Askeland D.R., Fulay P.P. Essentials of Materials Science & Engineering

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SUMMARY

V Toughness refers to the ability of materials to absorb energy before they fracture.

Tensile toughness is equal to the area under the true or engineering stress-true

strain curve. The impact toughness is measured using the impact test. This could be

very di¤erent from the tensile toughness. Fracture toughness describes how easily a

crack or ﬂaw in a material propagates. The plane strain fracture toughness K

is a

common result of these tests.

V Weibull statistics are used to describe and characterize the variability in the

strength of brittle materials. The Weibull modulus is a measure of the variability of

the strength of a material.

V The fatigue test permits us to understand how a material performs when a cyclical

stress is applied. Knowledge of the rate of crack growth can help determine fatigue

life.

V Microstructural analysis of fractured surfaces can lead to better insights into the

origin and cause of fracture. Di¤erent microstructural features are associated with

ductile and brittle fracture as well as fatigue failure.

V The creep test provides information on the load-carrying ability of a material at

high temperatures. Creep rate and rupture time are important properties obtained

from these tests.

GLOSSARY

Beach or clamshell marks Patterns often seen on a component subjected to fatigue. Normally

formed when the load is changed during service or when the loading is intermittent, perhaps per-

mitting time for oxidation inside the crack.

Chevron pattern A common fracture feature produced by separate crack fronts propagating at

di¤erent levels in the material.

Climb Movement of a dislocation perpendicular to its slip plane by the di¤usion of atoms to or

from the dislocation line.

Conchoidal fracture Fracture surface containing a very smooth mirror zone near the origin of

the fracture, with tear lines comprising the remainder of the surface. This is typical of amorphous

materials.

Creep A time dependent, permanent deformation at high temperatures, occurring at constant

load or constant stress.

Creep rate The rate at which a material deforms when a stress is applied at a high temperature.

Creep test Measures the resistance of a material to deformation and failure when subjected to a

static load below the yield strength at an elevated temperature.

Delamination The process by which di¤erent layers in a composite will begin to debond.

Endurance limit An older concept that deﬁned a stress below which a material will not fail in a

fatigue test. Factors as corrosion or occasional overloading can cause materials to fail at stresses

below the assumed endurance limit.

Endurance ratio The endurance limit divided by the tensile strength of the material. The ratio is

about 0.5 for many ferrous metals. See the cautionary note on endurance limit.

Fatigue life The number of cycles permitted at a particular stress before a material fails by

fatigue.

C HA P T E R 7 Fracture Mechanics, Fatigue, and Creep Behavior220

Fatigue strength The stress required to cause failure by fatigue in a given number of cycles, such

as 500 million cycles.

Fatigue test Measures the resistance of a material to failure when a stress below the yield

strength is repeatedly applied.

Fracture mechanics The study of a material’s ability to withstand stress in the presence of

a ﬂaw.

Fracture toughness The resistance of a material to failure in the presence of a ﬂaw.

Griffith flaw A crack or ﬂaw in a material that concentrates and magniﬁes the applied stress.

Impact test Measures the ability of a material to absorb the sudden application of a load

without breaking. The Charpy and Izod tests are commonly used impact tests.

Intergranular In between grains or along the grain boundaries.

Microvoids Development of small holes in a material. These form when a high stress causes

separation of the metal at grain boundaries or interfaces between the metal and inclusions.

Notch sensitivity Measures the e¤ect of a notch, scratch, or other imperfection on a material’s

properties, such as toughness or fatigue life.

Rotating cantilever beam test An older test for fatigue testing.

Rupture time The time required for a specimen to fail by creep at a particular temperature and

stress.

S-N curve (also known as the W

€

ohler curve) A graph showing stress as a function of number of

cycles in fatigue.

Shot peening A process in which metal spheres are shot at a component. This leads to a re-

sidual compressive stress at the surface of a component and this enhances fatigue life.

Stress-corrosion A phenomenon in which materials react with corrosive chemicals in the envi-

ronment, leading to the formation of cracks and lowering of strength.

Striations Patterns seen on a fractured surface of a fatigued sample. These are on a much ﬁner

scale than beach marks and show the position of the crack tip after each cycle.

Tempering A glass heat treatment that makes the glass safer; it does so by creating a com-

pressive stress layer at the surface.

Toughness A qualitative measure of the energy required to cause fracture of a material. A ma-

terial that resists failure by impact is said to be tough. One measure of toughness is the area under

the true stress-strain curve (tensile toughness), another is the impact energy measured during an

impact test (impact toughness). The ability of materials containing ﬂaws to withstand load is

known as fracture toughness.

Transgranular Meaning across the grains (e.g., a transgranular fracture would be fracture in

which cracks would go through the grains).

Weibull distribution A mathematical distribution showing the probability of failure or survival

of a material as a function of the stress.

Weibull modulus (m) A parameter related to the Weibull distribution. It is an indicator of the

variability of the strength of materials resulting from a distribution of ﬂaw sizes.

€

ohler curve Graph showing fatigue stress as a function of number of cycles (also known as the

S-N curve).

Glossary 221

PROBLEMS

Section 7-1 Fracture Mechanics

Section 7-2 The Importance of Fracture

Mechanics

7-1 Alumina Al

is a brittle ceramic with low

toughness. Suppose that ﬁbers of silicon carbide

SiC, another brittle ceramic with low toughness,

could be embedded within the alumina. Would

doing this a¤ect the toughness of the ceramic ma-

trix composite? Explain.

7-2 A ceramic matrix composite contains internal ﬂaws

as large as 0.001 cm in length. The plane strain

fracture toughness of the composite is 45 MPa

ﬃﬃﬃﬃ

and the tensile strength is 550 MPa. Will the stress

cause the composite to fail before the tensile

strength is reached? Assume that f ¼ 1.

7-3 An aluminum alloy that has a plane strain fracture

toughness of 27.5 MPa

ﬃﬃﬃﬃ

fails when a stress of

290 MPa is applied. Observation of the fracture

surface indicates that fracture began at the surface

of the part. Estimate the size of the ﬂaw that ini-

tiated fracture. Assume that f ¼ 1:1.

7-4 A polymer that contains internal ﬂaws 1 mm in

length fails at a stress of 25 MPa. Determine the

plane strain fracture toughness of the polymer.

Assume that f ¼ 1.

7-5 A ceramic part for a jet engine has a yield strength

of 517 MPa and a plane strain fracture toughness

of 5.5 MPa

ﬃﬃﬃﬃ

. To be sure that the part does not

fail, we plan to assure that the maximum applied

stress is only one-third the yield strength. We use a

nondestructive test that will detect any internal

ﬂaws greater than 0.125 cm long. Assuming that

f ¼ 1:4, does our nondestructive test have the re-

quired sensitivity? Explain.

7-6 Assume that the critical stress intensity factor or

fracture toughness ðK

Þ for a partially stabilized

zirconia is 10 MPa-m

1=2

. If there is a plate of this

ceramic with a sharp edge notch 100 mm deep and

subjected to a stress of 300 MPa, will this plate be

able to withstand this stress?

7-7 Assume that the critical stress intensity factor or

fracture toughness ðK

Þ for a partially stabilized

zirconia is 10 MPa-m

1=2

. If there is a plate of this

ceramic with an internal notch 100 mm deep and

subjected to a stress of 300 MPa, will this plate be

able to withstand this stress?

Section 7-3 Microstructural Features of Fracture

in Metallic Materials

Section 7-4 Microstructural Features of Fracture

in Ceramics, Glasses, and Composites

7-8 Concrete has exceptional strength in compression

but it fails rather easily in tension. Explain why.

7-9 What controls the strength of glasses? What can be

done to enhance the strength of silicate glasses?

Section 7-5 Weibull Statistics for Failure

Strength Analysis

7-10 Sketch a schematic of the strength of ceramics

and that of metals and alloys as a function of

probability of failure. Explain the di¤erences you

anticipate.

7-11 Why does the strength of ceramics vary consid-

erably with the size of ceramic components?

7-12 Explain the signiﬁcance of the Weibull dis-

tribution.

Section 7-6 Fatigue

Section 7-7 Results of the Fatigue Test

Section 7-8 Application of Fatigue Testing

7-13 A cylindrical tool steel specimen that is 15 cm

long and 0.625 cm in diameter rotates as a canti-

lever beam and is to be designed so that failure

never occurs. Assuming that the maximum tensile

and compressive stresses are equal, determine the

maximum load that can be applied to the end of

the beam. (See Figure 7-17.)

7-14 A 2-cm-diameter, 20-cm-long bar of an acetal

polymer (Figure 7-26) is loaded on one end and

Figure 7-26 The S-N fatigue curve for an acetal

polymer (for Problems 7-14, 7-16, and 7-17).

C HA P T E R 7 Fracture Mechanics, Fatigue, and Creep Behavior222

is expected to survive one million cycles of load-

ing, with equal maximum tensile and compressive

stresses, during its lifetime. What is the maximum

permissible load that can be applied?

7-15 A cyclical load of 6672 N is to be exerted at the

end of a 25-cm-long aluminum beam (Figure

7-17). The bar must survive for at least 10

cycles. What is the minimum diameter of the bar?

7-16 A cylindrical acetal polymer bar 20 cm long and

1.5 cm in diameter is subjected to a vibrational

load at a frequency of 500 vibrations per minute,

with a load of 50 N. How many hours will the

part survive before breaking? (See Figure 7-26.)

7-17 Suppose that we would like a part produced from

the acetal polymer shown in Figure 7-26 to sur-

vive for one million cycles under conditions that

provide for equal compressive and tensile

stresses. What is the fatigue strength, or max-

imum stress amplitude, required? What are the

maximum stress, the minimum stress, and the

mean stress on the part during its use? What ef-

fect would the frequency of the stress application

have on your answers? Explain.

7-18 Explain how fatigue failure occurs even if the

material does not see overall stress levels higher

than the yield strength.

7-19 A fatigue test is conducted on an aluminum alloy

at a frequency of 100 Hz. If the number of cycles

is 10

, how much time will this fatigue test take?

How much will be the time if this test were con-

ducted for 10

cycles?

7-20 How much time will a piezoelectric fatigue test-

ing machine take to conduct a fatigue test on a

titanium alloy for 10

cycles? Assume that the

frequency of this test is 10 kHz.

Section 7-9 Creep, Stress Rupture, and Stress

Corrosion

7-21 Deﬁne the term ‘‘creep’’ and di¤erentiate creep

from stress relaxation.

7-22 What is meant by the terms ‘‘stress rupture’’

and ‘‘stress corrosion?’’

7-23 What is the di¤erence between failure of a ma-

terial by creep and that by stress rupture?

Design Problems

7-24 A hook (Figure 7-27) for hoisting containers

of ore in a mine is to be designed using a non-

Figure 7-17 (Repeated for Problems 7-13 and 7-15) The stress-number of cycles to failure (S-N) curves for a

tool steel and an aluminum alloy.

Figure 7-27 Schematic of a hook (for Problem 7-24).

Problems 223

ferrous (not based on iron) material. (A non-

ferrous material is used because iron and steel

could cause a spark that would ignite explosive

gases in the mine.) The hook must support a

load of 111,200 N, and a factor of safety of 2

should be used. We have determined that the

cross-section labeled ‘‘?’’ is the most critical

area; the rest of the device is already well over-

designed. Determine the design requirements

for this device and, based on the mechanical

property data given in Chapters 13 and 14 and

the metal/alloy prices obtained from such sour-

ces as your local newspapers, the internet web-

site of London Metal Exchange or The Wall

Street Journal, design the hook and select an

economical material for the hook.

7-25 A support rod for the landing gear of a private

airplane is subjected to a tensile load during

landing. The loads are predicted to be as high as

177,920 N. Because the rod is crucial and fail-

ure could lead to a loss of life, the rod is to be

designed with a factor of safety of 4 (that is,

designed so that the rod is capable of support-

ing loads four times as great as expected). Op-

eration of the system also produces loads that

may induce cracks in the rod. Our non-

destructive testing equipment can detect any

crack greater than 0.05 cm deep. Based on the

materials given in Table 7-1, design the support

rod and the material, and justify your answer.

7-26 A lightweight rotating shaft for a pump on the

national aerospace plane is to be designed to

support a cyclical load of 66,720 N during serv-

ice. The maximum stress is the same in both

tension and compression. The endurance limits

or fatigue strengths for several candidate mate-

rials are shown here. Design the shaft, including

an appropriate material, and justify your sol-

ution.

Material

Endurance Limit/

Fatigue Strength

(MPa)

Al-Mn alloy 110

Al-Mg-Zn alloy 225

Cu-Be alloy 295

Mg-Mn alloy 80

Be alloy 180

Tungsten alloy 320

7-27 A ductile cast-iron bar is to support a load of

177,920 N in a heat-treating furnace used to

make malleable cast iron. The bar is located in

a spot that is continuously exposed to 500



Design the bar so that it can operate for at least

10 years without failing.

C HA P T E R 7 Fracture Mechanics, Fatigue, and Creep Behavior224

Strain Hardening and

Annealing

Have You Ever Wondered?

9 Why does bending a copper wire make it stronger?

9 What type of steel improves the crashworthiness of cars?

9 How are aluminum beverage cans made?

9 Why do thermoplastics get stronger when strained?

9 Why is it that the strength of the metallic material around a weld could be lower than that of the

surrounding material?

In this chapter, we will learn how the strength of

metals and alloys is influenced by mechanical

processing and heat treatments. In Chapter 4, we

learned about the different techniques that can

strengthen metals and alloys (e.g., enhancing dis-

location density, decreasing grain size, alloying,

etc.). In this chapter, we will learn how to enhance

the strength of metals and alloys using cold

working, a process by which a metallic material is

simultaneously deformed and strengthened. We

will also see how hot working can be used to shape

metals and alloys by deformation at high temper-

atures without strengthening. We will learn how

the annealing heat treatment can be used to

225

enhance ductility and counter the increase in

hardness caused by cold working. The strength-

ening we obtain during cold working, which is

brought about by increasing the dislocation den-

sity, is called strain hardening or work hardening.

By controlling the thermo-mechanical processing

(i.e., combinations of mechanical processing and

heat treatment), we are able to process metallic

materials into a usable shape yet still improve

and control their mechanical properties.

The topics discussed in this chapter pertain

particularly to metals and alloys. Strain hardening

(obtained by multiplication of dislocations) re-

quires that the materials have ductility. We use

strain hardening as a tool to enhance strength of

a material. We have to counter the effects of

strain hardening in manufacturing processes. For

example, when we draw a wire or extrude a tube,

strain hardening can occur and we have to ensure

that the product still has acceptable ductility.

Cars and trucks are made by stamping out a ma-

terial known as sheet steel. This process leads to

aerodynamic and aesthetically pleasing car chas-

sis. The sheet steel used must exhibit an ability

to stretch and bend easily during stamping.

However, we must ultimately produce a strong

steel that can withstand minor bumps and major

impacts. The increase in the strength of steel as a

result of strain hardening helps us in this regard.

Furthermore, for better crashworthiness we must

use steels that exhibit rapid strain hardening dur-

ing impact loading.

What about polyme rs, glasses, and ceramics?

Do they also exhibit strain hardening? We will

show that the deformation of thermoplastic poly-

mers often produces a strengthening effect.

However, the mechanism of deformation strength-

ening is completely different in polymers than

that in metallic materials. The strength of most

brittle materials such as ceramics and glasses

depends upon the flaws and flaw-size distribution

(Chapters 6 and 7). Therefore, inorganic glasses

and ceramics do not respond well to strain hard-

ening. We, therefore, consider different strategies

to strengthen these materials. In this context, we

will learn the principles of tempering and an-

nealing of glasses. These processes make glass

stronger and safer. We will also examine con-

ditions under which ceramic materials can show

large (several hundred percent) plastic deforma-

tions. Thus, all ceramic materials are not intrin-

sically brittle! There are conditions under which

many ceramics can exhibit considerable ductility.

We begin by discussing strain hardening in

metallic materials in the context of stress-strain

curves.

8-1 Relationship of Cold Working to the Stress-Strain Curve

A stress-strain curve for a ductile metallic material is shown in Figure 8-1(a). If we apply

a stress s

that is greater than the yield strength (s

), it causes a permanent deformation

or strain. When the stress is removed, it leaves behind a strain of e

. If we make a tensile

test sample from the metallic material that had been previously stressed to s

and retest

that material, we obtain the stress-strain curve shown in Figure 8-1(b). Our new test

specimen would begin to deform plastically or ﬂow at stress level s

. We deﬁne ﬂow

stress as the stress that is needed to initiate plastic ﬂow in a previously deformed mate-

rial. Thus, s

is now the ﬂow stress of the material. If we continue to apply a stress until

we reach s

, then release the stress and again retest the metallic material, the new ﬂow

stress is s

. Each time we apply a higher stress, the ﬂow stress and tensile strength in-

crease and the ductility decreases. We eventually strengthen the metallic material until

C HA P T E R 8 Strain Hardening and Annealing226

the ﬂow stress, tensile, and breaking strengths are equal and there is no ductility [Figure

8-1(c)]. At this point, the metallic material can be plastically deformed no further. Fig-

ures 8-1(d) and (e) are related to springback, a concept that is discussed a bit later in this

section.

By applying a stress that exceeds the original yield strength of the metallic material,

we have strain hardened or cold worked the metallic material, while simultaneously

deforming it. This is the basis for many manufacturing techniques, such as wire

drawing. Figure 8-2 illustrates several manufacturing processes that make use of both

Figure 8-1 Development of strain hardening from the stress-strain diagram. (a) A specimen is

stressed beyond the yield strength before the stress is removed. (b) Now the specimen has a

higher yield strength and tensile strength, but lower ductility. (c) By repeating the procedure,

the strength continues to increase and the ductility continues to decrease until the alloy

becomes very brittle. (d) Note the total strain and the elastic strain recovery lead to remnant

plastic strain and (e) illustration of springback. (This article was published in Engineering

Materials I, Second Edition, M.F. Ashby and D.R.H. Jones. Copyright > Butterworth-

Heinemann (1996). )

8-1 Relationship of Cold Working to the Stress-Strain Curve 227

Figure 8-2 Manufacturing processes that make use of cold working as well as hot working.

Common metalworking methods. (a) Rolling. (b) Forging (open and closed die). (c) Extrusion

(direct and indirect). (d) Wire drawing. (e) Stamping. (Adapted from Mechanical Behavior of

Materials by Meyers, M.A. & Chawla, K.K. 1999, Prentice Hall.) (Source: Adapted from

Mechanical Behavior of Materials, by M.A. Meyers and K.K. Chawla, p. 292, Fig. 6-1.

Upper Saddle River, NJ.)

C HA P T E R 8 Strain Hardening and Annealing228

cold-working and hot-working processes. We will discuss the di¤erence between hot

working and cold working later in this chapter (Section 8-7). Many techniques are used

to simultaneously shape and strengthen a material by cold working (Figure 8-2). For

example, rolling is used to produce metal plate, sheet, or foil. Forging deforms the metal

into a die cavity, producing relatively complex shapes such as automotive crankshafts

or connecting rods. In drawing, a metallic rod is pulled through a die to produce a wire

or ﬁber. In extrusion, a material is pushed through a die to form products of uniform

cross-sections, including rods, tubes, or aluminum trims for doors or windows. Deep

drawing is used to form the body of aluminum beverage cans. Stretch forming and

bending are used to shape sheet material. Thus, cold working is an e¤ective way of

shaping metallic materials while simultaneously increasing their strength. The down

side of this process is the loss of ductility. If you take a metal wire and bend it re-

peatedly it will harden and eventually break because of strain hardening. Strain hard-

ening is used in many products, especially those that are not going to be exposed to

very high temperatures. For example, an aluminum beverage can derives almost 70% of

its strength as a result of strain hardening that occurs during its fabrication. Some of the

strength of aluminum cans also comes from the alloying elements (e.g., Mg) added.

Note that many of the processes such as rolling, can be conducted using both cold and

hot working. The pros and cons of using each will be discussed later in this chapter.

Strain-Hardening Exponent (n) The response of a metallic material to cold working is

given by the strain-hardening exponent, n, which is the slope of the plastic portion of the

true stress-true strain curve in Figure 8-3 when a logarithmic scale is used:

¼ Ke

ð8-1aÞ

ln s

¼ ln K þ n ln e

ð8-1bÞ

The constant K (strength coe‰cient) is equal to the stress when e

¼ 1. The strain-

hardening exponent is relatively low for HCP metals, but is higher for BCC and, par-

ticularly, for FCC metals (Table 8-1). Metals with a low strain-hardening exponent

respond poorly to cold working. If we take a copper wire and bend, the bent wire is

stronger as a result of strain hardening.

Figure 8-3

The true stress-true strain curves for metals with large

and small strain-hardening exponents. Larger degrees of

strengthening are obtained for a given strain for the

metal with the larger n.

8-1 Relationship of Cold Working to the Stress-Strain Curve 229

Askeland D.R., Fulay P.P. Essentials of Materials Science &amp; Engineering

Подождите немного. Документ загружается.

Askeland D.R., Fulay P.P. Essentials of Materials Science & Engineering