificial aging. In dispersion hardening, fine second particles are mixed with matrix powder, consolidated, and pressed in powder metallurgy techniques. For dispersion hardening, second phase need to have very low solubility at all temperatures.

E.g.: oxides, carbides, nitrides, borides etc.

Dislocation moving through matrix embedded with foreign particles can either cut through the particles or bend around and bypass them. Cutting of particles is easier for small particles which can be considered as segregated solute atoms. Effective strengthening is achieved in the bending process, when the particles are submicroscopic in size

Fiber strengthening

Second phase can be introduced into matrix in fiber form too.

Requisite for fiber strengthening:

Fiber material – high strength and high modulus

Matrix material – ductile and non-reactive with fiber material

E.g.: fiber material – Al2O3, boron, graphite, metal, glass, etc;    matrix material – metals, polymers

Mechanism of strengthening is different from other methods.

Higher modulus fibers carry load, ductile matrix distributes load to fibers. Interface between matrix and fibers thus play an important role. Strengthening analysis involves application of continuum, not dislocation concepts as in other methods of strengthening

Cold work will lead to:

•       Increase of Yielding Strength

•       Increase of Tensile Strength

•       Reduction of Elongation

•       Material becomes stronger but more brittle

Plastic deformation occurs when large numbers of dislocations move and multiply so as to result in macroscopic deformation. In other words, it is the movement of dislocations in the material which allows for deformation. If we want to enhance a material's mechanical properties (i.e. increase the yield and tensile strength), we simply need to introduce a mechanism which prohibits the mobility of these dislocations. Whatever the mechanism may be, (work hardening, grain size reduction, etc.) they all hinder dislocation motion and render the material stronger than previously.

The stress required to cause dislocation motion is orders of magnitude lower than the theoretical stress required to shift an entire plane of atoms, so this mode of stress relief is energetically favorable. Hence, the hardness and strength (both yield and tensile) critically depend on the ease with which dislocations move. Pinning points, or locations in the crystal that oppose the motion of dislocations, can be introduced into the lattice to reduce dislocation mobility, thereby increasing mechanical strength.

Dislocations may be pinned due to stress field interactions with other dislocations and solute particles, creating physical barriers from second phase precipitates forming along grain boundaries. There are four main strengthening mechanisms for metals, each is a method to prevent dislocation motion and propagation, or make it energetically unfavorable for the dislocation to move. For a material that has been strengthened, by some processing method, the amount of force required to start irreversible (plastic) deformation is greater than it was for the original material.

In amorphous materials such as polymers, amorphous ceramics (glass), and amorphous metals, the lack of long range order leads to yielding via mechanisms such as brittle fracture, crazing, and shear band formation. In these systems, strengthening mechanisms do not involve dislocations, but rather consist of modifications to the chemical structure and processing of the constituent material.

The strength of materials cannot infinitely increase. Each of the mechanisms explained below involves some trade-off by which other material properties are compromised in the process of strengthening.

Dislocations and Strengthening Mechanisms

Dislocations and Strengthening Mechanisms

Plastic deformation –Dislocations

Permanent plastic deformation is due to shear process–atoms change their neighbors. Inter-atomic forces and crystal structure plays an important role during plastic deformation. Cumulative movement of dislocations leads to gross plastic deformation. Edge dislocation move by slip and climb, while screw dislocation move by slip and cross-slip.

During their movement, dislocations tend to interact. The interaction is very complex because of number of dislocations moving over many slip systems in different directions  Dislocations moving on parallel planes may annihilate each other, resulting in either vacancies or interstitials. Dislocations moving on non-parallel planes hinder each other’s movement by producing sharp breaks–jog (break out of slip plane), kink(break in slip plane) . Other hindrances to dislocation motion–interstitiall and substitutional atoms, foreign particles, grain  boundaries, external grain surface, and change in structure due to phase change.

Material strength can be increased by arresting dislocation motion

Plastic deformation mechanisms -Slip

Mainly two kinds :slip and twinning.

•       Slip is prominent among the two. It involves sliding of blocks of crystal over other along slip planes.

•       Slip occurs when shear stress applied exceeds a critical value.

•       Slip occurs most readily in specific directions(slip directions)on certain crystallographic planes.Feasible combination of a slip plane together with a slip direction is considered as a slip system.

•       During slip each atom usually moves same integral number of atomic distances along the slip plane

Extent of slip depends on many factors-external load and the corresponding value of shear stress produced by it, crystal structure, orientation of active slip planes with the direction of shearing stresses generated. Slip occurs when shear stress applied exceeds a critical value. For single crystal, Schmid defined critical shear stress,which can be expressed as:

Both factors τ and σ are measured in stress, which is calculated the same as pressure by dividing force by area. φ and λ are angles usually measured in degrees.

 In a poly-crystalline material, individual grains provide a mutual geometrical constraint on one other, and this precludes plastic deformation at low applied stresses.  Slip in polycrystalline material involves 

generation, movement and (re-) arrangement of dislocations. During deformation, mechanical integrity and coherency are maintained along the grain boundaries. A minimum of five independent slip systems must be operative for a polycrystalline solid to exhibit ductility and maintain grain boundary integrity–von Mises. On the other hand, crystal deform by twinning.

Strengthening mechanisms of material can be increased by hindering  dislocation, which is responsible for plastic deformation.Different ways to hinder dislocation motion/Strengthening mechanisms:

In single-phase materials

-Grain size reduction

-Solid solution strengthening

-Strain hardening

In multi-phase materials

-Precipitation strengthening

-Dispersion strengthening

-Fiber strengthening

-Martnsite strengthening

Strengthening by Grain size reduction

 It is based on the fact that dislocations will experience hindrances while trying to move from a grain in to the next because of abrupt change in orientation of planes. Hindrances can be two types: forcible change of slip direction, and discontinuous slip plane.  Smaller the grain size, often a dislocation encounters a hindrance. Yield strength of material will be increased.  Yield strength is related to grain size(diameter, d)as Hall-Petch relation:

Grain size can be tailored by controlled cooling or by plastic deformation followed by appropriate heat treatment

Solid solution strengthening

Impure foreign atoms in a single phase material produces lattice strains which can anchor the  dislocations. Effectiveness of this strengthening depends on two factors –size difference and volume fraction of solute. Solute atoms interact with dislocations in many ways:

-elastic interaction

-modulus interaction

-stacking-fault interaction

-electrical interaction

-short-range order interaction

-long-range order interaction

Elastic, modulus, and long-range order interactions are of long-range i.e. they are relatively insensitive to temperature and continue to act about 0.6Tm     

Yield point phenomenon

Localized, heterogeneous type of transition from elastic to plastic deformation marked by abrupt elastic-plastic transition–Yield point phenomenon. It characterizes that material needs higher stress to initiate plastic flow than to continue it.

The bands are called Lüders bands/Hartmann lines/stretcher stains, and generally are approximately 45 to the tensile axis.

Occurrence of yield point is associated with presence of small amounts of interstitial or substitutional impurities. It’s been found that either unlocking of dislocations by a high stress for the case of strong pinning or generation of new dislocations are the reasons for yield-point phenomenon. Magnitude of yield-point effect will depend on energy of interaction between solute atoms and dislocations and on the concentration of solute atoms at the dislocations.

Fracture is the separation of a single body into pieces by an imposed stress. Information about plastic deformation and fracture is given in this article. As polycrystalline material is made up of many grains which may have second phase particles and grain boundaries. It is therefore easier to study plastic deformation in a single crystal to eliminate the effects of grain boundaries and second phase particles

Plastic deformation mechanisms –Twinning

It results when a portion of crystal takes up an orientation that is related to the orientation of the rest of

The important role of twinning in plastic deformation is that it causes changes in plane orientation the untwined lattice in a definite, symmetrical way so that further slip can occur. Twinning also occurs in a definite direction on a specific plane for each crystal structure

Deformation by Slip. 

If a single crystal of a metal is stressed in tension beyond its elastic limit, it elongates slightly, a step appears on the surface indicating relative displacement of one part of the crystal with respect to the rest, and the elongation stops. Increasing the load will cause movement on another parallel plane, resulting in another step. It is as if neighboring thin sections of the crystal had slipped past one another like sliding cards on a deck. Each successive elongation requires a higher stress and results in the appearance of another step. With progressive increase of the load, a stage is reached which causes the material to fracture.

Sliding occurs in certain planes of atoms in the crystal and along certain directions in these planes. Thus the mechanism is a new type of flow that depends upon the perfectly repetitive structure of the crystal . It allows the atoms in one face of a slip plane to shear away from their original neighbors in the other face, to slide in an organized way along this face carrying their own half of the crystal with them, and finally to join up again with a new set of neighbors as nearly perfect as before. The movement in the crystal takes place along planes having highest atomic density with greatest distance between similar parallel planes and in the direction of close-packed atoms. This can be simply stated as: Slip occurs on planes that have h ighest planer density of atoms and in the direction with highest linear density of atoms.

Slip occurs in directions in which the atoms are most closely packed since this requires the least amount of energy. As shown in the figure, close-packed rows are vertically further apart from each other (d1) than rows that are not close-packed (d2), therefore they can slip past each other with less interference.

Black bars between atoms show the slope of the path of atoms. Since the slope is less steep in case of closed-packed rows, less force is required for a given horizontal displacement. In addition, less displacement (D1 < D2) is required by the atoms to move from one stable position (before slip) to other stable position (after slip).

To get a better grasp of this, think of gluing ping pong balls to two boards in a widely spaced pattern as shown in above figure. Put the boards together, ping pong balls to ping pong balls, and begin to tilt the bottom board. You will have to go to a very steep angle before the top board will slip from its position of the nestled ping pong balls. Now do the experiment again, but this time gluing the balls very close together. The top board will now slip at a much lesser angle.

Mechanism of Elastic Deformation

Mechanism of Elastic Deformation

Elastic deformation is reversible. Once the applied forces are removed, the object returns to its original shape. Elastomers and shape memory metals such as Nitinol exhibit large elastic deformation ranges, as does rubber. However elasticity is nonlinear in these materials. Normal metals, ceramics and most crystals show linear elasticity and a smaller elastic range.

The initial straight line (OP)of the curve characterizes proportional relationship between the stress and the deformation (strain). The stress value at the point P is called the limit of proportionality:

σ_p= F_P / S₀

This behavior conforms to the Hook’s Law .i,e, σ = E*δ

Where E is a constant, known as Young’s  Modulus or Modulus of Elasticity.

The value of Young’s Modulus is determined mainly by the nature of the material and is nearly insensitive to the heat treatment and composition. Modulus of elasticity determines stiffness - resistance of a body to elastic deformation caused by an applied force. The line OE in the Stress-Strain curve indicates the range of elastic deformation – removal of the load at any point of this part of the curve results in return of the specimen length to its original value. The elastic behavior is characterized by the elasticity limit (stress value at the point E):

σ_el =  F_E / S₀

For the most materials the points P and E coincide and therefore σ_el=σ_p.

Mechanism of Plastic Deformation

Yield stress, Shear strength of Perfect and Real Crystals   

Critical Resolved Shear Stress(CRSS).

Critical resolved shear stress is the component of shear stress, resolved in the direction of slip in a grain. It is a constant for a given crystal. Since this is a threshold value, it is called critical; and being a component of the applied stress, it is said to be resolved.

Crystalline materials tend to deform or fail by the relative motion of planes of atoms under the action of stress. This motion is induced by the component of stresses acting across the slip planes. The deformation process is a collective motion of adjacent slip planes. But all the planes do not start deforming simultaneously. The first slip in a single plane occurs when the shear stress across the plane exceeds CRSS.

Temperature and crystal geometry influence the minimum stress required to cause the shear. 

A pure crystalline solid, when pulled along different orientations, requires different amounts of load in each instance for the very first slip to occur though the stress required for the planes to slip remains same. This implies that the Critical Resolved Shear Stress is greatly influenced by the orientation of the slip plane with the tensile axis.

Schmid's Law states that the critically resolved shear stress (τ) is equal to the force applied to the material (σ) multiplied by the cosine of the angle with the glide plane (φ) and the cosine of the angle with the glide direction (λ).

Resolved shear stress is given by τ = σ cos Φ cos λ where σ is the magnitude of the applied tensile stress, Φ is the angle between the normal of the slip plane and the direction of the applied force and λ is the angle between the slip plane direction and the direction of the applied force.

Hence critical resolved shear stress is given by,

  

 _max

Plastic Deformation and Fracture

When sufficient load is applied to a material, it will cause the material to change shape or deform. A temporary shape change that is self-reversing after the force is removed, so that the object returns to its original shape. The change in shape of a material at low stress that is recoverable after the stress is removed is called elastic deformation. Elastic deformation involves stretching of the bonds (but the atoms do not slip past each other or twin which requires breaking of bonds).

As shown in the graph above, when the stress is sufficient to permanently deform the metal, it is called plastic deformation. Plastic deformation involves the breaking and remaking of atomic bonds. Plastic deformation may take place by slip, twinning or a combination of both methods.