Precipitation and the Bauschinger Effect in Al-Ge-Si Alloys

Wei Gana, Richard Bogerb, Frédéric Barlatc and Robert H. Wagonerd*

a Simulia Central Region , Minneapolis/St. Paul Office, 539 Bielenberg Drive, Suite 110, Woodbury, MN 55125

b Simulia Central Region, Cincinnati Office, 9075 Centre Pointe Drive, Suite 410, West Chester, OH 45069

c Pohang University of Science and Technology, Graduate Institute of Ferrous Technology, San 31 Hyoja-Dong, Nam-Gu, Pohang, Gyeongbuk, 790-784, KOREA

d The Ohio State University, Department of Materials Science and Engineering, 2041 College Road, Columbus, OH 43210, USA

* Corresponding Author. Tel.: +1 614 292 2079; Fax: +1 614 292 6530. E-mail address: wagoner.2@osu.

Abstract

Dilute Al-Ge-Si alloys were created from the melt and processed to obtain wrought sheets suitable for solutionizing and aging to obtain a range of hardness. Al-Ge-Si was selected as a model material because the thermodynamically stable precipitates have diamond cubic crystal structures which are incoherent with the matrix and are thus non-shearable, even at very small sizes. This is in contrast to commercial age-hardenable aluminum alloys which have coherent, metastable, shearable precipitates at early stages of aging. Aging curves at temperatures of 120, 160, 200 and 240 deg. C were established, along with the precipitate spacing, size, and morphology. The role of non-shearable precipitates on the strength of the Baushinger effect was revealed using novel, large-strain tension/compression tests. Even for these very dilute alloys, precipitates were found to contribute twice the grain boundary contribution to the Bauschinger effect. The Baushinger effect increases dramatically from the underaged to the peak aged condition and remains the same through the overaged condition. This behavior contrasts with that of model Al-Cu alloys, for which the maximum Bauschinger effect is seen at peak aging and decreases afterwards, and with that of commercial alloy 2524, for which the maximum Bauschinger effect occurs in the overaged condition.

March 17, 2009To be submitted to Metallurgical and Materials Transactions A

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1. INTRODUCTION

Many commercial aluminum alloys contain second phase particles for strengthening as obstacles for dislocation movement. The stress heterogeneity caused by the particles during deformation also gives rise to a transient hardening response upon reverse or non-proportional loading, and effect we refer to here as the “Bauschinger effect” [1], although this term is often used in the more limited sense of a reduced yield stress upon a stress reversal. An accurate description of precipitation strengthening and its role in reverse yielding has importance for simulation of many sheet forming operations, where stress reversals and non-proportional strain paths are common. Springack simulation is particularly sensitive to accurate prediction of stress under such conditions [REF: Geng and Wagoner].

[Wei – I would suggest a rewritten version of the introduction of the B-E in the next 2 paragraphs using what you have done here, plus some from Richard Boger’s. His is too long for this paper, but the ideas and references should be mentioned. Yours is a bit too short. You can refer to his paper if necessary. The basic idea is that there is the continuum-type stress inhomogeneity / composite model, which you have shown (REF) is insignificant for alloys with small volume fractions of second phase particle, with effects from grain boundaries and other sources generally being even smaller. The other idea is in some way related to dislocations being impeded and stored in some polarized way that build up high local stresses and strains which are released upon a stress reversal. The basic idea is from Orowan, etc. and you have cited TEM evidence for versions of it. This model can produce significant effects for small volume fractions of particles if they are spaced closely enough, analogous to the usual Orowan looping mechanism for monotonic deformation. The question really is, how does the storage of the polarized dislocation structures relate to precipitate spacing and size when the precipitates are non-shearable, i.e. when the confounding effects of coherency, etc., are removed from the problem?]

The study of the Bauschinger effect falls into two categories: continuum composite models and microstructure based analysis. Continuum composite models do not have intrinsic length scale. The size effect of microstructural features cannot be considered in those models. Furthermore, they cannot explain the Bauschinger effect in pure single crystal materials where no second phase or grain texture effect is present [2, 3]. The shortcomings of the continuum composite models as applied to precipitate-strengthened alloys motivate the microstructure based Bauschinger effect analysis.

TEM observations have revealed complex dislocation interactions during stress reversal or path changes [4-13]. When the loading direction is changed, dislocation structures may untangle, disintegrate and then form new patterns. Semi-phenomenological models have been constructued to simulate the influence of dislocation cell structure and slip

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band evolution on the Bauschinger effect [6, 9, 14-16]. The dislocation structure descriptions in these models remain qualitative and are difficult to verify. It has been shown that dislocation cell structure does not have determining effect on the Bauschinger effect [17]. Instead, the form of the dislocation substructure is determined by the same single-dislocation interactions that control the mechanical evolution of strength via dislocation density.

[Wei, you need a little introduction to at least the Bate/Wilson papers and Liu and Barlat paper which show that the B-E is strongest in Al-Cu alloys at peak aging. Also need to mention briefly Boger’s result that complex commercial alloys seem to have a B effect that continues to grow well into the overaging conditions. Because both kinds of alloys have precipitates that change character – i.e. coherent/incoherent and Xl structure – during aging, it is impossible to separate these effects from precipitate size and spacing alone. There might be a few other references that can support these ideas from Boger’s paper / thesis and yours.]

Age-hardened Al-Ge-Si alloys have finely spaced Ge-Si precipitates [18, 19] of stable, incoherent, non-shearable [21], fixed-composition diamond-cubic crystal structure [20, 21]. No array of metastable phases are present, in contrast with commercial age-hardened alloys. Very significant strengthening occurs during aging for very small volume fractions of precipitates. These properties allow the inherent characteristics of “hard pins” strengthening in terms of forward and reverse yield and hardening to be revealed experimentally.

[I think that the form that the introduction takes will really depend on a decision about whether these two paper – i.e. Boger and Gan – go in together or not. If separate, the introductions need to be more complete. If together, each one can do certain aspects and refer to the other for others. In particular, I think the representations of the B effect are of interest for both, and I would like to see my idea of an energy term (integral of delta-sigma x delta epsilon after a reversal) used to characterize the overall strength of the B effect. In this way we can easily quantify how small the composite model is (at the strongest) vs. what is seen in practice. Also, how much does this term vary with aging, volume fraction, etc.]

2. EXPERIMENTS

Dilure Al-Ge-Si alloys were cast, homogenized and rolled to 2mm thickness at the Alcoa Technical Center [22]. Sheets were solution heat treated at 500 0C [for what time?], water quenched and aged for various times at temperatures of 120, 160, 200 or 240 degrees C. Micro-hardness data were collected at various aging times in order to identify under aged (UA), peak aged (PA) and over aged (OA) conditions. Samples were examined using TEM to reveal the precipitate structure and were tested in tension and reverse tension/compression tests. These aspects are presented in more detail in this

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section.

2.1.Materials

Three melt chemistries were cast into ingots with nominal dimensions of 2”x10”x14” (50mm x 250mm x 350mm), homogenized for 8 hours at 5000C, and forced-air cooled. Hot rolling at 4400C was carried out using 12 passes from the initial thickness of 2” (50mm) to a final thickness of 0.2”. Finally, cold rolling was performed, reducing the strip to 0.08” (2mm) in 3 passes.

The three materials have small alloy concentrations, with combined atomic percentages of germanium and silicon less than one percent. Because the alloy concentrations and production quantities were small, precise alloy content could not be obtained. The compositions of the three materials were measured at Alcoa® [23], Table 1. Al-1%Ge-Si has the highest Ge and Si concentrations, with a Ge/Si atomic ratio near to 1:1. Table 2 summarizes the germanium and silicon concentrations for the three alloys in atomic, weight and volume percentages. [How is the volume obtained? From pure Ge and Si crystals? What about Ge-Si? Can we say that Ge+Si volume percentages in Table 2 is the same as the volume fraction of precipitates at peak aging and beyond, when I suppose virtually all of these elements is out of solution? Does that agree with the TEM work?]

Table 1 Atomic compositions of Al-Ge-Si alloys

Table 2 Atomic, weight and volume percentages of the Ge, Si elements

Atomic Percent Weight Percent Volume PercentGe Si Ge+Si Ge Si Ge+Si Ge Si Ge+Si

Al-1%Ge-Si 0.49% 0.50% 0.99% 1.30% 0.51% 1.81% 0.66% 0.59% 1.25%Al-0.4%Ge-Si 0.19% 0.16% 0.36% 0.51% 0.17% 0.68% 0.26% 0.20% 0.46%Al-0.2%Ge-Si 0.07% 0.16% 0.24% 0.19% 0.17% 0.36% 0.10% 0.20% 0.29%

2.2.Aging study

Test coupons (30mm x 30mm) were sheared from the rolled sheets, solutionized in air at 500 0C for one hour, quenched in water, and blow-dried. These coupons were then aged using a Scientific, Isotemp® Model 725F furnace. A redundant metal sheet was preheated in the oven and the samples were placed on top of it in order increase the temperature rise rate in test coupons for more precise determination of aging times.

Al Ge Si Fe Cu Zn TiAl-1%Ge-Si Balanced 0.49% 0.50% 0.03% 0.01% 0.03% 0.02%Al-0.4%Ge-Si Balanced 0.19% 0.16% 0.03% 0.00% 0.01% 0.01%Al-0.2%Ge-Si Balanced 0.07% 0.16% 0.02% 0.00% 0.01% 0.01%

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The microstructures of the as-received and heat-treated samples were examined using a Philips CM200 transmission electron microscope (TEM) at 200KV. To obtain TEM samples, small material coupons were first mechanically thinned to a thickness of about 120um, then electro-polished in 70% methanol and 30% Nitric acid to a final thickness of 150nm at the center of the sample.

Aging was conducted at 1200C, 1600C, 2000C and 2400C. The Vicker’s hardness profile versus aging time curves are plotted in Figure 1, along with Vicker’s hardness of 47 for the solution treated material. [Where are the results for the other alloys? You should show as much of that as you can – there may be interest in this. Don’t disregard you data, show it but explain why you continue in more detail for the richest alloy. For example, the aging curves for each alloy at one temperature could be compared. Also, as I recall, we did get some small ability to separate ppt spacing vs size effects on the B effect, which should be very interesting, even if very limited in extent.] When aged at 1200C and 1600C, none of the material achieve an over aged (OA) condition after weeks in the oven. At 2000C the material hardness dropped after one day of aging. Higher aging temperature (2400C) producted faster aging, but the precipitates were unevenly distributed, as will be shown later in this section.

[Will stop playing with the actual words here. You can get the idea from the foregoing paragraphs, that I modified. For the remainder the content will probably change some, so it won’t help to work on the words right now.]

There was no detectable hardness change for solution heat treated samples measured after several months at room temperature, suggesting that natural aging process is not significant. Pure aluminum has a Vicker’s hardness number of 15, one-third of the solution heat treated material. [Find a table relating Hv to UTS. Probably 1/3 doesn’t mean such a large difference in stress. Best to cite these estimated UTS’s, also.] The difference is caused by the solution hardening effect of the solutes inside of the matrix. [Can you check whether this makes sense with simple solute models? Also, what is the softest Hv you ever saw for long aging at the highest temperature? How close is it to the pure Al value?]

TEM tests were performed to examine the microstructure of the as-received Al-1%Ge-Si material, Figure 2. Coarse, evenly distributed precipitates are apparent. [What is the YS, UTS, Hv for this material? Oh, I see below. What if this is aged at high temp for a long time to really coarsen the precipitates, remove dislocations and keep all solutes out of solution? Also, what is the solubility of Ge and Si in Al at Room T? I have been assuming almost zero. Is it true?] The average size of those particles is 0.5~1.0 um. [Where is the procedure for quantifying the precipitates presented? We need to have average size, average spacing, etc., as shown much later, in Figure 8. I would suggest introducing a table soon after Figure 2b to contain all this data for the various conditions where it is available. Or maybe the plots like Fig 8 are sufficient, but I think it should come very soon, right with the TEM info.] Figure 2b reveals the dense dislocation networks inside of the material. They are the result of the cold rolling operation during the production of the flat sheet. Those dislocation networks give very high hardness of

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the as-received material (HV=72). However, when solution heat treated (one hour at 500 0C), the dislocation networks disappeared. Most of the area inside of the grain becomes clear (free of precipitates), although few big inclusions can be observed near the grain boundary.

When the solution heat treated material was aged at 1200C, precipitation occurred. Figure 3a is a TEM micrograph at the junction of three grains. Some large particles along grain boundaries can be easily identified. A more detailed image (Figure 3b) shows the newly formed precipitates inside of the grain, along with a big particle on the grain boundary. The big particle is an order of magnitude larger than the ones inside which are only about 10 nm in size. There is a precipitate free zone (PFZ) near the grain boundary, because grain boundaries provide an excellent channel for pipe diffusion [20]. The solutes near boundaries will be attracted into and transported along the channel. Once a particle forms on the boundary it can grow rapidly. This is the reason that much bigger precipitates were observed on the grain boundary than the grain interior. Inside of grain, there is a fine distribution of precipitates, although some area may have few slightly bigger precipitates and form PFZ as shown at the center of Figure 3c. Most of the precipitates are equiaxed in shape and evenly distributed, Figure 3d, and they are the focus of the quantitative TEM measurements.

The precipitate size (d), spacing ( ) and volume fraction (f) for the aged material are reported in Figure 3d. The average precipitate size, d, for the aging condition is obtained by taking the arithmetic mean of all the measured individual particle sizes, which is defined as the square root of the product of the maximum and minimum diameters of the particle ( ). The total volume fraction of the precipitates can be calculated by [24]:

(Equation 1)

where A is the area of micrograph and N is the total number of particles in that area. The foil thickness, t, can be measured using the CBED method [25, 26]. Once the particle size and volume fraction are known, the inter particle spacing, , can be calculated through Equation 2 [27]:

(Equation 2)

It can be seen from the 1200C and 1600C aging curve (Figure 1) that the material has not arrived at its peak aged condition. An over aged condition is desired to compare the Bauschinger response under different precipitate structure. Therefore, higher temperature aging was conducted to expedite the aging process.

Figure 4a to c show the precipitate structures of the material after aging times of 0.5 hour, 12 hours and one week under 2000C. According to the aging curve in Figure 1 these conditions represent the under aged, peak aged and over aged conditions respectively. Almost all the precipitates at the over aged condition grow into equiaxed shape. No laths or plates were observed. As expected, the over aged sample contains bigger precipitates than then peak aged one. However, while some grow bigger others shrink or dissapear.

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As a result there is a wider range of precipitate size, as shown in Figure 5.

Aging at 2400C was also attempted to accelerate the aging process. The sample microstructures are provided in Figure 6. There are two limitations with this aging temperature. The first one is that the aging process happens so fast that it takes only 5 minutes to for the material to arrive at the under aged condition. This would make the aging process harder to control and more difficult to achieve the exact aging condition. The other disadvantage is that the over aged sample displays predominantly lath shaped precipitates as shown in Figure 6. Those laths make the quantitative measurement uncertain. For the above considerations 2400C aging is not suitable for current research. Instead, 2000C is selected as the aging temperature for a complete precipitate structure and mechanical behavior correlation study.

All the quantitative precipitate measurement results for Al-1%Ge-Si are summarized in Figure 7a. Each label contains three numbers, d, , f, respectively. It is interesting to note that the peak aged materials at different temperatures have similar average precipitate size of about 16 nm. Also, the precipitate volume fractions approach the equilibrium value of 1.25%. That means nearly all the solutes have come out of the matrix at the peak aged condition.

The precipitate structure parameters are plotted in Figure 8a to c with respect to , a time quantity corrected for aging temperature, defined as

(Equation 3)

where t is the aging time, T is the aging temperature and refers to the activation energy which equals to 117 kJ/mol [28]. The four hardening curves in Figure 7a would reduce to one master curve when they are plotted against Figure7b. Figure 8a shows that precipitate size always increases with aging. The precipitate size for the SHT condition is equal to zero since there is no precipitate present at that condition. For the same reason, the particle spacing for SHT conditions is equal to infinity. This data point cannot be plotted in Figure 8b, but the trend for particle spacing evolution is apparent: it decreases first, arrives at a minimum near peak aging and then goes up again upon over aging. The development of precipitate volume fraction follows a similar trend as precipitate size initially. However, it does not change further after peak aging.

The precipitate structures of the aged Al-0.2%Ge-Si alloy are provided in Figure 9. The precipitate distribution is not uniform for this material. It makes the quantitative precipitate size and volume fraction measurement difficult and unreliable. Similar uneven precipitate distribution was observed for the aged Al-0.4%Ge-Si alloy. Both alloys have low alloy content and therefore have small precipitate concentration when aged, which gives a marginal contribution to the total strength. Because there is little strength increase from the solution heat treated condition to the peak aged condition, the study of precipitate strengthening mechanisms become difficult to carry out. Therefore mechanical strengthening studies will concentrate on the Al-1%Ge-Si material which has

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larger precipitate hardening effect and more uniform precipitate distribution.

2.3.Tensile results

Tensile tests were performed to get the yield stress and hardening rate of aged materials. They were conducted at a nominal initial strain rate of 1.7×10-3/sec at a constant crosshead speed. Each condition contains three repeated tests and the average stress strain response is reported here, with a standard deviation of about 5 MPa.

The engineering stress strain curves for the under aged, peak aged and over aged conditions are shown in Figure 10. Both the yield stress and tensile stress of the over aged sample are smaller than the peak aged one. The under aged material has higher tensile stress than the other two conditions although its yield stress is low. Because of less precipitates, the underaged material has lower initial hardening rate and less dislocation generation. At the same time, it has more solute content remaining in the matrix. Those solutes can store higher density of dislocations and thus contribute to the strain hardening. Therefore the balance of dislocation generation and annihilation is delayed, causing the increased ductility in higher tensile strength in the under-aged material.

The work hardening rates of the aged materials are plotted against strain and in Figure 11a and b. The solution heat treated Al-1%Ge-Si material always have a higher hardening rate than pure aluminum at the same strain (Figure 11a), because the solid solutes in the matrix increases the ability of the material to store higher density of dislocations [29, 30]. When under aged, the material displays higher initially hardening rate. However the rate decreases fast, and only after 2.5% strain it is already lower than the solution heat treated case. Upon further aging, the work hardening rate continues to decrease, but still higher than the pure aluminum. The results show that: 1) the presence of Ge and Si elements in the solution increase the material’s ability to store dislocation. 2) precipitation process suppresses strain hardening by taking solutes out of the matrix.

It is apparent from Figure 11b that all the aged Al-1%Ge-Si materials have higher initial work hardening rate than the solution heat treated material. This confirms that the precipitates in the aged materials are non-shearable. Dislocation by-passing leaves dislocation loops around the non-shearable particles and thus increase the initial hardening rate [29]. The hardening rate of the peak aged and overaged materials decrease 6 times faster than the solution heat treated material, because of the lack of solutes and the quick saturation of dislocation densities. The fast initial dislocation generation by non-shearable precipitates coupled with the reduced ability of dislocation storage are the reasons for the dramatic decrease in ductility in the aged Al-1%Ge-Si materials.

The monotonic loading results show that the hardening contribution from precipitates increase fast initially, but saturates rapidly after 3~5% strain. Because of the presence of precipitate, the strain hardening rate is suppressed by taking solutes out of the matrix.

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2.4. Tension compression testing

The study on the Bauschinger effect was performed through the tension/compression testing of the sheet materials [31, 32]. Because of buckling, sheet samples are often unstable during compression. The in plane tension/compression method developed at the Ohio State University successfully overcame the buckling problem by using side constraints. Following the optimized testing guidelines the achievable compression strain could be as large as -0.20 [32].

A schematic of the sample dimensions are shown in Figure 12a. This dog-bone shape of the sample has been optimized for minimum buckling and bigger attainable compressive strain. The two side plates are used to clamp the sample and the friction is minimized by sandwiching a Teflon® sheet between the specimen and side plates. The side restraining forces of 4 KN are applied by a hydraulic pump through four sets of steel rollers, Figure12b. Because the sample is sandwiched by two side plates there left little room to mount a mechanical extensometer for strain measurement. Therefore a non-contact EIRTM laser extensometer [33] is used to measure the strain during deformation. Prior loading, two small pieces (2 mm x 2 mm) of reflecting tape are attached to the same side of the sample and a laser light is projected onto it to measure their separation distance. This distance is recorded all the time during loading and this information is used to calculate the strain [32]. The recorded stress needs to be corrected for biaxial effects and friction because of the side constraints to avoid buckling [31, 32].

This new tension/compression test has the advantages of simple tooling, easy alignment, and smoother compressive flow. Although special specimen design is used and some data corrections are necessary this test is still a very powerful tool to study the material response on reverse loading.

The tension/compression tests were conducted for Al-1%Ge-Si materials aged at 2000C to UA, PA, OA conditions. These conditions were selected because TEM examinations show uniform precipitate distribution and more accurate precipitate size, spacing, volume fraction information is available for them. Therefore, better correlation of precipitate structure and the Bauschinger effect is attainable for those materials.

The magnitude of the Bauschinger effect can be evaluated using the Bauschinger factor, defined as [34, 35]:

(Equation 4)

where is the forward stress before strain path change and is the signed yield stress after the path change. If there is no Bauschinger effect, =- and . When the Bauschinger transition is so significant that the material yields at zero stress upon the path change, . The 0.2% offset yield stress is widely used for determining . However, analysis has shown that the elastic effect from particles happens within 0.4%

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reverse strain [Refer to Wei’s thesis]. Using 0.4% offset yield stress the short term effect of the elastic interaction of a particle and the matrix can be avoided. The 0.4% offset stress is also proven effective in the study of the Bauschinger behavior of Mg alloys [36]. It is thus used in this work to evaluate and .

The Bauschinger factors of the Al-1%Ge-Si alloy are shown in Figure 13 in three aging conditions. Because of precipitates their Bauschinger factors are all above the value of solution heat treated material which is indicated in the figure as the dashed horizontal line. The peak aged and over aged conditions give larger Bauschinger factor because they have larger volume percentage of precipitates than the under aged condition. The present results show that there is little difference in the Bauschinger transition between peak aged and over aged conditions, consistent with results reported for Al 2524 and Al 6013 alloys [37].

3. ANALYSIS OF THE BAUSCHINGER EFFECT

Studies have shown that any factor that causes heterogeneous deformation inside of the sample will contribute to the Bauschinger effect [38, 39]. For the aged Al-1%Ge-Si materials, the Bauschinger effect is determined by grain boundary hardening, grain texture and precipitates. The total contribution to the Bauschinger factor from the first two sources together can be obtained through the tension/compression testing of solution heat treated samples. They produce a Bauschinger factor of 0.06 after a pre-strain of 3.5%. However the grain boundary and orientation effects are dependent on each other and their contributions to the Bauschinger factor cannot be separated. The precipitates inside of the grains are the third source for the Bauschinger effect. They cause the additional 0.15 increase of the Bauschinger factor in the peak and over aged materials, i.e. approximately 2/3 of the total effect.

To help understand the precipitate effect on monotonic hardening and the Bauschinger effect, a 3D elastic inclusion model was constructed as shown in Figure 14. This “continuum composite” model consists of an elastic particle sitting at the center of an elastic-plastic matrix. It is a more general and realistic form of Eshelby theory [40-44]. Because of symmetry considerations only a quarter of the full model is simulated.

The simulated loading and reverse loading behavior from the elastic inclusion FEA model is shown in Figure 15. The result shows that the predicted monotonic hardening curve has a much lower yield stress than the measurement. This indicates the FEA model is not capable of capturing the precipitate effect on initial yield stress increase as is well known (Orowan effects [45, 46]). Meanwhile, the reverse loading curve from FEA simulation reaches the monotonic curve almost immediately after reverse loading. The Bauschinger factor, , is equal to 0.004 for this case, two orders of magnitude smaller than

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experiment. The predicted response is in contrast to the measured Bauschinger effect which displays substantial backstress evolution upon the loading direction change. These results demonstrate that the origin of the Bauschinger effect is clearly not a continuum effect.

Table 3 summarizes the measured backstress ( ) and Bauschinger factor for the Al-

1%Ge-Si materials. The backstress for the solution heat treated materials is only 2.5 MPa. It comes from grain boundaries and textures. The under aged material has a similar particle spacing as the over aged case. However its backstress and Bauschinger factor are both smaller. This suggests that Bauschinger process is not controlled by the precipitate spacing. The peak aged and over aged materials have similar Bauschinger factors, even though the precipitate spacings are 60% different. These results suggest that particle spacing does not have significant impact on the Bauschinger effect. The total volume fraction of precipitates appears to have more profound effect on the materials response upon reverse loading. With the same precipitate volume fraction, the over aged and peak aged material displays similar backstress and Bauschinger factors.

Table 3 Bauschinger effect of the aged Al-1%Ge-Si materials

d (nm) λ (nm) f (%) (MPa) (MPa)SHT - - - 86 2.5 0.06UA 9.4 390.5 0.2 139 10.6 0.15PA 15.7 227.4 1.2 154 16.4 0.21OA 25.9 371.7 1.2 146 15.6 0.21

Besides Bauschinger factor, a strain based parameter, , was also used to quantify the magnitude of the Bauschinger effect. It measures the amount of reverse loading strain when the slope of the stress strain curve reaches two times of the monotonic slope. This quantity describes how long the Bauschinger transition lasts and it is called here the “Bauschinger strain”. The Bauschinger strains for the SHT, UA, PA and OA Al-1%Ge-Si materials are equal to 0.8%, 1.7%, 2.6% and 2.3% respectively. These values are consistent with the Bauschinger factors reported in Table 3 where the UA sample has less Bauschinger effect among the three aged conditions and all the aged samples have larger Bauschinger effect than the solutionized material. The predicted Bauschinger strains from the elastic inclusion FEA model are all below 0.1% for the aged materials. It shows again that the continuum model is inadequate to reproduce the profound Bauschinger transition seen in experiments.

The reverse hardening curves for the aged AG-1%Ge-Si materials are plotted in Figure16a. The y axis represents the ratio of the reverse stress over the forward stress. It describes how fast a material approaches its monotonic strength upon reverse loading. The figure shows that the OA sample experienced nearly the same Bauschinger transition as the PA sample, although its precipitate size is 60% larger. Measured Bauschinger transitions have been reported for commercial Al 2524 alloy, Figure 16b [37]. The over

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aged condition for the commercial material actually has more Bauschinger effect than the PA condition. The Bauschinger response of the OA sample is contrary to the Orowan theory, which says that with larger precipitate spacing in the over aged condition; the dislocation should bypass the precipitates more easily. As a result less dislocation accumulation and smaller Bauschinger effect should be present. However, current experimental results on Al-1%Ge-Si and commercial Al alloys do not support the theory. Therefore, precipitate spacing does not appear to be the dominant factor for the Bauschinger effect in the studied alloys.

The Bauschinger factors and strains for the SHT and aged materials in Table 3 are plotted in Figure 17 a and b. The OOA condition in those figures refers to the aging condition of two weeks at 1600C plus one week at 2400C. The results show that the value using 0.4% offset strain becomes larger with aging, and then saturates after peak aging. Its evolution seems to relate with that of precipitate volume fraction, Figure 8c. However, if using 0.2% offset strain to measure , the Bauschinger factor drops at the OOA condition. These results suggest that the maximum Bauschinger effect occurs after peak aging, at a condition between PA and OOA. The evolution of the Bauschinger strains with aging is presented in Figure 17b. Three types of Bauschinger strain values are measured. is the amount of reverse strain when the hardening rate during reverse loading reaches two times of the monotonic rate, k. is a similar variable except that it uses 4k to determine the Bauschinger strain. measures the amount of reverse strain when the reverse stress reach the same magnitude as . It was found that all three parameters increase initially from SHT to UA and PA, but drops after peak aging. The development of the Bauschinger strain appears to inversely correlate to precipitate spacing, Figure 8b.

From the experimental data and simulation results, it is concluded that precipitate is the major source for the Bauschinger effect in these aged alloys, although grain boundary hardening and orientation effect also have contributions. The Bauschinger effect cannot be explained through the Eshelby nor the Orowan theories. It is related to the plastic interactions between dislocations and obstacles. Particle size, spacing and volume fraction all have impact on the Bauschinger effect. For the studied alloys, the Bauschinger strain is closely correlated to the Bauschinger factor.

4. CONCLUSIONS

Two kinds of conclusions were reached, the first with respect to purely microstructural features associated with aging of Al-Ge-Si alloys, and the second with respect to microstructural sources of the reverse yield and hardening (generalized Bauschinger effect).

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Microstructural Features Associated with Aging of Al-1at%Ge-Si

1. Under most aging conditions tested, the morphology of the Ge-Si precipitates remains nearly equiaxed. The precipitate size increases monotonically with again, while the size distribution widens.

2. Some large particles (up to 10 times larger than intra-grain particles) form at grain boundaries, accompanied by adjacent precipitate-free regions.

3. Al-0.2at%Ge-Si and Al-0.4at%Ge-Si have inhomogenously distributed precipitates and more irregularly-shaped laths and plates. For this reason, these alloys were not tested extensively.

4. The aging characteristics at three temperatures may be plotted on a single master curve using a reduced temperature-time variable based on published values of the activation energy of diffusion of germanium in aluminum. This verifies the assumption that a single mechanical mechanism for dislocation bypass occurs over a wide range of precipitate sizes.

5. Consistent with the Orowan equation, the precipitate spacing passes through a minimum at the peak aging condition. Concurrently, the volume fraction of precipitates increases dramatically to its full value, and it maintains a plateau thereafter.

Microstructural Contributions to Reverse Strength and Hardening of Al-1at%Ge-Si

6. Based on measurements and the literature, the reverse yielding at PA and OA conditions is attributable to precipitates (β=0.15, ~70% of the total) and grain effects (β=0.06, ~30% of the total).

7. Reverse yielding and flow cannot be predicted by continuum composite models (Eshelby theory), which under-predict the effect by two orders of magnitude. The continuum composite contributions to changes in reverse yield stress can be neglected by choosing a slightly larger strain offset, 0.4%, to define yield.

8. The Bauschinger factor (β) increases with aging up to the PA condition, but does not decrease significantly with over-aging, even though the particle spacing increases by 60%. Therefore, the Bauschinger effect cannot be directly correlated with monotonic strength or simple Orowan effects. The Bauschinger factor is more closely related to the precipitate volume fraction, rather than size or spacing.

9. The strain range of the altered reverse hardening curve (as defined by hardening slope) is closely correlated with the Bauschinger factor for this alloy. This result does not appear to extend to other aluminum aging systems nor to other measures of Bauschinger strain range [37].

13

ACKNLOWLEDGEMENTS

NSF (two projects should be cited here)OSCRobert HylandAlcoaRichard Boger [If not a co-author. You two should decide if you want to be co-authors on the two papers or not. It is up to you. Which way you go will change the way the introductions read. Also, if we submit the two papers together, that should be considered. It looks like they might be ready around the same time.]

14

REFERENCES

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2. Edwards E.H. and Washburn J., Strain hardening of latent slip systems in zinc crystals, Journal of Metals, 6 (11), p.1239-1242, 1955

3. Wang M.Z., Lin S., Li C.H., and al. et, A study of latent hardening behavior in aluminum single crystals, Scripta Materialia, 35 (10), p.1183-1188, 1996

4. Rauch E.F. and Schmitt J.H., Dislocation substructures in mild steel deformed in simple shear, Materials Science and Engineering. A, Structural Materials : Properties, Microstructure and Processing, 113, p.441-448, 1989

5. Hasegawa T., Yako T., and Kocks U. F., Forward and reverse rearrangements of dislocations in tangled walls, Materials Science and Engineering, 81, p.189-99, 1986

6. Hu Z., Rauch E. F., and Teodosiu C., Work-hardening behavior of mild steel under stress reversal at large strains, International Journal of Plasticity, 8 (7), p.839-56, 1992

7. Nesterova E. V., Bacroix B., and Teodosiu C., Experimental observation of microstructure evolution under strain-path changes in low-carbon IF steel, Materials Science & Engineering A: Structural Materials, 309-310, p.495-9, 2001

8. Schmitt J.H., Aernoudt E., and Baudelet B., Yield loci for polycrystalline metals without texture, Mater Sci Eng, 75 (1-2), p.13-20, 1985

9. Rauch E. F., The flow law of mild steel under montonic or complex strain path, Solid State Phenomena, 23-24, p.317-448, 1992

10. Kocks U.F., Hasegawa T., and Scattergood R. O., On the origin of cell walls of lattice misorientations during deformation, Scripta metall., 14, p.449-454, 1980

11. Mughrabi H., Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals, Acta Metall, 31 (9), p.1367-1379, 1983

12. Wilson D. V. and Bate P.S., Influences of cell walls and grain boundaries on transient responses of an IF steel to changes in strain path, Acta Metall. Mater., 42 (1099-1111), 1994

13. Strauven Y. and Aernoudt E., Directional strain softening in ferritic steel, Acta Metall, 35, p.1029-1036, 1987

14. Peeters B., Seefeldt M., Teodosiu C., and others and, Work hardening/softening behaviour of b.c.c. polycrystals during changing strain path: I. An integrated model based on substructure and texture evolution, and its predictions of the stress-strain behaviour of an IF steel during two-stage strain paths, Acta Materialia, 49, p.1607-1619, 2001

15. Peeters B., et al., Work hardening/softening behaviour of b.c.c. polycrystals during changing strain path: II. TEM observations of dislocations sheets in an IF steel during two-stage strain paths and their representations in terms of dislocation densities, Acta Materialia, 49, p.1621-1632, 2001

16. Bouvier S., Alves J.L., Oliveira M.C., and Menezes L.F., Modelling of anisotropic work-hardening behavior of metallic materials subjected to strain-path changes, Computational Materials Science, 32, p.301-315, 2005

17. Vincze G., Rauch E.F., Gracio J.J., and al. et, A comparison of the mechanical behaviour of an AA1050 and a low carbon steel deformed upon strain reversal, Acta Materialia, 53 (4), p.1005-1013, 2005

18. Hornbogen E., Mukhopadhyay A.K., and Starke E.A., An exploratory-study of hardening in AL-(SI,GE) alloys, Z METALLKD, 83 (8), p.577-584, 1992

19. Hornbogen E., Mukhopadhyay A.K., and Starke E.A., Precipitation hardening of AL-(SI,GE) alloys, Scripta Metall Mater, 27 (6), p.733-738, 1992

20. Martin J.W., Precipitation Hardening. 2nd ed. 1998: Butterworth-Heinemann.21. Radmilovic V., Mitlin D., Tolley A.J., and al. et, Resistance to shape refinement of precipitates in

Al-(Si,Ge) alloys during thermal cycling, Metall Mater Trans A, 34 (3), p.543-551, 200322. Barlat F., Materials Science Division, Alcoa Technical Center, 100 Technical Drive, Alcoa Center,

PA 15069, USA, 2005

15

23. Contino J.M. and DeCapite D., Alcoa Inc, Alcoa Technical Center, 100 Technical Drive, Alcoa Center, PA 15069, USA, 2005

24. Underwood E.E. and Starke E.A., Quantitative stereological methods for analyzing important microstructural features in fatigue of metals and alloys, in Fatigue Mechanisms, Proceedings of an ASTM-NBS-NSF symposium, A.S. 675, Editor. 1978: Kansas city, Mo. p. 633-682.

25. Allen S.M., Foil Thickness measurements from convergent-beam diffraction patterns, Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties, 43 (2), p.325-335, 1981

26. Kelly P.M., Jostsons A., Blake R.G., and Napier J.G., Determination of foil thickness by scanning transmission electron microscopy, Phys Status Solidi (A) Appl Res., 31 (2), p.771-780, 1975

27. Guo Z.L. and Sha W., Quantification of precipitation hardening and evolution of precipitates, Mater. Trans., 43 (6), p.1273-1282, 2002

28. Zumkley T. and Mehrer H., Diffusion of Ge in binary and ternary Al-(Si, Ge) solid-solution alloys, Z. Metallkd., 89 (7), p.454-463, 1998

29. Deschamps A., Dumont D., Brechet Y., and al. et, Process modeling of age-hardening aluminum alloys: from microstructure evolution to mechanical and fracture properties, in Proceeding of the James T. Stanley honorary symposium on aluminum alloys, Indianapolis, USA,

30. Cheng L. M., Poole W. J., Embury J. D., and Lloyd D. J., The influence of precipitation on the work-hardening behavior of the aluminum alloys AA6111 and AA730, Metallurgical and Materials Transactions A, 34, p.2473-2481, 2003

31. Balakrishnan V., Measurement of in-plane Bauschinger effect in metal sheet, Department of Materials Science and Engineering, The Ohio State University, 1999

32. Boger R.K., Wagoner R.H., and al. et, Continuous, large strain, tension/compression testing of sheet material, International Journal of Plasticity, 21 (12), p.2319-2343, 2005

33. Laser extensometer model LE-01, Electronic Instrument Research, PO Box 678 o Irwin, PA 15642, 2005

34. Abel A., Historical perspectives and some of the main features of the Bauschinger effect, Materials Forum, 10 (1), p.11-26, 1987

35. Abel A. and Muir H., The Bauschinger effect and discontinuous yielding, Philosophical Magazine, 26 (2), p.489-504, 1972

36. Lou X.Y., Evolution of Hardening in AZ31B Mg Sheet, The Materials Science and Engineering, The Ohio State University, 2005

37. Boger R.K., Influence of hardening precipitates on the deformation of aluminum alloys, Materials science and engineering, The Ohio State University, 2005

38. Gan W., Zhang P., Wagoner R.H., and Daehn G.S., The Effect of Load Redistribution in Transient Plastic Flow, submitted to The Metallurgical & Materials Transactions A, 8/27/05, 2005

39. Hu X.Y., Chao W., Margolin H., and al. et, The bauschinger effect and the stresses in a strained single-crystal, Scripta Metallurgica et Materialia, 27 (7), p.865-870, 1992

40. Barlat F. and Liu J., Precipitate-induced anisotropy in binary Al-Cu alloys, Materials Science & Engineering A: Structural Materials, (A1), p.47-61, 1998

41. Bate P.S., Roberts W.T., and Wilson D.V., The plastic anisotropy of two-phase aluminum alloys-I. Anisotropy in unidirectional deformation, Acta Metallurgica, 29, p.1797-1814, 1981

42. Brown L. M. and Stobbs W. M., The work-hardening of copper-silica. I. A model based on internal stresses, with no plastic relaxation, Philosophical Magazine, 23 (185), p.1185-99, 1971

43. Embury J. D., Plastic flow in dispersion hardened materials, Metallurgical Transactions A, 16, p.2191-200, 1985

44. Eshelby J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London A, 241, p.376-96, 1957

45. Orowan E., Discussion on Internal Stresses. In Symp. Internal Stresses in Metals and Alloys. 1948, London: The Institute of Metals. 451-453.

46. Orowan E., Causes and effects of internal stresses, in Symposium on Internal Stresses and Fatigue in Metals, Detroit, Elsevier, 1959

16

FIGURE CAPTIONS

Figure 1. Aging curves of Al-1%Ge-Si alloyFigure 2. Microstructure of Al-1%Ge-Si, as-received: a) overview, b)

dislocation networksFigure 3. TEM micrographs of Al-1%Ge-Si, aged for one week at 1200C: a)

grain junction, b) grain boundary area, c) grain interior, d) fine precipitates inside of grain

Figure 4. TEM micrographs of Al-1%Ge-Si, aged at 2000C for: a) 0.5 hours (UA), b) 12 hours (PA), c) one week

Figure 5. Precipitate size distribution of Al-1%Ge-Si aged at 2000CFigure 6. TEM micrographs of Al-1%Ge-Si, aged at 2400C for 2 hoursFigure 7. Aging curves for Al-1%Ge-Si: a) with quantitative precipitate

measurement results, b) master hardening curveFigure 8. Evolution of precipitate characteristics: a) size, b) spacing, and c)

volume fractionFigure 9. TEM micrographs of Al-0.2%Ge-Si, aged at 2000C for: a) 8 hours,

b) 8 hours (higher magnification.)Figure 10. Tensile curves of Al-1%Ge-Si aged at 2000CFigure 11. The evolution of work hardening rate: a) vs. , b) vs.

.Figure 12. Setup of the Tension/compression test [33]: a) Sample dimensions,

b) overview of the setupFigure 13. Bauschinger factors of the aged Al-1%Ge-Si materialsFigure 14. Continuum finite element model for precipitate hardening.Figure 15. Comparison of the measured and simulated Bauschinger effect.Figure 16. Reverse hardening curves for various aging conditions: a) Al-1%Ge-

Si,Figure 17. Measured Bauschinger parameters with aging: a) Bauschinger factor,

b) Bauschinger strain

17

40

45

50

55

60

65

70

10-2 10-1 100 101 102 103

Vic

ker's

Har

dnes

s (H

V)

Time (hour)

Al-1%Ge-Si

2400C

2000C1600C

1200CSHT

Figure 1. Aging curves of Al-1%Ge-Si alloy

18

10 um 100 nm(a) (b)

Figure 2. Microstructure of Al-1%Ge-Si, as-received: a) overview, b) dislocation networks

19

2 um 200 nm(a) (b)

200 nm 50 nm

(c) (d)

Figure 3. TEM micrographs of Al-1%Ge-Si, aged for one week at 1200C: a) grain junction, b) grain boundary area, c) grain interior, d) fine precipitates inside of grain

20

d=7.1 nmλ=236 nmf=0.26%

100 nm 100 nm (a) (b)

100 nm (c)

Figure 4. TEM micrographs of Al-1%Ge-Si, aged at 2000C for: a) 0.5 hours (UA), b) 12 hours (PA), c) one week

21

d=9.4 nmλ=390 nmf=0.17%

d=15.7 nmλ=227 nmf=1.22%

d=25.9 nmλ=372 nmf=1.24%

0%

10%

20%

30%

40%

50%

60%

70%

80%

5 10 15 20 25 30 35 40 45 50

UAPAOA

Per

cent

age

Diameter (nm)

Figure 5. Precipitate size distribution of Al-1%Ge-Si aged at 2000C

22

1 um

Figure 6. TEM micrographs of Al-1%Ge-Si, aged at 2400C for 2 hours

23

40

45

50

55

60

65

70

10-2 10-1 100 101 102 103

Vic

ker's

Har

dnes

s (H

V)

Time (hour)

Al-1%Ge-Si

2400C

2000C1600C

1200C

SHT

10, 262, 0.41%

9.4, 390, 0.17%

18.4, 264, 1.24%

26.1, 373, 1.25%

15.7, 227, 1.22%

15.2, 229, 1.14%

7.1, 236, 0.26%

25.9, 372, 1.24%

7.9, 268, 0.25%

d, , f =

(a)

40

45

50

55

60

65

70

10-16 10-15 10-14 10-13 10-12 10-11 10-10

Vic

ker's

Har

dnes

s (H

V)

Al-1%GeSi

2400C

2000C1600C

1200C

SHT

(b)

Figure 7. Aging curves for Al-1%Ge-Si: a) with quantitative precipitate measurement results, b) master hardening curve

24

0

5

10

15

20

25

30

10-19 10-17 10-15 10-13 10-11

d (n

m)

Al-1%Ge-Si

2400C2000C1600C1200CSHT

200

250

300

350

400

450

500

10-15 10-14 10-13 10-12 10-11

(n

m)

Al-1%Ge-Si

2400C2000C1600C1200C

(a) (b)

0

0.5

1

1.5

10-19 10-17 10-15 10-13 10-11

f (%

)

Al-1%Ge-Si

2400C2000C1600C1200CSHT

(c)

Figure 8. Evolution of precipitate characteristics: a) size, b) spacing, and c) volume fraction

25

2 um 200 nm(a) (b)

Figure 9. TEM micrographs of Al-0.2%Ge-Si, aged at 2000C for: a) 8 hours, b) 8 hours (higher magnification.)

26

0

40

80

120

160

0 0.05 0.1 0.15 0.2 0.25 0.3

Eng

inee

ring

Stre

ss (M

Pa)

Engineering Strain

Al-1%Ge-Si

2000C aging

OA

PAUA

SHT

Figure 10. Tensile curves of Al-1%Ge-Si aged at 2000C

27

0

500

1000

1500

2000

2500

3000

0 0.05 0.1 0.15

dd

e(M

Pa)

True Strain

Al-1%Ge-Si

2000C aging

OA

PAUA SHT

Al

(a)

0

500

1000

1500

2000

2500

3000

0 50 100 150 200

dd

e(M

Pa)

(MPa)

Al-1%Ge-Si

2000C aging

OAPA

UA

SHTAl

(b)

Figure 11. The evolution of work hardening rate: a) vs. , b) vs. .

28

G

B

W L

G = 36.8 mm, W = 15.2 mmB = 50.8 mm, L > 3 mm

Figure 12. Setup of the Tension/compression test [32]: a) Sample dimensions, b) overview of the setup

29

b)

a)

Hydraulic pump

Laser extensometer

0

0.06

0.12

0.18

0.24

0.3

UA PA OA

Bau

schi

nger

Fac

tor,

Bet

a

Al-1%Ge-Si

2000C aging

Figure 13. Bauschinger factors of the aged Al-1%Ge-Si materials

30

Figure 14. Continuum finite element model for precipitate hardening.

31

0

20

40

60

80

100

120

140

160

180

200

0 0.05 0.1 0.15 0.2

True

Stre

ss(M

Pa)

True Strain

Measured, monotonic

Al-1%Ge-Si, 2000C, PA

Measured, Reverse

FEA Reverse

FEA, monotonic

d, , f =15.7, 227, 1.22%

Figure 15. Comparison of the measured and simulated Bauschinger effect.

32

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1

r/

f

Reverse Plastic Strain

UA

PAOA

Al-1%Ge-Si

2000C Aging

(a)

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1

r/

f

Reverse Plastic Strain

UA

PA

OA

Al 2524

(b)

Figure 16. Reverse hardening curves for various aging conditions: a) Al-1%Ge-Si, b)Al 2524 [37]

33

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

10-19 10-17 10-15 10-13 10-11 10-9

Al-1%Ge-Si

UA PA OAOOA

SHT

0.2%

0.4%

(a)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

10-19 10-17 10-15 10-13 10-11 10-9

Al-1%Ge-Si

UA PA OAOOA

SHT

2k

4k

s

(b)

Figure 17. Measured Bauschinger parameters with aging: a) Bauschinger factor, b) Bauschinger strain

34