Constitutive description of creep behavior of Mg-4 Al-1Ca alloy
Creep behavior of an advanced magnesium alloy AX41 (4 wt.% Al, 1 wt.% Ca, Mg balanced) was investigated in temperature interval from 343 to 673 K and stresses from 2 to 200 MPa. Compressive creep experiments with stepwise loading were used in order to obtain stress dependence of the creep rate in in...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Zitieren: | Constitutive description of creep behavior of Mg-4Al-1Ca alloy / K. Milicka, F. Dobes // Проблемы прочности. — 2008. — № 1. — С. 36-39. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-484032013-08-19T15:57:13Z Constitutive description of creep behavior of Mg-4 Al-1Ca alloy Milicka, K. Dobes, F. Научно-технический раздел Creep behavior of an advanced magnesium alloy AX41 (4 wt.% Al, 1 wt.% Ca, Mg balanced) was investigated in temperature interval from 343 to 673 K and stresses from 2 to 200 MPa. Compressive creep experiments with stepwise loading were used in order to obtain stress dependence of the creep rate in interval from 10~9 to 10~3 iT 1 fo r a given temperature. All stress dependences can be well described by the Garofalo sinh relationship with natural exponent n = 5. An analysis ofthe parameters of this relationship has shown that lattice diffusion controls creep at all experimental conditions. While climb-controlled creep mechanism is decisive at lower stresses and higher temperatures, glide-controlled mechanisms act at higher stresses and lower temperatures. A typical power-law breakdown is observed at intermediate stresses and temperatures. Выполнены исследования ползучести оптимизированного магниевого сплава AX41 (4 вес.% Al, 1 вес.% Ca, Mg - баланс) в температурном диапазоне 343...673 K и уровнях напряжений 2...200 МПа. Были проведены испытания на ползучесть при ступенчатом нагружении сжимающей нагрузкой с целью определения зависимости скорости ползучести от напряжения в диапазоне 10-9...10-3 с-1 для данной температуры. Все вышеуказанные зависимости хорошо описывались уравнением Барафоло (типа sinh) с показателем степени n = 5. Анализ параметров этого уравнения показал, что ползучесть во всех проведенных экспериментах определяется диффузией решетки. При низких уровнях напряжений и высоких температурах определяющим является механизм восхождения, а при высоких уровнях напряжений и более низких температурах - механизм скольжения. В промежуточном диапазоне напряжений и температур наблюдается характерное отклонение экспериментальных точек от степенной зависимости. 2008 Article Constitutive description of creep behavior of Mg-4Al-1Ca alloy / K. Milicka, F. Dobes // Проблемы прочности. — 2008. — № 1. — С. 36-39. — Бібліогр.: 5 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48403 539. 4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Milicka, K. Dobes, F. Constitutive description of creep behavior of Mg-4 Al-1Ca alloy Проблемы прочности |
| description |
Creep behavior of an advanced magnesium alloy AX41 (4 wt.% Al, 1 wt.% Ca, Mg balanced) was investigated in temperature interval from 343 to 673 K and stresses from 2 to 200 MPa. Compressive creep experiments with stepwise loading were used in order to obtain stress dependence of the creep rate in interval from 10~9 to 10~3 iT 1 fo r a given temperature. All stress dependences can be well described by the Garofalo sinh relationship with natural exponent n = 5. An analysis ofthe parameters of this relationship has shown that lattice diffusion controls creep at all experimental conditions. While climb-controlled creep mechanism is decisive at lower stresses
and higher temperatures, glide-controlled mechanisms act at higher stresses and lower temperatures. A typical power-law breakdown is observed at intermediate stresses and temperatures. |
| format |
Article |
| author |
Milicka, K. Dobes, F. |
| author_facet |
Milicka, K. Dobes, F. |
| author_sort |
Milicka, K. |
| title |
Constitutive description of creep behavior of Mg-4 Al-1Ca alloy |
| title_short |
Constitutive description of creep behavior of Mg-4 Al-1Ca alloy |
| title_full |
Constitutive description of creep behavior of Mg-4 Al-1Ca alloy |
| title_fullStr |
Constitutive description of creep behavior of Mg-4 Al-1Ca alloy |
| title_full_unstemmed |
Constitutive description of creep behavior of Mg-4 Al-1Ca alloy |
| title_sort |
constitutive description of creep behavior of mg-4 al-1ca alloy |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2008 |
| topic_facet |
Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/48403 |
| citation_txt |
Constitutive description of creep behavior of Mg-4Al-1Ca alloy / K. Milicka, F. Dobes // Проблемы прочности. — 2008. — № 1. — С. 36-39. — Бібліогр.: 5 назв. — англ. |
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Проблемы прочности |
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2025-07-04T08:50:06Z |
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1836705652234256384 |
| fulltext |
UDC 539. 4
C o n s t i tu t iv e D e s c r ip t io n o f C r e e p B e h a v io r o f M g - 4 A l - 1 C a A llo y
K . M ilick a 1a and F . D o b es1b
1 Institute o f Physics o f Materials, Academy o f Sciences o f the Czech Republic, Brno, Czech
Republic
a milicka@ipm.cz, b dobes@ipm.cz
Creep behavior o f an advanced magnesium alloy AX41 (4 wt.% Al, 1 wt.% Ca, Mg balanced) was
investigated in temperature interval from 343 to 673 K and stresses from 2 to 200 MPa.
Compressive creep experiments with stepwise loading were used in order to obtain stress
dependence o f the creep rate in interval from 10~9 to 10~3 iT 1 fo r a given temperature. All stress
dependences can be well described by the Garofalo sinh relationship with natural exponent n = 5.
An analysis ofthe parameters o f this relationship has shown that lattice diffusion controls creep at
all experimental conditions. While climb-controlled creep mechanism is decisive at lower stresses
and higher temperatures, glide-controlled mechanisms act at higher stresses and lower temperatures.
A typical power-law breakdown is observed at intermediate stresses and temperatures.
K e y w o r d s : m agnesium a lloys, creep, constitu tive creep equation o f creep, creep
m echanism s.
In troduction . The M g -A l-C a alloys are developed as a cheaper alternative o f the
alloys containing rare earth m etals for applications at elevated temperatures. M echanical
properties o f these alloys, nam ely their creep resistance, are im proved b y precipitates o f
M g17A l12 and M g2Ca. How ever, effective developm ent o f this type o f m agnesium alloys is
im peded by the lack o f experim ental data as w ell as detailed know ledge o f m echanism s
governing their creep behavior at elevated temperatures. In the present study, som e results
o f creep behavior investigation o f a representative o f this alloy group, i.e ., the alloy
A X 41, are sum marized for a w ide interval o f temperatures and stresses.
E x p er im en ta l. M agnesium a lloy A X 41 w ith nom inal com position (in wt.% ) 4 A l,
1 Ca and M g balanced w as cast in Zentrum ftr Funktionwerkstoffe in Clausthal
Zellerfeld, Germany. Parallelepiped specim ens w ith 6 X 6 m m cross section and 12 mm
height were annealed at 673 K for 24 h and cooled in air and then heated at 353 K for 16 h.
The average size o f regular grains d = 0 .037 m m resulted from the h igh temperature
treatment.
C om pressive creep tests w ith stepw ise loading w ere used, in order to obtain stress
_9 _3 _1
dependence o f the creep rate in interval from 10 to 10 s for a g iven temperature. In
any step, the constant loading w as hold until the creep rate reached stationary or
quasi-stationary value. This rate w as then assigned to the true stress o corresponding to
the last strain value in the step. The loadings o f consequent steps were chosen randomly.
The tests were m ostly conducted till the strain reached a value £ = 0.15. Suitability o f the
used stepw ise procedure w as verified by a com parison o f obtained creep rates at a g iven
stress leve l w ith those resulting from conventional com pressive tests under constant stress.
D ifferences o f these values lay in scatter error.
The tests w ere perform ed in purified and dried argon atm osphere. Identical
temperature regim e w as applied before each test in order to elim inate eventual influence
o f temperature on second phase’s precipitation during the test. In all cases, the sam ple was
kept approxim ately 10 h at the testing temperature before the test w as started. The strain
w as m easured w ith the sensitivity 10_5. For the stepw ise stress creep experim ents and
evaluation o f their results, special software w as developed.
© K. MILICKA, F. DOBES, 2008
36 ISSN 0556-171X. npo6n.eubi npounocmu, 2008, N 1
mailto:milicka@ipm.cz
mailto:dobes@ipm.cz
Constitutive Description o f Creep Behavior o f M g-4A l-!C a Alloy
R esults. Creep behavior o f the alloy w as investigated at temperatures from 343 to
673 K. Stress dependences o f the creep rate £ are illustrated in both conventional
coordinate system s, i.e ., b i- and sem i-logarithm ic, in Fig. 1a and 1b. From the shape o f
dependences, no sim ple relationships, pow er law or exponential, can be chosen for their
description in the entire experim ental interval o f conditions. For sm all stresses and higher
temperatures the N orton pow er-law relation
£ « o ( 1)
w ith n = 5 seem s to be suitable for the description, the exponential relationship can be
rather w ell applied at low er temperatures and higher stresses. A t intermediate testing
conditions, neither o f both relationships is applicable. In principle, such behavior can be
w ell described by G arofalo’s sinh formula, w hich is conform ing to both these basic
descriptions in accord w ith above stress dependence o f the rate £.
b
Fig. 1. Stress dependences o f creep rate in bi-logarithmic (a) and semi-logarithmic (b) coordinates.
ISSN 0556-171X. Проблемы прочности, 2008, N2 1 37
K. Milicka and F. Dobes
The Garofalo equation has a form [1]
S = A (sinh[B o ])n (2 )
w here parameters A and B depend on temperature T on ly and exponent n is
considered to be natural number and temperature dependence o f the parameter A can be
written as
QA oc exp
R T (3)
w here Q is the activation energy and R the gas constant. For values B o < 0 .8, Eq. (2)
transfers to pow er-law relationship w ith stress exponent n and for B o > 1 .2 to the
exponential relationship w ith the function argument nB o .
Values o f the exponent n from 3 to 7 w ere proved in data treatment. Statistically, the
best agreem ent w as obtained by description for the exponent n = 5. U sing this value,
optim um treatment o f the stress dependences o f the rate s has confirm ed good
applicability o f both Eqs. (2) and (3) - see drawn curves in Fig. 1a and 1b w hich
correspond to these equations.
D ependence o f the parameter A on reciprocal temperature is plotted in Fig. 2. A
straight line can be drawn through calculated values in chosen coordinate system , w hich
confirm s valid ity o f Eq. (3). The activation energy Q = 137kJ/m ol results from the slope
o f the straight line. This value is very close to the activation enthalpy o f self-d iffusion o f
m agnesium A H Sd = 135 kJ/m ol [2].
Temperature dependence o f the parameter B is plotted in the Fig. 3. The dependence
has a convex shape; the parameter B reaches values from 0.021 to 0.035 w ith the
m inim um at approxim ately at 450 K.
10J / T [ K'1] T[K]
Fig. 2 Fig. 3
Fig. 2. Temperature dependence o f the parameter A.
Fig. 3. Temperature dependence o f the parameter B.
D iscussion . The activation energy Q obtained from temperature dependence o f
parameter A [cf. Fig. 2 and Eq. (3)] is very c lose to the activation enthalpy o f lattice
diffusion in M g. Probably, there are no data o f diffusion in the investigated m agnesium
alloy A X 41. H ow ever, it can be expected that the enthalpy o f lattice diffusion in the
investigated a lloy does not differ substantially from that in pure m agnesium . Therefore,
one can assum e that the value o f the energy Q supports an expectation that the creep
behavior o f the alloy is controlled by diffusion processes under all experimental conditions.
38 ISSN 0556-171X. npo6n.eubi npounocmu, 2008, № 1
Constitutive Description o f Creep Behavior o f M g-4 A l-lC a Alloy
A natural exponent n = 5 w as revealed to be the m ost convenient stress exponent in
the pow er-law part o f the stress dependences o f the creep rate £. From phenom enological
point o f v iew , such exponent is usually connected w ith the m etal-type (C lass II) creep
behavior [3]. A s the m ost probable m echanism controlling creep, respecting also the value
o f the energy Q, com bined m echanism o f clim b and glide o f d islocations can be
considered (see e.g ., [4]).
Exponential expression o f the stress dependences o f rate £ is frequently attributed to
therm ally activated glide o f dislocations. W ith respect to the controlling role o f lattice
diffusion, the non-conservative glide should be the major m echanism in the interval o f the
validity o f exponential dependence. A very sim ple concept o f non-conservative m otion o f
jogs on screw dislocation segm ents [5] can be accepted. Then, the apparent activation
energy o f creep Q c = [—6 ln £ /3 (1 R T )]o should depend on the stress due to the
temperature dependence o f the parameter B.
It can be seen from Fig. la that the shape o f stress dependences at the highest
temperatures indicates possib le threshold behavior since a strong bend o f the rate £
towards low er values appears w hen the stress decrease to a certain value (~ threshold
stress o th). Therefore, an attempt w as perform ed to describe these dependences by the
m odified Garofalo relationship
£ = A {s in h [B (o —o th ) ] } 5 , (4)
w hich are illustrated in Fig. la by dashed lines drawn for 673 and 623 K. However,
acceptable positive values o f o th w ere obtained from optim izing procedures on ly at
temperatures from 473 to 673 K.
C onclusions. F ollow ing conclusions can be drawn from the investigation o f creep
behavior o f the A X 41 alloy in temperature interval from 343 to 673 K:
• Stress dependences o f the m inim um creep rate £ can be w ell described by the
Garofalo equation (2).
• Obtained parameters o f this relationship can be w ell physically interpreted.
• Lattice diffusion controls creep behavior o f the A X 41 alloy in the entire
experim ental interval.
Acknowledgment. The work was supported by Project 106/06/1354 o f the Grant Agency of
the Czech Republic.
1. G. Garofalo, Trans. AIME, 227, 351 (1963).
2. P. G. Shewmon, Trans. AIME, 206, 918 (1956).
3. O. D. Sherby and P. M. Burke, Prog. Mat. Sci., 13, 325 (1968).
4. H. J. Frost and M. F. Ashby, Deformation-Mechanisms Maps. The Plasticity and Creep o f
Metals and Ceramics, Chapter 2, Pergamon Press, Oxford (1982).
5. J. Cadek, Creep in Metallic Materials, Chapter 9, Elsevier, Oxford; Academia, Prague (1988).
Received 28. 06. 2007
ISSN 0556-171X. n poôëeu u npouHocmu, 2008, № 1 39
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