A model of fatigue crack propagation in metals
A model of the formation and evolution of a local plastic deformation zone at the crack tip is proposed based on the analysis of the main physical processes taking place in a metallic material under the action of cyclic loads. An equation offatigue crack growth rate curves, which explicitly accounts...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2009
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| Цитувати: | A model of fatigue crack propagation in metals / T.Yu. Yakovleva, L.E. Matokhnyuk // Проблемы прочности. — 2009. — № 1. — С. 35-43. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859835245482737664 |
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| author | Yakovleva, T.Yu. Matokhnyuk, L.E. |
| author_facet | Yakovleva, T.Yu. Matokhnyuk, L.E. |
| citation_txt | A model of fatigue crack propagation in metals / T.Yu. Yakovleva, L.E. Matokhnyuk // Проблемы прочности. — 2009. — № 1. — С. 35-43. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | A model of the formation and evolution of a local plastic deformation zone at the crack tip is proposed based on the analysis of the main physical processes taking place in a metallic material under the action of cyclic loads. An equation offatigue crack growth rate curves, which explicitly accountsfor the loadingfrequency, was derived. The equation applies to the whole range ofcrack lengths from short cracks to macroscopic ones.
На основании анализа основных физических процессов, протекающих в металлах при воздействии циклических нагрузок, предложена модель формирования и развития зоны локальной пластической деформации в окрестности вершины трещины. Выведено уравнение, описывающее скорость роста усталостной трещины, которое в явном виде учитывает влияние частоты нагружения. Предложенное уравнение применяется для широкого диапазона длин трещины: от коротких до макротрещин.
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| first_indexed | 2025-12-07T15:34:23Z |
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| fulltext |
UDC 539.4
A Model of Fatigue Crack Propagation in Metals
T. Y u. Y akovleva and L. E. M ato k h n y u k
Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine,
Kiev, Ukraine
A model o f the formation and evolution o f a local plastic deformation zone at the crack tip is
proposed based on the analysis o f the main physical processes taking place in a metallic material
under the action o f cyclic loads. An equation o f fatigue crack growth rate curves, which explicitly
accounts fo r the loading frequency, was derived. The equation applies to the whole range o f crack
lengths from short cracks to macroscopic ones.
K e y w o r d s : local plastic deformation, surface energy, fatigue strength, fatigue-
crack growth resistance, loading frequency.
In tro d u c tio n . Fracture o f a m aterial and structural element under external
therm om echanical loading is a two-stage process. The first stage involves damage
accumulation in the material and comes to an end when the parameters o f the
local plastic deformation zone reach their critical values, which corresponds to the
beginning o f the formation o f one or several cracks. The second stage is
characterized by the crack propagation up to a complete body failure. Nowadays,
there are attempts to describe the entire process o f fatigue fracture from a single
perspective, w ith the leading role given to the process zones w hich are formed
both during the first (incubation) period and at the crack growth stage [1-6]. The
growing fatigue crack is regarded as a sharp notch and its growth is m odeled as
repeated crack initiation events which follow the same laws as those governing
the initiation o f the prim ary crack.
The m ajor characteristics o f the loading conditions include the frequency of
the acting load. The few models considering the frequency either contain it in an
implicit form [7], or cover only one or several materials [8-10], or are difficult to
apply in practice [11].
Based on the above, what seems topical to us is the creation o f unified
models covering the w idest possible range o f factors that influence the fatigue
fracture process, relying on the analysis o f physical processes that take place in a
metallic material, and having a sufficiently simple, easy-to-use mathematical
form.
P hysical F o u n d a tio n s o f th e F ra c tu re M odel. Earlier we analyzed
experim ental data, both our own and those from literature, on the processes o f
fatigue damage accumulation and fatigue crack propagation in m etallic materials
using such techniques as optical, transm ission electron, and scanning electron
microscopies combined w ith a quantitative data processing and the determination
o f the residual electrical resistivity and internal friction. This made it possible to
establish basic general laws for the evolution o f the m aterial structure and
variation o f the fractographic characteristics under cyclic loading. Detailed results
o f these investigations are given in [12]. Here we outline only the key issues.
© T. Yu. YAKOVLEVA, L. E. MATOKHNYUK, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 1 35
T. Yu. Yakovleva and L. E. Matokhnyuk
The m ain distinction o f the structural changes occurring during the period of
fatigue damage accumulation is their local nature. Progressive microplastic
deformation is observed in a lim ited num ber o f m icrovolum es, along w ith a m uch
larger num ber o f non-progressive zones o f structural changes appearing in the
material. The microvolumes of the maximum structural changes have a dislocation
structure different from that o f the original m aterial and are surrounded by a zone
o f m ild changes, which is sim ilar to a transition zone to the rest o f the m aterial,
being almost in the same state as before loading. The extent o f the structural
changes in different microvolumes depends significantly on the sensitivity of
their crystalline structure to the direction of the loading axis, as well as on the
local stress concentration, nonuniform ity in terms o f impurities and alloying
elements, and closeness to the free material surface.
The increase in the degree o f localization o f the m aterial restructuring with
rising duration o f loading was revealed by means o f direct strain measurements
[13], Barkhausen noise analysis [14], and Fourier methods [15, 16]. Fracture
occurs when a certain critical state o f the structure is attained in the sites of
localization of deformation.
As the loading frequency increases, the num ber o f defects accumulated over
a loading cycle, as well as the size o f the zones with m arked structural changes,
decreases. The im peded realization o f the plastic deformation micromechanisms
because o f the shorter cycle duration under high-frequency loading is m ade up for
by the activation o f the micromechanisms that are less energetically feasible
under low frequencies. Still, the basic laws o f damage accumulation described
above hold true.
The presence o f the static com ponent under cyclic loading and an increase in
the stress ratio R result in smaller degrees o f localization o f deformation, which
shows up in a slight reduction o f the m aterial volume that underw ent no structural
changes [12].
The dislocation structure o f the plastic deformation zone at the tip o f the
m ain crack in the near-threshold range o f the stress intensity factor AK is the
next logical stage in the evolution o f the structure formed during the fatigue
damage accumulation in the original material. The m aterial exhibits quantitative
rather than qualitative differences between the dislocation structure formed in the
fracture zone and the local microzones in the original m aterial m ost heavily
deformed during the incubation period o f the fatigue fracture. The plastic
deformation process in the fracture zone engulfs almost entire microvolume
located in the area affected by the crack tip.
Comparison o f the fracture surface and the corresponding dislocation structure
suggests that the length o f the preparatory period preceding the material fracture
has a significant effect on the crack growth rate both prior to the initiation and
during the propagation o f the prim ary crack. Fractographic investigations [17]
and direct observations o f the fatigue-crack growth process [18] show the
possibility o f using the “m icrocrack at the notch-tip” m odel to represent the
process o f the macrocrack extension increment. For this model, the tip o f a
macrocrack at its blunting stage plays the role o f the notch.
A t the stage o f propagation o f the m ain crack, as well as during the
incubation period, the growth o f the loading frequency is accompanied by the
36 ISSN 0556-171X. npodxeMbi npounocmu, 2009, N 1
A Model o f Fatigue Crack Propagation in Metals
reduction o f the element size in the substructure being formed. The band width in
a band structure [19] and the depth o f the plastic deformation zone [20] increase
less intensively w ith AK as compared w ith their increase under low-frequency
loading.
Analysis o f the research findings summarized here allows us to draw the
following conclusions.
1. Zones o f progressive local plastic deformation (LPD zones) can be
regarded as parts o f some “quasi-phase,” which differ in properties from the
remaining material and, consequently, their specific surface energy depends on
the coordinates.
2. The size o f these zones depends on the local stress state, micromechanisms
o f plastic deformation, num ber o f cycles, and loading frequency, and the local
fracture o f the material occurs as a result o f the loss o f its capacity for further
plastic deformation.
3. The evolution o f the LPD zones in a given m aterial during the incubation
period and the active period o f fatigue fracture is governed by common laws.
4. The fatigue-crack growth rate is m ainly determined by the duration o f the
preparatory period in the restructuring o f the LPD zone material, and this
duration, in turn, depends on the material properties and levels o f nominal
stresses.
5. The loading frequency has a similar im pact on the integral macroscopic
and local (structural and fractographic) characteristics o f the fatigue fracture.
The M odel o f M ateria l F ra c tu re u n d e r Cyclic L oading. Consider a model
for the behavior o f a m etallic material subjected to a cyclic load o f arbitrary
magnitude w ith the frequency f taking into account the above research findings
on the related physical processes. To this end, we make the following preliminary
assumptions:
(i) the LPD zone material is a continuous medium whose physical-mechanical
properties, including the specific surface energy, are functions o f the coordinates
and time;
(ii) the current m ean radius o f this zone depends linearly on the m ean rate of
the m icroplastic deformation process and time;
(iii) the exact nature and mechanisms o f the structure evolution are reflected
in changes in the specific surface energy.
Starting from the above assumptions, we first analyzed the equilibrium
conditions for the system L P D z o n e - r e m a in in g m a te r ia l v o lu m e taking into
account the presence o f an interfacial area and then the energy balance w ithin the
LPD zone.
In the case studied, under the ultimate equilibrium conditions the component
inducing macroscopically elastic deformation should be considered together with
three additional components. These are the d is s ip a t iv e force [21], w hich is related
to the irreversible energy dissipation within a cycle and depends on the cycle
characteristics, and the components dependent on the resulting surface curvature
within the LPD zone and the magnitudes o f the interaction forces acting along the
interface between the m ain volume and the LPD zone. The latter components are
linked to the size o f the LPD zone and the value o f the specific surface energy a
accumulated within this zone after N loading cycles, i.e., they depend on the
ISSN 0556-І7ІХ. Проблемыг прочности, 2009, № І з?
T. Yu. Yakovleva and L. E. Matokhnyuk
duration o f loading. The stresses 0 in the case under study can also be presented
as a sum o f the o e component inducing m acroelastic deformation and the o md
component introduced to account for the energy dissipation and the presence of
the interface between the LPD zone and the remaining material. We present o md
as a sum o f three components, two o f them being dependent on the duration of
loading and the third one on the cycle characteristics:
0 = 0 e + ° md , (!)
where
0 md = 0 md 1 + 0 md 2 + 0 md3 .
W hen analyzing variation o f the internal energy within the LPD zone with
time t , we also considered two conditional components: the first one, linked to
the size o f the plastic deformation zone, and the second one, linked to the
evolution o f the structural m orphology within this zone and, therefore, variation
o f the specific surface energy a . In the same manner, we also divide the work of
external forces into two conditional components. The first one, being the work of
the elastic deformation within one loading cycle, is equal to zero. The second
component is the work done over the time t to bring the LPD microvolum e to a
nearly spherical shape w ith a characteristic linear dimension, e.g., m ean radius.
The LPD zone expansion continues as long as the decrease in its energy due to
the stress relaxation caused by the structural evolution is greater than the increase
in this energy caused by the growth o f the geometric dimension and the specific
surface energy. The critical mom ent is when the sum o f changes in the energy
equals zero, which corresponds to certain critical values o f the zone size and
specific surface energy. A further decrease in the energy is only possible through
fracture in the zone, i.e., the appearance o f a prim ary microcrack. The condition
for attaining the m aximum o f the function o f several variables is the equality to
zero o f the partial derivatives, and the local fracture criteria are the critical values
o f the LPD zone radius and specific surface energy. As a result, we arrive at a
relationship that is a constitutive equation for the material in the state of
instability accounting for the cyclic loading rate and stress ratio:
0 a = 0 e + a 0
4 7 + b 0 f N F : + c 0 i f
(2)
where
E 0) tan p d a
3 v f b 0 = k .
d N ’
0 e k° el— 1,
I E r d a
3v0 dT
k = 1— k
= k .
E 0) tan p d a
1+ R
al R
3 dv 0
2
p is the phase shift angle between the stress and strain, E m and E r represent the
circumferential elastic m odulus and relaxation modulus, respectively, [2 2 ], k a/R
characterizes the m aterial sensitivity to the static stress component, 0 ej— 1 is the
38 ISSN 0556-171X. npodxeMbi npounocmu, 2009, N9 1
A Model o f Fatigue Crack Propagation in Metals
true elastic limit for fully-reversed cycles, and v 0 is the mean rate o f microplastic
deformation processes.
Further loading will lead to the onset o f fracture. Reduced to its simplest
form, this relationship is a fatigue curve equation with two coefficients for given
stress-controlled loading conditions:
Dividing all the terms in Eqs. (2) and (3) by the value o f the corresponding
modulus, we obtain equations o f similar form for the strain-controlled loading
conditions.
Keeping in m ind the above results, we consider the material state after the
onset o f the fatigue microcrack propagation under conditions o f uniaxial tension.
The boundary o f the LPD zone is itself an inner stress raiser and so, i f we do
not dwell on the specific micromechanisms depending on numerous factors, the
m ost probable direction o f the local fracture is from the boundary o f the LPD
zone into its inner volume at some angle to the loading axis in the plane o f the
maximum local tensile stresses (Fig. 1). I f 2 l is the length o f the initial
microcrack, which corresponds to the first instantaneous event o f local fracture,
we arrive at the problem o f a crack, which is m odeled by a slant slot in the tensile
stress field [23].
Fig. 1. Crack growth scheme: (/) primary crack; (2) secondary LPD zone; (3) transition zone.
N ow consider the material state in the vicinity o f the point r , 6 (where r , 6
is the local polar coordinate system in the crack cross-section), w hich belongs to a
m icrozone exhibiting the above listed characteristics, namely, m ost intense
structural changes, highest stresses, and their small gradient. We will call this
microzone se c o n d a r y L P D z o n e (Fig. 1), in contrast to the prim ary one formed
P,
P
1 2 3
ISSN 0556-171X. Проблемыг прочности, 2009, № l 39
T. Yu. Yakovleva and L. E. Matokhnyuk
during the incubation period. Then if r ~ r /2 [r is the distance from the crack
tip for which a ar/ k ( r ) = a ar/ik max holds true], the local stresses a ar/ik (and
strains £ ar/ik ) within the microvolum e in question weakly depend on A r [24]. If
the value o f the stress intensity factor is given, we can write the known expression
for local stresses in the central point o f the secondary LPD zone:
a ar/ik
A K
■J2nr
0 = F ( r */ p ) 0 ik ( e m P), (4)
A K = ^ A K n , A K n = a a 0/ ik 4 H l Y , 0 ik ( e ) = ^ 0 ik/n ( e ),
where i, k = x , y , z , n = I, I I I I I characterizes the three basic modes o f crack-tip
opening displacement (mode I is the opening, mode II is the in-plane shear, and
m ode III is the out-of-plane shear), 0 ik and W are functions o f the angles e
and P , respectively, P is the angle betw een the loading axis and the fracture
propagation direction (Fig. 1), Y is the correction function dependent on the
ratio o f l to the specim en width, F is the function dependent on the ratio r / p ,
w here p is the crack tip radius, and a a is the am plitude o f nom inal
stresses. Further, we w ill omit the indices i and k to avoid too lengthy
designations o f stresses.
W riting these stresses as a function o f the num ber o f cycles required to
fracture the secondary zone,
a er a or
r - 1— 1 A K O
4 f + ( b ar + c a r 4 f X ^ = (5)
we can present the function differential as a dependence o f the crack growth rate
on A K :
d l = 2( A K - A K e - a a k ) 2
d N H !~F\2
O 2 ( b ar + c a r y f )
A K = k A K - 1 , (6)
where
2
1 + R a erV2Hr
k = 1 - k a / - 1 ~ T ~ , A K e = ^ , a AKO
a a r Ĵ 2 n r
O
or on the crack length:
dl_
d N
i— V2HT i—
a a 0 » h 1 Y — o (a er + a a r y f )
O 2
( b ar + c a r 4 f )2
(7)
n n
2
2
40 ISSN 0556-171X. npodxeMbi npounocmu, 2009, N9 1
A Model o f Fatigue Crack Propagation in Metals
Here, the parameters o er , a o r , b o r , and c or have the same physical and
mathematical m eaning as in Eq. (2), but refer to the microzone o f the m aximum
structural changes in the vicinity o f the point r , 6 at the crack tip, k a/_1 has the
same m eaning as in Eq. (2) and refers to the amplitude o f external load, and
A K _1 is the stress intensity factor for fully-reversed loading w ith a given crack
growth rate.
The resulting equations can be reduced to a m odified Paris law
d l 9
— = A f ( A K _ A K ue ) \ (8)
i.e., expressed as a function o f A K . Here, the expressions for the coefficient and
the addend account for the loading frequency and the expression for A K
incorporates the stress ratio.
Similarly, we can simplify the relation between the crack growth rate and
crack length:
d N = A f (B o 4 l _ C o ) 2 , B o = o a ^ Y ,
_ r ^9)
C o = ^ ( o er a o r y f ) .
Thus, based on the unified physical approach to describing the formation of
the local plastic deformation zone during the fatigue fracture incubation and
propagation periods, we obtained fatigue curve equations and dependences o f the
crack growth rate on A K and crack length that take into account the loading
frequency and stress ratio. Physically, the equations for the crack growth rate are
the constitutive equations o f a material at the tip o f a growing crack at the instant
o f time preceding the next onset o f the crack growth.
The validity o f the equations obtained was verified on a large volume o f test
data on nickel-, titanium-, and aluminum-based alloys and steels. Equations o f the
fatigue-crack growth curves (7) and (8) enable description o f the fatigue-crack
growth behavior, in particular at the stages o f short crack development and stable
or unstable crack growth, as well as conditions o f the crack growth retardation up
to the complete arrest.
The m athematical consequences of the equations are analytic dependences of
the crack growth rate vs crack length, threshold stress-intensity factor A K th vs
frequency f , crack growth rate d l / d N vs frequency f for AK = const, and
cyclic crack-growth resistance characteristics A K th and A K ^ vs structural
element size d.
1. V. V. Panasyuk and V. P. Sylovanyuk, “A computational model o f fatigue
fracture o f m aterials,” F iz .-K h im . M ek h . M a te r . , No. 3, 44-54 (2003).
2. O. P. Ostash and V. V. Panasyuk, “Initiation o f fatigue macrocracks in
notched specim ens,” S tre n g th M a te r ., 32, No. 5, 417-426 (2000).
ISSN 0556-171X. Проблемы прочности, 2009, N2 1 41
T. Yu. Yakovleva and L. E. Matokhnyuk
3. O. P. Ostash, V. V. Panasyuk, and E. M. Kostyk, “A unified m odel of
initiation and growth o f fatigue macrocracks. Pt. 2. Application o f strain-based
fracture mechanics parameters at the crack initiation stage,” F iz .-K h im .
M ekh . M a te r . , No. 3, 5 -14 (1998).
4. O. P. Ostash, V. V. Panasyuk, and E. M. Kostyk, “A unified m odel of
initiation and growth o f fatigue macrocracks. Pt. 3. M acrocrack growth
stage,” F iz .-K h im . M ekh . M a t e r , No. 3, 55-66 (1999).
5. O. P. Ostash and I. M. Andreiko, “Cyclic crack growth resistance of
high-strength cast irons at m acrocrack nucleation and grow th stages,”
F iz .-K h im . M ek h . M a te r . , No. 1, 57-62 (2001).
6 . V. P. Golub and A. V. Plashchinskaya, “Subcritical growth o f fatigue cracks
in thin plates with a stress concentrator,” in: Proc. o f the Int. Conf. on L ife
A s s e s s m e n t a n d M a n a g e m e n t f o r S tr u c tu r a l E le m e n ts (Kiev, 2000), Vol. 1,
Kiev (2000), pp. 93-99.
7. S. Kocanda, Z m e c z e n io w e N is z c z e n ie M e ta l i , W idaw nictw o Naukowo-
Techniczne, W arzawa (1972).
8 . X. Q. Shi, H. L. J. Pang, W. Zhou, and Z. P. Wang, “A modified
energy-based low cycle fatigue m odel for eutectic solder alloy,” S cr. M a te r . ,
41, No. 3, 289-296 (1999).
9. F. V. Antunes, J. M. Ferreira, C. M. Branco, and J. Burne, “Influence of
stress state on high-temperature fatigue crack growth in Inconel 718,” F a tig u e
F ra c t. E n g . M a te r . S tru c t., 24, No. 2, 127-135 (2001).
10. A. B. O. Soboyejo, S. Shademan, M. Foster, et al., “A m ultiparameter
approach to the prediction o f fatigue crack growth in metallic m aterials,”
F a tig u e F ra c t. E n g . M a te r . S tr u c t., 24, No. 3, 225-241 (2001).
11. A. T. Yokobori and T. Isogai, “Fatigue crack growth and dislocation
dynamics,” J. J a p . S oc . S tr e n g th F ra c t. M a te r . , 34, No. 1, 1-10 (2000).
12. T. Yu. Yakovleva, L o c a l P la s t ic D e fo rm a tio n a n d F a tig u e o f M e ta ls [in
Russian], Naukova Dumka, Kiev (2003).
13. A. V. G ur’ev and V. Ya. Mitin, “Features o f development o f nonuniform
microscopic strains and fatigue damage accum ulation in carbon steels,”
S tre n g th M a te r . , 10, No. 11, 1263-1267 (1978).
14. C. Buque, W. Tirsher, and Ch. Blochwitz, “Rauschen in mechanische
ermüdeten N ickeleinkristallen,” Z. M e ta ll ik , 86 , No. 10, 671-681 (1995).
15. T. Yu. Yakovleva and L. E. Matokhnyuk, “Estimation o f degradation o f a
metallic material structure using the Fourier analysis m ethod,” in: Proc. of
the Int. Conf. on L ife A s s e s s m e n t a n d M a n a g e m e n t f o r S tr u c tu r a l E le m e n ts
(Kiev, 2000), Vol. 1, Kiev (2000), pp. 193-197.
16. T. Yu. Yakovleva, “Application o f the methods o f Fourier optics for
quantitative analysis o f the evolution o f structural states o f metals under
conditions o f cyclic loading,” S tre n g th M a te r . , 32, No. 2, 162-167 (2000).
17. M. D. Halliday, P. Poole, and P. Bowen, “N ew perspective on sleep band
decohesion as fracture event during fatigue crack growth in both small and
long cracks,” M a te r . S ci. T ech n o l., 15, No. 4, 382-390 (1999).
42 ISSN 0556-171X. npoöxeMbi npounocmu, 2009, N 1
A Model o f Fatigue Crack Propagation in Metals
18. A. Sugeta, M. Jono, and Y. Uematsu, “Observation o f fatigue crack growth
behavior using an atomic force m icroscope,” in: Proc. o f the Seventh Int.
Congress on F a tig u e '9 9 (Beijing, P. R. China, 8 -12 June, 1999), Vol. 4,
H igher Education Press, Beijing (1999), pp. 2783-2788.
19. L. E. M atokhnyuk and T. Yu. Yakovleva, “Influence o f loading frequency
on the rules and mechanisms o f fatigue crack growth in titanium alloys.
Report 2,” S tre n g th M a te r . , 20, No. 1, 25-36 (1988).
20. T. Yu. Yakovleva and L. E. Matokhnyuk, “The influence o f the cyclic
loading rate on the plastic zone depth in VNS-25 alloy,” S tre n g th M a te r . , 34,
No. 2, 150-152 (2002).
21. L. D. Landau and E. M. Lifshitz, C on tin u u m M e c h a n ic s [in Russian],
Gostekhizdat, M oscow -Leningrad (1953).
22. C. Zener, E la s t ic i ty a n d I n e la s tic i ty o f M e ta ls , Chicago (1948).
23. L. M. Kachanov, F u n d a m e n ta ls o f F r a c tu r e M e c h a n ic s [in Russian], Nauka,
GRFML, M oscow (1974).
24. G. Pluvinage, “N otch fracture m echanics,” F iz .-K h im . M ekh . M a te r . , No. 6 ,
7 -20 (1998).
Received 11. 06. 2008
ISSN 0556-171X. Проблемыг прочности, 2009, № 1 43
|
| id | nasplib_isofts_kiev_ua-123456789-48478 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T15:34:23Z |
| publishDate | 2009 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Yakovleva, T.Yu. Matokhnyuk, L.E. 2013-08-20T04:35:39Z 2013-08-20T04:35:39Z 2009 A model of fatigue crack propagation in metals / T.Yu. Yakovleva, L.E. Matokhnyuk // Проблемы прочности. — 2009. — № 1. — С. 35-43. — Бібліогр.: 24 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48478 539.4 A model of the formation and evolution of a local plastic deformation zone at the crack tip is proposed based on the analysis of the main physical processes taking place in a metallic material under the action of cyclic loads. An equation offatigue crack growth rate curves, which explicitly accountsfor the loadingfrequency, was derived. The equation applies to the whole range ofcrack lengths from short cracks to macroscopic ones. На основании анализа основных физических процессов, протекающих в металлах при воздействии циклических нагрузок, предложена модель формирования и развития зоны локальной пластической деформации в окрестности вершины трещины. Выведено уравнение, описывающее скорость роста усталостной трещины, которое в явном виде учитывает влияние частоты нагружения. Предложенное уравнение применяется для широкого диапазона длин трещины: от коротких до макротрещин. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел A model of fatigue crack propagation in metals Модель роста усталостной трещины в металлах Article published earlier |
| spellingShingle | A model of fatigue crack propagation in metals Yakovleva, T.Yu. Matokhnyuk, L.E. Научно-технический раздел |
| title | A model of fatigue crack propagation in metals |
| title_alt | Модель роста усталостной трещины в металлах |
| title_full | A model of fatigue crack propagation in metals |
| title_fullStr | A model of fatigue crack propagation in metals |
| title_full_unstemmed | A model of fatigue crack propagation in metals |
| title_short | A model of fatigue crack propagation in metals |
| title_sort | model of fatigue crack propagation in metals |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/48478 |
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