Influence of dispersoids on the creep behavior of dispersión strengthened aluminum materials

The creep behavior of a rapidly solidified Al-6.5%Fe-0.6%V-1.3%Si dispersión strengthened material containing 16 volume % of dispersoids has been studied by means of tensile tests at high temperatures from 483 to 821 K. The imposed strain rates ranged from 2.5 • 10" to 10~ s". The microstructure was very fine, consisting of submicron grains and small hard round-shaped dispersoids of about 54 nm. The creep behavior was characterized by high apparent stress exponents and high activation energies that are not accurately predicted by models from the literature. Therefore, a creep equation is developed to describe the creep behavior of the studied aluminum dispersión strengthened material and bther materials with similar microstructures. The proposed equation is a generalization of conventional slip creep equations without the use of a threshold stress.

Al-Fe alloys with ternary additions of transition metáis have promised lightweight structural materials due to their low diffusivity in the aluminum matrix and have been studied extensively (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18).The addition of silicon to these systems allowed the formation of a large volume fraction of very fine, rounded and thermally stable suicides (19)(20).These alloys are specially creep resistant due to the much slower coarsening rate of the suicides.These alloys and other dispersión strengthened materials present an "anomalous" creep behavior compared to puré metáis and dispersion-free alloys, referring to the high apparent stress exponent and activation energy valúes when tested at high temperatures.
The stress exponent for creep of these materials is much higher than 5, extending over several decades in strain rate.On the other hand, the activation energy for creep is much higher than that for lattice self-diffusion (21-24).These two creep parameters, n and Q, are determined from the general creep equation where ¿ is the strain rate, A PL is a material constant, o is the stress, n is the stress exponent, Q is the activation energy for creep, E is Young's modulus, R is the gas constant and T is the temperature.The stress exponent and activation energy obtained experimentally from é vs o/E curves at different temperatures using eq.[1] are normally referred as apparent, n ap and <2 ap , respectively.
At constant structure creep tests, as expected in dispersion-strengthened alloys, the following equation can be used in the power law creep región (21 and 25): In this equation, X is the subgrain size and b is Burgers vector.The constant A\ is^equal to 10 9 and D L = D 0 exp(-Q L /RT) is the lattice self-diffusion coefficient, where D 0 is the preexponential constant and Q L is the activation energy for lattice selfdiffusion.
The activation energies for creep and the stress exponents of dispersion-strengthened materials are often found to be too high to be explained by this equation.A formal representation of the creep data for such materials can be obtained by introducing a threshold stress, a 0 , into eq.[1], Below this stress, creep deformation is assumed to be negligible.This assumption leads to an arbitrarily high apparent stress exponent on log é -log a plots in the vicinity of o 0 .By curve fitting, consistent sets of valúes for Q and n (where n can be 2, 3, 5 or 8) can usually be found which enable eq.[1] to describe the creep data within a certain range of experimental conditions (21)(22)(23)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35).The inadequacies of this parametric approach are however quite evident: the parameter a 0 is not a good material constant as it often varies with both temperature and applied stress.
The purpose of this paper is to study the creep behavior of a rapidly solidified extruded Al-Fe-V-Si dispersión strengthened material and to develop a phenomenological relation that permits a quantitative prediction for dispersión strengthened materials that do not show threshold stress-like behavior.The predictions of the new equation are compared with the creep data of both the extruded material studied in this work and a rolled material of similar composition that was previously investigated (46).

MATERIAL AND EXPERIMENTAL PROCEDURE
An extruded material of composition Al-6.5%Fe-0.6%V-1.3^Si(in mass percent) was studied.The abbreviated denomination is "extruded AFV-16%".The material denomination is given by the initials of the elements present except for silicon.The percent amount following those initials corresponds to the volume fraction of dispersoids in the material.
The material was obtained at Allied-Signal laboratories.It was rapidly solidified by "planar flow casting", producing ribbons of approximately 25 \xm in thickness and 50 mm in width at cooling rates of uptol0 6 K/s(47).
The ribbons were then comminuted to powder and were processed by a powder metallurgy route.The powders were first sieved to have particles smaller than about 200 ¡im and then degassified and hot pressed at 623 K in vacuum.Billets of 279 mm in diameter were obtained.The ingots were preheated at 673 K and extruded at an extrusión ratio of 9.8:1 to obtain bars of 89 mm in diameter.
Cylindrical tensile samples of 4.8 mm in diameter and 19 mm gauge length were machined parallel to the extrusión direction.

RESULTS
The microstructure of the extruded AFV-16% material was found to consist of very fine grains and small and rounded dispersoids.The grain size is about 0.7 |iim and the dispersoids, of approximately 54 nm, are homogeneously distributed in the matrix.The vast majority of dispersoids found are of the Al, 2 (Fe, V) 3 Si phase, being the rest of the Al 13 (Fe,V) 4 phase.The microstructure after testing at temperaturas up to 673 K showed that the grain and dispersoid sizes remain very fine.The microstructure of the material remains homogeneous after tensile testing.
In order to charaeterize the creep behavior of the dispersión strengthened material, strain rate-flow stress data at different temperatures were obtained by means of strain rate changes.The tests started at the highest strain rate of 10 2 s 1 until constant flow stress is reached.Then, decreasing steps of an order of magnitude in strain rate were imposed.The material showed a typical constant substructure deformation behavior since, after a change in strain rate, a new steady state was quickly developed after a small deformation (25).
Figure 1 shows a plot of logarithm of the true strain rate, é, as a function of logarithm of the true flow stress, a, for the extruded AFV-16% material.The flow stresses range from 41 to 258 MPa for applied strain rates ranging from 2.5 -10" 6 to 10~2 s 1 and temperatures ranging from 483 to 821 K.
The apparent stress exponent, n ap , and the apparent activation energy, <2 ap , are directly obtained from figure 1, <3ln¿ " ap ancr ftp= W ap R l [3,4] where R is the gas constant.To avoid extrapolations, the activation energy for creep was determined at a constant strain rate of 10~4 s 1 .
Valúes of the Young's modulus for puré aluminum at different temperatures were used (48).
Figure 2 shows the apparent activation energy and the apparent stress exponent as a function of temperature for the extruded AFV-16% material in the temperature range 483 to 821 K.The large activation energy valúes found at high temperatures (up to 550 kJ/mol) do not correspond to activation energies of any kind of diffusivity that may control deformation in these systems.Thus, these very high valúes of activation energies should be rationalized to explain the creep behavior.The stress exponent valúes, on the other hand, decrease with increasing temperature from 44 at 483 K to 19 at 821 K.These high valúes are in contrast to non-reinforced materials that usually show a stress exponent of about 5 at elevated temperatures which remain unchanged in a wide range of temperatures.These stress exponents are even higher than that of 8, cofresponding to the creep model under constant substructure conditions (25).
It is of interest to note that the anomalously high valúes of n ap and Q ap are also found in dispersión and particulate reinforced materials (21-24).However, they are not encountered in puré metáis and solid solutions (49).Fig. 2.-La energía de activación aparente y el exponente de la tensión aparente en función de la temperatura de ensayo del material AFV-16% extruido.

DISCUSSION
Several attempts have been made in the literature to rationalize the high valúes of n ap and <2 ap often observed in dispersión strengthened materials.An usual approach is to fit the creep data considering some creep mechanism and incorporating a threshold stress.The threshold stress is then related to that particular mechanism chosen.For example, the stress necessary to start the motion of dislocations if slip creep is considered.The most common slip creep mechanisms incorporating a threshold stress used in the literature to predict the creep data are those referred to materials where the substructure is supposed to change with stress (n = 5) (24, 28-29) and those where the microstructure does not change with stress (n = 8) (23, 32-33, 46, 50).An analysis of the present creep data was made by means of both mechanisms.The best fit was obtained by incorporating a threshold stress, G 0 , into the constant structure equation (eq.[2]).An agreement within an order of magnitude in strain rate between the experimental data and the prediction of eq.[2] was found for the extruded AFV-16% material (51).Similar results were also found for a rolled AFV-27% material previously studied ( 46).However, the threshold stresses used were found to strongly depend on temperature.The variation of threshold stress in the range 573 to 823 K was 12 and 4 times for the rolled AFV-27% and extruded AFV-16% materials, respectively (46 and 51).This strong dependence on temperature of the threshold stress cannot be justified by microstructifral changes and has not a physical meaning.Therefore, the threshold stress remains a fitting parameter.Considering the important structural applications of dispersion-strengthened alloys this is a serious practical limitation and its use should be avoided when extrapolating to lower stresses and/or higher temperatures.
As an interesting alternative to the use of a threshold stress, Arzt et al. developed a model where an attractive interaction of dislocations and precipitates is considered (42)(43).The result of this attractive interaction is that dislocations remain attached to the dispersoids after local climbing until an equilibrium position, given by the strength of the interaction and the resolved shear stress, is reached.This mechanism is characterized by means of the parameters /:, a relaxation parameter, which gives the strength of the attractive interaction, and x d , which gives the detachment shear stress necessary for dislocations to bypass the dispersoids without noticing the attractive interaction.
In order to compare the experimental data of the dispersión strengthened material with predictions from the Arzt model, valúes for k and x d were obtained as a function of temperature to obtain the best correlation.Figure 3 shows the temperature dependence of k for the extruded AFV-16% material.It can be seen that h is strongly temperature dependent.This temperature dependence of k is not considered in the model.Similar dependence was obtained for T d .This may conclude that this model is not appropriate to predict the creep behavior of this material.In addition, a study conducted on the rolled AFV-27% material (46) revealed that inconsistent sets of k and T d valúes had to be used to predict either the apparent activation energy or the strain rate, but not both simultaneously.Moreover, the preexponential constant that had to be used to fit the creep data, was orders of magnitude higher than that predicted by the model.
Other authors approached the problem of the anomalous creep behavior by considering the deformation of dispersoids (36)(37) or the load transfer between particles and matrix (38-39).However, the load transfer mechanism should be less important in this material than in whisker reinforced materials.On the other hand, TEM observations of deformed samples showed no deformation of the dispersoids (51).Moreover, in most dispersión strengthened materials the particles are impenetrable for dislocations and their concurrent deformation cannot occur.These results do not support the approach of Nix et al.It is, therefore, concluded that the models given in the literature do not satisfactorily predict the creep data of the dispersión strengthened aluminum materials considered in this work.A new approach is developed in this work that is an alternative to existing models.

Alternative creep equation for dispersión strengthened materials
It is well established that the creep behavior of puré aluminum is characterized by a stress exponent of about 5 in the power law región.In addition, the activation energy for creep corresponds to that for lattice self-diffusion.Therefore, all creep data for puré aluminum at different temperatures can be superimposed into a single line in a representation of lattice diffusion compensated strain rate versus Young's modulus compensated stress in logarithmic scale.If the microstructure of the aluminum remains constant, a stress exponent of 8 would be found in this representation.As any creep data of puré aluminum lies along this single line, it is true that the creep data corresponding to a particular fixed strain rate for different temperatures lie also along the same line, thus showing the same stress exponent.Therefore, it would be sufficient to consider the creep data at a fixed strain rate to know the operating deformation mechanism for puré aluminum and other metáis and alloys.
To better describe the creep behavior of dispersión strengthened materials, let us define the "skeleton line" as the linie joining the creep data corresponding to the same reference strain rate (for example at 10~4 s 1 ) at different temperatures.Figure 4 shows the skeleton line of the extruded AFV-16% material obtained at a constant strain rate of 10~4 s" 1 .In addition, a skeleton line of a previously tested Al-Fe-V-Si material denominated "rolled AFV-27%" ( 46) is also incorporated into the figure.The choice of another strain rate does not alter the results.The lines in the figure are drawn from data at different testing temperatures.
Three distinct temperature ranges can be differentiated.At intermedíate temperatures, power law breakdown occurs as shown by the curvature of the skeleton line at about é/D L = 10 13 nr 2 .The power law región, /.<?., the región at the highest temperatures, can be divided into two regions according to changes in the microstructure.Up to about 723 K the microstructure does not change during testing.At higher temperatures some microstructural coarsening takes place as a result of the higher diffusivity of the different elements present in the material.Only the creep data in the power law región will be considered in the following.-Lattice diffusion-compensated strain rate as a function of modulus-compensated stress for the extruded AFV-16% and rolled AFV-27% materials showing their "skeleton lines" at a constant strain rateof lO^s 1 .
The slope of the skeleton line is a stress exponent that will be named h.A valué of h -8 is observed for the extruded AFV-16% material in the power-law regime.This valué of 8 agrees with the valué of the stress exponent of the constant microstructure model, as given by eq.[2].In contrast, the rolled AFV-27% material shows a decreasing valué from h = 8 to about h = 5, or lower, for increasing temperatures.This lowering of h for the rolled AFV-27% material is attributed to increasing microstructural coarsening and heterogeneization at increasing temperatures.
The valué of h is defined by the expression: <9ln $ 'A dm{%) [5] According to this definition, h is a stress exponent that can be obtained from data at constant strain rate.The stress exponent, h, can be related to the apparent stress exponent, w ap , the apparent activation energy, Q ap , and the lattice diffusion activation energy, Q LJ using the following relations for n üp and £ ap ,

M%)
Q a p= n ap-R \ Applying the chain rule for partial derivatives, the following relation is derived: Therefore, when n ap = /z, then Q ap = Q L .In other words, if creep is exclusively controlled by lattice diffusion, n ap = h = n and the creep behavior is described by eq.[1] as for puré aluminum.It also follows from this equation that an increase of n ap is accompanied by an increase of Q ap , as it is observed for the studied dispersión strengthened materials.
It is our contention that the high valúes of n ap observed in dispersion-strengthened materials are attributed to an additional dependence of stress with strain rate from the presence of dispersoids.This is to be expected since the high n ap and Q ap valúes are observed in dispersion-strengthened materials and not in puré metáis and alloys.According to this view, the interaction between dislocations and particles is a factor that influences slip creep.This can be considered as the core of the present approach.The magnitude of this interaction is described by a stress exponent, ñ, given by the relation: ñ = n ap ~h or, n^" = h + ñ ap [7] In other words, the dislocation-dispersoid interaction raises the stress exponent by a valué of ñ.Therefore, h is determined by the matrix behavior and ñ by the dislocation-dispersoid interaction.The exponent ñ can be, therefore, obtained for the extruded AFV-16% material by substracting the slope of the skeleton line from the apparent stress exponent, both experimentally determined from figures 4 and 1, respectively.The introduction of ñ implies changes in the activation energy and in the pre-exponential constant of eq.[1].Equation [7] together with eq.[6] predict that both the experimental apparent stress exponent and the activation energy are simultaneously increased for dispersión strengthened materials by means of ñ.
Similarly to the detachment model ( 42), it is our contention that the valué of the parameter characterizing the dislocation-dispersoid interaction, ñ, is dependent on the particular dispersoid-matrix interface.Thus, vary for different materials.
The most general creep equation of our approach can be derived by introducing eqs.[6] and [7] into the general creep equation (eq.[1]): where A is a material constant.Rearranging eq.[8], the different contributions of matrix and dispersoids can be separated: RT h, [9] It is readily apparent that the larger the interaction, i.e., the ñ valué, the more creep resistant is the material.
When the material deforms at high temperature maintaining its microstructure constant, a more explicit equation can be written: t = ±¿ OL •!H£f: [10]   where X is the interparticle distance.
In summary, the apparent activation energy corresponds to that for self-diffusion of the matrix altered by the presence of dispersoids.The exponent ñ causes an "amplification" of the strain rate dependence on temperature, predicting high apparent activation energy valúes.There is no need to invoke the operation of a threshold stress to rationalize the high apparent stress exponent and apparent activation energy valúes.Equation [8] presents also clearly the new approach by showing the two parameters, h and ñ, describing the creep behavior of dispersión strengthened materials.These two parameters are related solely to the matrix behavior and the presence of dispersoids, respectively.Therefore, eq.[8] is a generalization of eq.[1] for dispersion-strengthened materials since for a non-reinforced material, ñ = 0 and eq.[8] becomes eq.[1].This equation describes the creep behavior of dispersión strengthened materials, not showing an apparent threshold stress, in a simple manner and is able to accurately predict the creep behavior, as long as there is no microstructural degradation and/or change in deformation mechanism, as will be shown in the following.

Predictive capability of the new equation
Equation [8] was used to analyze and predict the creep behavior of the extruded AFV-16% and rolled AFV-27% materials.For the extruded AFV-16% material a valué of h = 8 was used, as shown in figure 4, that is consistent with a constant microstructure slip creep mechanism, in contrast to a valué of 5 implying stress dependent subgrain formation during creep.Valúes of A = 9.M0 84 s" 1 and ñ = 14 were obtained by a minimum squares regression method to fit the experimental data.The valué of A is large because it is inversely proportional to the term a/E raised to the n ap exponent which is about 23.
Figure 5 shows the strain rate vs the flow stress at five different temperatures for the extruded AFV-16% material.The predicted curves from eq. [8], using the previous valúes, correlate well with data at all temperatures except at the lowest temperature, 623 K, where a lower creep rate is predicted.This can be associated with pipe and grain boundary diffusion that is believed to become important for fine grain size at intermedíate temperatures.This can be taken into account by considering an effective diffusivity in eq.[8] instead of the lattice self-diffusivity used.The small disagreement at 821 K is attributed to microstructural changes involving coarsening of dispersoids.The relation between the creep rate and the microstructural parameters will be considered later.
Figure 6 shows the strain rate as a function of the stress at five different temperatures for the rolled AFV-27% alloy previously investigated (46).The following valúes of constants have been used: h = 8, ñ = 12.5 and A = 3.8-10 79 s 1 .The figure shows experimental valúes of é and a at different temperatures and the prediction of eq.[8] given as straight lines.The agreement between predicted valúes and experimental data is good except at 573 and 773 K, due to the effective diffusivity and microstructural changes similar to those occurring in the extruded AFV-16% material, respectively.
The small difference in ñ valúes for the two materials (ñ = 12.5 for the rolled AFV-27% material and ñ = 14 for the extruded AFV-16% material) would indicate a slightly higher efficiency of the extruded AFV-16% dispersoids to hinder the motion of dislocations.The preexponential constant A is also 4 orders of magnitude larger for the extruded AFV-16% material but it represents only about 30 MPa in the stress axis, due to the large apparent stress exponent.
Another simple method to predict the creep behavior needs just three creep data: two at the same strain rate and at two different temperatures, and another one at a different strain rate for an ío-1 -The strain rate as a function of stress for the extruded AFV-16% material at various temperatures.The lines are the predicted curves from eq. [8].
already tested temperature.The valúes of h and n ap are obtained from the two creep data at the same strain rate and from the two creep data at the same temperature, respectively.The valué of ñ can be calculated from these valúes by means of eq.[7], and <2 ap by means of eq.[6].The constant A can be calculated by introducing the h and ñ valúes into eq.[8], using a single experimental creep datum (one é and o for a given T).As long as there is no change in microstructure and/or deformation mechanism, the given valúes of Q ap , n ap and A are constant and can be introduced into eq.[8] to predict the creep behavior.
Apart from explaining the high valúes of Q ap and n ap , our approach also explains the simultaneously strong temperature dependence of these parameters with temperature due to microstructural degradation involving coarsening and heterogeneization of the microstructure occurring at high temperatures.For constant ñ, according to eqs.[6] and [7], a decrease of h causes a decrease of n ap and an increase of <2 ap .
The skeleton line, except for the preexponential constant, follows the constant microstructure equation (eq.[2]), as long as the interparticle distance is smaller than the equilibrium subgrain size for the flow stress, given by the relation (25 and 52): b {E [11] where A is approximately 7 for puré aluminum.Therefore, the change of h can be quantified if microstructural changes are known.The valué of h can be related to the microstructure*as follows: An experimental valué of h = 7.4 corresponded to the rolled AFV-27% material at 673 K.The prediction at 723 K, as a result of microstructure coarsening, is therefore: h = 7.4 -2.4 = 5, that is the experimental valué at 723 K.The new Q ap valué can be obtained through eq.[7], using ñ = 12.5 for this material: Similar agreement can be obtained for the extruded AFV-16% material.Assuming an increase of X of 15 % from 721 to 774 K, it is obtained Mi « -1.9.Therefore, while at 721 K an apparent activation energy Q ap = 142(14 + 8) / 8 = 391 kJ/mol is predicted, a valué of Q ap = 142(14 + 6.1) / 6.1 = 468 kJ/mol is obtained at 774 K which is, again, cióse to the experimentally measured.Assuming again the same small increase of X of 15 % from 774 to 821 K, it is obtained M « -1.6.A valué for Q ap = 142(14 + 4.5) / 4.5 = 584 kJ/mol is obtained at 821 K which is, again, cióse to the experimental valué.This agreement gives an added support to the prediction capability of our approach.
It is worth noting that small changes in the microstructure, which are difficult to avoid in most families of dispersión strengthened alloys, cause strong changes in the creep behavior, Le., in the creep resistance, n ap and, specially, in <2 ap .
In conclusión, the phenomenological model developed in this work describes well the creep behavior of the Al-Fe-V-Si materials.It can be also applied to the study of other dispersión strengthened materials.

SUMMARY AND CONCLUSIONS
If the microstructure remains constant, AX = 0, and h = 8.If the microstructure coarsens, h < 8, since the derivative of X of eq.[12] is negative.This drop of h induces a drop of n ap (eq.[7]) and an increase of Q ap (eq.[6]).
An example of the effect of a microstructural change on Q ap is given in the following for the rolled AFV-27% material at é = 10' 4 s A and at 673 and 723 K. Stresses corresponding to a strain rate of 10 4 s 1 are considered although, as mentioned, any other strain rate can be considered.Assuming an increase of X of 25 % the correction for h from eq. [12], using the stress valúes from ( 46 threshold stress-like behavior.This equation is a generalization of conventional slip creep equations and does not contain a threshold stress.The creep behavior of the matrix is characterized by h, the slope of the Une that relates the lattice diffusion compensated strain rate and the modulus compensated stress at a constant strain rate.This line is called the skeleton line.An exponent ñ is introduced that characterizes a dislocationdispersoid interaction which is temperature independent.The effect of the exponent ñ is to increase the apparent stress exponent and the apparent activation energy respect to the valúes related to the matrix.The creep equation correctly predicts the creep behavior of aluminum dispersionstrengthened materials.It explains the high valúes of <2 ap and n ap , and, moreover, the simultaneous strong temperature dependence of these parameters that is due to microstructural degradation. Rev. Metal.Madrid, 33 (5), 1997 325 (c) Consejo Superior de Investigaciones Científicas Licencia Creative Commons 3.0 España (by-nc) http://revistademetalurgia.revistas.csic.esF. Carreño et al. / Influence of dispersoids on the creep...
Fig 5.-The strain rate as a function of stress for the extruded AFV-16% material at various temperatures.The lines are the predicted curves from eq.[8].
Fig 6.-The strain rate as a function of stress for the rolled AFV-27% material at various temperatures.The lines are the predicted curves from eq.[8].
) is -The microstructure of the extruded Al-Fe-V-Si material investigated was very fine.The dispersoids (about 54 nm) pin the grain boundaries limiting the aluminum matrix grain size to a valué of about 0.7 \im.-High apparent stress exponents, ranging from 44 at 483 K to 19 at 821 K, and high apparent activation energy valúes, up to 550 kJ/mol, were observed.These high n ap and Q ap valúes are in contrast to those of non-reinforced materials.-The various models existent in the literature do not satisfactorily explain these high n ap and <2 ap valúes.A new creep equation has been developed for dispersion-strengthened materials that do not show Rev. Metal.Madrid, 33 (5), 1997 331 (c) Consejo Superior de Investigaciones Científicas Licencia Creative Commons 3.0 España (by-nc) http://revistademetalurgia.revistas.csic.esF. Car reno et al. / Influence of dispersólas on the creep...