Super Plasticity

Dr.R.Narayanasamy, Professor,

Department of Production Engineering,National Institute of Technology, Tiruchirappalli – 620 015.

Tamil Nadu, India

Super Plasticity

• It is a deformation process that produces essentially neck-free elongations of many hundreds of percent in metallic materials in tension.

(Or)• It is a deformation process which produce neck free

high elongation in tension.For super plasticity, the material should have a) Stable ultra fine grain sizeb) Temperature of deformation greater than or equal to

0.4 Tm (absolute melting point)

Constitutive Relationship

Where K and m are constants dependent on temperature and grain size.m – strain rate sensitivitym determines the stability of the flow

Tensile test

Where t – trueN – nominal or Engineering

Constitutive Relationship

Where K’ and N are strain hardening exponents m – strain rate sensitivityFor temperature below 0.4 Tm,

M ~ 0, N lies between 0.1 to 0.3

For super plastic deformation, N ~ 0 and m varies from 0.3 to 0.9

Constitutive Relationship

For a linear Newtonian – Viscous material, N=0 and m = 1

For temperature and grain size dependence

Where K – constantL- Grain size

A – constant varies from 2 to 3Q – activation energy

R- Boltzmann’s constantT – absolute temperature

Constitutive Relationship

For isothermal deformation

A and B are constants

Tensile test

• Strain rate ἐ = (V/l) = velocity/length of specimen

Sigmodidal curve - Variation of flow stress with strain rateStage 2 – has maximum strain rate sensitivity. The range over which super plasticity occurs

Shape of the deforming specimen

Strain hardening dominant

Strong rate sensitivity (Diffuse necking) – extreme elongation

Plastic instability

The on setting of necking when m = 0For plastic stability

and are the incremental changes in true stress and instantaneous cross sectional area. Neglecting second order terms, we get

Plastic instability

For constant volume principle

For stability

Instability starts when

Plastic instability

For linear Newtonian Viscous material, (N=0 and m=1)

Where

Plastic instability

For this material the rate of loss of area at any cross section is dependent only on the load and is independent of the cross sectional area

Plastic instability

Partial derivatives are coefficients which depends on specimen history.

The flow is stable δA doesn’t increase with deformation.

For stability

.

Stability criterion

Plastic instability

When m >0.5, there is no necking For super plastic materials m varies from 0.3 to

0.9 and N~0.We know that,

Plastic instability

When m increases from 0.3 to 0.9, (1-m)/(m) decreases from 2.33 to 0.11As m = 1, the dependence of dA/dt on A decreases. The extreme elongation for super plastic materials is the result of the very high resistance to neck growth.

Plastic instabilityThe geometry of neck formation

Type 1 – involves the formation of several active necks during uniform deformation.

Type 2- when a number of active necks are growing concurrently, one becomes dominant which grows to produce failure.

Plastic instabilityThe elongation of super plastic materials

Take β=0 (because rupture takes place in the smallest area of cross section)

Plastic instabilityThe elongation of super plastic materials

Plastic instability

The strain rate sensitivity index m

The slope of curve

The variation of strain rate sensitivity index with

Plastic instabilityThe strain rate sensitivity index m

The stress relation tests yield most satisfactory fundamental data (because of the very small strains)

Where C & D are constants. Slope of & should yield a straight line graph is (m/m-1)

Physical significance of m value

The disagreement in them value (by various methods) is due to:

a) Necking.b) The difference in the defect structure because of

various strain employed.c) A wide variation in m value over the strain rate.d) Grain growth.e) The sign and the magnitude of the strain rate

change involved.

Properties of various alloysAlloy M value % elongation Temperature application

Ti-6Al-4V 0.85 1000 1023-1273

Ti-5Al- 2.5 Sn 0.72 450 1173-1373

Ti - 8 Mn 0.95 140 853-1173

Ti pure(commercial) 0.8 ------ 1173

Ti-6Al-5Zn-4Mo-7Cu-0.25Si

----- 300 1073

Al-4Cu-0.7Mg-2.0Ni Aircraft engine cylinder

Al-4Cu-1.5Mg-2.0Ni Jet engine compressor

Applications of various alloysAlloy application

Ti 99.2 % Pure Air frames , aircraft engines

Ti- 8 Al-1 Mo- 1 V Air frame and jet engine parts

Ti- 6 Al – 2 Sn- 4 Zr – 2 Mo Jet engine compressor parts and cases

Ti-5 Al – 5 Sn – 2 Zr – 2 Mo – 0.25 Si Jet engine compressor parts and cases

Ti – 6 Al – 4 V Disks for aircraft turbine and compressor (widely used ppt. hardenable)

Ti – 6 Al – 6 V -2 Sn Structural aircrafts parts

Ti – 8 Mn Aircraft sheet components

Ti – 3 Al -2.5 V Aircraft hydraulic component

Mechanical properties

Variation of σt for three grain sizes

Mechanical properties

• Region II with (m> 0.3) over which super plasticity occurs .

• Beyond ϵ̇* , m decreases.• II a region over which an

optimal super plasticity deformation occurs . The material exhibits work hardening .

• II b decreases with increase ϵ̇t

Region/Range in which super plasticity is slowly being lost .

Necessary condition for super plastic forming

1. Duplex and multiphase structure (which have stable grain size and resistance to grain growth)

2. The type of phase or phase and their distribution .

3. The grain boundary condition .4. Temperature , strain rate and grain size .

Above condition influence the degree of super plasticity .

Necessary condition for super plastic forming

5. Lower the eutectic (or equivalent) temperature , better the super plasticity properties .

6. Ternary eutectics are more super plastic than binaries .

7. Strain rate should match the velocity of diffusion processes . This improves the super plasticity .

Necessary condition for super plastic forming

8. Coarse grained structure and dissolved second phase – eliminates strain rate sensitivity (m) and high elongation .

9. non-deformable second phase particle found in dispersion hardening alloys- eliminates the effect of fine grain size and lead to cavitation .

10. Undissolved carbides (martensite in Fe-C system ) prevent superplasticity .

Production of ultrafine grain size

1. Cold/hot work the commercial pure metal and produce fine grain sizes stabilize the grain sizes by dispersion of impure particles which pin the grain boundaries predominantly .

Production of ultrafine grain size2 . When the alloy contains second phase particles

• We know that where R= radius of grain r= radius of second phase particle f= volume fraction of second phase particle

Production of ultrafine grain size2 . When the alloy contains second phase particles

• The above relation shows that the minimum grain size that can be obtained depends on

a) A smaller “r”b) More “f ”(high f) when second phase particle are present , the

grain boundary area is eliminated (where the boundary intersects the particle) . This leads to a decrease in the grain boundary energy .

2 . When the alloy contains second phase particles

When the decrease in grain boundary energy is more , the system results in grain growth . (this is structural super plasticity)

Zr addition in Al alloys is helpful .

Production of ultrafine grain size

3. (a). cast alloys of eutectic/eutectoid or poly phase

(b). Work them by about 60-70% to get an intimate mixture of phases .

(c). Stable ultra fine grains of less than 10 µm. can be obtained when particles are relatively

coarse and well separated . This is extensively employed ex. Zn-Al , Al-Cu

Production of ultrafine grain sizeFor Ni base super alloys

• Power metallurgy route because of several advantages .

• Segregation and bonding makes unsuitable in conventional method .

a) Compact alloy powder (after mixing)b) Hot extrude grain refinement is obtained spinodal decomposition

Production of ultrafine grain sizeVariable of deformation

a) Strain rate uniform strain and secondary creep rate increases with decrease in grain size . where L = grain size b = constant varies from 2 to 3

Production of ultrafine grain sizeVariable of deformation

• Increase in strain rate beyond ϵ̇t , is equivalent to increases in the grain size which has a deleterious effect on super plasticity .

• The strain rate increases exponentially with temperature .

Production of ultrafine grain sizeVariable of deformation

Straini. Finer grain material exhibits greater recovery

σI = stress at zero strain for a given strain rate α =slowly varies with strain rateii. Super plastic deformation is essentially strain

independent when structural changes are absent .

Production of ultrafine grain size Strain rate sensitivity index “m”

1. m increases with decreasing grain size2. m increases with increasing temperature 3. In many alloy system maximum value of ‘m‘ is reached at a

temperature just below the phase boundary defining the upper limit of the two phase field .

Production of ultrafine grain size Strain rate sensitivity index “m”

4. The temperature dependence of ‘m’ is more in region II compared with region I or III .

5. ‘m’ is independent of strain rate and dependent of temperature

ex. Zn-Al eutectoid alloy.

Reference book

• K. A. Padmanabhan, Davis , Super plasticity .

Thank you