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Strain localization and damage mechanisms during bending of AA6016 sheet
Materials Science & Engineering A 559 (2013) 812–821
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Strain localization and damage mechanisms during bending of AA6016 sheet a,n ¨ Laurent Mattei a, Dominique Daniel b, Gilles Guiglionda b, Helmut Klocker , Julian Driver a a b
Ecole Nationale Supe´rieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42000 Saint-Etienne, France Constellium, Centre de recherches de Voreppe, 725 rue Aristide Berge s, BP 27, 38341 Voreppe Cedex, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 June 2012 Received in revised form 6 September 2012 Accepted 7 September 2012 Available online 16 September 2012
The bendability of AA6016 sheets is a critical parameter for many automotive applications. In this experimental study the origins of damage and its evolution are characterized using interrupted and insitu bending tests to correlate microstructural evolution with damage development. Local strains were estimated by optical and scanning microscopy (EBSD). Together with the load-displacement plots, they provided a set of physical parameters characterizing crack initiation. In particular, it is shown that
Keywords: Aluminum alloys Bendability Damage kinetics EBSD and optical observations
(1) crack initiation occurs at the maximum of the rigidity–displacement curve; (2) cracking is preceded by strain localization in the form of macro-shear bands which induce surface roughening. Local necking then occurs in some surface grains and leads to ductile intergranular crack propagation. The sequence of microscopic changes at the grain scale up to and beyond crack initiation have been characterized and quantified in terms of local grain strains, coarse intragranular slip and shear band evolution over several grains. & 2012 Elsevier B.V. All rights reserved.
1. Introduction Aluminum alloys are increasingly used in automotive structural applications because of their combination of low density, high strength and good formability. Bending is important in the shaping of complex parts, and it is also critical in the joining of outer skins to inner sheet panels by hemming. Appropriate strength levels for automotive aluminum panels are achieved by a combination of alloy composition and thermo mechanical treatment [1,2], and several experimental studies concern the influence of alloy composition on bend performance of Al 6xxx automotive sheet [3–6]. The bendability has been shown to decrease with increasing copper, iron and Si content. In particular Davidkov et al. [7] have recently investigated the major role of Mg2Si and AlCuMgSi Q phase particles on the bending response of 2 AA6016 grades. Most theoretical analyses attribute damage during bending to the development of surface roughness and intense strain localization. Several authors conclude that shear bands initiate at points of strain concentration induced by initial thickness heterogeneity [8–10]. Other authors have analyzed the effects of thermal softening on shear banding [11,12]. Crystal plasticity simulations have also been used essentially to analyze the effect of particular
n
Corresponding author. Tel.: þ33 4 77 42 0078; fax: þ33 4 77 42 0000. ¨ E-mail address: [email protected] (H. Klocker).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.09.028
textures on the formability and bendability of sheet metal [13–19]. Probably the most important result of these studies is the close relationship between surface roughening and strain localization. But strain localization is difficult to characterize experimentally. Thus most experimental studies have compared different alloys based on macroscopic measurements (bending angle), whereas theoretical damage analyses focus on local behavior (shear band pattern). The present work aims to quantify damage evolution during bending of AA6016 sheet in terms of strain localization by the use of in-situ and interrupted tests. The kinetics of damage development during bending is determined. Original quantitative measurements based on optical and electron metallographies for shear banding are also developed.
2. Experimental 2.1. Material and microstructure The chemical composition of AA6016 alloy sheet is given in Table 1. The industrial sheet was obtained from cast ingots hot rolled to a thickness of 2 mm, then cold rolled to the final gauge of 1 mm. The sheet was solution heat treated at 560 1C followed by a forced air quench to room temperature and natural aging for 1 week. The initial grain size was characterized by optical metallography and found to be homogeneous throughout the sheet thickness. The mean grain dimensions are 47 mm in the rolling direction, 30 mm in
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the transverse direction and 24 mm in the normal direction. Crystallographic texture was characterized by electron backscatter diffraction (EBSD) measurements and found to be weak with a small cube component peak. 6016 alloys contain intermetallic iron-rich and Mg2Si particles whose size and spatial distribution (mean surface fraction 1.16%) were characterized in previous work [20]. These intermetallic particles exhibit equal dimensions in the rolling (RD) and transverse (TD) direction (1.39 mm) and a height of 2.9 mm. Standard tensile tests were used to determine the initial yield strength (143 MPa). The large strain behavior to strains of 1 was characterized by plane strain compression tests on bonded samples [20]. Only very small yield anisotropy is observed [21]. The flow stress during large strains of 6016 alloy may be described by an extended Voce law [22] given by
s ¼ s0 þðs1 s0 Þð1edep Þ þ aep
ð1Þ
where ep is the accumulated plastic strain. s0 and sN are the initial yield stress and the saturation stress in the classical Voce law, respectively. d describes hardening at small strains and the additional term aep describes hardening at large strains. The constants are given in Table 2.
Table 1 Chemical composition of analyzed alloy.
6016
Si (%)
Fe (%)
Cu (%)
Mn (%)
Mg (%)
1.05
0.24
0.06
0.17
0.39
Table 2 Extended Voce law parameters of T4 6016 aluminum alloy.
s0 (MPa)
rN (MPa)
d
a (MPa)
143
282
16
146.4
813
2.2. Plane strain bending tests Several tests to characterize bending performance have been described in the literature [23–25]. In the present work, two planestrain bending tests were used for characterizing damage development on 6016T4 sheet. First standardized bending tests were carried out in accordance with the guidelines proposed by Daimler-Chrysler [26] and DIN 50 111 with a test set-up shown in Fig. 1. Samples of size 60 60 mm2 were machined from the sheet and tested in two directions (parallel and perpendicular to the rolling direction). The tests were performed on a standard tension/compression testing machine. The geometrical characteristics of the test set-up are given in Table 3. The punch speed was initially 10 mm/min until a preforce of 30 N was reached, then increased to 20 mm/min. During the bending test the applied force F and the punch displacement U were recorded continuously. The test was automatically stopped when the force dropped by more than 15 N from the maximum force. Interrupted bending tests on the same geometry were used to characterize the relation between damage development and microstructural evolution. An original in-situ bending test was also developed for scanning electron microscopy observations of surface damage evolution. Fig. 2 shows this bending module based on a Kamrath tensile machine as used in a Zeiss Supra FEG SEM. In this test facility, the punch is fixed and the rolls move. The displacement and the load applied to the rolls are recorded continuously. The punch radius (Rp ¼ 0.2 mm) is the same as in the standardized test. The geometrical characteristics of the test setup are given in Table 4. Note that small-scale SEM in-situ bend tests are particularly useful for characterizing the damage mechanisms but do not always allow reproducible damage quantification.
2.3. Strain maps and strain localization 2.3.1. Strain maps In the present work the relationship between damage evolution during bending and strain localization (shear bands) was analyzed experimentally over a large number of grains under
Fig. 1. Bending test: (a) overall view of the test, (b) bent sample with observed sections and (c) punch.
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plane strain conditions. The strain distribution was measured in the mid-section (BB’ in Fig. 1) of the bent samples. The shape factor of each individual grain was determined as the ratio between maximum and minimum Feret radii. The assumption of plane strain deformation in the sample mid-section gives the mean value of the equivalent von Mises strain in each grain as 1 l e ¼ pffiffiffi log ð2Þ l 3 0 where l and l0 are respectively the initial and current values of the grain shape factor. Two methods were used to characterize the individual grain shape: optical micrography after chemical etching and EBSD observations by reconstruction of the individual grains. The parameters used for the EBSD observations are given in Table 5. For the reconstruction of individual grains, misorientations larger than 101 were identified as grain boundaries. Another method of quantifying strain localization is by digital image correlation as used by Davidkov et al. [27] on continuous cast AA5754 sheet samples. This method was not applied here because of the large out-of-plane movements. 2.3.2. Coarse slip Crystallographic glide leads to the formation of coarse slip bands inside the grains with traces observable by scanning electron microscopy. Fig. 3 shows band contrast maps of bent samples. Band contrast maps are particularly well adapted for visualizing coarse slip bands. But, to quantify their density, orientation maps (as Euler angles) were preferred. The density of coarse slip bands was determined from binary misorientation maps using cut-off angles between 21 and 101. Misorientations larger than 101 were
associated to grain boundaries. An area of 250 mm 300 mm close to the outer surface of bent specimens (section BB0 in Fig. 1) was analyzed to give the density of coarse slip bands defined as the relative number of black pixels in the binary image.
3. Results 3.1. The general kinetics of damage development during bending 3.1.1. A macroscopic criterion for failure during bending Fig. 4a shows a typical load displacement curve for the 6016T4 sheet. The scatter is extremely small, thus only one curve is represented. First the punch displacement at failure Uf (12.8 mm) and the minimum bending angle bf after elastic unloading (bf ¼281) were determined. Since F and U are measured continuously, it is possible to plot out the apparent rigidity (dF/dU) as a function of the displacement U as in Fig. 4b. The overall rigidity exhibits a clear maximum at 0.92Uf. For other samples, the bending test was stopped at different punch displacements and the damage was observed in the
Table 4 Characteristics of the new in-situ bending test. Parameter
Value
Sheet width Sheet height Radius of the punch Rp Radius of the rolls Roll gap
33 mm 10 mm 0.2 mm 5.75 mm 4.5 mm
Table 3 Characteristics of standard bending test. Parameter
Value
Sheet width and length Radius of the punch Rp Radius of the rolls Roll gap Maximum punch displacement umax Punch velocity during preload Preload Punch velocity during bending Test stop for a load drop of
60 mm 0.2 mm 15 mm 2nt mm 14.2 mm 10 mm/min 30 N 20 mm/min 15 N
Table 5 Parameters used in EBSD acquisition. Undeformed sample Bent sample Magnification Step size (mm) Binning Gain Number of frames Resolution in Hough space
100 5 44 High 2 60
Fig. 2. In-situ bending test: (a) overall view of the test and (b) bent sample with the observed section.
500 1 44 High 3 60–90
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Fig. 3. Band contrast observations (step 1 mm) in section BB0 after interrupted bending test for several punch displacements of 0.6Uf, 0.85Uf, 0.96Uf, Uf.
Fig. 4. Bending test: (a) typical load displacement curve of the punch and (b) typical variation of the overall rigidity as a function of the punch displacement.
midsection of different samples (Fig. 1). Fig. 5 shows optical micrographs (section BB0 ) corresponding to different punch displacements. At this scale, damage is observed only on the outer skin submitted to tension. At relatively small punch displacements (0.6Uf), surface instabilities become visible. Between 0.6Uf and 0.91Uf, the intensity of the surface undulations increases, but no surface cracks are observed. A crack develops ‘‘suddenly’’ at a punch displacement of 0.92Uf corresponding to the maximum of the overall rigidity. Crack formation during a standard bend test occurs when the overall rigidity attains a maximum. To our knowledge, this macroscopic criterion for bend cracking (dF/dU maximum) does not appear to have been observed before.
3.1.2. Strain localization as the motor of damage development Several simulations assumed surface undulations to be the cause of strain localization [8]. Other authors considered the surface undulations as a consequence of strain localization [13–18]. The importance of surface roughness on bend performance was
first examined by Lloyd [28] using a Cantilever Beam Test. He bent specimens to an intermediate angle, then polished off the surface topography and measured the bend angle that could be obtained. Intermediate polishing appeared to enhance bendability. In the present work, to analyze the influence of surface roughness on damage development during bending, three test series were run (Fig. 6). In the first series, samples with an industrial surface finish were bent to failure at an angle b1 ¼281. For the second and third test series samples were first polished to a mirror finish (P4000) prior to bending. One part of these samples (series 2) was bent to failure at an angle of b2 ¼ 211 and the punch displacement U2. In the third series bending was stopped at a punch displacement larger than 0.6U2 and the surface re-polished to a mirror finish. Then the new bend angle b3 was determined and found to be 211, i.e. identical to b2. We conclude that for an initially mirror polished sample, intermediate polishing does not improve the bendability. Initial surface roughness (undulations) favors the development of strain localization [7,26]. But eliminating the surface roughness
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Fig. 5. Observations of bent specimens (section BB0 ) at different punch displacement. Development of a wavy surface (a, b, e, f), surface cracks (c, d, g, h).
Fig. 6. Bending tests run for analyzing influence of surface roughness on bendability.
at an intermediate bending angle does not enhance the bendability compared to an initial mirror surface finish. Fig. 7 shows an optical micrograph of a sample bent to the minimum bend angle. Strain localization leads locally to significant changes in grain shape and orientation. Grain rotation and grain deformation at the outer surface lead to surface undulations. It is therefore concluded that strain localization controls damage development and leads to the formation of surface cracks.
3.1.3. Observation of surface cracks The mechanisms leading to the development of surface cracks were characterized by the in-situ bend test. Fig. 8 shows the free surface (section AA0 ) of a bent specimen. Grains deform by slip on particular crystallographic systems, and shear typically accompanies stretching. In most grains only one set of coarse bands is visible at the free surface. But close to the outer surface, grains with two visible sets of coarse bands are observed. Strain localization leads to ‘‘necking’’ of these surface grains. This neck causes an intergranular crack to propagate (Fig. 8b, c) and leads to final failure. Davidkov et al. [7] have also observed this final intergranular failure mode in a similar alloy. Some of the adjacent grains can move perpendicular to the surface without significant deformation. This relative motion of two surface grains also causes an intergranular crack to propagate (Fig. 8b). In Fig. 8 surface cracks are observed, but no cavitation is observed before crack initiation. In summary, we observe that the basic damage mechanism consists of very intense localized necking in some grains which then initiates intergranular crack propagation to final failure. 3.2. Quantification of strain localization and damage development The previous section showed that strain localization is the motor of damage development. Once strain becomes localized, eliminating the surface roughness does not eliminate the damage. It is therefore important to characterize and quantify strain localization.
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Fig. 7. Optical observation in section BB0 of a specimen bent to failure: (a) grain deformation and rotation, (b) grain necking at the outer surface and (c) development of a crack.
Fig. 8. In-situ observations of bent specimen in section AA0 : (a) overall view of the bent specimen, (b) grain movement without straining, (c and d) grain ‘‘necking’’ due to multiple slip.
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3.2.1. Shear banding Strain localization was characterized in the mid section of specimens bent at different punch displacements. Fig. 9 shows optical micrographs of the microstructures before and after
Fig. 9. Optical micrograph (section BB0 ) of the initial microstructure and after bending to failure ({RD, ND}¼ rolling axes).
bending. In the initial microstructure, the grains are quasi-equiaxed. During bending, the grains at the outer surface rotate and stretch parallel to the overall tension direction. The determination of the mean strain in each grain was based on EBSD observations. Fig. 10 shows Euler angle maps of two bent samples. The mean strain, given by the variation of the shape factor, was determined in each grain (Eq. (2)) and mapped out in Fig. 11. This figure also reveals elongated zones of higher deformation (indicated in red) that we assimilate to shear bands. This technique allows characterizing the geometry of the shear bands. The strain localizes in small bands (2 or 3 grain width) which form an angle of about 401 with the local tension axis for all punch displacements. Strains about unity are attained in the shear bands. Table 6 summarizes the observed evolution of the shear band characteristics. During bending, the major axis of the grains in the shear bands aligns with the tension axis. This realignment leads to a decrease in the band width. The mean value of the von Mises strain increases with the punch displacement. But, close to failure (0.96Uf–Uf) a sudden decrease (or plateau) in the mean strain is observed indicating that the grains in the shear bands either stop elongating or, more frequently, can fragment adopting a more equi-axed shape. This evolution will become clear by observing the throughthickness distribution of the von Mises strain.
3.2.2. Coarse slip bands Fig. 3 shows band contrast maps obtained in the midsection of bent samples. At small punch displacements, only one set of coarse bands is visible in most grains. For punch displacements larger than 0.92Uf a high density of grains with two sets of coarse bands are observed. As described above the density of coarse bands was determined in a small area (250 mm 300 mm) close to the outer surface of different bent samples (Fig. 1). Fig. 12 shows the evolution of this surface fraction as a function of the punch displacement. First the density of coarse slip bands increases linearly with the punch displacement. Between 0.93Uf and 0.96Uf a sharp increase of the density of coarse slip bands is observed. This increase is followed by a plateau. The sharp increase of the coarse slip band density may be correlated with the band contrast observations (Fig. 3). For small punch displacements, a homogeneous density of coarse slip bands (one visible set of coarse bands) is observed in the characterized area. Close to failure (40.92Uf), the density of coarse slip bands increases very rapidly. Subsequent unloading of the surface grains due to cracking leads to an increased strain in the underlying grains.
Fig. 10. Euler angle map in section BB0 of samples bent to (a) 0.7Uf, (b) Uf.
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Fig. 11. Strain distribution determined by the grain shape based on the Euler angle map (Fig. 7a). Black zones correspond to non indexed pixels in the EBSD acquisition. Shear bands are indicated in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 6 Shear bands observed in bent specimens. Uf is the punch displacement at failure and a is the angle between the shear band the tension axis. U/Uf
0.70 0.85 0.96 1.00
Shear band Width (mm)
a (deg.)
Strain
106.3 91.9 81.1 77.5
39.2 46.8 35.4 41.6
0.88 0.97 1.07 1.07
Fig. 13. Density of surface undulations as a function of the normalized punch displacement.
Fig. 12. Surface fraction of coarse slip bands as a function of the normalized punch displacement.
Table 7 Linear density of surface undulations as a function of the punch displacement. U/Uf Linear density (mm 1)
0.5 0.6 0.7 0.8 0.85 0.9 0.91 0.92 0.94 0.96 0.98 0 0 3.8 6 6 6 5.9 7.5 5.2 6.7 5.9
3.2.3. Evolution of surface undulations During bending, surface roughness increases by the formation of surface undulations aligned for several milimeters parallel to the bend axis. When visualized in any section perpendicular to this axis their density remains effectively constant [29] and therefore any section can be chosen to obtain statistically relevant results. In practice the mid-section was chosen. We propose a very simple method to characterize the density of surface undulations at the outer skin by light microscopy. The linear density of surface undulations is defined as the number of valleys deeper than 10 mm per unit length at the outer skin. This 10 mm depth corresponds roughly to half the grain size and was adopted as an
Fig. 14. Apparent mean value of strain: (a) typical optical micrograph used to determine the mean value of the strain concentric circular sectors and (b) apparent mean value of the mean strain as function of the distance from the neutral axis y.
empirical criterion after testing different depths. Table 7 and Fig. 13 represent this density of surface undulations as a function of the punch displacement. At small punch displacements no surface undulations are observed. Between 0.6Uf and 0.8Uf, the density of surface undulations increases rapidly corresponding to an increasing number of shear bands. This sharp increase is followed by a plateau corresponding to a constant number density of shear bands. Close to failure, the density of surface undulations seems at first glance almost chaotic or at least due to measuring artifacts. These rapid variations may be explained by considering the through-thickness distribution of the von Mises strain.
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3.2.4. Through-thickness distribution of von Mises strain The strain distribution in the mid section of bent samples was also characterized by optical micrography after chemical etching. The mean von Mises strain e in each grain has been determined by the grain shape factor (Eq. (2)). The optical micrographs also allowed determining the local curvature of the bent samples. The mean value EðyÞ of the strain distribution for a given distance y to the neutral axis has been determined in an angular sector Df corresponding to a constant curvature (Fig. 14a): Z 1 EðyÞ ¼ o e 4 ¼ e ðy, fÞdf ð3Þ
Df
Df
the strain increases proportional to the punch displacement. At 0.9Uf, a sudden increase in the plateau value is observed followed by the appearance of a ‘‘macro’’ crack at 0.92Uf. After crack formation, the apparent value of mean strain decreases. Since, the strain is based on the grain shape factor, a decrease indicates more equi-axed grain shapes. At 0.92Uf, some grains at the outer surface neck down to a much reduced thickness, leading to crack formation. Crack formation leads to a decrease in the plateau strain and a decrease of the density of surface undulations.
4. Summary and discussion
eðy, fÞ is the local strain (Eq. (2)) determined by the grain shape factor. y and f are respectively the distance from the neutral axis and the polar angle. Fig. 14b shows this mean value E as a function of the distance from the neutral axis for several punch displacements. Pure bending would lead to a logarithmic (quasi-linear) strain distribution. bending
E
¼ lnð1þ y=rÞ
ð4Þ
where r is the radius of curvature of the neutral axis. Close to the neutral axis (yE 0) the strain varies effectively linearly with the distance y from the neutral axis. But close to the outer surface (yZ300 mm) strain localization leads to a plateau strain of the grains. Fig. 15 presents the value of this plateau strain as a function of the punch displacement. Between 0.6Uf and 0.9Uf,
Fig. 15. Plateau value of apparent mean strain (Fig. 13) at the outer surface as a function of the punch displacement.
Fig. 16 summarizes the evolution of normalized values of the set of measured parameters. Strain localization is measurable for punch displacements above 0.6Uf. Measurable surface undulations start to form about the same punch displacement. The number of shear bands increases and the linear density of surface undulations increases. At 0.8Uf, a stable number of shear bands and a plateau value for the surface undulations are reached. In most grains only a single system of coarse slip bands is visible. The outermost grains elongate strongly in the local tensile direction. The strain in the outermost grains (eplateau), the strain in the shear bands (esb) and surface fraction of coarse slip bands (fcsb) exhibit a similar evolution. Close to 0.92Uf, some grains at the outer surface (and only these grains) reach the failure strain (AB on Fig. 15b) and neck into two distinct parts (BC on Fig. 15b). At 0.92Uf a macro crack is observed, leading to a decrease of the overall rigidity (K ¼dF/dU). At this stage, the strain in the shear bands continues to increase. Thus no general grain split is observed. The outer-most region of the sheet loses its stress carrying capacity. The resulting load transfer to inner grain layers leads to increased strain and the density of coarse slip bands (C-D) increases rapidly. The final stage of rapid loss in overall rigidity (U40.96Uf) corresponds to generalized multiple surface cracking. The apparent strain in the shear bands decreases because grains exhibit a more equi-axed shaped and the surface density of coarse slip bands increases more slowly as the overall deformation is accommodated by generalized surface crack formation. Several, simple, independent measures at different scales have been introduced to quantify damage development during bending. The maximum of the overall rigidity (K ¼dF/du) perfectly indicates the appearance of the first crack. Strain maps were determined independently from EBSD observations followed by grain reconstruction and from optical micrographs. These strain maps are based on the shape factor evolution of the individual
Fig. 16. Variables normalized by their maximum as a function of the punch displacement: (1) strain in shear bands, (2) plateau value of apparent strain, (3) density of surface instabilities, (4) surface fraction of coarse slip bands and (5) overall rigidity (dF/du).
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grains. The through-thickness distribution of the equivalent strain exhibits a plateau. The analysis of this plateau value allows detecting the microscopic necking of the outer-most grains and the formation of the first crack. This simple result is very important, because the strain in the shear bands continues increasing after surface crack initiation with decreasing rigidity. The analysis of the shear band strain and the micro shear band density are used to characterize the propagation of damage to the sheet center.
5. Conclusions An experimental study of the local mechanisms of damage evolution during large strain bending of AA 6016 has been carried out. Interrupted and in-situ bend tests combined with optical and SEM metallography enable one to characterize the relations between strain localization and damage development. The overall rigidity and the plateau value of the surface strain give two simple independent measures for characterizing the onset of cracking of the surface grains. The local strain measurements show that after unloading of surface grains (at maximum rigidity) only a small increase in the punch displacement leads to final failure. The bendability is thus controlled essentially by the strain to failure of the surface grains. This strain corresponds to that required for necking down to near-zero thickness. The mechanisms of strain localization and damage were analyzed. Strain localization was shown to be the motor for damage evolution and the formation of surface undulations. Damage development obeys the following sequence: (1) strain localization by grain-scale shear bands, (2) formation of surface undulations, (3) necking of particular surface grains and (4) intergranular propagation of a crack. Some cracks are initiated by quasi-rigid body movement of adjacent grains.
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Strain localization and damage mechanisms during bending of AA6016 sheet a,n ¨ Laurent Mattei a, Dominique Daniel b, Gilles Guiglionda b, Helmut Klocker , Julian Driver a a b
Ecole Nationale Supe´rieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42000 Saint-Etienne, France Constellium, Centre de recherches de Voreppe, 725 rue Aristide Berge s, BP 27, 38341 Voreppe Cedex, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 June 2012 Received in revised form 6 September 2012 Accepted 7 September 2012 Available online 16 September 2012
The bendability of AA6016 sheets is a critical parameter for many automotive applications. In this experimental study the origins of damage and its evolution are characterized using interrupted and insitu bending tests to correlate microstructural evolution with damage development. Local strains were estimated by optical and scanning microscopy (EBSD). Together with the load-displacement plots, they provided a set of physical parameters characterizing crack initiation. In particular, it is shown that
Keywords: Aluminum alloys Bendability Damage kinetics EBSD and optical observations
(1) crack initiation occurs at the maximum of the rigidity–displacement curve; (2) cracking is preceded by strain localization in the form of macro-shear bands which induce surface roughening. Local necking then occurs in some surface grains and leads to ductile intergranular crack propagation. The sequence of microscopic changes at the grain scale up to and beyond crack initiation have been characterized and quantified in terms of local grain strains, coarse intragranular slip and shear band evolution over several grains. & 2012 Elsevier B.V. All rights reserved.
1. Introduction Aluminum alloys are increasingly used in automotive structural applications because of their combination of low density, high strength and good formability. Bending is important in the shaping of complex parts, and it is also critical in the joining of outer skins to inner sheet panels by hemming. Appropriate strength levels for automotive aluminum panels are achieved by a combination of alloy composition and thermo mechanical treatment [1,2], and several experimental studies concern the influence of alloy composition on bend performance of Al 6xxx automotive sheet [3–6]. The bendability has been shown to decrease with increasing copper, iron and Si content. In particular Davidkov et al. [7] have recently investigated the major role of Mg2Si and AlCuMgSi Q phase particles on the bending response of 2 AA6016 grades. Most theoretical analyses attribute damage during bending to the development of surface roughness and intense strain localization. Several authors conclude that shear bands initiate at points of strain concentration induced by initial thickness heterogeneity [8–10]. Other authors have analyzed the effects of thermal softening on shear banding [11,12]. Crystal plasticity simulations have also been used essentially to analyze the effect of particular
n
Corresponding author. Tel.: þ33 4 77 42 0078; fax: þ33 4 77 42 0000. ¨ E-mail address: [email protected] (H. Klocker).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.09.028
textures on the formability and bendability of sheet metal [13–19]. Probably the most important result of these studies is the close relationship between surface roughening and strain localization. But strain localization is difficult to characterize experimentally. Thus most experimental studies have compared different alloys based on macroscopic measurements (bending angle), whereas theoretical damage analyses focus on local behavior (shear band pattern). The present work aims to quantify damage evolution during bending of AA6016 sheet in terms of strain localization by the use of in-situ and interrupted tests. The kinetics of damage development during bending is determined. Original quantitative measurements based on optical and electron metallographies for shear banding are also developed.
2. Experimental 2.1. Material and microstructure The chemical composition of AA6016 alloy sheet is given in Table 1. The industrial sheet was obtained from cast ingots hot rolled to a thickness of 2 mm, then cold rolled to the final gauge of 1 mm. The sheet was solution heat treated at 560 1C followed by a forced air quench to room temperature and natural aging for 1 week. The initial grain size was characterized by optical metallography and found to be homogeneous throughout the sheet thickness. The mean grain dimensions are 47 mm in the rolling direction, 30 mm in
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the transverse direction and 24 mm in the normal direction. Crystallographic texture was characterized by electron backscatter diffraction (EBSD) measurements and found to be weak with a small cube component peak. 6016 alloys contain intermetallic iron-rich and Mg2Si particles whose size and spatial distribution (mean surface fraction 1.16%) were characterized in previous work [20]. These intermetallic particles exhibit equal dimensions in the rolling (RD) and transverse (TD) direction (1.39 mm) and a height of 2.9 mm. Standard tensile tests were used to determine the initial yield strength (143 MPa). The large strain behavior to strains of 1 was characterized by plane strain compression tests on bonded samples [20]. Only very small yield anisotropy is observed [21]. The flow stress during large strains of 6016 alloy may be described by an extended Voce law [22] given by
s ¼ s0 þðs1 s0 Þð1edep Þ þ aep
ð1Þ
where ep is the accumulated plastic strain. s0 and sN are the initial yield stress and the saturation stress in the classical Voce law, respectively. d describes hardening at small strains and the additional term aep describes hardening at large strains. The constants are given in Table 2.
Table 1 Chemical composition of analyzed alloy.
6016
Si (%)
Fe (%)
Cu (%)
Mn (%)
Mg (%)
1.05
0.24
0.06
0.17
0.39
Table 2 Extended Voce law parameters of T4 6016 aluminum alloy.
s0 (MPa)
rN (MPa)
d
a (MPa)
143
282
16
146.4
813
2.2. Plane strain bending tests Several tests to characterize bending performance have been described in the literature [23–25]. In the present work, two planestrain bending tests were used for characterizing damage development on 6016T4 sheet. First standardized bending tests were carried out in accordance with the guidelines proposed by Daimler-Chrysler [26] and DIN 50 111 with a test set-up shown in Fig. 1. Samples of size 60 60 mm2 were machined from the sheet and tested in two directions (parallel and perpendicular to the rolling direction). The tests were performed on a standard tension/compression testing machine. The geometrical characteristics of the test set-up are given in Table 3. The punch speed was initially 10 mm/min until a preforce of 30 N was reached, then increased to 20 mm/min. During the bending test the applied force F and the punch displacement U were recorded continuously. The test was automatically stopped when the force dropped by more than 15 N from the maximum force. Interrupted bending tests on the same geometry were used to characterize the relation between damage development and microstructural evolution. An original in-situ bending test was also developed for scanning electron microscopy observations of surface damage evolution. Fig. 2 shows this bending module based on a Kamrath tensile machine as used in a Zeiss Supra FEG SEM. In this test facility, the punch is fixed and the rolls move. The displacement and the load applied to the rolls are recorded continuously. The punch radius (Rp ¼ 0.2 mm) is the same as in the standardized test. The geometrical characteristics of the test setup are given in Table 4. Note that small-scale SEM in-situ bend tests are particularly useful for characterizing the damage mechanisms but do not always allow reproducible damage quantification.
2.3. Strain maps and strain localization 2.3.1. Strain maps In the present work the relationship between damage evolution during bending and strain localization (shear bands) was analyzed experimentally over a large number of grains under
Fig. 1. Bending test: (a) overall view of the test, (b) bent sample with observed sections and (c) punch.
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plane strain conditions. The strain distribution was measured in the mid-section (BB’ in Fig. 1) of the bent samples. The shape factor of each individual grain was determined as the ratio between maximum and minimum Feret radii. The assumption of plane strain deformation in the sample mid-section gives the mean value of the equivalent von Mises strain in each grain as 1 l e ¼ pffiffiffi log ð2Þ l 3 0 where l and l0 are respectively the initial and current values of the grain shape factor. Two methods were used to characterize the individual grain shape: optical micrography after chemical etching and EBSD observations by reconstruction of the individual grains. The parameters used for the EBSD observations are given in Table 5. For the reconstruction of individual grains, misorientations larger than 101 were identified as grain boundaries. Another method of quantifying strain localization is by digital image correlation as used by Davidkov et al. [27] on continuous cast AA5754 sheet samples. This method was not applied here because of the large out-of-plane movements. 2.3.2. Coarse slip Crystallographic glide leads to the formation of coarse slip bands inside the grains with traces observable by scanning electron microscopy. Fig. 3 shows band contrast maps of bent samples. Band contrast maps are particularly well adapted for visualizing coarse slip bands. But, to quantify their density, orientation maps (as Euler angles) were preferred. The density of coarse slip bands was determined from binary misorientation maps using cut-off angles between 21 and 101. Misorientations larger than 101 were
associated to grain boundaries. An area of 250 mm 300 mm close to the outer surface of bent specimens (section BB0 in Fig. 1) was analyzed to give the density of coarse slip bands defined as the relative number of black pixels in the binary image.
3. Results 3.1. The general kinetics of damage development during bending 3.1.1. A macroscopic criterion for failure during bending Fig. 4a shows a typical load displacement curve for the 6016T4 sheet. The scatter is extremely small, thus only one curve is represented. First the punch displacement at failure Uf (12.8 mm) and the minimum bending angle bf after elastic unloading (bf ¼281) were determined. Since F and U are measured continuously, it is possible to plot out the apparent rigidity (dF/dU) as a function of the displacement U as in Fig. 4b. The overall rigidity exhibits a clear maximum at 0.92Uf. For other samples, the bending test was stopped at different punch displacements and the damage was observed in the
Table 4 Characteristics of the new in-situ bending test. Parameter
Value
Sheet width Sheet height Radius of the punch Rp Radius of the rolls Roll gap
33 mm 10 mm 0.2 mm 5.75 mm 4.5 mm
Table 3 Characteristics of standard bending test. Parameter
Value
Sheet width and length Radius of the punch Rp Radius of the rolls Roll gap Maximum punch displacement umax Punch velocity during preload Preload Punch velocity during bending Test stop for a load drop of
60 mm 0.2 mm 15 mm 2nt mm 14.2 mm 10 mm/min 30 N 20 mm/min 15 N
Table 5 Parameters used in EBSD acquisition. Undeformed sample Bent sample Magnification Step size (mm) Binning Gain Number of frames Resolution in Hough space
100 5 44 High 2 60
Fig. 2. In-situ bending test: (a) overall view of the test and (b) bent sample with the observed section.
500 1 44 High 3 60–90
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Fig. 3. Band contrast observations (step 1 mm) in section BB0 after interrupted bending test for several punch displacements of 0.6Uf, 0.85Uf, 0.96Uf, Uf.
Fig. 4. Bending test: (a) typical load displacement curve of the punch and (b) typical variation of the overall rigidity as a function of the punch displacement.
midsection of different samples (Fig. 1). Fig. 5 shows optical micrographs (section BB0 ) corresponding to different punch displacements. At this scale, damage is observed only on the outer skin submitted to tension. At relatively small punch displacements (0.6Uf), surface instabilities become visible. Between 0.6Uf and 0.91Uf, the intensity of the surface undulations increases, but no surface cracks are observed. A crack develops ‘‘suddenly’’ at a punch displacement of 0.92Uf corresponding to the maximum of the overall rigidity. Crack formation during a standard bend test occurs when the overall rigidity attains a maximum. To our knowledge, this macroscopic criterion for bend cracking (dF/dU maximum) does not appear to have been observed before.
3.1.2. Strain localization as the motor of damage development Several simulations assumed surface undulations to be the cause of strain localization [8]. Other authors considered the surface undulations as a consequence of strain localization [13–18]. The importance of surface roughness on bend performance was
first examined by Lloyd [28] using a Cantilever Beam Test. He bent specimens to an intermediate angle, then polished off the surface topography and measured the bend angle that could be obtained. Intermediate polishing appeared to enhance bendability. In the present work, to analyze the influence of surface roughness on damage development during bending, three test series were run (Fig. 6). In the first series, samples with an industrial surface finish were bent to failure at an angle b1 ¼281. For the second and third test series samples were first polished to a mirror finish (P4000) prior to bending. One part of these samples (series 2) was bent to failure at an angle of b2 ¼ 211 and the punch displacement U2. In the third series bending was stopped at a punch displacement larger than 0.6U2 and the surface re-polished to a mirror finish. Then the new bend angle b3 was determined and found to be 211, i.e. identical to b2. We conclude that for an initially mirror polished sample, intermediate polishing does not improve the bendability. Initial surface roughness (undulations) favors the development of strain localization [7,26]. But eliminating the surface roughness
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Fig. 5. Observations of bent specimens (section BB0 ) at different punch displacement. Development of a wavy surface (a, b, e, f), surface cracks (c, d, g, h).
Fig. 6. Bending tests run for analyzing influence of surface roughness on bendability.
at an intermediate bending angle does not enhance the bendability compared to an initial mirror surface finish. Fig. 7 shows an optical micrograph of a sample bent to the minimum bend angle. Strain localization leads locally to significant changes in grain shape and orientation. Grain rotation and grain deformation at the outer surface lead to surface undulations. It is therefore concluded that strain localization controls damage development and leads to the formation of surface cracks.
3.1.3. Observation of surface cracks The mechanisms leading to the development of surface cracks were characterized by the in-situ bend test. Fig. 8 shows the free surface (section AA0 ) of a bent specimen. Grains deform by slip on particular crystallographic systems, and shear typically accompanies stretching. In most grains only one set of coarse bands is visible at the free surface. But close to the outer surface, grains with two visible sets of coarse bands are observed. Strain localization leads to ‘‘necking’’ of these surface grains. This neck causes an intergranular crack to propagate (Fig. 8b, c) and leads to final failure. Davidkov et al. [7] have also observed this final intergranular failure mode in a similar alloy. Some of the adjacent grains can move perpendicular to the surface without significant deformation. This relative motion of two surface grains also causes an intergranular crack to propagate (Fig. 8b). In Fig. 8 surface cracks are observed, but no cavitation is observed before crack initiation. In summary, we observe that the basic damage mechanism consists of very intense localized necking in some grains which then initiates intergranular crack propagation to final failure. 3.2. Quantification of strain localization and damage development The previous section showed that strain localization is the motor of damage development. Once strain becomes localized, eliminating the surface roughness does not eliminate the damage. It is therefore important to characterize and quantify strain localization.
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Fig. 7. Optical observation in section BB0 of a specimen bent to failure: (a) grain deformation and rotation, (b) grain necking at the outer surface and (c) development of a crack.
Fig. 8. In-situ observations of bent specimen in section AA0 : (a) overall view of the bent specimen, (b) grain movement without straining, (c and d) grain ‘‘necking’’ due to multiple slip.
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3.2.1. Shear banding Strain localization was characterized in the mid section of specimens bent at different punch displacements. Fig. 9 shows optical micrographs of the microstructures before and after
Fig. 9. Optical micrograph (section BB0 ) of the initial microstructure and after bending to failure ({RD, ND}¼ rolling axes).
bending. In the initial microstructure, the grains are quasi-equiaxed. During bending, the grains at the outer surface rotate and stretch parallel to the overall tension direction. The determination of the mean strain in each grain was based on EBSD observations. Fig. 10 shows Euler angle maps of two bent samples. The mean strain, given by the variation of the shape factor, was determined in each grain (Eq. (2)) and mapped out in Fig. 11. This figure also reveals elongated zones of higher deformation (indicated in red) that we assimilate to shear bands. This technique allows characterizing the geometry of the shear bands. The strain localizes in small bands (2 or 3 grain width) which form an angle of about 401 with the local tension axis for all punch displacements. Strains about unity are attained in the shear bands. Table 6 summarizes the observed evolution of the shear band characteristics. During bending, the major axis of the grains in the shear bands aligns with the tension axis. This realignment leads to a decrease in the band width. The mean value of the von Mises strain increases with the punch displacement. But, close to failure (0.96Uf–Uf) a sudden decrease (or plateau) in the mean strain is observed indicating that the grains in the shear bands either stop elongating or, more frequently, can fragment adopting a more equi-axed shape. This evolution will become clear by observing the throughthickness distribution of the von Mises strain.
3.2.2. Coarse slip bands Fig. 3 shows band contrast maps obtained in the midsection of bent samples. At small punch displacements, only one set of coarse bands is visible in most grains. For punch displacements larger than 0.92Uf a high density of grains with two sets of coarse bands are observed. As described above the density of coarse bands was determined in a small area (250 mm 300 mm) close to the outer surface of different bent samples (Fig. 1). Fig. 12 shows the evolution of this surface fraction as a function of the punch displacement. First the density of coarse slip bands increases linearly with the punch displacement. Between 0.93Uf and 0.96Uf a sharp increase of the density of coarse slip bands is observed. This increase is followed by a plateau. The sharp increase of the coarse slip band density may be correlated with the band contrast observations (Fig. 3). For small punch displacements, a homogeneous density of coarse slip bands (one visible set of coarse bands) is observed in the characterized area. Close to failure (40.92Uf), the density of coarse slip bands increases very rapidly. Subsequent unloading of the surface grains due to cracking leads to an increased strain in the underlying grains.
Fig. 10. Euler angle map in section BB0 of samples bent to (a) 0.7Uf, (b) Uf.
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Fig. 11. Strain distribution determined by the grain shape based on the Euler angle map (Fig. 7a). Black zones correspond to non indexed pixels in the EBSD acquisition. Shear bands are indicated in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 6 Shear bands observed in bent specimens. Uf is the punch displacement at failure and a is the angle between the shear band the tension axis. U/Uf
0.70 0.85 0.96 1.00
Shear band Width (mm)
a (deg.)
Strain
106.3 91.9 81.1 77.5
39.2 46.8 35.4 41.6
0.88 0.97 1.07 1.07
Fig. 13. Density of surface undulations as a function of the normalized punch displacement.
Fig. 12. Surface fraction of coarse slip bands as a function of the normalized punch displacement.
Table 7 Linear density of surface undulations as a function of the punch displacement. U/Uf Linear density (mm 1)
0.5 0.6 0.7 0.8 0.85 0.9 0.91 0.92 0.94 0.96 0.98 0 0 3.8 6 6 6 5.9 7.5 5.2 6.7 5.9
3.2.3. Evolution of surface undulations During bending, surface roughness increases by the formation of surface undulations aligned for several milimeters parallel to the bend axis. When visualized in any section perpendicular to this axis their density remains effectively constant [29] and therefore any section can be chosen to obtain statistically relevant results. In practice the mid-section was chosen. We propose a very simple method to characterize the density of surface undulations at the outer skin by light microscopy. The linear density of surface undulations is defined as the number of valleys deeper than 10 mm per unit length at the outer skin. This 10 mm depth corresponds roughly to half the grain size and was adopted as an
Fig. 14. Apparent mean value of strain: (a) typical optical micrograph used to determine the mean value of the strain concentric circular sectors and (b) apparent mean value of the mean strain as function of the distance from the neutral axis y.
empirical criterion after testing different depths. Table 7 and Fig. 13 represent this density of surface undulations as a function of the punch displacement. At small punch displacements no surface undulations are observed. Between 0.6Uf and 0.8Uf, the density of surface undulations increases rapidly corresponding to an increasing number of shear bands. This sharp increase is followed by a plateau corresponding to a constant number density of shear bands. Close to failure, the density of surface undulations seems at first glance almost chaotic or at least due to measuring artifacts. These rapid variations may be explained by considering the through-thickness distribution of the von Mises strain.
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3.2.4. Through-thickness distribution of von Mises strain The strain distribution in the mid section of bent samples was also characterized by optical micrography after chemical etching. The mean von Mises strain e in each grain has been determined by the grain shape factor (Eq. (2)). The optical micrographs also allowed determining the local curvature of the bent samples. The mean value EðyÞ of the strain distribution for a given distance y to the neutral axis has been determined in an angular sector Df corresponding to a constant curvature (Fig. 14a): Z 1 EðyÞ ¼ o e 4 ¼ e ðy, fÞdf ð3Þ
Df
Df
the strain increases proportional to the punch displacement. At 0.9Uf, a sudden increase in the plateau value is observed followed by the appearance of a ‘‘macro’’ crack at 0.92Uf. After crack formation, the apparent value of mean strain decreases. Since, the strain is based on the grain shape factor, a decrease indicates more equi-axed grain shapes. At 0.92Uf, some grains at the outer surface neck down to a much reduced thickness, leading to crack formation. Crack formation leads to a decrease in the plateau strain and a decrease of the density of surface undulations.
4. Summary and discussion
eðy, fÞ is the local strain (Eq. (2)) determined by the grain shape factor. y and f are respectively the distance from the neutral axis and the polar angle. Fig. 14b shows this mean value E as a function of the distance from the neutral axis for several punch displacements. Pure bending would lead to a logarithmic (quasi-linear) strain distribution. bending
E
¼ lnð1þ y=rÞ
ð4Þ
where r is the radius of curvature of the neutral axis. Close to the neutral axis (yE 0) the strain varies effectively linearly with the distance y from the neutral axis. But close to the outer surface (yZ300 mm) strain localization leads to a plateau strain of the grains. Fig. 15 presents the value of this plateau strain as a function of the punch displacement. Between 0.6Uf and 0.9Uf,
Fig. 15. Plateau value of apparent mean strain (Fig. 13) at the outer surface as a function of the punch displacement.
Fig. 16 summarizes the evolution of normalized values of the set of measured parameters. Strain localization is measurable for punch displacements above 0.6Uf. Measurable surface undulations start to form about the same punch displacement. The number of shear bands increases and the linear density of surface undulations increases. At 0.8Uf, a stable number of shear bands and a plateau value for the surface undulations are reached. In most grains only a single system of coarse slip bands is visible. The outermost grains elongate strongly in the local tensile direction. The strain in the outermost grains (eplateau), the strain in the shear bands (esb) and surface fraction of coarse slip bands (fcsb) exhibit a similar evolution. Close to 0.92Uf, some grains at the outer surface (and only these grains) reach the failure strain (AB on Fig. 15b) and neck into two distinct parts (BC on Fig. 15b). At 0.92Uf a macro crack is observed, leading to a decrease of the overall rigidity (K ¼dF/dU). At this stage, the strain in the shear bands continues to increase. Thus no general grain split is observed. The outer-most region of the sheet loses its stress carrying capacity. The resulting load transfer to inner grain layers leads to increased strain and the density of coarse slip bands (C-D) increases rapidly. The final stage of rapid loss in overall rigidity (U40.96Uf) corresponds to generalized multiple surface cracking. The apparent strain in the shear bands decreases because grains exhibit a more equi-axed shaped and the surface density of coarse slip bands increases more slowly as the overall deformation is accommodated by generalized surface crack formation. Several, simple, independent measures at different scales have been introduced to quantify damage development during bending. The maximum of the overall rigidity (K ¼dF/du) perfectly indicates the appearance of the first crack. Strain maps were determined independently from EBSD observations followed by grain reconstruction and from optical micrographs. These strain maps are based on the shape factor evolution of the individual
Fig. 16. Variables normalized by their maximum as a function of the punch displacement: (1) strain in shear bands, (2) plateau value of apparent strain, (3) density of surface instabilities, (4) surface fraction of coarse slip bands and (5) overall rigidity (dF/du).
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grains. The through-thickness distribution of the equivalent strain exhibits a plateau. The analysis of this plateau value allows detecting the microscopic necking of the outer-most grains and the formation of the first crack. This simple result is very important, because the strain in the shear bands continues increasing after surface crack initiation with decreasing rigidity. The analysis of the shear band strain and the micro shear band density are used to characterize the propagation of damage to the sheet center.
5. Conclusions An experimental study of the local mechanisms of damage evolution during large strain bending of AA 6016 has been carried out. Interrupted and in-situ bend tests combined with optical and SEM metallography enable one to characterize the relations between strain localization and damage development. The overall rigidity and the plateau value of the surface strain give two simple independent measures for characterizing the onset of cracking of the surface grains. The local strain measurements show that after unloading of surface grains (at maximum rigidity) only a small increase in the punch displacement leads to final failure. The bendability is thus controlled essentially by the strain to failure of the surface grains. This strain corresponds to that required for necking down to near-zero thickness. The mechanisms of strain localization and damage were analyzed. Strain localization was shown to be the motor for damage evolution and the formation of surface undulations. Damage development obeys the following sequence: (1) strain localization by grain-scale shear bands, (2) formation of surface undulations, (3) necking of particular surface grains and (4) intergranular propagation of a crack. Some cracks are initiated by quasi-rigid body movement of adjacent grains.
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