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Application of X-ray microtomography to analysis of cavitation in AZ61 magnesium alloy during hot deformation
Materials Science and Engineering A 528 (2011) 2610–2619
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Application of X-ray microtomography to analysis of cavitation in AZ61 magnesium alloy during hot deformation H.M.M.A. Rashed a , J.D. Robson a,∗ , P.S. Bate a , B. Davis b a b
Materials Science Centre, University of Manchester, Grosvenor Street, Manchester M1 7HS, UK Magnesium Elektron North America, 1001 College Street, P.O. Box 258, Madison, IL 62060, USA
a r t i c l e
i n f o
Article history: Received 21 September 2010 Received in revised form 26 November 2010 Accepted 26 November 2010 Available online 4 December 2010 Keywords: Magnesium alloys Tomography Superplasticity Failure
a b s t r a c t The efficiency of particles in acting as cavity formation sites during hot deformation was investigated for a fine-grained wrought magnesium–aluminium–zinc (AZ series) alloy using X-ray micro tomography. Two methodologies were developed to determine the particle/cavity association from 3-dimensional data, each clearly demonstrating that particles act as a major formation site for cavitation. The particles forming cavities were identified and characterised. It is shown that progressively smaller particles nucleate cavities as strain increases. This is due to concurrent grain growth which reduces the critical particle diameter for cavity nucleation during testing, leading to a continuous cavity nucleation. Particle agglomerates are shown to be particularly potent sites for cavity formation, leading to large and complex shaped cavities even if the individual particles within the agglomerate are below the critical particle diameter for cavity nucleation. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The formability of magnesium alloys, which is poor at room temperature due to limited slip system activity, is greatly enhanced at elevated temperatures. Furthermore, under suitable conditions, many magnesium alloys are capable of superplastic deformation. Formability can be further improved by thermo-mechanical treatments to refine microstructure [1,2] and by addition of appropriate alloying elements [3]. Second phase particles, present in all commercial magnesium alloys either as a result of impurities or deliberate alloying additions, have an important influence on microstructural evolution during hot deformation and hence formability. They may act to pin grain boundaries preventing grain growth [4], or they may provide particle-stimulated nucleation (PSN) sites for recrystallized grains [5]. Alternatively, these particles may be detrimental by developing local stresses surrounding them during deformation, promoting the nucleation of cavities [6]. Cavity formation and coalescence often ultimately limits the strains achievable during severe hot deformation or superplastic forming. Understanding the role of microstructure in controlling cavity nucleation and growth is therefore critical to improve the hot forming performance of magnesium alloys. Lee and Huang have performed an extensive study on growth of cavities in an extruded AZ31 alloy but the sources of cavities remained was not uniquely
∗ Corresponding author. Tel.: +44 1613063560. E-mail address: [email protected] (J.D. Robson). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.11.083
identified [7]. Recent studies have highlighted the role of accommodation processes such as grain boundary sliding during deformation in contributing to cavity formation in an AZ61 alloy [8]. However, the role of particles in contributing to and controlling cavity formation in magnesium alloys during hot deformation remains unclear, and is the focus of the present paper. Traditional 2-dimensional (2D) imaging techniques such as scanning electron microscopy (SEM) have some critical limitations in attempting to correlate cavity characteristics and locations to those of particles. In addition to stereological issues inherent in any sectioning technique that makes it difficult to unambiguously determine any association between cavities and particles, the specimen preparation required for SEM or optical microscopy can also introduce artefacts, such as cavities formed by particle pull-out. Both of these problems can be countered with the aid of the Xray tomography. This allows complete 3-dimensional (3D) data to be obtained for interrogation. Furthermore, no further sample preparation of mechanical test specimens is required prior to Xray tomography, eliminating the chance of introducing artefacts. In this study, X-ray tomography was applied for the first time to determine the relationships between particles and cavity evolution during hot deformation of an aluminium–zinc (AZ) wrought magnesium alloy containing an enhanced number of coarse particles. An important part of this work has been to compare results from alternative methods to interrogate the 3D dataset and provide a quantitative assessment of the influence of particles on cavitation. In this work, sufficient resolution was obtained using laboratory X-rays. However, it is recognized that X-ray tomography performed
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on a synchrotron beam-line offers the potential for imaging cavities and other defects in the very early stages of formation when they are below the resolution limits of laboratory X-ray equipment.
2. Experimental The AZ61 alloy (Al 5.7, Zn 1.02, Mn 1.03, Fe 0.003 and Ni 0.001 wt.%) used in this study, was provided by Magnesium Elektron, UK in chill-cast plate form. This alloy contains a higher concentration of Mn than usual for commercial AZ61, which promotes formation of a higher volume fraction of constituent particles. The alloy was homogenised at 420 ◦ C for 24 h in an argon gas atmosphere and hot rolled at 400 ◦ C from a thickness of 25 mm to 2 mm by a total of 19 passes to obtain a refined microstructure. The rolling was accomplished with an equal compressive strain of 0.12 in each pass and the work-piece was rolled uni-directionally in the first seven passes followed by cross-rolling in the remaining passes. The work-piece was reheated for 5–10 min following each pass since heat was dissipated quickly during the contact with the cold rolls. The sizes of the grains of the alloy in rolled condition were determined from optical micrographs using ImageJ [9] software and the linear intercept method. Specimens for optical microscopy were prepared by standard metallographic methods followed by etching using acetic-picric solution (4.2 g picric acid, 10 ml water, 10 ml acetic acid and 70 ml methanol) for 10–15 s to reveal grain boundaries. Unetched specimens were examined using a Philips XL30 field emission gun scanning electron microscope and energy dispersive X-ray spectroscopy (EDX) was used to measure the composition of the second phase particles in the rolled plates. Tensile specimens were then prepared from the rolled plates, keeping the tensile axis direction along the rolling direction of the final pass, with a gage width of 6.3 mm and length of 12 mm with simple square tag ends (no blend radius at the ends of the gage) and uniaxial tensile tests were performed using a custom-built tensile machine (made by Alcan International Ltd.) containing an electrical resistance-heated furnace chamber. Two types of uniaxial tensile tests were carried out. The first was a perturbed-rate test in which the specimens were deformed to failure at different temperatures ˙ of 5 × 10−4 s−1 (300, 350, 400 and 450 ◦ C) at a base strain rate (ε) with a ±10% variation of nominal strain rate applied for every 0.1 strain step. These tests were used to determine the strain rate sensitivity (m) values at different true strain levels from the slope of true stress–strain (–ε) curves. Details of the process can be found elsewhere [10]. The elongation to failure (ef ) values were determined from the deformed gage length using callipers. Grain sizes at the gage region near the failed surface were also determined after metallographic preparation using ImageJ. The second test type was performed at a fixed temperature of 350 ◦ C to different pre-set strains – ranging from 0.80 to 1.05 – at a constant strain rate of 5 × 10−4 s−1 . These tests were used to study cavity evolution with increasing strain. An area of approximately 1.3 mm2 from the middle of the gage sections of the specimens deformed to different pre-set strains were scanned using an Xradia MicroXCT tomography machine. X-rays are sent from a cone beam source to the rotating sample and the transmitted beams are then recorded by the detector. Full details of the technique are presented elsewhere [11]. The accelerating voltage used was 75 kV, power was 10 W and an optical lens magnification of 20× successfully resolved the features present in the material. Absorption mode was used by keeping the sample stage very close to the detector. During the rotation of the specimen stage from 0 to 180, a total of 723 images were acquired, with radiographs (projected profiles) captured at every 0.25◦ using
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a 50 s exposure time for each radiograph. The collected projections were reconstructed, using Feldkamp–Davis–Kress (FDK) algorithm for cone beam geometry [12], by calculating the spatial distribution of attenuation coefficients of each voxel (volume element). During reconstruction, each voxel was assigned to a specific grey value depending on the average attenuation coefficient of that voxel which was dependent on the attenuation coefficients of matrix, particles and cavities. Particles and cavity regions had distinct levels of grey-values from the matrix material. Matrix material had grey-values within a range of 30k to 36k for the 16 bit data and values smaller and greater than this range corresponded to cavities and particles respectively. The volume of each voxel in the reconstructed tomography data set was 1.22 m3 . 3D images of the particles and cavities were produced in Avizo software [13], after segmenting particles and cavities using the incorporated segmentation module. For quantitative analysis, preprocessing steps were carried out. The raw tomography data were first loaded in ImageJ software. Then, only particle regions and only cavity regions were segmented by applying a threshold to certain grey-values and saved as raw files. A Matlab routine [14] was used to identify and tag particle and cavity regions for analysis. 3. Methods developed for cavitation analysis Two methods were developed to analyse the tomography data and determine the tendency for particle–cavity association: (a) the spatial correlation function and (b) the particle–cavity normalised intersection distribution. Both methods were performed on the same data set since each gives distinct information. The spatial correlation function gives the distribution of spacing (or the probability of finding a given spacing) between particle and cavity voxels and can thus be used to investigate any tendency for clustering of particles and cavities. The normalised intersection distribution is determined by measuring the intersection (overlap) between particles and cavities as the particles are artificially dilated. This provides a measure of the proximity of particle and cavity surfaces, which can be compared against that expected for a random distribution. 3.1. Spatial correlation function A program was developed in Fortran to calculate the particle–cavity correlation function. Correlation is used in statistics to find out the linear association between two events and a correlation function can be used to get the correlation of two features as a function of distance; i.e., the relative probability of two features being separated by a given distance can be determined. Consider single regions of cavity and particle (xc and xp ) which are separated by a vector x (Fig. 1(a)). Now, the relative probability can be calculated for a given value of x that there is a particle and cavity with separation x. Consider a function defined for particles, p(x), which is equal to one if there is a particle at position x or zero if there is not. A similar function, c(x), can be defined pertaining to cavities. The un-normalised particle–cavity correlation is given by:
f (x) =
p(x) · c(x + x)dx
(1)
˚
where ˚ is the spatial domain over which the integral is being evaluated. To get the normalised, relative probability of a particle cavity separation of x, the function f needs to be divided by the product of fractions of particles and cavities. Using Fast Fourier Transform, the above mentioned convolution integral can be solved efficiently as: F = P · C∗
(2)
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Fig. 1. (a) A schematic representation of the method applied in correlation estimation. Positions of a particle (xp ) and a cavity (xc ) in 3D space are marked and the distance, x, between them is shown. (b) A series of schematic drawings showing the steps in calculating the particle–cavity intersections by dilation: (i) shows the particle and cavity regions; (ii) shows the dilation of the particle regions by the dashed circles; (iii) shows the intersections of the dilated particle and cavity regions and (iv) shows only the intersected regions (marked 1 and 2).
where F, P and C are the Fourier transforms of f, p and c, respectively, and * denotes the complex conjugate. To interpret the result, f can be plotted as a function of radius: r = |x| = (x12 + x22 + x32 )
1/2
(3)
where x12 , x22 , x32 are the components of x in three orthogonal directions defined as the Euclidean distance between two points in 3D space. 3.2. Particle–cavity normalised intersection distribution To determine the fraction of particle and cavity voxels in contact, a dilation and intersection checking routine was developed in Matlab. 3D arrays defining the coordinates of all particle and cavity voxels were first generated. After constructing the 3D arrays, particle regions were dilated by a predefined distance and a check for cavity regions intersecting the dilated particle regions was performed. The number of intersected regions was then divided by the total number of cavity regions to get normalised data for each predefined dilation. A schematic presentation of the steps followed is shown and explained in Fig. 1(b). 4. Results
only particles greater than 1.8 m in size due to the resolution limits inherent in the data. The size distribution was estimated from the longest major axis of each particle region, considering each region as a spheroid, and this distance will be denoted as the diameter hereafter. Approximately 31,000 particles of various sizes were detected after removing single voxels present in the volume to reduce noise of data and the corresponding size distribution is plotted in Fig. 3 as a probability distribution function of particle diameter (dp ), using the Epanechnikov kernel [17]. It is apparent from the plot that the peak corresponds to a mode particle size of approximately 3 m, with 4% of the particles in the range 10–40 m. These apparently very large particles were actually agglomerates of smaller particles, as will be shown later. The results plotted in Fig. 4(a) show the true stress–strain curves from specimens tested at different temperatures with strain rate perturbations around a base rate of 5 × 10−4 s−1 . Average strain rate sensitivity (m) values derived from these data, annotated on the plot, varied from 0.24 to 0.33, but showed no systematic variation with temperature. As expected, the flow stress decreased with an increase of test temperature. The elongation to failure was highest at 400 ◦ C. At 450 ◦ C, extensive grain growth together with cavity development led to a slightly lower strain rate sensitivity and less resistance to diffuse necking hindering further enhancement of the
4.1. Hot deformation properties Optical micrographs of the as-rolled material are shown in Fig. 2. Recrystallization during hot rolling resulted in an equiaxed microstructure with an average grain size of approximately 8 m. Second phase particles were distributed mostly along the recrystallized grain boundaries, likely to be a result of boundary pinning by the particles. Compositions of these particles were determined using EDX and at least 30 particles were analysed. The extrapolation method was used to determine the compositions from EDX data to diminish any effect of matrix magnesium [15]. Using the JMatPro thermodynamic software [16] and the MgData database, the composition of the stable phases were also determined at different temperatures and Al11 Mn4 was predicted as the dominant stable precipitate phase at the homogenisation temperature under equilibrium condition. Experimental measurements showed the particles contained approximately 71 at.% Al and 28 at.% Mn, with minor content (0.65 at.%) of Fe, which was close to the predicted Al11 Mn4 stoichiometry. From the tomography data set, a sub-volume of 500 m × 500 m × 700 m was cropped, and the volume fractions and size distribution of particles were measured. This analysis considers
Fig. 2. An optical micrograph of hot rolled microstructure. A heterogeneous mixture of refined equiaxed grains is evident.
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Table 1 Grain sizes at the deformed gage region at different temperatures. Errors are shown as the 95% confidence level (mean ± 2× standard error).
Fig. 3. A semi-log plot of the probability distribution function of the particle diameter (dp ). The peak corresponds to the maximum occurrence of sizes at nearly 2–3 m.
elongation to failure at this high temperature. The sizes of the grains were measured from the gage regions of the failed specimens and are shown in Table 1. A considerable growth of the grains, except at 300 ◦ C, was observed during deformation. The apparent activation energy (Qapp ) of deformation can be calculated from the flow stress dependency at elevated temperature using the following equation [18]:
Q
ε˙ = A n exp −
RT
mQ + m ln A1 + mε˙ RT
350 ◦ C
400 ◦ C
450 ◦ C
10.96 ± 1.96
15.21 ± 2.64
20.02 ± 2.68
35.32 ± 5.90
near the fracture surface. Macroscopically, there was very little evidence of neck formation prior to failure; though at 350 and 400 ◦ C, the reduction of area was comparatively low signifying most cavitation occurred at these temperature. It is notable that at 300 ◦ C, there was no large cavity coalescences near the fracture surface and at 450 ◦ C, the specimen failed by coupled action of cavitation and diffuse necking. Fig. 5 shows the evolution of the cavities in the unetched SEM images of the gage regions close to the failed surface at different pre-set strain values deformed at 350 ◦ C under a constant strain rate of 5 × 10−4 s−1 . Several characteristics are common at all strains. There are some single cavities appearing close to particles (marked A). However, a similar number of isolated cavities is observed which are not obviously formed close to any particles (marked B). With an increase in strain, more coalesced cavities are developed in the microstructure (marked C). It is obvious from these images that the number density of cavities had increased during deformation to a higher strain. The existence of small cavities, even at the strain of 1.05, implies a continuous nucleation of cavities during deformation. The SEM observations suggest that particles act as a source of formation of cavities but do not allow a quantitative determination of particle/cavity correlation to be made due to sectioning effects.
(4) 4.2. Analysis of cavities
After rearranging, ln =
300 ◦ C
(5)
where A and A1 (= 1/Am ) are constants, n = (1/m) is the stress exponent and R is the molar gas constant. The peak flow stresses of the alloys at different temperatures were used to plot ln against 1000/RT to obtain the slope mQ (Fig. 4(b)). Using this value, the activation energies were determined from the average strain rate sensitivity values of the alloy at different temperatures. The estimated Qapp (by averaging the activation energies at different temperatures) was 89.7 ± 14.8 kJ mol−1 . Failed specimens were observed optically and found to contain a high fraction of large cavities, except at 300 ◦ C, near to the fracture surface. Strong evidence for cavity coalescence was observed
X-ray micro tomography was performed on the deformed regions of the specimens tested at 350 ◦ C from 0.80 to 1.05 strains, with tomographs recorded from the mid-length position along the gage length. The ambiguity of particle–cavity association in a 2D section, showed in Fig. 5, can be illustrated using the tomography data by creating an imaginary 2D surface in the 3D volume. Fig. 6(a) shows an example of such a surface for the specimen strained up to 1.05 (95% of the failure strain). In this 2D section, three cavities (A, B and C) appear not to be connected with any particles. However, the tomography data permits investigation of the 3D volume just below the surface and it can be seen that when this is done cavity regions A and B are indeed connected to particles (Fig. 6(b)), although cavity C is not.
Fig. 4. (a) True stress–strain plots for temperatures 300–450 ◦ C at the strain rate of 5 × 10−4 s−1 and corresponding strain rate sensitivity values (m) are shown. (b) A plot of logarithmic flow stress against temperature to determine the activation energy of deformation. The obtained slope is shown by the linear equation.
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Fig. 5. SEM images of the gauge surfaces of the specimens pre-strained to (a) 0.80, (b) 0.90, (c) 1.00 and (d) 1.05 at 350 ◦ C under a constant strain rate of 5 × 10−4 s−1 . Cavities are marked as A if they are close to any particles or B if they are located far from particles. Large coalesced cavities are marked as C.
4.2.1. Qualitative analysis of tomography data A series of 3D images were extracted from the 3D volumes recorded for material tested to a strain of 1.05. Fig. 7(a) shows the distribution of particles and cavities in a sub-volume of 350 m × 430 m × 400 m. The particles were found to be distributed throughout the whole volume, with evidence of some clustering and alignment of particle stringers in the rolling direction (parallel to the tensile axis). Regions of intense cavitation appear
to be associated with regions containing the greatest number of particles. Like the particles, the cavities are also distributed in illdefined stringers aligned along the tensile axis (Fig. 7(b)). Many of the cavities have complex morphologies that may be a result of cavity coalescence. Most of the cavities are not equiaxed, and the long axis is generally near parallel to the tensile axis. Fig. 8 shows magnified images of some typical cavity/particle features. Two cavities (marked A and B) were observed to have
Fig. 6. (a) A 2D surface view of a random area of the 3D volume of AZ61H at ε = 1.05. A, B and C cavity regions are identified not to be connected with any particle. (b) But, if the view is transformed into a 3D view by extending the depth below the surface, particles are found to be attached to the cavity regions of A and B. Cavity region C is still observed to be not connected with any particle.
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Fig. 7. Reconstructed 3D sub-volumes of 350 m × 430 m × 400 m of AZ61H at ε = 1.05 showing (a) the particles and the cavities, and (b) only cavities.
emerged from the particle–matrix interface of a single particle and have grown fastest in the direction of the tensile axis. Another cavity (marked C), formed from a particle in a plane behind that of the first can be seen to have grown towards and coalesced with cavity B. The original morphology of the individual cavities, which is roughly cylindrical with a long axis aligned close to the tensile axis, is preserved. More advanced coalescence of a number of cavities can change the cavity morphology, making it more complex, and examples of this is shown in Fig. 8(b). Here, several cavities have coalesced together and formed a large cavity of irregular shape. The large cavity has a roughly oblate spheroidal morphology, but with several branches in different directions that presumably are remnants of the original constituent cavities. Different sizes of particles were observed to act as the cavity formation sites. Most of the particles could be classified to be spheroidal in shape. Qualitatively, it was observed that agglomerations of small particles (Fig. 9(a)) were more potent in causing extensive cavitation than single large particles, with regions containing high cavity fractions and extensive coalesced cavities (Fig. 9(b)). The tomography data (Fig. 9(a)) suggests there is an
interconnected network of particles. However, it should be bourne in mind that particles that are within the spatial resolution distance (1.22 m3 ) from each other may erroneously be connected in the image rendering process. The SEM observations suggest that features such as that observed in Fig. 9(a) consist of agglomerations of isolated particles with separation less than the spatial resolution of the micro-tomography. However, effectively these agglomerations do seem to behave as one very large interconnected “super-particle” and the constraint placed on deformation about such regions appears to be responsible for the high levels of local cavitation. Given the high number density of particles capable of initiating cavitation, it was always found to be the case that the largest cavities were formed by cavity coalescence. Cavity shape tended to evolve as the cavities grew. The smallest cavities were near spherical in shape, consistent with a diffusion controlled growth mechanism. Larger cavities tended to become elongated in the direction of the tensile axis, indicative of plasticity controlled growth. The largest cavities have complex morphologies associated with coalescence as already discussed.
Fig. 8. 3D images from a specimen deformed to a strain of 1.05 at 350 ◦ C showing (a) the growth of three cavities emerging from two particles and coalescences of them and (b) a large cavity, exhibiting branches in different directions, formed by the coalescences of smaller cavities.
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Fig. 9. 3D rendered images showing (a) an agglomeration of particles and (b) the effect of agglomeration on cavitation. These particles nucleated closely-spaced cavities which have coalesced to form a large cavity. Table 2 Cavity volume fractions at 350 for different pre-set strains.
size, and this is attributed to extensive cavity coalescence in this strain interval.
Strain
0.8
0.9
1
1.05
Cavity volume fractions, %
0.18
0.47
0.49
0.9
4.2.2. Size distributions of cavities From the raw data, a sub-volume of 500 m × 500 m × 700 m was cropped, and the volume fractions and size distributions of cavities were measured. The cavity volume fractions are shown in Table 2. At the largest strain, the cavity volume fraction approached 1%, but it should be noted that this is an average over the whole gage length. All the size distributions were estimated from the longest major axis (dcav ) of each cavity region, a similar approach as applied to particle size estimation. About 19,000 cavities were detected in the specimen deformed to a strain of 1.05, while only 7500 were detected at the strain of 0.80. The cavity size distributions at different strains are shown in Fig. 10. For all strains, the mode cavity size is similar and is approximately 3 m. An important feature of size distributions is that the proportion of small cavities (<5 m) has decreased during straining. However, the number of small cavities still increases continuously with strain because the total cavity number increases by a factor of 3 between strains of 0.80 and 1.05. Fig. 10 also reveals that between strains of 1.00 and 1.05 there is a large increase in the proportion of cavities greater than 20 m in
Fig. 10. Probability distribution plots of the diameters (dcav ) of cavities for different levels of deformation.
4.3. Measurements of association of particles and cavities Using Matlab and Fortran routines (discussed in Section 3), two relationships between particles and cavities were established for a sub-volume of 500 m × 500 m × 700 m to be compared with random sets of particle and cavity regions contained in a subvolume of same dimension. If cavities were not associated with particles, the position of the cavities would be random, i.e., no preferential location for cavities close to particles would occur. In view of this, random coordinates of the particle and cavity regions were generated in Matlab followed by tagging and analysing in a procedure identical to the one carried out for experimental data. The sizes of the random regions were chosen to mimic the experimental data. From the correlation plot (Fig. 11(a)), the radial distance between particle and cavity voxels is shown up to maximum distance of 50 m. A peak was obtained at a radial distance of approximately 5–8 m which corresponds to the occurrence of maximum number of pairs of voxels (of particles and cavities) separated from each other by that distance. The correlation plot does not provide the information on particle/cavity association in a straightforward way since it considers each voxel present in the sub-volume instead of regions of particles or cavities (here, the term region means a particle or cavity containing connected voxels of similar type). To understand the origin of the peak, a particle of 3 m and a cavity of 3 m can be considered since the mode size of the particle and cavity regions was close to 3 m. In this case, the distance between voxels in a particle and voxels in a connecting cavity would vary from the minimum distance between two voxels (∼1 m) to 6 m, the distance from a voxel at the far side of the particle to that at the far side of the connected cavity. The mean separation will depend on the particle and cavity shape, but will lie between these extremes (and would be 3.18 m for perfectly spherical particles and cavities). Given that this distance will increase for non-spherical particles and cavities, the measured peak is indicative of a preference for cavities and particles to be in close association. On the other hand, if the distribution of cavities is random, no such peak is observed. In contrast to the correlation method, the dilation-andintersection method considers regions of particles and cavities containing more than one voxel in each type of region. Calculated by this method, nearly 90% of the cavities (Fig. 11(b)) had their edges connected with particle edges by a single voxel distance. With an increase of distance from particle edges, the fraction of cavities
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Fig. 11. (a) A semi-log correlation function (f(p–c)) plot showing the distribution between particle (p) and cavity (c) voxels separated by a pre-defined radial distance, r. (b) The number of overlaps of cavity and particle regions (Nintn ) normalised by the total number of cavities (Ncav ) in the sub-volume are shown. The dashed lines show probable distributions if the particles and cavities are randomly located in the sub-volume.
attached to particles approaches to unity. This implies that though some cavities (approximately 10%) were not physically attached to any particles, they were located a short distance from particles. Now, for a random distribution of cavities, a parabolic shape curve is obtained with only 1% of the total cavities at a distance of 1.22 m from particle edges compared to the 90% intersections obtained at 1.22 m distance in the experimental data. Finally, only the particles with neighbouring cavities were identified in a cropped sub-volume and their frequencies were recorded for a bin width of 1 m. The estimated number of particles truly attached to cavities (Np−c ) for each bin width was normalised by the number of particles (Np ) present in that size range in the cropped sub-volume. Fig. 12 shows two distributions of particles at the strains of 0.90 and 1.05 plotted using this methodology. At a strain of 0.90, a greater fraction of particles larger than 10 m were associated with cavities compared to small particles (<10 m). However, not all the large particles had connected cavities. Nevertheless, at a strain of 1.05, more than 50% of the large particles were associated with cavities and the contribution in assisting cavity formation by the small particles (<10 m) was increased by nearly 4 times compared to that at the strain of 0.90. These results confirm that nucleation of cavities is a continuous process and large particles,
generally, form more cavities prior to small particles. Interestingly, this figure also shows that even at the highest strain not all the large particles form cavities. 5. Discussion 5.1. Hot deformation behaviour The m-values showed a dependency on temperature, increasing to a maximum at 400 ◦ C (m = 0.33) and dropping slightly at 450 ◦ C (m = 0.32). This was directly related to the grain growth that occurred during deformation and the extensive grain growth (Table 1) at 450 ◦ C is expected to be the cause of the reduction in average m value at this temperature. Previous studies of AZ31 [7] with a similar starting grain size led to m values greater than measured here (0.30–0.55) in the temperature range 200–400 ◦ C. Greater elongations, up to 400% [19] were measured in AZ31 deformed under similar conditions to the present work, where GBS and limited grain growth were observed. AZ31 contains far fewer coarse particles than the AZ61H used in the present work. Microstructural instability occurring from concurrent grain growth and particle induced cavitation are expected to be the cause of the lower m reported here. The measured Qapp is close to the activation energy for grain boundary diffusion of magnesium (QGB = 92 kJ mol−1 ) [18] for the temperature range investigated. The estimated stress exponent (n) values, determined using the relation n = 1/m, ranged from 3.00 to 4.20. In previous studies of an AM60 Mg alloy, a value of n, close to 2, was shown to be consistent with grain boundary sliding (GBS) as the dominating deformation mechanism, with an m value of 3 or above indicating a combination of slip and GBS [20]. This implies that in the current study GBS and slip occur and grain boundary diffusion acts as the accommodation process of deformation. 5.2. Cavitation characteristics
Fig. 12. Plots of the size distributions of particles associated with cavities (N(p–c) ) normalised by the total number of particles (Np ) at each size group at the strain of (a) 0.90 and (b) 1.05.
Both the correlation and the dilation methods applied to the 3D tomography data show that there is a strong association of cavities with particles after deformation at 350 ◦ C For example, Fig. 11(b) demonstrates that approximately 90% cavities are associated directly with particles. During deformation, a local discontinuity in strain develops across the particle/matrix interface, leading to a concentration of stress in the surrounding area. If this stress fails to relax quickly, cavity can nucleate at the boundary.
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Table 3 Materials constants and parameters used in the current study [18]. ˝ (m3 )
␦Dgb (m3 s−1 )
k (kJ mol−1 )
2.33 × 10−28
5 × 10−12
1.38 × 10−23
Grain boundary particles limit the stress–relief process and become an effective source of cavity formation. The competition between stress concentration and relaxation mechanisms leads to a critical particle diameter (dpcrit ) below which a particle will not assist in cavity formation. This supposition leads to the consideration of a critical diffusion length below which local stresses can be relaxed quickly. Needleman and Rice [21], based on grain boundary diffusion, proposed an expression for the critical particle diameter
dpcrit
=
8˝ıDgb kT ε˙
1/3 (6)
where ˝ is the atomic volume and k is Boltzmann’s constant. The maximum flow stress () was 30 MPa at 350 ◦ C. Using the values of the parameters from Table 3, the critical particle diameter was approximately 10 m at 350 ◦ C. This value is three times higher than the value predicted by Mussi et al. [22] for a AZ91 alloy at 250 ◦ C under a strain rate of 10−3 s−1 . However, since nucleation of a cavity depends on diffusional processes, the critical diffusion length required to relax stress concentration varies strongly with test parameters. In the current study, a significant fraction (4%) of particles are greater than dpcrit and thus would be expected to contribute to cavity formation. However, the tomography data also reveals that particles smaller than the predicted dpcrit also nucleated cavities (Fig. 12). A local increase in stress is expected due to concurrent growth of grains. Such an increase in stress allows comparatively small cavities to become stable after formation [23]. Therefore, NR cannot truly reflect the minimum size of a particle required to nucleate a cavity if an alloy experiences grain growth during deformation. As a consequence, at higher strains, particles much smaller than NR were associated with cavities. The current results are consistent with the supposition that cavitation initially occurs at larger particles. As the grains grow, cavities of small size can become stable after nucleation and dpcrit determined by Needleman and Rice does not reflect the actual critical particle diameter. This leads to the observed continuous nucleation of cavities at progressively smaller particles as grain growth advances. It is noteworthy that if relief of stress concentration is maintained by grain boundary diffusion throughout deformation and grain growth is prevented, the probability of failure by cavitation may be very low, since the critical particle size will remain large (and may be above the size of the largest particles present). This situation was observed in AZ91 by Mussi et al. [22], where the grain size remained small throughout deformation and grain boundary diffusion was effective in relieving stress concentrations around particles. In some random regions in the volume, agglomeration of the particles was observed (Fig. 9a). Agglomeration had a significant effect on formation of a cavity. Cavities nucleated from closely spaced particles coalesce rapidly, resulting in formation of a large cavity. If the spacing of the agglomerated particles is less than the critical particle diameter required for nucleation of a cavity, nucleation may occur from a particle (within the cluster) having a diameter less than the critical diameter since the relaxation of local stress is hindered by the surrounding particles. Therefore, the degree of agglomeration is an important factor in an alloy containing coarse particles since particles smaller than the critical particle
diameter required for nucleation of a cavity may assist in cavity formation depending on spacing of the agglomerated particles. Lee and Huang [7] had argued that nucleation of cavities was not a continuous process after observing a plateau in the total number density of cavities after a certain strain. On the other hand, in the current study, formation of cavities was a continuous process since the number density of cavities increased continuously up to the failure strain. This difference is likely to be due to the much higher fraction of coarse to fine particles in the AZ61H alloy studied here. As already discussed, it is the activation of progressively smaller particles as effective cavity nucleation sites due to grain growth which leads to the observed continuous nucleation of cavities. 6. Conclusions A high manganese variant of AZ61 alloy, with a grain size of 8 m, was studied during hot deformation in the range 300–450 ◦ C. This alloy contained a continuous distribution of Al11 Mn4 particles of mode size 3 m, with some large particle clusters present greater than 10 m in size. The following conclusions were drawn: • Strain rate sensitivity values varied from 0.24 to 0.33 with the highest value obtained at 400 ◦ C. The dominant diffusion process expected during deformation was estimated as grain boundary diffusion. • At 300 ◦ C and 450 ◦ C, the failure of the material occurred by neck formation. In the later case, a diffuse neck coupled with cavity development was observed. At 350 and 400 ◦ C, cavity dominated failure was observed. • X-ray micro tomography was used to provide a detailed study of cavitation during deformation at 350 ◦ C. Particles were identified as the prime source of cavity formation. 3D rendered images revealed cavities are closely connected with particles and two methodologies were developed to quantify the association of particles and cavities. • The critical particle diameter for cavity formation varied depending on grain size. Smaller particles become increasingly effective as cavity formation as the grain size increases and an increase in flow stress allowed smaller cavities to become stable. • Cavity nucleation was identified as a continuous process throughout deformation at 350 ◦ Cwhich was dependent on the availability of cavity formation sites. • The degree of agglomeration of particles is an influential factor in controlling cavitation, since even small particles were observed to nucleate cavities when surrounded by other particles that inhibit stress relaxation processes. Acknowledgements The work was performed with support from the EPSRC portfolio partnership on Light Alloys for Environmentally Sustainable Transport (EP/D029201/1) and Magnesium Elektron, UK. References [1] W.J. Kim, S.I. Hong, Y.S. Kim, S.H. Min, H.T. Jeong, J.D. Lee, Acta Materialia 51 (2003) 3293–3307. [2] N. Stanford, M.R. Barnett, Journal of Alloys and Compounds 466 (2008) 182–188. [3] F. Zarandi, G. Seale, R. Verma, E. Essadiqi, S. Yue, Materials Science and Engineering A 496 (2008) 159–168. [4] S.W. Xu, N. Matsumoto, S. Kamado, T. Honma, Y. Kojima, Materials Science and Engineering A 523 (2009) 47–52. [5] J.D. Robson, D.T. Henry, B. Davis, Acta Materialia 57 (2009) 2739–2747. [6] A.H. Chokshi, A.K. Mukherjee, Acta Metallurgica 37 (1989) 3007–3017. [7] C.J. Lee, J.C. Huang, Acta Materialia 52 (2004) 3111–3122. [8] Y. Takigawa, J.V. Aguirre, E.M. Taleff, K. Higashi, Materials Science and Engineering A 497 (2008) 139–146. [9] M. Abramoff, P. Magelhaes, S. Ram, Biophotonics International 11 (2004) 36–42.
H.M.M.A. Rashed et al. / Materials Science and Engineering A 528 (2011) 2610–2619 [10] P.S. Bate, F.J. Humphreys, N. Ridley, B. Zhang, Acta Materialia 53 (2005) 3059–3069. [11] S.R. Stock, International Materials Reviews 53 (2008) 129–181. [12] L.A. Feldkamp, L.C. Davis, J.W. Kress, Journal of the Optical Society of America A 1 (1984) 612–619. [13] VSG, Avizo 5.1 3D Visualization Software User Manual, VSG, Burlington, MA, 2010, http://www.vsg3d.com. [14] T. J. Marrow, Personal communication, University of Manchester, 2009. [15] G. Lorimer, G. Cliff, P. Champness, C. Dickinson, F. Hasan, P Kenway, in: D. Williams, D. Joy (Eds.), Analytical Electron Microscopy, San Francisco Press, San Francisco, 1984, pp. 153–156. [16] N. Saunders, Z. Guo, X. Li, A. Miodownik, J.-P. Schillé, JOM 55 (2003) 60–65.
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[17] B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman & Hall/CRC, London, 1992. [18] H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps: The Plasticity Creep of Metals and Ceramics, Pergamon Press, Oxford, 1982. [19] R. Panicker, A.H. Chokshi, R.K. Mishra, R. Verma, P.E. Krajewski, Acta Materialia 57 (2009) 3683–3693. [20] J. del Valle, O. Ruano, Acta Materialia 55 (2007) 455–466. [21] A. Needleman, J.R. Rice, Acta Metallurgica 28 (1980) 1315–1332. [22] A. Mussi, J.J. Blandin, L. Salvo, E.F. Rauch, Acta Materialia 54 (2006) 3801–3809. [23] N. Ridley, D. Livesey, A. Mukherjee, Journal of Materials Science 19 (1984) 1321–1332.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Application of X-ray microtomography to analysis of cavitation in AZ61 magnesium alloy during hot deformation H.M.M.A. Rashed a , J.D. Robson a,∗ , P.S. Bate a , B. Davis b a b
Materials Science Centre, University of Manchester, Grosvenor Street, Manchester M1 7HS, UK Magnesium Elektron North America, 1001 College Street, P.O. Box 258, Madison, IL 62060, USA
a r t i c l e
i n f o
Article history: Received 21 September 2010 Received in revised form 26 November 2010 Accepted 26 November 2010 Available online 4 December 2010 Keywords: Magnesium alloys Tomography Superplasticity Failure
a b s t r a c t The efficiency of particles in acting as cavity formation sites during hot deformation was investigated for a fine-grained wrought magnesium–aluminium–zinc (AZ series) alloy using X-ray micro tomography. Two methodologies were developed to determine the particle/cavity association from 3-dimensional data, each clearly demonstrating that particles act as a major formation site for cavitation. The particles forming cavities were identified and characterised. It is shown that progressively smaller particles nucleate cavities as strain increases. This is due to concurrent grain growth which reduces the critical particle diameter for cavity nucleation during testing, leading to a continuous cavity nucleation. Particle agglomerates are shown to be particularly potent sites for cavity formation, leading to large and complex shaped cavities even if the individual particles within the agglomerate are below the critical particle diameter for cavity nucleation. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The formability of magnesium alloys, which is poor at room temperature due to limited slip system activity, is greatly enhanced at elevated temperatures. Furthermore, under suitable conditions, many magnesium alloys are capable of superplastic deformation. Formability can be further improved by thermo-mechanical treatments to refine microstructure [1,2] and by addition of appropriate alloying elements [3]. Second phase particles, present in all commercial magnesium alloys either as a result of impurities or deliberate alloying additions, have an important influence on microstructural evolution during hot deformation and hence formability. They may act to pin grain boundaries preventing grain growth [4], or they may provide particle-stimulated nucleation (PSN) sites for recrystallized grains [5]. Alternatively, these particles may be detrimental by developing local stresses surrounding them during deformation, promoting the nucleation of cavities [6]. Cavity formation and coalescence often ultimately limits the strains achievable during severe hot deformation or superplastic forming. Understanding the role of microstructure in controlling cavity nucleation and growth is therefore critical to improve the hot forming performance of magnesium alloys. Lee and Huang have performed an extensive study on growth of cavities in an extruded AZ31 alloy but the sources of cavities remained was not uniquely
∗ Corresponding author. Tel.: +44 1613063560. E-mail address: [email protected] (J.D. Robson). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.11.083
identified [7]. Recent studies have highlighted the role of accommodation processes such as grain boundary sliding during deformation in contributing to cavity formation in an AZ61 alloy [8]. However, the role of particles in contributing to and controlling cavity formation in magnesium alloys during hot deformation remains unclear, and is the focus of the present paper. Traditional 2-dimensional (2D) imaging techniques such as scanning electron microscopy (SEM) have some critical limitations in attempting to correlate cavity characteristics and locations to those of particles. In addition to stereological issues inherent in any sectioning technique that makes it difficult to unambiguously determine any association between cavities and particles, the specimen preparation required for SEM or optical microscopy can also introduce artefacts, such as cavities formed by particle pull-out. Both of these problems can be countered with the aid of the Xray tomography. This allows complete 3-dimensional (3D) data to be obtained for interrogation. Furthermore, no further sample preparation of mechanical test specimens is required prior to Xray tomography, eliminating the chance of introducing artefacts. In this study, X-ray tomography was applied for the first time to determine the relationships between particles and cavity evolution during hot deformation of an aluminium–zinc (AZ) wrought magnesium alloy containing an enhanced number of coarse particles. An important part of this work has been to compare results from alternative methods to interrogate the 3D dataset and provide a quantitative assessment of the influence of particles on cavitation. In this work, sufficient resolution was obtained using laboratory X-rays. However, it is recognized that X-ray tomography performed
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on a synchrotron beam-line offers the potential for imaging cavities and other defects in the very early stages of formation when they are below the resolution limits of laboratory X-ray equipment.
2. Experimental The AZ61 alloy (Al 5.7, Zn 1.02, Mn 1.03, Fe 0.003 and Ni 0.001 wt.%) used in this study, was provided by Magnesium Elektron, UK in chill-cast plate form. This alloy contains a higher concentration of Mn than usual for commercial AZ61, which promotes formation of a higher volume fraction of constituent particles. The alloy was homogenised at 420 ◦ C for 24 h in an argon gas atmosphere and hot rolled at 400 ◦ C from a thickness of 25 mm to 2 mm by a total of 19 passes to obtain a refined microstructure. The rolling was accomplished with an equal compressive strain of 0.12 in each pass and the work-piece was rolled uni-directionally in the first seven passes followed by cross-rolling in the remaining passes. The work-piece was reheated for 5–10 min following each pass since heat was dissipated quickly during the contact with the cold rolls. The sizes of the grains of the alloy in rolled condition were determined from optical micrographs using ImageJ [9] software and the linear intercept method. Specimens for optical microscopy were prepared by standard metallographic methods followed by etching using acetic-picric solution (4.2 g picric acid, 10 ml water, 10 ml acetic acid and 70 ml methanol) for 10–15 s to reveal grain boundaries. Unetched specimens were examined using a Philips XL30 field emission gun scanning electron microscope and energy dispersive X-ray spectroscopy (EDX) was used to measure the composition of the second phase particles in the rolled plates. Tensile specimens were then prepared from the rolled plates, keeping the tensile axis direction along the rolling direction of the final pass, with a gage width of 6.3 mm and length of 12 mm with simple square tag ends (no blend radius at the ends of the gage) and uniaxial tensile tests were performed using a custom-built tensile machine (made by Alcan International Ltd.) containing an electrical resistance-heated furnace chamber. Two types of uniaxial tensile tests were carried out. The first was a perturbed-rate test in which the specimens were deformed to failure at different temperatures ˙ of 5 × 10−4 s−1 (300, 350, 400 and 450 ◦ C) at a base strain rate (ε) with a ±10% variation of nominal strain rate applied for every 0.1 strain step. These tests were used to determine the strain rate sensitivity (m) values at different true strain levels from the slope of true stress–strain (–ε) curves. Details of the process can be found elsewhere [10]. The elongation to failure (ef ) values were determined from the deformed gage length using callipers. Grain sizes at the gage region near the failed surface were also determined after metallographic preparation using ImageJ. The second test type was performed at a fixed temperature of 350 ◦ C to different pre-set strains – ranging from 0.80 to 1.05 – at a constant strain rate of 5 × 10−4 s−1 . These tests were used to study cavity evolution with increasing strain. An area of approximately 1.3 mm2 from the middle of the gage sections of the specimens deformed to different pre-set strains were scanned using an Xradia MicroXCT tomography machine. X-rays are sent from a cone beam source to the rotating sample and the transmitted beams are then recorded by the detector. Full details of the technique are presented elsewhere [11]. The accelerating voltage used was 75 kV, power was 10 W and an optical lens magnification of 20× successfully resolved the features present in the material. Absorption mode was used by keeping the sample stage very close to the detector. During the rotation of the specimen stage from 0 to 180, a total of 723 images were acquired, with radiographs (projected profiles) captured at every 0.25◦ using
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a 50 s exposure time for each radiograph. The collected projections were reconstructed, using Feldkamp–Davis–Kress (FDK) algorithm for cone beam geometry [12], by calculating the spatial distribution of attenuation coefficients of each voxel (volume element). During reconstruction, each voxel was assigned to a specific grey value depending on the average attenuation coefficient of that voxel which was dependent on the attenuation coefficients of matrix, particles and cavities. Particles and cavity regions had distinct levels of grey-values from the matrix material. Matrix material had grey-values within a range of 30k to 36k for the 16 bit data and values smaller and greater than this range corresponded to cavities and particles respectively. The volume of each voxel in the reconstructed tomography data set was 1.22 m3 . 3D images of the particles and cavities were produced in Avizo software [13], after segmenting particles and cavities using the incorporated segmentation module. For quantitative analysis, preprocessing steps were carried out. The raw tomography data were first loaded in ImageJ software. Then, only particle regions and only cavity regions were segmented by applying a threshold to certain grey-values and saved as raw files. A Matlab routine [14] was used to identify and tag particle and cavity regions for analysis. 3. Methods developed for cavitation analysis Two methods were developed to analyse the tomography data and determine the tendency for particle–cavity association: (a) the spatial correlation function and (b) the particle–cavity normalised intersection distribution. Both methods were performed on the same data set since each gives distinct information. The spatial correlation function gives the distribution of spacing (or the probability of finding a given spacing) between particle and cavity voxels and can thus be used to investigate any tendency for clustering of particles and cavities. The normalised intersection distribution is determined by measuring the intersection (overlap) between particles and cavities as the particles are artificially dilated. This provides a measure of the proximity of particle and cavity surfaces, which can be compared against that expected for a random distribution. 3.1. Spatial correlation function A program was developed in Fortran to calculate the particle–cavity correlation function. Correlation is used in statistics to find out the linear association between two events and a correlation function can be used to get the correlation of two features as a function of distance; i.e., the relative probability of two features being separated by a given distance can be determined. Consider single regions of cavity and particle (xc and xp ) which are separated by a vector x (Fig. 1(a)). Now, the relative probability can be calculated for a given value of x that there is a particle and cavity with separation x. Consider a function defined for particles, p(x), which is equal to one if there is a particle at position x or zero if there is not. A similar function, c(x), can be defined pertaining to cavities. The un-normalised particle–cavity correlation is given by:
f (x) =
p(x) · c(x + x)dx
(1)
˚
where ˚ is the spatial domain over which the integral is being evaluated. To get the normalised, relative probability of a particle cavity separation of x, the function f needs to be divided by the product of fractions of particles and cavities. Using Fast Fourier Transform, the above mentioned convolution integral can be solved efficiently as: F = P · C∗
(2)
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Fig. 1. (a) A schematic representation of the method applied in correlation estimation. Positions of a particle (xp ) and a cavity (xc ) in 3D space are marked and the distance, x, between them is shown. (b) A series of schematic drawings showing the steps in calculating the particle–cavity intersections by dilation: (i) shows the particle and cavity regions; (ii) shows the dilation of the particle regions by the dashed circles; (iii) shows the intersections of the dilated particle and cavity regions and (iv) shows only the intersected regions (marked 1 and 2).
where F, P and C are the Fourier transforms of f, p and c, respectively, and * denotes the complex conjugate. To interpret the result, f can be plotted as a function of radius: r = |x| = (x12 + x22 + x32 )
1/2
(3)
where x12 , x22 , x32 are the components of x in three orthogonal directions defined as the Euclidean distance between two points in 3D space. 3.2. Particle–cavity normalised intersection distribution To determine the fraction of particle and cavity voxels in contact, a dilation and intersection checking routine was developed in Matlab. 3D arrays defining the coordinates of all particle and cavity voxels were first generated. After constructing the 3D arrays, particle regions were dilated by a predefined distance and a check for cavity regions intersecting the dilated particle regions was performed. The number of intersected regions was then divided by the total number of cavity regions to get normalised data for each predefined dilation. A schematic presentation of the steps followed is shown and explained in Fig. 1(b). 4. Results
only particles greater than 1.8 m in size due to the resolution limits inherent in the data. The size distribution was estimated from the longest major axis of each particle region, considering each region as a spheroid, and this distance will be denoted as the diameter hereafter. Approximately 31,000 particles of various sizes were detected after removing single voxels present in the volume to reduce noise of data and the corresponding size distribution is plotted in Fig. 3 as a probability distribution function of particle diameter (dp ), using the Epanechnikov kernel [17]. It is apparent from the plot that the peak corresponds to a mode particle size of approximately 3 m, with 4% of the particles in the range 10–40 m. These apparently very large particles were actually agglomerates of smaller particles, as will be shown later. The results plotted in Fig. 4(a) show the true stress–strain curves from specimens tested at different temperatures with strain rate perturbations around a base rate of 5 × 10−4 s−1 . Average strain rate sensitivity (m) values derived from these data, annotated on the plot, varied from 0.24 to 0.33, but showed no systematic variation with temperature. As expected, the flow stress decreased with an increase of test temperature. The elongation to failure was highest at 400 ◦ C. At 450 ◦ C, extensive grain growth together with cavity development led to a slightly lower strain rate sensitivity and less resistance to diffuse necking hindering further enhancement of the
4.1. Hot deformation properties Optical micrographs of the as-rolled material are shown in Fig. 2. Recrystallization during hot rolling resulted in an equiaxed microstructure with an average grain size of approximately 8 m. Second phase particles were distributed mostly along the recrystallized grain boundaries, likely to be a result of boundary pinning by the particles. Compositions of these particles were determined using EDX and at least 30 particles were analysed. The extrapolation method was used to determine the compositions from EDX data to diminish any effect of matrix magnesium [15]. Using the JMatPro thermodynamic software [16] and the MgData database, the composition of the stable phases were also determined at different temperatures and Al11 Mn4 was predicted as the dominant stable precipitate phase at the homogenisation temperature under equilibrium condition. Experimental measurements showed the particles contained approximately 71 at.% Al and 28 at.% Mn, with minor content (0.65 at.%) of Fe, which was close to the predicted Al11 Mn4 stoichiometry. From the tomography data set, a sub-volume of 500 m × 500 m × 700 m was cropped, and the volume fractions and size distribution of particles were measured. This analysis considers
Fig. 2. An optical micrograph of hot rolled microstructure. A heterogeneous mixture of refined equiaxed grains is evident.
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Table 1 Grain sizes at the deformed gage region at different temperatures. Errors are shown as the 95% confidence level (mean ± 2× standard error).
Fig. 3. A semi-log plot of the probability distribution function of the particle diameter (dp ). The peak corresponds to the maximum occurrence of sizes at nearly 2–3 m.
elongation to failure at this high temperature. The sizes of the grains were measured from the gage regions of the failed specimens and are shown in Table 1. A considerable growth of the grains, except at 300 ◦ C, was observed during deformation. The apparent activation energy (Qapp ) of deformation can be calculated from the flow stress dependency at elevated temperature using the following equation [18]:
Q
ε˙ = A n exp −
RT
mQ + m ln A1 + mε˙ RT
350 ◦ C
400 ◦ C
450 ◦ C
10.96 ± 1.96
15.21 ± 2.64
20.02 ± 2.68
35.32 ± 5.90
near the fracture surface. Macroscopically, there was very little evidence of neck formation prior to failure; though at 350 and 400 ◦ C, the reduction of area was comparatively low signifying most cavitation occurred at these temperature. It is notable that at 300 ◦ C, there was no large cavity coalescences near the fracture surface and at 450 ◦ C, the specimen failed by coupled action of cavitation and diffuse necking. Fig. 5 shows the evolution of the cavities in the unetched SEM images of the gage regions close to the failed surface at different pre-set strain values deformed at 350 ◦ C under a constant strain rate of 5 × 10−4 s−1 . Several characteristics are common at all strains. There are some single cavities appearing close to particles (marked A). However, a similar number of isolated cavities is observed which are not obviously formed close to any particles (marked B). With an increase in strain, more coalesced cavities are developed in the microstructure (marked C). It is obvious from these images that the number density of cavities had increased during deformation to a higher strain. The existence of small cavities, even at the strain of 1.05, implies a continuous nucleation of cavities during deformation. The SEM observations suggest that particles act as a source of formation of cavities but do not allow a quantitative determination of particle/cavity correlation to be made due to sectioning effects.
(4) 4.2. Analysis of cavities
After rearranging, ln =
300 ◦ C
(5)
where A and A1 (= 1/Am ) are constants, n = (1/m) is the stress exponent and R is the molar gas constant. The peak flow stresses of the alloys at different temperatures were used to plot ln against 1000/RT to obtain the slope mQ (Fig. 4(b)). Using this value, the activation energies were determined from the average strain rate sensitivity values of the alloy at different temperatures. The estimated Qapp (by averaging the activation energies at different temperatures) was 89.7 ± 14.8 kJ mol−1 . Failed specimens were observed optically and found to contain a high fraction of large cavities, except at 300 ◦ C, near to the fracture surface. Strong evidence for cavity coalescence was observed
X-ray micro tomography was performed on the deformed regions of the specimens tested at 350 ◦ C from 0.80 to 1.05 strains, with tomographs recorded from the mid-length position along the gage length. The ambiguity of particle–cavity association in a 2D section, showed in Fig. 5, can be illustrated using the tomography data by creating an imaginary 2D surface in the 3D volume. Fig. 6(a) shows an example of such a surface for the specimen strained up to 1.05 (95% of the failure strain). In this 2D section, three cavities (A, B and C) appear not to be connected with any particles. However, the tomography data permits investigation of the 3D volume just below the surface and it can be seen that when this is done cavity regions A and B are indeed connected to particles (Fig. 6(b)), although cavity C is not.
Fig. 4. (a) True stress–strain plots for temperatures 300–450 ◦ C at the strain rate of 5 × 10−4 s−1 and corresponding strain rate sensitivity values (m) are shown. (b) A plot of logarithmic flow stress against temperature to determine the activation energy of deformation. The obtained slope is shown by the linear equation.
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Fig. 5. SEM images of the gauge surfaces of the specimens pre-strained to (a) 0.80, (b) 0.90, (c) 1.00 and (d) 1.05 at 350 ◦ C under a constant strain rate of 5 × 10−4 s−1 . Cavities are marked as A if they are close to any particles or B if they are located far from particles. Large coalesced cavities are marked as C.
4.2.1. Qualitative analysis of tomography data A series of 3D images were extracted from the 3D volumes recorded for material tested to a strain of 1.05. Fig. 7(a) shows the distribution of particles and cavities in a sub-volume of 350 m × 430 m × 400 m. The particles were found to be distributed throughout the whole volume, with evidence of some clustering and alignment of particle stringers in the rolling direction (parallel to the tensile axis). Regions of intense cavitation appear
to be associated with regions containing the greatest number of particles. Like the particles, the cavities are also distributed in illdefined stringers aligned along the tensile axis (Fig. 7(b)). Many of the cavities have complex morphologies that may be a result of cavity coalescence. Most of the cavities are not equiaxed, and the long axis is generally near parallel to the tensile axis. Fig. 8 shows magnified images of some typical cavity/particle features. Two cavities (marked A and B) were observed to have
Fig. 6. (a) A 2D surface view of a random area of the 3D volume of AZ61H at ε = 1.05. A, B and C cavity regions are identified not to be connected with any particle. (b) But, if the view is transformed into a 3D view by extending the depth below the surface, particles are found to be attached to the cavity regions of A and B. Cavity region C is still observed to be not connected with any particle.
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Fig. 7. Reconstructed 3D sub-volumes of 350 m × 430 m × 400 m of AZ61H at ε = 1.05 showing (a) the particles and the cavities, and (b) only cavities.
emerged from the particle–matrix interface of a single particle and have grown fastest in the direction of the tensile axis. Another cavity (marked C), formed from a particle in a plane behind that of the first can be seen to have grown towards and coalesced with cavity B. The original morphology of the individual cavities, which is roughly cylindrical with a long axis aligned close to the tensile axis, is preserved. More advanced coalescence of a number of cavities can change the cavity morphology, making it more complex, and examples of this is shown in Fig. 8(b). Here, several cavities have coalesced together and formed a large cavity of irregular shape. The large cavity has a roughly oblate spheroidal morphology, but with several branches in different directions that presumably are remnants of the original constituent cavities. Different sizes of particles were observed to act as the cavity formation sites. Most of the particles could be classified to be spheroidal in shape. Qualitatively, it was observed that agglomerations of small particles (Fig. 9(a)) were more potent in causing extensive cavitation than single large particles, with regions containing high cavity fractions and extensive coalesced cavities (Fig. 9(b)). The tomography data (Fig. 9(a)) suggests there is an
interconnected network of particles. However, it should be bourne in mind that particles that are within the spatial resolution distance (1.22 m3 ) from each other may erroneously be connected in the image rendering process. The SEM observations suggest that features such as that observed in Fig. 9(a) consist of agglomerations of isolated particles with separation less than the spatial resolution of the micro-tomography. However, effectively these agglomerations do seem to behave as one very large interconnected “super-particle” and the constraint placed on deformation about such regions appears to be responsible for the high levels of local cavitation. Given the high number density of particles capable of initiating cavitation, it was always found to be the case that the largest cavities were formed by cavity coalescence. Cavity shape tended to evolve as the cavities grew. The smallest cavities were near spherical in shape, consistent with a diffusion controlled growth mechanism. Larger cavities tended to become elongated in the direction of the tensile axis, indicative of plasticity controlled growth. The largest cavities have complex morphologies associated with coalescence as already discussed.
Fig. 8. 3D images from a specimen deformed to a strain of 1.05 at 350 ◦ C showing (a) the growth of three cavities emerging from two particles and coalescences of them and (b) a large cavity, exhibiting branches in different directions, formed by the coalescences of smaller cavities.
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Fig. 9. 3D rendered images showing (a) an agglomeration of particles and (b) the effect of agglomeration on cavitation. These particles nucleated closely-spaced cavities which have coalesced to form a large cavity. Table 2 Cavity volume fractions at 350 for different pre-set strains.
size, and this is attributed to extensive cavity coalescence in this strain interval.
Strain
0.8
0.9
1
1.05
Cavity volume fractions, %
0.18
0.47
0.49
0.9
4.2.2. Size distributions of cavities From the raw data, a sub-volume of 500 m × 500 m × 700 m was cropped, and the volume fractions and size distributions of cavities were measured. The cavity volume fractions are shown in Table 2. At the largest strain, the cavity volume fraction approached 1%, but it should be noted that this is an average over the whole gage length. All the size distributions were estimated from the longest major axis (dcav ) of each cavity region, a similar approach as applied to particle size estimation. About 19,000 cavities were detected in the specimen deformed to a strain of 1.05, while only 7500 were detected at the strain of 0.80. The cavity size distributions at different strains are shown in Fig. 10. For all strains, the mode cavity size is similar and is approximately 3 m. An important feature of size distributions is that the proportion of small cavities (<5 m) has decreased during straining. However, the number of small cavities still increases continuously with strain because the total cavity number increases by a factor of 3 between strains of 0.80 and 1.05. Fig. 10 also reveals that between strains of 1.00 and 1.05 there is a large increase in the proportion of cavities greater than 20 m in
Fig. 10. Probability distribution plots of the diameters (dcav ) of cavities for different levels of deformation.
4.3. Measurements of association of particles and cavities Using Matlab and Fortran routines (discussed in Section 3), two relationships between particles and cavities were established for a sub-volume of 500 m × 500 m × 700 m to be compared with random sets of particle and cavity regions contained in a subvolume of same dimension. If cavities were not associated with particles, the position of the cavities would be random, i.e., no preferential location for cavities close to particles would occur. In view of this, random coordinates of the particle and cavity regions were generated in Matlab followed by tagging and analysing in a procedure identical to the one carried out for experimental data. The sizes of the random regions were chosen to mimic the experimental data. From the correlation plot (Fig. 11(a)), the radial distance between particle and cavity voxels is shown up to maximum distance of 50 m. A peak was obtained at a radial distance of approximately 5–8 m which corresponds to the occurrence of maximum number of pairs of voxels (of particles and cavities) separated from each other by that distance. The correlation plot does not provide the information on particle/cavity association in a straightforward way since it considers each voxel present in the sub-volume instead of regions of particles or cavities (here, the term region means a particle or cavity containing connected voxels of similar type). To understand the origin of the peak, a particle of 3 m and a cavity of 3 m can be considered since the mode size of the particle and cavity regions was close to 3 m. In this case, the distance between voxels in a particle and voxels in a connecting cavity would vary from the minimum distance between two voxels (∼1 m) to 6 m, the distance from a voxel at the far side of the particle to that at the far side of the connected cavity. The mean separation will depend on the particle and cavity shape, but will lie between these extremes (and would be 3.18 m for perfectly spherical particles and cavities). Given that this distance will increase for non-spherical particles and cavities, the measured peak is indicative of a preference for cavities and particles to be in close association. On the other hand, if the distribution of cavities is random, no such peak is observed. In contrast to the correlation method, the dilation-andintersection method considers regions of particles and cavities containing more than one voxel in each type of region. Calculated by this method, nearly 90% of the cavities (Fig. 11(b)) had their edges connected with particle edges by a single voxel distance. With an increase of distance from particle edges, the fraction of cavities
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Fig. 11. (a) A semi-log correlation function (f(p–c)) plot showing the distribution between particle (p) and cavity (c) voxels separated by a pre-defined radial distance, r. (b) The number of overlaps of cavity and particle regions (Nintn ) normalised by the total number of cavities (Ncav ) in the sub-volume are shown. The dashed lines show probable distributions if the particles and cavities are randomly located in the sub-volume.
attached to particles approaches to unity. This implies that though some cavities (approximately 10%) were not physically attached to any particles, they were located a short distance from particles. Now, for a random distribution of cavities, a parabolic shape curve is obtained with only 1% of the total cavities at a distance of 1.22 m from particle edges compared to the 90% intersections obtained at 1.22 m distance in the experimental data. Finally, only the particles with neighbouring cavities were identified in a cropped sub-volume and their frequencies were recorded for a bin width of 1 m. The estimated number of particles truly attached to cavities (Np−c ) for each bin width was normalised by the number of particles (Np ) present in that size range in the cropped sub-volume. Fig. 12 shows two distributions of particles at the strains of 0.90 and 1.05 plotted using this methodology. At a strain of 0.90, a greater fraction of particles larger than 10 m were associated with cavities compared to small particles (<10 m). However, not all the large particles had connected cavities. Nevertheless, at a strain of 1.05, more than 50% of the large particles were associated with cavities and the contribution in assisting cavity formation by the small particles (<10 m) was increased by nearly 4 times compared to that at the strain of 0.90. These results confirm that nucleation of cavities is a continuous process and large particles,
generally, form more cavities prior to small particles. Interestingly, this figure also shows that even at the highest strain not all the large particles form cavities. 5. Discussion 5.1. Hot deformation behaviour The m-values showed a dependency on temperature, increasing to a maximum at 400 ◦ C (m = 0.33) and dropping slightly at 450 ◦ C (m = 0.32). This was directly related to the grain growth that occurred during deformation and the extensive grain growth (Table 1) at 450 ◦ C is expected to be the cause of the reduction in average m value at this temperature. Previous studies of AZ31 [7] with a similar starting grain size led to m values greater than measured here (0.30–0.55) in the temperature range 200–400 ◦ C. Greater elongations, up to 400% [19] were measured in AZ31 deformed under similar conditions to the present work, where GBS and limited grain growth were observed. AZ31 contains far fewer coarse particles than the AZ61H used in the present work. Microstructural instability occurring from concurrent grain growth and particle induced cavitation are expected to be the cause of the lower m reported here. The measured Qapp is close to the activation energy for grain boundary diffusion of magnesium (QGB = 92 kJ mol−1 ) [18] for the temperature range investigated. The estimated stress exponent (n) values, determined using the relation n = 1/m, ranged from 3.00 to 4.20. In previous studies of an AM60 Mg alloy, a value of n, close to 2, was shown to be consistent with grain boundary sliding (GBS) as the dominating deformation mechanism, with an m value of 3 or above indicating a combination of slip and GBS [20]. This implies that in the current study GBS and slip occur and grain boundary diffusion acts as the accommodation process of deformation. 5.2. Cavitation characteristics
Fig. 12. Plots of the size distributions of particles associated with cavities (N(p–c) ) normalised by the total number of particles (Np ) at each size group at the strain of (a) 0.90 and (b) 1.05.
Both the correlation and the dilation methods applied to the 3D tomography data show that there is a strong association of cavities with particles after deformation at 350 ◦ C For example, Fig. 11(b) demonstrates that approximately 90% cavities are associated directly with particles. During deformation, a local discontinuity in strain develops across the particle/matrix interface, leading to a concentration of stress in the surrounding area. If this stress fails to relax quickly, cavity can nucleate at the boundary.
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Table 3 Materials constants and parameters used in the current study [18]. ˝ (m3 )
␦Dgb (m3 s−1 )
k (kJ mol−1 )
2.33 × 10−28
5 × 10−12
1.38 × 10−23
Grain boundary particles limit the stress–relief process and become an effective source of cavity formation. The competition between stress concentration and relaxation mechanisms leads to a critical particle diameter (dpcrit ) below which a particle will not assist in cavity formation. This supposition leads to the consideration of a critical diffusion length below which local stresses can be relaxed quickly. Needleman and Rice [21], based on grain boundary diffusion, proposed an expression for the critical particle diameter
dpcrit
=
8˝ıDgb kT ε˙
1/3 (6)
where ˝ is the atomic volume and k is Boltzmann’s constant. The maximum flow stress () was 30 MPa at 350 ◦ C. Using the values of the parameters from Table 3, the critical particle diameter was approximately 10 m at 350 ◦ C. This value is three times higher than the value predicted by Mussi et al. [22] for a AZ91 alloy at 250 ◦ C under a strain rate of 10−3 s−1 . However, since nucleation of a cavity depends on diffusional processes, the critical diffusion length required to relax stress concentration varies strongly with test parameters. In the current study, a significant fraction (4%) of particles are greater than dpcrit and thus would be expected to contribute to cavity formation. However, the tomography data also reveals that particles smaller than the predicted dpcrit also nucleated cavities (Fig. 12). A local increase in stress is expected due to concurrent growth of grains. Such an increase in stress allows comparatively small cavities to become stable after formation [23]. Therefore, NR cannot truly reflect the minimum size of a particle required to nucleate a cavity if an alloy experiences grain growth during deformation. As a consequence, at higher strains, particles much smaller than NR were associated with cavities. The current results are consistent with the supposition that cavitation initially occurs at larger particles. As the grains grow, cavities of small size can become stable after nucleation and dpcrit determined by Needleman and Rice does not reflect the actual critical particle diameter. This leads to the observed continuous nucleation of cavities at progressively smaller particles as grain growth advances. It is noteworthy that if relief of stress concentration is maintained by grain boundary diffusion throughout deformation and grain growth is prevented, the probability of failure by cavitation may be very low, since the critical particle size will remain large (and may be above the size of the largest particles present). This situation was observed in AZ91 by Mussi et al. [22], where the grain size remained small throughout deformation and grain boundary diffusion was effective in relieving stress concentrations around particles. In some random regions in the volume, agglomeration of the particles was observed (Fig. 9a). Agglomeration had a significant effect on formation of a cavity. Cavities nucleated from closely spaced particles coalesce rapidly, resulting in formation of a large cavity. If the spacing of the agglomerated particles is less than the critical particle diameter required for nucleation of a cavity, nucleation may occur from a particle (within the cluster) having a diameter less than the critical diameter since the relaxation of local stress is hindered by the surrounding particles. Therefore, the degree of agglomeration is an important factor in an alloy containing coarse particles since particles smaller than the critical particle
diameter required for nucleation of a cavity may assist in cavity formation depending on spacing of the agglomerated particles. Lee and Huang [7] had argued that nucleation of cavities was not a continuous process after observing a plateau in the total number density of cavities after a certain strain. On the other hand, in the current study, formation of cavities was a continuous process since the number density of cavities increased continuously up to the failure strain. This difference is likely to be due to the much higher fraction of coarse to fine particles in the AZ61H alloy studied here. As already discussed, it is the activation of progressively smaller particles as effective cavity nucleation sites due to grain growth which leads to the observed continuous nucleation of cavities. 6. Conclusions A high manganese variant of AZ61 alloy, with a grain size of 8 m, was studied during hot deformation in the range 300–450 ◦ C. This alloy contained a continuous distribution of Al11 Mn4 particles of mode size 3 m, with some large particle clusters present greater than 10 m in size. The following conclusions were drawn: • Strain rate sensitivity values varied from 0.24 to 0.33 with the highest value obtained at 400 ◦ C. The dominant diffusion process expected during deformation was estimated as grain boundary diffusion. • At 300 ◦ C and 450 ◦ C, the failure of the material occurred by neck formation. In the later case, a diffuse neck coupled with cavity development was observed. At 350 and 400 ◦ C, cavity dominated failure was observed. • X-ray micro tomography was used to provide a detailed study of cavitation during deformation at 350 ◦ C. Particles were identified as the prime source of cavity formation. 3D rendered images revealed cavities are closely connected with particles and two methodologies were developed to quantify the association of particles and cavities. • The critical particle diameter for cavity formation varied depending on grain size. Smaller particles become increasingly effective as cavity formation as the grain size increases and an increase in flow stress allowed smaller cavities to become stable. • Cavity nucleation was identified as a continuous process throughout deformation at 350 ◦ Cwhich was dependent on the availability of cavity formation sites. • The degree of agglomeration of particles is an influential factor in controlling cavitation, since even small particles were observed to nucleate cavities when surrounded by other particles that inhibit stress relaxation processes. Acknowledgements The work was performed with support from the EPSRC portfolio partnership on Light Alloys for Environmentally Sustainable Transport (EP/D029201/1) and Magnesium Elektron, UK. References [1] W.J. Kim, S.I. Hong, Y.S. Kim, S.H. Min, H.T. Jeong, J.D. Lee, Acta Materialia 51 (2003) 3293–3307. [2] N. Stanford, M.R. Barnett, Journal of Alloys and Compounds 466 (2008) 182–188. [3] F. Zarandi, G. Seale, R. Verma, E. Essadiqi, S. Yue, Materials Science and Engineering A 496 (2008) 159–168. [4] S.W. Xu, N. Matsumoto, S. Kamado, T. Honma, Y. Kojima, Materials Science and Engineering A 523 (2009) 47–52. [5] J.D. Robson, D.T. Henry, B. Davis, Acta Materialia 57 (2009) 2739–2747. [6] A.H. Chokshi, A.K. Mukherjee, Acta Metallurgica 37 (1989) 3007–3017. [7] C.J. Lee, J.C. Huang, Acta Materialia 52 (2004) 3111–3122. [8] Y. Takigawa, J.V. Aguirre, E.M. Taleff, K. Higashi, Materials Science and Engineering A 497 (2008) 139–146. [9] M. Abramoff, P. Magelhaes, S. Ram, Biophotonics International 11 (2004) 36–42.
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