U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

NBS Special Publication 702

Standards and Metadata

Requirements for Computerization of

Selected Mechanical Properties of

Metallic Materials

Jack H. Westbrook

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TM he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

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Gailhersburg, MD 20899. "Some divisions within the center are located at Boulder, CO 80303. Located at Boulder, CO, with some elements at Gaithersburg, MD.
NBS Special Publication 702

Standards and Metadata

Requirements for Computerization of

Selected Mechanical Properties of

Metallic Materials

Jack H. Westbrook

General Electric Corporation

Work Sponsored by:

National Bureau of Standards and

US. Army DARCOM

August 1985

U.S. Department of Commerce

Malcolm Baldrige, Secretary

National Bureau of Standards

Ernest Ambler, Director
Library of Congress U.S. Government Printing Office Catalog Card Number 85-600585 Washington: 1985

National Bureau of Standards

Special Publication 702

Natl. Bur. Stand. (U.S.), Spec. Publ. 702, 47 pages (Aug. 1985)

CODEN: XNBSAV

For sale by the Superintendent

of Documents,

U.S. Government Printing Office, Washington, DC 20402
FOREWORD

Over the past few years, a number of activities have been started with the ultimate goal being to develop

easy-to-use materials data systems which contain a large amount of data on a wide variety of materials. In 1982, a meeting of experts on materials, data systems, and databases was held in Fairfield Glade, Tennessee. The

report of that workshop

Computerized Materials Data Systems —concluded that no major barriers existed to developing such systems and recommended that work begin immediately.

Since then, The Metal Properties Council, Inc. and the National Bureau of Standards have taken many

steps toward realizing the goals set forth in that report. Work has begun on building databases of evaluated data on mechanical properties and corrosion. Workshops have been held in various industries for engineers who are

potential users to determine their precise needs for materials data. The Metal Properties Council has established

the National Materials Property Data Network, Inc. as the focal point for industrial involvement, and that group has already raised substantial industry support. A project to build a demonstration system has started under the sponsorship of the National Bureau of Standards and the Office of Scientific and Technical Information of the Department of Energy.

One of the major areas of concern are the materials data themselves since most mechanical and corrosion

properties are not intrinsic but rather result from standard tests which over the years have been correlated to service performance. Questions have been raised concerning the adequacy of these tests with respect to computer storage and delivery of the data. Many tests have several variations, and often the tests themselves

change in time. Consequently, combining data generated by two similar but not equivalent test methods may

or may not be valid engineering practice.

This report is an attempt to identify some of the issues and problems relating to standards of mechanical

properties of metallic materials. The work was sponsored by the Office of Standard Reference Data of NBS

using funds provided by the U.S. Army DARCOM. It is anticipated that the discussion and recommendations

given here, while representing one view, may also be used to generate action within the engineering standards

c ommunity to look into the coming age of computerized materials data and to address the associated issues.

David R. Lide, Jr. Director

Standard Reference Data

iii
EXECUTIVE SUMMARY

To assist in building a computerized information system on the engineering properties of materials, the

standards and metadata requirements for a representative group of mechanical property categories are considered. These categories include: tensile behavior, hardness numbers, notch-bar impact test parameters and

fatigue properties. For each property group, definitions of terms, synonyms (and non-synonyms), standard test methods, standards for reporting data, precision and accuracy, and correlations of properties are addressed.

The principal findings and recommendations are as follows. Existing test methods are generally adequate

for the properties considered but better standards are needed for data reporting. Appraisal of materials

variability and testing machine variability would be assisted by access to standard reference materials, certified as to their mechanical properties. All properties considered for inclusion in a computerized system can be

categorized as: parameters for direct search, parameters retrievable with extraction of all data stored for a given

material, and parameters which are derived from an analytical representation of experimental data. Drafting of some general standards on computerized file structures and metadata files suitable for the engineering field is advised.

Recommendations

The recommendations set forth below apply strictly only to the specific mechanical properties examined

in the study. Many, however, are broadly generalizable to all standards and metadata requirements for computerized data on engineering properties of metallic materials.

Testing Standards

1. Adequate ASTM standards exist for the several mechanical property groups examined, except for

fatigue. Here standards need to be issued for rotational fatigue, plane bending, and torsion, or one of

the existing foreign standards should be endorsed.

2. ASTM standards are often inadequate in the extent to which information to be reported is specified.

Since computerized data systems have enhanced capability for both merger and intercomparison of

separate data sets, it is imperative that testing and reporting standards be improved so as to permit such

treatments of the data. It is suggested that ASTM E 21. 1 1-79 be used as a starting point for reporting

data.

3. Wherever data obtained from foreign tests are to be included in an information system, careful comparison needs to be made of standardized test methods to assess the possibility for interconversion.

4. There is a need for a complete compilation of all definitions used in ASTM standards on mechanical

property testing including resolution of conflicting definitions. Such a list would allow more uniform

nomenclature in databases as they are built.

Computerization Standards

ASTM should consider the advisability of drafting some general standards on computerized file structures, metadata files, etc. These could then be made particular by existing committees focused on individual materials or test methods. An example of such standards is the classification of different classes of mechanical property

data included in databases. One possible scheme shown below would distinguish three broad classes of these

data based on how engineers might search databases.

Classes of Data

Three broad classes of properties data may be distinguished:

1. Parameters for Direct Search —examples include yield strength, fatigue strength at N cycles, Charpy

V-notch impact strength, elastic modulus, etc.

2. Parameters Retrievable with Extraction of all Data Stored for a Given Material —examples include

hardness values, tensile elongation, reduction in area, etc. In other words, these are data which it might

iv
be desirable to the user to know but which would rarely if ever be involved in a search for materials

exhibiting a specified profile of properties.

3. Parameters Derivedfrom an Analytical Representation ofExperimental Data —examples include impact

transition temperature, Ramberg-Osgood exponent, fatigue life parameters, etc. The concept here is that the database manager may choose to store the pertinent raw experimental data in the file and then

subject these to a certain type of analysis to yield the derived parameters. The user of the database may

be permitted to access and search upon only the derived parameters or, alternatively, to retrieve a whole data set for a particular material together with its analytical representation but not individual

data points.

In any specific computerized system, allocation of individual parameters to the above three data classes depends in part on the database management system being used and in part on user preference decisions built into the information systems design. However, ASTM may wish to differentiate in their standards the data

reporting requirements according to these three classes.

Other Recommendations

Specific Database Comparisons —The observations and conclusions reported here result from a broad

reconnaissance of the general literature on mechanical properties. Once work on an integrated data system has

started and specific candidate databases have been identified, their terminology, referenced test methods, etc., need to be checked against the dictionaries, cross-references, and other assists advocated here.

Standard Reference Materials —A great need exists for standard reference materials for the several mechanical properties considered here. None exist within the national NBS collection and none anywhere for tensile and fatigue behavior. Only for hardness and impact data have standard reference materials been privately

developed.

Extension of this Study —Implementation of any broad materials information system covering several overlapping data compilations will require extension of the above pattern of information and analysis, not only

in the remaining important mechanical behaviors—torsion, compression, fracture (toughness and crack growth

rate), creep and stress rupture, stress corrosion and corrosion-fatigue—but also in other property areas

electrical, magnetic, processibility, safety and health, etc. However, because of the relative newness of certain

of these areas, the multiplicity of terms and test methods, coupled with the paucity of standards, will make the

extension of the study more difficult. Yet the results of such a study could provide the basis for a standard

covering presentation of engineering property data for any purpose whatsoever.

v
CONTENTS

Page

Foreword iii Executive Summary and Recommendations iv Introduction 1 Chapter 1 - Tensile Behavior 4

Chapter 2 - Hardness Numbers 16 Chapter 3 - Notch Bar Impact Test Parameters 23

Chapter 4 - Fatigue Properties 30

List of Figures

Page

Chapter 1

Figure 1. Relationship of stress-strain curve to kinetic modulus 4

Figure 2. Stress-strain relationship showing 0.1% and 0.2% proof stress, and 5 proportional limit Figure 3. Stress-strain diagram for determination of yield strength by the offset method. 7 Figure 4. Stress-strain diagram for determination of yield strength by the

extension-under-load method 7 Figure 5. Tensile strength versus hardness for 4340 and 8630 steel 13

Chapter 2

Figure 1. Correlation lines for metals and ionic crystals relating hardness numbers and

yield stresses 20

Figure 2. Correlation of hardnesses and elastic moduli for pure fee metals and covalent

crystals 21 Figure 3. Vickers hardness softening coefficient (B) for metals (including low-expansion

alloy, Nilo 36) and thermal coefficient of expansion 21

Chapter 3

Figure 1 . Dimensional details of Izod and Charpy test specimens as called for in ASTM E23-82 23

Figure 2. Schematic of the hyperbolic tangent function representing the temperature

dependence of impact toughness 24

Figure 3. Reproducibility of impact test results derived from extensive testing

of AMMRC 27

Figure 4. Variation in impact behavior of a steel tempered to various strength levels ... 28

Figure 5. Correlation between fracture toughness Klc and Charpy V-notch- impact

strength in the upper shelf region 28
Chapter 4

Page

Figure 1 . Typical fatigue loadings and definitions of stress terms 31 Figure 2. Typical constant-life fatigue diagram for heat-treated AISI 4340 alloy steel (bar), Ftu =125 ksi 33

Figure 3. Cyclic stress-strain curve drawn through stable loop tips 34

Figure 4. Cyclic stress-plastic strain plot, 1020 H. R. Steel 34

Figure 5. Strain amplitude versus reversals to failure, 1020 H. R. Steel 34

Figure 6. S-N diagram retrieved in the condition of smooth bar specimen, S35C alloy

in JIS Standard; <ry = 20-50 kg/mm2

, in air, temperature =0-30°, mean stress

<rm =0, and rotating bending or axial loading 36

Figure 7. Distribution of fatigue lifetimes. Results of simulated service tests of front suspension torsion bar springs of 5260H steel. Size of hexagonal bar section was 32 mm (1.25 in). Mean service life 134,000 cycles; standard deviation

37,000 cycles; coefficient of variation 0.28 38

Figure 8. Relation of tensile strength and fatigue limit retrieved in the condition of

carbon steel, smooth bar specimen, in air, temperature =0-30°, and rotating

bending. 38

List of Tables

Page

Chapter 1

Table 1. Recommended values for rounding test data 12

Chapter 2

Table 1. Rockwell test scales, indenting conditions, and typical applications 18 Table 2. Standard Brinell Test Loads 18 Table 3. Repeatability of the Rockwell hardness test 19 Table 4. Repeatability of the Vickers hardness test 19

Chapter 4

Table 1. Coefficients of variation experienced in testing for mechanical properties 37

vii
V
INTRODUCTION

Current thinking on building an effective computerized information system covering the engineering

properties of materials envisions the merger or electronic linkage (networking) of several existing machinereadable databases [1,2]*. By a network system we understand a system of inter-connected, independent,

machine-readable databases accessed by the user via a socalled "gateway" computer.' The gateway connects

the user to that database or databases which best answers his query; performs search, retrieval and display

functions; and offers a modest variety of post-processing operations—graphics, statistical analysis, re- formatting, etc. In order that the system appear to the user as a virtually integrated single database it is essential that transparent means be implanted to assure the interconvertibility of all material and property descriptors.

The need for "translation" of descriptors and interpretation of data values goes beyond the requirements

implied by any particular set of independent databases. Study of the materials/properties coverage offered by

any chosen set of candidate databases would undoubtedly disclose both broad gaps in certain parts of the

materials/properties matrix and isolated omissions of data for certain key properties of materials which would

have to be filled by extraction from the literature [3]. Thus, an even broader array of descriptors would be

introduced which would require conversion to the standard terms of the computerized system.

Whichever aspect of the development of a computerized materials properties system is considered

merger of separate databases, concurrent use of several in a linked system, or incorporation of new, additional

data, there are numerous problems of definition to be addressed before the integration of data of different origin can be made intelligible and effective for the user of the system. The generic term to cover all descriptive,

cross-reference, or indexed forms of data needed to identify and define a specific set of data values in a computerized database is "metadata" [4-6].

Although the range of metadata required for materials and properties in a full-blown system is quite large,

this study confines attention to certain mechanical properties of metals with the thought that the findings and

recommendations arrived at would not only have value in themselves but also that collectively they might

serve as a model for what is needed in other materials/property areas. Mechanical properties of metallic materials have been identified in several studies [1,2] as the first and most

important component of any comprehensive system of computerized engineering materials information. Existing machine-readable files of mechanical properties, not to mention the general literature, are not readily

integrable because of their use of different terminology, definitions, units, test methods, etc. What is needed

then is a system support dictionary which will show, wherever possible, the synonyms —words, phrases, or symbols—for each pertinent property. Furthermore by providing, as one of the "helps" in a network, a

definition of each important term, a system would aid the user in the interpretation of data and in ascertaining

the degree of incongruency of non-synonymous terms. Provision of exemplary sets of such definitions and

synonym lists are an important output of this study. It was further anticipated that other major results of this study would be:

• encouragement of full reporting of all the necessary metadata for data recording and

• strengthening of the use of standard methods of materials testing and data analysis.

There are three main uses to be made of metadata of this type within a computerized data system:

1 . The availability in the system of a synonym dictionary which will be used, transparent to the user, to "translate" user terms (such as property designations and units), to standardized internal system terms during search and retrieval.

2. The availability of a series of content directories covering such areas as terms, test methods, and

property titles for user viewing purposes, either prior to or during search and retrieval activities.

3. The availability of a "HELP" thesaurus, including term definitions, relationships, etc., with associated

explanatory text as covered in this report, to support the user in the intellectual aspects of accessing

and utilizing the system of databases. The specific task statement for this study included:

1 . Develop definitions of nomenclature and properties, referenced wherever possible to existing stan- dards.

Figures in brackets indicate literature references. 'This concept embraces both direct access to the network itself as well as down-loading any arbitrarily customized subset(s) of the whole

for use "off-line" in a personal computer.

1
2. Recommend new standards for reporting data.

3. Consider the desirability of recommending standard reference materials for mechanical property

determination.

4. Compile a dictionary of synonyms and cross-reference terms to mechanical properties in order to

facilitate entry to an information system.

5. Recommend standard test methods

a. where none satisfactory are found, define the need

b. where rigorous tests are impractical, because of time or cost limitations, recommend correlative

tests.

6. Distinguish, where appropriate, between properties which should be searchable vs. those which are merely retrievable with the entire record for a given material.

The organization of this report is as follows. The specific mechanical property categories considered

include:

• tensile behavior

• hardness numbers

• notch bar impact test parameters

• fatigue properties

These property categories are representative of the types of mechanical property tests most commonly

conducted and of the property parameters most frequently recorded. The tensile test shows the response of a

material (usually as a cylindrical or flat sheet specimen) to uniaxial tensile loading. Not only are many service

parts loaded essentially in pure tension but experience has shown that results of the tensile test may be used to a degree to predict behaviors under more complex circumstances. Hardness numbers are derived from indenting a material with an indentor of known geometry under a specified load. This crude but quick and

inexpensive test is very widely used, especially as an inspection tool, and often correlates well with other

mechanical properties. Notch bar impact tests measure the ability of a material to absorb energy under a rapidly

applied load and convey information not imparted by the tensile parameters. Fatigue tests measure the

resistance of a material to repeated application of stress or strain, a characteristic important in many cases of

moving machinery, for example. Each of the above categories is considered in a separate chapter with

individual referencing, figure numbers, etc., so as to facilitate later extension of the work to other mechanical

property groups in a possible supplement to the study. It is not the intent to prepare, at this time, a concise

treatise on all mechanical properties but rather to present a reconnaisance of the problems of database

compatibility and "user friendliness" in computer networking in that subject area, with only sufficient general

background as to make the report intelligible on its own.

Clearly there is much more work like this to be done. Other property areas—even some closely related to those reported on here such as fracture toughness and crack growth rates—are equally or even more important

for similar examination. Even collectively, what has been done to date represents only a generalized model

approach. In planning the interconnection of two or more specific databases one must consider what particular

terms, test methods, and derived parameters still lie outside the definitions and equivalency lists presented here. Furthermore, designation of a particular application area or user community for the system might modify the

scope of mechanical property coverage.

Finally, despite the above limitations, the extent of the study has been such that some broad recommendations can be offered. These are summarized in the executive summary at the beginning.

References

[1] Graham, J. A., "The Metal Properties Council Activities on a National Materials Property Data Net- work," in "An On-Line Materials Property Base", J. A. Graham, ed. (American Society of Mechanical Engineers, New York, 1983), pp. 1-14.

[2] Westbrook, J. H., and Rumble, J. R., eds. "Computerized Materials Data Systems," Nov. 1982, available

from OSRD, National Bureau of Standards, Gaithersburg, MD 20899.

[3] Westbrook, J. H., "Extraction and Compilation of Numerical and Factual Data," AGARD Lecture

Series #130 Development and Use of Numerical and Factual Databases, Neuilly sur Seine, France

(1984).

2
[4] Date, C. J. "Introduction to Database Systems", 3d ed. Addison-Wesley, Reading, MA (1981).

[5] McCarthy, J. L., "Metadata Management for Large Statistical Databases," Proc. 8th Int. Conf. on Very

Large Databases, Mexico City (1982) 234-243.

[6] Westbrook, J. H., "Some Considerations in the Design of Properties Files for a Computerized Materials

Information System" Proc. 9th Int. CODATA Conf, Jerusalem, Israel, June 1984 (to be published).

3
Chapter 1

TENSILE BEHAVIOR

Introduction

The behavior of a material when subjected to uniaxial tensile loading is perhaps the most common and

most informative of mechanical property tests. Basically, the deformation of the material is observed as it is incrementally stressed through the elastic and plastic regions to ultimate failure. From the specimen dimensions

and the load-deformation response, a number of different parameters may be derived (yield strength, elongation, ultimate strength, etc.) which have been adopted as descriptive of the material behavior. Such data are used for comparison of materials, for alloy development, for quality control, and for some aspects of design.

Definitions are provided in ASTM Standard E6-81, [1] extracts from which are shown below.

Definitions ([1] except as noted)

Figures 1 to 4 will aid in the interpretation of these definitions and in appreciating the distinction between

synonyms and non-synonymous terms to be discussed subsequently.

elastic limit [FL~*] { —the greatest stress which a material is capable of sustaining without any permanent

strain remaining upon complete release of the stress. ASTM Note—Due to practical consideration in determining the elastic limit, measurements of strain,

using a small load rather than zero load, are usually taken as the initial and final reference.

elongation —the increase in gage length (Note 1) of a tension test specimen, usually expressed as percentage

of the original gage length.

ASTM Note 1 —The increase in gage length may be determined either at or after fracture, as specified for the material under test. ASTM Note 2—The term elongation, when applied to metals, generally means measurement after fracture; when applied to plastics and elastomers, measurement at fracture. Such interpretation is usually

applicable to values of elongation reported in the literature when no further qualification is given.

ASTM Note 3 —In reporting values of elongation the gage length shall be stated.

modulus of elasticity [FL'2

] —the ratio of stress to corresponding strain below the proportional limit. (Author's note: for other types of modulus, secant modulus, tangent modulus, etc., see fig. 1)

Kinetic Modulus

Figure 1. Relationship of stress-strain curve to kinetic modulus (after Kasper et al., SAE Tech Paper 790003 (1979)).

'Dimensional analysis; F = force, L = lineal dimension
Poisson's ratio —the absolute value of the ratio of transverse strain to the corresponding axial strain resulting from uniformly distributed axial stress below the proportional limit of the material.

ASTM Note 1 —Above the proportional limit, the ratio of transverse strain to axial strain will depend on

the average stress and on the stress range for which it is measured and, hence, should not be regarded as Poisson's ratio. If this ratio is reported, nevertheless, as a value of "Poisson's ratio" for stresses beyond the

proportional limit, the range of stress should be stated. ASTM Note 2—Poisson's ratio will have more than one value if the material is not isotropic.

proof stress [FL ~ 2

] —the stress that will cause a specified small permanent set in a material. (From ASM

Handbook, 9th ed.) (See fig. 2.)

proportional limit [FL _2] —the greatest stress which a material is capable of sustaining without any deviation from proportionality of stress to strain (Hooke's law). (See fig. 2 .) ASTM Note—Many experiments have shown that values observed for the proportional limit vary greatly

with the sensitivity and accuracy of the testing equipment, eccentricity of loading, the scale to which the

stress-strain diagram is plotted, and other factors. When determination of proportional limit is required, the

procedure and the sensitivity of the test equipment should be specified.

Ol 02 0 3 0 4 STRAIN

Figure 2. Stress-strain relationship showing 0.1% and 0.2% proof stress, and proportional limit

(after Merriman, "Concise Encyclopedia of Metallurgy" McDonald and Evans (1965)).

reduction of area—the difference between the original cross-sectional area of a tension test specimen and

the area of its smallest cross section (Note 1). The reduction of area is usually expressed as a percentage of the

original cross-sectional area of the specimen.

ASTM Note 1—The smallest cross section may be measured at or after fracture as specified for the

material under test. ASTM Note 2—The term reduction of area when applied to metals generally means measurement after

fracture; when applied to plastics and elastomers, measurement at fracture. Such interpretation is usually

applicable to values for reduction of area reported in the literature when no further qualification is given.

strain-hardening exponent (n)—the exponent in the empirical relationship between true stress and true

strain, <x = Ken

. It is computed as the slope of the assumed linear relationship between logarithm true stress and

logarithm true strain.

2 [2]

: True stress is load divided by instantaneous cross-sectional area [prior to necking, <r = S(l +e)] and true strain is the natural logarithm of the ratio of the length at the moment of observation to the original gage length, [e = ln(l +e)].
strain rate exponent* (m) —the exponent in the empirical relationship between true stress and strain rate,

ar = Kem

, taken at constant strain, e. It is computed as the slope of the assumed linear relationship between

logarithm true stress and logarithm true strain rate.

tensile strength [FL~ 2

] —the maximum tensile stress which a material is capable of sustaining. Tensile

strength is calculated from the maximum load during a tension test carried to rupture and the original

cross-sectional area of the specimen.

true fracture stress [FL ~*]—the true normal stress on the minimum cross-sectional area at the beginning of

fracture. (Author's note: This value must be corrected for the effect of triaxial stress once necking has begun.

One such correction has been suggested by Bridgman.)

ASTM Note—This term usually applies to tension tests of unnotched specimens.

yield point [FL ~*\ —the first stress in a material, less than the maximum attainable stress, at which an

increase in strain occurs without an increase in stress. ASTM Note—It should be noted that only materials that exhibit the unique phenomenon of yielding have

a "yield point."

yield strength [FL _2] —the stress at which a material exhibits a specified limiting deviation from the

proportionality of stress to strain. The deviation is expressed in terms of strain.

ASTM Note—It is customary to determine yield strength by:

(a) Offset Method (usually a strain of 0.2% is specified), (see fig. 3) (b) Total-Extension-Under-Load Method (see fig. 4; usually a strain of 0.5% is specified although

other values of strain may be used). An equation for calculating strain is:

x = [Y/E +specified offset (strain)] X 100

where:

x = limiting strain, in percent,

Y = specified yield strength, in psi, and

E= nominal modulus of elasticity of the material, in psi.

(This strain, x, is multiplied by the gage length to determine the total extension under load.)

Whenever yield strength is specified, the method of test must be stated along with the percent offset or the

total strain under load. The values obtained by the two methods may differ.

} Not defined by ASTM; composed by author.

6
om = Specified Offset

Figure 3. Stress-strain diagram for determination ofyield strength by the offset method (ASTM A-370-77).

om = Specified Extension Under Load

Figure 4. Stress-strain diagram for determination ofyield strength by the extension-under-load method (ASTM A-370-77).

7
Data Analysis

Where it is desired to have a more complete analytical description of tensile behavior, other methods can

be employed. For engineering stress-strain properties beyond yielding, the so-called Ramberg-Osgood equation [3]

4 is often used:

e = S/E +0.002 (S/Sy )

r (1)

where e = strain Sy =0.2% offset yield stress S =stress r = Ramberg-Osgood exponent5 E = elastic modulus

Analytical methods for determination of r are discussed in Mil Handbook 5 [4]. In the plastic region, true stress and true strain are related by an empirical expression

o- = o-0€

n (2)

where cr = true stress

o-0 =a constant

e = true strain n =strain hardening exponent

Analogously, engineering stress-strain in the plastic region may be represented by a power law, up to the point

of maximum load

S = Aep (3)

where A =strain hardening coefficient

p =strain hardening exponent

The functional equivalence of eq (3) and eq (1) is readily seen by algebraic manipulation.

Even when no attempt is made to record the full stress-strain curve, notation is frequently made of the

strain hardening exponent n or p. Likewise strain rate sensitivity is measured by the exponent, m, in the

expression

<T = Kem

(4)

where e = strain rate K = constant

By modification of the test specimen or apparatus, it is possible to conduct a tensile test under conditions

of plane strain to which many practical sheet forming operations approximate. Such tests, as described by Sang

and Nishikawa [5] can yield both the plane strain limit strain and the ductility in plane strain.

It should be noted that, in analysis of experimental data according to equations such as (1) to (4) involving

exponentials, least squares treatment of linear relations in a log-log plot biases the results due to the fact that equal weight is given to the least accurate portion of the records, the low values of strain or strain rate.

Synonyms

In design of computerized systems it is important, both in the loading of data from diverse sources as well

as to accommodate the varied terminology employed by different users, that the system be provided with

thesauri which allow automatic translation of terms frequently encountered. To this end we list here

synonymous terms for each of the major parameters associated with each class of properties. Also noted are other terms of possible relevance which should not be confused with the parameter in question.

4 Other functional representations have also been proposed, for example: Voce <t = a + (b —a)[ 1 — exp( — ce)] and Swift cr = c(a + e)n where a,b,c and n are constants and e is true strain.

5 n is often used but is replaced here by r to avoid confusion with the strain hardening exponent n.

8
Synonymous Terms

Yield Strength

Yield

Y.S.

Tensile yield

Proof stress P.S.

F,„

Not Synonymous

Yield point

Upper yield

Lower yield

Flow stress

Tensile Strength

Ultimate strength

U.T.S.

U.S.

Tensile strength

Ultimate tensile strength

Maximum tensile stress Tenacity

Tensile ultimate

Ftu

True Fracture Stress Breaking strength

Breaking stress Fracture strength Fracture stress

Rupture strength

Modulus of rupture

Maximum fiber stress

Rupture strength

Modulus of rupture

Rupture modulus

Modulus of Elasticity

Elastic modulus

Young's modulus

Modulus of extensibility

Stretch modulus

Monotonic modulus

Static modulus

Tensile modulus

Coefficient of elasticity

Tangent modulus

Secant modulus

Chord modulus

Initial tangent modulus

Dynamic modulus

Kinetic modulus

Elongation

Elongation at break

Elongation at fracture

Ductility

Tensile ductility

Tensile elongation

e

True fracture ductility

Reduction ofArea

R.A.

Area reduction

Reduction in area

Poisson s Ratio

Poisson's ratio Plastic strain ratio Poisson's number

Proportional Limit

Limit of proportionality Elastic limit

Elastic Limit

Proportional limit

9
Strain Rate Exponent

Strain rate sensitivity

m

Strain Hardening Exponent

n

Standard Test Methods

The tensile test is based upon well-established test methods, both because of its long history of use and its wide application. The basic test method for tension testing of metallic materials is ASTM E8-82 [6]. This

document is supplemented by the following ASTM test methods:

Those specific to various material classes:

Ref.

Steel A370 [7] Copper alloys B598 [8] Aluminum and magnesium alloys B557 [9] Aluminum and magnesium alloys (metric) B557M [10]

Those specific to form:

Foil E345 [11] Fasteners F606 [12]

Wire F113, F219 [13,14]

Those specific to particular test conditions:

Sharp notch sheet E338 [15] Sharp notch cylindrical bar E602 [16] Elevated temperature E21 [17]

Those specific to particular parameters:

Plastic strain ratio E517 [18]

Poisson's ratio El 32 [19] Young's modulus E231 [20] Young's modulus, tangent El 11 [21]

modulus and chord modulus

Strain hardening exponent E646 [2]

These procedural standards provide for testing of foil, sheet, plate, wire and round specimens in both

standard and subsizes. A point of importance is that for the common cylindrical test bars the gage length to diameter ratio needs be maintained at 4: 1 if elongation values are to be comparable. It should be noted further

that European and Japanese practice is for a 5:1 ratio, which has been adopted for ISO standards and may

become future ASTM practice. One way of estimating 5D elongation from 4D data is described below under

correlations

Standards for Reporting Data

In order that tensile data be fully assessable they must be completely documented; that is, it is necessary

that results be accompanied by a full description of material, specimen, test method, and data reduction

techniques. Curiously, despite all the detail provided on recommended test methods in ASTM standards for

tensile testing, most such standards are silent or carry only implied guidance as to reporting of data. A notable

10
exception is that on elevated temperature tensile testing [17], the pertinent section of which is quoted in full below because of its useful detail:

11. Report

11.1 The report shall include the following:

11.1.1 Description of material tested, including method of manufacture,

type and size of product, and other pertinent processing information, as well

as heat treatment, microstructure, and chemical composition.

11.1.2 Specimen dimensions, including cross-sectional dimensions, fillet radius, length of reduced section, adjusted length of reduced section (if used),

type of end connection, and whether machined, partially machined, or as

cast.11.1.3 Temperature of test. 11.1.4 Strain rate during yielding and strain rate after yielding.

11.1.5 Yield strength, if required, and drop-of-beam yield point if such a

yield point occurs.

11.1.5.1 When one or more values of yield strength are required, the

amount of the offsets should be shown with the numerical values.

11.1.5.2 If the extensometer was attached to the specimen shoulders, this fact should be stated in a footnote to the values.

11.1.5.3 If an extensometer was not attached directly to the specimen, the

value should be listed as approximate yield strength (offset =0.2%).

11.1.6 Tensile strength.

11.1.7 Elongation and gage length. If elongation was measured from gage

marks not on the reduced section of the specimen this fact should be included

in the designation of the quantity, for example "elongation from shoulder

measurements" or "elongation from overall measurements." If elongation was measured from the extensometer record at fracture instead of after fracture, this should be noted.

11.1.8 Reduction of area for specimens with circular cross section.

11.1.9 Time to attain test temperature and time at temperature before

testing. 11.1.10 Other special conditions, such as nonstandard atmosphere and

heating methods, exceptions to required dimensional accuracy and axiality of

loading, amount and duration of temperature overshoot.

11.1.11 Location and description of fracture. The description should in- clude any defects, evidence of corrosion, and type of fracture (such as cup

and cone, brittle, shear). 11.1.12 Identification of equipment used including make and capacity of

testing machine, make and class of extensometer, make and size of furnace,

type of temperature controller, and description of thermocouples including

material, wire size, attachment, technique and shielding. 11.1.13 Name of tester and date of test.

While this text might in general be taken as a model for reporting of tensile data, it too is incomplete in some

respects:

a) orientation and location of the sample relative to the original stock (e.g. rolling direction, location

in a casting, forging, etc.). b) surface finish in gage length (variability in test results in specimens of high strength and low ductility is particularly attributable to this factor).

c) method of calculating or determining specific parameters (often covered in specification of test method but should appear in reporting of data where pertinent).

1 !
d) estimated precision of the results. e) recommendations for rounding of test data. An example from ASTM's steel testing standard is appropriate:

Table 1. Recommended values for rounding test data

Test Quantity Test Data Range

Level of Rounded ValueA

up to 50 000 psi, excl. 100 psi 50 000 to 100 000 psi, excl. 500 psi Yield Point, 100 000 psi and above 1000 psi Yield Strength, Tensile Strength up to 500 MPa, excl. 1 MPa

500 to 1000 MPa, excl. 5 MPa

1000 MPa and above 10 MPa

Elongation 0 to 10%, excl. 0.5%

10% and above 1%

Reduction of Area 0 to 10%, excl. 0.5%

10% and above 1%

A Round test data to the nearest integral multiple of the values in this column. If the data value is exactly midway between two rounded values, round to the higher values.

Precision and Accuracy

Despite the long history of use of tensile testing, no body of reliable test data exists to form a basis for determination of precision and accuracy. Almost every ASTM tensile testing standard comments on this point

and notes that precision is "being established." No such results have been found in its literature. Standard

reference materials* available for testing of tensile parameters, with certified values of their tensile data, would

be very valuable in establishing accuracy and precision and in distinguishing between material variability and

test variability. None such exists at present. It is recommended that the Standard Reference Materials Program

at NBS investigate the feasibility of producing and certifying such standards.

Correlations

Hardness. The property which is most often correlated with tensile parameters is hardness, largely

because of its convenience as a quality control tool. A typical result is shown in figure 5. Unfortunately such

correlations are not broadly generalizable but are restricted to a narrow family of materials with similar elastic constants, work hardening characteristics, etc. Nonetheless if this restriction be realized and accepted, the

correlation can be a very useful one. A particular problem with such correlations arises with the possible

absence of through-hardening in large sections of certain steels resulting in a hardness gradient. Other kinds of

gradients in the thickness direction (grain size, texture, residual stresses, etc.) can also affect the correlation

between tensile properties and surface indentation hardness.

Elongation, Round to Flat. A procedure for conversion of percent elongation in a standard cylindrical

tensile bar to that for a standard flat test specimen is incorporated in ASTM standard for testing of steel [7]. This relationship is expressed as:

ef =eG(4.47 VX/L)3

where ef = elongation in flat specimen of gage length L and cross-sectional area A

eQ =elongation in cylindrical specimen with 2" gage length and 0.500" diameter

a=a constant characteristic of the test material

Elongation, conversion of 4D to 5D elongations [22,23]. Two steel alloys are compared to illustrate differ- ences in material response to testing. The numbers shown in the calculations and tables below pertain only to the specific materials used for illustration and are not to be applied elsewhere. The approach, however, is generalizable.

12
46

44

42

40

38

3634

3230

28

26

242220

1 8

1 6

I 4

I 2

1 0

*

*

A*

/

A

r

1 1 A • 8630 steel, quenched and tempered

o 8630 steel, normalized A 8630 steel, quenched and tempered - A 8630 steel, normalized _ 8630 steel, quenched and tempered

8630 steel, normalized

i i i i i i i 1 i i 100 120 140 160 180 200

Ultimate tensile strength, ksi

220

Figure 5. Tensile strength versus hardness for 4340 and 8630 steel. Reference curve plotted from ANC-5

"Strength of Aircraft Elements," Govt. Printing Office, Washington, DC (1955) p. 4.

Adjusted only for strain in the increased gage length, the values of elongation in 5D are as shown below:

elongation %

Measured Calculated Measured

at 4D for 5D from 4D at 5D

Low alloy steel 16.0 13.8 14.5 Carbon steel 31.0 27.4 27.5

It would be expected that the tensile strength, yield strength, and reduction in area would be the same for two specimens tested, if one assumes no strain in the added gage length. A more accurate assumption is that the unit strain in the added length is equal to the "uniform strain" where uniform strain is defined as the unit

strain before neck down. However, it can be shown that significant differences in tensile properties of some

materials occur in specimens taken side by side. In the case of carbon steels, the tensile results are within the expected range of repeatability for uniform material and the calculated result for elongation in 5D agrees very

well with the measured result. For low alloy steels, the agreement is not good when the 4D properties are used directly. The calculated

value for 5 D is 13.8 while the measured is 14.5. However, the yield strength is lower and the reduction in area

is higher for the 5D specimen than for the 4D specimen indicating that the material responds differently. A

higher elongation is to be expected for the 5D material even if the same gage length is used for both specimens.

Therefore, the difference between the calculated and measured 5D elongation is qualitatively consistent with

the difference in the strain of the two specimens as shown by the other tensile properties.

Material Properties 4D gage length 5D gage length

Low Tensile Strength (T) ksi 154.0 156.0 Alloy Yield Strength (Y) ksi 139.0 135.0

Steel Elongation (E) percent 16.0 14.5 Red. of Area (R) percent 48.6 50.1

To quantitatively estimate this difference, the uniform strain is calculated from the yield strength, tensile strength and the reduction of area of each material separately using an empirical formula (1) below. Then the

elongation for each material is calculated at 4D and the measured elongation at 4D multiplied by the ratio of

13
these calculated values to adjust for material differences [formula (2)]. Then this adjusted elongation is used to calculate the elongation at 5D using the other tensile properties measured on the material tested at 5D [formula

(3)]. It is possible to estimate the elongation at 5D from that measured at 4D with useful accuracy for normal

structural steels using the following scheme (only for structural steels):

4.33(1 +0.01U)084 -pO.84—

U°'

51 ^

Solve for U

For 4D: U' =4.8 16%

For 5D: U" = 5.242%

U= , *f +0.001 E

2 (2) Ve2 +r2 V '

Solve for E

For 4D: E'= 15.32% in 4D

For 5D: E" = 16.21% in 4D

Measured elongation in 4D corrected for material difference is:

(16.0) (j||^ = 16.93%

E5D =0.8 E4D +0.2U (3)

Sample Calculation:

Using (2)

U =^=(16

f

3)2 + (0.001)(16.93)

2 = 5.706%

V(16.93)2 + (50.1)

2

From (3) E5D = (0.8)( 1 6.93) + (0.2)(5.706) = 14.7%

As is shown, the calculated value of 14.7 now agrees well with the value of 14.5 obtained from actual

testing using a 5D gage length.

Modulus of Elasticity . The value derived from the tensile test itself is sometimes referred to as the static modulus. Alternatively a dynamic modulus may be determined in one or the other of two different types of

experiment. In the first a specimen is put in resonance (Kilocycle frequencies and about 0.01 kg/mm2 peak

stress) and the modulus calculated from the theory of resonance. In the second, wave pulses, whose wavelength

is small compared to specimen dimensions, are propagated through a specimen and their transit time measured.

Frequencies are in megacycles and peak stresses are about 0.001 kg/mm2 or less. Dynamic values do not always

agree closely with static values of the modulus. Attenuation due to grain size effects is one complication. A

definitive comparison of modulus data obtained by tests over a wide variety of materials with these techniques

has not yet been attempted. It must also be remarked that elastic modulus may also be obtained by x-ray

diffraction techniques even with very small samples. In general, however, these results are less precise and may

not conform to the more direct, mechanically derived values because they sample only an arbitrary fraction of

randomly (?) oriented grains whose orientations happen to be favored for diffraction of the x-rays.

References

[1] ASTM E6-81 "Standard Definitions of Terms Relating to Methods of Mechanical Testing".

[2] ASTM E646-78 "Tensile Strain-Hardening Exponents (n-values) of Metallic Sheet Materials".

[3] Ramberg, W. and Osgood, W. R., "Description of Stress-Strain Curves by Three Parameters" NACA

TN 902, July 1943.

14
, Military Standardization Handbook, Mil Handbook 5C, "Metallic Materials and Elements for Aerospace Vehicle Structures" (1976) with supplements.

Sang, H. and Nishikawa, Y., "A Plane Strain Tensile Apparatus" /. Metals (1983) 30. ASTM E8-82 "Tension Testing of Metallic Materials".

ASTM A370-77 "Mechanical Testing of Steel Products".

ASTM B598-74 "Offset Yield Strength for Copper Alloys".

ASTM B557-81 "Tension Testing of Wrought and Cast Aluminum and Magnesium Alloy Products".

ASTM B557M-81 "Tension Testing Wrought and Cast Aluminum and Magnesium Alloy Products

(Metric)".

ASTM E345-81 "Tension Testing of Metallic Foil".

ASTM F606-79A "Conducting Tests to Determine the Mechanical Properties of Fasteners. . . ." ASTM Fl 13-65 "Stiffness Testing of Wire for Electron Devices and Lamps".

ASTM F2 19-79 "Testing Fine Round and Flat Wire for Electron Devices and Lamps".

ASTM E338-81 "Sharp Notch Testing of High-Strength Sheet Materials".

ASTM E602-81 "Sharp Notch Testing with Cylindrical Specimens".

ASTM E21-79 "Elevated Temperature Tension Test of Metallic Materials".

ASTM E5 17-81 "Plastic Strain Ratio r for Sheet Metal".

ASTM El 32-61 "Poisson's Ratio at Room Temperature".

ASTM E231-69 "Static Determination of Young's Modulus at Low and Elevated Temperatures".

ASTM El 11-82 "Young's Modulus, Tangent Modulus and Chord Modulus".

AK Schmieder (private communications).

Rudolf, W. . "Comparison of Mechanical Properties Determined According to DIN Norms and to ASTM

Specifications" Praktiker (4), (1981) 80.

15
Chapter 2

HARDNESS NUMBERS

Introduction

Hardness differs from most other mechanical properties of metals in that it is never used directly in a design

calculation and only seldom is a parameter involved in final materials selection. Nonetheless it is one of the most

frequently used (an estimated 50 million tests performed each day in the United States [1]) and most frequently

recorded mechanical characteristics and hence cannot be ignored. Yet it is scoffed at by many scientists as being an unanalyzable complex of many mechanical properties and not susceptible to fundamental interpretation. The

explanation for this apparent contradiction may be found in the many practical advantages attendant to the

hardness test:

• simplicity of application with saving of labor, time and expense

• convenience—simple, often portable, equipment sometimes permitting testing in situ

• non-destructiveness

• small effective sample size

• direct correlation with service performance

These attractive features make it preeminent for two broad classes of application: initial screening for deter- mination of suitability of a material for a given purpose and maintenance of product uniformity (i.e. processing

and compositional controls).

Systematic tests for measurement of hardness date back at least to Reaumur (1722). The methods that have

been devised over the years include a) abrasion, b) penetration, c) elastic, d) magnetic, and e) electrical types.

Of these, the penetration or indentation type is far and away the most widely used; the remainder of the

discussion will be confined to this type.

Common to all the indentation tests is the concept that an indenter of known geometry is impressed upon

a flat, smooth surface of the specimen and subjected to a known load, applied perpendicular to the specimen

surface. The extent of penetration is determined either concurrently or subsequently by measurement of the

depth or diametral extent of the indentation produced. The various standard tests which have been developed over the years differ primarily in indenter material and geometry, load and method of loading, and means of

characterizing the resultant indentation. For these reasons, as well as the fact that any hardness test is measuring

a combination of mechanical properties, the interconvertibility of the different hardness scales is usually poor

and always questionable.

Socalled micro-indentation hardness testing, using loads less than 1 kg, is more often applied in scientific studies than engineering work (except for coatings) and therefore will not be discussed here.

Indentation Hardness 1 —the hardness as evaluated from measurements of area or depth of the indentation

made by pressing a specified indenter into the surface of a material under specified static loading conditions.

Brinell Hardness Test

2 —an indentation hardness test using calibrated machines to force a hard ball, under

specified conditions, into the surface of a material under test and to measure the diameter of the resulting

impression after removal of the load.

Brinell Hardness Number, HB1 —a number related to the applied load and to the surface area of the

permanent impression made by a ball indenter computed from the equation:

Definitions

HB = 2P/ttD(D - VD2 -d

2

)

where:

P = applied load, kgf,

D= diameter of the ball, mm, and

d = mean diameter of the impression, mm.

Ball diameter

Load

Duration of loading

3000 kgf

10 to 15 s

10 mm

'See ASTM E6-81

2 Sec ASTM E10-78

16
For other conditions, the hardness numbers and symbol HB are supplemented by numbers indicating the

test conditions in the following order: diameter of ball, load, and duration of loading.

Rockwell Hardness Test*—an indentation hardness test using a calibrated machine to force a diamond

spheroconical penetrator (diamond penetrator), or hard steel ball under specified conditions, into the surface

of the material under test in two operations, and to measure the permanent depth of the impression under the

specified conditions of minor and major loads.

Rockwell Hardness Number, HR 3 —a number derived from the net increase in the depth of impression as the load on a penetrator is increased from a fixed minor load to a major load and then returned to the minor

load. This number must always be associated with a particular scale symbol which implies the penetrator, load,

and dial used in the test.

Note 1 —Penetrators for the Rockwell hardness test include a diamond spheroconical penetrator having an included angle of 120° with a spherical tip having a radius of 0.20 mm and steel balls of several specified

diameters.

Note 2—Rockwell hardness numbers are always quoted with a scale symbol representing the penetrator,

load, and dial used.

Vickers Hardness Test*—an indentation hardness test using calibrated machines to force a square-based

pyramidal diamond indenter having specified face angles, under a predetermined load, into the surface of the

material under test and to measure the diagonals of the resulting impression after removal of the load.

Vickers Hardness Number, HV4—a number related to the applied load and the surface area of the per- manent impression made by a square based pyramidal diamond indenter having included face angles of 136° computed from the equation:

HV= 2P sin (a/2)/d2 =1.8544P/d2

where:

P =load, kgf,

d =mean diagonal of impression, mm, and a = face angle of diamond =136°

NOTE—The Vickers pyramid hardness number is followed by the symbol HV with a suffix number

denoting the load and a second suffix number indicating the duration of loading when the latter differs from the normal loading time, which is 10 to 15 s.

Synonyms

Vickers hardness number

VHN

HV

Diamond Pyramid Hardness (DPH)5 DHN

DPN5

Brinell hardness number

Brinell

BHN

HB

Rc

Rockwell hardness number

HRC, HRB, etc.

3 See ASTM E18-79

"See ASTM E92-82

5 Some writers distinguish DPH and DPN from HV or VHN in that projected rather than pyramidal area is used in calculating the hardness number. This is by no means the general practice.

17
Standard Test Methods

The three principal indentation hardness techniques have been thoroughly defined by the standards setting

bodies as follows:

ASTM B.S. ISO

Brinell E10-78 240-1962 R6505-1981

Rockwell E18-79 891-1962 R80-1968, 2713-1973

Vickers E92-82 427-1961 R8 1-1967

R192-1971

R399-1964

In addition to specifying indenter geometry tolerances, loading, calibration and readout procedures, the

other important factors covered by the standard test methods are the preparation of the specimen surface and

the requisite size of the effective sample relative to the size of the indentation. The latter requirement implies

a minimum thickness of the specimen, a minimum separation of indentations and a minimum spacing of any

indentation from the edge of the specimen. Factors that may not be adequately controlled, despite conformance

otherwise with the testing specification, include vibration, rate of loading or time of indentation. Choice of a load/ball combination inappropriate to the hardness level of the specimen may also be a factor in ball indentation. For the Rockwell test, the combinations of table 1 are specified.

Table 1. Rockwell test scales, indenting conditions, and typical applications

Scale Symbol

Penetrator Major

Load,

kgi

Dial Fig- ures Typical Applications of Scales

B '/ih-in. (1.588-mm) ball 100 red Copper alloys, soft steels, aluminum alloys, malleable iron. C diamond 150 black

etc. Steel, hard cast irons, pearlitic malleable iron, titanium, deep

case hardened steel, and other materials harder than B 100 A diamond 60 black Cemented carbides, thin steel, and shallow case-hardened

steel. D diamond inn black Thin steel and medium case hardened steel, and pearlitic malleable iron. E

l/x-in. (3.175-mm) ball 100 red Cast iron, aluminum and magnesium alloys, bearing metals. F V,H-in. (1.588-mm) ball 60 red Annealed copper alloys, thin soft sheet metals. G fts-in. (1.588-mm) ball 15(1 red Malleable irons, copper-mckel-zinc and cupro-nickel alloys. Upper limit G 92 to avoid possible flattening of ball.

11 '/x-in. (3.175-mm) ball 60 red Aluminum, zinc, lead. K 'A-in. (3.175-mm) ball 150 red

1 'A-in. (6.350-mm) ball 60 red M Vt-in. (6.350-mm) ball 100 red Bearing metals and other very soft or thin materials. Use

P 'A-in. (6.350-mm) ball 150 red smallest ball and heaviest load that does not give anvil R

l/2-in. ( 12.70-mm) ball 60 red effect. s '/.-in. (12.70-mm) ball 11)0 red V l/2-in. (12.70-mm) ball 150 red

For the Brinell test, the load is selected for a particular ball diameter to give the ratio of indentation diameter

to ball diameter approximating the ideal of .375.

Table 2. Standard Brinell Test Loads (ASTM E10-78)

Ball Diameter, Recommended Range,

mm Load, kgf HB

10 3000 96 to 600

10 1500 48 to 300

11) 500 16 to 100

18
Standards for Reporting Data

The data report should include beside the hardness number, the test conditions regarding load, indenter

and time of loading whenever these differ from conditions required by the testing specifications. In addition,

although not called out in these documents, assurance should be given that processing conditions were such as to yield a homogeneous specimen, both laterally in the test surface and in depth (at least to distances sensed by

the penetrating indenter).

Precision and Accuracy

Examples of the repeatability which should be achievable under the Rockwell and Vickers tests are shown

in tables 3 and 4. Standard reference blocks, referred to in the tables, having certified hardness values and

exceptional uniformity, are available from many hardness tester manufacturers.

Table 3. Repeatability of the Rockwell hardness test

Range of Standardized Hardness Test Blocks

The Repeatability" of

the Machine Shall Be Not Greater Than:

Rockwell C Scale: 20 to 30 2.0 35 to 55 1.5 59 to 65 1.0 Rockwell B Scale: 40 to 59 2.5 60 to 79 2.0 80 to 100 2.0 Rockwell JON Scale: 40 to 50 2.0 55 to 73 1.5 75 to 80 1.0 Rockwell 30T Scale: 43 to 56 2.5 57 to 70, incl 2.0 Over 70 to 82 2.0

* The repeatability of machines on Rockwell or Rockwell

superficial hardness scales other than those given in Table 20

shall be the equivalent converted difference in hardness for those scales, except for the 15N and I5T scales. In the case of the 15N and 15T scales, the repeatability shall be no

greater than 1.0 for all ranges. Example—At C 60, typical readings of a series of impressions might range from 59 to 60, 59.5 to 60.5, 60 to 61, etc. Thus, converted A-scale values corresponding to C 59 to 60

(see Table II of Standard Tables E 140) would be A 80.7 to 81.2 and the repeatability for the A-scale would be 0.5.

Table 4. Repeatability of the Vickers hardness test

Range of Standardized Hardness of Test Blocks

The Repeatability of

the Machine Should

be Less Than:

Examples of Equivalents in Hardness

Units

100 to 240, incl 4% 0{dAM

8 at 100 HV; 16 at 200 HV

Over 240 to 600, incl 3%o(dAU 18 at 300 HV; 36 at 600 HV

Over 600 2%o[dAM 28 at 700 HV

" d = (d, + d, + ... + rfr,)/5. * In all cases the repeatability is the percentage given or 1 |xm (0.001 mm), whichever is the greater.

19
Correlations

Because of the great variety of hardness tests in use and the existence of different scales for the same basic

test, there is naturally a great desire for interconversion. Yet recognition of the fact that hardness is not a fundamental property but a combination of several properties whose mix changes from test to test foredooms

any exact conversion to failure. For example, differences in elastic modulus or in strain hardening capacity of

different metals will inevitably cause differences in the hardness conversion relationships. Even differences in the state of cold work of a single material will affect the conversion. Despite these difficulties, hardness

conversion tables for various families of materials have been published by the standardizing bodies (ASTM

E 140-79 and BS860). All such tables, charts or graphs should be employed with great caution and viewed as estimates only, in the absence of a direct, ad hoc calibration for the particular material and pair of tests at hand.

Correlations of hardness with other properties of a material are also inexact for the same reason but are nonetheless useful. For example, the fact that electrical and magnetic properties are sensitive to composition,

mechanical and thermal treatment as is hardness opens the way to non-contact measurement of relative hardness. Such comparative techniques are generally satisfactory for inspection control of a given material or

for scrap sorting.

Correlations of hardness with other mechanical properties are more direct and in that sense more useful even though inexact and perhaps confined to a narrow family of materials. Examples are shown in figures 1 to 3.

Figure 1. Correlation lines for metals and ionic crystals relating hardness numbers and yield stresses (after J. H. Westbrook [2]).

20
10 ;

10

BULK MODULUS

SLOPE ^2 - 7

/

I SiC

G« ^ /

/

I

Si

GoSb> / T >I

/

/"r*— In At

Al Sb /

1

Go At

- InP

-In Sb

Sn(gr»y) /

V /

i r

o

' Pd S Al

10 ;

YOUNG'S MODULUS

SLOPE I

10* ELASTIC MODULUS (kg/mm 2 )

Figure 2. Correlation of hardnesses and elastic moduli for pure fee metals and covalent crystals (after J. J. Gilman [2]).

4

10 20 30

COEFFICIENT OF EXPANSION x I0 6

Figure 3. Vickers hardness softening coefficient (B) for metals (including low-expansion alloy, Nilo 36) and thermal coefficient of expansion

(Petty and O'Neill, Metallurgia, Jan. 1961 [3]).

21
References

[1] Petty, E. R., "Hardness Testing" in Techniques of Metals Research v, part 2, R. F. Bunshah, ed., Interscience, NY (1971) 157.

[2] Westbrook, J. H., and Conrad, H., eds., "The Science of Hardness Testing and Its Research Applications," ASM, Metals Park, OH (1973).

[3] O'Neill, H., "Hardness Measurement of Metals and Alloys," Chapman and Hall, London (1967).

[4] Williams, S. R., "Hardness and Hardness Measurements," ASM, Cleveland, OH (1942).

22
Chapter 3

NOTCH BAR IMPACT TEST PARAMETERS

Introduction

It was discovered quite early that catastrophic failures sometimes occurred in structural members where

the mean stress was clearly well below the yield stress as measured in a conventional tensile test. In practice

such failures were alarming, not just because they were not predictable from prior testing, but also because little warning by way of deformation preceded failure and the failure itself was a low energy process. Further

experience indicated that failures of this type, particularly in ferrous materials, were associated with the

presence of notches, with high rates of loading and with low temperatures. Such observations were not always

correctly interpreted: notches introduce extra rigidity, not simply stress concentration; high strain rates are not

intrinsically embrittling but they do raise the temperature at which brittle failure occurs. In any event both

materials engineers and designers finally recognized that a new type of test was needed to characterize this behavior [1]. The beam loaded impact test, as a measure of toughness or energy absorption capacity, was introduced by

Tetmajer in 1883 and brought to its current form by Izod in 1903 and Charpy in 1904. The latter tests differ both in mode of loading (cantilever beam vs simple beam) and in notch geometry (V-notch vs U-notch vs keyhole notch) as shown in figure 1 . Although the original hope that parameters from such tests might be used

directly in design calculations has now been vitiated, the value of the Charpy V-notch (CVN) test as a reliable comparative measure of the impact behavior of materials has never been greater. It is only this form of impact

test that will be addressed here.

Charpy U-notch specimen

Figure 1. Dimensional details of Izod and Charpy test specimens as called for in ASTM E23-82 (from ASM Handbook, 8th ed.).

23
An important aspect of this test is that steels and other strong materials frequently exhibit a suddenly

reduced capacity for energy absorption as the temperature is lowered in the vicinity of room temperature. This

characteristic behavior has led to some debate as to which parameters of the impact strength-temperature curve

are most useful in characterizing material behavior or should the entire curve be somehow represented

analytically. Oldfield [2] has proposed representing the Charpy-temperature characteristic by the function

Y=A+ B tanh

where Y is the fracture property (CVN energy, % shear, or lateral expansion), A, B, C and T0 are constants and T is the test temperature. From the representation shown in figure 2, it may be seen that A + B and A —

may be taken as the upper and lower shelf energies respectively and that T0 is the transition temperature

corresponding to an energy median definition (see below). Not only was this function found to give a fair representation of a wide variety of impact data but the fitting parameters can be transformed by a specified

procedure [2] to produce an analogous function predicting the fracture toughness relationship, both mean

values and tolerance bounds.

-c | + c

T

o TEMPERATURE, T

Figure 2. Schematic of the hyperbolic tangent function representing the temperature dependence of impact toughness (after Oldfield [3]).

Mention must also be made of the so-called "instrumented Charpy impact test" which can provide

load-time information as well as energy absorption [4]. This additional information is derived from strain gages

applied to the Charpy striker and read out through an oscilloscope. By analysis of the load-time trace, the total energy absorbed can be divided into the energy required to initiate fracture, the energy to propagate brittle fracture and the energy associated with the shear-lip formation.

Definitions'

Impact Value —The energy absorbed in breaking the specimen, equal to the difference between the energy

in the striking member of the impact apparatus at the instant of impact with the specimen and the energy

remaining after breaking.

'Neither ASTM E6-81 (Standard Definitions of Terms Relating to Methods of Mechanical Testing) nor ASTM E23-82 (Notched Bar Impact Testing) contains these definitions in explicit form. These definitions have been composed by the author.

24
Transition Temperature —That temperature at which a material exhibits a transition from ductile to brittle behavior as variously defined:

Average Energy Transition Temperature —The temperature corresponding to the median between the maximum energy (high temperature region) and the minimum energy (low temperature region).

Temperature for Stated Energy Absorption —The temperature at which an arbitrary level of energy is absorbed, typically 15 or 30 ft. lbs. Gross [5] has suggested that this level should be increased with

increasing tensile strength so as to ensure a constant notch ductility (lateral expansion).

Average Temperature Transition Temperature —The median temperature of the transition temperature

range.

Fracture Appearance Transition Temperature (FA TT) —The temperature at which the ratio of the area of fibrous (shear) to crystalline (cleavage) fracture is at a specified level, e.g. equal parts—50% FATT;

or 100% shear— 100% FATT.

Lateral Expansion Transition Temperature —The temperature at which the lateral expansion in the

fractured specimen (increase in specimen width on the compression side, opposite the notch) is some

specified amount.

Brittle Fracture Transition Temperature —Temperature at which maximum load first equals load to

brittle fracture (determinable from the instrumented Charpy test).

Nil Ductility Transition Temperature (NDTT) —A transition temperature, derived from a drop weight

test, defined as the maximum temperature where a standard drop weight specimen fractures when

tested as specified in ASTM E208. This parameter does not relate to the Charpy notch bar impact test.

Upper Shelf Energy —The level of the energy plateau above the transition temperature.

Lower Shelf Energy —The level of the energy plateau below the transition temperature.

Per Cent Shear Fracture —A subjective determination of the relative cross-sectional area of the impact

specimen exhibiting shear (ductile or fibrous) fracture.

Synonyms

Charpy V-Notch Impact Strength

Synonymous Terms

notch toughness

impact strength

Charpy V-notch

CVN

impact toughness

impact value

Charpy V-notch impact

Charpy V-notch IE

Charpy V-impact energy

Charpy strength

impact energy

Cv

Not Synonymous

fracture toughness

Izod strength

Izod impact strength

DT strength

Standard Test Methods

„ The basic ASTM method for notched bar impact testing of metallic materials is ASTM E23-82. This is supplemented by the following ASTM methods which also bear on impact testing:

ASTM A370-77 Mechanical Testing of Steel Products

ASTM A673-82 Sampling Procedure for Impact Testing of Structural Steel ASTM A327-72 Impact Testing of Cast Irons

25
Numerous factors can affect the results obtained from the Charpy impact test. The most important are:

Specimen-related

notch dimensions2

tool marks left in notch

specimen size Machine-rela ted

rigidity linear velocity of pendulum (16 to 19 ft/sec)

anti-jamming provisions3 energy range

4

relative mass of tup and anvil

geometry of tup and hammer ("C"-type vs "U"-type)

The ISO standard corresponding to ASTM E23 is R442-1965. In general R442's allowable variations in geometric tolerances and its failure to specify rigid mounting of the machine to an adequate foundation are such

as to yield impact values different by as much as 20% from those obtained under the ASTM specification.

Standards for Reporting Data

ASTM E23-82 calls for reporting of various factors in addition to energy values themselves. Among these

are: type of specimen

size of specimen

temperature

presence of anti-jamming features

Particular specifications may also call for recording

orientation of specimen relative to processing direction nature of sampling

fracture appearance

lateral expansion

average energy value

minimum energy value

The writer also recommends that the yield strength or hardness be recorded as a crude measure of the result of heat treatment and other processing in establishing equivalent structures.

Precision and Accuracy

Tests run by the Army Materials and Mechanics Research Center (AMMRC) under carefully controlled

conditions show that the Charpy V-notch impact test is both reliable and highly reproducible. The results on

1200 specimens of a single heat of steel, heat-treated to three different hardness levels and tested in two different machines, are shown in figure 3. The spreads in impact energy observed were essentially independent of the

test machine and were typically within ±10% at the highest impact strength level and ±15% at the lowest

impact strength level tested. Still, heat-to-heat variations, differences in processing history and sampling

location can add considerably to the spread in test results even when the testing is most rigorously controlled.

The AMMRC laboratory has continued to be active in establishing the reliability of this test and calibration of

test machines. Calibration specimens of AISI 4340 are available at the 15, 30 (formerly), and 70 ft-lb levels, and

current work with ASTM Committee 28.07 is being conducted for the 150 ft-lb level. No determination of

precision or accuracy in impact testing yet bears ASTM imprimatur.

2 Modest variation in notch dimensions from those of standard specimens have been shown by Fahey [6] to lead to ±5% changes in impact energy in high energy specimens ( — 76 ft lbs) and +27%, — 14% in low energy specimens (~ 12.5 ft lbs).

3The broken pieces of the test specimen must be free to leave the machine with a minimum of interference and not rebound into the pendulum before the pendulum completes its swing.

The energy values from the test should be within 80% of the machine capacity, typically 220 ft lbs.

26
43 to 46 HRC 32.5 to 36.5 HRC 26 to 29 HRC

100

Charpy machine a - 50 n

E

32

—

1

100

Ti"T-ri

!00

- 50 2

E "I J I—

I

10 12 14 Impact energy, fflb44 48 52 Impact energy, fflb

56 76 80 84 Impact energy, fflb

100

Charpy

machine b

50

1

100

J- "fl TTh

12 14 Impact energy, fflb48 52 Impact energy, fflb

76 80 84 Impact energy, fflb

Charpy

test averages

Machine A

Machine B

43 to 46 HRC 32.5 to 36.5 HRC 26 to 29 HRC

12.7 fflb 17.2 J 48.6 fflb 65.9 J 78.4 fflb 106.3 J

12.6 fflb 17.1 J 49.1 fflb 66.6 J 77.9 fflb 105.6 J Comparison of test results from two Charpy impact machines manufactured by two companies. 1 200 specimens were made from a single heat of aircraft-quality 4340 steel. Specimens were hardened and tempered to three hardness levels: 43 to 46 HRC, 32.5 to 36.5 HRC and 26 to 29 HRC. 200 specimens at each of the three hardness levels were tested at 21 °C (70 °F) on each of the impact machines. (Ref 1)

Figure 3. Reproducibility of impact test results derived from extensive testing of AMMRC (from ASM Handbook, 9th ed.).

The Community Bureau of Preference (BCR) of the European Economic Community (EEC) has also been

working to establish reliable reference materials for the notch-bar impact test. Working with four different laboratories in the EEC, the BCR had round robin tests on AISI 4340 steel conducted to ascertain the

contribution to scatter of heat treatment, testing laboratory, sample direction, and steel making and refining

practices [7]. The major finding of this study is that increased purity and homogeneity of the steel afforded by

electroslag remelting as compared to vacuum arc remelting or normal air melting increased the mean impact

energy (at the 100 J, 74 ft-lb level), reduced the difference between the longitudinal and transverse directions,

and narrowed the dispersion of the results.

Correlations

Notch bar impact behavior is not predictable from parameters from simpler tests such as tensile ductility.

Specimens exhibiting equal ductility will frequently be found to have radically different notch impact strengths.

Another illustration of the unique character of the notch toughness parameter is found in figure 4 which shows

the variation in impact behavior of a medium carbon steel tempered to various strength levels. Significant

variations are seen in the upper shelf energy, much lesser changes in transition temperature, and almost no

change in the lower shelf energy. Of much greater importance is the use of impact energy measurements to predict plane strain fracture toughness, Klc , because of the greater complexity and expense of the latter test. Such correlations have been reported by Barsom and Rolfe [8], Groves and Wallace [9], Goode et al. [10], and

Wullaert [11]. An example is shown in figure 5. Much further work needs to be done to establish fully the

conditions under which reliable correlations may be expected.

27
Temperature, °F

-200 -150 -100 -50 0 50 100 Temperature, C

Yield strength A B C 0 E MPa 650 740 890 1025 1220

ksi 94 107 129 149 177

Figure 4. Variation in impact behavior of a steel tempered to various strength levels (from ASM Handbook, 9th ed.).

Figure 5. Correlation between fracture toughness K/c and Charpy V-notch-impact strength in the upper shelf region

(after Barsom and Rolfe [8]).

28
Concluding Remarks

In considering what numbers should be stored in a computer file to describe some property, compromise

must always be effected between those fundamental parameters that are most meaningful and the values one

is likely to find available for a broad range of materials. This is certainly true of the notch impact situation. While one might desire the full characterization of the impact-temperature curve or the additional information

afforded by the instrumented Charpy test, what one is most likely to find tabulated is a simple impact energy

value, usually at room temperature, or a transition temperature. In any event, it is most important, however

skimpy the impact data themselves may be, that the other descriptive parameters relative to the test or the

specimen be included in the computer file as well.

It is recommended that standard test procedures for notched bar impact behavior include explicit defini- tions of critical terms and the reporting requirement of some parameter characterizing the strength level of the

specimen.

References

[1] Hoyt, S. L., "Notch Bar Testing—Theory and Practice," ASTM Symp. on Impact Testing, STP 176,

(1955) 3.

[2] Oldfield, W., "Development of Fracture Toughness Reference Curves," /. Eng. and Materials Technology 102 (1980) 107.

[3] Oldfield, W. and Marston, T. U., "Fracture Toughness Prediction Method for Ferritic Steels,"

SMIRT-7, Post Conference Seminar (1983).

[4] Turner, C. E., "Measurement of Fracture Toughness by Instrumented Impact Test," fm. Impact Testing,

ASTM STP 466 (1970) 93.

[5] Gross, J. H., "Effect of Strength and Thickness on Notch Ductility," ibid. p. 21.

[6] Fahey, N. H., "Effects of Variables in Charpy Impact Testing," Materials Research and Standards 1, No. 11 (1961) 872.

[7] Helms, R. and Ledworuski, S., "Reference Material for Proof Tests of Method and Apparatus for Notched-Bar Impact Tests," fm. Production and Use of Reference Materials, B. F. Schmitt, ed., Bundesanstalt fur Materialprufung, Berlin (1980).

[8] Barsom, J. M., and Rolfe, S. T., "Correlations Between KIc and Charpy V-Notch Test Results in the

Transition Temperature Range," fm. Impact Testing, ASTM STP 466 (1970) 281.

[9] Groves, M. T., and Wallace, J. F., "Cast Steel Plane Fracture Toughness, Charpy V-Notch and Dynamic

Tear Test Correlations," /. Steel Castings Res., No. 70 (1975) 1. [10] Goode, R. W. et al., "Metallurgical Characteristics of High Strength Structural Materials," NRL Report

6607 (Sept. 1967).

[11] Wullaert, R. H., "Fracture Toughness Predictions from Charpy V-Notch Data," AIME Meeting,

Denver, CO (Feb. 1978).

29
Chapter 4

FATIGUE PROPERTIES

Introduction

Fatigue is the progressive damage suffered by a material subjected to repeated application of stress. At some point the loading regime leads to the formation of a crack. This crack grows in extent with each

successive application of tensile stress until the remaining, uncracked portion is unable to carry the load, at which time sudden, complete fracture occurs. Systematic testing and analysis of the fatigue phenomenon has

been going on since the pioneering work of Wohler over a century ago. Much information has been gained, to the point that general precepts can be laid down that will help avoid

fatigue failure, and the beginnings of a quantitative approach to engineering design from a fatigue viewpoint

have been established. However, fundamental understanding is still somewhat limited as is our ability to deal

with complex stress (strain) history and concomitant effects of environment, surface condition, etc. Not only

is the process inherently probabilistic, but the many variables may differently affect the initiation and propagation of a crack.

We will consider here only fatigue properties associated with conventional room temperature testing. The

important but more complex behaviors associated with high temperature fatigue, stress-corrosion fatigue,

fretting fatigue and complex loading will not be treated, because so little consensus has yet been achieved in these areas with respect to definitions and test methods. Existing ASTM standards do not read on these more

complex behaviors and loading conditions, excepting appendix X4 to E606-80 which provides "guidance" for elevated temperature, low cycle fatigue testing. The Fatigue Design and Evaluation Steering Committee of the

Society of Automotive Engineers (SAE) has also been active in these areas with respect to standardizing test methods, collecting and analyzing data, etc. Thomas [13] and Coffin [14] have provided useful overviews of

high temperature fatigue with respect to testing standards and phenomenology, respectively.

Definitions (From ASTM E206-72 or E5 13-74 except where noted)

cycle —one complete sequence of values of stress or strain that is repeated periodically.

hysteresis diagram —the stress-strain path during one cycle.

fatigue —the process of progressive localized permanent structural change occurring in a material subjected to conditions which produce fluctuating stresses and strains at some point or points and which may

culminate in cracks or complete fracture after a sufficient number of fluctuations. (ASTM Notes omitted)

fatigue life, N—the number of cycles of stress or strain of a specified character that a given specimen

sustains before failure of a specified nature occurs.

S-N diagram —a plot of stress against the number of cycles to failure. The stress can be Smin , Smax, or Sa = [one half the range of stress, (Smax — Sm, n)/2]. (See fig. 1 for graphical representation of these definitions.)

The diagram indicates the S-N relationship for a specified value of Sm = [mean stress, (Smm -hSmax)/2],

A = [Sa /Sm] or R = [S mm/Smax] and a specified probabililty of survival. For N a log scale is almost always used. For S a linear scale is used most often, but a log scale is sometimes used.

fatigue strength at N cycles, S [FL ^—a hypothetical value of stress for failure at exactly N cycles as determined from an S-N diagram. The value of S thus determined is subject to the same conditions as those

which apply to the S-N diagram.

(ASTM Note omitted)

median fatigue life —the middlemost of the observed fatigue life values, arranged in order of magnitude,

of the individual specimens in a group tested under identical conditions.

(ASTM Note omitted)

30
Tensile Loading- Minimum

Stress Less than Zero

Completely Reversed Loading

0 ! 2 2

Cycles

Figure 1. Typical fatigue loadings and definitions of stress terms.

range of stress, Sr [FL *] —the algebraic difference between the maximum and minimum stresses in one

cycle, that is Sr =Smax -Smin .

stress ratio, A or R —the algebraic ratio of two specified stress values in a stress cycle. Two commonly used

stress ratios are: The ratio of the alternating stress amplitude to the mean stress, that is, A = Sa/Sm (1)

and the ratio of the minimum stress to the maximum stress, that is, R = Smj n/Smax (2)

median fatigue strength at N cycles [FL *\ —an estimate of the stress level at which 50 percent of the

population would survive N cycles.

Note—The estimate of the median fatigue strength is derived from a particular point of the fatigue life distribution, since there is no test procedure by which a frequency distribution of fatigue strength at N

cycles can be directly observed.

Note—This is a special case of the more general definition (see immediately below).

fatigue strength for p percent survival at N cycles [FL _2

] —an estimate of the stress level at which p percent

of the population would survive N cycles; p may be any number, such as 95, 90, etc.

31
Note—The estimates of the fatigue strengths for p percent survival values are derived from particular

points of the fatigue life distribution, since there is no test procedure by which a frequency distribution of

fatigue strengths at N cycles can be directly observed.

fatigue limit, Sf[FL "-'] —the limiting value of the median fatigue strength as N becomes very large.

Note—Certain materials and environments preclude the attainment of a fatigue limit. Values tabulated as "fatigue limits" in the literature are frequently (but not always) values of Sn for 50 percent survival at N

cycles of stress in which Sm =0.

cycle ratio, C—the ratio of the nunmber of stress cycles, n, of a specified character to the hypothetical

fatigue life, N, obtained from the S-N diagram, for stress cycles of the same character, that is, C = n/N.

fatigue notch factor, Kf —the ratio of the fatigue strength of a specimen with no stress concentration to the

fatigue strength at the same number of cycles with stress concentration for the same conditions.

Note—In specifying Kf it is necessary to specify the geometry and the values of Smax, Sm, and N for which

it is computed.

constant life fatigue diagram —a plot (usually on rectangular coordinates) of a family of curves, each of

which is for a single fatigue life, N, relating Sm, Smax and/or Smjn to the mean stress Sm . The constant life fatigue

diagram is generally derived from a family of S-N curves, each of which represents a different stress ratio (A

or R) for a 50 percent probability of survival. (See fig. 2.) Author's note: This is also referred to as a modified

Goodman diagram.

cyclic stress-strain curve

x —the cyclic stress-strain curve is defined as the locus of tips of stable "true"

stress-strain hysteresis loops obtained from companion test specimens tested under axial cyclic strain control. See figure 3.

cyclic yield strength (0.2% crys )

1 —is the stress to cause 0.2% inelastic strain as measured on a cyclic

stress-strain curve. It is usually determined by constructing a line parallel to the slope of the cyclic stress-strain curve at zero stress through 0.2% strain and zero stress. The stress where the constructed line intercepts the

cyclic stress-strain curve is taken as the 0.2% cyclic yield strength.

cyclic strain hardening exponent (n ')

1 —is the power to which "true" plastic strain amplitude must be raised

to be proportional to "true" stress amplitude. It is taken as the slope of the log Acr/2 versus log Aep/2 plot,

where Aep/2 and Acr/2 are measured from cyclically stable hysteresis loops.

Ao-/2 = K'(Aep/2)

n

'

where Aep/2 = "true" plastic strain amplitude. The line defined by this equation is illustrated in figure 4.

cyclic strength coefficient (K') x —is the "true" stress at a "true" plastic strain of unity in eq 11. It may be

necessary to extrapolate as indicated in figure 4.

fatigue ductility exponent (c)

1 —is the power to which the life in reversals must be raised to be proportional

to the "true" strain amplitude. It is taken as the slope of the log (Aep/2) versus log (2Nf) plot. (See fig. 5.)

fatigue ductility coefficient (e'f )

x —is the "true" strain required to cause failure in one reversal. It is taken as the intercept of the log (Acr/2) versus log (2Nf) plot. (See fig. 5.)

fatigue strength exponent (b)

1 —is the power to which life in reversals must be raised to be proportional to "true" stress amplitude. It is taken as the slope of the log (Acr/2) versus log (2Nf) plot.

fatigue strength coefficient (&f )

x —is the "true" stress required to cause failure in one reversal. It is taken

as the intercept of the log (Acr/2) versus log (2Nf) plot at 2Nf = 1.

transition fatigue life (2N,) X —is the life where elastic and plastic components of the total strain are equal.

It is the life at which the plastic and elastic strain-life lines cross. (See fig. 5.)

'From SAE J1099 [1].

32
A= 4.0 R = -0.6

2.33 -0.4

15

-0.2 0.67

0.2 0.43

0.4 0.25

0.6

0.11 0.8 0

1.0

£

V)E

3

EX

a

i i i i i i i

Test Conditions

Unnotched —

A=oo

A=I.O

Notched ; Kt =3.3 A=oo

A=I.O A=0.25

-140 -120 -100 -80 -60 -40 -20 0 20 40 60

Minimum Stress, ksi

80 100 120 140 160 180 200

Correlative Information for Figure 2

Product Form : Rolled Bar, 1-1/8 inches diameter

Properties

:

Specimen Details:

TUS, ksi 125.0

150.2

Unnotched:

0.400-inch diameter

TYS, ksi Temp. F

RT (Unnotched)

RT (Notched)

Notched, V-Groove, K,=3.3

0.450-inch gross diameter

0.400-inch net diameter

0.010-inch root radius, r 60° flank angle, w

Test Parameters

:

Loading—Axial Frequency —2000 to 2500 cpm

Temperature—RT

Atmosphere—Air

KN =2.34, p = 0.0023 inch, where KN = 1 +

K,-l

TT —bi V r

Surface Condition : Unnotched:

Notched: Hand polished to 10 microinches RMS

Lathe turned to 10 microinches RMS

Figure 2. Typical constant-life fatigue diagram for heat-treated AISI 4340 alloy steel (bar), Flu =125 ksi. (from Mil Handbook 5).

33
CYCLIC STRESSSTRAIN CURVE

Figure 3. Cyclic stress-strain curve drawn through stable loop tips [1].

10 6

wQUJQ

3

< 10

CO

LU

cr\-co3

IX

10'

CYCLIC STRENGTH

COEFFICIENT- -4+ - pfn=

J n'- CYCLIC STRAIN HARDENING - EXPONENT 1 |_

(CORRECTED FOR

NECKING)

0.001 0.01 0.10 "TRUE" PLASTIC STRAIN AMPLITUDE

Figure 4. Cyclic stress-plastic strain plot, 1020 H. R. Steel. [1].

10

1 0

0.1

0.01

AC

V" 2

1.0

= % (2N,A e f' (2N, )

-STRAIN-LIF

c

E

PLAST

En —

1.0

IC STRAIN -L FE^\^

ELAiSTIC STRAIN -LIFE ^ \ ~-—

LUD

D

Q.5

<z

iUJE 0.001

00001

10° 10

1 102 10

3 10* 10' 10°

LIFE, REVERSALS TO FAILURE, 2N,

Figure 5. Strain amplitude versus reversals to failure. 1020 H. R. Steel. [1].

34
maximum strain, emM—the greatest algebraic value of strain in a cycle, tensile strain being considered

positive and compressive strain negative.

mean strain , em—the algebraic average of the maximum and minimum strains in one cycle.

minimum strain , —the least algebraic value of strain in a cycle, tensile strain being considered positive

and compressive strain negative.

reversal —the point at which the first derivative of the stress or strain-time function changes sign. For

constant amplitude cycling, the number of reversals is equal to twice the number of cycles.

strain amplitude —one half the range of any strain cycle.

strain range, Ae—the algebraic difference between the maximum and minimum strains in one cycle.

Note—The strain range is often separated into elastic and plastic components. For many metals and alloys,

the elastic strain range, Aee , is equal to the stress range divided by the modulus of elasticity with the plastic strain range, Aep

, taken as the difference between the strain range and the elastic strain range (see 2.2).

strain ratio —the algebraic ratio of two specified strain values in a strain cycle. Two commonly used ratios are (a) A€ , the ratio of the strain amplitude to the mean strain, and (b) Re , the ratio of the minimum strain to the maximum strain.

Synonyms

fatigue life endurance

fatigue limit endurance limit endurance strength

cycle ratio fatigue ratio endurance ratio

range of stress stress range

endurance range

fatigue range

fatigue notch factor

fatigue strength reduction factor

Standard Test Methods

There are many test methods for studying fatigue behavior which have become broadly used over the

years, among them:

rotating testing - in which the specimen is bent about a neutral plane which rotates with respect

to the test piece. The specimen may be subjected to 3 point, 4 point or cantilever

loading

plane bending - in which the specimen is repeatedly bent about a particular neutral plane

torsion - in which the specimen is subjected to twisting in alternating directions about a

fixed axis

axial stressing - in which the material is uniaxially loaded and is cycled between tension and

compression or between two levels of tension. Both stress and strain control of

the cyclic amplitude are practiced

35
Curiously, although all the above testing techniques are widely practiced and results reported thereon, ASTM

has written testing standards only for tests of the axial loading type:

E466-82 Constant amplitude axial fatigue where strains are predominantly elastic both upon initial loading and throughout the test

E606-80 Constant amplitude low cycle fatigue where strains may be inelastic but are not time

dependent

Standards setting bodies in other countries have prepared standards for the other types of test, e.g., the Japanese

JIS Z 2274 (1974), German DIN 50113, and British BS 3518, Pt.2 for rotating bending fatigue. Such tests are not in general correctable with axially stressed tests as may be seen from figure 6. Testing may also be complicated by the introduction of notches, multiaxial stressing, use of more elaborate

loading regimes than simple sawtooth or sinusoidal—hold times, spectral loading simulative of service, etc., or

the provision of creep and environmental conditions. Such matters are beyond the scope of this report.

10

7 S35C

Failure

Rotating

bending

— m ^

• m

Rev ersed"

;ion- tpress

•

•Nss ten" con

• on

1 10 Number of cycles

Figure 6. S-N diagram retrieved in the condition of smooth bar specimen, S35C alloy in JIS Standard; cr, =20-50 kg/mm 2

, in air, temperature =0-30°, mean stress <r m =0, and rotating bending or axial loading [6]

Standards for Reporting Data

The sensitivity of fatigue behavior to numerous factors is such that a very detailed recording of these is essential to permit full analysis of the text results or intercomparison of two sets of experiments. These matters

are covered in ASTM 468-82 (cyclic stress), ASTM 606-80 (cyclic strain) and are also discussed by Radziminski

et al. [9] and by Uenishi et al. [6]. The pertinent factors desirable or essential to include with the test report

comprise:

material

designation

form and section size heat number and manufacturer

melting practice

thermal and mechanical processing

chemical composition

mechanical properties (hardness, tensile, and impact)

microstructure

specimen

geometry and dimensions

orientation relative to processing

preparation technique

surface condition

theoretical stress concentration factor

critical stress intensity factor

36
testing

experimental design

machine

test method

loading conditions

frequency of loading (if other than a sinusoidal stress cycle is used, the shape should be described)

ambient conditions

test termination

criteria crack incidence

crack propagation rate

total strain

failure "run-out"

location of fracture

appearance of fracture

Presentation of the test results themselves may be tabular or graphical, either the common S-N curves or €-N curves or one form or another of the so-called constant life diagram. (Fig. 2.) Increasingly, an analytical approach is being taken, especially for strain controlled testing. True strain can be viewed as the sum of an elastic component and a plastic component. It therefore can be shown [1] that each

of these components of true strain amplitude,

Ae/2 = Aee/2 + Aep/2 , (4)

can be related to the number of reversals to failure (2Nf) in a strain-controlled fatigue test, giving:

Ae/2 = (o-f/E)(2Nf)

b + eK2Nf)

c (5)

Thus four fatigue constants cr'f, e'f, b, c and the elastic modulus can describe the whole of fatigue life, both low

cycle and long-life data. This set of constants, therefore constitutes the preferred parameters for characterizing

fatigue behavior.

A useful discussion of data requirements for characterizing the fatigue behavior of a material, including

fatigue data analysis, combining data from multiple sources and regression analysis of fatigue data is presented

in Mil Handbook 5 [11].

Precision and Accuracy

Fatigue is intrinsically a probabilistic phenomenon and is further complicated by extraordinary sensitivity to a large number of factors as just reviewed. It is therefore not surprising that a substantially larger coefficient

of variation (the standard deviation divided by the mean value) is experienced with fatigue data than with other

mechanical properties. Some representative results are shown in table 1.

Table 1. Coefficients of variation experienced in testing for mechanical properties [5].

Mechanical Property Coefficient of Variation

Elastic Modulus 0.03 Ultimate Tensile Strength 0.05

Brinell Hardness 0.05 Tensile Yield Strength 0.07 Fracture Toughness 0.07 Fatigue Strength 0.08 to 1.0

Another view of the typical scatter to be expected is afforded by the histogram of figure 7 for 300 parts in 25

lots of a spring steel, 5160H. The coefficient of variation for this set of experiments was 0.28 in terms of fatigue

life; naturally, near the fatigue limit this approach is meaningless and coefficient of variation there should be

calculated for the fatigue limit. Generally speaking, the scatter in fatigue data tends to increase with increasing

37
strength, decreasing purity and homogeneity and decreasing sample size. A special standard practice (E739-80)

has been issued by ASTM for statistical analysis of linear or linearized stress-life or strain-life fatigue data.

40 r

1

50 10C 150 200 250

Service life, 1000 cycles

Figure 7. Distribution offatigue lifetimes. Results of simulated service tests offront suspension torsion bar springs of 5260H steel. Size of hexagonal bar section was 32 mm (1.25 in). Mean service life 134,000 cycles; standard deviation 37,000 cycles; coefficient of variation 0.28

(after Boardman [5]).

Correlations

The correlation between monotonic properties of materials and their cyclic behavior depends on whether

we are considering alternating stress loading (usually elastic) or alternating strain loading (predominantly

plastic). A good correlation is often obtained for alternating stress tests between the fatigue limit and the tensile strength as shown in figure 8. Low cycle (high stress, strain control) fatigue data tend to relate more to the

ductility of the material than to its strength. Apart from these crude empirical generalizations it is not yet

possible to predict fatigue behavior from simpler and quicker tests. The lack of good correlations between the

various types of fatigue tests has already been cited.

Rotati ng

Dendi ng

"J

<•

o m

o

o

»

20 Tensile strength (Kg/mm2

) 100

Figure 8. Relation of tensile strength and fatigue limit retrieved in the condition of carbon steel, smooth bar specimen, in air, temperature =0-30°, and rotating bending (after Uenishi et al. [6]).

References

[1] , "Technical Report on Fatigue Properties," SAE J 1099 Society of Automotive Engineers

(1977).

[2] Graham, J. A., ed., "Fatigue Design Handbook," Society of Automotive Engineers, Inc., 400 Commonwealth Drive, Warrendale, PA 15096 (1968).

[3] Jaske, C. E., Fedderson, C. E., Davies, K. B., Rice, R. C, "Analysis of Fatigue, Fatigue Crack Propagation and Fracture Data," NASA CR 13233. Battelle-Columbus Labs, Columbus, OH (Nov. 1973).

[4] Sandor, B. I., "Fundamentals of Cyclic Stress and Strain," U. Wisconsin Press, Madison, WI.

[5] Boardman, B. E., "Fatigue Resistance of Steels," fm. ASM Metals Handbook 9th ed., p. 665, American

Society for Metals, Metals Park, OH (1978).

38
Uenishi, M., et al., "Computer Program System for Fatigue Strength Analysis," /. Jap. Soc. for Metals

(1980) 1108. Koehler, J., Heckel, K., and Munich, T. U., "Scatter and Statistical Size Effect in the Fatigue Behavior

of Metallic Specimens," Proc. 2nd Int. Conf. on Mechanical Behavior of Materials, ASM (1980) 193.

, "NRIM Fatigue Data Sheet Series," National Research Institute for Metals, Tokyo, Japan

(1978-).

Radziminski, J. B., et al., "Fatigue Data Bank and Data Analysis Investigation," U. Illinois Report, NTIS

PB-240261, June 1973. Dabell, B. J., and Hill, S. J., "The Use of Computers in Fatigue Design and Development," Int. J. of

Fatigue 1 (1979) 29.

, Military Standardization Handbook, 5C, "Metallic Materials and Elements for Aerospace

Vehicle Structures," 15 Sept. 1976, 2 vols with later supplements.

Swanson, S., ed., "Handbook of Fatigue Testing," ASTM STP 566 (1974) 232 pp. Thomas, G. B. "Standards for High Temperature Fatigue" in "Measurement of High Temperature

Mechanical Properties of Metals," Loveday, M. S., Day, M. F. and Dyson, B. F. eds., National

Physical Laboratory (1982).

Coffin, L. F. "Overview of Temperature and Environmental Effects on Fatigue of Structural Metals,

Proc. 27th Sagamore Army Materials Research Conf. (1982).

39
1
NBS-114A (rev. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS/SP-702

2. Performing Organ. Report No. 3. Publication Date August 1985

4. TITLE AND SUBTITLE

STANDARDS AND METADATA REQUIREMENTS FOR COMPUTERIZATION OF SELECTED MECHANICAL

PROPERTIES OF METALLIC MATERIALS

5. AUTHOR(S)

J 0 Ho Westbrook

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. **tfxfcK*k>§W*G^8Kx3*^^ General Electric Corporation

jtef#MMZ^%R)QQmm®fr Materials Information Services 8. TyP e of Report & period covered

^KH^0iJ«&*xxH*** 120 Erie Boulevard Final

. Schenectady, NY | 9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

U.So Army DARCOM NBS

Code DRCLD Office of Standard Reference Data

5001 Eisenhower Avenue A323 Physics Building

Alexandria, VA 22333 Gai thersburg, MP 20899

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 85-600585

] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here) To assist in building a computerized information system on the engineering properties

of materials, the standards and metadata requirements for a representative group of

mechanical property categories are considered 0 These categories include: tensile

behavior, hardness numbers, notch-bar impact test parameters, and fatigue properties.

For each property group, definitions of terms, synonyms (and non-synonyms), standard

test methods, standards for reporting data, precision and accuracy, and correlations of

properties are addressed.

The principal findings and recommendations are as follows 0 Existing test methods are generally adequate for the properties considered, but better standards are needed for

data reporting,. Appraisal of materials variability and testing machine variability

would be assisted by access to standard reference materials, certified as to their

mechanical propertieSo All properties considered for inclusion in a computerized

system can be categorized as parameters for direct search, parameters retrievable with

extraction of all data stored for a given material, and parameters which are derived

from an analytical representation of experimental data. Drafting of some general

standards on computerized file structures and metadata files suitable for the engineering field is advised.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

computerized materials data; fatigue; hardness; materials data; materials metadata;

materials property; mechanical properties; notch-bar impact test; tensile behavior;

tensile strength

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