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Research Papers

Thermally Induced Mechanical Response of Metal Foam During Laser Forming

[+] Author and Article Information
Tizian Bucher

Advanced Manufacturing Laboratory,
Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: tb2430@columbia.edu

Adelaide Young

Advanced Manufacturing Laboratory,
Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: agy2107@columbia.edu

Min Zhang

Mem. ASME
Laser Processing Research Center,
School of Mechanical and
Electrical Engineering,
Soochow University,
Suzhou 215021, Jiangsu, China
e-mail: mzhang@aliyun.com

Chang Jun Chen

Mem. ASME
Laser Processing Research Center,
School of Mechanical and
Electrical Engineering,
Soochow University,
Suzhou 215021, Jiangsu, China
e-mail: chjchen2001@aliyun.com

Y. Lawrence Yao

Fellow ASME
Advanced Manufacturing Laboratory,
Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: yly1@columbia.edu

1Corresponding author.

Manuscript received March 31, 2017; final manuscript received January 4, 2018; published online February 12, 2018. Assoc. Editor: Hongqiang Chen.

J. Manuf. Sci. Eng 140(4), 041004 (Feb 12, 2018) (12 pages) Paper No: MANU-17-1200; doi: 10.1115/1.4038995 History: Received March 31, 2017; Revised January 04, 2018

To date, metal foam products have rarely made it past the prototype stage. The reason is that few methods exist to manufacture metal foam into the shapes required in engineering applications. Laser forming is currently the only method with a high geometrical flexibility that is able to shape arbitrarily sized parts. However, the process is still poorly understood when used on metal foam, and many issues regarding the foam's mechanical response have not yet been addressed. In this study, the mechanical behavior of metal foam during laser forming was characterized by measuring its strain response via digital image correlation (DIC). The resulting data were used to verify whether the temperature gradient mechanism (TGM), well established in solid sheet metal forming, is valid for metal foam, as has always been assumed without experimental proof. Additionally, the behavior of metal foam at large bending angles was studied, and the impact of laser-induced imperfections on its mechanical performance was investigated. The mechanical response was numerically simulated using models with different levels of geometrical approximation. It was shown that bending is primarily caused by compression-induced shortening, achieved via cell crushing near the laser irradiated surface. Since this mechanism differs from the traditional TGM, where bending is caused by plastic compressive strains near the laser irradiated surface, a modified temperature gradient mechanism (MTGM) was proposed. The densification occurring in MTGM locally alters the material properties of the metal foam, limiting the maximum achievable bending angle, without significantly impacting its mechanical performance.

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Figures

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Fig. 1

Uniaxial compressive stress–strain data (engineering) of four compression specimens (curves 1–4) made with the same metal foam that was used in this study [22]. The stress–strain curve can be divided into three segments: (1) a linear regime, followed by (2) a plateau where cell crushing occurs and a large amount of energy is absorbed, followed by (3) foam densification. Due to their crushability, metal foams can withstand much lower compressive stresses than solid metals.

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Fig. 2

Two approaches were used to model metal foam. In the first (equivalent) model, shown in (a), a solid geometry was used and equivalent foam properties were assigned. In the second (Kelvin) model, shown in (b), the foam geometry was explicitly modeled, and solid aluminum properties were assigned. The cavity geometry was approximated by a Kelvin-cell geometry.

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Fig. 3

(a) Experimental setup. The laser was scanned in x-direction. The bottom specimen surface was spray-painted white with a black speckle pattern. Digital images were taken in between consecutive laser scans. (b) Example strain distribution (εyy, Lagrangian strain) on the bottom surface of a laser formed specimen at a bending angle of 45 deg. The strain was only extracted on the clamped half of the specimen above the bending axis to avoid effects related to out-of-plane rotations [34].

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Fig. 4

Section of the top surface of the specimen on the laser scan line (a) before laser forming, (b) after 1 scan, and (c) after 10 scans at 90 W and 5 mm/s. Even at this low power, localized melting of thin cell walls occurred, marked in white. Melting started after the first scan and progressed with each consecutive scan, forming u-shaped trenches in the cell walls and reducing the amount of compressible material. Melting stopped once the thickness of the remaining cell wall sections increased.

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Fig. 5

Cross section of a foam specimen after five laser scans at 180 W and 10 mm/s. The laser was scanned into the page. The white arrows show where cell walls were bent during laser forming, indicating that the foam cannot withstand high compressive stresses.

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Fig. 6

Comparison of the tensile strain (εyy) on the bottom surface (determined via DIC) in 4-point bending and laser forming (at 180 W and 10 mm/s). εyy is the strain resulting from a combination of cell collapsing and cell wall deformation. Standard errors are shown, calculated over all the pixels of the averaged areas (see Sec. 3). In 4-point bending, the strain increased exponentially before a catastrophic failure, whereas in laser forming there was a stable linear strain growth with increasing bending angle. Laser forming yielded a larger maximum εyy, due to heat-induced softening, yet εyy did not grow proportionally to the bending angle, and hence tensile stretching cannot be the main cause of bending.

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Fig. 7

Strain distributions (εyy) in (a) metal foam during 4-point bending, (b), metal foam during laser forming, and (c) a steel sheet during laser forming. (d) Ratio of top surface (compressive) strain over bottom surface (tensile) strain at the bending axis, calculated for all three simulations. In 4-point bending, bending was equally caused by compressive and tensile strains. In laser forming, the large ratios indicate that compressive deformation was the main cause for bending.

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Fig. 8

Relative density distribution after a single scan at 180 W and 10 mm/s. The baseline relative density is 0.112, and a relative density of 1 indicates complete densification. Densification occurred throughout the top 80% of the foam, leaving only a small tensile region on the bottom surface. Therefore, laser forming shifts the neutral axis downward, and deformation is dominated by compressive shortening.

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Fig. 9

(a) Experimental and (b) numerical bending angles and tensile strain data (εyy) at large bending angles. “High” refers to the condition 180 W 10 mm/s, “low” refers to 90 W 5 mm/s. Standard errors are shown for the strain results, calculated over all the pixels of the averaged area (see Sec. 3). In both the experiment and the simulation, the bending angle and strain plots leveled off at a large number of scans. In the numerical simulation, the limit at 180 W and 10 mm/s was reached at a larger bending angle, since the model did not consider melting, as well as changes in the moment of area, laser absorption and thermal conductivity with increasing densification.

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Fig. 10

Comparison of numerical data before and after correcting for density dependence. Without correction, both the bending angle and strain increment decreased only slightly with increasing scans, induced by tensile strain hardening on the bottom surface. After incorporating density-dependent variables, a distinct limiting behavior could be observed.

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Fig. 11

Bottom surface of a specimen scanned at 90 W and 5 mm/s at bending angles of (a) 1 deg, (b) 11.6 deg, and (c) 16.3 deg. Due to some naturally occurring stress concentrations, microcracks already occurred at low bending angles of 1 deg. As the bending angle became larger, those microcracks increased in size, and new microcracks formed ((b) and (c)). However, the microcracks remained isolated from each other at this stage and thus hardly affected the structural integrity of the foam.

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Fig. 12

(a) Foam specimen at a bending angle of 45 deg, after being laser formed at 180 W and 10 mm/s, with a cross section shown in (b). At large bending angles, the isolated cracks on the bottom surface grew larger and started to coalesce, shown in (a). In close proximity to the bending axis, cells at the top surface were crushed significantly, shown in (b), but the foam was still far away from complete densification.

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Fig. 13

Resistance curves determined using the J-integral method, ASTM 813-89, for a closed-cell foam with a very similar composition and porosity [38]. The white and black data points represent two test specimens. Unlike in a brittle material, where the JR-value would be horizontal beyond an unstable crack length, it keeps on increasing in metal foam, indicating that the foam fracture toughness is maintained even as the crack grows larger. Therefore, microcracks do not lead to an unstable fracture, and even larger cracks do not completely remove the structural integrity of the foam.

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Fig. 14

Fracture surfaces in (a) mechanically fractured and (b) laser formed metal foam specimens. The fracture surface in (a) consists of a mix of dimples and clean surfaces with sharp edges, indicating a mix of ductile and brittle fracture. The material on the surface of (b), on the other hand, appears to have been stretched severely, indicating a more ductile fracture.

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Fig. 15

Relative density distribution at a bending angle of 45 deg. The baseline relative density is 0.112, and a relative density of 1 indicates complete densification. The densified region was highly localized around the bending axis. Over a small area close to the top surface, the relative density increased by a factor of 2.5, which is still far away from complete densification. Foam expansion occurred close to the bottom surface, coinciding with the region where cracks appeared in Fig. 12(a).

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Fig. 16

Bending angles predicted by the Kelvin model in comparison with the predictions of the equivalent model and the experimental values. Standard errors are shown for the experimental data. Due to its superior geometrical accuracy, the Kelvin model yielded results that were closer to the experimental results. Nevertheless, the model still overestimated the bending angle, particularly at the high condition (180 W, 10 mm/s), since it did not account for melting, as well as changes in the laser absorption (due to using an uncoupled modeling approach).

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Fig. 17

Thermal strain distribution in a micro-CT based “voxel” model during a laser scan at 90 W and 5 mm/s. The downward deformation represents the initial counter-bending that occurs during the laser scan. The voxel model has a higher level of geometrical accuracy, which could potentially be used to predict crack-initiation sites and cell wall bending.

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