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APPENDIX 2: STRENGTH AND DYNAMIC FATIGUE TESTS 821

Dangers

●

Modifying the ﬂaw distribution on the specimen tensile surfaces through

improper handling procedures

●

Testing in such a manner (speed or environment) that allows slow crack

growth to occur during the test

APPENDIX 2: STRENGTH AND DYNAMIC FATIGUE TESTS

Strength tests are tests in which the strength of specimens (ﬁnal components or

specially fabricated test specimens) is measured at a constant loading rate. For

inert strength measurements, the loading rate is high and the specimens are tested

in an inert environment to minimize slow crack growth. In contrast, dynamic

fatigue tests

4,49

are strength tests that are conducted in an active environment

over a wide range of loading rates to quantify parameters that describe slow

crack growth. Setting aside for the moment issues of environment, loading rate,

and natural ﬂaw distribution versus indentation ﬂaws, all of which are addressed

below, the mechanics associated with measuring strength are the same for inert

strength, Weibull distribution, or dynamic fatigue.

Bend Tests. Strength tests are usually conducted under uniaxial

60–63

or bi-

axial

64–68

bending conditions. The stress states associated with both of these

bending geometries are well known, so data analysis is straightforward. A brief

discussion of the advantages and disadvantages of each of these stress tests

follows.

The most commonly used uniaxial bend test is called the 4-point bend test.

This test, which is thoroughly described in the ASTM standard C 1161-94,

consists of a rectangular parallelepiped specimen in a loading ﬁxture that con-

sists of two parallel cylindrical loading pins in contact with one face of the

specimen and two more widely spaced cylindrical loading pins in contact with

the opposite face. The loading pins are perpendicular to and are spaced sym-

metrically about the center point of the specimen’s long axis. This loading ge-

ometry has the advantage of generating a uniform, uniaxial stress longitudinally

on the tensile side of the bend bar; the size of the uniform tensile region matches

the spacing of the narrowly spaced loading cylinders. The large region of uni-

form tensile stress makes the 4-point bend geometry much preferable to the 3-

point bend geometry, also described in ASTM standard C 1161-94.

In the

3-point bend geometry, the tensile stress is largest at the center of the specimen

but drops off immediately as a function of distance away from the center. There-

fore, in the 4-point bend geometry, a much larger population of initial defects

is sampled at maximum stress than is sampled in the 3-point bend geometry.

Edge failures pose a problem in uniaxial testing. The process of machining

specimen material into bars unavoidably generates machining damage along the

edges of the specimens. If the stress intensity at one of the machining ﬂaws is

greater than the stress intensity values at the ﬂaws of interest, the specimen will

fail from the machining ﬂaw. This gives rise to a couple of difﬁculties. On the

simplest level, if specimens that fail from the edge are ignored in the analysis,

edge failures still involve time and material that are wasted. On a more subtle

level, the question arises whether it is legitimate to ignore data from specimens

that fail from the edge? How can it be determined whether a specimen failed

822 RELIABILITY AND LIFE FOR BRITTLE MATERIALS

from a ﬂaw that resulted from specimen manufacture or whether it failed from

a ﬂaw of interest that happened to lie near or at an edge? Certainly, in the latter

case, discarding the data is not appropriate. Clearly, it would be better to avoid

edge failures altogether. Two ways of accomplishing this for uniaxial bending

involve either machine chamfering or hand rounding specimen edges on the

tensile surface or use of a standard ﬂaw large enough to be the source of failure.

Edge modiﬁcation requires that the 90

⬚ corners along the longitudinal tensile

edges of the specimen be machined away or rounded the length of the specimen.

This approach greatly reduces the probability of edge failures by eliminating the

high stress concentrating effect of the corner. However, it reduces the tensile

surface area of the specimen and adds both machining expense and time to the

specimen preparation. In addition, a sloppy chamfering or rounding job can

cause more damage than it relieves. Nevertheless, if carefully done, chamfering

or hand rounding corners can nearly eliminate edge failures. The second ap-

proach to reduce edge failures through the use of large standard sized ﬂaws will

be discussed below for both uniaxial and biaxial bend tests. At this point, it is

sufﬁcient to say that the use of standard ﬂaws clearly is not a solution to edge

failures if the purpose of the strength tests is to obtain a Weibull distribution

(see Appendix 1). However, standard ﬂaws can be very useful in dynamic fatigue

experiments.

Biaxial tests generate an equi-biaxial stress state on the tensile surface of

disk-shaped specimens.

64–68

This is accomplished through the use of a test ge-

ometry in which a ring composed of small balls* (e.g., tungsten carbide balls)

is placed in contact with one side of the specimen. This ring has a radius some-

what smaller than the radius of the specimen disk. On the other side of the disk,

a ring or circular ﬂat (e.g., a tungsten carbide ball that has had a ﬂat machined

onto it) is pressed against the specimen. When the ﬂat is pressed against the

specimen, an equi-biaxial tensile stress with a radius equal to the radius of the

small ﬂat is generated on the tensile surface of the specimen. The literature

contains descriptions of biaxial test conﬁgurations in which a ball, rather than a

ﬂat or ring, is used to apply the load.

Like the 3-point bend test, point loading

under biaxial conditions generates tensile stresses that fall monotonically from

the center of the specimen; there is no region of high uniform tensile stress like

that which occurs when a ﬂat is used. Therefore, ﬂat-on-ring rather than ball-

on-ring loading is recommended.

Biaxial loading has several major advantages. First, because the stress is equi-

biaxial, the most severe ﬂaw will cause failure regardless of its orientation in

the specimen. Second, because the loading geometry is circularly symmetric,

alignment in the plane of the disk is less of a problem than for uniaxial bend

tests. Third, because the high stress region is in the center of the disk and the

stress at the edge of the specimen is only about 30% of the maximum stress,

edge failures are almost completely eliminated. However, these beneﬁts can be

offset by the fact that biaxial testing requires much more material that uniaxial

testing.

*A solid ring of a somewhat compliant material may also be used.

22,68

APPENDIX 2: STRENGTH AND DYNAMIC FATIGUE TESTS 823

Both uniaxial and biaxial bend tests are subject to errors resulting from load-

ing train misalignment and friction. The ASTM standards address both of these

issues. Here we only mention the existence of the problems and commend the

standards to the attention of the reader.

Standard Flaws. If it is not necessary to measure strengths from ﬂaws rep-

resentative of the ﬂaw population in the ﬁnal components, i.e., to determine the

Weibull distribution, it is usually beneﬁcial to generate a large, uniform ﬂaw

from which the specimen will fail. Such ﬂaws can greatly reduce scatter in the

strength data, allowing trends to be observed that might be obscured by the

scatter resulting from the natural ﬂaw population. Typically, such ﬂaws are gen-

erated by use of a Vickers indenter to place an indentation impression in the

center of what will be the high tensile stress region of the specimen. When

indentations are used, their depths should remain fairly shallow, since the tensile

stress in the bend test decreases with depth into the specimen. A rule of thumb

is that the indentation impression, including cracks, should be less than one-

fourth the thickness of the specimen. Examining the fracture surface of a bend

specimen after testing can verify this.

It is important to be aware that indentations leave a residual stress ﬁeld around

the indentation impression. Therefore, strength tests on indented specimens

must take into account both the applied far-ﬁeld stresses as well as the local

residual stresses at the indentation. In the dynamic fatigue measurements,

the residual stress ﬁeld results in an expression usually expressed in terms of

⬘ ⫽ (3N ⫹ 2)/4 rather than N (see Eq. 2).

A residual ﬁeld also typically

surrounds natural ﬂaws.

The residual stress associated with point ﬂaws is iden-

tical in form to that around an indentation. Even many surface scratches can be

treated as a series of point ﬂaws, due to the nonuniform crack formation that

occurs along the length of the scratch.

Dynamic Fatigue Measurements. As stated at the beginning of this appen-

dix, dynamic fatigue tests are simply strength tests that have been made in the

environment of interest as a function of stressing rate. Therefore, the discussion

regarding uniaxial and biaxial strength tests applies directly to dynamic fatigue

tests. The purpose of dynamic fatigue measurements is to quantify crack growth

parameters. For the power law crack growth expression, it is particularly nec-

essary to determine N. As mentioned above, dynamic fatigue experiments are

usually conducted on indented specimens to minimize scatter in the strength.

From Eq. 2, we see that evaluating N

⬘ requires that the independent axis be

plotted as log( ). For even moderate values of N, the slope of the dynamic˙

␴

fatigue curve will be shallow (e.g., for N ⫽ 30, 1/(N⬘ ⫺ 1) ⬇ 0.05). Conse-

quently, to obtain accurate values for N

⬘, it is necessary to take the dynamic

fatigue data over as wide a stressing rate as possible. We recommend taking the

data over ﬁve orders of magnitude in stressing rate, if possible. Data taken over

less than three orders of magnitude should not be trusted. An analysis of the

conﬁdence with which N

⬘ (or N) is known (see Appendix 3) will give guidance

as to whether the stressing rate range was large enough.

It should be mentioned that recent work suggests that dynamic fatigue mea-

surements made at too high a velocity could give values for N that are somewhat

too low.

70,71

The reported work reﬂects ongoing research, and a discussion of it

824 RELIABILITY AND LIFE FOR BRITTLE MATERIALS

lies outside the scope of this chapter; the upper velocity at which this effect

occurs is dependent upon both material and environment. In addition, it is not

clear that the variation in N is generally large enough to detect experimentally.

At any rate, any proposed error in N that would result from measuring dynamic

fatigue at too high a stressing rate would result in a conservative lifetime pre-

diction. Therefore, at this time, we recommend as wide a stressing rate range as

possible.

Indented Inert Strength. Indented inert strength measurements are made

with indented specimens rather than specimens that will fail from their natural

ﬂaw population. As stated earlier in this appendix, inert strength measurements

need to be made at a high loading rate in an inert (e.g., N

gas) environment. It

is worth mentioning that regular dry nitrogen gas is sufﬁcient; there is no meas-

urable advantage in going to a super dry gas as long as the loading rate is high.

Best Practices

●

For either uniaxial or biaxial bend tests, articulated, self-aligning ﬁxtures

should be used to minimize extraneous stresses (see ASTM Standard C

1161-94 for uniaxial testing

62,63

and Refs 64, 65, 67, 68 for a discussion

of biaxial testing).

●

Inert strength tests require high loading rate and inert environment. En-

closing the test rig in a glove bag and ﬂowing N

gas through the bag is

a simple way to achieve an inert environment.

●

To minimize edge failures in bend bars, the edges can be rounded or

chamfered.

●

Vickers indentations are useful in reducing scatter in bend tests. In uni-

axial tests, the indentation should be oriented so that one set of diagonal

cracks will be perpendicular to the stress axis.

●

Dynamic fatigue tests should be made over as wide a range of stressing

rates as possible. Three orders of magnitude is the minimum range that

should be considered.

Dangers

●

3-point bend or ball-on-circle tests should be avoided in favor of 4-point

bend or ﬂat-on-circle tests.

●

Do not use indentations for Weibull strength tests.

●

In biaxial tests, do not use a rigid punch as the ﬂat.

APPENDIX 3: CONFIDENCE LIMITS

The lifetime analysis presented above is based on three sets of experimental

data: (1) dynamic fatigue data for indented specimens, (2) inert strength data for

indented specimens, and (3) inert strength distribution for the strength-limiting

ﬂaws (Weibull data). To estimate the conﬁdence in a lifetime prediction based

on Eq. (3) and these three data sets, i.e., the lifetime at a particular level of

conﬁdence, we need to determine the distribution of lifetimes that results from

the experimental uncertainties in these data sets. The nonparametric bootstrap

technique

21,22,50–52

is ideal for this purpose. The nonparametric bootstrap tech-

REFERENCES 825

nique involves the creation of a collection of simulated data sets based upon the

original data. If the original data set contained n data points, the simulated data

sets also contain n values and are generated by the random selection of values

from the original data set. After each value is selected to provide a simulated

data point, it is returned to the original data pool so that every value selected

for the simulated sets is selected out of the full collection of n values (i.e., a

select and replace procedure). The new set of data is called a bootstrap sample.

This procedure is repeated a large number of times and the statistic of interest

is determined.

The requirement for the original data set is that the data be independent and

identically distributed (iid). Clearly, if the data for the Weibull distribution and

the indented inert strength are taken properly, they meet this criterion. Equally

clearly, the dynamic fatigue data do not; the strength values depend upon the

stressing rate. To use the bootstrap technique to simulate dynamic fatigue data,

the following steps are taken. First, a linear regression analysis is performed on

the dynamic fatigue data, regressing the logarithm of the fracture stress versus

the logarithm of the stressing rate. The residuals of this regression analysis,

namely, the failure stress minus the best-ﬁt value, do meet the iid requirement.

Therefore, for each loading rate, residuals are chosen using the select and replace

procedure previously described. A fatigue stress is calculated from the selected

residual and the ﬁtted line and associated with the loading rate to simulate a

dynamic fatigue data set. A new estimate of lifetime can be made from each

simulated set of Weibull, indented inert strength and dynamic fatigue data. This

procedure can be repeated thousands of times to generate a distribution of life-

times. The value of the lifetime at any arbitrary conﬁdence level, y% (e.g., 99%),

is the lifetime such that y% of the lifetime estimates are greater than this value.

Best Practice

●

The bootstrap technique should be used to evaluate the conﬁdence limits

for the parameters from each of the three data sets as well as the conﬁ-

dence limits for the overall lifetime. This can alert the user to problems

in a particular experimental procedure (e.g., a wide enough loading rate

range in the dynamic fatigue experiment).

Acknowledgment

The authors gratefully acknowledge the critical reviews of the manuscript and

the most helpful suggestions of S. J. Dapkunas and S. M. Wiederhorn.

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West Conshohocken, PA, 2001.

PART 6

MANUFACTURING

HandbookofMaterialsSelection.EditedbyMyerKutz

831

CHAPTER 29

INTERACTION OF MATERIALS

SELECTION, DESIGN, AND

MANUFACTURING PROCESSES

Ronald A. Kohser

Department of Metallurgical Engineering

University of Missouri-Rolla

Rolla, Missouri

1 MANUFACTURING OBJECTIVE 831

2 VARIOUS APPROACHES 832

3 DESIGN 833

4 MATERIAL SELECTION 836

5 SELECTION OF FABRICATION

PROCESS 837

6 COMPLETING THE SYSTEM:

SECONDARY PROCESSING 838

7 SELECTION OF ‘‘BEST’’

SYSTEM 839

8 INTERRELATIONSHIP

EXAMPLES 840

1 MANUFACTURING OBJECTIVE

Manufacturing operations are targeted toward the production of products or com-

ponents that will adequately perform their intended task. Implicit in this state-

ment is the generation of parts with the required geometrical shape and precision.

Further, these parts must be made from selected materials, with internal struc-

tures and companion properties that have been optimized for the speciﬁc service

environment that the product must withstand. The ideal product is one that is

‘‘just good enough.’’ Anything better will usually incur added cost through

higher-grade materials, enhanced processing, or improved properties that may

not be necessary. Anything worse, and we may encounter product failure, dis-

satisﬁed customers, and possible unemployment.

As shown in Fig. 1, nearly every manufactured item goes through a series of

activities that include elements of design, material selection, process selection,

manufacture, evaluation (and possible failure analysis) and feedback. Along the

way, multiple alternatives are considered, and a number of decisions must be

made. Many of these decisions are judgmental in nature, not black and white,

and the consequences can be highly interrelated.

Consider the following assignment. Send a group of engineering students to

a local discount department store. Ask them to identify the speciﬁc toaster that

HandbookofMaterialsSelection.EditedbyMyerKutz