FUNDAMENTALS OF FRACTURE

8.3 Ductile Fracture • 253
Simple fracture is the separation of a body into two or more pieces in response to an imposed
stress that is static (i.e., constant or slowly changing with time) and at temperatures
that are low relative to the melting temperature of the material. Fracture can also occur
from fatigue (when cyclic stresses are imposed) and creep (time-dependent deformation,
normally at elevated temperatures); the topics of fatigue and creep are covered later
in this chapter (Sections 8.7 through 8.15). Although applied stresses may be tensile,
compressive, shear, or torsional (or combinations of these), the present discussion will
be confined to fractures that result from uniaxial tensile loads. For metals, two fracture
modes are possible: ductile and brittle. Classification is based on the ability of a material
to experience plastic deformation. Ductile metals typically exhibit substantial plastic deformation
with high energy absorption before fracture. However, there is normally little
or no plastic deformation with low energy absorption accompanying a brittle fracture.
The tensile stress–strain behaviors of both fracture types may be reviewed in Figure 6.13.
Ductile and brittle are relative terms; whether a particular fracture is one mode or the
other depends on the situation. Ductility may be quantified in terms of percent elongation
(Equation 6.11) and percent reduction in area (Equation 6.12). Furthermore, ductility is a
function of temperature of the material, the strain rate, and the stress state. The disposition
of normally ductile materials to fail in a brittle manner is discussed in Section 8.6.
Any fracture process involves two steps—crack formation and propagation—in
response to an imposed stress. The mode of fracture is highly dependent on the
mechanism of crack propagation. Ductile fracture is characterized by extensive plastic
deformation in the vicinity of an advancing crack. Furthermore, the process proceeds
relatively slowly as the crack length is extended. Such a crack is often said to be stable—
that is, it resists any further extension unless there is an increase in the applied stress.
In addition, there typically is evidence of appreciable gross deformation at the fracture
surfaces (e.g., twisting and tearing). However, for brittle fracture, cracks may spread
extremely rapidly, with very little accompanying plastic deformation. Such cracks may
be said to be unstable, and crack propagation, once started, continues spontaneously
without an increase in magnitude of the applied stress.
Ductile fracture is almost always preferred to brittle fracture for two reasons:
First, brittle fracture occurs suddenly and catastrophically without any warning; this is
a consequence of the spontaneous and rapid crack propagation. However, for ductile
fracture, the presence of plastic deformation gives warning that failure is imminent,
allowing preventive measures to be taken. Second, more strain energy is required to
induce ductile fracture inasmuch as these materials are generally tougher. Under the
action of an applied tensile stress, many metal alloys are ductile, whereas ceramics are
typically brittle, and polymers may exhibit a range of behaviors.
ductile fracture,
brittle fracture
8.2 FUNDAMENTALS OF FRACTURE
Fracture
8.3 DUCTILE FRACTURE
Ductile fracture surfaces have distinctive features on both macroscopic and microscopic
levels. Figure 8.1 shows schematic representations for two characteristic macroscopic
fracture profiles. The configuration shown in Figure 8.1a is found for extremely soft
metals, such as pure gold and lead at room temperature, 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 8.1b, where fracture is preceded by only a moderate amount of necking.
The fracture process normally occurs in several stages (Figure 8.2). First, after necking

WHY STUDY Failure?

The design of a component or structure often calls

upon the engineer to minimize the possibility of failure.

Thus, it is important to understand the mechanics of

the various failure modes—fracture, fatigue, and

creep—and, in addition, be familiar with appropriate

design principles that may be employed to prevent inservice

failures. For example, in Sections M.14 through

M.16 of the Mechanical Engineering Online Support

Module, we discuss material selection and processing issues

relating to the fatigue of an automobile valve spring.

WHY STUDY Failure?

Learning Objectives

After studying this chapter, you should be able to do the following:

1. Describe the mechanism of crack propagation

for both ductile and brittle modes of fracture.

2. Explain why the strengths of brittle materials

are much lower than predicted by theoretical

calculations.

3. Define fracture toughness in terms of (a) a

brief statement and (b) an equation; define all

parameters in this equation.

4. Make a distinction between fracture toughness

and plane strain fracture toughness.

5. Name and describe the two impact fracture

testing techniques.

6. Define fatigue and specify the conditions under

which it occurs.

7. From a fatigue plot for some material, determine

(a) the fatigue lifetime (at a specified stress

level) and (b) the fatigue strength (at a

specified number of cycles).

8. Define creep and specify the conditions under

which it occurs.

9. Given a creep plot for some material, determine

(a) the steady-state creep rate and (b) the

rupture lifetime.

The failure of engineering materials is almost always an undesirable event for several

reasons; these include putting human lives in jeopardy, causing economic losses, and

interfering with the availability of products and services. Even though the causes of

failure and the behavior of materials may be known, prevention of failures is difficult

to guarantee. The usual causes are improper materials selection and processing and

inadequate design of the component or its misuse. Also, damage can occur to structural

parts during service, and regular inspection and repair or replacement are critical to safe

design. It is the responsibility of the engineer to anticipate and plan for possible failure

and, in the event that failure does occur, to assess its cause and then take appropriate

preventive measures against future incidents.

The following topics are addressed in this chapter: simple fracture (both ductile

and brittle modes), fundamentals of fracture mechanics, fracture toughness testing,

the ductile-to-brittle transition, fatigue, and creep. These discussions include failure

mechanisms, testing techniques, and methods by which failure may be prevented or

controlled.

8.1 INTRODUCTION

Concept Check 8.1 Cite two situations in which the possibility of failure is part of the

design of a component or product.

[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]

252 •

Tutorial Video:

Cyclical

Fatigue Failure

What are Some

Real-World Examples

of Failure?

Fatigue Failure Analysis

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Even if you design mechanical components satisfying mechanical strength criteria it may fail due to a phenomenon called fatigue. Historically many design disasters have happened by neglecting effect of Fatigue.In this video lecture we will learn how to predict and quantify fatigue effect.

Detailed description of above video lecture is given below

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A Wire Breaking problem

To understand what is fatigue let’s consider this metal wire. You have to break it. So how will you break it? Will you pull it from both ends or will you bend the wire upward and downward repetitively.

Fig.1 Two methods to break metal wire, Either bend it upward and downward repetitively or pull it

Your answer is obviously the second option. Because this method requires less effort compared to the first case. This is a well known example of fatigue failure. So how does material fail due to fatigue? To get answer for this question let us have a close look at stress variation in wire cross section.

Reason Behind Fatigue Failure - Crack Propagation

When you bend it downwards bending stress induced is in the wire cross section. There will be tension at top area and compression at bottom area. When wire is at equilibrium there will not be any stress on wire cross section. When wire is bending upwards there will be compression at top and tension at bottom.

Fig.2 Stress variation in wire cross-section, as wire is bent downward and upward

So if you trace stress induced at a point with respect to time it will vary like this. As a fluctuating stress with time.

Fig.3 Stress variation at a point is plttod on stress vs time graph

Initially the point will have positive stress, after that zero, then negative stress. The same cycle repeats again and again. Such fluctuating stress is root cause of fatigue failure. When such fluctuating load act on a material it will initiate something called micro crack. This crack will begin to grow with fluctuating load and over time it will cause an abrupt failure. Unlike failure due to static load failure due to fatigue happens without any warning, it does not make necking. And the failure is unpredictable.

Fatigue Failure in Real Life Engineering Problems

Fig.4 Some practical cases which could result in fatigue failure, if not designed properly

The same phenomenon can happen for axle of this motor where it is undergoing fluctuating stress due to gravity effect of this mass. A rail wheel when it is in contact with with the track produces a high contact stress, but when the wheel rotates stress gets relieved. When it comes back to original position again contact stress arises. So this also is a case of fluctuating stress case. Again will lead to fatigue failure if we do not design it carefully. Same is the case with a gear pair. Here contact stress arised at contact point fluctuates with time.

Effect of Stress Amplitude on Number of Cycles - S N Curve

This is the most important part in fatigue analysis. Relationship between stress amplitude and number of cycles it can execute before it fails. As you can guess as stress amplitude increases number of cycles for failure decreases. We will draw number of cycles in x axis, Stress amplitude in y axis. Both in logarithmic scale. Let’s start with the maximum stress a material can withstand, its ultimate stress. So this will happen, as you increase the stress even before completing one cycle the material will get broken. If you decrease the stress amplitude it will execute more number of cycles before it fails. Decreasing stress further even more number of cycles.

Fig.5 Number of cylces for fatigue failure increases with decrease in stress amplitude

So this will follow a trend like this, but not forever. You can see after particular stress amplitude, even with slight decrease in stress number of cycles required to make it fail increases drastically.

Fig.6 Stress amplitude Vs number of cycles, green region represents safe design area

Or in short if you have stress amplitude below this limit number of cycles to make to fail jumps ton infinity. Or material never fails after this limit. the material never fails. This limit is known as endurance limit; below endurance limit it is safe to operate the material. Engineers always try to design their components by keeping stress amplitude below endurance limit. You can see that endurance limit is way below ultimate stress value.

Fatigue Failure, when there is no Complete Stress Reversal

The case we discussed had complete stress reversal. What will be maximum stress limit for this case ?. When stress reversal does not happen. It has got a mean value and amplitude.

Fig.7 Fluctuating stress case which is not fully reversed

For this purpose we have to use something called Goodman diagram. Where mean value of stress is drawn on x axis. Amplitude of stress is drawn on y axis. When mean value of zero, we know safe stress limit is same as endurance limit. When amplitude of stress is zero, it is same as a static loading condition. So safe limit for tension is ultimate tensile stress at tension and safe limit for compression is ultimate tensile stress for compression. According to Goodman analysis safe stress amplitude limits for other cases lie on straight lines connecting this points. So for a particular stress mean value, we can find what’s the maximum allowable safe stress limit from this diagram. It will be here.

Fig.8 Use of Goodman diagram to find safe stress amplitude when stresmm mean value is not zero

Similar analysis can be done considering, safe limit of amplitude zero condition as yield strength of material. This is known as Soberberg diagram. Generally Goodman analysis is the most preferred one.