1. Elastic & Plastic behavior of Materials….(Contd)
Lecture 3

2. Plastic Deformation: Atomic Perspective
1. Initial
Initial state F
2. Large load
bond stretch
and planes sheared
Large load applied
3. Unload
planes still stretched
Load removed dp
de+p de F d
non-linear
elastic + plastic de
Plastic means permanent!!
linear elastic dp
deformation occurs by breaking and re-arrangement of atomic bonds (crystalline materials by motion of defects)

3. Plastic deformation: Plastic deformation:
stress not proportional to strain
deformation is not reversible
The mechanism of this deformation is different for crystalline and amorphous (noncrystalline) materials. For crystalline solids, deformation is accomplished by means of a process called slip, which involves the motion of dislocations. Plastic deformation in noncrystalline solids (as well as liquids) occurs by a viscous flow mechanism.

4. Plastic Deformation by Slip Process
The usual method of plastic deformation in metals is by the gliding of blocks of the crystal over one another along definite crystallographic planes (slip planes) which is known as Slip.
Slip occurs mainly by the mechanism of dislocation movement.
Slip occurs most readily in specific directions on certain crystallographic planes.

5. Stress-strain behavior in the plastic region
With the increase in stress beyond the proportional limit (point A), the strain begins to increase more rapidly for each increment in stress. Consequently, the slope becomes smaller and smaller, until, and point B, the curve becomes horizontal. A
stress
strain B C D E
yield point
proportional limit
From B, considerable elongation of the test bar occurs with no noticeable increase in the tensile load. This phenomenon is called yielding of the material and point B is called the yield point.
In the region from B to C the material becomes perfectly plastic, which means that it deforms without an increase in the applied load.

6. Yielding and yield strength
The yield stress or yield strength, sy , is a measure of resistance to plastic deformation of material.
It is the stress that a material can withstand before starting visible permanent change. So, it is the stress that divides the elastic and plastic behavior of material.
Although plastic deformation begins after the proportional limit, it is difficult to determine.
For this reason, yield point is commonly recognized as the point where plastic deformation starts.
σy =Pe /Ao
For designing a component that must support a force during use, we must select a material that has a high yield stress so that the component does not plastically deform.
Alternately, for giving shape to a component using a deformation process, the applied stress must exceed the yield stress to cause a permanent change in the shape of the material.

7. stress
strain
stress-strain curves for ferrous and nonferrous materials
ferrous materials
nonferrous materials
yield point
 For most nonferrous metals and some ferrous alloys (e.g., cast irons), the elastic to plastic transition is a gradual one, where no well-defined yield point is available.
determining the 0.2% offset yield strength in gray cast ion
 In such cases, an offset stress, or proof stress, sP , is calculated.
The offset is chosen for a stress that causes a permanent strain of 0.2 or 0.35 per cent.

8. Strain or work hardening
Stress
 If a material is deformed plastically and the stress is then released, the material ends up with a net, permanent strain.
sy1
sy2
strain
hardening
permanent strain
unload
 If the stress is reapplied, the material again responds elastically at the beginning up to a new yield point that is higher than the original yield point. This is due to strain or work hardening of material.
Re-apply load
 It is the strengthening of a metal by plastic deformation. This strengthening occurs because of dislocation movements and dislocation generation within the crystal structure of the material

9. Loading beyond yield point
After undergoing the large strain during yielding (point C), the steel begins to strain harden and the plastic deformation becomes more and more difficult.
With deformation, the number of dislocations inside the material is increased, which hinder further dislocation movement, and the material becomes stronger.
Elongation in the test specimen in this region requires an increase in the tensile load, and therefore the stress-strain diagram has a positive slope from C to D.
The load eventually reach the maximum value and the corresponding stress (at point D) is known as the ultimate tensile strength (UTS) or simply the tensile strength (TS) of the material.
Further stretching of the bar is actually accompanied by a reduction in the load, and fracture finally occurs at point E.
tensile strength
fracture A
stress
strain B C D E

10. Formation of necking during plastic deformation
Beyond the point M, necking occurs at the sample and stress decreases to eventual fracture.
fracture strength
 During necking, pores and other defects start to form or propagate, accumulate, and multiply, and reduce the effective cross-section of the material.
 When the cross-section can hold the applied load no more, fracture or material takes place.
necking

11. Ductility
Ductility is a measure of the degree of plastic deformation that has been sustained at fracture. Ductility is normally expressed in percentage and usually measured as either percent elongation in length or percent reduction in area.
Percent reduction
Percent elongation
A0 is the original cross-sectional area and Af is the cross-sectional area at thepoint of fracture
Lf the fracture length and lo and is the original gauge length

12. Ductility: Graphical representation
A material that experiences very little or no plastic deformation upon fracture is termed brittle.
 Small %E
 Material is brittle, if %E < 5%
 Larger %E
 Materials is ductile, if %E > 5%

13. A knowledge on ductility of materials is important:
 It indicates to a designer the degree to which the structure will deform plastically before fracture.
The designer of a component would prefer a material that display at least some ductility so that, if the applied stress is too high, the component deforms before it breaks.
 It specifies the degree of allowable deformation during fabrication operations.
The fabricator wants a ductile material so they can form complicated shapes without breaking the material in the process.

14. Ductility vs. Malleability
Ductility is a solid material's ability to deform under tensile stress; this is often characterized by the material's ability to be stretched into a wire. (Au,Pt, Al etc.)
Malleability, a similar property, is a material's ability to deform under compressive stress; this is often characterized by the material's ability to form a thin sheet by hammering or rolling.
Both of these mechanical properties are aspects of plasticity, the extent to which a solid material can be plastically deformed without fracture. Also, these material properties are dependent on temperature and pressure.

15. Toughness
Toughness: ability of a material to absorb energy up to fracture (Area under the strain-stress curve up to fracture). Units: the energy per unit volume, e.g. J/m3
Strain
Stress
Low toughness
(High Carbon Spring Steel)
High toughness
(Medium carbon SS)
Low toughness
(unreinforced polymers)

16.  sel2 sy2 sy2 s ds Uelastic = s de = E 2E =  2E Ur =
Modulus of resilience
Total work of elastic deformation is a measure of resilience.
Given: s = Ee, ds = Ede
( E ≠ E(s) in the elastic region )
Uelastic = s de = 
epl
s ds E
sel2 2E
sy2
= 
 Resilient materials have high yield strengths and low modulus of elasticity.
 Suitable to use in spring applications.
Ur =
sy2 2E
Modulus of resilience