(at lower temperatures, T < T melt /3) • Simple tension test:
Chapter 6- 14
y • Stress at which
plastic deformation has when
p = 0.002=0.2% (just a rule of thumb or convention)
p = 0.002
Chapter 6- 15
Room T values Based on data in Table B4, Callister 6e ag = aged .
a = annealed hr = hot rolled cd = cold drawn cw = cold worked qt = quenched & tempered Chapter 6- 16
• Maximum possible engineering stress in tension.
Adapted from Fig. 6.11, Callister 6e.
Work Example Problem 6.3
• Metals: occurs when noticeable necking • Ceramics: starts.
occurs when crack propagation starts.
• Polymers: occurs when polymer backbones aligned and about to break.
are Chapter 6- 17
TS(ceram) ~ TS (met) ~ TS(comp) >> TS(poly) Room T values Based on data in Table B4, Callister 6e ag = aged .
a = annealed hr = hot rolled cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers.
Chapter 6- 18
• Plastic tensile strain at failure:
%EL L f L o L o x100
Adapted from Fig. 6.13, Callister 6e.
• Another ductility measure:
%AR A o A f x100
%AR and %EL are often comparable.
--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck. Chapter 6 19
Chapter 6- 19
modulus of resilience
Resilient materials, with high yield strength and low modulus of elasticity, are used in spring applications.
Chapter 6- 19
• Energy to break a unit volume of material • Approximate by the area under the stress-strain curve.
• Toughness can be measured with an impact test (Izod or Charpy) tensile stress,
smaller toughness (ceramics) larger toughness (metals, PMCs) smaller toughness- unreinforced polymers Engineering tensile strain,
Chapter 6 20
Toughness can be measured with an impact test (Izod or Charpy) Chapter 6 20
Instantaneous area If volume of material is conserved during deformation:
A i l i =A 0 l 0
( 1 e ),
T F A i
l i l
0 Instantaneous gauge length 1 e ) necking
vali d u nti l n e ck i ng poi n t Chapter 6- 22
A cylindrical specimen of steel having an original diameter of 12.8mm (0.505 in) is tensile tested to fracture and found to have an engineering fracture strength Determine: b) The true stress at fracture
of 460 MPa (67,000 psi). If its cross-sectional diameter at fracture is 10.7mm (0.422 in). a) The ductility in terms of percent reduction in area
Chapter 6- 22
• An increase in
due to plastic deformation.
• Curve fit to the stress-strain response:
strain K K and n can be found from tables or tensile tests
Chapter 6 22
• Resistance to permanently indenting the surface.
• Large hardness means: --resistance to plastic deformation or cracking in compression.
--better wear properties.
Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.) Chapter 6 21
Brinell, uses 10 mm sphere of steel or tungsten carbide 2
2 Rockwell and Superficial Rockwell, uses a diamond cone (Brale indenter) or steel spheres Vickers microhardness, uses a diamond pyramid
1 2 Knoop microhardness, uses a diamond pyramid
Chapter 6- 21
There is a linear relation between the tensile strength and hardness of a metal (especially for cast iron, steel and brass) For most steels:
) 3 .
Chapter 6- 21
• Design uncertainties mean we do not push the limit.
• Factor of safety, N
working N y
Often N is between 1.2 and 4 • Ex: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5.
working y N 220, 000N d 2 / 4
5 Chapter 6 23
• Stress and strain : These are size-independent measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often shows a linear relation between stress and strain.
To minimize deformation, select a material with a large elastic modulus (E or G).
• Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches
• Toughness : The energy needed to break a unit volume of material.
• Ductility : The plastic strain at failure.
Note: For materials selection cases related to mechanical behavior, see slides 22-4 to 22-10.
Chapter 6 24