Sep 19, 2018

AMIE Material Science Solved Question Papers Summer 2005: Q3

  (Answer FIVE questions, taking AA'Y TWO from Group A      ANY TWO from Group B and ALL from Group C        Irigures in the bracket indicate full marks)
                            Group A  
Q.3. (a) Explain Lever Rule with a Tie Line.       
Find the weight percentage of pro-eutectoid ferrite just above the eutectoid temperature of a 0-3 C-steel.                              (2  2)       
(b) Derive the relationship between True Strain and Engineer- ing Strain. What is Resilience ? Why is it important for spring material ?                                                                        2  (1  1)1       
(c) Describe Yield Point Phenomenon. Draw the engineering stress-strain diagram of Glass. Why does necking occur during ten- sion test of a ductile material ?                                    (2  2  2) 
(d) Justify :
(i) Zinc is not as ductile as copper  (2 x 3)        
(ii) Cold working increases hardness of materials       
(iii) Steel is a brittle material at sub-zero atmosphere.    

Ans. (a) Lever rule : Lever rule is an adaptation of the mechani- cal lever force calculations, applied to thermal equilibrium diagrams to obtain the proportion of constituents present for a given composition.  
If two constituents A and B, are separated by a distance x in the diagram, then any composition between them, say distance y from A, will have x- y proportion of constituent A and y proportion of B. 

Fig. 7. Determination of amount of phases by lever rule 
Percentage of liquid phase= XZ/XY *100.
Percentage of solid phase= ZY/XY*100
The numerical values of  X Y, ZY and XZ are inserted  and the amount of phases is determined. The values of phases are as under.
the percentage of liquid phase= 13/28×100= 45.40
  The percentage of solid phase = 15/28×100 = 53.60
Hence the amount of solid is proportional to the distance from the fulcrum to be end of lever marking the liquid composition.

(B) Engineering Strain = dl/l
True Strain= l (Integration)lo dl/l
True Strain l (Integration)lo (Engineering Strain).
where l is the instantaneous length of the specimen and lo is the original length.   
Resilience :  Resilience is the capacity of a material to absorb or store energy, and to resist shock and impact.  It is measured by the amount of energy absorbed per unit volume. in stressing a material upto elastic limit.  This property is important in materials used for springs.       
           The maximum energy which can be stored in a body upto elastic limit is called proof resilience. Proof resilience per unit volume is called modulus of resilience.  Thus. the energy stored per unit volume at elastic limit is the modulus of resilence.        
          The materials having high resilience are used for springs.  The elastic limit of annealed copper is very low, thus it is not used for springs.  But cold- worked copper has much high elastic limit (and resilience) and thus it is used for springs.  Hence resilience is associated with high elastic limit.  Resilience is also of importance for materials required to bear shocks and vibrations.     
(c) yield point phenomenon : A specimen of mild steel during tensile deformation behaves elastically up to a certain high load and then it suddenly yields plastically to a lower value. The first higher point at which yield starts js called the upper yield point and the lower point at which considerable srrain occurs is termed as the lower yield point.  The important feature to notice from this curve is that the stress required to maintain plastic flow immediately after yielding has started is lower than that required to start it. After which the specimen work hardens and the curve rises steadily and smoothly.  This yield point phenomenons in mild steel is explained by the dislocation theory. 
The engineering stress-strain diagram of Glass.

Necking occurs during tension test of ductile muterial :       
The stages in the development of a ductile "cup-and-cone" fracture are illustrated in Fig. 9. Necking begins at the point of plastic instability where the increase in strength due to strain-hardening fails to compensate for the decrease in cross-sectional area Fig.  9 (a)).  This occvrs at maximum load.  The formation of a neck introduces a triaxial state of stress in the region.  A hydrostatic component of tension acts along the axis of the specimen at the centre of rhe necked region.  Many fine cavities form in this region Fig.  9 (b)). and under continued straining these grow the coalesce into a central crack Fig.  9 (c)J. This crack grows in a direction perpendicular to the axis of the specimen until it approaches the surface of the specimen.  It then propagates to the surface of the specimen in a direction'roughly 45o to the tensile axis to form the cone part of the fracture Fig.  9 (d)).

(d) (i) Zinc is not as ductile as copper : Zinc is bluish white metal. It is brittle at ordinary temperatures, but is malleable and ductile between lOOoC to 150oC. At 200oC it becomes brittle again and can be easily powdered. On the other hand copper is red in colour and has a crystalline structure and forms FCC structure. It is highly ductile and malleable and has a very high tenacity. It is very good conductor of heat and electricity, its conductivity being almost as much as that of silver. So. that Zinc is not as ductile as Copper.
(ii) The important change in properties is tl increase in strength of metals.  As deformation goes on increasing, the resistance of metal to further deformation increases constantly. The ductility of metal goes on decreasing simultaneously. The phenomenon is called strain hardening. Again. as the temperature of cold working increases the rate of strain hardening decreases. The hardness of all metals increases with cold work, Fig. 10.       
        Cold working produces elongation of grains in principal direction of working, which leads to changes in tensile properties.  Usually there is decrease in ductility, with cold working.

(iii) In slowly cooled carbon steels, the overall hardness and duc- tility of the steel are determined by the relative proportions of the soft, ductile ferrite and the hard, brittle cementite. The cementite content in- creases with increasing carbon content, resulting in an increase of hard- ness and a decrease of ductility, as we go from low carbon to high carbon steels. A rivet should have good deformability, and hence has a low carbon content. In contrast, a file should have high hardness and wear resistance and hence has a high carbon content. Even though we may increase the hardness by increasing the carbon further, the alloy becomes two brittle to be useful above 1-4 carbon. A rail has 0-6 carbon. It combines some toughness with some hardness and wear resistance.

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