Lec.

1:
Introduction to Fracture Mechanics

An oil tanker that fractured in a brittle manner by crack

propagation around its girth. (Photography by Neal Boenzi.
Reprinted with permission from The New York Times.)
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- Brittle fracture of normally ductile materials, such as that shown
in the above photograph for this chapter, has demonstrated the
need for a better understanding of the mechanisms of fracture.

- Extensive research endeavors over the past several decades have

led to the evolution of the field of fracture mechanics.

- This subject allows quantification of the relationships between

material properties, stress level, the presence of crack-producing
flaws, and crack propagation mechanisms.

- Design engineers are now better equipped to anticipate, and thus

prevent, structural failures.

- The present chapter centers on some of the fundamental

principles of the mechanics of fracture. X
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- The failures often occurred under conditions of low stresses (several
ships failed suddenly while in the harbor) which made them seemingly
inexplicable.

- As a result of extensive investigations were initiated in many countries,

especially in USA.

- This work reveals that here again, flaws and stress concentrations
(and to a certain extent internal stresses) were responsible for failure.

- The fractures were truly brittle: they were accompanied by very little
plastic deformation.

- It turned out that the brittle fracture of a steel was promoted by low
temperatures and by conditions of triaxial stress such as may exist at a
sharp notch or flaw.

- Under these circumstances, structural steel can fracture by cleavage

without noticeable plastic deformation. X 3
- Above certain temperature, the transition temperature, the steel
behave in a ductile manner.

- The transition temperature may go up as a result of heat cycle during

the welding process.

- After the World War II, the use of high strength steels has increased
considerably.

- These materials are often selected to realize weight savings.

- Simultaneously, stress analysis methods were developed which enable

a more reliable determination of local stresses.

- This permitted safety factors to be reduced resulting in further weight

savings.

- Consequently, structures designed in high strength materials have only

low margins of safety. X4
- This means that service stresses (sometimes with the aid of aggressive
environment) may be high enough to induce cracks, particularly if pre-
existing flaws or high stress concentrations are present.

- The high strength materials have a low crack resistance (fracture

toughness): the residual strength under the presence of cracks is low.

- When only small cracks exist, structures designed in high strength

materials may fail at stresses below the highest service stress they were
designed for.

- Low stress fractures induced by small cracks are, in many aspects, very
similar to the brittle fractures of welded low-strength steel structures.

- Very little plastic deformation is involved: the fracture is brittle in an

engineering sense, although the micromechanism of separation is the
same as in ductile fracture. X

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- The occurrence of low stress fracture in high strength materials
induced the development of Fracture Mechanics.

- Engineering fracture mechanics can deliver the methodology to

compensate the inadequacies of conventional design concepts.

- The conventional design criteria are based on tensile strength, yield

strength and buckling stress.

- These criteria are adequate for many engineering structures, but they
are insufficient when there is the likelihood of cracks.

- Now, after a period of development, fracture mechanics have

become a useful tool in design with high strength materials.

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(1) Ductile Brittle Transition Temperature (DBTT):
- One of the primary functions of Charpy and Izod tests is to
determine whether or not a material experiences a ductile-to-
brittle transition with decreasing temperature and, if so, the range
of temperatures over which it occurs.

- The ductile-to-brittle transition is related to the temperature

dependence of the measured impact energy absorption.

- This transition is represented for a steel by curve A in Fig.(1).

- Frequently, the percent shear fracture is plotted as a function of

temperature—curve B in Fig.(1).
- In addition to the ductile-to-brittle transition represented in
Fig.(1), two other general types of impact energy-versus-
temperature behavior have been observed; these are represented
schematically by the upper and lower curves of Fig.(3).
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Fig.(1): Temperature dependence of the Charpy V-notch impact energy
(curve A) and percent shear fracture (curve B) for an A283 steel.
(Reprinted from Welding Journal. Used by permission of the American
Welding Society.)
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- As the temperature is lowered, the impact energy drops suddenly
over a relatively narrow temperature range, below which the
energy has a constant but small value; that is, the mode of fracture
is brittle.
- For many alloys, there is a range of temperatures over which the
ductile-to-brittle transition occurs (Fig.(1)); this presents some
difficulty in specifying a single ductile-to-brittle transition
temperature.

- Alternatively, appearance of the failure surface is indicative of the

nature of fracture and may be used in transition temperature
determinations.
- For ductile fracture, this surface appears fibrous or dull (or of
shear character), as in the steel specimen of Fig.(2) that was tested
at 79°C. x
99
- Conversely, totally brittle surfaces have a granular (shiny) texture (or
cleavage character) (the – 59°C specimen, Fig.(2)).

- Over the ductile-to-brittle transition, features of both types will exist (in
Fig.(2), displayed by specimens tested at – 12°C, 4°C, 16°C, and 24°C).
- 59 - 12 4 16 24 79

Fig.(2): Photograph of fracture surfaces of A36 steel Charpy V-notch specimens

tested at indicated temperatures (in °C). (From R.W. Hertzberg, Deformation and
Fracture Mechanics of Engineering Materials, 3rd edition, Fig. 9.6, p. 329.
Copyright © 1989 by John Wiley & Sons, Inc., New York. Reprinted by
permission of John Wiley & Sons, Inc.) x
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- No explicit criterion has been established, and so this temperature is
often defined as that temperature at which the CVN energy assumes some
value (e.g., 20 J or 15 ft-lbf), or corresponding to some given fracture
appearance (e.g., 50% fibrous fracture).

- Matters are further complicated inasmuch as a different transition

temperature may be realized for each of these criteria.

- Perhaps the most conservative transition temperature is that at which

the fracture surface becomes 100% fibrous; on this basis, the transition
temperature is approximately 110°C (230°F) for the steel alloy that is the
subject of Fig.(1).

- Structures constructed from alloys that exhibit this ductile-to-brittle

behavior should be used only at temperatures above the transition
temperature, to avoid brittle and catastrophic failure.
x
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- Classic examples of this type of failure occurred, with disastrous
consequences, during World War II when a number of welded
transport ships, away from combat, suddenly and precipitously split
in half.

- The vessels were constructed of a steel alloy that possessed

adequate ductility according to room-temperature tensile tests.

- The brittle fractures occurred at relatively low ambient

temperatures, at about 4°C (40°F), in the vicinity of the transition
temperature of the alloy.

- Each fracture crack originated at some point of stress

concentration, probably a sharp corner or fabrication defect, and
then propagated around the entire girth of the ship. x
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Fig.(3): Schematic curves for the three general types of impact
energy-versus-temperature behavior.
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- Here, it may be noted that low-strength FCC metals (some
aluminum and copper alloys) and most HCP metals do not
experience a ductile-to-brittle transition (corresponding
to the upper curve of Fig.(3), and retain high impact energies (i.e.,
remain ductile) with decreasing temperature.

- For high-strength materials (e.g., high-strength steels and titanium

alloys), the impact energy is also relatively insensitive to
temperature (the lower curve of Fig.(3)); however, these materials
are also very brittle, as reflected by their low impact energy
values.

- And, of course, the characteristic ductile-to-brittle transition is

represented by the middle curve of Fig.(3).

X 14
- As noted, this behavior is typically found in low-strength steels
that have the BCC crystal structure.

- For these low-strength steels, the transition temperature is

sensitive to both alloy composition and microstructure.

- For example, decreasing the average grain size results in a

lowering of the transition temperature.

- Most ceramics and polymers also experience a ductile-to-brittle

transition.

- For ceramic materials, the transition occurs only at elevated

temperatures, ordinarily in excess of 1000°C (1850°F).

x
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- Hence, refining the grain size both strengthens and toughens steels. In
contrast, increasing the carbon content while increasing the strength of
steels, also raises the CVN transition of steels, as indicated in Fig.(4).

Fig.(4): Influence of carbon content on the Charpy V-notch (CVN) energy-

versus temperature behavior for steel. (Reprinted with permission from
ASM International, Metals Park, OH 44073-9989, USA; J. A. Reinbolt and
W. J. Harris, Jr., “Effect of Alloying Elements on Notch Toughness of
Pearlitic Steels,” Transactions of ASM, Vol. 43, 1951.)
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Change in impact transition curves with increasing pearlite content in
normalized carbon steels.
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