second phase particle distribution and its ... - wit press · nucleation sites during forming...

Second phase particle distribution and its effect on the formability of aluminum alloys

Z. Chen Department of Mechanical Engineering, University of New Brunswick, Canada

Abstract

Aluminum alloys have been increasingly used in the automotive industry for fuel economy. The existence of second phase particles in aluminum alloys provides damage nucleation sites during formation processes and limits the formability. Characterization of second phase particle distribution and its effect on the formability of aluminum alloys is of great importance.

Distribution of Fe- and Mn-based second phase particles in Al-Mg alloys AA5182 and AA5754 is captured using microscopy and image analysis. Spatial tessellation of particle images is conducted to quantify particle distribution, such as particle size, shape (aspect ratio) and clustering. Large particles are found more often in AA5182 than AA5754. The obtained particle distribution is then applied to a so-called damage percolation model to predict formability of both alloys in stretch flanging. Keywords: aluminum sheet, ductile fracture, formability, second phase particles, microstructure, heterogeneity.

1 Introduction

Modern automotive industry instigates more and more usage of new high-strength-to-weight ratio metal alloys such as aluminum and high strength steel in the fabrication of structural components. Application of advanced lightweight alloys contributes efficiently to the effort in reducing emission and promoting fuel economy in the auto industry. However, compared with traditional steel, aluminum exhibits limited formability due to ductile fracture caused by the existence of second phase particles. Experimental study showed that distribution of second phase particles in aluminum alloys is strongly inhomogeneous [1],

© 2005 WIT Press WIT Transactions on Engineering Sciences, Vol 51, www.witpress.com, ISSN 1743-3533 (on-line)

Computational Methods and Experiments in Material Characterisation II 53

both in size and spacing. Existence of second phase particles provides damage nucleation sites during forming processes and limits the formability of aluminum alloys. Characterization of second phase particle distribution and its effect on the formability of aluminum alloys is of great importance. For this reason we conduct the current research.

Void nucleation occurs at second phase particles through particle debonding and/or particle cracking during straining. Subsequent growth and coalescence of nucleated voids will finally trigger ductile fracture in aluminum alloys. Although Gurson’s [2] model and many other micromechanics models have been introduced in the numerical simulation of aluminum sheet forming processes, selection of void nucleation strain in each simulation is somewhat arbitrary, with lack of experimental background. Further more, Gurson’s material model only involves the value of particle areal (volumetric) fraction, it is therefore unable to examine the effect of heterogeneity of particle distribution on the forming behaviour of aluminum sheet alloys.

The current paper reports our recent work in characterizing the heterogeneous particle distribution in automotive aluminum-magnesium sheet alloys, AA5182 and AA5754, and their effect on the formability of these sheet alloys. To employ quantified particle distribution in formability prediction, a so-called combined FE/damage percolation model recently developed by the author [3] is adopted.

2 Quantification of heterogeneous particle distribution

Two automotive Al-Mg sheet alloys, AA5182 and AA5754 are studied as received and O-tempered. The chemical compositions for both alloys are listed in Table 1.

Table 1: Nominal chemical composition of AA5182 and AA5754, wt% [4].

Alloy Si Fe Mg Mn Cu Ti AA5182 0.08 0.3 4.6 0.33 0.04 AA5754 0.06 0.21 3.2 0.2 0.01

The accuracy and precision of quantitative stereology is highly dependent on

the quality and consistency of metallographic specimen preparation, as discussed by Pilkey [5]. Rectangular samples were sheared from the as-received sheet and set in 25 mm cold mounts. Epoxy was used to mount the samples to minimize residual stress from the mounting process. Metallographic specimens were prepared of sufficient size so that particle fields can be extracted from areas well away from the sheared edges. The requirement to obtain large-scale high-resolution metallographic fields dictated that the specimen surfaces be virtually perfectly flat and free of scratches. In order to maintain high quality and repeatability, sample preparation was carried out using vibratory polishing equipment at the Alcan Kingston Research and Development Centre (Now


54 Computational Methods and Experiments in Material Characterisation II

Novelis Global Technology Centre). Detailed grinding and polishing procedures can be seen in [3].

To prevent variations in field illumination from affecting the measurements, a 1000-series pure aluminum sample was employed as a standard background to achieve a background-correcting image. To avoid further inaccuracy, the background image has been acquired by averaging 15 images taken from different spots on the surface of the standard sample. The adverse effect of video noise is minimized through an image averaging algorithm, where ten frames are acquired in rapid succession and then averaged to reduce gray scale fluctuations [3].

Table 2: Mechanical properties of AA5182 and AA5754 from uniaxial tensile tests [4].

Fe- and Mn-based particles of 2 micron to 20 micron in diameter were found

in these materials. Generally, AA5182 has higher particle content compared with AA5754 due to higher magnesium and iron contents. Particle distribution has been quantified through the sheet thickness using image analysis. Particle fields were captured for each alloy using a roughly 3.5 mm x 1.6 mm plane image. This large-scale image was constructed from 98 smaller scale images with a magnification of 150 using an optical microscope and a digital camera. Particle data was obtained by image analysis using ImagePro Plus v4.5 software.

Figure 1: A small-scale particle dilation tessellation for a particle field of AA5182.

Particle distribution data used in the damage percolation model include particle size, neighbouring particle list (first order cluster), neighbouring particle cluster list (second order cluster). To achieve this data, a so-called particle dilation (or matrix-erosion) tessellation technique has been adopted in the current work [5, 6], which is based on the so-called matrix erosion technique. In this tessellation, a particle dilation algorithm is applied to partition the particle field (Fig. 1). This tessellation scheme entails dilation of the particles at constant rates

Material AA5182 1.6 mm AA5754 1.6 mm σ0 (MPa) 117.34 102.78 E (GPa) 71.71 71.17 ν 0.33 0.33



until they impinge upon each other, with the skeletonized field corresponding to the respective boundaries of impingement. Conceptually, an equivalent tessellation is obtained by incrementally removing a single width of pixels from the matrix surrounding each particle in a digital particle field until a shell of matrix material remains after the impingement of neighbouring particles. This tessellation method is attractive since the original particle shape and orientation are reflected by the tessellated images and it is well suited for use in digital image processing.

2.1 Tessellated particle field

Employing the particle dilation tessellation technique, large-scale tessellated particle fields were obtained from the four Al-Mg microstructures, using metallographic specimens in various planes of view. Figures 2 and 3 show the cropped tessellations for the 1.0 and 1.6 mm AA5182 and AA5754 in the rolling-thickness planes.

In general, AA5182 exhibits a higher particle areal fraction and particle size than AA5754. In contrast, AA5754 displayed higher numbers of particles per unit area. These observations demonstrated that AA5182 contains much larger particles, which should lead to earlier damage nucleation during deformation [7, 8]. The higher degree of particle clustering in the AA5182 microstructures (Fig. 2) should also lead to higher damage rates [9, 10].

400 µm (a)

400 µm (b)

Figure 2: Large-scale high-resolution spatial tessellation for AA5182 sheet particle field, rolling-thickness view: (a) 1.0 mm thickness; (b) 1.6 mm thickness.



400 µm (a)

400 µm (b)

Figure 3: Large-scale high-resolution spatial tessellation for AA5754 sheet particle field, rolling-thickness view: (a) 1.0 mm thickness; (b) 1.6 mm thickness.

Particle field data extracted by the tessellation software includes: (a) particle size, location, and orientation; (b) nearest neighbouring particle list and spacing; and (c) cluster list (particles comprising each cluster). The determination of which particles comprise a cluster is based on the inter-particle dilational spacing data, which will be addressed shortly. It is worth mentioning that the particle field data was obtained based on an elliptical simplification. Each of the irregular shaped particles was simplified as being an ellipse of the same area as the particle in the tessellation data. Ellipses were oriented vertically or horizontally about its centroid based on the initial orientation of the semi-axes. The ellipse was rotated such that its semi-axes aligned with the nearest horizontal or vertical axes of the image, as illustrated in Fig. 4.

x

y θ y

x

aa

r r

(a) (b)

Figure 4: Re-orientation of the simplified ellipse representation of a particle: (a) before realignment; (b) after realignment.



2.2 Inter-particle dilational spacing

The software developed by Pilkey [5] is used to extract useful information from the tessellated digital images. During each particle dilation step, the software records when each particle feature merges or touches another dilating particle feature. First contact or agglomeration between a particle and one of its neighbours defines then a nearest neighbour. Knowing the pixel size, the software can then determine the nearest neighbour spacing based upon the number of dilations performed. Dilational counting measures are then tabulated during the construction of a matrix erosion spatial tessellation and represented by a histogram of inter-particle dilational spacing (IPDS) frequencies. Given that a matrix erosion tessellation algorithm involves repeated particle dilational passes, equivalent to matrix erosion passes, the number of distinct features that disappear from the particle field during each dilation pass is recorded as a frequency. The disappearance of a feature occurs when it agglomerates with another feature (i.e. dilating neighbours come in contact). At the start of the spatial tessellation process, each particle represents a feature. By recognizing that each particle dilation pass is of characteristic length in a digital image, the agglomeration frequencies can be plotted against dilational distance to produce an IPDS frequency spectrum. It follows that local peaks in the frequency of dilational merging events are indicative of characteristic spacings within the tessellated particle field. The dilating features which agglomerate at the smallest of these characteristic spacings are referred to as first order clusters, while successive IPDS peaks signify so-called second, third and higher orders of particle clusters [5].

Figures 5 and 6 display the IPDS spectra for each of the particle fields presented in the preceding section. It is observed that the through-thickness longitudinal section for each sheet exhibits the prominent first-order cluster peak occurring at an IPDS of 2µm. This suggests that a relatively large number of closely spaced particles are available to promote void nucleation and subsequent coalescence.

(a) (b)

Figure 5: IPDS of AA5182 sheets in the rolling (longitudinal)-thickness view planes: (a) 1.0 mm sheet; (b) 1.6 mm sheet.



(a) (b)

Figure 6: IPDS of AA5754 sheets in the rolling (longitudinal)-thickness view planes: (a) 1.0 mm sheet; (b) 1.6 mm sheet.

2.3 Particle size distribution

The particle size distribution is an important microstructural parameter impacting ductile fracture. Figures 7 and 8 show the measured particle size distributions in the rolling-thickness view plane for the alloys. In these figures, particle size is plotted in terms of particle area in the section plane. It is observed that AA5182 possesses more large particles beyond 25 µm2, compared to AA5754, for all sections. This is attributed to the higher Fe and Si levels in AA5182 (Table 1).

AA5182, 1.0 mm rolling-thickness

0

10

20

30

40

0 10 20 30 40Particle size (µm2)

Freq

uenc

y (%

)

AA5182, 1.6 mmrolling-thickness

0

10

20

30

40


Freq

uenc

y (%

)

(a) (b)

Figure 7: Normalized histograms of particle size in rolling-thickness view plane: AA5182.




0

10

20

30

40

50

60


Freq

uenc

y (%

)


0

10

20

30

40

50

60


Freq

uenc

y (%

)

(a) (b)

Figure 8: Normalized histograms of particle size in rolling-thickness view plane: AA5754.

Distribution of particle aspect ratio was also extracted from image tessellation, as reported in [3]. However, this parameter hasn’t been considered in the current work for simplicity.

3 Formability prediction

A so-called combined FE/damage percolation model developed recently by the author [3] was employed to simulate stretch flanging process of these alloys. Stretch flanging is such a forming process that a blank with an inner cutout hole, clamped at outer edge, deforms under a downward motion of a circular cylindrical punch. This process, due to repeated bending/unbending effect as the material flows around the punch profile, is believed to be damage-sensitive. The model uses damage-based Gurson’s [2] model to account for the global softening of the material in the finite element calculation, whilst the local damage development and fracture is examined within the measured particle field at individual particle. To achieve this goal, the FE calculated stress/strain and porosity histories have been exerted onto the local particle distribution, where nucleation, growth and coalescence of voids are controlled by appropriate criteria. Catastrophic failure of stretch flanges was predicted at the onset of ductile fracture, and formability predicted as the limit punch depth to fracture. Details of the forming designations and combined model can be seen in [3]. It is revealed that void nucleation dominates the catastrophic ductile fracture, no significant void growth and coalescence has been observed at the onset of failure [3]. Also found from the experimental test, thinner 1.0 mm sheet exhibits cutout edge necking which is believed to be induced by other failure mechanisms than



damage-based ductile fracture. Consequently, different levels of void nucleation strain have been adopted in the combined model to correlate the model results with the experimental ones for the 1.6 mm sheet only. Figure 9 shows damage development within a large scale particle field of AA5754 predicted by the combined model, at which void coalescence reaches to a critical level to trigger catastrophic failure, and the limit punch depth has been determined.

Figure 9: Critical moment at which void coalescence within measured particle distribution triggers catastrophic failure, AA5754, 1.6 mm sheet: (a) corresponding finite element mesh; (b) damage development within the area of interest; grey ellipses show coalesced voids.

Figure 10 depicts the predicted the flanging formability against three levels of void nucleation strain for both alloys. It is seen that nucleation strain of 0.6 provides good model results in comparison with experimental results.

AA5182, 1.6 mm0

10

20

30

40

50

60

70

80

0.2 0.3 0.4 0.5 0.6 0.7εN

Lim

itpu

nch

dept

h(m

m)

Experimental:Radial crack at cutoutCircumferential crack at punch nose

Radial crack Circumferentialcrack

AA5754, 1.6 mm0

10

20

30

40

50

60

70

80

0.2 0.3 0.4 0.5 0.6 0.7εN

Lim

itpu

nch

dept

h(m

m)

Experimental:Radial crack at cutoutCircumferential crack at punch nose

(a) (b)

Figure 10: Limit punch depth predicted for the 1.6 mm sheet by the combined model at different levels of void nucleation strain: (a) AA5182, (b) AA5754.



Acknowledgements

This research was supported by the Natural Science and Engineering Research Council of Canada, the New Brunswick Innovation Foundation, and the University of New Brunswick.

References

[1] Pilkey, A.K., Fowler J.P., Worswick M.J., Burger G. and Lloyd D.J., Characterizing particle contributions in model aluminum alloy systems, Microstructural Science, Vol. 22, ASM, 1995.

[2] Gurson A.L., Porous rigid-plastic materials containing rigid inclusions-yield function, plastic potential, and void nucleation, Ph.D. Thesis, Brown University, Providence, RI, the United States, 1975.

[3] Chen Zengtao, Heterogeneous particle distribution and its effect on ductile fracture, Ph.D. Thesis, University of Waterloo, Waterloo, Canada, 2004.

[4] Finn M.J., Private communications, 1999. [5] Pilkey A.K., Effect of second phase particle clustering on aluminum-

silicon alloy sheet formability, Ph.D. Thesis, Carleton University, Ottawa, Canada, 1997.

[6] Shehata M.T. and Boyd J.D., Measurement of spatial distribution of inclusions, In: Inclusions and Their Influence on Materials Behaviour, ASM International, Metals Park, 123-131, 1988.

[7] Gurland J., Observations on the fracture of cementite particles in a spheroidized 1.05% steel deformed at room temperature, Acta Metall., 20, 735-741, 1972.

[8] Fisher J.R. and Gurland J., Void nucleation in spheroidized carbon steels, Part I: Experimental, Metal Science, 15, 185-192, 1981.

[9] Horstemeyer M.F., Matalanis M.M., Sieber A.M. and Botos M.L., Micromechanical finite element calculations of temperature and void configuration effects on void growth and coalescence, Int. J. Plasticity, 16, 979-1015, 2000.

[10] Worswick, M.J., Pilkey A.K., Thomson C.I.A., Lloyd D.J. and Burger G., Percolation damage predictions based on measured second phase particle distributions, Microstructural Science, Vol. 26, 507-514, 1998.



second phase particle distribution and its ... - wit press · nucleation sites during forming...

Documents