review of creep in magnesium matrix composites seminar title: by: farid labib supervised by: prof....

Review of creep in Magnesium matrix composites

Seminar title:

By:Farid Labib

Supervised by:Prof. R. Mahmudi

Prof. H. R. Ghasemi

Main Mechanisms of Creep in metals:

• Dislocation slip and climb• Grain boundary sliding• Diffusional flow

Stage I: Primary CreepStrain rate decreases as strain increases.Resistance to plastic deformation: strainhardening

Stage II: Secondary (steady-state) Creep(used as design tool)Strain rate minimum and constantBalance between recovery = strainhardening. Fracture will not occur.

Stage III: Tertiary Creep (failure-rupture)Strain rate increases. reduction in cross-sectionalarea due to voids, neckingreduce

M. E. Kassner, M. T. Perez-Prado, Fundamentals of Creep In Metals and Alloys, 2004

Dislocation slip and climb:

Dislocation climb is the mechanism responsible to achieve the desired balance between recovery and strain hardening during secondary creep. dislocations must escape from tangled regions by a process called dislocation climb.

At low temperatures, dislocation slip dominates. (high temp. diffusion is dominates)


As temperature increases atoms have more thermal energy (proportional to RT) and the equilibrium concentration of vacancies in a metal increases exponentially

Q is the activation energy for vacancy creation and movement, (or the activation energy for self-diffusion).

Dislocation climb requires diffusion vacancies or self-diffusion. So the rate is control by atomic diffusion

At intermediate and higher temperatures (at high stresses), dislocation climb dominates

Climb is, however, still the basic controlling mechanism in steady-state creep of solid solution alloys


Above about 0.6 TM the grain boundary region is thought to have a lower shear strength than the grains themselves, probably due to the looser atomic packing at grain boundaries

Grain boundary sliding:

Rounded and wedge shaped voids are seen mainly at the grain boundaries

the grains in polycrystalline metals are able to move relative to each other.

Occurs due to increasing the temperature and stress and/or decreasing the strain rate.


The boundary sliding may account for 10% to 65% of the total creep strain

Ball-Hutchinson model of GBS accommodated by dislocation movement: (Sub-grain formation)


• Diffusion occurs through the main body of the grains

• Rate of the creep can be reduced by increasing the size of the grains

Diffusion Creep or Dislocation CreepCoble Nabarro-herring

• Diffusion occurs through the grain boundaries

• creep rates is reduced by increasing grain size, as structure with larger grains have fewer grain boundaries.

Coble

Nabarro-herring


The fastest mechanism will control the creep behavior, the slowest mechanism will control the creep deformation

More than one creep mechanism will operate at the same time (In parallel), but they operate independently each other.


A metal matrix composite (MMC) is composite material with at least two constituent, one being a metal. The other material may be a different metal or another material, such as a ceramic or organic compound. When at least three materials are present, it is called a hybrid composite.

where K and are the bulk and shear moduli, respectively, and f is the volume fraction of reinforcing particles.

E. Kroner, Z. Phys., 1958, 151, 504. B. Budiansky, J. Mech. Phys. Solids, 1965, 13, 223.

A model to predict the creep rate of a same sized aligned short fiber MMC

Strengthening Mechanisms in Metal Matrix composites:

Direct strengthening: Under an applied load, the load is transferred from the weaker matrix, across the matrix/reinforcement interface, to the typically higher stiffness reinforcement. In this manner, strengthening takes place by the reinforcement “carrying” much of the applied load. [1]

Indirect strengthening: the thermal mismatch between the high expansion metallic matrix and the low expansion ceramic is typically quite high. Thus, upon cooling, dislocations form at the reinforcement/matrix interface due to the thermal mismatch. In this manner, thermally induced dislocation punching results in “indirect strengthening” of the matrix. [2]

[2] K. K. Chawla, M. Metzger, J. Mater. Sci., 1972, 7, 34.[1] V. C. Nardone, K. M. Prewo, Scripta Metall., 1989, 23, 291.

Interfacial sliding may be affected by internal thermal stresses arising at the interfaces on heating the specimen to the test temperature (the thermal expansion coefficients of the metallic matrix and the ceramic particles differ considerably). Since SiC particles are very rigid, interfacial sliding is not accommodated sufficiently and, hence, cavities form at interfaces. [3]

[3] Florian Moll, Frantisek Chmelik, Pavel Lukac, Barry Leslie Mordike, Karl-Ulrich Kainer, Materials Science and Engineering A291 (2000) 246–249

[1] Y.-L. Shen, M. Finot, A. Needleman, S. Suresh, Acta Metall. Mater., 1995, 43, 1701

in the presence of thermal stresses a lower slope is observed at the early stage of deformation, due to the slightly lower apparent Young's modulus arising from prior plastic deformation. [1]

[2] LIU CHENG, ZHANG FAN, ZHANG GUODING, JOURNAL OF MATERIALS SCIENCE 39 (2004) 2923 – 2925

[2]

[3] V. SKLENICKA, M. PAHUTOVA , K. KUCHAROVA, M. SVOBODA, T.G. LANGDON, Metall. Mater. Trans. A 2002, Vol 33,13, pp 883-889

[3]

Predicted tensile stress-strain curves for the Al/SiC/20p composite with the variousreinforcement shapes.[1]

[1] Y.-L. Shen, M. Finot, A. Needleman, S. Suresh, Acta Metall. Mater., 1995, 43, 1701

unit-cylinder and double-Cone particles result in, respectively, the highest and lowest degrees of disturbance of the local plastic flow paths in the matrix.

An enhanced creep resistance was also obtained with the higher aspect ratio whiskers than with particles, presumably due to more effective load transfer from the matrix to the high stiffness reinforcement [2]

[2] D. Webster, Metall. Mater. Trans., 1982, 13A, 1511±1519.

With an increase in volume fraction, higher elastic modulus, macroscopic yield and tensile strengths were observed, coupled with lower ductility

void nucleation

composite, which may result from processing of composites with fairly coarse particulate reinforcement, do not contribute to load transfer or strengthening and would decrease strength.

N. Chawla, C. Andres, J. W. Jones, J. E. Allison, Metall. Mater. Trans., 1998, 29A, 2843.

M. Habibnejad-Korayema, R. Mahmudi, W.J. Pooleb, Materials Science and Engineering A 519 (2009) 198–203.

Yield stress improvement of the composites could be predicted by the following equation:

where the strengthening coefficient ofˇ is 1.25, is the difference between CTE of matrix and reinforcement, and T is the difference between the processing and the test temperatures

where Gm is the shear modulus of matrix, b is the Burgers vector, is the inter-particle spacing, and dp is the average diameter of particles

where K is the Hall-Petch coefficient and is the matrix grain diameter. The parameter K was calculated from the slope of

Hall-Petch − plot using different grain sizes of the rolled Mg–2Al2O3 material before and after annealing and their corresponding yield stress values

Assuming a well bonded particle

M. Habibnejad-Korayema, R. Mahmudi,W.J. Pooleb, Materials Science and Engineering A 519 (2009) 198–203.

The addition of nano-particles resulted in significant improvements in both hardness and tensile properties. However, this caused a considerable reduction in the ductility of the composites relative to the monolithic materials

CTE mismatch between the matrix and the particles was themost effective one

M. Habibnejad-Korayema, R. Mahmudi,W.J. Pooleb, Materials Science and Engineering A 519 (2009) 198–203.

Transition from quasi-cleavage fracture to amore advanced brittle state

Creep experiments on pure Mg at temperatures up to 600 K ∼ have shown that, as in f.c.c. metals, the steady state creep rate is related to the applied stress through a power-law in which the stress exponent is 1 at very low stresses, 5 over a wide range of ∼ ∼intermediate stresses and with a breakdown in the power-law behavior at very high stresses. [1]

[1] S . S . VAGARALI and T. G. LANGDON, Acta Metall. 29(1981) 1969.

They have been interpreted in terms of transitions from diffusion creep at the lowest stresses, dislocation climb with basal slip at intermediate stresses and power-law breakdown at very high stresses, where the diffusion creep and dislocation climb regions have activation energies of 135 kJ mol−1 ∼ which is equal to the value for lattice self-diffusion in magnesium

pyramidal slip mode can offer five independent slip systems to enhance ductility.Therefore, deformation of Mg polycrystals is normally required prismatic and pyramidal slip system

[2] X. W. Wei, X. T. Zu, H. Fu and W. L. Zhou, Materials Science and Technology 2006 VOL 22 NO 8 907

[2]

In many experiments on MMCs, the secondary stage is of a sufficiently short duration that it is best described as a minimum creep rate.

K.-T. Park, E.J. Lavernia, and F.A. Mohamed: Acta Metall., 1990, vol. 38, pp. 2149-59.

The Creep Curves in MMCs

• an abrupt and possibly poorly defined minimum creep rate is not an intrinsic property of all MMCs.


extent of the steady-state stage is also often of a very short duration in the creep of unreinforced powder metallurgy (PM) materials

relatively short duration of the steady-state stage in the creep of MMCs is not necessarily related to the advent of damage mechanisms within the matrix such as the occurrence of debonding at the interfaces between the matrix and the reinforcement.


The Nature of the Threshold Stress in MMCs

1) the particulates used as the reinforcements, which may have diameters of up to 20 m, cannot represent the source of the threshold stresses measured experimentally Attention has, therefore, focused instead on the presence of fine oxide particles, with sizes in the nanometer range, which may exist in MMCs fabricated using standard PM techniques.[1, 2]

[1] K.-T. Park, E.J. Lavernia, and F.A. Mohamed: Acta Metall., 1990, vol. 38, pp. 2149-59.[2] F.A. Mohamed, K.-T. Park, and E.J. Lavernia: Mater. Sci. Eng., 1992, vol. A150, pp. 21-35.

2) It is possible also that load transfer to the reinforcement may account for the origin of the threshold stress. based on creep experiments on Al-based composites, in which the values of the measured threshold stresses were dependent upon the precise volume fractions of the reinforcement. [3]

[3] A.B. Pandey, R.S. Mishra, and Y.R. Mahajan: Acta Metall. Mater., 1992, vol. 40, pp. 2045-52.

3) reinforcing particulates may crack as a result of the thermo-mechanical processing, thereby giving fine SiC particles with sizes of 100 nm. [4]

[4] Y. Li and F.A. Mohamed: Acta Mater., 1997, vol. 45, pp. 4775-85.

[1] K.-T. Park, E.J. Lavernia, and F.A. Mohamed: Acta Metall., 1990, vol. 38, pp. 2149-59.[2] K.-T. Park, E.J. Lavernia, and F.A. Mohamed: Acta Metall., 1994, vol. 42, pp. 667-78.

Threshold stresses in this composite are not associated primarily with a transfer of load from the metallic matrix to the ceramic reinforcement. Experimental

It has been shown that attractive interactions between these particles and moving dislocations may account for the measured threshold stresses in the high-temperature creep of MMCs

A higher volume of reinforcement may lead to the presence of a larger number of nanoparticles and higher threshold stress values.

significant values for the threshold stresses were observed in an Al 6061-20 vol pct Al2O3(p) and in an Al 7005-20 vol pct Al2O3(p) composite, both were fabricated using an ingot metallurgy (IM) procedure. [3]

[3] Y. Li and T.G. Langdon: Acta Mater., 1998, vol. 46, pp. 1143-55.

[2] A.B. Pandey, R.S. Mishra, and Y.R. Mahajan: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 305-16.

An extrapolation of against plot to a creep rate of s−1, which is in the range of the lowest measurable strain by a creep test machine, can then give the threshold stress for each temperature level. The true or effective stress exponents “n” in equation can then be obtained from the slope of against . [1]

Calculating the threshold stress

threshold stress for this composite is essentially independent of temperature for the condition where n =8.

[1] Y. Li, T.G. Langdon, Scr. Mater. 36 (12) (1997) 1457–1460.

[2]

B.Q. Han, D.C. Dunand, Materials Science and Engineering A300 (2001) 235–244

Q0 is an energy which has been tentatively associated with the binding energy between dislocations and obstacles in the glide plane.

It is well documented that the values for the apparent stress exponent and the apparent activation energy are often exceptionally high and variable in creep experiments on MMCs. threshold stress is incorporated into the analysisthese high and variable values for na and Qa are reduced to lower and constant values

for simple unreinforced materials: n=3 representing viscous glide of dislocations [1] n=5 representing climb of dislocations (lattice diffusion) [2] n=7 representing low temperature climb (core diffusion) [4]

n=8 representing (lattice diffusion) controlled by constant substructure model in which microstructure remain constant during creep [3]

When n=3, the anticipated activation energy is close to the value for the inter-diffusion energy of solute atoms. When n=5, 8 the anticipated activation energy is close to the value for the self-diffusion in the crystalline lattice.

[1] J. Weertman: J. Appl. Phys., 1957, vol. 28, pp. 1185-87. [2] J. Weertman: J. Appl. Phys., 1957, vol. 28, pp. 362-64.[3] O.D. Sherby, R.H. Klundt, and A.K. Miller: Metall. Trans. A, 1977, vol. 8A, pp. 843-50.[4] Sherby OD, Klundt RH, Miller AK. Flow stress, subgrain size, and subgrain stability at elevated temperature. Metall Trans A 1977;8(6):843–50.

[1] O.D. Sherby, R.H. Klundt, and A.K. Miller: Metall. Trans. A, 1977, vol. 8A, pp. 843-50..

Metal-based composites reinforced with ceramic particulates may have a fine substructure which develops during processing and they anticipated this would be invariant with stress, thereby inferring that the creep data for MMCs may be successfully analyzed using the constant substructure model where n=8. [1]

Al-4 pct Mg MMC

[2] A.B. Pandey, R.S. Mishra, and Y.R. Mahajan: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 305-16.

[2]

n=8

n=24

n=8

[3] Y. Li and T.G. Langdon: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 1271-73.

viscous glideQ = 125 kJ/molInter-diffusion of Mg atoms in anAl lattice (130.5 kJ/ mol)

kJ/ mol


[1] Al 6061 alloy MMC

n=8

Inter-diffusion of Mg in an Al lattice

viscous glideQ = 150 kJ/molInter-diffusion of Mg atoms in anAl lattice (130.5 kJ/ mol)

[1] Y. Li, T. G. Langdon, Mater. Sci. Eng., 1998, A245, 1±9.[2] P. Yavari, F. A. Mohamed, T. G. Langdon, Acta Metall., 1981, 29, 1495.[3] Y. Li and T.G. Langdon: Acta Mater., 1998, vol. 46, pp. 1143-55.

creep properties of the MMCs are governed by creep in the matrix material.

whereas values of n of 3 or 5 give threshold stresses which exhibit a consistent dependence on temperature, a value of n =8 may lead either to negative threshold stresses or to threshold stresses showing no significant variation with temperature.

[1] Y. Li, T. G. Langdon, Mater. Sci. Eng., 1998, A245, 1±9.

In class M (pure metal type) materials dislocation climb is the rate-controlling mechanism, with a stress exponent of around 5 and an activation energy similar to the value for self-diffusion in the matrix. In class A (alloy type) metals, viscous dislocation glide is the rate-controlling mechanism, with a stress exponent of around 3 and an activation energy associated with the viscous drag of the solute atmospheres. [1]

It should be noted that in unreinforced solid solution alloys a transition exists between class M behavior at low stresses to class A behavior at higher stresses.[2]

[2] P. Yavari, F. A. Mohamed, T. G. Langdon, Acta Metall., 1981, 29, 1495.

in dilute solid-solution alloys, representing either glide or climb as the rate-controlling process it is possible to modify the standard approach for solid solution alloys. in order to describe the two different classes of behavior in the MMCs [3]

e is the solute-solvent size differencec is the concentration of the solvent, is the stacking fault energy of the matrix alloy Dg is the appropriate diffusion coefficient for glide


[1] Y. Li and T.G. Langdon: Acta Mater., 1997, vol. 45, pp. 4797-4806.[2] Y. Li and T.G. Langdon: Acta Mater., 1998, vol. 46, pp. 1143-55.

[1] [2]

Effect of Processing Procedure on the Creep Properties of MMCs

[1] K.-T. Park, E.J. Lavernia, and F.A. Mohamed: Acta Metall., 1990, vol. 38, pp. 2149-59.


It is apparent from Figure 16 that the PM composite is consistently stronger than the IM material under these testing conditions.

the higher apparent strength recorded in Figure 16 for the PM composite is due only to the occurrence of a higher value for the threshold stress.

It was shown earlier by calculation that the change in slope in Figure 17 is associated with the breakaway of dislocations from their solute atmospheres

n (AZ 91) 5 .2

n (Pure magnesium) 8

n (AZ 91 −20 vol pct Al 2O 3 fiber) 8

n (QE22 − 20 vol pct Al 2 O3 fiber )>20

ε c°

εm° ¿(1− α)n

0<α <1

For the AZ 91 composite:

0.7 to 0.9𝑛=3

V. SKLENICKA, M. PAHUTOVA , K. KUCHAROVA, M. SVOBODA, T.G. LANGDON, Metall. Mater. Trans. A 2002, Vol 33,13, pp 883-889

– squeeze casting

V. SKLENICKA, M. PAHUTOVA , K. KUCHAROVA, M. SVOBODA, T.G. LANGDON, Metall. Mater. Trans. A 2002, Vol 33,13, pp 883-889

1) Massive precipitates along grain boundaries.2) Continuous precipitates of bcc in grain interiors. (platelets, responsible for age hardening)3) discontinuous precipitates of bcc in grain interiors. (cellular, detrimental to the age-hardening)

Mg17 Al12

massive precipitates often form a continuous interconnection among the alumina short fibers

MgO particles in the vicinity of fibers

In the composite, the fibers act as nucleation centers in the precipitation process promoting precipitation of Al2Nd, Mg(Ag)12Nd, and Mg3Ag phases

During the creep exposure, theMg(Ag)12Nd particles at fibers grew slightly

At temperatures above 423 K, these particles are replaced by hexagonal phase or tetragonal Mg(Ag)12Nd precipitates, which nucleate often on dislocations,

The creep resistance of squeeze-cast AZ 91 and QE 22 magnesium alloys reinforced with 20 vol pct Al2O3 short is shown to be significantly improved by comparison with the unreinforced alloy

Higher stresses ~> the sudden weakening of composites ~> dominance of the load transfer

Creep resistance of AZ91 composite > Creep resistance of AZ91 alloy ~> good adhesion between carbon fiber surfaces and the matrix ~> load transfer

Creep resistance of QE22 composite < Creep resistance of QE22 alloy ~> interfacial reaction and debonding

A strong bonding between carbon fibre surfaces and MgO reaction zones and SiC/matrix interfaces (Fig. 3a) implies very important role of the load transfer in creep strengthening of the AZ91 alloy

M. Svoboda, M. Pahutova, K. Kucharova, V. Sklenicka, K.U. Kainer, Materials Letters 39 _1999. 179–183

AZ 91∧QE 22− 15 % volume SiC +7 % volume short carbon fibers +2 % vol Si − squeeze casting

The creep resistance of the MMCs is poor by comparison to the unreinforced QE22 alloy.

QE 22− 15 % volume SiC – PM

[1] Florian Moll, Frantisek Chmelik, Pavel Lukac, Barry Leslie Mordike, Karl-Ulrich Kainer, Materials Science and Engineering A291 (2000) 246–249

Interfacial sliding may be affected by internal thermal stresses arising at the interfaces on heating the specimen to the test temperature (the thermal expansion coefficients of the metallic matrix and the ceramic particles differ considerably). Since SiC particles are very rigid, interfacial sliding is not accommodated sufficiently and, hence, cavities form at interfaces. [1]

It is concluded that fibre cracking andror breakage are not mechanisms controlling the damage process in the high temperature creep of magnesium-based metal matrix composites

- squeeze casting- machining

M. Pahutovaa, J. Brezina a, K. Kucharovaa, V. Sklenicka a, T.G. Langdon, Materials Letters 39 1999. 179–183

Inspection reveals a large number of Al2O3 short-fibre breaks and fibre fragmentation due to the high mechanical and thermal loads. Fibre damage was clearly evident in a subsurface zone to approximately 100 m below the specimen surface.

Damage A ~> crackingDamage B ~> breakage

15%vol. Saffil short fibers and 5% vol. SiC particulates 10%vol. Saffil short fibers and 10% vol. SiC particulates 10%vol. Saffil short fibers and 15% vol. SiC particulates

(longitudinal direction) the plane containing random fiber orientation was parallel to the loading direction

A.K. Mondal , S. Kumar, Composites Science and Technology 68 (2008) 3251–3258


Initially the matrix deforms slowly with the generation and movement of dislocations. The movement of dislocations is hindered by the rigid network of the fibers and dislocation pile-ups are formed. As the formation of pile-ups is continued, the local stress around the fibers is increased accordingly. The increase in local stress concentration leads to the fiber fracture. This helps the dislocations start moving, inducing failure of further fibers, thereby accelerating the deformation.


the broken fibers in the plastic deformation zone are clogged, i.e., all broken fibers are totally entrapped and segregated below and surrounding the indenter so that the further movement of the indenter is slowed down. The broken fibers also change their orientation and tend to align in the direction of flow within the bulk material


Viscous glide as well as climb of dislocation is found to be the dominant creep mechanism in the stress and temperature range employed for all the composites.

B.Q. Han, D.C. Dunand, Materials Science and Engineering A300 (2001) 235–244

low-stress regime ~> (Qapp = 48 kJ/ mol) = 1/2 energy of grain boundary diffusion in pure magnesium (Qgb = 92 kJ/ mol)high-stress regime ~> (Qapp = 230 to 325 kJ /mol ) >> activation energy of lattice diffusion in magnesium (Q1=35 kJ/mol(

) – squeeze casting

.

The low-stress behavior can be described by an existing model of grain-boundary sliding inhibited by grain-boundaries dispersoids

The high-stress behavior ~> threshold stress ~> dislocation climb

A. Arunachaleswaran, I.M. Pereira, H. Dieringa, Y. Huang, N. Hort, B.K. Dhindaw,, K.U. Kainer, Materials Science and Engineering A 460–461 (2007) 268–276

AE42+alumina short fibers (Saffil)and SiC particles (SiCp)-squeeze casting-T4

The stress exponents calculated were very high, revealing threshold creep behavior as expected from these hybrid composites. The values of effective stress exponents were in general, between the range of 3–7 strongly indicating, that‘viscous glide and high temperature climb of dislocations’ as the predominant creep mechanism involved.

The T4 heat-treatment could not provide any remarkable variationin the creep behavior of these composites, thus, it is suggested from the study that these composites be used in its as-cast state.

X. W. Wei, X. T. Zu, H. Fu and W. L. Zhou, Materials Science and Technology 2006 VOL 22 NO 8 907

Mg–14Li–Al–(5-10-15)%vol. MgO/Mg2Si & Mg–14Li–Al - casting

For Mg–14Li–Aln= 4.95Q= 76.67 kJ/mol

For Mg–14Li–Al- MgO/Mg2Si n= 7.38-9.42Q= 109.9-135.2 kJ/mol

The compressive creep rate is controlled by dislocation climb and diffusion of Li in the testing materials.

It is possible that the interparticle spacing of the MgO/Mg2Si particulates is smaller than the average subgrain size, leading to a constant structure condition.

The more content of MgO/Mg2Si particulates, the smaller interparticle spacing of the MgO/Mg2Si particulates. Constant structure implies that the barrier spacing to a dislocation motion (i.e. either subgrain size stabilised by particles or the interparticle space) is independent of the applied stress. A stress exponent of >8 is reasonable for the Mg–14Li–Al–MgO/Mg2Si composites because a constant structure presents in the form of subgrains pinned by the MgO/Mg2Si particulates or by the presence of the particulates alone if they are closely spaced and are effective dislocation barriers.

Thank for your attention!

review of creep in magnesium matrix composites seminar title: by: farid labib supervised by: prof....

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