# Chapter 6

### PLASTIC (PERMANENT) DEFORMATION

(at lower temperatures, T < T melt /3) • Simple tension test:

Proportional limit

Chapter 6- 14

### YIELD STRENGTH,

y

y • Stress at which

### noticeable

occurred.

tensile stress,

plastic deformation has when

e

p = 0.002=0.2% (just a rule of thumb or convention)

e

p = 0.002

engineering strain,

e

Chapter 6- 15

>>

>>

### y(polymers)

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

### TENSILE STRENGTH, TS

• 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

### TENSILE STRENGTH: COMPARISON

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

### DUCTILITY, %EL

• 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

• Note:

A o

%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

### RESILIENCE

modulus of resilience

U r

 1 2 

y

e

y

 1 2 

y

  

E y

    2

y

2

E

Resilient materials, with high yield strength and low modulus of elasticity, are used in spring applications.

Chapter 6- 19

### TOUGHNESS

• 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,

e

Chapter 6 20

### TOUGHNESS

Toughness can be measured with an impact test (Izod or Charpy) Chapter 6 20

### TRUE STRESS & TRUE STRAIN

Instantaneous area If volume of material is conserved during deformation:

A i l i =A 0 l 0

Then 

True

 

Stress

( 1  e  ),  

T

e 

T F A i

 ,

True Strain

 e

T

 ln

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

### EXAMPLE PROBLEM 6.4

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 

f

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

y

### HARDENING

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

### HARDNESS

• 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

P

### HARDNESS

Brinell, uses 10 mm sphere of steel or tungsten carbide 2

P

HB

 

D

D

D

2 

d

2  Rockwell and Superficial Rockwell, uses a diamond cone (Brale indenter) or steel spheres Vickers microhardness, uses a diamond pyramid

HV

 1 .

854

P

/

d

1 2 Knoop microhardness, uses a diamond pyramid

HK

 14 .

2

P

/

l

2

Chapter 6- 21

### HARDNESS and TENSILE STRENGTH

There is a linear relation between the tensile strength and hardness of a metal (especially for cast iron, steel and brass) For most steels:

TS

(

MPa

)  3 .

45 

HB TS

(

psi

)  500 

HB

Chapter 6- 21

### DESIGN OR SAFETY FACTORS

• 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

### SUMMARY

• 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

y .

• 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