Localization of plastic deformation and fracture in aluminum polycrystals
The effect of the grain size as a basic structural parameter on plastic strain macrolocalization has been studied for polycrystalline aluminum. The mathematical form of the above dependence has been verified. The limiting cases have been defined both for small- and coarse-grain ranges. The effect of...
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| Опубліковано в: : | Проблемы прочности |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2008
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| Цитувати: | Localization of plastic deformation and fracture in aluminum polycrystals / N.V. Zarikovskaya, L.B. Zuev // Проблемы прочности. — 2008. — № 1. — С. 52-55. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859858253881540608 |
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| author | Zarikovskaya, N.V. Zuev, L.B. |
| author_facet | Zarikovskaya, N.V. Zuev, L.B. |
| citation_txt | Localization of plastic deformation and fracture in aluminum polycrystals / N.V. Zarikovskaya, L.B. Zuev // Проблемы прочности. — 2008. — № 1. — С. 52-55. — Бібліогр.: 4 назв. — англ. |
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| container_title | Проблемы прочности |
| description | The effect of the grain size as a basic structural parameter on plastic strain macrolocalization has been studied for polycrystalline aluminum. The mathematical form of the above dependence has been verified. The limiting cases have been defined both for small- and coarse-grain ranges. The effect of sample dimension on the macrolocalization period has been considered.
Исследовано влияние размера зерна как основного параметра структуры на макролокализацию пластической деформации в поликристаллическом алюминии. Выполнена проверка математической записи указанной зависимости. Определены предельные случаи для областей малых и больших размеров зерен. Рассмотрено влияние размера образца на период макролокализации.
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| first_indexed | 2025-12-07T15:44:35Z |
| format | Article |
| fulltext |
UDC 539. 4
L o c a liz a t io n o f P la s t ic D e fo r m a t io n a n d F r a c tu r e in A lu m in u m P o ly c r y s ta ls
N . V . Z a rik o v sk a y a 1,a and L . B . Z u ev2,b
1 Institute o f Strength Physics and Materials Science, Siberian Branch o f the Russian Academy of
Sciences, Tomsk, Russia
2 Tomsk State University o f Control Systems and Radioelectronics, Tomsk, Russia
a chepko-znv@mail.ru, b lbz@ispms.tsc.ru
The effect o f the grain size as a basic structural parameter on plastic strain macrolocalization has
been studied fo r polycrystalline aluminum. The mathematical form o f the above dependence has
been verified. The limiting cases have been defined both fo r small- and coarse-grain ranges. The
effect o f sample dimension on the macrolocalization period has been considered.
K eyw ords: plastic deform ation localization, polycrystalline aluminum, deform ation curve,
autowave, spatial period, failure.
In trod u ction . The plastic deform ation o f polycrystalline materials is an essential
and often a defining factor in m any technological processes. A t present significant
progress has been m ade in the physical theory o f plasticity. A significant volum e o f
experim ental data on the distinctive features o f deform ation and fracture has been
obtained for polycrystalline alum inum.
Plastic flow tends to localize at all the stages. The form o f localization patterns
varies from the y ie ld lim it to fracture depending on the prevailing law o f w ork hardening.
Our experim ental investigations suggest that the observed regularities exhibited by
plastic flow are the result o f self-organization o f the deform ing m edium . A ccording to
Zuev and D anilov [1 ], the above regularities can be considered as w aves o f localized
plastic deform ation.
E xp er im en ta l P roced ure. The uniaxial tension tests w ere perform ed for a w ide
range o f m ono- and polycrystals using an Instron-1185 testing m achine w ith load F =
10 kN and loading rate £ = 3.3-10 6 m/s.
L ocalized strain zones on the test specim en w ere revealed by the m ethod o f
double-exposure speckle interferometry [ 1], w hich y ie ld s distributions o f plastic strain
tensor com ponents [ 1].
Out o f five types o f deform ation localization patterns on ly three are observed on the
flow curve o f polycrystalline aluminum, namely:
• A t the stage o f linear w ork hardening a set o f m obile nuclei o f localized plastic
deform ation originates in the test specim en and m oves in a regular fashion, thereby
form ing a running w ave.
• A t the stage o f parabolic w ork hardening a set o f im m obile nuclei o f deform ation
localization em erges in the test specim en.
• A t the pre-failure stage localized plastic deform ation nuclei merge together,
resulting in necking and v iscou s failure o f the test specim en.
The distribution patterns o f plastic strain tensor com ponents are show n £ xx in Fig. 1
for polycrystalline alum inum both at the linear and the parabolic work hardening stage.
The observed regularities o f plastic flow localization are com m on to all deform ing
materials [1, 2]. It is found that plastic deform ation tends to localize in certain zones o f
the deform ing specim en and is characterized by m acroscopic scale, i.e ., w avelength X.
It has been found that X depends on material parameters, i.e ., length scale, crystal
lattice geometry, grain size, etc. Therefore, to determine the dependence o f X on the grain
size and dim ensions o f a polycrystalline material is o f particular interest.
© N. V. Z A R IK O V SK A Y A , L. B. Z U EV , 2008
52 ISSN 0556-171X. Проблемы прочности, 2008, № 1
mailto:chepko-znv@mail.ru
mailto:lbz@ispms.tsc.ru
Localization o f Plastic Deformation and Fracture
Fig. 1. Space-time distributions o f the elongation component obtained for polycrystalline aluminum
having a grain size D = 190 [im: (a) linear stage at e = 4.8-5.6%; (b) parabolic stage at
e = 8 .0- 8 .8%.
The tests w ere conducted using A 85 aluminum sam ples w hose grain size w as easily
varied from 0.008 to 10 m m by the m ethod o f co llective recrystallization.
G rain S ize D ep en d en ce o f L oca liza tion W avelen gth for P o lycrysta llin e
A lu m in u m . Figure 2 show s X as a function o f the grain size D. N um erical processing o f
the above dependence y ields the fo llow ing equation:
dX /dD = aX — bX2 ( 1)
where a and b are the positive dim ensional constants [3].
The solution to the above equation is as follow s:
X =
1+ C exp(— aD ) (2 )
w here X 0 = a /b , and C is a non-dim ensional integration constant.
Fig. 2. Wavelength X dependence on the grain size D for polycrystalline aluminum.
Equation (2) describes, w ith a sufficient accuracy, a set o f experim ental X (D ) data
in a w ide interval o f D values (correlation coefficient R = 0 .98). The curve in Fig. 2 m ay
be subdivided into three portions [3]: 1) as D goes up to 0.5 m m , X grow s exponentially
up to X eaD (Fig. 3a); 2) in the range 0.5 < D < 2 .5 m m the dependence takes on the
logarithm ic form (X ln D ) (Fig. 3b); 3) at D > 2 .5 m m , X b ecom es constant (X ^ X 0 ~
15 mm).
ISSN 0556-171X. npoôëeMbi npounocmu, 2008, N 1 53
N. V. Zarikovskaya and L. B. Zuev
Fig. 3. Limiting cases o f the wavelength dependence on grain size: (a) D < 0.5 mm; (b) D > 0.5 mm.
The effect o f sam ple geom etry (in particular, the sam ple thickness) on the m acro
localization period w as exam ined for alum inum sam ples having grain size D < 0.5 mm.
It can be seen in Fig. 4, w ith increasing sam ple thickness, X grow s as w ell.
N um erical processing o f experim ental data y ielded constants a = 1.1 mm 1 and
_2 _1 _2
b = 0.2 m for 2X 10X 50-mm sam ples and a = 1.5 mm and b = 0 .2 m for
5X 10X 50-mm sam ples. Evidently, b is unaffected by the sam ple thickness.
Fig. 4. Grain size dependence o f macrolocalization periods on the sample thickness: lines 1 and 2
correspond to tl = 5 mm and t2 = 2 mm, respectively.
D istin ctive F eatu res o f D eform ation M acro loca liza tion at th e P refractu re Stage.
In order to get a holistic picture o f deform ation for polycrystalline aluminum, the final
stage o f the process, i.e ., the prefracture stage, has been explored. It w as show n earlier [4]
that the m ost striking feature o f the plastic deform ation localization reveals itse lf at the
latter stage.
The prefracture stage is a parabolic one, i.e., the stress-strain dependence for this
stage has the form o ~ £ n (where n is the parabola exponent). It has been show n that
w ith n < 0.5 the localized deform ation nuclei m ove along the sam ple at a velocity V [4],
V (n ) = V0 (n _ q )2 . (3)
A t the parabolic stage (n » 0 .5) the localized deform ation nuclei becom e m otionless
(V = 0), w hile at the linear stage (n = 1) they m ove synchronously w ith different velocities.
The nuclei locations w ere plotted in the X ( t ) or X (£ ) coordinates, w here X is the
nucleus’ coordinate, t is the deform ation tim e, and £ is the deform ation (Fig. 5).
54 ISSN 0556-171X. npodxeMbi npounocmu, 2008, N9 1
Localization o f Plastic Deformation and Fracture
X, mm n=0.4 n=0.32
36
34
32
30
28
26
24
22
20
1»
16
14
12
10
3700 3BQ0 3900 4000 4100 4200 43 M 4400 4500
t S
Fig. 5. Positions o f localization nuclei vs. time.
It can be seen from the p lot that w ith n < 0.4 the n u c le i’s trajectories w ould form a
bundle w h ose pole pinpoints the location o f future fracture.
The velocity o f a nucleus can be defined from the slope o f the straight line. A lso , it
should be noted that the nuclei m ove w ith different velocities, som e o f them disappearing
altogether.
Thus, one can predict the place o f future fracture long before the beginning o f
visib le necking.
1. L. B. Zuev and V. I. Danilov, Phil. Mag. A , 79, 43 (1999).
2. L. B. Zuev, Ann. Phys., 3, 965 (2001).
3. L. B. Zuev, B. S. Semukhin, and N. V. Zarikovskaya, Int. J. Solids Struct., 40, 941 (2003).
4. L. B. Zuev and V. I. Danilov, Tech. Phys., 50, 1636 (2005).
Received 28. 06. 2007
ISSN 0556-171X. npoôëeMbi npounocmu, 2008, N 1 55
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| id | nasplib_isofts_kiev_ua-123456789-48461 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T15:44:35Z |
| publishDate | 2008 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Zarikovskaya, N.V. Zuev, L.B. 2013-08-19T19:56:03Z 2013-08-19T19:56:03Z 2008 Localization of plastic deformation and fracture in aluminum polycrystals / N.V. Zarikovskaya, L.B. Zuev // Проблемы прочности. — 2008. — № 1. — С. 52-55. — Бібліогр.: 4 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48461 539. 4 The effect of the grain size as a basic structural parameter on plastic strain macrolocalization has been studied for polycrystalline aluminum. The mathematical form of the above dependence has been verified. The limiting cases have been defined both for small- and coarse-grain ranges. The effect of sample dimension on the macrolocalization period has been considered. Исследовано влияние размера зерна как основного параметра структуры на макролокализацию пластической деформации в поликристаллическом алюминии. Выполнена проверка математической записи указанной зависимости. Определены предельные случаи для областей малых и больших размеров зерен. Рассмотрено влияние размера образца на период макролокализации. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Localization of plastic deformation and fracture in aluminum polycrystals Локализация пластической деформации и разрушение поликристаллов алюминия Article published earlier |
| spellingShingle | Localization of plastic deformation and fracture in aluminum polycrystals Zarikovskaya, N.V. Zuev, L.B. Научно-технический раздел |
| title | Localization of plastic deformation and fracture in aluminum polycrystals |
| title_alt | Локализация пластической деформации и разрушение поликристаллов алюминия |
| title_full | Localization of plastic deformation and fracture in aluminum polycrystals |
| title_fullStr | Localization of plastic deformation and fracture in aluminum polycrystals |
| title_full_unstemmed | Localization of plastic deformation and fracture in aluminum polycrystals |
| title_short | Localization of plastic deformation and fracture in aluminum polycrystals |
| title_sort | localization of plastic deformation and fracture in aluminum polycrystals |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/48461 |
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