Introduction : Mechanical Metallurgy - PPT, Engineering, Semester Notes

 Page 1


• The various engineering and true stress-strain properties 
obtainable from a tension test are summarized by the 
categorized listing of Table 1.1.   
• Note that the engineering fracture strain e
f
 and the % 
elongation are only different ways of stating the same 
quantity.  Also, the %RA and e
f  
can be calculated from each 
other. 
• Note that the strength coefficient H determines the 
magnitude of the true stress in the large strain region of the 
stress-strain curve, and so it is included as a measure of 
strength.   
• The strain hardening exponent n is a measure of the rate of 
strain hardening. 
Page 2


• The various engineering and true stress-strain properties 
obtainable from a tension test are summarized by the 
categorized listing of Table 1.1.   
• Note that the engineering fracture strain e
f
 and the % 
elongation are only different ways of stating the same 
quantity.  Also, the %RA and e
f  
can be calculated from each 
other. 
• Note that the strength coefficient H determines the 
magnitude of the true stress in the large strain region of the 
stress-strain curve, and so it is included as a measure of 
strength.   
• The strain hardening exponent n is a measure of the rate of 
strain hardening. 
Table 1.1  Materials Properties Obtainable from Tension Tests 
Category Engineering Property True Stress-Strain
Property
Elastic
Constants
Elastic modulus, E
Poisson's ratio, ?
Strength
Proportional limit, s
p
Yield strength, s
y
Ultimate tensile strength, s
µ
Engineering fracture strength, s
ƒ
True fracture strength, s
f
Strength coefficient, H or K
Ductility
Percent elongation, 100 ?
ƒ
Reduction in area, %RA
True fracture strain, ??
ƒ
Energy Capacity
Resilience, ?u
r
Tensile toughness, u
t
True toughness, ?u
ƒ
Strain hardening Strain hardening
Ratio,  s
µ
/ s
?
Strain hardening
exponent, ?n
Page 3


• The various engineering and true stress-strain properties 
obtainable from a tension test are summarized by the 
categorized listing of Table 1.1.   
• Note that the engineering fracture strain e
f
 and the % 
elongation are only different ways of stating the same 
quantity.  Also, the %RA and e
f  
can be calculated from each 
other. 
• Note that the strength coefficient H determines the 
magnitude of the true stress in the large strain region of the 
stress-strain curve, and so it is included as a measure of 
strength.   
• The strain hardening exponent n is a measure of the rate of 
strain hardening. 
Table 1.1  Materials Properties Obtainable from Tension Tests 
Category Engineering Property True Stress-Strain
Property
Elastic
Constants
Elastic modulus, E
Poisson's ratio, ?
Strength
Proportional limit, s
p
Yield strength, s
y
Ultimate tensile strength, s
µ
Engineering fracture strength, s
ƒ
True fracture strength, s
f
Strength coefficient, H or K
Ductility
Percent elongation, 100 ?
ƒ
Reduction in area, %RA
True fracture strain, ??
ƒ
Energy Capacity
Resilience, ?u
r
Tensile toughness, u
t
True toughness, ?u
ƒ
Strain hardening Strain hardening
Ratio,  s
µ
/ s
?
Strain hardening
exponent, ?n
Modulus of Elasticity 
 
•The slope of the initial portion of the stress-strain curve is 
the modulus of elasticity, or Young’s Modulus.  The 
modulus of elasticity is a measure of the stiffness of the 
material.  It is an important design value. 
 
•The modulus of elasticity is determined by the building 
forces between atoms.  It is only slightly affected by 
alloying. 
Page 4


• The various engineering and true stress-strain properties 
obtainable from a tension test are summarized by the 
categorized listing of Table 1.1.   
• Note that the engineering fracture strain e
f
 and the % 
elongation are only different ways of stating the same 
quantity.  Also, the %RA and e
f  
can be calculated from each 
other. 
• Note that the strength coefficient H determines the 
magnitude of the true stress in the large strain region of the 
stress-strain curve, and so it is included as a measure of 
strength.   
• The strain hardening exponent n is a measure of the rate of 
strain hardening. 
Table 1.1  Materials Properties Obtainable from Tension Tests 
Category Engineering Property True Stress-Strain
Property
Elastic
Constants
Elastic modulus, E
Poisson's ratio, ?
Strength
Proportional limit, s
p
Yield strength, s
y
Ultimate tensile strength, s
µ
Engineering fracture strength, s
ƒ
True fracture strength, s
f
Strength coefficient, H or K
Ductility
Percent elongation, 100 ?
ƒ
Reduction in area, %RA
True fracture strain, ??
ƒ
Energy Capacity
Resilience, ?u
r
Tensile toughness, u
t
True toughness, ?u
ƒ
Strain hardening Strain hardening
Ratio,  s
µ
/ s
?
Strain hardening
exponent, ?n
Modulus of Elasticity 
 
•The slope of the initial portion of the stress-strain curve is 
the modulus of elasticity, or Young’s Modulus.  The 
modulus of elasticity is a measure of the stiffness of the 
material.  It is an important design value. 
 
•The modulus of elasticity is determined by the building 
forces between atoms.  It is only slightly affected by 
alloying. 
Measures of Yielding 
 
• Yielding defines the point at which plastic deformation begins.  
This point may be difficult to determine in some materials, which 
have gradual transition from elastic to plastic behavior.  Therefore, 
various criteria (depends on the sensitivity of the strain 
measurements) are used to define yielding.   
1. Proportional Limit - This is the highest stress at which stress is 
directly proportional to strain. 
 
2. Elastic Limit - This is the greatest stress the material can 
withstand without any measurable permanent strain remaining on 
the complete release of the load. 
 
3. Yield Strength - This is the stress required to produce a small 
(0.2% strain) specified amount of plastic deformation.  
Page 5


• The various engineering and true stress-strain properties 
obtainable from a tension test are summarized by the 
categorized listing of Table 1.1.   
• Note that the engineering fracture strain e
f
 and the % 
elongation are only different ways of stating the same 
quantity.  Also, the %RA and e
f  
can be calculated from each 
other. 
• Note that the strength coefficient H determines the 
magnitude of the true stress in the large strain region of the 
stress-strain curve, and so it is included as a measure of 
strength.   
• The strain hardening exponent n is a measure of the rate of 
strain hardening. 
Table 1.1  Materials Properties Obtainable from Tension Tests 
Category Engineering Property True Stress-Strain
Property
Elastic
Constants
Elastic modulus, E
Poisson's ratio, ?
Strength
Proportional limit, s
p
Yield strength, s
y
Ultimate tensile strength, s
µ
Engineering fracture strength, s
ƒ
True fracture strength, s
f
Strength coefficient, H or K
Ductility
Percent elongation, 100 ?
ƒ
Reduction in area, %RA
True fracture strain, ??
ƒ
Energy Capacity
Resilience, ?u
r
Tensile toughness, u
t
True toughness, ?u
ƒ
Strain hardening Strain hardening
Ratio,  s
µ
/ s
?
Strain hardening
exponent, ?n
Modulus of Elasticity 
 
•The slope of the initial portion of the stress-strain curve is 
the modulus of elasticity, or Young’s Modulus.  The 
modulus of elasticity is a measure of the stiffness of the 
material.  It is an important design value. 
 
•The modulus of elasticity is determined by the building 
forces between atoms.  It is only slightly affected by 
alloying. 
Measures of Yielding 
 
• Yielding defines the point at which plastic deformation begins.  
This point may be difficult to determine in some materials, which 
have gradual transition from elastic to plastic behavior.  Therefore, 
various criteria (depends on the sensitivity of the strain 
measurements) are used to define yielding.   
1. Proportional Limit - This is the highest stress at which stress is 
directly proportional to strain. 
 
2. Elastic Limit - This is the greatest stress the material can 
withstand without any measurable permanent strain remaining on 
the complete release of the load. 
 
3. Yield Strength - This is the stress required to produce a small 
(0.2% strain) specified amount of plastic deformation.  
(a) 
Figure 1-13. (a) Typical stress-strain (type II) behavior for a metal showing 
elastic and plastic deformations, the proportional limit P, and the yield 
strength s
y
, as determined using the 0.002 strain offset method.  
(b) Representative stress-strain (type IV) behavior found for some steels 
demonstrating the yield drop (point) phenomenon. 
(a) 
(b)