ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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9. G.R. Irwin, Plastic Zone near a Crack and Fracture Toughness, Proc. Seventh Sagamore Ordnance

Materials Research Conference, Syracuse University Press, 1960, p IV63–IV78

10. R.D. Venter and D.W. Hoeppner, “Crack and Fracture Behavior in Tough Ductile Materials,” report

submitted to the Atomic Energy Control Board of Canada, Oct 1985

11. “Fracture Mechanics Tests, Part 1: Method for Determination of K

, Critical CTOD and Critical J

Values of Metallic Materials,” BS 7448: Part 1, The British Standards Institution, 1991

12. “Standard Test Method for Crack Tip Opening Displacement (CTOD) Fracture Toughness

Measurement,” E 1290-93, Annual Book of ASTM Standards, Vol 03.01, ASTM, 1999, p 831–840

13. J.R. Rice, A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches

and Cracks, J. Appl. Mech., Vol 35, 1968, p 379–386

14. D.J. Hayes, “Some Applications of Elastic Plastic Analysis to Fracture Mechanics,” Ph.D. thesis,

University of London, 1970

15. J.M. Krafft, A.M. Sullivan, and R.W. Boyle, Effect of Dimensions on Fast Fracture Instability of

Notched Sheets, Proc., Crack Propagation Symposium, Vol I, College of Aeronautics, Cranfield,

England, 1961, p 8–28

16. D.E. McCabe and R.H. Heyer, R-Curve Determination Using a Crack-Line-Wedge-Loaded (CLWL)

Specimen, Fracture Toughness Evaluation by R-Curve Methods, STP 527, 1973, p 17–35

17. D.A. Sarno, J.P. Bruner, and G.E. Kampschaefer, Fracture Toughness of 5% Nickel Steel Weldments,

Weld J., Vol 53, 1974, p 486

18. P.C. Paris, H. Tada, A. Zahoor, and H. Ernst, The Theory of Instability of the Tearing Mode of Elastic-

Plastic Crack Growth, Elastic-Plastic Fracture, STP 668, J.D. Landes, J.A. Begley, and G.A. Clarke,

Ed., ASTM, 1977, p 5–36

19. S.D. Antolovich and G.R. Chanai, Errors Associated with Fracture Toughness Testing, Paper II-242,

Third Int. Conf. Fracture, Verein Deutscher Eisenhüttenleute, Dusseldorf, 1975, p 1–5

20. J.D. Landes and J.A. Begley, Test Results from J-Integral Studies—An Attempt to Develop a J-Integral

Test Procedure, Fracture Analysis, STP 560, ASTM, 1974, p 170–186

21. “Standard Test Method for J

, A Measure of Fracture Toughness,” E 813, Annual Book of ASTM

Standards, Vol 03.01, ASTM, (before 1998)

22. “Standard Test Method for Measurement of Fracture Toughness,” E 1820-99, Annual Book of ASTM

Standards, Vol 03.01, ASTM, 1999, p 972–1005

23. P.C. Paris, The Fracture Mechanics Approach to Fatigue, Fatigue—An Interdisciplinary Approach,

Syracuse University Press, 1964, p 107–133

24. “Standard Test Method for Measurement of Fatigue Crack Growth Rates,” E 647-95a, Annual Book of

ASTM Standards, Vol 03.01, ASTM, 1999, p 577–613

25. R.O. Ritchie and and R.H. Dauskardt, Cyclic Fatigue of Ceramics: A Fracture Mechanics Approach to

Subcritical Crack Growth and Lite Production, J.Ceram. Soc. J., Vol 99, 1991, p 1047–1062

Fracture Toughness Testing

John D. Landes, University of Tennessee, Knoxville

Introduction

FRACTURE TOUGHNESS is defined as a “generic term for measures of resistance to extension of a crack”

(Ref 1). The term fracture toughness is usually associated with the fracture mechanics methods that deal with

the effect of defects on the load-bearing capacity of structural components. Fracture toughness is an empirical

material property that is determined by one or more of a number of standard fracture toughness test methods. In

the United States, the standard test methods for fracture toughness testing are developed by ASTM (formerly

the American Society for Testing and Materials). These standards are developed by volunteer committees and

are subjected to consensus balloting. This means that all objecting points of view to any part of the standard

must be accounted for. Other industrial countries have equivalent standards writing organizations that develop

fracture toughness test standards. In addition, international bodies such as the International Organization for

Standardization (ISO) develop fracture toughness test standards that have an influence on products intended for

the international market. In this review of fracture toughness testing, the ASTM approach is emphasized to

provide a consistent point of view.

The standard fracture toughness test methods were written primarily for the testing of metallic materials.

Toughness testing of nonmetals is also important. For many nonmetals, standards are developed based on

procedures, analyses, and methods used for metallic fracture toughness tests with some possible modification to

account for special needs of the nonmetal material behavior. Fracture toughness test methods written

specifically for a particular nonmetal are relatively new. Therefore, this review emphasizes those standards

written for metals without intent to make them apply exclusively to metals. A short discussion of fracture

toughness testing for ceramics and polymers is included at the end of this article.

General Fracture Toughness Behavior. As a general background before discussing the details of fracture

toughness testing and analysis, fracture toughness behavior and the parameters used to describe it are discussed.

Fracture toughness is defined as resistance to the propagation of a crack. This propagation is often thought to be

unstable, resulting in a complete separation of the component into two or more pieces. Actually, the fracture

event can be stable or unstable. With unstable crack extension, often associated with a brittle fracture event, the

fracture occurs at a well-defined point, and the fracture characterization can be given by a single value of the

fracture parameter. With stable crack extension, often associated with a ductile fracture process, the fracture is

an ongoing process that cannot be readily described by a point (Ref 2). This fracture process is characterized by

a crack growth resistance curve, or R-curve. This is a plot of a fracture parameter versus the ductile crack

extension, Δa. An example K-based R-curve is shown in Fig. 1. Sometimes a single point is chosen on the R-

curve to describe the entire process; this is mostly done for convenience and does not give a complete

quantitative description of the fracture behavior.

Fig. 1 Schematic of K-based crack resistance, R, curve with definition of K

Whether the fracture is ductile or brittle does not directly influence the deformation process that a component or

specimen might undergo during the measurement of toughness (Ref 2). The deformation process is generally

described as being linear-elastic or nonlinear. This determines which parameter is used in the fracture toughness

test characterization. All loading begins as linear-elastic. For this, the primary fracture parameter is the well-

known crack-tip stress-intensity factor, K (Ref 3). If the toughness is relatively high, the loading may progress

from linear-elastic to nonlinear during the toughness measurement, and a nonlinear parameter is needed. The

nonlinear parameters that are most often used in toughness testing are the J-integral (Ref 4), labeled J, and the

crack tip opening displacement (CTOD), labeled δ (Ref 5). Because all loading starts as linear-elastic, the

nonlinear parameters are all written as a sum of a linear component and a nonlinear component. This is

illustrated with the individual descriptions of the various methods in this article.

Test Methods Covered. The test methods covered include linear-elastic and nonlinear loading, slow and rapid

loading, crack initiation, and crack arrest. The development of the test methods followed a chronological

pattern; that is, a standard was written for a particular technology soon after that technology was developed.

Standards written in this manner tend to become exclusive to a particular procedure or parameter. Because most

fracture toughness tests use the same specimens and procedures, this exclusive nature of each new standard did

not allow much flexibility in the determination of a fracture toughness value. The newer approach is to write

standards to encompass all parameters and measures of toughness into a single test procedure. This approach is

labeled the common fracture toughness test method approach and has resulted in a new standard developed by

ASTM as well as similar standards from organizations in other countries. The test standards for fracture

toughness testing are not completed; revision and expansion of existing standards are in progress at this time. It

is a requirement of ASTM that standards be reevaluated every five years and be updated if necessary.

Therefore, work on revising and updating standards is continually in progress.

The fracture toughness test is generally conducted on a test specimen containing a preexisting defect; usually

the defect is a sharp crack introduced by fatigue loading and called the precrack. The test is conducted on a

machine that loads the specimen at a prescribed rate. Measurements of load and a displacement value are taken

during the test. The data resulting from these measurements are subjected to an analysis procedure to evaluate

the desired toughness parameters. These toughness results are then subjected to qualification procedures (or

validity criteria) to see if they meet the conditions for which the toughness parameters can be accepted. Values

meeting these qualification conditions are labeled as acceptable standard measures of fracture toughness. The

standard fracture toughness test, thus, has these ingredients: test specimens, types, and preparation; loading

machine, test fixture, and instrumentation requirements; measurement taking; data analysis; and qualification of

results. The following sections discuss the various standard fracture toughness test methods following this

format. The fracture toughness test methods written as ASTM standards follow a prescribed format. It is not

always easy to determine the step-by-step procedure required to conduct the test from the standard. The

sections below, which describe the various methods, follow a format of a step-by-step procedure rather than the

format of the actual standards. The application of the fracture toughness result to the evaluation of structural

components containing defects is not explicitly covered in the ASTM standard test methods, nor is it covered in

this article. The description of the fracture toughness test methods follows a somewhat chronological outline,

beginning with the methods that use the linear-elastic parameter K. After this, the methods that use the

nonlinear parameters J and δ are discussed. Next, some of the work in progress to update the standards and the

newest standards is discussed. Finally, a brief overview of fracture toughness testing for ceramic and polymer

materials is given (see the articles “Fracture Resistance Testing of Plastics” and “Fracture Toughness of

Ceramics and Ceramic Matrix Composites” in this Volume for additional information about testing of these

materials).

References cited in this section

1. “Standard Terminology Relating to Fracture Testing,” E 616, Annual Book of ASTM Standards, Vol

3.01, ASTM

2. J.D. Landes and R. Herrera, Micro-mechanisms of Elastic/Plastic Fracture Toughness, J

, Proc. 1987

ASM Materials Science Seminar, ASM International, 1989, p 111–130

3. G.R. Irwin, Analysis of Stresses and Strains near the End of a Crack Traversing a Plate, J. Appl. Mech.,

Vol 6, 1957, p 361–364

4. J.R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentrations by

Notches and Cracks, J. Appl. Mech., Vol 35, 1968, p 379–386

5. A.A. Wells, Unstable Crack Propagation in Metals: Cleavage and Fast Fracture, Proc. Cranfield Crack

Propagation Symposium, Vol 1, Paper 84, 1961

Fracture Toughness Testing

John D. Landes, University of Tennessee, Knoxville

Linear-Elastic Fracture Toughness Testing

Fracture mechanics and fracture toughness testing began with a strictly linear-elastic methodology using the

crack-tip stress-intensity factor, K. Later, nonlinear parameters were developed. However, the first test methods

developed used the linear-elastic parameters and were based on K. These methods are described first in this

article.

The linear-elastic methods of fracture toughness testing are used to measure a single-point fracture toughness

value. For fracture by a brittle mechanism, this is no problem. Fracture occurs at a distinct point, and the

fracture toughness measurement is taken as a value of the fracture parameter at that point. For fracture by a

ductile mechanism, the fracture is a process, and the fracture toughness measurement is an R-curve. To get a

single value for this fracture toughness, a point on the R-curve must be chosen. This usually involves a

construction procedure. The ASTM E 399 K

standard fracture toughness test method, which is described next,

gives an example of a construction procedure that is used to get a single-point measurement of fracture

toughness on the R-curve.

Plane-Strain Fracture Toughness (K

) Test (ASTM E 399)

The first fracture toughness test that was written as a standard was the K

test method, ASTM E 399. This test

measures fracture toughness that develops under predominantly linear-elastic loading with the crack-tip region

subjected to near-plane-strain constraint conditions through the thickness. The test was developed for

essentially ductile fracture conditions, but can also be used for brittle fracture. As a ductile fracture test, a single

point to define the fracture toughness is desired. To accomplish this, a point where the ductile crack extension

equals 2% of the original crack length is identified. This criterion is illustrated schematically with a K-R curve

in Fig. 1. This criterion gives a somewhat size-dependent measurement, and so validity criteria are chosen to

minimize the size effects as well as to restrict the loading to essentially the linear-elastic regime. The various

elements of the K

test are discussed in a little more detail than are some of the other tests for fracture

toughness measurement. In this way, the K

test can serve as a model for the other discussions. The details of

this test can be found in Ref 6.

Test Specimen Selection. The first element of the test is the selection of a test specimen. Five different

specimen geometries are allowed (Fig. 2). These are the single edge-notched bend specimen, SE(B), compact

specimen, C(T), arc-shaped tension specimen, A(T), disk-shaped compact specimen, DC(T), and the arc-shaped

bend specimen, A(B). Many of these specimen geometries are used in the other standards as well. The

acronyms are standard ASTM nomenclature given in Ref 1. The bend and compact specimens (Fig. 2a and b,

respectively) are traditional fracture toughness specimens used in nearly every fracture toughness test method.

The other three are special geometries that represent structural component forms. Therefore, most fracture

toughness tests are conducted with either the edge-notched bend or compact specimens. The choice between the

bend and compact specimen is based on the following:

• The amount of material available (the bend takes more)

• Machining capabilities (the compact has more detail and costs more to machine)

• The loading equipment available for testing (discussed next)

All of the specimens for the K

test must be precracked in fatigue before testing. This means that a sharp crack

is developed at the end of a notch by repeated loading and unloading of the specimen, that is, fatigue loading.

Refer to ASTM E 399 (Ref 6) for details on precracking.

Fig. 2 Specimen types used in the K

test (ASTM E 399). (a) Single edge-notched bend, SE(B). (b)

Compact specimen, C(T). (c) Arc-shaped tension specimen, A(T). (d) Disk-shaped compact specimen,

DC(T). (e) Arc-shaped bend specimen, A(B)

The choice of the specimen also requires a choice of the size. Because the validity criteria depend on the size of

the specimen, it is important to select a sufficient specimen size before conducting the test. However, the

validity criteria cannot be evaluated until the test is completed; therefore, choosing the correct size is a guess

that may turn out to be wrong. There are guidelines (Ref 6) for choosing a correct size, but no guarantee that the

chosen size will pass the validity requirement. The test specimens must also be chosen so that the proper

material is sampled. This means that the location in the material source and the orientation of the sample must

be correct and accounted for. The ASTM standards have a letter system to specify orientation (Ref 1). As the

specimens are being prepared, requirements for tolerances on such things as locations of surfaces, size and

location of the notch and pin holes, and surface finishes must be followed.

Loading Machines and Instrumentation. The next step in the test procedure is the choice of a loading machine

and the preparation of loading fixtures and instrumentation for recording the test data. Most tests are conducted

on either closed-loop servo-hydraulic machines or constant-rate crosshead drive machines. The first machines

allow load, displacement, or other transducer control but are more expensive. They are preferred for pre-

cracking, which is usually done at a constant load range so load control is desired. The second type of loading

machine is less expensive and may give more stability but allows only crosshead control. Because this is

required in most of the fracture toughness tests, this type of machine is quite satisfactory for the actual fracture

toughness testing but is not so good for precracking.

Loading fixtures must be designed for the test. Two types can be used ( 3); choice of loading fixture depends on

the test specimen chosen. The bend specimens SE(B) and A(B) use a bend fixture. The tension specimens C(T),

DC(T), and A(T) require a pin-and-clevis loading. Note in Fig. 3(a) that the bend loading is three point; this is

the case for all bend- loaded specimens. Also note in Fig. 3(b) that the clevis has a loading flat at the bottom of

the pin hole. This allows free rotation of the specimen arms during the test and is essential for getting good

results.

Fig. 3 Test fixtures for the K

test specimens. (a) Fixtures for the bend test. (b) Clevises for the compact

specimen

For the K

test, a continuous measurement of load and displacement is required during testing. The load is

measured by a load cell, which should be on all loading machines. The measurement of displacement is usually

done with a strain-gaged clip gage that is positioned over the mouth of the crack in the specimen. An example

of a clip gage is shown in Fig. 4. Figure 3(a) shows the bend specimen with a clip gage in place. The standards

give guidelines for the accuracies and working requirements of the load and displacement gages used in the

tests.

Fig. 4 An example clip gage for displacement measurement (all dimensions in mm)

The loading of the specimen is done at a prescribed rate. It must be done fast enough so that any environmental

or temperature interactions are not a problem. On the other hand, it must be done slowly enough so that it is not

considered a dynamically loaded test. For the K

test, the load must be applied at a rate so that the increase in K

is given by the range 0.55 to 2.75 MPA /s The loading is done in displacement control, which usually

means test machine crosshead control. During the loading, the load and displacement are measured

continuously. This can be done autographically or digitally.

Test Data and Analysis. The load-and-displacement record provides the basic data of the test. The data are then

analyzed to determine a provisional K

value, labeled K

. This provisional value is determined from a

provisional load, P

, and the crack length. The P

value is determined with a secant line of reduced slope on

the load-and-displacement record (Fig. 5). The construction for P

involves drawing the original loading slope

of the load-versus-displacement record. A slope of 5% less than the original (secant slope) is then drawn. For a

monotonically increasing load, the P

is taken where the 5% secant slope intersects the load-versus-

displacement curve; this is illustrated as type I in Fig. 5. For other records in which an instability or other

maximum load is reached before the 5% secant, the maximum load reached up to and including the possible

intersection of the 5% secant is the P

. Type II illustrated in Fig. 5 is an example of one of the other types of

load-versus-displacement records. The 5% secant corresponds to about 2% ductile crack extension; this may be

physical crack extension or effective crack extension related to plastic zone development. Unstable failure

before reaching the 5% offset also marks a measurement point for P

at the maximum load reached at the point

of instability.

Fig. 5 Typical load-versus-displacement record for the two types of K

testing

The P

value is used to determine the corresponding K

value. This is calculated from the equation:

K = P f(a/W)/

(Eq 1)

where P is load, B and W are specimen thickness and width, and f(a/W) is a calibration function that depends on

the ratio of crack length to specimen width, a/W, and is given in the standard. For the calculation of K, a crack

length value, a, is required. This comes from a physical measurement on the fracture surface of a broken

specimen half. The specimen must be fractured into halves if it is not already that way from the test. The crack

length is measured to the tip of the precrack using an averaging formula given in the test standard. This value of

crack length normalized with width, W, is used in the calibration function f(a/W) to determine the K

value.

The K

is a provisional K value that may be the K

if it passes the validity requirements. The first of the two

major validity requirements is quantified as:

(Eq 2)

which limits the R-curve behavior to an essentially flat trend and ensures some physical crack extension. The

second requirement is:

(Eq 3)

which guarantees linear-elastic loading and plane-strain thickness. P

max

is the maximum value of load reached

during the test. An example of P

max

is shown in Fig. 5; σ

is the 0.2% offset yield strength. Other validity

requirements relating to specimen preparation, precracking, and crack front straightness must also be met.