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Effect of particles on the formation of deformation twins in a magnesium-based alloy
Materials Science and Engineering A 516 (2009) 226–234
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Effect of particles on the formation of deformation twins in a magnesium-based alloy N. Stanford ∗ , M.R. Barnett Centre for Material and Fibre Innovation, Deakin University, Pigdons Road, Geelong 3217, Australia
a r t i c l e
i n f o
Article history: Received 3 December 2008 Received in revised form 6 March 2009 Accepted 1 April 2009 Keywords: Magnesium alloys Precipitation Twinning Deformation
a b s t r a c t The deformation behaviour of the age hardenable alloy Mg–5%Zn after different precipitation treatments has been examined. It has been found that during compressive deformation, fine particles increase the number of twins that form, but reduce the size and total volume fraction of twins. Visco-plastic selfconsistent modelling has been used to show that the presence of precipitates hardens the twin and prismatic slip systems more than the basal slip system. It is proposed that because the {1 0 1¯ 2} twin requires basal slip to accommodate the twinning shear, this twin type will always be hardened equal to, or more than, the basal slip system in response to precipitation. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
1. Introduction Magnesium and its alloys can deform by both slip and twinning [1]. Of the twinning modes that are possible in hexagonal metals, {1 0 1¯ 2} and {1 0 1¯ 1} are commonly observed in Mg alloys, and {1 0 1¯ 3} can be observed in coarse grained materials [2] and single crystals of certain orientations [3]. Although the twinning behaviour of magnesium is well studied, the interaction of particles and twins is not so well characterised. There are really only three studies [4–6] that examine the twinning of magnesium in the presence of precipitates. Gharghouri et al. [6] studied a Mg–7.7 at.%Al binary and showed that after the matrix surrounding a precipitate underwent twinning, no rotation of the precipitates was observed. This is in direct disagreement with the observations by Clarke [4] who showed that a rigid body rotation of approximately 10◦ about 1 1 2¯ 0 occurred in precipitates after matrix twinning. Gharghouri et al. [6] have also shown that twins can change their apparent habit plane to avoid intersection with a particle. Clarke [4,5] studied two binary alloys, Mg–Zn and Mg–Al. These studies suggested that certain particles could be sheared by the twinning transformation, and also that {1 0 1¯ 2} twins could be suppressed by particles at high enough volume fractions. The latter observation is of interest because the relative contribution of slip and twinning to the deformation will determine not only the flow stress but may also impact on the ductility of the alloy. However, the observations about twin fractions made in that study were quali-
∗ Corresponding author. Tel.: +61 3 52272169. E-mail address: [email protected] (N. Stanford).
tative. With the advent of modern techniques such as EBSD this observation can be re-examined quantitatively, and its effect on the mechanical properties of the alloy can be more fully examined. The current study was therefore designed to investigate the effect of particles on the room temperature deformation behaviour of a magnesium-based alloy. In particular, the development of {1 0 1¯ 2} twins is examined.
2. Experimental method The starting material for this study was a 2 kg cast ingot with a composition of Mg 5 wt.%Zn. Billets were machined from the cast ingot and given a two step solution treatment of 2 h at 330 ◦ C, then 6 h at 400 ◦ C, followed by an immediate cold water quench. In order to refine the grain size and develop a strong texture, the billets were extruded at 400 ◦ C at a ram speed of 1 mm/s and a reduction ratio of 30. The extrusion temperature was chosen to be in the single-phase region of the Mg–Zn equilibrium diagram. To avoid precipitation during cooling, the extrudates were water cooled immediately on exiting the extrusion die. The grain size resulting from this procedure was 30 m, and the material was precipitate-free. After extrusion, specimens were given a range of precipitation heat treatments that were chosen directly from the ageing curves in Ref. [4] and were 10 h at 250 ◦ C, 18 h at 200 ◦ C, 8 days at 150 ◦ C and 32 days at 110 ◦ C. For mechanical testing, tensile specimens with a 3.5 mm diameter and 12 mm guage length were machined from the extrudate. Compression specimens of 8 mm height and 5.4 mm diameter were also cut from the extrudate. Mechanical testing was carried out on an Instron 30 kN screw driven tensile tester equipped with a non-contact video extensometer.
0921-5093/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.04.001
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Table 1 Summary of the average tensile and compressive behaviours of the specimens after the ageing treatments shown. Yield point determined from 0.002 offset. Strength refers to the highest engineering strength measurement made on the tensile or compressive loads. Brackets show one standard deviation for the measurements. Sample As-ext 10 h 250 ◦ C 18 h 200 ◦ C 8 days 150 ◦ C 32 days 110 ◦ C As-ext 10 h 250 ◦ C 18 h 200 ◦ C 8 days 150 ◦ C 32 days 110 ◦ C
Comp Comp Comp Comp Comp Tens. Tens. Tens. Tens. Tens.
Yield pt. (MPa)
Strength (MPa)
Uniform strain (%)
88 (13.5) 98 (10.6) 116 (13.4) 176 (2.1) 150 (4.9) 153 (6.6) 154 (6.7) 230 (14.2) 282 (0.7) 305 (7.1)
477 (14.8) 473 (5.7) 481 (9.9) 499 (0.7) 451 (3.5) 214 (6.5) 218 (6.2) 257 (8.0) 299 (2.1) 317 (4.2)
20.8 (1.2) 26.6 (2.7) 25.2 (0.3) 13.2 (0.1) 14.0 (0.7) 13.6 (0.8) 11.2 (1.4) 3.8 (0.4) 3.3 (0.2) 2.7 (0.1)
A summary of the tensile and compressive mechanical behaviours is detailed in Table 1. The compressive behaviour of the specimens (Fig. 1b) do not show as large a difference as the tensile behaviours. The compressive yield point is increased after precipitation treatment, with the lower ageing temperatures having a larger strengthening effect. The specimens aged at the higher temperatures of 200 and 250 ◦ C showed lower work hardening rates between the strains of 0.05 and 0.1, and showed higher strains to failure compared to the asextruded condition. The specimens aged at the lower temperatures showed a lower failure strain compared to the as-extruded condition. 3.2. Texture and microstructure
Fig. 1. Typical stress–strain curves for samples tested in (a) tension and (b) compression. Full details of results including standard deviations are given in Table 1.
For metallographic observation, specimens were polished using standard metallographic techniques followed by a 5 min polish using Struers OPS colloidal silica. For optical microscopy specimens were etched with acetic picral (100 mL ethanol, 10 mL H2 O, 6 g picric acid and 5 mL acetic acid). For electron microscopy, specimens were electro-polished in 5% nitric acid in ethanol at 20 V for 30–45 s. Specimens were then chemically cleaned in the same solution for 5–10 s with no applied voltage. Electron backscattered diffraction (EBSD) was carried out on a Leo 1530 field emission scanning electron microscope equipped with HKL analysis software. Specimens for transmission electron microscopy (TEM) were prepared using a Gatan plasma ion polishing system. TEM was carried out on a JEOL 2100 at 200 kV. 3. Results 3.1. Mechanical properties Typical examples of the tensile and compressive behaviour of specimens after the different aging treatments are shown in Fig. 1. The curves for the tensile behaviour show a particularly large difference between the as-extruded and aged specimens. With decreasing aging temperature, the tensile yield point of the specimens increases, with the yield point and UTS of the samples aged at 150 ◦ C and 110 ◦ C being almost twice that of the as-extruded specimen. The tensile ductility of the specimens aged at 150 and 200 ◦ C are significantly decreased compared to the as-extruded condition.
The deformed microstructures of the tensile and compressive specimens were examined after failure, and typical microstructures are given in Fig. 2. Tensile deformation of the as-extruded specimens resulted in the formation of a large number of twins both in the region of uniform elongation as well as in the necked region, Fig. 2a and b, respectively. The specimens aged at 200 ◦ C and below showed necking at low tensile strains of approximately 4% elongation. For these specimens, in the regions of uniform elongation that correspond to strains of less than 4%, minimal twinning was observed, Fig. 2c. However, in the necked regions extensive twinning was observed, Fig. 2d. In order to examine the evolution of the twinned microstructure, additional specimens were deformed in compression to a strain of 5%. These specimens were examined optically, but EBSD showed more clearly the shape and volume fraction of twins in the microstructure. Examples of these microstructures are given in Fig. 3 which shows the same sized area for both specimens, and each was measured using the same step size of 0.75 m. It can be seen that these specimens show extensive twinning even at these low strain levels. It is also evident from these micrographs that qualitatively, the twins appear to be smaller and more numerous in the aged specimen compared to the as-extruded condition. For the area examined, the aged specimen showed more twins, 1574, compared to the same sized area in the as-extruded condition which had 931 twins. The twins in the aged specimen had an average area of 29.0 m2 compared to 52.6 m2 in the as-extruded condition. This corresponds to equivalent circle diameters of 3.2 and 5.1 m, respectively. By eye, the twins in the aged specimen appear to have a higher aspect ratio than those in the as-extruded condition. However, the aspect ratio of the largest 400 twins in each of the specimens is quite close, being 3.7 for the as-extruded and 4.1 for the aged specimen. The texture of the as-extruded material was measured using EBSD, Fig. 4. It can be seen that a strong basal texture has developed, and that there is negligible material with
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Fig. 2. Optical micrographs of specimens deformed to failure. (a) Region of uniform elongation in as-extruded specimen after tensile deformation. (b) Necked region behind fracture surface in as-extruded specimen tensile deformed to failure. (c) Region of uniform elongation (∼4% strain) in specimen aged at 150 ◦ C after tensile deformation. (d) Necked region behind fracture surface in specimen aged at 150 ◦ C after tensile deformation.
orientations close to the [0 0 0 1] corner of the inverse pole figure. EBSD was also used to examine the deformation texture of selected specimens compressed to 5% strain, Fig. 4. It can be seen that there is a marked difference in the intensity of the texture at the 0 0 0 1 axis between the two specimens. The aged specimen shows a much weaker 0 0 0 1 intensity compared to the as-extruded condition. Since the texture was sharp in the starting material, with virtually no grains lying near 0 0 0 1, it can be assumed that all of the material found at this orientation in the deformed texture originates from {1 0 1¯ 2} twinning. This texture data can therefore be used to estimate the volume fraction of twins in the microstructure, and this is detailed in Fig. 4. These results show that there is a significant difference in the volume fraction of {1 0 1¯ 2} twins resulting from deformation of materials after precipitation ageing. For the same strain level of 5% compression, the as-extruded specimen had 55% twin fraction, while the aged specimen had 38% twin fraction.
of the rods, electron micrographs were taken with a [0 0 0 1] zone axis—parallel to the long axis of the precipitates. To measure the length of the precipitates, micrographs were taken in the [1 0 1¯ 2] axis perpendicular to the long axis of the precipitates. With decreasing aging temperature the precipitates became smaller and more closely spaced, Table 2. In addition to the precipitates that form within the grains, grain boundary precipitation was also observed see Fig. 5a. In order to examine more fully the interaction of twins and precipitates, a specimen deformed in compression to 5% strain was examined in the TEM. This specimen was prepared in the same way as the one shown in Fig. 3b, and exhibited extensive {1 0 1¯ 2} twinning. The interaction of the precipitates with the twins was found to be minimal. There was not any boundary pinning of the twin boundary with precipitates, and there was no change in precipitate shape or orientation where the precipitates crossed the twin boundaries. 4. Discussion
3.3. Transmission electron microscopy 4.1. Modelling the deformation modes The precipitation behaviour of this system is well characterised, and will not be repeated here. A brief summary will be given for completeness sake. As described by Chun and Byrne [7], aging of this alloy produces a transition phase known as MgZn having a hexagonal crystal structure (hP12) with lattice parameters of a = 0.52 nm and c = 0.85 nm. Due to the close matching of the a lattice parameter of the precipitate and the c lattice parameter of the matrix, the precipitates form into rods that lie parallel to the c-axis, Fig. 5. In addition to these rods some plates also form on the basal planes, but this was not a common feature of the precipitation in the cases studied here. To measure the spacing between the rods and the diameter
Visco-plastic self-consistent (VPSC) modelling was used to examine the effect of the precipitation treatment on the relative activity of the four main deformation modes. For this purpose, only the specimen aged at 150 ◦ C was compared to the as-extruded (precipitate-free) case because this specimen showed a large difference in mechanical properties. The four deformation modes considered were basal slip, prismatic slip, second order pyramidal c + a slip and {1 0 1¯ 2} twinning. For this modelling work, the starting texture comprising 800 grains was taken from a subset of the texture data measured using EBSD as shown in Fig. 4.
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Fig. 3. EBSD orientation map of the deformed microstructures after compression to a strain of 5% for (a) as-extruded specimen and (b) specimen aged at 150 ◦ C.
As a starting point, the values determined in Ref. [8] were taken for the critical resolved shear stress (CRSS) and the hardening parameters of the four deformation modes (see Table 3). During the fitting procedure, the hardening values were not altered because
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Fig. 5. Transmission electron micrographs. (a) Precipitates formed in specimen aged at 110 ◦ C for 32 days. (b) Specimen aged at 150 ◦ C and deformed to 5% strain in compression. Micrograph shows {1 0 1¯ 2} twin, with common 1 1 2¯ 0 zone axis. Note higher magnification in (b).
Table 2 Effect of aging treatment on the size and distribution of the precipitates measured using TEM. Aging treatment
Precipitate length (nm)
Precipitate diameter (nm)
10 h 250 ◦ C 18 h 200 ◦ C 8 days 150 ◦ C 32 days 110 ◦ C
600 400 120 150
50 40 20 10
Precipitate spacing (nm) 200 150 80 40
there were only essentially 2 curves on which the fitting could be carried out. Instead, the CRSS for basal slip was assigned a value of 1, and the other modes scaled accordingly. The original fit for the compression curve of the as-extruded condition using the values from Ref. [8] is shown in Fig. 6a. It is clear that in compression there is a poor fit to the experimental data. The high work hardening that is typical of magnesium when deformed in this orientation with this Table 3 Vocé hardening parameters used for the VPSC modelling. 0 = critical resolved shear stress for deformation mode. SF = scaling factor applied to fit experimentally measured values. Deformation mode
Fig. 4. Textures measured using EBSD. (a) Starting texture. (b) Texture after compression to 5% strain of the as-extruded material. (c) Texture after compression to 5% strain of specimen aged at 150 ◦ C.
Basal slip Prismatic slip c + a slip {1 0 1¯ 2} twinning
As-ext. (SF = 18)
Aged (SF = 20)
Both conditions
0
0
1
1 3 12 1
1 7 12 4
0
0.5 40 2.0 20 2.3 800 0 0
1 3.0 1.2 0 0
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Fig. 6. VPSC modelling of the deformation behaviour of the as-extruded and aged specimens. Solid lines represent the experimental data of the conditions indicated. The dotted lines represent modelling data; model parameters for each simulation shown on the left.
texture type is not well described by these parameters. The strain of about 5% where the experimental and predicted data diverge corresponds to the region where c + a slip becomes prominent in the model prediction. Raising the CRSS of c + a slip to 12 (compared to a value of 1 for basal slip) reduced its activity at higher stains, and resulted in a better fit, Fig. 6c. This high value for the CRSS for c + a slip virtually eliminated its activity during the simulations in both tension and compression, indicating that in this alloy c + a slip may not be operative at room temperature. Comparing the compressive behaviour of the aged and asextruded conditions (Fig. 1), it can be seen that the aged specimen has a higher flow stress, and that the work hardening rate is lower. The lower work hardening rate indicates that the deformation modes have not hardened equally in response to the presence of the precipitates. If the hardening affected each system equally, a scaling factor would see the curves closely overlap. Increasing the CRSS for twinning from 1 to 4 (compared to basal slip) reduced the twin fraction predicted by the simulation, and reduced the work hardening rate to approximate the experimental data, Fig. 6e. This indicates that the twinning has been hardened by the precipitation more than the basal slip system has. This result is entirely consistent with the microstructural examinations detailed in the results sec-
tion. The experimentally determined twin fraction of 55% is close to the predicted value of 58% after 5% compressive deformation. In the aged specimen, the predicted value was 46%, compared to the measured value of 38%. Microstructurally, the total twin fraction in the aged specimens is smaller because the twins that from are smaller, rather than a smaller number of them forming. In this respect, reducing the predicted twin fraction by increasing the CRSS for twinning does not simulate the microstructural changes that result from ageing, but does simulate the flow stress and textural changes likely to take place by reducing the total twinned volume at a given strain. Looking now to the tensile behaviour of the aged specimen, increasing the twinning CRSS for twinning to 2 does not significantly effect the predicted flow stress for tension because the texture was such that the twin fraction is minimal. However, applying the same scaling factor as the compressive test, the yield and flow stress of the model prediction are too low. Since c + a slip has been found to be of negligible effect on the deformation in this case, it must be that the prismatic slip system has been hardened. This has been simulated in Fig. 6f where the prismatic CRSS has been increased from 3 to 7 relative to the basal CRSS of 1. This increase has minimal effect on the flow stress in compression, but increases
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the flow stress in tension to a value closer to that measured experimentally (given the same scaling factor as that for compression). The VPSC modelling has suggested that precipitation has hardened the prismatic slip and {1 0 1¯ 2} twin systems more than it has the basal slip system. However, the necessity to increase the scaling factor from 18 to 20 after the aging treatment shows that the basal system too has been hardened by about 10% by precipitation. In the following sections the mechanisms of precipitation hardening on these individual deformation modes are discussed in more detail. 4.2. Precipitation strengthening of slip An interesting outcome of the VPSC modelling is the conclusion that the prismatic slip system is more strongly hardened than the basal slip system in response to the precipitates formed in this alloy, that is, thin rods that grow parallel to the c-axis. These precipitates are incoherent, and not sheared by dislocation motion, Fig. 5b. It is therefore appropriate to view precipitate hardening in this case as an Orowan hardening mechanism in which the dislocations loop around particles as they bypass them. The increase in critical resolved shear stress (CRSS) resulting from precipitates is described mathematically by the Orowan–Ashby equation [9]: =
0.13Gb r ln b
(1)
where G is the shear modulus = 15 GPa; b is the Burgers vector = 0.32 nm; is the inter-particle spacing; r is the particle radius. Examination of this equation reveals that for maximum strengthening a small inter-particle spacing is required and to a lesser extent that the precipitates be large. Let us consider the particle distribution in this system to be a hexagonal array with the rods on the prismatic planes. Dislocations bowing between precipitates on the basal and prismatic planes are shown schematically in Fig. 7a and b. It can be seen that many more precipitates per unit area intersect the basal plane compared to the prismatic plane. The inter-particle spacings are different, as are the effective particle diameters. For the basal plane the effective particle diameter is the width of the rods (D), while the effective particle diameter for an edge dislocation on the prismatic plane is the length of the rods (L). From the schematic representation of the precipitates in this system, it is clear that the end-to-end spacing of the rods (I) is a critical parameter in determining the hardening for edge disloca-
Fig. 8. (a) Relationship between the diameter (D) and spacing (S) of precipitates as a function of length (L) measured using TEM. (b) Orowan strengthening (Eq. (1)) of the prismatic and basal slip systems as a function of precipitate length for a volume fraction of 3% precipitates.
tions on the prismatic plane. However, measurement of this spacing is difficult in the TEM because of overlap between rods on different planes. In order to estimate the end-to-end spacing (I) based on the measurements of L and D made using TEM, the schematic shown in Fig. 7c was used to mathematically determine the end-to-end spacing of the rods. The volume of the array is determined by the spacing and length of the precipitates: √ 3 3 Vol = (S + D)2 (I + L) (2) 2 The total volume of the three precipitates in the array is determined assuming a cylindrical precipitate shape: Vol precipitates =
Fig. 7. Schematic illustration of the different particle morphologies intercepted by (a) edge dislocations on the prismatic plane and (b) edge or screw dislocations on the basal plane. (c) Schematic diagram of the volume distribution of rod shaped precipitates on the prismatic planes used to determine the inter-particle spacing, see text for further details. (d) Schematic illustration of the particle morphology intercepted by screw dislocations on the prismatic plane.
3 D2 L 4
(3)
With increasing aging temperature, the precipitates thicken and lengthen. So too their spacing increases. The length (L), width (D) and spacing (S) of the precipitates after different aging treatments have been measured with TEM, and are given in Table 2. The relationship between the diameter and spacing as a function of the width are shown graphically in Fig. 8a. The relationship between the length and width/spacing of the precipitates is used to solve Eq. (2) for a volume fraction of 3% precipitates (estimated from the binary phase diagram [10]), and therefore determine the end-to-end parti-
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Table 4 The effect of precipitation on the critical resolved shear stress (CRSS) of the three dominant deformation modes predicted by VPSC modelling and the Orowan equation for a precipitate of 125 nm in length. CRSS for deformation mode Basal slip Prismatic slip Twining
As-ext
Aged
0 VPSC
18 MPa 54 MPa 18 MPa
20 MPa 140 MPa 80 MPa
2 MPa 86 MPa 62 MPa
0 Orowan 40 MPa 70 MPa –
cle spacing (I). Using the end-to-end particle spacing (I), the Orowan equation has been used to estimate the hardening on the prismatic and basal planes as a function of precipitate length, Fig. 8b. It is clear that the prismatic plane is strengthened more than the basal plane by this arrangement of rods for edge-type dislocations. If we consider the case of a precipitate length of 125 nm (Table 4), which is close to the case for ageing at 150 ◦ C, the strengthening on the prismatic plane is predicted by the Orowan equation to be 70 MPa, while the strengthening on the basal plane is 40 MPa (see Fig. 8b). From the VPSC modelling, the CRSS on the basal plane is predicted to increase by a value of 2 MPa, and the CRSS for prismatic slip was predicted to increase by 86 MPa. Although the quantitative predictions for the rise in CRSS are different for the two mathematical approaches, it still remains that the needle shaped precipitates strengthen the prismatic slip system more than the basal slip system. It should also be noted that the value for I (and therefore the Orowan strengthening prediction) is strongly effected by the volume fraction term. Increasing the volume fraction above 3.8% for the particle size distribution results in the end-to-end spacing becoming zero, representing a continuous phase. Reducing the volume fraction to below 2.6% yields end-to-end spacing values approximately equal to the inter-particles spacing S. This results in the basal plane being hardened more than the prismatic plane at particle lengths above 125 nm. Let us now consider screw dislocations on the prismatic plane, Fig. 7d. The effective spacing between particles is S, and the particle diameter is D. Applying the Orowan equation (Eq. (1)) we see that the predicted strengthening for a screw dislocation on the prismatic plane is identical to the strengthening predicted for the basal plane. However, in this situation the dislocation must travel the length of the rod before being able to bypass it. The stress required to bow the dislocation between the precipitates remains the same as it travels this length, and is unlikely therefore to increase the CRSS. In reality, it is most likely that any portion of a dislocation that has a screw character will simply cross-slip onto the basal plane in order to bypass precipitates. Taking these two factors into consideration, it appears that the edge dislocations are principally responsible for the increased hardening observed on the prismatic planes after age hardening. Finally, we should consider the possible impact of solid solution softening of the prismatic slip system on these calculations. Akhtar and Teghtsoonian [11] have shown that the addition of Zn into the Mg matrix will harden the basal slip system, but soften the prismatic slip system. At room temperature, their data shows a reduction in the CRSS for prismatic slip of approximately 12.5 MPa for each additional atomic percent of Zn. This is probably a large over-estimate, since the data shown in Ref. [11] appears to be reaching a plateau, and the compositions used in this study exceed those measured in Ref. [11]. However, we can use the data to give an idea of the magnitude of the effect. From the Mg–Zn phase diagram we can estimate that when fully in solid solution, the alloy used here has 1.9 at.%Zn in the matrix. Fully aged, the matrix composition is around 0.7 at.%Zn. Therefore, the increase in the CRSS for prismatic slip resulting from Zn depletion in the matrix of aged specimens can be estimated to be a maximum of 15 MPa. So although this phe-
Fig. 9. Schematic illustration of the interaction of {1 0 1¯ 2} twins with the rod-shaped precipitates formed in this system. See text for further details.
nomenon may account for some of the increased hardening found on the prismatic slip system after ageing, the magnitude of this effect is much smaller than the hardening from the precipitates. 4.3. Precipitate twin interactions The EBSD and optical microscopy data presented in the results section has shown that extensive {1 0 1¯ 2} twinning occurs during compression, but that the twins are smaller and have a lower volume fraction in the precipitate-containing microstructure. This reduces the total volume fraction of twins in the age-hardened condition. These observations suggest that twins can easily form in precipitate-containing alloys, but that their growth is limited. In other words, the {1 0 1¯ 2} twin is growth limited, not nucleation limited in the presence of particles. In a particle-free matrix the {1 0 1¯ 2} twin can easily grow laterally, and in some cases can consume entire grains. In the case of an age-hardened alloy, if the lateral growth is limited then the grain is subject to higher stress because the imposed strain cannot be accommodated by the twin. This high stress state enables the nucleation of new twins within the grain to accommodate applied strain. This accounts for the formation of more twins in the age-hardened condition, and also their smaller size. Clearly, the next question is why should precipitates inhibit twin growth? A schematic representation of {1 0 1¯ 2} twinning and a precipitate are shown in Fig. 9. Since the particle is not sheared during the twinning, as the twinning ledge approaches the particle there will be some back-stress resulting from the rigid particle inhibiting the free shear of the moving twin ledge. This back-stress must be overcome by the applied stress. When the shear takes place at the interface between the matrix and the precipitate, the movement of atoms toward the precipitate must be accommodated by the surrounding material. This is most likely accomplished by basal slip away from the particle/matrix interface. However, it can be seen that basal slip too would be inhibited by the precipitate for this geometry. It might therefore be that the shear is accommodated by basal slip inside the twin, rather than in the parent material. This may also account for the observation of stacking faults (see Fig. 10) within some twins—the stacking faults may help to accommodate the twin shear at the particle/matrix interface. As a matter of interest, stacking faults have also been observed by the authors inside twins in the particle-containing alloy Mg 1.6 wt.%Mn. The need for additional basal slip on a local scale around
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Fig. 10. Transmission electron micrograph of parent (upper) and twin (lower) in specimen aged at 150 ◦ C and deformed to 5% strain in compression. The micrograph is taken on the common 1 1 2¯ 0 zone axis. Parent orientation evident from the alignment of precipitates in the [0 0 0 1] direction. Note stacking faults and basal dislocations in the twinned region.
the precipitates is likely to increase the stress required to form the twin. An additional contribution of the precipitates to the increased CRSS for twinning is through the accommodation of the twinning shear by the surrounding matrix. This is distinct from the accommodation described in the previous paragraph that occurs over the scale of nanometers. Accommodation of large twins microscopically occurs across 10s of micrometers. Observations by Roberts and Partridge [12] have shown that the thickening of the {1 0 1¯ 2} twin in magnesium is accommodated by significant amounts of basal slip. These accommodation mechanisms explain why the twin system is hardened more by precipitation than the basal slip system is. Basal slip is inhibited by precipitates. The {1 0 1¯ 2} twin system is inhibited by the need to shear around particles, in addition to the restriction in the basal slip that accommodates its growth. It therefore follows that if the basal slip system is hardened by some increment, then the twin must be hardened by at least that same amount. From this perspective it appears likely that precipitation will always harden the {1 0 1¯ 2} twin system equal to, or more than, the basal slip system. The final point of discussion regarding twins and precipitates is the observation that the particles do not appear to be rotated by the twinning shear. One might expect that after a twin consumes a particle and its surroundings that the particle too is rotated by this angle. However, rotations were not observed in this study, e.g. Figs. 5 and 10. With the problem of foil warping and poor contrast on the appropriate zone axis, it is difficult to measure small angles in this system. In addition to these microscopical hindrances, the particles formed in these samples do not show the sharp and well-defined edges that other precipitates such Mg17 Al12 do [6]. For these reasons it is difficult to say if there is a genuine rigid body rotation in micrographs such as the one shown in Fig. 5b. However, we can use the stacking faults on the basal planes in the micrograph of Fig. 10 to provide some approximation of the rotation of particles after twinning has occurred. During ageing, the particles form with their long axis parallel to the c-axis of the parent orientation. After {1 0 1¯ 2} twinning, the matrix is rotated by 86.3◦ about 1 1 2¯ 0. If there is no rigid body rotation, there will be a 3.7◦ deviation between the basal plane of the twinned material and the precipitate. However, the precipitate could rotate in response to the twinning shear, and a schematic representation of this is shown in Fig. 11. The full rigid body rotation, assuming the particle shears with the matrix, can be calculated as
follows (see Fig. 11): shear = =
x h
(4)
tan ˇ =
h x
(5)
tan =
x + x = tan ˇ + h
(6)
˛=−ˇ
(7)
where is the twinning shear = 0.13 for {1 0 1¯ 2} twinning in Mg, ˇ the angle between the long axis of the precipitate and the twin plane before twinning (=46.8◦ for the case studied here), and ˛ is the rotation angle due to twinning shear. The angle ˇ between the {1 0 1¯ 2} twin plane and the {0 0 0 1} of the parent = 46.8◦ , and so the full rigid body rotation ˛ = 3.3◦ (note that if the long axis of the precipitate was perpendicular to the twinning plane, then ˇ would be 0◦ , and the full rigid body rotation would be tan−1 = 7.4◦ ). The deviation between the basal plane of the twin and the precipitate is 3.7◦ –3.3◦ = 0.4◦ in the case of a full rigid body rotation. These two possible cases are shown in Fig. 12. The micrograph in Fig. 10 shows stacking faults on the basal plane in the twinned region. These features provide a convenient local scale determination of the existence of a rigid body rotation. If the stacking faults (basal planes) in the twinned matrix are misoriented by about 4◦ compared to the precipitates long-axis then there has been no rigid body rotation of the precipitate. However, if the stacking faults are closely aligned with the precipitates, then it is likely that the full theoretical rotation has occurred during twinning. It can be seen from Fig. 10 that the former is observed experimentally, that the stacking faults are misoriented compared
Fig. 11. Geometry of rigid body rotation of a particle due to twinning shear. See text for further details.
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Fig. 12. Illustration of the misorientation between precipitates and the basal plane of the twin for the two cases of no rotation and full rotation of a particle due to the twinning shear.
to the precipitates. This indicates that there has been negligible rigid body rotation associated with the twinning of the material surrounding these precipitates. During deformation by slip, rigid body rotation of particles with respect to the slip plane is readily observed, e.g. [13]. Slip and twinning both apply a shear to the crystal on a well defined plane and a known direction, but only in the case of twinning does this result in the formation of a region with a different orientation compared to the parent grain. It may be that in the case of twinning the orientation change across the twin boundary introduces sufficient additional slip systems that the material can flow around the particle, negating the need for the particle to rotate. Also, in the case of slip it is probably common for the entire matrix along the length of the precipitate to be deforming, whereas in twinning a shear front propagates from one end of the precipitate to the other. Clearly, examination of the interaction of twins with precipitates of different sizes, morphologies, and crystallographic orientations are needed before we can fully describe how these features of the microstructure effect macroscopic deformation behaviour in metals that mechanically twin. 5. Conclusions The effect of precipitation on the deformation behaviour of a binary Mg–Zn alloy has been studied. The following conclusions have been made: • The yield strength and flow stress were significantly increased by precipitation hardening. The yield point was increased by more than 150 MPa in tension and 60 MPa in compression, through precipitation heat treatments.
• EBSD analysis showed that the alloy age hardened at 150 ◦ C produced a larger number of twins in response to 5% compression, compared to the precipitate-free specimens. These twins in the age-hardened alloy were smaller, and had a lower total volume fraction. • Transmission electron microscopy showed that in response to compressive deformation, the precipitates are not sheared by either slip or twinning activity. The precipitates did not show any rigid body rotation after the twinning shear. • Visco-plastic self-consistent (VPSC) modelling was used to show that the prismatic planes are hardened more by the precipitation than the basal planes. This has been attributed to the small end-to-end spacing between the rod-shaped precipitates at the volume fractions found in this alloy. • VPSC modelling also showed that the {1 0 1¯ 2} twin system was hardened more than the basal slip system by precipitation. This is consistent with the lower work hardening rate and lower twin fraction in age-hardened specimens. This behaviour has been attributed to the need for accommodation of the twinning shear around precipitates, and also macroscopically within the parent grain. • It is proposed that because the {1 0 1¯ 2} twin requires basal slip to accommodate the shape change, this twin type will always be hardened equal to, or more than, the basal slip system in response to precipitation. Acknowledgements The work described in this paper was funded by the Australian Research Council through the Centre of Excellence for Design in Light Metals. The authors would also like to thank R.A. Lebensohn and C.N. Tomé who developed the VPSC5 code and kindly allowed us to use it. Finally, the first author would like to give special thanks to Dr. Dominic Phelan who suggested that counting twins would be a very effective way of showing that there are, in fact, more in one micrograph than another. References [1] W.H. Hosford, The Mechanics of Crystals and Textures Polycrystals, Oxford University Press, 1993. [2] Z. Keshavarz, PhD Thesis, Deakin University (2007). [3] R.E. Reed-Hill, W.D. Robertson, Acta Metall. 5 (1957) 717. [4] J.B. Clarke, Acta Metall. 13 (1965) 1281. [5] J.B. Clarke, Acta Metall. 16 (1968) 141. [6] M.A. Gharghouri, G.C. Weatherly, J.D. Embury, Phil. Mag. A 78 (1998) 1137. [7] J.S. Chun, J.G. Byrne, J. Mater. Sci. 4 (1969) 861. [8] J. Bohlen, M.R. Nurnberg, J.W. Senn, D. Letzig, S.R. Agnew, Acta Mater. 55 (2007) 2101. [9] G.E. Deiter, Mechanical Metallurgy, McGraw-Hill, 1988. [10] E.A. Brandes, G.B. Brook (Eds.), Smithells Light Metals Handbook, ButterworthHeinemann, 1998, p. 150. [11] A. Akhtar, E. Teghtsoonian, Acta Metall. 17 (1969) 1351. [12] E. Roberts, P.G. Partridge, Acta Metall. 14 (1966) 513. [13] P. Bate, W.T. Roberts, D.V. Wilson, Acta Metall. 29 (1981) 1797.
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effect of particles on the formation of deformation twins in a magnesium-based alloy N. Stanford ∗ , M.R. Barnett Centre for Material and Fibre Innovation, Deakin University, Pigdons Road, Geelong 3217, Australia
a r t i c l e
i n f o
Article history: Received 3 December 2008 Received in revised form 6 March 2009 Accepted 1 April 2009 Keywords: Magnesium alloys Precipitation Twinning Deformation
a b s t r a c t The deformation behaviour of the age hardenable alloy Mg–5%Zn after different precipitation treatments has been examined. It has been found that during compressive deformation, fine particles increase the number of twins that form, but reduce the size and total volume fraction of twins. Visco-plastic selfconsistent modelling has been used to show that the presence of precipitates hardens the twin and prismatic slip systems more than the basal slip system. It is proposed that because the {1 0 1¯ 2} twin requires basal slip to accommodate the twinning shear, this twin type will always be hardened equal to, or more than, the basal slip system in response to precipitation. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
1. Introduction Magnesium and its alloys can deform by both slip and twinning [1]. Of the twinning modes that are possible in hexagonal metals, {1 0 1¯ 2} and {1 0 1¯ 1} are commonly observed in Mg alloys, and {1 0 1¯ 3} can be observed in coarse grained materials [2] and single crystals of certain orientations [3]. Although the twinning behaviour of magnesium is well studied, the interaction of particles and twins is not so well characterised. There are really only three studies [4–6] that examine the twinning of magnesium in the presence of precipitates. Gharghouri et al. [6] studied a Mg–7.7 at.%Al binary and showed that after the matrix surrounding a precipitate underwent twinning, no rotation of the precipitates was observed. This is in direct disagreement with the observations by Clarke [4] who showed that a rigid body rotation of approximately 10◦ about 1 1 2¯ 0 occurred in precipitates after matrix twinning. Gharghouri et al. [6] have also shown that twins can change their apparent habit plane to avoid intersection with a particle. Clarke [4,5] studied two binary alloys, Mg–Zn and Mg–Al. These studies suggested that certain particles could be sheared by the twinning transformation, and also that {1 0 1¯ 2} twins could be suppressed by particles at high enough volume fractions. The latter observation is of interest because the relative contribution of slip and twinning to the deformation will determine not only the flow stress but may also impact on the ductility of the alloy. However, the observations about twin fractions made in that study were quali-
∗ Corresponding author. Tel.: +61 3 52272169. E-mail address: [email protected] (N. Stanford).
tative. With the advent of modern techniques such as EBSD this observation can be re-examined quantitatively, and its effect on the mechanical properties of the alloy can be more fully examined. The current study was therefore designed to investigate the effect of particles on the room temperature deformation behaviour of a magnesium-based alloy. In particular, the development of {1 0 1¯ 2} twins is examined.
2. Experimental method The starting material for this study was a 2 kg cast ingot with a composition of Mg 5 wt.%Zn. Billets were machined from the cast ingot and given a two step solution treatment of 2 h at 330 ◦ C, then 6 h at 400 ◦ C, followed by an immediate cold water quench. In order to refine the grain size and develop a strong texture, the billets were extruded at 400 ◦ C at a ram speed of 1 mm/s and a reduction ratio of 30. The extrusion temperature was chosen to be in the single-phase region of the Mg–Zn equilibrium diagram. To avoid precipitation during cooling, the extrudates were water cooled immediately on exiting the extrusion die. The grain size resulting from this procedure was 30 m, and the material was precipitate-free. After extrusion, specimens were given a range of precipitation heat treatments that were chosen directly from the ageing curves in Ref. [4] and were 10 h at 250 ◦ C, 18 h at 200 ◦ C, 8 days at 150 ◦ C and 32 days at 110 ◦ C. For mechanical testing, tensile specimens with a 3.5 mm diameter and 12 mm guage length were machined from the extrudate. Compression specimens of 8 mm height and 5.4 mm diameter were also cut from the extrudate. Mechanical testing was carried out on an Instron 30 kN screw driven tensile tester equipped with a non-contact video extensometer.
0921-5093/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.04.001
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Table 1 Summary of the average tensile and compressive behaviours of the specimens after the ageing treatments shown. Yield point determined from 0.002 offset. Strength refers to the highest engineering strength measurement made on the tensile or compressive loads. Brackets show one standard deviation for the measurements. Sample As-ext 10 h 250 ◦ C 18 h 200 ◦ C 8 days 150 ◦ C 32 days 110 ◦ C As-ext 10 h 250 ◦ C 18 h 200 ◦ C 8 days 150 ◦ C 32 days 110 ◦ C
Comp Comp Comp Comp Comp Tens. Tens. Tens. Tens. Tens.
Yield pt. (MPa)
Strength (MPa)
Uniform strain (%)
88 (13.5) 98 (10.6) 116 (13.4) 176 (2.1) 150 (4.9) 153 (6.6) 154 (6.7) 230 (14.2) 282 (0.7) 305 (7.1)
477 (14.8) 473 (5.7) 481 (9.9) 499 (0.7) 451 (3.5) 214 (6.5) 218 (6.2) 257 (8.0) 299 (2.1) 317 (4.2)
20.8 (1.2) 26.6 (2.7) 25.2 (0.3) 13.2 (0.1) 14.0 (0.7) 13.6 (0.8) 11.2 (1.4) 3.8 (0.4) 3.3 (0.2) 2.7 (0.1)
A summary of the tensile and compressive mechanical behaviours is detailed in Table 1. The compressive behaviour of the specimens (Fig. 1b) do not show as large a difference as the tensile behaviours. The compressive yield point is increased after precipitation treatment, with the lower ageing temperatures having a larger strengthening effect. The specimens aged at the higher temperatures of 200 and 250 ◦ C showed lower work hardening rates between the strains of 0.05 and 0.1, and showed higher strains to failure compared to the asextruded condition. The specimens aged at the lower temperatures showed a lower failure strain compared to the as-extruded condition. 3.2. Texture and microstructure
Fig. 1. Typical stress–strain curves for samples tested in (a) tension and (b) compression. Full details of results including standard deviations are given in Table 1.
For metallographic observation, specimens were polished using standard metallographic techniques followed by a 5 min polish using Struers OPS colloidal silica. For optical microscopy specimens were etched with acetic picral (100 mL ethanol, 10 mL H2 O, 6 g picric acid and 5 mL acetic acid). For electron microscopy, specimens were electro-polished in 5% nitric acid in ethanol at 20 V for 30–45 s. Specimens were then chemically cleaned in the same solution for 5–10 s with no applied voltage. Electron backscattered diffraction (EBSD) was carried out on a Leo 1530 field emission scanning electron microscope equipped with HKL analysis software. Specimens for transmission electron microscopy (TEM) were prepared using a Gatan plasma ion polishing system. TEM was carried out on a JEOL 2100 at 200 kV. 3. Results 3.1. Mechanical properties Typical examples of the tensile and compressive behaviour of specimens after the different aging treatments are shown in Fig. 1. The curves for the tensile behaviour show a particularly large difference between the as-extruded and aged specimens. With decreasing aging temperature, the tensile yield point of the specimens increases, with the yield point and UTS of the samples aged at 150 ◦ C and 110 ◦ C being almost twice that of the as-extruded specimen. The tensile ductility of the specimens aged at 150 and 200 ◦ C are significantly decreased compared to the as-extruded condition.
The deformed microstructures of the tensile and compressive specimens were examined after failure, and typical microstructures are given in Fig. 2. Tensile deformation of the as-extruded specimens resulted in the formation of a large number of twins both in the region of uniform elongation as well as in the necked region, Fig. 2a and b, respectively. The specimens aged at 200 ◦ C and below showed necking at low tensile strains of approximately 4% elongation. For these specimens, in the regions of uniform elongation that correspond to strains of less than 4%, minimal twinning was observed, Fig. 2c. However, in the necked regions extensive twinning was observed, Fig. 2d. In order to examine the evolution of the twinned microstructure, additional specimens were deformed in compression to a strain of 5%. These specimens were examined optically, but EBSD showed more clearly the shape and volume fraction of twins in the microstructure. Examples of these microstructures are given in Fig. 3 which shows the same sized area for both specimens, and each was measured using the same step size of 0.75 m. It can be seen that these specimens show extensive twinning even at these low strain levels. It is also evident from these micrographs that qualitatively, the twins appear to be smaller and more numerous in the aged specimen compared to the as-extruded condition. For the area examined, the aged specimen showed more twins, 1574, compared to the same sized area in the as-extruded condition which had 931 twins. The twins in the aged specimen had an average area of 29.0 m2 compared to 52.6 m2 in the as-extruded condition. This corresponds to equivalent circle diameters of 3.2 and 5.1 m, respectively. By eye, the twins in the aged specimen appear to have a higher aspect ratio than those in the as-extruded condition. However, the aspect ratio of the largest 400 twins in each of the specimens is quite close, being 3.7 for the as-extruded and 4.1 for the aged specimen. The texture of the as-extruded material was measured using EBSD, Fig. 4. It can be seen that a strong basal texture has developed, and that there is negligible material with
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Fig. 2. Optical micrographs of specimens deformed to failure. (a) Region of uniform elongation in as-extruded specimen after tensile deformation. (b) Necked region behind fracture surface in as-extruded specimen tensile deformed to failure. (c) Region of uniform elongation (∼4% strain) in specimen aged at 150 ◦ C after tensile deformation. (d) Necked region behind fracture surface in specimen aged at 150 ◦ C after tensile deformation.
orientations close to the [0 0 0 1] corner of the inverse pole figure. EBSD was also used to examine the deformation texture of selected specimens compressed to 5% strain, Fig. 4. It can be seen that there is a marked difference in the intensity of the texture at the 0 0 0 1 axis between the two specimens. The aged specimen shows a much weaker 0 0 0 1 intensity compared to the as-extruded condition. Since the texture was sharp in the starting material, with virtually no grains lying near 0 0 0 1, it can be assumed that all of the material found at this orientation in the deformed texture originates from {1 0 1¯ 2} twinning. This texture data can therefore be used to estimate the volume fraction of twins in the microstructure, and this is detailed in Fig. 4. These results show that there is a significant difference in the volume fraction of {1 0 1¯ 2} twins resulting from deformation of materials after precipitation ageing. For the same strain level of 5% compression, the as-extruded specimen had 55% twin fraction, while the aged specimen had 38% twin fraction.
of the rods, electron micrographs were taken with a [0 0 0 1] zone axis—parallel to the long axis of the precipitates. To measure the length of the precipitates, micrographs were taken in the [1 0 1¯ 2] axis perpendicular to the long axis of the precipitates. With decreasing aging temperature the precipitates became smaller and more closely spaced, Table 2. In addition to the precipitates that form within the grains, grain boundary precipitation was also observed see Fig. 5a. In order to examine more fully the interaction of twins and precipitates, a specimen deformed in compression to 5% strain was examined in the TEM. This specimen was prepared in the same way as the one shown in Fig. 3b, and exhibited extensive {1 0 1¯ 2} twinning. The interaction of the precipitates with the twins was found to be minimal. There was not any boundary pinning of the twin boundary with precipitates, and there was no change in precipitate shape or orientation where the precipitates crossed the twin boundaries. 4. Discussion
3.3. Transmission electron microscopy 4.1. Modelling the deformation modes The precipitation behaviour of this system is well characterised, and will not be repeated here. A brief summary will be given for completeness sake. As described by Chun and Byrne [7], aging of this alloy produces a transition phase known as MgZn having a hexagonal crystal structure (hP12) with lattice parameters of a = 0.52 nm and c = 0.85 nm. Due to the close matching of the a lattice parameter of the precipitate and the c lattice parameter of the matrix, the precipitates form into rods that lie parallel to the c-axis, Fig. 5. In addition to these rods some plates also form on the basal planes, but this was not a common feature of the precipitation in the cases studied here. To measure the spacing between the rods and the diameter
Visco-plastic self-consistent (VPSC) modelling was used to examine the effect of the precipitation treatment on the relative activity of the four main deformation modes. For this purpose, only the specimen aged at 150 ◦ C was compared to the as-extruded (precipitate-free) case because this specimen showed a large difference in mechanical properties. The four deformation modes considered were basal slip, prismatic slip, second order pyramidal c + a slip and {1 0 1¯ 2} twinning. For this modelling work, the starting texture comprising 800 grains was taken from a subset of the texture data measured using EBSD as shown in Fig. 4.
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Fig. 3. EBSD orientation map of the deformed microstructures after compression to a strain of 5% for (a) as-extruded specimen and (b) specimen aged at 150 ◦ C.
As a starting point, the values determined in Ref. [8] were taken for the critical resolved shear stress (CRSS) and the hardening parameters of the four deformation modes (see Table 3). During the fitting procedure, the hardening values were not altered because
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Fig. 5. Transmission electron micrographs. (a) Precipitates formed in specimen aged at 110 ◦ C for 32 days. (b) Specimen aged at 150 ◦ C and deformed to 5% strain in compression. Micrograph shows {1 0 1¯ 2} twin, with common 1 1 2¯ 0 zone axis. Note higher magnification in (b).
Table 2 Effect of aging treatment on the size and distribution of the precipitates measured using TEM. Aging treatment
Precipitate length (nm)
Precipitate diameter (nm)
10 h 250 ◦ C 18 h 200 ◦ C 8 days 150 ◦ C 32 days 110 ◦ C
600 400 120 150
50 40 20 10
Precipitate spacing (nm) 200 150 80 40
there were only essentially 2 curves on which the fitting could be carried out. Instead, the CRSS for basal slip was assigned a value of 1, and the other modes scaled accordingly. The original fit for the compression curve of the as-extruded condition using the values from Ref. [8] is shown in Fig. 6a. It is clear that in compression there is a poor fit to the experimental data. The high work hardening that is typical of magnesium when deformed in this orientation with this Table 3 Vocé hardening parameters used for the VPSC modelling. 0 = critical resolved shear stress for deformation mode. SF = scaling factor applied to fit experimentally measured values. Deformation mode
Fig. 4. Textures measured using EBSD. (a) Starting texture. (b) Texture after compression to 5% strain of the as-extruded material. (c) Texture after compression to 5% strain of specimen aged at 150 ◦ C.
Basal slip Prismatic slip c + a slip {1 0 1¯ 2} twinning
As-ext. (SF = 18)
Aged (SF = 20)
Both conditions
0
0
1
1 3 12 1
1 7 12 4
0
0.5 40 2.0 20 2.3 800 0 0
1 3.0 1.2 0 0
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Fig. 6. VPSC modelling of the deformation behaviour of the as-extruded and aged specimens. Solid lines represent the experimental data of the conditions indicated. The dotted lines represent modelling data; model parameters for each simulation shown on the left.
texture type is not well described by these parameters. The strain of about 5% where the experimental and predicted data diverge corresponds to the region where c + a slip becomes prominent in the model prediction. Raising the CRSS of c + a slip to 12 (compared to a value of 1 for basal slip) reduced its activity at higher stains, and resulted in a better fit, Fig. 6c. This high value for the CRSS for c + a slip virtually eliminated its activity during the simulations in both tension and compression, indicating that in this alloy c + a slip may not be operative at room temperature. Comparing the compressive behaviour of the aged and asextruded conditions (Fig. 1), it can be seen that the aged specimen has a higher flow stress, and that the work hardening rate is lower. The lower work hardening rate indicates that the deformation modes have not hardened equally in response to the presence of the precipitates. If the hardening affected each system equally, a scaling factor would see the curves closely overlap. Increasing the CRSS for twinning from 1 to 4 (compared to basal slip) reduced the twin fraction predicted by the simulation, and reduced the work hardening rate to approximate the experimental data, Fig. 6e. This indicates that the twinning has been hardened by the precipitation more than the basal slip system has. This result is entirely consistent with the microstructural examinations detailed in the results sec-
tion. The experimentally determined twin fraction of 55% is close to the predicted value of 58% after 5% compressive deformation. In the aged specimen, the predicted value was 46%, compared to the measured value of 38%. Microstructurally, the total twin fraction in the aged specimens is smaller because the twins that from are smaller, rather than a smaller number of them forming. In this respect, reducing the predicted twin fraction by increasing the CRSS for twinning does not simulate the microstructural changes that result from ageing, but does simulate the flow stress and textural changes likely to take place by reducing the total twinned volume at a given strain. Looking now to the tensile behaviour of the aged specimen, increasing the twinning CRSS for twinning to 2 does not significantly effect the predicted flow stress for tension because the texture was such that the twin fraction is minimal. However, applying the same scaling factor as the compressive test, the yield and flow stress of the model prediction are too low. Since c + a slip has been found to be of negligible effect on the deformation in this case, it must be that the prismatic slip system has been hardened. This has been simulated in Fig. 6f where the prismatic CRSS has been increased from 3 to 7 relative to the basal CRSS of 1. This increase has minimal effect on the flow stress in compression, but increases
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the flow stress in tension to a value closer to that measured experimentally (given the same scaling factor as that for compression). The VPSC modelling has suggested that precipitation has hardened the prismatic slip and {1 0 1¯ 2} twin systems more than it has the basal slip system. However, the necessity to increase the scaling factor from 18 to 20 after the aging treatment shows that the basal system too has been hardened by about 10% by precipitation. In the following sections the mechanisms of precipitation hardening on these individual deformation modes are discussed in more detail. 4.2. Precipitation strengthening of slip An interesting outcome of the VPSC modelling is the conclusion that the prismatic slip system is more strongly hardened than the basal slip system in response to the precipitates formed in this alloy, that is, thin rods that grow parallel to the c-axis. These precipitates are incoherent, and not sheared by dislocation motion, Fig. 5b. It is therefore appropriate to view precipitate hardening in this case as an Orowan hardening mechanism in which the dislocations loop around particles as they bypass them. The increase in critical resolved shear stress (CRSS) resulting from precipitates is described mathematically by the Orowan–Ashby equation [9]: =
0.13Gb r ln b
(1)
where G is the shear modulus = 15 GPa; b is the Burgers vector = 0.32 nm; is the inter-particle spacing; r is the particle radius. Examination of this equation reveals that for maximum strengthening a small inter-particle spacing is required and to a lesser extent that the precipitates be large. Let us consider the particle distribution in this system to be a hexagonal array with the rods on the prismatic planes. Dislocations bowing between precipitates on the basal and prismatic planes are shown schematically in Fig. 7a and b. It can be seen that many more precipitates per unit area intersect the basal plane compared to the prismatic plane. The inter-particle spacings are different, as are the effective particle diameters. For the basal plane the effective particle diameter is the width of the rods (D), while the effective particle diameter for an edge dislocation on the prismatic plane is the length of the rods (L). From the schematic representation of the precipitates in this system, it is clear that the end-to-end spacing of the rods (I) is a critical parameter in determining the hardening for edge disloca-
Fig. 8. (a) Relationship between the diameter (D) and spacing (S) of precipitates as a function of length (L) measured using TEM. (b) Orowan strengthening (Eq. (1)) of the prismatic and basal slip systems as a function of precipitate length for a volume fraction of 3% precipitates.
tions on the prismatic plane. However, measurement of this spacing is difficult in the TEM because of overlap between rods on different planes. In order to estimate the end-to-end spacing (I) based on the measurements of L and D made using TEM, the schematic shown in Fig. 7c was used to mathematically determine the end-to-end spacing of the rods. The volume of the array is determined by the spacing and length of the precipitates: √ 3 3 Vol = (S + D)2 (I + L) (2) 2 The total volume of the three precipitates in the array is determined assuming a cylindrical precipitate shape: Vol precipitates =
Fig. 7. Schematic illustration of the different particle morphologies intercepted by (a) edge dislocations on the prismatic plane and (b) edge or screw dislocations on the basal plane. (c) Schematic diagram of the volume distribution of rod shaped precipitates on the prismatic planes used to determine the inter-particle spacing, see text for further details. (d) Schematic illustration of the particle morphology intercepted by screw dislocations on the prismatic plane.
3 D2 L 4
(3)
With increasing aging temperature, the precipitates thicken and lengthen. So too their spacing increases. The length (L), width (D) and spacing (S) of the precipitates after different aging treatments have been measured with TEM, and are given in Table 2. The relationship between the diameter and spacing as a function of the width are shown graphically in Fig. 8a. The relationship between the length and width/spacing of the precipitates is used to solve Eq. (2) for a volume fraction of 3% precipitates (estimated from the binary phase diagram [10]), and therefore determine the end-to-end parti-
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Table 4 The effect of precipitation on the critical resolved shear stress (CRSS) of the three dominant deformation modes predicted by VPSC modelling and the Orowan equation for a precipitate of 125 nm in length. CRSS for deformation mode Basal slip Prismatic slip Twining
As-ext
Aged
0 VPSC
18 MPa 54 MPa 18 MPa
20 MPa 140 MPa 80 MPa
2 MPa 86 MPa 62 MPa
0 Orowan 40 MPa 70 MPa –
cle spacing (I). Using the end-to-end particle spacing (I), the Orowan equation has been used to estimate the hardening on the prismatic and basal planes as a function of precipitate length, Fig. 8b. It is clear that the prismatic plane is strengthened more than the basal plane by this arrangement of rods for edge-type dislocations. If we consider the case of a precipitate length of 125 nm (Table 4), which is close to the case for ageing at 150 ◦ C, the strengthening on the prismatic plane is predicted by the Orowan equation to be 70 MPa, while the strengthening on the basal plane is 40 MPa (see Fig. 8b). From the VPSC modelling, the CRSS on the basal plane is predicted to increase by a value of 2 MPa, and the CRSS for prismatic slip was predicted to increase by 86 MPa. Although the quantitative predictions for the rise in CRSS are different for the two mathematical approaches, it still remains that the needle shaped precipitates strengthen the prismatic slip system more than the basal slip system. It should also be noted that the value for I (and therefore the Orowan strengthening prediction) is strongly effected by the volume fraction term. Increasing the volume fraction above 3.8% for the particle size distribution results in the end-to-end spacing becoming zero, representing a continuous phase. Reducing the volume fraction to below 2.6% yields end-to-end spacing values approximately equal to the inter-particles spacing S. This results in the basal plane being hardened more than the prismatic plane at particle lengths above 125 nm. Let us now consider screw dislocations on the prismatic plane, Fig. 7d. The effective spacing between particles is S, and the particle diameter is D. Applying the Orowan equation (Eq. (1)) we see that the predicted strengthening for a screw dislocation on the prismatic plane is identical to the strengthening predicted for the basal plane. However, in this situation the dislocation must travel the length of the rod before being able to bypass it. The stress required to bow the dislocation between the precipitates remains the same as it travels this length, and is unlikely therefore to increase the CRSS. In reality, it is most likely that any portion of a dislocation that has a screw character will simply cross-slip onto the basal plane in order to bypass precipitates. Taking these two factors into consideration, it appears that the edge dislocations are principally responsible for the increased hardening observed on the prismatic planes after age hardening. Finally, we should consider the possible impact of solid solution softening of the prismatic slip system on these calculations. Akhtar and Teghtsoonian [11] have shown that the addition of Zn into the Mg matrix will harden the basal slip system, but soften the prismatic slip system. At room temperature, their data shows a reduction in the CRSS for prismatic slip of approximately 12.5 MPa for each additional atomic percent of Zn. This is probably a large over-estimate, since the data shown in Ref. [11] appears to be reaching a plateau, and the compositions used in this study exceed those measured in Ref. [11]. However, we can use the data to give an idea of the magnitude of the effect. From the Mg–Zn phase diagram we can estimate that when fully in solid solution, the alloy used here has 1.9 at.%Zn in the matrix. Fully aged, the matrix composition is around 0.7 at.%Zn. Therefore, the increase in the CRSS for prismatic slip resulting from Zn depletion in the matrix of aged specimens can be estimated to be a maximum of 15 MPa. So although this phe-
Fig. 9. Schematic illustration of the interaction of {1 0 1¯ 2} twins with the rod-shaped precipitates formed in this system. See text for further details.
nomenon may account for some of the increased hardening found on the prismatic slip system after ageing, the magnitude of this effect is much smaller than the hardening from the precipitates. 4.3. Precipitate twin interactions The EBSD and optical microscopy data presented in the results section has shown that extensive {1 0 1¯ 2} twinning occurs during compression, but that the twins are smaller and have a lower volume fraction in the precipitate-containing microstructure. This reduces the total volume fraction of twins in the age-hardened condition. These observations suggest that twins can easily form in precipitate-containing alloys, but that their growth is limited. In other words, the {1 0 1¯ 2} twin is growth limited, not nucleation limited in the presence of particles. In a particle-free matrix the {1 0 1¯ 2} twin can easily grow laterally, and in some cases can consume entire grains. In the case of an age-hardened alloy, if the lateral growth is limited then the grain is subject to higher stress because the imposed strain cannot be accommodated by the twin. This high stress state enables the nucleation of new twins within the grain to accommodate applied strain. This accounts for the formation of more twins in the age-hardened condition, and also their smaller size. Clearly, the next question is why should precipitates inhibit twin growth? A schematic representation of {1 0 1¯ 2} twinning and a precipitate are shown in Fig. 9. Since the particle is not sheared during the twinning, as the twinning ledge approaches the particle there will be some back-stress resulting from the rigid particle inhibiting the free shear of the moving twin ledge. This back-stress must be overcome by the applied stress. When the shear takes place at the interface between the matrix and the precipitate, the movement of atoms toward the precipitate must be accommodated by the surrounding material. This is most likely accomplished by basal slip away from the particle/matrix interface. However, it can be seen that basal slip too would be inhibited by the precipitate for this geometry. It might therefore be that the shear is accommodated by basal slip inside the twin, rather than in the parent material. This may also account for the observation of stacking faults (see Fig. 10) within some twins—the stacking faults may help to accommodate the twin shear at the particle/matrix interface. As a matter of interest, stacking faults have also been observed by the authors inside twins in the particle-containing alloy Mg 1.6 wt.%Mn. The need for additional basal slip on a local scale around
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Fig. 10. Transmission electron micrograph of parent (upper) and twin (lower) in specimen aged at 150 ◦ C and deformed to 5% strain in compression. The micrograph is taken on the common 1 1 2¯ 0 zone axis. Parent orientation evident from the alignment of precipitates in the [0 0 0 1] direction. Note stacking faults and basal dislocations in the twinned region.
the precipitates is likely to increase the stress required to form the twin. An additional contribution of the precipitates to the increased CRSS for twinning is through the accommodation of the twinning shear by the surrounding matrix. This is distinct from the accommodation described in the previous paragraph that occurs over the scale of nanometers. Accommodation of large twins microscopically occurs across 10s of micrometers. Observations by Roberts and Partridge [12] have shown that the thickening of the {1 0 1¯ 2} twin in magnesium is accommodated by significant amounts of basal slip. These accommodation mechanisms explain why the twin system is hardened more by precipitation than the basal slip system is. Basal slip is inhibited by precipitates. The {1 0 1¯ 2} twin system is inhibited by the need to shear around particles, in addition to the restriction in the basal slip that accommodates its growth. It therefore follows that if the basal slip system is hardened by some increment, then the twin must be hardened by at least that same amount. From this perspective it appears likely that precipitation will always harden the {1 0 1¯ 2} twin system equal to, or more than, the basal slip system. The final point of discussion regarding twins and precipitates is the observation that the particles do not appear to be rotated by the twinning shear. One might expect that after a twin consumes a particle and its surroundings that the particle too is rotated by this angle. However, rotations were not observed in this study, e.g. Figs. 5 and 10. With the problem of foil warping and poor contrast on the appropriate zone axis, it is difficult to measure small angles in this system. In addition to these microscopical hindrances, the particles formed in these samples do not show the sharp and well-defined edges that other precipitates such Mg17 Al12 do [6]. For these reasons it is difficult to say if there is a genuine rigid body rotation in micrographs such as the one shown in Fig. 5b. However, we can use the stacking faults on the basal planes in the micrograph of Fig. 10 to provide some approximation of the rotation of particles after twinning has occurred. During ageing, the particles form with their long axis parallel to the c-axis of the parent orientation. After {1 0 1¯ 2} twinning, the matrix is rotated by 86.3◦ about 1 1 2¯ 0. If there is no rigid body rotation, there will be a 3.7◦ deviation between the basal plane of the twinned material and the precipitate. However, the precipitate could rotate in response to the twinning shear, and a schematic representation of this is shown in Fig. 11. The full rigid body rotation, assuming the particle shears with the matrix, can be calculated as
follows (see Fig. 11): shear = =
x h
(4)
tan ˇ =
h x
(5)
tan =
x + x = tan ˇ + h
(6)
˛=−ˇ
(7)
where is the twinning shear = 0.13 for {1 0 1¯ 2} twinning in Mg, ˇ the angle between the long axis of the precipitate and the twin plane before twinning (=46.8◦ for the case studied here), and ˛ is the rotation angle due to twinning shear. The angle ˇ between the {1 0 1¯ 2} twin plane and the {0 0 0 1} of the parent = 46.8◦ , and so the full rigid body rotation ˛ = 3.3◦ (note that if the long axis of the precipitate was perpendicular to the twinning plane, then ˇ would be 0◦ , and the full rigid body rotation would be tan−1 = 7.4◦ ). The deviation between the basal plane of the twin and the precipitate is 3.7◦ –3.3◦ = 0.4◦ in the case of a full rigid body rotation. These two possible cases are shown in Fig. 12. The micrograph in Fig. 10 shows stacking faults on the basal plane in the twinned region. These features provide a convenient local scale determination of the existence of a rigid body rotation. If the stacking faults (basal planes) in the twinned matrix are misoriented by about 4◦ compared to the precipitates long-axis then there has been no rigid body rotation of the precipitate. However, if the stacking faults are closely aligned with the precipitates, then it is likely that the full theoretical rotation has occurred during twinning. It can be seen from Fig. 10 that the former is observed experimentally, that the stacking faults are misoriented compared
Fig. 11. Geometry of rigid body rotation of a particle due to twinning shear. See text for further details.
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Fig. 12. Illustration of the misorientation between precipitates and the basal plane of the twin for the two cases of no rotation and full rotation of a particle due to the twinning shear.
to the precipitates. This indicates that there has been negligible rigid body rotation associated with the twinning of the material surrounding these precipitates. During deformation by slip, rigid body rotation of particles with respect to the slip plane is readily observed, e.g. [13]. Slip and twinning both apply a shear to the crystal on a well defined plane and a known direction, but only in the case of twinning does this result in the formation of a region with a different orientation compared to the parent grain. It may be that in the case of twinning the orientation change across the twin boundary introduces sufficient additional slip systems that the material can flow around the particle, negating the need for the particle to rotate. Also, in the case of slip it is probably common for the entire matrix along the length of the precipitate to be deforming, whereas in twinning a shear front propagates from one end of the precipitate to the other. Clearly, examination of the interaction of twins with precipitates of different sizes, morphologies, and crystallographic orientations are needed before we can fully describe how these features of the microstructure effect macroscopic deformation behaviour in metals that mechanically twin. 5. Conclusions The effect of precipitation on the deformation behaviour of a binary Mg–Zn alloy has been studied. The following conclusions have been made: • The yield strength and flow stress were significantly increased by precipitation hardening. The yield point was increased by more than 150 MPa in tension and 60 MPa in compression, through precipitation heat treatments.
• EBSD analysis showed that the alloy age hardened at 150 ◦ C produced a larger number of twins in response to 5% compression, compared to the precipitate-free specimens. These twins in the age-hardened alloy were smaller, and had a lower total volume fraction. • Transmission electron microscopy showed that in response to compressive deformation, the precipitates are not sheared by either slip or twinning activity. The precipitates did not show any rigid body rotation after the twinning shear. • Visco-plastic self-consistent (VPSC) modelling was used to show that the prismatic planes are hardened more by the precipitation than the basal planes. This has been attributed to the small end-to-end spacing between the rod-shaped precipitates at the volume fractions found in this alloy. • VPSC modelling also showed that the {1 0 1¯ 2} twin system was hardened more than the basal slip system by precipitation. This is consistent with the lower work hardening rate and lower twin fraction in age-hardened specimens. This behaviour has been attributed to the need for accommodation of the twinning shear around precipitates, and also macroscopically within the parent grain. • It is proposed that because the {1 0 1¯ 2} twin requires basal slip to accommodate the shape change, this twin type will always be hardened equal to, or more than, the basal slip system in response to precipitation. Acknowledgements The work described in this paper was funded by the Australian Research Council through the Centre of Excellence for Design in Light Metals. The authors would also like to thank R.A. Lebensohn and C.N. Tomé who developed the VPSC5 code and kindly allowed us to use it. Finally, the first author would like to give special thanks to Dr. Dominic Phelan who suggested that counting twins would be a very effective way of showing that there are, in fact, more in one micrograph than another. References [1] W.H. Hosford, The Mechanics of Crystals and Textures Polycrystals, Oxford University Press, 1993. [2] Z. Keshavarz, PhD Thesis, Deakin University (2007). [3] R.E. Reed-Hill, W.D. Robertson, Acta Metall. 5 (1957) 717. [4] J.B. Clarke, Acta Metall. 13 (1965) 1281. [5] J.B. Clarke, Acta Metall. 16 (1968) 141. [6] M.A. Gharghouri, G.C. Weatherly, J.D. Embury, Phil. Mag. A 78 (1998) 1137. [7] J.S. Chun, J.G. Byrne, J. Mater. Sci. 4 (1969) 861. [8] J. Bohlen, M.R. Nurnberg, J.W. Senn, D. Letzig, S.R. Agnew, Acta Mater. 55 (2007) 2101. [9] G.E. Deiter, Mechanical Metallurgy, McGraw-Hill, 1988. [10] E.A. Brandes, G.B. Brook (Eds.), Smithells Light Metals Handbook, ButterworthHeinemann, 1998, p. 150. [11] A. Akhtar, E. Teghtsoonian, Acta Metall. 17 (1969) 1351. [12] E. Roberts, P.G. Partridge, Acta Metall. 14 (1966) 513. [13] P. Bate, W.T. Roberts, D.V. Wilson, Acta Metall. 29 (1981) 1797.