An Examination of Anisotropic Void Evolution in Aluminum Alloy 7075

An Examination of Anisotropic Void Evolution in

Aluminum Alloy 7075

Helena Jin1∗, Wei-Yang Lu1, James W. Foulk III1,Alejandro Mota1, George Johnson2, John Korellis1

1Mechanics of Materials DepartmentSandia National LaboratoriesLivermore CA 94550, USA

2Department of Mechanical EngineeringUniversity of California, Berkeley

Berkeley CA 94720, USA

March 21, 2013

Abstract

This paper investigates the anisotropy of void evolution and its relation with ductility in the highstrength rolled aluminum alloy 7075-T7351. Smooth tension specimens are extracted from three prin-cipal material orientations, i.e. rolling (R), transverse (T), and short transverse (S). The mechanicalbehavior of these specimens is characterized and the varying ductility in the three orientations is clearlyobserved. Electron Backscattered Diffraction (EBSD), optical microscopy, and Scanning Electron Mi-croscopy (SEM) are employed to characterize the grain structure and the size, location, and chemicalcomposition of the intermetallic particles. In-situ X-ray Tomography (XCT) experiments are performedto obtain tomographic images of the specimens at critical loading steps. The radiographs acquired duringthe tensile test are then reconstructed and examined through quantitative analysis to partition particlesand voids. These tomographic images enable us to visualize void evolution as the specimens are loadedalong material orientations. The tomographic images clearly illustrate anisotropy in the void evolutionand highlight the importance of local coalescence in developing 1D and 2D void structures prior to globalcoalescence. Fractography confirms tomography. These findings motivate model forms with appropri-ate internal variables to adequately describe the dominant mechanisms which govern anisotropic voidevolution.

Keywords: anisotropy, void evolution, X-ray tomography

1 Introduction

Aluminum alloy 7075 has high strength that is comparable to many steels. It also has good resistance to cor-

rosion. It is often used both the aerospace, automotive, and other industries for structural components where

∗[email protected]

1

H.Jin, W.Lu, J.Foulk, A.Mota, G.Johnson, J.Korellis Anisotropic Void Evolution in Aluminum 7075

the combination of high strength and good corrosion resistance is required [1]. In order to understand design

margins of complex machined parts subjects to mult-axial loadings, we must understand the dominant mech-

anisms governing fracture and failure. Candidate wrought aluminum alloys typically develop microstructural

anisotropy during rolling and extrusion processes where they undergo large plastic deformations [2]. The

damage and failure process is heavily influenced by anisotropic defect structures. Consequently, they exhibit

pronounced anisotropy in fracture and failure properties along different orientations [3, 4].

It has long been accepted that ductile failure is associated with void nucleation, growth and coalescence

[5–9]. For a recent review of growth and coalescence, we refer the reader to Benzerga and Leblond [10]. Prior

works have necessarily relied on empirical and simplified assumptions for modeling the complex process of

void evolution in structural alloys. Although more recent works have included plastic anisotropy and non-

spherical voids [10], the inclusion of anisotropic defect structures and the requisite micromechanics which may

include local coalescence within 1D and 2D defect structures requires experimental discovery. Unfortunately,

few experiments efforts have attempted to elucidate the evolution of anisotropic failure process in wrought

aluminum alloys to aid the necessary (dominant) model forms. Moreover, these limited experimental works

rely on interrupted testing and destructive sectioning [11–13]. In an effort to provide novel microstructural

experimental data for the development of micromechanics-based failure models, we aim to develop a non-

destructive technique to characterize anisotropic damage evolution under loading.

X-Ray Computed Tomography (XCT) is a very attractive 3D imaging technique which enables the vi-

sualization of microstructure features inside a specimen. Previously, this technique was mainly limited to

medical and biological applications due to its low spatial resolution. Recent advances in terms of resolution

and portable light source availability have made microXCT and nanoXCT a valuable technique for character-

izing the internal damage of a specimen [14]. In recent years, there is an increasing amount of research in this

area from all over the world, especially from French researchers at European Synchrotron Radiation Facility

(ESRF). Babout et al. have used high resolution XCT to assess the damage in two model metallic matrix

composites during monotonic and cycling loading, mostly focusing on the observation of cracked particles

and fatigue [15]. Qian et al. have applied microXCT to visualize the ductile fracture process in an Al-Si

alloy, where crack views on different cross sections were provided[16] . Morgeneyer et al. investigated void

evolution in Kahn tear tests to study anisotropy in the fracture toughness of Al 2139 sheet [17]. Jordon et al.

employed microscopy and fractography to study the damage induced-anisotropy in Al 7075-T651[13]. More

recently, Maire et al. compared the damage evolution in three different aluminum alloys with quantitative

analysis of in-situ X-ray tomographic data [18]. Given that the dominant mechanisms may depend on the

2


material, processing, orientation, and loading, additional studies are needed to adequately understand the

anisotropic damage evolution that leads to ultimate material failure in rolled aluminum alloys.

We are motivated to first investigate the discrepancy in the tensile ductility of the aluminum alloy

7075-T7351 in the rolling (R), transverse (T), and short transverse (S) orientations. Although the smooth

specimens will not evolve the fields at notches and crack tips, the work is a necessary step in developing the

relevant micromechanics that span triaxility. Rather than fit the kinetics of a particular mechanism, we seek

to determine which mechanisms are dominant. Specifically, we seek to understand anisotropic void evolution

in different material orientations with emphasis on the importance of local coalescence.

Section 2 explores the mechanical characterization of specimens extracted in the rolling (R), transverse

(T), and short transverse (S) orientations. Microstructural characterization through microscopy and diffrac-

tion is presented in Section 3. Section 4 details the in-situ testing procedure at the Advanced Light Source

(ALS). A quantitative methodology for delineating voids and particles is presented in Section 5. Section 6

illustrates specific cases of void evolution in the R, T, and S orientations. Those results are discussed in

Section 7 with the aid of fractography. Finally, our contribution is noted in Section 8.

2 Mechanical Characterization of Specimens

Certified 100 mm thick wrought plate of aluminum alloy 7075-T7351 is selected as the material for this study.

To fully study the microstructure and mechanical properties of this type of material, tensile specimens

are extracted using the Electron Discharged Machining (EDM) method from all three principal material

directions, i.e. rolling (R), transverse (T), and short transverse (S). The tensile specimens have gage section

diameter of 1.25 mm and gage length of 10.0 mm. Figure 1(a)-(b) show the locations of the extracted

specimens in three principal orientations and the designed uniform tensile specimens, respectively.

(a)

(b)

Figure 1: (a) Locations of specimens extracted from three principal directions. (b) Designed uniform tensilespecimen.

The mechanical properties of the specimens are characterized with an MTS 858 table top system under

3


displacement control, as shown in Figure 2(a). An extensometer with gage length of 7.50 mm is used to

measure the displacement. Ball joints are inserted to assure precise alignment of the specimen during loading.

A strain rate of 0.0004 s−1 is applied to simulate quasi-static loading. Three specimens along each orientation

are tested under same loading condition using the MTS system. The stress- strain curves are consistent with

each other and only one curve from each orientation is plotted in Figure 2(b) to represent the behavior of that

orientation. The anisotropy of ductility in three orientations is clearly demonstrated in this figure, although

the yield and ultimate tensile stresses are very close to each other. The rolling direction is the most ductile

with an ultimate strain over 12%. The transverse direction has an ultimate strain of slightly above 10%,

which is slightly less than that of the rolling direction. The short transverse direction is the least ductile

with an ultimate strain of less than 7%.

(a) (b)

400

300

200

100

0

F/A0

(MPa

)

0.120.080.040.00L/L0

Rolling Transverse Short Transverse

Figure 2: (a) MTS set-up of experiment. (b) Stress-strain curves for specimens in different orientations.

3 Microstructural Characterization of Specimens

To link microstructural details to mechanical properties, the virgin material from all three orientations

is carefully examined using Electron Backscattered Diffraction (EBSD), optical microscopy, and Scanning

Electron Microscopy (SEM) to study the grain structures of the material. The material surface is first

mechanically polished down to 3 µm finish using a standard polishing procedure and then slightly etched

using Keller’s agent to disclose the grain boundary. Figures 3(a) and (b) show the EBSD images of the virgin

material in the T-S and T-R planes. The EBSD images clearly show that the grains are elongated along the

rolling direction with an average size of 200 µm. The grain size is ∼ 80 µm in the transverse direction (T)

4


and ∼ 30 µm in the short transverse (S) direction.

R

TS

T

100 μm 100 μm (a) (b)

Figure 3: EBSD images of the virgin material showing grain structures in the (a) S-T plane and (b) R-Tplane.

Figure 4(a) is an optical image of specimen in the T-R plane under 200× showing the grain structures

and constituent particles that are aligned in the form of stringers along the rolling direction. Figure 4(b) is

an optical image of the specimen in the T-S plane under 500× showing the grain structure and the shape

and size of particles. It is, however, difficult to distinguish different intermetallics in the optical images. For

this purpose, an SEM image of roughly the same area is acquired using the Backscattered Electron Imaging

(BEI) mode. Shown in Figure 4(c), the intensity of each pixel is dependent on the atomic weight of the

elements in the sample. In Figure 4(c), the white large particles in the BEI images are Fe-rich constituent

particles, mostly Al7Cu2Fe, Al6(Fe,Mn). The dark particles are Mg-rich particles, mostly Mg2Si [19]. The

smaller circular spots are either particles or dispersoids. Energy-dispersive X-ray (EDX) spectrums are also

acquired on both the dark and white particles. The results are consistent with the BEI images.

MgSi2-rich

Fe-rich

20 μm (a) (b) (c)

R

T

S

T

S

T

Figure 4: Optical images of (a) T-R plane at 200× and (b) T-S plane at 500× showing grain structures andconstituent particles; (c) BEI image of the same area as (b) showing the composition of the intermetallicparticles.

5


4 In-situ XCT Imaging during Tensile Testing

In this study, the in-situ XCT experiment is performed at the Advanced Light Source (ALS) at Lawrence

Berkeley National Laboratory (LBNL). The light source is a monochromatic X-ray beam with 21 keV of

energy applied. To study void evolution, the XCT imaging capability is coupled with in-situ tensile testing

of the specimen. Figure 5(a) shows the schematic of in-situ XCT experiment. The specimen is mounted on

a rotating stage located between the X-ray source and CCD detector. The apparatus records a radiograph

of the projection of the material body after a period of X-ray transmission at each i-th increment. As the

specimen rotates through 180 degrees, N radiographs are recorded at different incremental angles. For this

study, 1440 radiographs are taken which results in an angular increment of 0.125 degrees. Each series of

radiographs are acquired in-situ at each j-th increment in the loading. Here, M is the number of loading

steps that were held under load for the XCT scan. The spatial resolution of XCT is on the order of a micron

and the voxel size is 0.9 µm. Each projection is ∼ 2500× 1800 voxels, which is approximately equivalent to

a projection area of 2.2 mm × 1.6 mm. The X-ray scan is performed in the middle of a slightly tapered gage

section to ensure sure that the specimen will neck and fail within the scanned area.

(a) (b)

Figure 5: Schematic of the in-situ XCT experiment. The load frame (b) contains a confocal displacementsensor (1) and a ball joint (2).

Figure 5(b) illustrates the loading frame used for our in-situ XCT experiment at ALS. The tensile test

loading frame, used in prior work [20] is centered precisely on the rotating stage in front of X-ray source.

The loading axis aligned with the axis of the rotation. Ball joints are inserted in the loading chain for precise

axial alignment. A new confocal displacement sensor [21] with micrometer resolution is installed to measure

the crosshead displacement in-situ. A polyester tube window of negligible X-Ray absorption transfers the

6


load (via compression) between the two grip ends of the specimen.

(a) (b) (c)

Figure 6: Engineering stress-strain curves in the (a) rolling, (b) transverse and (c) short transverse directions.

Figure 6 shows the engineering stress-strain curves for the specimens loaded along the different directions.

The critical loading steps where XCT scans are performed are marked on the curve as: 1-undeformed, 2-yield

point, 3-hardening, 4-maximum load, 5-necking and 6-material failure. Given a series of of i-th radiographs

at each j-th loading increment, we seek to develop a quantitative methodology for distinguishing particles

and voids from the aluminum matrix. We need to establish guidelines for quantifying and visualizing void

evolution.

5 Quantitative Analysis of Tomography Data

A series of radiographs are acquired in-situ at each incremental load step for each specimen during the

tensile test as shown in Figure 6. Data obtained from XCT consist of gray-scale 2D images with a voxel

size of 0.9 µm per pixel which show attenuation to soft X-rays (21 keV). This attenuation can be correlated

to the mass density of the material, with bright areas being zones of higher density (particles) than dark

areas (voids). These images are processed further using the Octopus reconstruction software to obtain full

3D representations that reveal the internal structure of the material [22]. Each voxel in the reconstructed

images has a 16-bit integer associated with it, its CT number, which is proportional to its average relative

attenuation to soft X-rays, and which henceforth will be referred to as attenuation.

In order to distinguish between the aluminum matrix, particles, and voids in the images it is necessary to

determine the ranges of values of their corresponding attenuation. First, start by constructing histograms of

attenuation values of regions that are visually devoid of bright or dark zones. The corresponding histograms

are normalized so that their mean is equal to zero and their standard deviation equal to one. Figure 7(a)

7


shows the results, from which it is evident that the distributions are close to a normal probability distribution.

By contrast, the attenuation distribution of a region in the scan that is outside the specimen is essentially a

Dirac δ, as shown in Figure 7(b). This indicates that the attenuation distribution in the matrix is a feature

of the matrix and not an artifact of the scanning or reconstruction processes.

(a) (b)

Figure 7: Scan S1 (a) Normalized distribution of attenuation values of aluminum matrix (µ = 0, σ = 1)compared with the normal distribution N(0, 1). (b) Distribution of attenuation values outside specimen.

Low (voids) and high (particles) density regions can then be extracted by filtering those voxels that

deviate from the normal distribution. A typical histogram of the distribution of the attenuation values for a

scan is shown in Figure 8. This histogram was produced by taking all the slices in the reconstruction of scan

T1 and extracting a rectangular parallelepiped that avoids the boundaries of the specimen. The boundary is

not included as it contains a high concentration of voxels with both low and high attenuation values, which

would bias the statistics. This effect does not seem to be a genuine structural feature of the specimen but

rather an artifact of either the scan or reconstruction.

Note that the histogram of Figure 8 still shows a rather smooth distribution of the attenuation values

but one that deviates significantly from a normal distribution. For comparison, a normal distribution with

the same mean and standard deviation is shown as a black line in the figure. A distribution with a more

pronounced peak than the normal distribution has high kurtosis, which means that there are significant

contributions to the standard deviation from outliers.

Given the very large size of the data sets (almost two billion voxels for this set alone), the statistics are

computed in a single pass by means of moments about zero that are transformed into moments about the

8


(a) (b)

Figure 8: Histogram of attenuation values for scan T1: (a) linear-linear scale; (b) linear-log scale.

mean as follows

µk :=1

N

N∑i=1

xki , µ̄3 := µ3 − 3µ1µ2 + 2µ31, µ̄4 := µ4 − 4µ1µ3 + 6µ2

1µ2 − 3µ41, (1)

µ := µ1, σ :=√µ2 − µ2

1, γ :=µ̄3

σ3, κ :=

µ̄4

σ4− 3, (2)

in which N is the number of voxels in a given set, xi the attenuation value for voxel i, µ is the mean, σ is the

standard deviation, γ is the skewness, and κ is the excess kurtosis, defined in a way that both the skewness

and kurtosis of the normal distribution are zero. The statistics for all the scans are summarized in Table 1.

Positive skewness means a distribution tilted toward −∞ and negative skewness means a distribution

tilted toward +∞, both with respect to a distribution with zero skewness. Note that all scans have relatively

low negative skewness, which means that their distributions of attenuation are highly symmetric, as it is

evident from the example in Figure 8. Kurtosis is a measure of the concentration of values around the mean.

A leptokurtic distribution (high kurtosis) has a high central peak and many outliers as compared with the

normal distribution. A platykurtic distribution (low kurtosis) has a flattened central peak and few outliers

as compared to the normal distribution. Note that the attenuation distributions for all scans are highly

leptokurtic, which means that they contain a significant amount of outliers and a high peak at the center,

as it is evident from Figure 8.

The distribution of attenuation values in the aluminum matrix follows closely that of the normal dis-

tribution, as seen in Figure 7(a); while the background is highly monochromatic, as shown in Figure 7(b).

These two observations indicate that the normal distribution of the matrix attenuation values is a feature

9


ScanNumber of Voxels Mean Std Dev Skewness Kurtosis

N µ σ γ κR1 2 301 320 960 30 978.9 628.4 -0.7 60.8R2 2 131 860 605 34 849.6 706.7 -0.5 42.1R3 1 974 380 079 34 432.9 588.5 -0.7 44.8R4 1 726 160 744 34 428.9 639.5 -0.7 30.2R5 1 542 430 692 34 435.3 693.5 -2.6 83.1R6 1 466 857 008 34 443.4 747.9 -3.5 96.1T1 1 904 894 496 34 819.6 698.2 -0.6 56.0T2 1 895 833 544 34 408.7 556.6 -1.5 91.3T3 1 891 507 845 34 411.9 556.6 -1.1 67.8T4 1 792 388 864 34 414.9 575.6 -1.2 66.1T5 1 557 048 744 34 417.6 748.2 -3.3 97.4T6 766 397 352 27 870.9 703.0 -4.6 118.9S1 2 084 499 200 34 222.2 533.0 -0.8 56.0S2 2 048 435 200 34 383.3 601.5 -0.8 54.2S3 1 954 356 000 34 385.1 633.9 -1.4 59.9S4 1 871 206 400 34 388.7 696.0 -2.5 81.5S5 1 846 365 204 34 389.5 744.4 -3.1 90.6S6 364 860 840 34 365.3 627.1 -0.3 8.1

Table 1: Statistics for all scans.

of the specimen. On the other hand, the high values of kurtosis observed in Table 1 for all scans indicate a

significant presence of outliers that are located toward the tails of the distributions. This is evident in the

semi-logarithmic plot of Figure 8. This suggests that in order to find the distribution of outliers contained

in the full histogram of a scan, such as the one in Figure 8, one would need first to identify the normal

distribution associated with the attenuation values of its matrix. Provided that this identification can be

performed, the distribution of outliers would be given by the difference between the full distribution and the

matrix normal distribution.

The identification of the normal distribution associated with the matrix was performed using two methods:

a least-squares fit using the central part of the histogram that has no obvious outliers (from µ−σ to µ+σ),

and the random sample and consensus approach or RANSAC, which finds a model from data that contains

a significant amount of outliers. The theory behind the RANSAC method is not addressed here; we defer

to Fischler and Bolles who first introduced this technique [23]. The results of using both the least-squares

and RANSAC approaches are shown in Figure 9. It shows the normalized scan histogram (circles), a normal

distribution with the same mean and standard deviation as the full distribution (black), the best-fitting

normal distribution found by RANSAC (blue), a normal distribution that was fitted by least-squares to the

central part (red), and the difference between the full distribution and the least-squares fit (green).

10


(a) (b)

Figure 9: Identification of matrix normal distribution for scan T1. Black, normal with µ and σ. Red,least-squares fit. Blue, RANSAC fit. Green, outlier distribution. (a) linear-linear scale; (b) linear-log scale.

The results shown in Figure 9 are typical in the sense that, in our computations, the least-squares

approach consistently produced better results than the RANSAC approach. Although the theory behind the

RANSAC method is sound and robust, it is known that in order to find the model that best fits the data

with a high probability, the RANSAC algorithm may require a large number of iterations. We found that

the computational expense associated with the RANSAC approach was not justified, especially considering

that in this case the location of outliers is known beforehand, and therefore one can quickly produce a good

fit by using least squares.

The central part of the outlier distribution computed in this manner sometimes yields small negative

values. These values are unrealistic and are associated with fits that have larger distribution values than the

original curve. These negative values can be ignored, as we are interested in outliers at the tails. With this in

mind, we now proceed to define the criterion that separates voids and particles from the aluminum matrix.

The green curve in Figure 9 indicates the difference between the full attenuation distribution and the normal

distribution associated with the matrix. Thus, it also indicates the attenuation distribution of outliers. Note

that the full normalized histogram is the only true probability density function (PDF) involved here, and

therefore

P [a ≤ X ≤ b] =

∫ b

a

f(x) dx,

∫ +∞

−∞f(x) dx = 1, f(x) = g(x) + h(x), (3)

in which X is a random attenuation value, f(x) represent the histogram (taken as a continuous function),

x is the attenuation (taken as continuous as well), and g(x) and h(x) are functions representing the matrix

11


and outlier attenuation distributions, respectively. It follows from these definitions that, given p ∈ [0, 1], the

attenuation value x with probability of being an outlier p and probability of being in the matrix 1 − p is

given by solutions of

p h(x) = (1− p) g(x), (4)

if such solutions exist. As an example, assume that p = 12 , which means finding attenuation values for

which it is equally likely that they are part of the matrix or outliers. The criterion (4) is reduced to finding

solutions for h(x) = g(x). In terms of Figure 9 this requires finding points where the green and red curves

intersect, if any such points exist. From the figure, in particular in the semi-logarithmic plot, it is clear that

two such points exist, one at each tail of the distribution. Thus, there are two attenuation values for which it

is equally likely that they correspond to matrix or outliers: one for voids for the left tail and one for particles

for the right tail.

Solving (4) for a given p does not pose significant computational challenges, as the histograms are repre-

sented as pairs of values (attenuation, distribution). Therefore finding solutions is relatively simple by using

interpolation between points.

The results of applying criterion (4) to determine the void volume fraction for all the scans are shown in

Figure 10. We remind the reader that the samples from each scan derive from a rectangular parallelepiped

that avoids the boundaries of the sample. For nearly all the scans, the region is nearly a cube (of varying size)

at the centerline. The selected confidence value of p = 0.90 gives reasonable assurance, with 90% probability,

that the attenuation threshold for each scan separates voids from the matrix. This confidence value is shown

as a circle in the figure. The limits of the error bars are for a confidence of 95% (lower limit) and 80% (upper

limit). The higher the confidence, the lower the computed void volume fraction. Issues with the sampling

and reconstruction of the short transverse case reveal a non-physical void volume fraction after failure (scan

6).

6 Observations of Damage Evolution

Although helpful in estimating the accuracy of a given model, the evolving void volume fraction shown

in Figure 10 cannot help the researcher determine the dominant mechanisms governing anisotropic void

evolution. To help the reader, case studies from specimens loaded along the three material orientations are

rendered along different using the ParaView visualization software [24]. Figure 11 shows voids distribution

and evolution for the specimen loaded in the transverse (T) orientation.

12


1 2 3 4 5 6Rolling Scan

0

2×10-3

4×10-3

6×10-3

8×10-3

1×10-2

Voi

d V

olum

e Fr

actio

n

1 2 3 4 5 6Long Transverse Scan

1 2 3 4 5 6Short Transverse Scan

Figure 10: Computed void volume fraction with 90% confidence for each specimen and scan using criterion(4). The error bar limits are for 95% confidence (lower) and 80% confidence (upper).

undeformed

(1)

RT RT RT RT

100 μm 100 μm 100 μm 100 μm (4) (5) (6) maximum load necking failure

Figure 11: A horizontal slice of the tomographic image of the specimen loaded along the transverse (T)direction. Step (1)-undeformed configuration; Step (4)-near maximum load; Step (5)-necking and Step (6)-material failure.

13


The intensity patterns of the tomographic images can reveal internal features of the material. 3D images

reconstructed from XCT radiograph contain rich information throughout the whole material body. To

observe and understand the void evolution at loading increments, the reconstructed 3D images are then

sliced and rendered. Figure 11 shows a horizontal slice of the tomographic images for the specimen loaded in

the transverse direction at loading steps of (1), (4), (5) and (6) as marked in Figure 6(b). The slice thickness

is equal to the spatial resolution of the scanner, 0.9 µm. From these series of slices, we can visualize the

void evolution that leads to material failure, as shown in the circled area near the surface of the bar. Some

initial voids exist in the original undeformed material and there is no dramatic void evolution in the earlier

steps (1)-(4). However, larger voids are clearly seen at loading step (5)-necking and material failure occurs

at step (6). These images confirm that voids do not necessarily nucleate and grow. Local coalescence along

stringers of particles can affect void evolution.

6.1 Rolling orientation

To understand the void evolution for the specimen loaded in the rolling direction, a sub-volume from the

acquired 3D image was selected. Figure 12(a) shows the center horizontal slice in the S-T plane of the 3D

tomogram for the specimen at the necking stage. An area of 450× 50 voxels (405× 45 µm2) as marked by

the white rectangle in Figure 12(a) is selected near the bar surface as an area of interest. This same area

is selected through 600 slices along the rolling direction, referring to this slice as the middle one. A total

sub-volume of 450×50×600 voxels (405×45×540 µm3) is built from these slices as a representative volume

as shown in Figure 12(b). Figure 12(c) shows 3D rendering of voids (orange color) and particles (white color)

in the R-T plane when the specimen is at the undeformed state. For each scan, the particles and voids are

defined through the mean and the standard deviation. To ensure high confidence, particles and voids are

filtered through µ + 3σ and µ − 3σ, respectively. The aluminum matrix is rendered transparent. Since the

image contains a finite sub-volume, the void and particle volume fraction appear to be higher in the rendered

images. In Figure 12(c), it can be seen that the existing voids are mostly aligned with particles. The void

and particle distribution tends to form cells which are highlighted by the dashed lines. The shape and size

of these cells are consistent with those of grains, as shown in EBSD and optical images in Figures 3 and 4.

These observations suggest that the voids are mostly aligned with particles along the grain boundaries.

Figures 12(d) and (e) show the void distribution in the R-T plane at the undeformed and necking states,

respectively. In this case, the necking state is show as scan (5) in Figure 6. The highlighted grain boundaries

in Figure 12(d) are stretched along the loading direction to simulate the tensile loading of the specimen.

14


R

600

voxe

ls

T

S

T

R

100 μm

T

R

T

R

T

S

(a) (b)

(c) (d) (e)100 μm 100 μm

100 μm

Figure 12: Void evolution for the specimen loaded in the rolling (R) direction. (a) A horizontal tomographicslice of the specimen in S-T plane at the necking state, marked as step (5) in Figure 6(a), showing thearea of interest; (b) sub-volume selected for image rendering; (c) 3D rendering of voids (orange color) andconstituent particles (white color) for the specimen in the undeformed state; (d) 3D rendering of voids inthe R-T plane in the undeformed state and (e) necking state.

15


R

S

100 μm

100 μm

R

TR

T

R

S

100 μm

100 μm

(a) (b)

(c)

(d)

(e)

100 μm

R

T

Figure 13: Void evolution for the specimen loaded in the transverse (T) direction. (a) A horizontal slice ofthe tomographic image in the S-R plane at the necking state, step (5) in Figure 6(b), depicts the selectedcross-section in the R-T plane. A 3D rendering of voids (orange) and constituent particles (white) for thespecimen in the undeformed (b) and necking state (c) illustrates local coalescence along a 1-D stringer.Figures (d) and (e) confirm the aspect ratio of the void stringer through views in the T-R and S-R planes,respectively.

They are then overlaid onto the rendered tomographic image in the necking state, as shown in Figure 12(e).

One can see that the void distribution in the necking state is mostly along the same grain boundaries.

Local coalescence between adjacent voids in the transverse direction is limited. Void stringers in the rolling

direction remain stable. Larger regions of coalescence are not noted in the R-T plane.

6.2 Transverse orientation

Figure 13 shows void distribution and evolution for the specimen loaded in the transverse direction. A center

slice in the S-R plane of the specimen at the necking state is shown in Figure 13(a). An area of 620 × 50

voxels (558× 45 µm2) as marked by the white rectangle in the image is selected as an area of interest. This

same area is selected through 400 slices, referring to this slice as the middle plane in the same manner as the

rolling direction. Thus, a total volume of 620×50×400 voxels (558×45×360 µm3) is built from these slices

to study the void evolution for the specimen loaded along the transverse direction. Figure 13(b) shows the

16


(b)

(a)

R

T

100 μm

R

T

R

S

(c)

(d)

(e)

R

T

R

S

100 μm

100 μm

100 μm

100 μm

Figure 14: Void evolution for the specimen loaded in the short transverse (S) direction. (a) A 2D tomographyslice of the specimen at the necking state in the T-R plane, showing the area used for vertical projectionsin the S-R plane; (b) 3D rendering of voids in the T-R plane and (c) in the S-R plane in the undeformedconfiguration; (d) 3D rendering of voids in the T-R plane and (e) in the S-R plane at the necking state.

3D rendering of voids and particles in the undeformed state. To ensure high confidence, inclusions and voids

are filtered through µ+3σ and µ−3σ, respectively. The voids and particles are mostly distributed along the

grain boundaries, similar to what has been shown in Figure 12(b). Figure 13(c) shows the 3D rendering of

voids in the T-R plane for the specimen in the necking state, as marked in scan (5) in Figure 6(b). Figures

13(d) and (e) are closer views of the white circled area in Figure 13(c), showing the details of void evolution

in the T-R and S-R planes, respectively. One can easily observe that void evolution is minimal along the

S and T directions. Local coalescence along the 1D stringers (aligned in R) is significant. We contrast the

the transverse orientation (T) to the prior rolling orientation (R). Both contain aligned 1D defect structures

loaded in different orientations.

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6.3 Short orientation

Figure 14 shows void distribution and evolution for the specimen loaded in the short transverse (S) direction.

A 2D slice of the specimen in the T-R plane at the necking state is shown in Figure 14(a). An area of 500×120

voxels (450×108 µm2) as marked in the white rectangle in the image is selected as area-of-interest. This same

area is selected through 100 slices, referring to this slice as the middle plane. Thus, a total representative

sub-volume of 500 × 120 × 100 voxels (450 × 108 × 90 µm3) is selected to study the void and particle

distribution when the specimen is loaded along the short transverse direction. Figures 14(b) and (c) show

the 3D rendering of voids for the undeformed state in the T-R and S-R planes, respectively. To ensure high

confidence, inclusions and voids are filtered through µ+ 3σ and µ− 3σ, respectively. One can observe that

the void distribution forms thin pancake-like layers in the T-R plane, perpendicular to the short transverse

direction. Please note that T-R plane shows defects from nominally three layers of grain boundaries. Side

views in the S-R plane illustrate the through-thickness location of the planar structures. Figures 14(d) and

(e) show the 3D rendering of voids at the necking state (scan 5, Figure 6(c), red) in the T-R and S-R planes,

respectively. Clearly, local coalescence along boundaries in the R-T plane is illustrated in Figures 14(d) and

(e). Limited void evolution occurs along the short transverse direction. Void nucleation and local coalescence

has planar preference perpendicular to the loading direction (transverse direction).

7 Discussion

Through this work, we have developed techniques to distinguish particles and voids and performed funda-

mental experiments for mechanistic discovery. We believe that the approach introduced in Section 5 is a

robust technique to partition the particles and voids in the material. The voxel size of the images being

0.9 µm, however, is insufficient to elucidate the mechanisms that lead to nucleation of the voids, namely, the

initial formation of a void from the debonding of the interface between a particle and the metallic matrix,

or the propagation and growth of a void from an already debonded interface that existed in the undamaged

material. In addition, the reliability of this type of quantitative analysis is highly sensitive to scan or re-

construction error. Reconstruction artifacts, such as wings, streaks or halos that propagate from voids and

particles enter the statistics as spurious outliers, compromising the analysis. Since we seek high confidence,

we filtered voids through µ− 3σ for the case studies illustrated in Section 6.

Experiments devoted to mechanistic discovery examine the undeformed reference (1), macroscopic yield

(2), strain hardening (3), peak-load (4), necking (5), and failure (6). Although limited, the knowledge gained

18


R

T

S

T

ST R

S R

T

ST

Rolling (R) Transverse (T) Short (S)

200x

2000

x

Figure 15: Fractographs of tensile specimens at 200× and 2000× aligned with the rolling (R), transverse(T), and short transverse (S) orientations.

through in-situ tomography can inform the functional forms employed to model the observed anisotropy in

7075-T7351 prior to global coalescence. Again, we emphasize that our goal was not to derive the kinetics

for a particular aspect of void evolution. We seek to elucidate the needed anisotropic mechanisms (internal

variables) needed to capture void evolution.

To aid our tomographic findings, fractographs of tensile specimens loaded in the rolling (R), transverse

(T), and short (S) orientations at 200× and 2000× are illustrated in Figure 15. Although Section 6 focuses

on events prior to global coalescence, features noted through tomography are confirmed via fractography.

The rolling direction illustrates larger voids that coalesce through a localized plastic instability [25]. In the

transverse direction, one can detect the 1D void stringers that run along the rolling direction. At 2000×,

the curved facets along the void stringer in Figure 15 confirm multiple nucleation sites along the 1D defect.

The short transverse direction confirms the role of 2D planar defects prior to coalescence through internal

necking. Increased magnification illustrates nucleation along a grain boundary bordered by larger particles.

Although helpful, the failure surfaces at 200× and 2000× cannot reflect temporal evolution. Multiple defect

populations are present and it is difficult to determine primary from secondary processes.

The observations in the rolling orientation point to void nucleation and growth. Nearly spherical voids

are prominent on the fracture surface. Although Figure 12 cannot provide the kinetics of growth, the

observations do indicate that (a) voids nucleate along stringers of particles and that (b) the process is stable

19


with minimal local coalescence. Based on EBSD and optical observations (see Figures 3 and 4), we position

those 1D defect structures along grain boundaries. Stability derives from the fact that void nucleation along

a 1D defect structure will shield neighboring defects and permit void growth via plastic deformation. This

process evolves until global coalescence. Regrettably, scans were not conducted prior to failure. Our findings

can only illuminate the nucleation and growth.

The transverse and the short transverse directions are less standard. Multiple populations of voids are

noted in Figure 15 for the transverse (T) and the short (S) orientations. To understand void evolution prior to

global coalescence, we rely on tomographic observations. We find that for the transverse direction, voids also

nucleate along 1D defect structures (stringers of particles). Unlike the rolling direction, void nucleation in the

transverse direction concentrates the load on adjacent particles within the stringer. Additional nucleation

and local coalescence ensues. Through this process of nucleation and local coalescence, 1D void structures

evolve and shield adjacent stringers (fore, aft) in the R-T plane . These 1D structures are evident in both the

tomography (Figure 13) and the fractography (Figure 15). Although the final void shape may be considered

ellipsoidal, the mechanistic process does not reflect the growth of an ellipsoidal void. Local coalescence, not

void growth, is the dominant process. We emphasize that due to the heterogeneity of defects in materials like

7075-T7351, there will always be local coalescence for any orientation. These observations, however, confirm

that for the transverse orientation, local coalescence is a dominant mechanism and may be considered a

proxy for 1-D void growth.

Perhaps the case that deviates the most from dilute void growth is the short transverse orientation (S).

The ductility is almost half of the rolling direction. Like the transverse direction, multiple defect populations

are present on the fracture surface. Tomography illustrates that planar defect structures are nucleated in

spacings (see Figure 14(e) and Figure 4(b)) consistent with grain boundaries. In-plane (T-R) stringers of

particles concentrate the load on a grain boundary populated with defects. Voids nucleate and coalesce

(locally) to form 2D defect structures that shield adjacent boundaries (above, below) in the S-R plane.

Although the final void shape may be idealized as an oblate spheroid, the mechanistic process does not

reflect the growth of a spheroidal void. Local coalescence, not void growth, is the dominant process. In the

short orientation, local coalescence may be considered a proxy for 2-D void growth.

The partition of ductile fracture into void nucleation, growth, and coalescence is perhaps too idealized for

the anisotropic defect structures observed in Al 7075-T7351. While the rolling orientation might be captured

with prior works, our work in the transverse and short orientations seeks to illustrate the importance of

local coalescence. The direction of loading can evolve 1D or 2D defect structures that concentrate and/or

20


shield local fields prior to global coalescence. Even the assertion that a particular model form is adequate

for a particular orientation requires proportional loading. Internal variables must be constructed to reflect

anisotropic damage in the event of non-proportional loading. Future work will seek to incorporate these

findings into model forms. Our goal is to address non-proportional loadings and/or loading orientations not

aligned with the material axes with an integrated experimental/computational effort.

8 Conclusions

This work examines the anisotropic damage evolution of the high strength aluminum alloy 7075-T7351 in

the rolling (R), transverse (T), and short transverse orientations (S). Specimens extracted and tested exhibit

varying ductility in these three orientations, with most ductility in the rolling direction and least ductility

in the short transverse direction. EBSD, optical microscopy, and SEM are employed to characterize the

grain structure and the size, location, and chemical composition of the intermetallic particles. In-situ X-ray

tomography is employed during the tensile loading of the specimens and tomographic images are collected at

critical increments of loading. The radiographs acquired during the tensile test are then reconstructed and

examined through quantitative analysis to partition particles and voids. Rendered images are probed to study

the mechanisms of anisotropic void evolution for specimens loaded in R, S, and T. These mechanisms are

confirmed through fractography. Through analysis, microscropy, diffraction, tomography, and fractography

of the rolled aluminum alloy 7075-T7351, we find:

1. One can partition particles and voids through the intersection of distributions for the entire body and

the aluminum matrix (devoid of particles/voids). Distributions for the entire body are shown to be

highly leptokurtic while distributions of the matrix are normal.

2. Void nucleation, growth, and local coalescence are aligned with particles that are distributed along

grain boundaries with preference to 1D stringers along the rolling direction. Void structures mirror

particle structures.

3. For the specimens loaded in the rolling direction, void nucleation and growth are dominant prior to

global coalescence. Voids nucleate along 1D stringers of particles and shield neighboring particles/voids.

Shielding stabilizes void growth and permits increased necking and ductility.

4. For the specimens loaded in the transverse direction, void nucleation and local coalescence are dominant

prior to global coalescence. Void nucleation along 1D stringers concentrates the load to further nucleate

21


additional voids. These voids locally coalesce to form 1D void structures that shield neighboring void

stringers but result in decreased ductility.

5. For the specimens loaded in the short transverse direction, void nucleation and local coalescence are also

dominant prior to global coalescence. Voids nucleate and concentrate the load on particle-rich bound-

aries. Planar, 2D void structures evolve through nucleation and local coalescence. These structures in

the R-T plane evolve early in the necking process and limit the ductility.

These findings emphasize the importance of local coalescence in void evolution of the transverse and short

transverse orientations. Models with appropriate internal variables to characterize the anisotropic damage

of rolled aluminum alloys such as 7075-T7351 should consider incorporating local coalescence in 1D and 2D

void structures to model the performance of structures under multi-axial and non-proportional loadings.

9 Acknowledgments

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation,

a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National

Nuclear Security Administration under contract DE-AC04-94AL85000. The authors greatly appreciate the

help from the staff members Alastair MacDowell, Dula Parkinson and Jamie Nasiatka at the Advanced Light

Source, Lawrence-Berkeley National Laboratory.

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An Examination of Anisotropic Void Evolution in Aluminum Alloy 7075

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