Idea Transcript
Chapter
7
/ Mechanical Properties
A
modern Rockwell hardness tester. (Photograph courtesy of
Wilson Instruments Division, Instron Corporation, originator of the Rockwell! Hardness Tester.)
Why Study Mechanical Properties? It is incumbent on engineers to understand how the various mechanical properties are measured and what these properties represent; they may be called upon to design structures / components using prede-
termined materials such that unacceptable levels of deformation and / or failure will not occur. We demonstrate this procedure with respect to the design of a tensile-testing apparatus in Design Example 7.1.
TRUE STRESS AND STRAIN 7 / Mechanical Properties
TS
M
Implies the material is getting weaker? F
Stress
7.11 ering ior to . The TS is nt M. nsets metry rmed rious urve.
True stress
Strain
TRUE STRAIN True strain of system
Assuming no volume change i.e.
RELATION BETWEEN TRUE STRESS AND STRAIN Stress Strain These are only valid to the onset of necking After that measurements at each point must be taken
!T "
True
Stress
M%
Corrected
M Engineering
Strain
n K# T
FIGURE 7.16 tensile enginee true stress–str begins at poin curve, which c Necking true curve. Th stress–strain c point the complex s neck region.
SIMPLE MODEL In some metals and alloys the true stress strain curve past the plastic point can be modelled / fitted to; 7.7 True Stress and Strain
Table 7.3 Tabulation of n and K Values (Equation 7.19) for Several Alloys K Material Low-carbon steel (annealed) Alloy steel (Type 4340, annealed) Stainless steel (Type 304, annealed) Aluminum (annealed) Aluminum alloy (Type 2024, heat treated) Copper (annealed) Brass (70Cu–30Zn, annealed)
n
MPa
psi
0.26
530
77,000
0.15
640
93,000
0.45
1275
185,000
0.20 0.16
180 690
26,000 100,000
0.54 0.49
315 895
46,000 130,000
Source: From Manufacturing Processes for Engineering Materials by
●
169
EXAMPLE A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile tested to fracture and found to have an engineering fracture strength ︎σf of 460 MPa. If its cross-sectional diameter at fracture is 10.7 mm, determine: (a)The ductility in terms of percent reduction in area. (b)The true stress at fracture.
30% 660 MPa
POLYMERS
r 7 / Mechanical Properties
10 60
A
8
A is
6
40
B is a plastic
30
4
B
C is highly elastic
20 2
10 0
Stress (1 0 3 psi)
Stress (MPa)
50
FIGURE 7.22 The stress–strain behavior fo brittle (curve A), plastic (curve B), and highly elastic (elastomeric) (cur ) polymers. aC brittle polymer
C 0
1
2
3
4 Strain
5
6
7
8
0
its an elastomer
y
stress at which fracture occurs (Figure 7.23); TS may be greater than o !y . Strength, for these plastic polymers, is normally taken as tensile stren 7.2 and Tables B.2, B.3, and B.4 in Appendix B give these mechanical for a number of polymeric materials.
THE YIELD POINT TENSILE STRENGTH FOR PLASTIC MATERIALS
FIGURE 7.23 Schematic stress–strain curve for a p polymer showing how yie tensile strengths are deter
TS
Stress
!y
The modulus and ductility are measured in the same way as for metals
For plastic polymers (B) the Yield Point is taken as the maximum point just beyond the linear section of the elastic region.
The tensile strength is taken as the stress at fracture
Strain
A LOOK IN TO WHY THESE MATERIALS ARE DIFFERENT 7.14 Macroscopic Deformation 12
80 4°C (4 0°F) 70
10
8
2 0°C (6 8°F) 3 0°C (8 6°F)
50 40
6
4 0°C (1 0 4°F)
30
4 5 0°C (1 2 2°F)
20
To 1.3 0 6 0°C (1 4 0°F)
10 0
0
0.1
0.2 Strain
FIGURE 7.24
The influence of temperature on the
2 0 0.3
Stress (1 0 3 psi)
Stress (MPa)
60
By Michael Sepe from Michael P. Sepe LLC From: Plastics Technology Issue: October 2011
HARDNESS
The ability of a material to resist localised plastic deformation. Originally comparison between materials (how easy was it for A to damage B). Mohs scale. 1 for Talc 10 for Diamond
HARDNESS TEST Most common form of mechanical measurement Cheap and no specific specimen needed Non destructive Other engineering quantise can be derived from it such as tensile strength
Brinell
10-mm sphere of steel or tungsten carbide
D
P d
HB !
2P ! D [D " ! D 2 " d 2 ]
ROCKWELL HARDNESS
Vickers microhardness
Diamond pyramid
Knoop microhardness
Diamond pyramid
d
1 3 6#
t l/b = 7.1 1 b/t = 4.0 0
Rockwell and Superficial Rockwell
a
#
Diamond cone !"#, $%, $&, $' in. diameter steel spheres
d1
1 2 0#
d1
P
HV ! 1.854P / d 21
b
P
HK ! 14.2P / l 2
l
" "
60 kg 100 kg Rockwell 150 kg 15 kg 30 kg Superficial Rockwell 45 kg
For the hardness formulas given, P (the applied load) is in kg, while D, d, d1 , and l are all in mm. Source: Adapted from H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior. Copyright 1965 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.
The most common form of harness test is the Rockwell harness test, In this test as with nearly all harness test an indenter is used to deform (damage) a material. The depth the indenter penetrates determines the harness of the material. There are several Rockwell harness scales and these depend on the shape and size of the indenter with the amount of force used to produce the indent. The Rockwell test uses steel spheres of diameters 1/16, 1/8, 1/4, 1/2 of an inch along with a diamond cone which is used for very hard materials. There are two types of Rockwell test, “the Rockwell” and the “superficial Rockwell”. The loads used for the Rockwell are 10 Kg for soft materials and 60, 100 and 150 Kg for harder materials. The loads used for the superficial are 3 Kg, 15 Kg, 30 kg, 45 Kg. These being assigned the numbers X, N, T, W. When a Rockwell test is performed a number and a letter are assigned to the material. The letter defines the test that was performed and a number which defines the harness of that material on the scale. The number ranges from 0-120, however 100 the scale overlaps with the previous and next scale, so that materials could be measure on two different scales. It is always best to use the scale which delivers a value in the mid range and this is the most accurate. The Rockwell scales can be used on materials from Metals to plastics. Some care needs to be taken when applying the tests. The sample must be thick enough to allow for all of the indentation to be expressed in the upper region of the sample. The spreading of any defects caused by the indentation must not reach the bottom surface, to insure this the sample must be 10x thicker than the indentation. The sample should be smooth and a distance of more than three indentation lengths should be left between the indentation are and sample edges or ridges.
7.16 Hardness
Table 7.5a
●
179
Rockwell Hardness Scales
Scale Symbol
Indenter
Major Load (kg)
A B C D E F G H K
Diamond !"# in. ball Diamond Diamond $% in. ball !"# in. ball !"# in. ball $% in. ball $% in. ball
60 100 150 100 100 60 150 60 150
80 HRB Represent a hardness of 80
Table 7.5b
Superficial Rockwell Hardness Scales
Scale Symbol
Indenter
Major Load (kg)
15N 30N 45N 15T 30T 45T 15W 30W 45W
Diamond Diamond Diamond !"# in. ball !"# in. ball !"# in. ball $% in. ball $% in. ball $% in. ball
15 30 45 15 30 45 15 30 45
on the B scale
The modern apparatus for making Rockwell hardness measurements (see the
FIGURE 7.30 Comparison of several hardness scales. (Adapted from G. F. Kinney, Engineering Properties and Applications of Plastics, p. 202. Copyright 1957 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
1 0,0 0 0
HARDNESS
10
5,0 0 0
2,0 0 0
1,0 0 0
80
1000 800 600
60
500 110
400 300 200
100
For cast iron, steel and brass
Diamond
100
200
100
50
20
20 0
60
Rockwell C
Rockwell B
Cutting tools
9 8
Topaz
7
Quartz
6
Orthoclase
5
Apatite
4 3
Fluorite Calcite
2
Gypsum
1
Talc
File hard
40
80
40 20 0
Knoop hardness
Nitrided steels
Corundum or sapphire
Easily machined steels
Brasses and aluminum alloys
Most plastics
10
5 Brinell hardness
Mohs hardness
HOWEVER
r 7 / Mechanical Properties Rockwell hardness
60 70 80 90
Different materials
1 0 0 HRB 20
30
40
Have different relations ships
5 0 HRC
between hardness and Tensile strength
250
1500 Steels
150
1000
100
Brass
Cast iron (nodular) 50
0
0
100
200
300
Brinell hardness number
400
0 500
Tensile strength (1 0 3 psi)
Tensile strength (MPa)
200
500
FIGURE 7.31 Relationships between hardness and tensile strength for steel, brass, and cast iron. (Data taken from Metals Handbook: Properties and Selection: Irons and Steels, Vol. 1, 9th edition, B. Bardes, Editor, American Society for Metals, 1978, pp. 36 and 461; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th edition, H. Baker, Managing Editor, American Society for Metals, 1979, p. 327.)
8 LECTURES
1 on Failure 2 on Phases 3 on Diffusion 2 on liquids
and other metals, polymers, and inorganic glasses at elevated temperatures. These highly ductile materials neck down to a point fracture, showing virtually 100% reduction in area. The most common type of tensile fracture profile for ductile metals is that represented in Figure 9.1b, which fracture is preceded by only a moderate amount
FIGURE 9.1 (a) Highly ductile fracture in which the specimen necks down to a point. (b) Moderately ductile fracture after some necking. (c) Brittle fracture without any A a very ductile fracture plastic deformation.
B a ductile fracture C a brittle fracture (a)
( b)
(c)
9.3 Ductile Fracture
(a)
(b)
(c)
237
FIGURE 9.2 Stages in the cup-and-cone fracture. (a) Initial necking. (b) Small cavity formation. (c) Coalescence of cavities to form a crack. (d ) Crack propagation. (e) Final shear fracture at a 45! angle relative to the tensile direction. (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, p. 468. Copyright 1976 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
Shear
Fibrous
(d)
●
(e)
of necking. The fracture process normally occurs in several stages (Figure 9.2). First, after necking begins, small cavities, or microvoids, form in the interior of the
STRESS CONCENTRATION 9.5b Principles of Fracture Mechanics (Concise Version)
●
241
0
m
Stress
t
a
X
X!
x
2a
x!
0
x
x!
Position along X–X!
(b)
(a) 0
FIGURE 9.7 (a) The geometry of surface and internal cracks. (b) Schematic stress profile along the line X – X $ in (a), demonstrating stress amplification at crack tip positions.
sectional area (perpendicular to this load). Due to their ability to amplify an applied
ba
a
250
●
Chapter 9 / Failure
Fibrillar bridges
Microvoids
(a)
Crack
( b)
FIGURE 9.17 Schematic drawings of (a) a craze showing microvoids and fibrillar bridges, and (b) a craze followed by a crack. (From J. W. S. Hearle, Polymers and Their Properties, Vol. 1, Fundamentals of Structure and Mechanics, Ellis Horwood, Ltd., Chichester, West Sussex, England, 1982.)
microstructural). Glassy thermoplastics are brittle at relatively low temperatures; as the temperature is raised, they become ductile in the vicinity of their glass transition temperatures and experience plastic yielding prior to fracture. This behav-
FATIGUE !max + 0 !
Stress Compression Tension
Chapter 9 / Failure
!min Time
(a)
!a !r
+ !m 0 !min
!
Stress Compression Tension
!max
FIGURE 9.23 Variation of stress with time that accounts for fatigue failures. (a) Reversed stress cycle, in which the stress alternates from a maximum tensile stress (#) to a maximum compressive stress ($) of equal magnitude. (b) Repeated stress cycle, in which maximum and minimum stresses are asymmetrical relative to the zero stress level; mean stress !m , range of stress !r , and stress amplitude !a are indicated. (c) Random stress cycle.
Time
(b)
+
!
Stress Compression Tension
DeHavilland Comet
Time
(c)
Also indicated in Figure 9.23b are several parameters used to characterize the
large or small fraction of the total fatigue life depending on nature of the test specimen; high stresses and the presence of n lived stage I. In polycrystalline metals, cracks normally extend grains during this propagation stage. The fatigue surface that is I propagation has a flat and featureless appearance.
FIGURE 9.28 Schematic represen I and II of fatigue crack propagat metals. (Copyright ASTM. Reprin
!
Stage II
Stage I
!
9.12a Crack Initiation and Propagation (Detailed Version) FIGURE 9.29 Fatigue crack propagation mechanism (stage II) by repetitive crack tip plastic blunting and sharpening; (a) zero or maximum compressive load, (b) small tensile load, (c) maximum tensile load, (d ) small compressive load, (e) zero or maximum compressive load, ( f ) small tensile load. The loading axis is vertical. (Copyright ASTM. Reprinted with permission.)
Zero Comp Max Compres
●
S-55
small Compres (a)
(d)
Max Compres
Small Tensile ( b)
(e)
Max Tensile
Small Tensile (c)
(f)
Eventually, a second propagation stage (stage II ) takes over, wherein the crack extension rate increases dramatically. Furthermore, at this point there is also a change in propagation direction to one that is roughly perpendicular to the applied
6
●
At this point it should be emphasized that although both beachmarks and striations are fatigue fracture surface features having similar appearances, they are nevertheless different, both in origin and size. There may be literally thousands of striations within a single beachmark. Often the cause of failure may be deduced after examination of the failure surfaces. The presence of beachmarks and/or striations on a fracture surface confirms that the cause of failure was fatigue. Nevertheless, the absence of either or both does not exclude fatigue as the cause of failure.
Chapter 9 / Failure FIGURE 9.30 Fracture surface of a rotating steel shaft that experienced fatigue failure. Beachmark ridges are visible in the photograph. (Reproduced with permission from D. J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.)
At this point it should be emphasized that although both beachmarks and striations are fatigue fracture surface features having similar appearances, they are nevertheless different, both in origin and size. There may be literally thousands of striations within a single beachmark. Often the cause of failure may be deduced after examination of the failure surfaces. The presence of beachmarks and/or striations on a fracture surface confirms that the cause of failure was fatigue. Nevertheless, the absence of either or both does not exclude fatigue as the cause of failure.
FIGURE 9.31 Transmission electron fractograph showing fatigue striations in aluminum. Magnification unknown. (From V. J. Colangelo and F. A. Heiser, Analysis of Metallurgical Failures, 2nd edition. Copyright 1987 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
FIGURE 9.31 Transmission electron fractograph showing fatigue striations in aluminum. Magnification unknown. (From V. J. Colangelo and F. A. Heiser, Analysis of Metallurgical Failures, 2nd edition. Copyright 1987 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.)
NOTICE SAME A Chapter 9 / Failure
!2 > !1 !1
Crack length a
●
!2 da dN a 1 , ! 2 da dN a 1 , ! 1
a1
a0
Cycles N
FIGURE 9.33 C versus the num stress levels $1 fatigue studies. rate da / dN is in crack length a1 levels.
Fatigue crack growth rate, ddNa (log scale)
9.13 Crack Propagation Rate
da dN
●
S-59
FIGURE 9.34 Schematic representation of logarithm fatigue crack propagation rate da / dN versus logarithm stress intensity factor range " K. The three regions of different crack growth response (I, II, and III) are indicated. (Reprinted with permission from ASM International, Metals Park, OH 44073-9989. W. G. Clark, Jr., ‘‘How Fatigue Crack Initiation and Growth Properties Affect Material Selection and Design Criteria,’’ Metals Engineering Quarterly, Vol. 14, No. 3, 1974.)
= A( K)m
Region I
Region II
Region III
Nonpropagating fatigue cracks
Linear relationship between da log K and log dN
Unstable crack growth
Stress intensity factor range, K (log scale)
rising temperature.
PHASE DIAGRAMS
10.3 PHASES
Also critical to the understanding of phase diagrams is the concept of a phase. A phase may be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics. Every pure material is considered to be a FIGURE 10.1 The solubility of sugar (C12H22O11 ) in a sugar–water syrup.
100 200
Temperature (°C)
150 60
Liquid solution + solid sugar
Liquid solution (syrup)
40
100
20 50 Sugar Water
0
0
20
40
60
80
100
100
80
60
40
20
0
Composition (wt%)
Temperature (°F)
Solubility limit
80
Composition (at% Ni) 1600
0
20
40
60
80
100
2800 1500 Liquid
1453 C 2600
Solidus line
Liquidus line 1300
! +L
2400
B 1200
2200
!
A
1100
2000
1085 C 1000 0 (Cu)
20
40
60
Composition (wt% Ni)
(a )
80
100 (Ni)
Temperature ( F)
1400 Temperature ( C)
The phase apted rams lloys, 1991. ed by ASM erials b) A f the phase which phase s are nt B.
10.6 Binary Isomorphous Systems
●
287
Composition (at% Ni) 1600
0
20
40
60
80
100
2800 1500 Liquid
1453 C 2600
Solidus line
Liquidus line 1300
! +L
2400
B 1200
2200
!
A
1100
2000
1085 C 1000 0 (Cu)
20
40
60
Composition (wt% Ni)
(a )
80
100 (Ni)
Temperature ( F)
1400 Temperature ( C)
The phase apted rams lloys, 1991. ed by ASM erials b) A f the phase which phase s are nt B.
10.6 Binary Isomorphous Systems
●
287
A
1100
2000
1085 C 1000 0
40
20
(Cu)
60
80
100
Composition (wt% Ni)
(Ni)
(a )
Liquid
Temperature ( C)
1300
Tie line
B
! + Liquid
! + Liquid
!
1200
R
S
!
20
40
30
CL C0 Composition (wt% Ni)
(b)
50
C!
alloys is shown in Figure 10.6 for the copper–silver system; this is eutectic phase diagram. A number of features of this phase diagr and worth noting. First of all, three single-phase regions are foun !, ", and liquid. The ! phase is a solid solution rich in copper; i solute component and an FCC crystal structure. The " phase s
400
50 300 40
30
200 0 (Cu)
20
40
60
Composition (wt% Ni)
80
100 (Ni)
Elongation (% in 5 0 mm [2 in.])
60 Tensile strength (ksi)
Tensile strength (MPa)
60
50
40
30
20
0 (Cu)
20
40
Composit
(a)
FIGURE 10.5 For the copper–nickel system, (a) tensile strength versus composition, and (b) ductility (%EL) versus composition at room temp A solid solution exists over all compositions for this system.
COPPER SILVER 10.10 Binary Eutectic Systems
●
293
Composition (at% Ag) 0
20
40
60
80
1200
100 2200
A
2000 Liquidus
1000
Liquid
1800 F
800
1600
! +L
!
7 7 9!C (TE)
B
"+L
E
8.0 (C! E)
7 1.9 (CE)
9 1.2 (C" E)
G
1400
"
1200 600 1000
Solvus ! + "
800
400
C
H 200
0
(Cu)
20
40
60
80
Composition (wt% Ag)
FIGURE 10.6 The copper–silver phase diagram. (Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski, Editor-in-Chief, 1990.
600
400 100 (Ag)
Temperature (!F)
Temperature (!C)
Solidus
IRON-IRON CARBIDE 10.18 The Iron–Iron Carbide (Fe–Fe 3C) Phase Diagram
●
303
Composition (at% C) 0
5
1538 C
10
20
25
1493 C
L
#
1400
2500 "+L
1394 C 1200 Temperature ( C)
15
1147 C 2.1 4
", Austenite
4.3 0
2000
1000 " + Fe 3 C
912 C
! + "
800
1500 727 C 0.7 6 0.0 2 2
600
! + Fe 3 C
!, Ferrite
Cementite (Fe 3 C) 400
0 (Fe)
1
2
3 4 Composition (wt% C)
5
6
FIGURE 10.26 The iron–iron carbide phase diagram. (Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski, Editor-in-Chief,
1000
6.7 0
Temperature ( F)
1600
r 10 / Phase Diagrams
308
Chapter 10 / Phase Diagrams
●
1100
1000
"
" + Fe 3 C
900
900
"
800
a # +"
"
7 2 7°C
b
700
"
#
! !
! ! ! + Fe 3 C
! !
c Temperature (°C)
"
x Temperature (°C)
FIGURE 10.28 Schematic 1100 representations of the microstructures for an iron–carbon alloy of eutectoid 1000 composition (0.76 wt% !C) above and below the eutectoid y temperature. M
! !
!
800
"
!
d N
Te
!
e O
f
700
!
# "
600
Fe 3 C
Pearlite
600
Fe 3 C Proeutectoid " Eutectoid "
400
x! 0
400
1.0 Composition (wt % C)
" + Fe 3 C
500
# + Fe 3 C
500
2.0
y 0
1.0
C0
Composition (wt % C)
2.0
FIGURE 10.31 representation microstructure iron–carbon al hypoeutectoid (containing les C) as it is cool the austenite p below the eute temperature.