The experimental and theoretical knowledge in this field is presented. The different relations which correlate the number of cyles to rupture with strain or strain-energy are given. The application of low-cycle fatigue concepts to the crack initiation and crack propagation are briefly studied

Bathias, C.

English

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https://ntrs.nasa.gov/search.jsp?R=19780011592 2020-03-22T04:19:00+00:00Z
NASA TECHNICAL MEMORANDUM
	 NASA TM-75226
DIFFERENT ASPECTS OF IOW-CYCLE FATIGUE
C. Bathias
Translation of "Diff4rents points de vue
Sur la fatigue oligocyclique", Mechnique
Materiaux Electri.cite, No. 323-324, Novem-
ber, 1976, pp. 3-5
(NASA-TI-75226)	 ^.IFFF.RFNT ASPECTS OF
N73-19535
Lnw-CYCLE FA T_I , 1 IE ('rational Aer^nauri::s an9
Space NIMinistration)	 12 p HC A02/1 F A01
	
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x,3/39 03646
t.1AR 1978
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NATIONAL AERONAUTICS AND SPACE ADI^aNISTRATION
WASHINGTON, D. C. 20546	 MARCH 1978
V
rf
I
STANDARD TITLE PAGE
J,,	 I	 . ornment Accession No. 3.	 Recrp-enr's Catalog No.
NASA TM-75226
FIGvo
4.	 Tale and Subt,tle 5. Report 
March 1978DIFFERENT ASPECTS OF LOW-CYCLE FATIGUE
6.	 Perh .min;, O,Sarr,sot,on Code
7.	 Author(&) 6.	 Performing Organisation Report No.
C.	 Bathias
10.	 Work Unit No.
Contract or Grant No.F11.
9.	 Pe,fo,m,ng Organisation Name and Address NASw-2791
SCITRAN 13.	 Type of Report and Period Covered
csox 5456
to Barb Translation
12.	 S^onsor;ng A envy Nome and Address
ionai Aeronautics and Spare Administration
ng Agenc y CodeWashington, D.C.	 [0546
15.	 Supplementary Notes
Translation of tt Differents points de vue sur
	 la fatigue oligocycliquett,
Mechnique Materiaux Electricite, No.
	 323-324, November, 1976, pp.
	 3-5
16.	 Abstract
In this introduction to low-cycle fatigue,
	 the experimental and theoretica
knowledge in this field is presented.
	 The different relations which cor-
relate the number of cycles to rupture with strain or strin-ene gy are
The application of low-cycle fatigue concepts to t^e crackgiven.
initiation and crack propagation are briefly studied.
17.	 Key words (Selected by Author(s))
	
18.	 Distribution Statement
Unclassified - Unlimited
19.
	 Security Closstf. (of this (eport)
	 20.	 Security Clossif. (of this pope)
	 21. No. of Pages	 122.	 P,,ce
Unclassified
	 Unclassified	 12
URi(;[Niu, PAGI; it TOF Pf.XAR QUAL ",
Q^ 1.)
DIFFFRENT ASPECTS OF LOW-CYCLE FATIGUE
by C. Bathias (UTC and SNIAS)
ABSTRACT
In this introduction to low-cycle fatigue we present the experimental 	 /3*
theoretical means used to study and predict fatigue leading to rupture
with a small number of cycles.
The different relationships between the number of cycles to rupture and
deformation or the energy dissipated through deformation are briefly
covered. The applications of low-cycle fatigue to crack initiation and
propagation are touched upon.
Author's English Abstract
In this introduction to low-cycle fatigue, the experimental and theoretical
knowledge in this field is presented. The different relations which
correlate the number of cycles to rupture with strain-energy are given.
The application of low-cycle fatigue concept to the crack initiation
an] crack propagation are briefly studied.
1. INVESTIGATION MF.T11OD
Low-cycle fatigue assumes several aspects the first of which is attached
to the etymological meaning of the words, to the low number of cycles
before rupture occurs, be it less than 50,000 cycles for Coffin (1), or
less than 100,000 cycles for Cazaud (2).
Regardless of the number of c ycles to which we refer, the main idea
distinguishing low-cycle fatigue from fatigue is based on the deformation
parameter involved in this investigation method instead of stress in
umbers in margin indicate pagination in original foreign text.
Woehler's method or instead of the stress intensity factor for studying
cracks using Paris' relationship.
The expression "low-cycle fatigue , " therefore implicitly assumes another
aspect associated with the investigation method itself and means of
computation used to study procedures connected with fissure initiation
and generation.
Present developments in low-cycle fatigue are undoubtedly tied to the
effectiveness of means of computation used, for predicting lifetimes
using Morrow's method (3) as well as determining crack propagation
velocities according to Tomkins (4) or evaluating the number of cycles
at crack initiation from the edge of a hole (5).
The advantage of this investigation method therefore exceeds the
scope of low-cycle ruptures 	 that gave it birth but also lies in
a specific concept for testing and computing damages from fatigue
starting with the imposed deformation or the energy dissipated through
deformation.
2. APPLICATIONS
For different reasons, low-cycle fatigue is of interest to metallurgists,
mechanics and physicists ^pecializing in solids.
From the standpoint of the evaluation of materials, we first derive a
life duration characterized by a number of cycles to rupture in terms of
the applied stress and of the environment, temperature in particular.
From the standpoint of the mechanical behavior of maLerials, the study
of cyclical cold-working leads to a knowledge of cyclical mechanical
properties: elastic limit, strengthening and cold-working coefficient.
-2-
iFrom a practical standpoint, the cyclic mechanical properties make it
possible to explain and to predict the behavior under fatigue, clearly
revealing the influence of thermal treatments and of the microstructure
in general.
Fin311y, from a fundamental point of view, low-cycle fatigue is approached
through the application of the theory of dislocations to cyclic
	 plastic
deformations, whether the latter are generalized or, on the contrary,
localized on the surface or at the leading edge of a fissure.
Low-cycle fatigue, a multi-discipline science, finds numerous applications
in the nuclear industry for nuclear vessels, in the aeronautics industry
for engines and landing gears, in the mechnical industry for all
problems dealing with optimization of structures, when there is a
concentration of stresses or strains.
It is true that there seem to be relatively few accidental ruptures of
parts in use caused by low-cycle fatigue. This low number of damages
is explained by the complete nature of the break, a break that takes place
within the lifetime with a small amount of dispersion relative to the
amount of endurance. Therefore, in this case, the probabilistic aspect
has less impo,tance than in the case of fatigue due to a large number
of cycles. The deterministic aspect dominates whether we are evaluating
an alloy or computing a structure. The engineer knows a priori that a
part submitted to low-cycle fatigue is destined to be ruined within
a more or less brief amount of time. Therefore, he will not seek to
determine an endurance range as in fatigue caused by a large number of
	 /4
cycles, but will seek a maximum lifetime as a function of stress, the
state of deformation or strain and of material properties.
For that purpose, we have available theoretical and experimental means
that will be explained in the following statements and that we will
-3-
ORIGMAL PAGE IS
OF POOR QUALITY
NEW
introduce with the help of a few examples to show the main points of
this subject.
3. THE MAIN POINTS OF T11FORF.TICAL AND E\PERiMENTAI. MEANS
Within the plastic range, under cyclical stresses, metal can harden,
1	 soften or remain stable. By observing the change in the mechanical
h y steresis lor;,;:, we determine a curve for cyclical metal hardening
which gives the stable state of the associated stresses and deformations.
Like the	 steady tension curve, the cyclic	 curve for metal hardening
is approximated by a power function of the form:
oa=K• (n'—
2
where a = alternate stress
a
Acp= amplitude of plastic deformation
R' = coefficient of cyclic 	 strengthening
n' = coefficient of cyclic 	 metal hardening
Figure 1 gives cyclic	 metal hardening curves for two aluminum alloys:
an A-114C1 in the T4 state and an A-1 1 2(N TO, meat-treated for 10 hours at
190 C and 22 Hours at 2030.
Results show that the A-114GI and A-1 1 ?CN alloys in the under- annealed
state gain strength under cyclical plastic deformation while the A-11?CN
alloy heat-treated to the maximum of its static properties has a tendency
to lose strength. These considerations tend to help select materials
to use, keeping in mind that, for a given elasticity limit, the more
an alloy increases in strength under cyclic, 	 stresses, the more it
is likely to remain in pla-e under large deformations.
-4-
cons
A.uaGi t• I_^ _.'_
4.woNret•^I-- cons
♦. UMN7{(E1
	
consp
ant
ant	
heat-treated at 1900C
for 10 hours
ant -_ hat-1rcated at 2030Cours
`^
Figure 1. Cyclic
	 Metal-Hardening Curves
Lifetime expressed in the number of cycles before rupture is given
respectively by Manson-Coffin's relationship if we only consider the
applied plastic deformation, or by Morrow's relationship if we consider
total deformation.
Ocp = e'f(2Nf)-c
2	 o'f
GE = e'f(2Nf)'C+— (2Nf)b
^	 E
where E	 = Young's modulus
NV	 = Number of alternations before rupture
A(. p = Amplitude of plastic deformation
At	 = Amplitude of total deformation I
I
-5-	 ptGE IS
(1RI p^UR QU ^yTL'Y►
E' 1 	 = coefficient of ductility under fatigue
01 	 = coefficient of resistance to fatigue.
The two above relations obtained experimentally show that ductile
metals with large e'f values generally show good resistance to applied
deformations. These same materials will not have as good a resistance to
applied stresses.
Results obtained for the two light alloys previously mentioned are
recorded in Figure 2. Although the elasticity limit for the A-112GN
alloy is greater than that for A-U4G1, we find that their behavior
is similar under low-cycle fatigue. Let us note that for lifetimes of
ver y
 short duration not exceeding ten cycles, the under-tempered A-U2GN
allo y is the hest.
O
A..gr.4TVA "	 t~l^at-Arvated at 190 C\\^	 AVIC-14 VW	 r 1 lours	 O
~ V rt-;EV'gted at 
2n 1 C
Ninire 2. Lifetinu, as a function of the aanlied deformation
Another approach to low-c ycle fatigue proposed byHalford and "sorrow
consists of determininf; lifetime as a function of the energv dissipated
through plastic deformation:
Wf -- NIAW
1I
e 11^
-6-
The energy of plastic deformation per cycl y
 L& is comput
with the area of the hysteresis loop, or for a sinusoids
1—n'
AW=2oaAcPll+n'
using the same notations as before.
Figure 3 gives results for the two light alloys studied.
the energy of plastic deformation before rupture increas
number of cycles before rupture in accordance with the c
law:
Wf = c(2Nf)3
► .u^cl t^ _
•, U104 n 1 Aa	 -- _
.MIN it(T).
	
'.r
I
1
M I
rigure 1.	 Lifetime as :a function of the energy dissipated throxigh
plastic deformation
The three approaches that we have just described, starting with
cyclic metal-hardening,, deformation and dissipated energy, represent
the key means used in studying low-cycle fatigue. They are covered in
deta-'l by Pineau, Lemaitre and Lieurade.
-7-
f^
i
Low-cycle fatigue lifetime under the effect of variable amplitude
stresses is difficult to determine. Miner's law based on the linear
accumulation of the damage does not give complete satisfaction. Landgraf
has recently proposed a relationship, similar to Miller's, introducing
damage per alternation (6), or-
1	 1 Arp1	 C
di --
2 N( i NIkAtt i
where
	 Nt = lifetime at the elastic /plastic transition.
There is a rupture when Id i = 1.
7o take into account the non-linear cumulation of damages, Chaboche
)xoposes a differential law (7) more elaborate than Landgraf's to
express basic damage.
Another attempt has been made by Thang Rui Ouoc (A), an attempt
according to which damage would be tied to the energy of plastic
deformation accumulated at each cvcle. Rupture would occur when:
Vi('- 2:i n; L W i
Let us finally note, as recalled above, that crack initiation and
propagation due to fatigue can be treated by considering that in both
cases, the processes result from localized low-cycle fatigue. Smith (9)
has thus shown that the number of cycles at initiation confirmsthe
following relationship:
Log Ni '- A + R Le7 (F p rnix t a; ^/I
Using a similar approach, lomkins shows that the fissuration velocity
associated with plastic deformation at the bottom of the crack is
expressed by the following relationship:
d1	 n^	 Y.1 2	
2(i+1Q
I k e p)
d 	 a 1211	 1
► RIG^AR
)V pW QU ALl rY-g- 
in which J. is the length of the crack, T is the rupture stress,
K is the strengthening coefficient and S is the coefficient of cyclic
metal hardening.
These two relationships were recently verified with steels (10, 11).
These marginal aspects of low-cycle fatigue will not be covered here
but it is good to mention them to properly show that the field of
fatigue is not only relegated to a technological question but that it
constitutes, by itself, a multi-discipline means of investigation.
BIBLIOGRAPHICAL REFERENCES
(1) L.F. Coffin - Manual on Low-Cycle Fatigue Testing, STP 465, 1969.
(2) R. Cazaud - Metal Fatigue, Dunod, 1969.
(3) .1. D. Morrow - Cyclic Plastic Strain Energy and Fatigue of Metals,
ASTM STP 378, 1969.
(4) B. Tomkins - Fatigue Failure - The Mechanics and Physics of
Fracture, 6-8 January 1975, Cambridge.
(5) D.F. Mowbray and J.E. Mc Connelee - Application of Finite
Element Stress Analysis and Stress-Strain Properties in Determining
Notch Fatigue Specimen Deformation and Life, ASTM STP 519, 1971.
(6) R.W. Landgraf - Cumulative Fatigue Damage l ender Complex Strain
Histories ASTM STP 519, 1971.
(7) J.L. Chaboche - A Differential Law of Fatigue Damage with Non-
Linear Accumulation, Revue fran aise de Wcanique Nr. 50-51
1974, pp. 71-82.
(8) Than Buic Quoc - Cycle Stress -_rain and Energy Variations under
Cumulation Damage Tests in LCF, Journal of Testing and Evaluation,
Volume 1, Nr. 1, .January 1973, pp. 58-64.
-9-
(9) K.N. Smith - P. Watson and T.H. Tapper - Journal of Materials,
vol. 5, 1970, p. 767.
(10) H.P. Lieurade - G. Sanz - M. Truchon - Study of Fatigue Crack
Initiation in High Strength Steel f;ecimens with Shape Defects
and nifferent Sizes. Contract DCRST 7371573.
(11) A. Pineau - Accommodation and Fissuration Mechanisms in Low-
Cycle Fatigue.
I


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