Crack Paths 2009

International Conference on

C R A CPKA T H S(CP 2009)

Vicenza (Italy), 23-25 September, 2009

University of Padua – Stradella S. Nicola, 3

ISBN: 978-88-95940-28-1

A Brief History of the CrackTip Stress Intensity Factor and

Its Application

Paul C. Paris

with the assistance of Thierry Palin-Luc

Arts et Metiers Paris Tech, Universite Bordeaux 1, LAMEFIP,Esplanade des Arts et

Metiers, 33405 Talence Cedex, France

pcparis30@gmail.com

Abstract The primary objective of this work is to discuss the origins, background

and development of the elastic crack tip stress intensity factor, K, as they occurred.

The further development of the three modes and the compilations of related formulas

in the literature are discussed. The origins of applications to static crack growth

stability, and sub-critical growth due to fatigue and environmental effects are

included. Significant events such as the formation of the ASTMcommittee on Fracture

Mechanics, the adoption of DamageTolerance Analysis by the aircraft industry using

Fracture Mechanics as a basis, and the further extension of the methods to large

scale plasticity conditions are presented. Finally a discussion of early predictions of

crack paths is discussed.

I N T R O D U C T I O N

The view of fracture from the point of view of mechanics was stated by Love [1] in

his authoritative work on Theory of Elasticity in the 1890s by “The conditions of

rupture are but vaguely understood,…” At that time Coulomb and Mohr’s theories

were followed by many without considering the effects of flaws or cracks in

materials. Most often structural failures were analyzed by metallurgists who knew

little about the mechanics of the effects of flaws. As a student in Engineering

Mechanics in the early 1950s, there were studies of failure due to excessive

deformations and various forms of instability but virtually nothing on fracture. Love’s

statement was still the case. However, the beginnings of background studies leading

to modern “Fracture Mechanics” approaches for analyzing the growth of cracks were

close.

Historically, some attempts were tried in the early 1900s but here only those

connected to and leading directly to current methods will be mentioned. The first was

that of Inglis [2] in 1913. He used elliptical-hyperbolic

coordinates to solve the elastic

stress problem of an elliptical hole in a plate. Then he tried to degenerate the ellipse

into a crack and his stress solution near the crack tip became unresolved. With the

assumption of a very small radius,ρ, at the tip of the ellipse of semi major axis,a,

applied, he did obtain the stress

σ,

and a remotely applied biaxial stress,

σmax =2σ a ρ, and noted the difficulty that it encountered with

concentration,

7

σ a was the important factor for flaw

considering,ρ =0. He was close to seeing that

size effects, but in discussion did not observe that.

Later, in 1920 (and 1924) Griffith [3] used the full stress solution of Inglis to calculate

G, the elastic potential energy made available in extending the crack per unit new

crack area. He did experiments on amorphous glass, cleverly measuring the surface

γ, (energy per unit surface area) as the resistance to crack growth and elastic

tension,

σ a for crack glass tubes and spheres

modulus, E, and predicted the value of

subjected to internal pressure using an energy balance approach. The critical energy

2γEπ, where the experimental values

σ a =

balance for crack growth was given as:

of fracturing strength of the left hand side averaged 239 and compared to

independently evaluated measure of 133 for the right hand side. This was an

astounding result for predicting the fracture strength from γ and E. Good luck was

also present since glass exhibits plasticity, resisting fracture, but this was perhaps

compensated by a reduction in surface energy due to water adhesion on new glass

surfaces, encouraging fracture. Moreover, Griffith undoubtedly was aided in this work

with discussions with G. I. Taylor whowas just downthe hall at Cambridge and who

communicated the paper to the Royal Society.

Between the 1920s and 1940s the attitude was present that Griffith’s analysis applied

only to perfectly brittle materials similar to glass and was often dismissed with metal

fracture where obvious plastic dissipation of energy accompanied crack growth.

However, in the late 1940s both Irwin [4] and Orowan [5] attempted to use the

Griffith energy balance method to explain failures of metal structures, especially the

T-1 Tankers and Liberty Ships which exhibited many failures during World War II.

Indeed, Orowannoted that the plastic energy rate for cleavage fracture was more than

γ, but still gave predominately elastic failures in very large steel

1000 times that for

plates. So both hoped to be able to apply a Griffith type elastic energy balance with a

plastic dissipation term added to assess fracture instability. The most applicable

analysis of this came from papers by Irwin which culminated in his 1954 work [5].

Indeed I attended a Symposium on Plasticity in 1953 at Brown University with the

great authorities present, where Captain Wendel P. Roop of the Navy discussed ship

failures and indicated that to his best knowledge “running fracture failures had

something to do with the energy available to drive the crack” but that anything further

was still vague. No one had any comments, which he solicited to explain his

statement. As a student in Mechanics I remained perplexed that the fracture failures of

structures were still “vaguely understood”.

T H ED E V E L O P M OE FNTTH EC R A CTKIPSTRESSFIELDC O N C E P T

At the U. S. Naval Research Laboratory (NRL), where Irwin was Superintendant of

the Mechanics Division, the group of people who assisted him were capable help in

his work on fracture analysis. In addition A. A. Wells then at the Brittish Welding

Institute made frequent lengthy visits in the early 1950s to N R Land drew his

attention to a method solving elastic crack problems by Westergaard [6]. Irwin [7]

used this to obtain the significant singularity term in the elastic crack tip stress field

series expansion. The form, which he first published was:

8

E G π ⎛ ⎝ ⎜

fijθ()

⎞ ⎠ ⎟

1 2

(1)

σ ij =

+terms of r12 and higher

2r

( except for a constant term σ0 parallel to the crack )

θ is measured from the extension of the crack

where r is measured from the crack tip,

line, and G is the Griffith available elastic energy rate per unit new crack extension

area or the so called “crack extension force”. For a uniformly stressed sheet the

1 2

⎞ ⎠ ⎟

⎛ ⎝ ⎜

original “elastic crack tip stress intensity factor” is E G

= σ a w,here in later

π

π to the other side of the equation to define the current “crack

times Irwin movedthe

tip stress intensity factor” as K = EG()12 = σ π a A.gain the significance of σ a , as

an expression of the fracture size effect, for the crack in the uniformly stressed sheet

(for the Griffith configuration) is noted. In addition Irwin gave the solutions for

several other configurations in this paper. Incidentally, Irwin used “K” to denote the

stress intensity factor to honor his long time friend and colleague Joseph A. Kies.

Meanwhile, just after Irwin’s publication (see submission dates of the papers),

Williams [8] had done a polar-coordinate eigen-function elastic solution of the crack

tip field in a somewhat similar fashion to Irwin but had not enterpreted its relation to

Griffith’s work and its further implications. However, the first known expansion of

the crack tip stress field was done by Sneddon [9] in 1946 for the “penny shaped

crack”, without realizing its important implication to fracture analysis.

The fact that different configurations of crack geometries and loading methods all had

the same local crack tip stress fields differing only in intensity, as indicated by the

form of the crack tip intensity factor, explained many previously unresolved

questions. For example with small scale yielding conditions (low nominal stresses on

the uncracked remaining section), one could reason that the plastic zone would be

completely embedded within the elastic crack tip stress field and would therefore be

similar between various crack configurations and identical for equal crack tip stress

intensity values for a given material and ambient conditions. This also explained the

thickness effect on the toughness of plates with through cracks in terms of plane stress

and plane strain, Paris [10] and Irwin [11] and the apparent (or effective) elastic crack

size as increased by the influence of plastic zone. Further, in an encyclopedic source

Irwin [12] also defined the three modes of crack tip stress fields and the elastic

analysis methods to determine their stress intensity factors,K

I , KI I , KIII . These results

were further extended by Irwin [13] published in 1960. The definition of the elastic

crack tip stress intensity factors and their corresponding stress fields was then

complete. These results were soon put to use in analyzing static failure of precracked

test pieces by various researchers.

T H EI N V O L V E M EONFTHISA U T H O R

In June 1955 just after I received m y M S degree, I took a Faculty SummerPosition

with the Boeing Companyin Seattle. It was a first experience with industry. They

asked me to study fracture in order to be sure the 707 commercial transport aircraft

would not experience the type of failures that had occurred with the pressure cabins of

British Comets. MayI admit nowthat I knewnothing about fracture but was afraid to

admit it then. The initial reaction was to read as much as possible on the subject,

about 120 papers in the first weeks there. Most of those papers madeno sense at all to

9

someone schooled in Mechanics. The only reasonable ones seemed to be those of

Irwin! With that background I requested some tests of the various thicknesses of

pressure cabin skin materials of both the 707 and KC135, its sister Air Force tanker

aircraft. A very surprising result was that the 707s material, 2024T-3, increased in

fracture toughness with increasing thickness, whereas the 7075T-6 of the KC135

decreased in toughness with increasing thickness. Moreover, the 2024 was also much

superior compared to 7075 in fracture resistance for equal thicknesses. The following

winter the Chief of Structural research asked me to attend the AIAAnational meeting

where he was presenting a paper using m y data from these tests with no credit to me. I

was requested to be there to answer questions he might be asked. M y reluctant

appearance for his presentation changed to enthusiasm after the meeting, when he

asked me to become a special consultant to Boeing, while still a graduate student at

Lehigh University. Consequently, I had funds to visit Irwin at the Naval Research

Laboratory and continue m y fracture studies. Irwin always welcomed m y visits and

our inspiring discussions, exchanging thoughts on howto understand our observations

of cracking. M y resolution of the thickness effects was that it was caused by the

constraint of plane strain vs. plane stress in the plastic zone at the crack tip, [10].

Irwin [11] agreed and later published his own data on thickness effects in 1960. M y

consulting and summer trips to Boeing continued into 1957. That fall I took a position

at University of Washington in Seattle to be closer to Boeing with a part time position

there as well.

Early in this Boeing experience, in 1955, Dr. E. Roweof Boeing asked me if the

Griffith-Irwin energy balance method could help to understand fatigue crack growth.

M yinitial reaction was that fatigue crack growth could not be explained by the energy

balance method. Later in 1957 when I first saw the crack tip stress field equations m y

reaction was immediate that the fluctuation of the crack tip stress intensity factor, K,

causing fluctuations of the crack tip stress field surrounding the plastic zone could

correlate growth rates [10]. At that time we had no data to prove that approach.

However by 1959 we had data from three independent sources on growth rates in

2024 and 7075 Aluminum Alloys and correlated the rates for each alloy. W ewrote a

paper showing the correlations using K and had it rejected by three leading journals. It

then became the subject of m y doctoral dissertation at Lehigh University where

Boeing gave me funding to expand that research. It grew into a whole group working

on various aspects of Fracture Mechanics, which had a significant impact on the

overall growth of that field. Later in the development of that group Irwin became a

Boeing University Distinguished Professor at Lehigh as well.

T H EA S T MSPECIALC O M M I T T E E

Late in the 1950s the American Society for Testing Materials (ASTM)was asked by

the military to form a special committee to resolve fracture problems with the Polaris

Submarine missile. They called together all of the about 10 top Fracture Mechanics

experts at that time to participate. The meetings not only worked on resolving the

missile issue but also resulted in this group exchanging research ideas and data by

special presentations to each-other. It greatly accelerated progress in the whole field.

Later it became the regular committee E-24 which developed the testing method for

K IC , plane strain fracture toughness, labeled method E-399. Moreover the committee

produced a book, ASTM-Special Technical Publication 381, “Fracture Toughness

Testing” [14] containing the basic background knowledge, testing methods and

10

practical applications. It provided a comprehensive state of the art assessment of the

field in 1964. M yown contribution in that book was a first extensive compilation of

crack stress analysis formulas and methods, which was later superceded by the Tada

[15] Handbook.

Again, Irwin [16] contributed by providing the solution for the elliptical shaped crack.

He did so by taking the displacement solution for an ellipsoidal cavity and

degenerated the ellipsoid into a flat crack after finding that the stress solution was

untenable. He also developed a solution for the edge crack, which checked and drew

attention to the solution from Wigglesworth [17]. These were key to developing K

approximations for the part through semi-elliptical surface flaws for many significant

practical applications, missile cases, etc. Other significant contributions are to

numerous to list here ( see [15] ), however those of Koiter [18], obtaining K by

assymtotic expansions; Bueckner [19] with his weight functions; Isida [20] using

series mapping methods; and finally Newman[21] for numerical methods for surface

flaws deserve special attention.

These efforts on obtaining K formulas and methods for their development provided

the A S T ME-24 committee with necessary background to develop standard test

methods for static failure and beyond for sub-critical crack growth.

T H EE A R LAYP P R O A C HTEOS UB-CRITICACLR A CGKR O W T H

By the time the first publication on fatigue crack growth using K occurred [22], it was

realized that for subcritical growth the nominal stresses are lower than for static

failure and that the reversed cyclic plastic zone in fatigue was smaller by another

factor of 4 so that the linear elastic fracture mechanics method was much better than

for applications to static failure. Further, problems, which occurred due to

environmental crack growth under static loading, were most prevalent in extremely

high strength metal alloys. H. H. Johnson’s original work in this field was done on H

11 tool steel for example, see his earlier references in [23]. He was the first to show

that for fatigue precracked tests, K could correlate static environmentally induce

growth rates from specimens at various nominal stress levels. He also demonstrated

that the activation energy for growth corresponded to that for hydrogen diffusion in

the metal lattice. It was somewhat later that B. F. Brown of the Naval Research

Laboratory did simple precracked cantilever beam tests and observed the threshold for

static environment cracking, K ISCC . Similarly, in the late-1960s Piper of Boeing

showed the precracked threshold K ISCC for 8-1-1 Titanium Alloy in salt water was less

than 20%of the static plane strain fracture toughness, K IC for this alloy. Only slightly

above that threshold,KISCC, the growth rates were more that an inch per hour. Prior to

these tests 8-1-1-Ti alloy was a candidate material for submarines and the U.S.

commercial supersonic transport aircraft (never built). This material was also used for

R. Bucci’s [24] dissertation to demonstrate environmentally enhanced fatigue crack

growth rates of this material in salt water of as muchas 1000 times faster than that in

inert environment. These sub-critical applications all showed that linear elastic

fracture mechanics employing K was clearly more accurately applied than for static

failure.

Also in the mid-1960s Lindner [25] found a fatigue crack growth threshold, in 7075 aluminum alloy, i.e. a level f

Δ K threshold Δ K below which n growth ccurs. La er it

11

was verified that the threshold does exist, but its definition is clouded by “overload

crack closure effects”, which may corrupt its true level. Such matters are still in

dispute [26]. However the work of Elber [27] originally demonstrated that crack

closure has a significant effect on fatigue crack growth rates. Muchhas been learned

about closure since Elber’s work in the late 1960s. This is perhaps best displayed by

Newman’s [28] finite element strip yield model of crack growth analysis with

variable amplitude loading. However, muchis left to be better understood in this area.

D A M A GT EO L E R A N OC FEA I R C R A FATN DO T H EARP P L I C A T I O N S

In late 1969 the event of a crash of a U. S, Air Force F-111 aircraft created a key use

of Fracture Mechanics in fixing and continued use of that aircraft with safety. The

solution involved “proof testing” at a high load to assure that no cracks larger than a

certain size are present. Then, for the largest of cracks, which would not fail during

the proof test, environmentally enhanced fatigue crack growth calculations were made

to ensure a calculated amount of safe flying life. With the success of this method

based on Fracture Mechanics calculations the U. S. Air Force made such methods a

design basis for all existing and future aircraft. Soon thereafter, the U. S.- F. A. A.

made such requirements also mandatory for all commercial aircraft. Damage

Tolerance Analysis became one of the largest applications of Linear Elastic Fracture

Mechanics based on the crack tip stress intensity factor, K.

Of course many other applications to various structural problems occured before the

mid-1970s. A typical example were pressure vessels where a “Leak Before Break”

approach could be used involving, K, as a basis of the analysis. The Nuclear Pressure

Vessel Code adopted an analysis using an assumed 1/4 of the wall thickness surface

flaw K analysis and K IC

values adjusted for material, temperature and irradiation

damage to assure safety. Again the many other applications are too numerous to be

listed here.

SPECIALE X T E N S I O NOSFE L A S T ISCTRESSINTENSITAYN A L Y S I S

Beyond the analysis of the single dominant singularity at a sharp elastic crack tip, the

additional series terms can be evaluated. The first of these is often called the T-stress

or σ0, mentioned earlier with Irwin’s crack tip field equations. In addition there are

the next terms in the series expansion of Irwin’s tip field method that should receive

equal attention [29]. Moreover, for blunted cracks the elastic field was computed by

Creager [30, 15] in his dissertation, which simply adjusts the center of the polar

coordinates ( to the focal point of a sharp ellipse or parabolic opening shape ) within

the notch. These extensions of the crack tip stress intensity concepts have received

little attention.

F R A C T U RM E C H A N IFCOSRH I G HT O U G H N EMSAST E R I A L S

Materials with high fracture toughness, K IC , and relatively low yield strength are

often not appropriate for analysis by linear elastic methods. There, static fracture may

occur only after net section yielding for manyapplications consequently linear elastic

methods are not appropriate. At the A S T Mmeeting in 1964, which produced S T P

381, a conclusion in the discussion period was that it would not be possible to treat

12

such topics for at least ten years before such analysis ( as soundly based as linear

elastic, K-methods ) might become available.

The prevailing method was first devised by Rice [31], who defined J as an integral

form, which is the intensity factor of crack tip plastic stress field for power hardening

material. The field is:

σij=σ0

n

(2)

⎛⎝⎜

J ⎞⎠⎟ n + 1 Σ i j θ , n ( ) ,

σ0ε0r

where n is the power hardening coefficient in the stress-strain law of the type:

ε =σ⎛⎝⎜ σ0⎞ ⎠⎟ n

. This so called H R Rfield was found by both Rice [32] and Hutchinson

ε0

[33]. It is noted that for n=1 (linear elastic material) this field reduces to the Irwin

K 2

E field equations (1), noted earlier, where J = G = . Therefore Irwin’s field equations

are simply a special case of this more general plastic crack tip stress field equations

and intensity factor, J. They have been used in the early to mid 1970s to characterize

static fracture instability, fatigue crack growth, creep crack growth, etc., which shall

be regarded as beyond the scope of this discussion.

T H O U G HOT NSC R A CPKA T H AS N DA B R U PCTH A N G EINSD I R E C T I O N

W ehave all seen cracks which change their direction of growth both slowly as they

grow and abrupt changes in direction. In 1963 Erdogan [34] published some test

results for inclined crack in tension and concluded that the crack extended changing

abruptly to the direction of maximumcircumferential tension as calculated from the

elastic crack tip stress equations. This conclusion caused me to withdraw m yname as

a coauthor of this work. The plastic material, which was tested, exhibited substantial

plasticity so that the real crack tip stresses would undoubtedly not be at exactly that

same angle for maximumcircumferential tension. Indeed if the material would have

been perfectly brittle the abrupt change in direction would have been to that which

γ, exactly the

would give maximumenergy release to overcome the cracks resistance,

energy per new surface created as Griffith proposed. However with a plastic stress

field and no means of calculating the maximumenergy direction at that time or the

maximumcircumferential stress direction or the maximumof any speculated critical

quantity proposed, it was not appropriate to make any claims about a proposed reason

for the “crack path” taken.

Further with materials that exhibit plasticity, slow stable growth prior to crack

instability is always the case, therefore the R-curve of material’s resistance is a

necessary approach to changes in direction toward an instability. It is admitted here

that such an analysis is so very complex that it looks quite unlikely. Perhaps some

light will be shed on this matter here?

For fatigue crack growth matters become even more complex with cycling of loads.

Intuition has made it seem that in fatigue the crack extends toward directions that tend

to be first mode cracking ( K II =KIII → 0 )as the crack progresses. Of course this

intuitive proposal is pure speculation. Beyond these thoughts better analyses will be

welcomed here.

13

A C K N O W L E D G E M E N T

The author acknowledges the Arts et Metiers Paris Tech and Foundation Arts et

Metiers for the financial support of Paul C. Paris’ stay at LAMEFIPin 2009. The

encouragement of Professor Ivan Iordanoff, Director of LAMEFIP, is also

acknowledged with thanks.

R E F E R E N C E S

[1] Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Dover, N e w York, p121, 1944, (4th ed. reproduced), (Editions 1893,1906, 1920,1927).

[2] Inglis, C. E., Proceedings Inst. Naval Architects, Vol. 60, 1913.

[3] Griffith, A. A., Phil. Trans. Roy. Soc., London, Series A. Vol.221, p. 163, 1920.

[4] Irwin, G. R., in Fracture of Metals, Amer. Soc. Metals, 1948.

[5] Irwin, G. R. and Kies, J. A.,The Welding Journal, Res. Suppl.Vol. 33, p.193,1954.

[6] Westergaard, H. M., Trans. of ASME,J. A. Mech., Series A,Vol.66, p.49, 1939.

[7] Irwin, G. R., Trans. of ASME,Jour. Appl. Mech.,Vol 24, p.361, 1957.

[8] Williams, M. L., Trans, of ASME,J. A. Mech.,Vol. 24, p.109, 1957.

[9] Sneddon, I. N., Proc. Roy. Soc. London, Ser. A, Vol.187, p.229, 1946.

[10] Paris, P. C., Document D2-2195, The Boeing Company,1957.

[11] Irwin, G. R., Jour. Basic Engin., Trans. ASME,Ser.D, Vol.82, No.2,p.417, 1960.

[12] Irwin, G. R., Fracture, Handbuch der Physik., Vol. VI, p. 551 Springer, 1958. [13] Irwin, G. R., Proc. of 1st Symp. on Naval Struct. Mech., p.557, Pergamon,1960.

[14] Paris, P. C., in Fracture Toughness Testing and Its Applications, Proceedings of

the Symposiumin Chicago in June 1964, A S T MSTP 381, 1965.

[15] Tada, H., Paris, P. C. and Irwin, G. R., The Stress Analysis of Cracks Handbook, 3rd edition, A S M EPress, 2000.

[16] Irwin, G. R., Trans. of ASME,Jour. Appl. Mech., Vol. 29, p.561,1962.

[17] Wigglesworth, L. A., Mathematica, Vol. 5, p. 67, 1957.

[18] Koiter, W. T., Trans. of ASME,J. A. Mech., Vol.32, p. 237, 1965 & also in [15].

[19] Bueckner, H. F., Z A M M V,ol. 50, p. 529, 1970 & also in [15].

[20] Isida, M., Engineering Fracture Mechanics, Vol. 7, p. 505, 1975 & also in [15].

[21] Newman,J. C. Jr., A S T MSTP 687, p.16, 1979.

[22] Paris, P. C., Gomez,M. P., and Anderson, W. E., The Trend in Engineering,

University of Washington (Seattle), 1961.

[23] Johnson, H. H., and Paris, P. C., Engin. Fract. Mech., Vol.1, No.1, Paper 1,

Pergamon Press, 1968.

[24] Bucci, R., PhD. Dissertation, Lehigh University, (P. C. Paris director), 1970.

[25] Lindner, B., M SDissertation, Lehigh U., (P. C. Paris director), 1965.

[26] Newman,J. C. Jr., Private Communication 2008.

[27] Elber, W., Journal of Engineering Fracture Mechanics,1970

[28] Newman,J. C. Jr., Comprehensive Structural Integrity, Vol. 4, Elsevier,2003.

[29] Paris, P. C., and Tada, H., Proc. of Internat. Conf. on Fatigue Dam. to Struct.

Materials V, Internat. Jour of Fatigue, 2005.

[30] Creager, M., and Paris, P. C., Int. Jour. of Fract. Mech., Vol. 3, p. 247, 1967.

[31] Rice, J. R., Trans. of ASME,Jour. Appl. Mech., Vol. 35, p.379, 1968.

[32] Rice, J. R., and Rosengren, G. F., Journ. of Mech. and Phys. of Solids,Vol.16,

p. 1, 1968.

[33] Hutchinson, J. W., Journ. of Mech. and Phys. of Solids, Vol.16, p. 13, 1968.

[34] Erdogan, F., and Sih, G. C., Trans.of ASME,Ser. D, Vol. 85,p. 519, 1963.

14

Influence of Hydrogen and Test Frequency on Fatigue Crack

Path

Yukitaka Murakami1and Saburo Matsuoka1

1 Kyushu University and The Research Center for Hydrogen Industrial Use and Storage

(HYDROGENIUS)A,IST, 744 Moto-Oka, Nishi-ku, Fukuoka, 819-0395 JAPAN

ymura@mech.kyushu-u.ac.jp

ABSTRACT.The present paper overviews the recent progress on H E obtained at

HYDROGENIUST.he influence of hydrogen and strong test frequency on fatigue crack

path is discussed with a particular attention. The mechanism of change in fatigue crack

path depending on test frequency is explained by the coupled effect of hydrogen induced

localized plasticity at crack tip and test frequency.

The test frequency of the fatigue test was switched from f = 2 Hz to f = 0.02 Hz and

the crack growth behaviour was observed by the replica method. These two step fatigue

tests were repeated and the variation of the crack growth behaviour by switching the

test pattern from f = 2 Hz to f = 0.02 Hz was investigated.

Particularly important phenomena are the localization of fatigue slip bands and also

strong frequency effects on fatigue crack growth rates. For example, with a decrease in

frequency of fatigue loading down to the level of 0.02 Hz, the fatigue crack growth rate

of a Cr-Mosteel was accelerated by 10 - 30 times. The same phenomenon also occurred

even in austenitic stainless steels at the frequency of the level of 0.001 Hz. Striation

morphology was also influenced by hydrogen.

The crack path of the hydrogen-uncharged specimen was monotonic and showed no

particular variation even after switching the test frequency from f = 2 Hz to 0.02 Hz and

also 0.02 Hz to 2 Hz. The monotonic moderate curving of the crack path was caused by

the growth of plastic zone size due to increase in the crack length, i.e. the stress

intensity factor range. Namely, the plane stress condition is gradually satisfied and the

crack extension by shear mode ahead of crack tip becomes dominant near specimen

surface. On the other hand, the crack of hydrogen-charged specimen grew in the

inclined direction under f = 2 Hz, though the crack grew straight under f = 0.02 Hz.

I N T R O D U C T I O N

In order to enable the “hydrogen society (or hydrogen economy)” in the near future, a

number of pressing technical problems must be solved. One important task for

mechanical engineers and material scientists is the development of materials and

systems which are capable of withstanding the effects of cyclic loading in hydrogen

environments. In the past much research has been concentrated on the phenomenon

15

known as hydrogen embrittlement [1-3]. Hydrogen effects on slip localization [2-4],

softening and hardening [4-12], hydrogen-dislocation interactions [12-14] and creep

[15] have been also reported. However, most research on H Eover the past 40 years has

paid insufficient attention to two points that are crucially important in the elucidation of

the true mechanism. One is that, in most studies, the hydrogen content of specimens was

not directly measured. Second, detailed studies that have quantified the influence of

hydrogen on fatigue crack growth behaviour, based on microscopic observations are

very rare; most studies have only examined the influence of hydrogen on tensile

properties[16-33]. In order to produce components which must perform satisfactorily in

service for up to 15 years, there is an urgent need for basic, reliable data on the fatigue

behaviour of candidate materials in hydrogen environments.

Twotypical fuel cell (FC) systems are the stationary FC system and the automotive

FC (Fuel Cell Vehicle, FCV)system. In the F C Vsystem, many components such as the

liner of high pressure hydrogen storage tank, valves, pressure sensors, hydrogen

accumulators, pipes, etc, are exposed to high pressure hydrogen environment for a long

period up to 15 years. Sufficient data have not been obtained on the content of hydrogen

which diffuses into metals during a long period of exposure to hydrogen. “Howmuch

hydrogen is contained in components in the fuel cell related system?” is a very

important question. But this question is difficult to answer.

M A T E R I A AL SN DE X P E R I M E N TMAELT H O D S

Materials and specimens

The material used in this study is a Cr-Mo steel JIS SCM435.Table 1 shows the

chemical compositions and the Vickers hardnesses (Load: 9.8 N) of these materials.

Hydrogen contents were measured by the thermal desorption spectrometry (TDS) using

a quadruple mass spectrometer. The measurement accuracy of the T D Sis 0.01 wppm.

Figures 1(a) and (b) show the fatigue specimen dimensions and the dimensions of the

small hole which was introduced into the specimen surface. After polishing with #2000

emery paper, the specimen surface was finished by buffing using colloidal SiO2 (0.04

m m )solution. A small artificial hole, 100 μ m diameter and 100 μ mdeep, was drilled

into the specimen surface as a fatigue crack growth starter. In the hydrogen-charged

specimens, the specimen surface was buffed after hydrogen charging, and the hole was

then introduced immediately.

Table 1 Chemical composition (w%, *wppm)and Vickers hardness H V

C Si

M n P

S Ni Cr M o Cu H V

SCM435 0.37 0.18 0.78 0.025 0.015 0.09 1.05 0.15 0.1 330

16

Figure 1. Dimensions of the fatigue test specimen and drilled hole

Method of hydrogen charging

Hydrogen was charged into the specimens of SCM435by soaking them in a 20%

ammoniumthiocyanate solution (NH4 SCN).

Method of fatigue testing

Fatigue tests of the hydrogen-charged and uncharged specimens were carried out at

room temperature in laboratory air. The fatigue tests for SCM435were conducted at a

stress ratio R = −1 and at a testing frequency between 0.02 Hz and 20 Hz.

Following the fatigue tests, in order to measure the hydrogen content remaining in

specimens, 0.8 m mthick disks were immediately cut from each specimen, under water

cooling. Then, hydrogen contents of disks were measured by TDS. Measurements were

carried out up to 800 °C at a heating rate of 0.5 °C/s.

R E S U L TASN DDISCUSSION

The basic mechanism of void growth in tensile test

The hydrogen-charged specimens show a peculiar void growth inside the specimen in

tensile test. Figure 2 shows an interesting difference of void growth behaviour between

the uncharged specimen (Fig. 2(a)) and the hydrogen-charged specimen (Fig. 2(b)). The

basic mechanism of the void growth lateral to tensile axis in the hydrogen-charged

specimen (Fig. 2(b) and (c)) can be considered consistent with that of fatigue crack

growth(Fig. 9).

17

UnchargedUncharged

Hydrogen-chargedHydrogen-charged

H

H

Inclusion

Inclusion

H

H

H

H H H

H

H

HHHHHHHH

H

20 μ m

500mm500mm

H

H

Voids are elongated in the direction perpendicular t the tensile axis. HydrogenHydrogen (a) Uncharg d (0.05p m)

H

(a) Nucleation

H

NeckingNecking

H

H

H

H

H H H H H H H

H

H H H H H H H

H

H

H

500mm500mm

H

Voids in longitudinal cross section of tensile fractured specimens. 20 μ m

(b) Growth

(b) Hydrogencharged(0.91ppm)

HH H H

H

ShearingShearing H

HH

H

H

H H

H

H

HH

H

•

H

H

• Nucleation of voids occurs at the lower true strain.

(c) Coalescence

Schematicillustration of nucleation, growth and

Hydrogen enhances

coalescence of voids.

Localized Slip Deformation.

* T. Matsuo, S. Matsuokaand Y. Murakami (2007)

Figure 2. Development of voids in tensile test of the hydrogen charged specimen of a

pipe line steel, JIS-SGP (0.078% carbon steel)[34]

Effect of Hydrogen on Fatigue Behaviour of Cr-Mosteel SCM435

Cr-Mo steel: JIS SCM435is a candidate material for the hydrogen storage cylinder of

hydrogen station equipped with 35MPa hydrogen supply to FCV. The effect of

hydrogen on fatigue crack behaviour of SCM435was investigated in details by H.

Tanaka et al [35]. In this paper, a part of their work will be introduced.

Figure 3 shows the relationship between crack length a and number of cycle N under

the tension- compression stress amplitude σa = 600 MPa. The fatigue crack growth rate

da/dN of the hydrogen charged specimens is much higher than the uncharged specimens.

Another important point is that da/dN increases with decreasing test frequency. It is

presumed that there is sufficient time for hydrogen to diffuse and concentrate at crack

tip under low test frequency.

Figure 4 shows the relationship between da/dN and stress intensity factor range ΔK.

Figure 5 shows the relationship between the acceleration of crack growth rate defined

by the ratio of da/dN with hydrogen to da/dN in air and the test frequency f. The most

important result in Figure 5 is that da/dN at Δ K < 17MPa√ m(da/dN = 1.0×10

8 m / c y c l e -1.0×10-7m/cycle) and f < 2Hz for the hydrogen charged specimens are

merged into one line regardless of the value off and the crack growth rates under these

conditions are 30 times higher than those for uncharged specimens.

This frequency tendency can also be confirmed by Fig. 5. This tendency can be

explained as follows. At very low crack growth rate da/dN <1.0×10-7m/cycle, hydrogen

18

has sufficient time to diffuse into the crack tip process zone, because the location of

crack tip does not move so much distance toward the direction of crack extension and

the crack tip stays inside the process zone until hydrogen concentrates. On the other

hand, for da/dN >1.0×10-7m/cycle, it is presumed that crack passes the process zone at

crack tip before hydrogen concentrates and the rate of acceleration of da/dN varies

depending on test frequency. However, regardless of the values of frequency, da/dN of

hydrogen charged specimens gradually merges to the line of da/dN of uncharged

specimens at higher value of da/dN, because crack grows much faster than hydrogen

diffusion to crack tip. Thus, the crack growth rate and hydrogen effect are mutually

coupled.

The dotted line of Fig. 4 shows approximately 30 times acceleration of fatigue crack

growth rate in presence of hydrogen and can be considered to be the upper bound of

hydrogen effect which should be used for the fatigue life prediction design of hydrogen

storage cylinder.

2000 3000 4567

f=0.2Hzf=0.2Hz

0.58ppm→0.49ppm0.58ppm→0.49ppm f=2Hzf=2Hz

f=20Hzf=20Hz

0.53ppm→0.27ppm0.53ppm→0.27ppm

Hydrogen-charged Uncharged (Hydrog ontent：0.01ppm) ：20Hz( = =100μm) U(

Hydrogen-charged

：20Hz(d=h=100μm)

：2Hz(d=h=100μm)

：0.2Hz(d=h=100μm)

0.58ppm→0.49ppm

1000

0

10000

20000

30000

40000

Numberof cycles，N

Figure 3. Relationship between crack length 2a and number of cycles N. σa = 600 MPa.

Material: SCM435(H. Tanaka, et al[40])

19

10*5

ll\"

Cgda/dNr(rm/cyacolre)cwakteh,

10*7

i Uncharged

\

(Hydrogencontent:

0.01 ppm)

6 Q6

Constant frequency

10*8

0 : f=2OHz

Frequency switched :

A zf=2Hz

El : f=0.02Hz

Hydrogen-charged

Constant frequency

9 : f=20Hz(0.53—>O.27ppm)

A : f=2Hz(0.58—>0.49ppm)

O : f=0.2Hz (0.58—>0.49ppm)

Frequencyswitched

V : f:2Hz(O.S8—>O.29ppm)

El : f=0.02Hz(0.58—>0.29ppm)

-10 10 10

20

30 40 50 60 708090100

Stress intensity factor range, A K ( M P a ~ / _ m )

Figure 4. Relationship between da/dNand AK. Material: S C M 4 3 5(H.Tanaka, et al[40])

5O

(0.56ppm

(056mm

i

i i

\l \ [ll]

lppm ‘

AK‘=. 17

(d/(1N)h/(da/dzv)air

I

TM'MPaJ'm

H”

l l

.Sppm)

052mm)

50 M P a f m

l

60 M P w / ‘ m

l

0.49ppm)

)

0.1

1

10

100

0.01

Test frequency, f (Hz)

Figure 5. Relationship between acceleration of crack growth rate (da/dN)h/(da/dN) air

and frequency f. Material: S C M 4 3 5(H. Tanaka, et al[40])

Figure 6 shows the crack shapes and slip bands morphologies. The crack of the

hydrogen charged specimen looks thinner than the uncharged specimens. The crack

paths of the hydrogen charged specimens tested under f : 0.2 and 2Hz are relatively

more linear than those of the uncharged specimens and also that of the hydrogen

20

charged specimen tested under f = 20Hz. The crack tip of the uncharged specimen has

many slip bands spreaded broad beside the crack line. On the other hand, the slip bands

of the hydrogen charged specimens are localized only at very narrow area beside the

crack line. Kanezaki, et al [36] reported the same slip localization at crack tip and linear

crack path in the fatigue of hydrogen charged austenitic stainless steels.

15μm15μm

15μm15μm

(a) Uncharged specimen,

σa =600MPa, f= 20 Hz (b) Hydrogen-charged specimen, σ

a = 600 MPa, f=20 Hz

10μm10μm15μm15μm

15μm15μm

(c) Hydrogen- charged specimen,

σa = 600 MPa, f = 2 Hz (d) Hydrogen-charged specimen,

σa = 600 MPa, f = 0.2 Hz

Figure 6. Slip bands and fatigue cracks in uncharged and hydrogen-charged specimens

at Δ K ≒ 2 0M P a √ m .Material: SCM435(H. Tanaka, et al [40])

In order to make clear the mechanism of slip bands localization and linear crack path

more in details, the following fatigue tests were carried out.

1. First, the fatigue test was carried out at f = 2Hz and the crack growth behaviour

was observed by the replica method.

2. Second, the test frequency of the fatigue test was switched to f = 0.02Hz and the

crack growth behaviour was observed by the replica method.

These two step fatigue tests were repeated and the variation of the crack growth

behaviour by switching the test pattern from 1 to 2 was observed. The results of these

tests were very interesting as described in the following.

Figures 7(a) and (b) show the overall crack growth paths. The crack path of the

uncharged specimens is monotonic and show no particular variation even after

switching the test frequency from f = 2Hz to 0.02Hz and also from 0.02Hz to 2Hz. The

monotonic moderate curving of the crack of Fig. 7(a) is caused by the growth of plastic

zone size due to increase in a, i.e. ΔK. Namely, the plane stress condition is gradually

satisfied and the crack extension by shear mode ahead of crack tip becomes dominant

near specimen surface. Figure 8 explains this mechanism caused by subsurface plane

strain condition and surface plane stress condition.

21

However, the crack of the hydrogen charged specimen for Δ K > 40MPa√m t,he

influence of switching the test frequency appears very clearly in the variation of slip

bands morphologies and crack path. The crack grows in the inclined direction under f =

2Hz, though the crack grows straight under f = 0.02Hz. Figure 7(c) is the magnification

of the localization of slip bands in the region off= 0.02Hz. As shown by the marks ■

and ▼ in Fig. 4, the da/dN under f = 0.02Hz in this region (■) is approximately 10 times

faster than da/dN under f = 2.0Hz. The cause for the difference between the inclined

crack growth for f = 2Hz and the linear crack growth for f = 0.02Hz can be interpreted

as follows.

(a) Crack path in the uncharged specimen.

(b) Crack path in the hydrogen-charged specimen.

Δ K ≒ 4 0 M P a √ m

0.02Hz

4 8 M P a √ m

5 5 M P a √ m

0.02Hz

2Hz

30μm30μm

Crack propagation

(c) Crack path and slip bands in the hydrogen-charged specimen

Figure 7. Fatigue crack path and slip bands for the test with two frequencies of 0.02 Hz

and 2 Hz at σa = 600 MPa, Material: SCM435 (H, Tanaka, et al [40])

As explained with respect to Fig. 6, hydrogen influences the localization of slip band

and decreases the plastic zone size at crack tip. As the test frequency f decreases, this

hydrogen effect is enhanced, resulting the plane strain condition with smaller plastic

zone size even at high ΔK.

22

Thus, the inclined crack growth behaviour under f = 2Hz in Fig. 7(b) and (c) is due to

large plastic zone size with less hydrogen effect which is almost similar to the case of

Fig. 7(a). It must be noted that these inclined cracks are made by shear mode fracture

and are inclined to specimen surface (see the mechanism explained in Fig. 8).

(a) Plane stress

(b) Plane strain

(e)Plastic zone produced at crack under no hydrogen (f)Plastic zone produced

at crack under hydrogen

(c) Schematic image of plastic zone at crack tip

(g) Nohydrogen effect

(h) Hydrogen effect

(d) Difference in fracture between plane stress

and plane strain

Figure 8. Hydrogen and frequency effects on plastic zone size

Hydrogen-induced striation formation mechanism

Based on the data for striation shape, which involves information on the crack growth

mechanism, we will discuss the mechanisms of crack tip opening, crack growth, and

decrease in H/s induced by hydrogen. W ewill also discuss the mechanisms related, not

only to the mechanism of hydrogen embrittlement in fatigue, but also to the basic

mechanism of hydrogen embrittlement in static fracture.

The distributions of maximumshear stress and of hydrostatic tensile stress, ahead of

the crack tip, under plane strain can be easily calculated by the elastic solution of crack.

In the case when there is no hydrogen, slip from the crack tip occurs in the 75.8°

direction, where the shear stress has its maximumunder plane strain. The slip in the

75.8° direction causes both crack tip blunting and crack growth at the initial stage of

loading. Under a given load level crack tip blunting occurs as a crack grows and, finally,

at the maximumload crack growth is saturated. This mechanism has been well known

in previous studies on metal fatigue [37-40]. On the other hand, for the case when

hydrogen is present, Sofronis et al. [41] showed, by numerical analysis of hydrogen

diffusion near the crack tip, that hydrogen diffuses to, and concentrates at, the region

23

where the hydrostatic tensile stress has its maximum.Tabata, Birmbaumand et al. [18]

suggested, through T E Mobservation of the interaction between dislocations and

hydrogen, that yield stress decreases as a function of hydrogen pressure. Considering

their experimental result, it is therefore presumed that yield stress decreases at a region

where hydrogen concentrates. As a result, crack tip blunting and crack growth both

occur during the whole load cycle. Namely, even if crack tip blunting occurs at a given

load level that is below the maximumload, further slip takes place at the growing crack

tip where hydrogen repeatedly concentrates. This further slip reduces crack tip blunting

in the 75.8° direction; both crack tip blunting and crack growth occur in a coupled

manner during the whole load cycle. As shown in Fig. 9, the fatigue crack growth

mechanism of ductile materials is based on striations formed by slip at a crack tip. This

differs from the static fracture mechanism of B C Cmetals. However, the diffusion and

concentration behaviour of hydrogen near a crack tip, or near a notch root, is similar in

both F C Cand B C Cmetals. Furthermore, with decreasing fatigue test frequency, there is

sufficient time for hydrogen to diffuse towards crack tips, and a large amount of

hydrogen concentrates near crack tips. As a result, a crack continues to grow before the

crack tip becomes fully blunt.

It is well knownthat there are three types of crack closure which control fatigue crack

growth [43-45]. From the viewpoint of plasticity-induced crack closure [42], it follows

from the above discussion that the amount of plastic deformation (plastic zone size) at

the maximumload, Pmax, is smaller in the presence of hydrogen than in its absence.

Figures 9(a) and (b) illustrate the effect of hydrogen on the crack closure mechanism

during one load cycle. Figure 9(a-2) shows the crack opening behavior on the way to

the maximumload in the absence of hydrogen. The crack tip opening displacement

reaches its saturated value at a given load level and crack growth ceases. As shown in

Fig. 9(b-2), however, hydrogen concentrates near the crack tip in the presence of

hydrogen. Hydrogen concentration enhances further crack opening by slip, and crack

growth continues. Since the corresponding plastic zone at the crack tip does not become

large, the plastic zone wake which remains on the fracture surface is shallow. Figure

9(c) and (d) are schematic illustrations of plastic zone wakes with and without hydrogen.

Ritchie et al. [46, 47] pointed out that the reason for the increase in crack growth rates

of a Cr-Mo steel, in a hydrogen gas environment, is the increase in ΔKeff due to the

absence of oxide induced crack closure. However, as shown in Fig. 9, hydrogen

influences all three types of crack closure mechanisms. In particular, the effect of

hydrogen on plasticity-induced crack closure is crucially important for all three types of

crack closure mechanism. This phenomenon results both in decrease in the height of

striation and in decrease in the crack opening load (decrease in ΔKop and increase in

ΔKeff).

As has been described in the previous paragraph, a crack grows continuously during

loading, in the presence of hydrogen, even before the crack opening displacement

reaches its maximumvalue. Consequently, the crack tip shape at the maximumload is

sharper in the presence of hydrogen than in its absence. The effect of hydrogen on

plastic deformation at a crack tip may be reduced during unloading. This is because the

stress field at the crack tip becomes compressive. Nevertheless, it is presumed that the

24