Effect of Laser Forming on the Fatigue Behavior of Metal Foams

Metal foam is a metallic material with cellular structure. It has the advantages of exceptional stiffness-to-weight ratio, excellent shock, and impact absorbing ability. It can also be used as fire and noise separator. Due to these advantages, metal foam has potential applications such as lightweight structures, protective casings, crush boxes, and many more industry applications [1]. However, applications often require complex geometry, and making metal foam into intricate geometry can be challenging. Traditional manufacturing process such as milling and sawing can easily damage the cell structure of metal foam [1,2]. 3D printing can readily produce metal foam parts into desired shape but is time-consuming. Powder metallurgy method requires initial investment in molds and is cost-inefficient for small volume production [3,4]. Metal foam is more commonly manufactured into generic shapes such as plates and slabs and further formed into the desired shape. Forming process is cost efficient due to reduced material waste, but conventional bending process can cause fracture and collapse of cell structure due to the high stiffness of the material [5]. Hydroforming has proven to cause excessive densification of the material. Therefore, an alternative forming method is crucial to the application of metal foam [6].

Laser forming is an alternative forming process for metal foam, which uses laser-induced thermal stress to bend the material. Laser forming has been demonstrated to achieve a high bending angle of metal foam without causing significant damage to the cell structure, and a modified temperature gradient mechanism (MTGM) was proposed to explain the bending mechanism [7]. Since its viability has been proven, laser forming’s effect on the material was investigated by multiple studies. Santo et al. [8] observed grain refinements of open-cell aluminum foam in the heat affected zone. Localized defects were also discovered at the heat affected zone but did not affect the bending efficiency. Zhang et al. [9] studied the energy absorbing behavior of metal foam after laser forming. Localized defects such as cell wall melting and cracks were demonstrated to cause minor decrease in energy absorbing ability of metal foam, and causing crush bands to form near the laser scanned surface under impact. Former studies indicated that laser forming is not only a viable process but also does not impose detrimental effects to the material. However, in applications, foam structures are often exposed to cyclic loading. This requires evaluation of the fatigue performance of metal foam after laser forming, which was paid little attention by the former studies.

Even though a fatigue study was yet to be performed on laser formed (LFed) metal foam, some efforts were paid toward the fatigue of metal foam. Harte et al. [10] established methods for both tension-to-tension and compression-to-compression fatigue of metal foam. In tension-to-tension fatigue, low-cycle fatigue failure of cell edges and cyclic ratcheting were observed, and the endurance ratio was found to be similar to solid aluminum alloy. Compressive fatigue tests featured progressive shortening of the specimen with a single crush band which broadens with increasing fatigue cycles. The progressive shortening also consisted of an initial slow incubation period until a strain of 2%, which defined the fatigue failure, followed by a faster and constant rate shortening. Fatigue strength was also demonstrated to be lower for tension–tension fatigue compared to compression–compression. Zhao et al. [11] conducted tension-to-tension fatigue tests on closed-cell aluminum foam and observed low repeatability of fatigue tests. A statistical damage model was proposed to describe the damage evolution of the foam. SEM investigations showed that damage initiations were located at different positions of the foam, governed by the irregularity of the foam microstructure. A compression-to-compression fatigue study on metal foam was conducted by Linul et al. [12] and similar scatter of data was seen in compressive fatigue test. The irregularity of cell structure was determined to contribute to the low repeatability of fatigue tests, and the number and sizes of large cells were found to have negative effect on the fatigue life. Hu et al. [13] conducted experimental and numerical studies on the effect of large cells on fatigue properties in closed-cell aluminum foam. A characteristic diameter was introduced to describe the fraction of large cells in foam material, and it was demonstrated that a large fraction of large cells has a major impact on the reduction of fatigue life of metal foams.

Attentions were paid to the fatigue of solid material after laser forming. These results could be relevant to the current study. Tensile and low-cycle fatigue tests were conducted on laser processed low carbon steel by Shen and Yao [14]. Despite little difference in tensile properties, the laser processed specimen has improved fatigue life, which is mainly contributed by the residual compressive strain during the laser forming process. However, in a study conducted by Mjali et al. [15], the fatigue life of titanium alloy plates decreased after laser forming. The reduction in fatigue life was attributed to the increase in tensile residual stress in the material. A total fatigue stress method was further proposed in analyzing the fatigue behavior of laser formed material. Zhang et al. [16] conducted numerical and experimental fatigue investigation on low carbon steel after laser forming and saw a decrease in the fatigue life. In addition to the increase to the tensile residual stress, they also attribute the fatigue life degradation to inhomogeneity at the boundary of the heat affected zone. Despite the various studies in fatigue behavior after laser forming, the concept in aforementioned literature was not sufficient to predict the fatigue performance of metal foam after laser forming, due to varying results and metal foam’s distinctive behavior under laser forming. In order to use laser forming in metal foam applications, it is necessary to evaluate the fatigue performance of laser formed metal foam.

The current study seeks to combine the study on laser forming and metal foam to investigate the fatigue performance of closed-cell aluminum foam before and after laser forming. Tension-to-tension fatigue tests were conducted to investigate the fatigue life difference between as-received specimen and specimen under two different laser scanning schemes. Strain measurements were performed to demonstrate the progressive lengthening in the tensile fatigue tests. The fractured surface was studied optically to explain the large scatter of fatigue life data. Numerical models for laser forming and fatigue were developed to demonstrate the residual stress and strain distribution after laser forming, as well as explaining the differences in fatigue life.

The mechanism of laser forming of metal foam has also been well studied. Bucher et al. proposed a MTGM to explain the bending of metal foam under laser forming [7]. When subjected to laser, metal foam develops a large temperature gradient on the top and bottom surface. The heat affected region right under the laser will try to expand due to heat expansion but is limited by the surrounding cold material due to the localized heating of laser. This will result in the plastic cell wall bending and collapsing under the laser, which is comparable to a compressive plastic deformation seen in solid material. The effective plastic compression makes the material shorter at the laser scanned area and will result in the foam bending toward the laser. This deformation also causes localized densification at the bending axis and shifts the neutral axis of the foam, limiting further bending. In addition to cell wall deformation, laser forming also causes defects such as cell wall melting and micro-cracks at the bottom surface at high bending angle. Fortunately, the defects and densification are only significant at large bending angle. When the bending angle is small, the assumptions in the isotropic crushable foam model still apply and the overall crushability of metal foam is maintained.

To understand the behavior of metal foam, various studies and tests have been conducted. Ashby et al. [1] conducted experiments on both tensile and compressive fatigue testing of metal foam. When subjected to tension–tension fatigue loading, metal foam typically undergoes initial cyclical ratcheting, featured by progressive lengthening at almost constant rate, as shown in Fig. 1. After which fatigue crack forms and progresses through the entire cross section until material separation.

Numerical studies were performed to simulate metal foam’s behavior under laser forming and fatigue loading. For the laser forming of metal foam, an equivalent homogenous solid model was used following the crushable foam model as explained in previous section. Sequentially coupled thermal–mechanical analysis was conducted in the commercial finite element analysis code abaqus. The heat flux of laser scans was applied on both sides of a dogbone foam specimen fixed at the center of the gauge length using a dflux user subroutine. Linear heat transfer element DC3D8 was used for the heat transfer analysis with a biased mesh to produce a finer mesh at the laser scanning path. Nodal temperature from the heat transfer analysis was then used in the mechanical analysis with linear stress element C3D8R and same mesh, along with the crushable foam model. Equivalent material properties were used and adopted from Ref. [7].

For the simulation of fatigue test, since the local plasticity needs to be considered, the porous structure of metal foam was approximated with regular Kelvin cells with 4 mm diameter and cell wall thickness of 0.15 mm to match the foam used in experiments. Initial uniaxial static loading response was simulated in abaqus using quadratic tetrahedron stress element C3D10, with maximum stress equal to the maximum stress in fatigue tests. The uniaxial stress data were combined with a sinusoidal signal with a frequency of 20 Hz and amplitude ranging from 0.1 to 1 and transformed into cyclic loading in the fe-safe module [21] to match the frequency and load amplitude in the experiment, where tension–tension fatigue life analysis was conducted following the strain-life method with Smith–Watson–Topper mean stress correction, as explained in the previous section. Since the foam structure was explicitly modeled, solid material properties were used in the fatigue analysis.

Metal foam used in this study was made using the melt-foaming method from AlSi₁₀ with TiH₂ as the foaming agent. The metal foam was manufactured by Havel Metal Foam into 10 mm-thick panels with cast skins on both sides with an average density of 500 kg/m³. Due to the lack of standard on foam material, ASTM C394/C394M-16 was used as a reference and a customized specimen geometry and fixture was designed and used. The metal foam panels were cut to I-shaped dogbone specimens. Contrary to a traditional dogbone specimen, the I-shaped dogbone specimen in this study does not have fillet at inside corners to prevent stress concentration due to the natural existence of stress concentration in the foam structure, and this was to increase the gripping of the dogbone with the fixture to prevent slipping during fatigue loading (Fig. 3(a)). In fact, experimental results showed that the dogbone specimen rarely fractured at the inside corners. The dogbone shape was cut with a gauge length of 60 mm and a gauge width of 20 mm using wire electrical discharge machining (wire EDM) to minimize deformation and residual stresses at the gauge length. The gripping section of the dogbone specimen has a width of 40 mm and a height of 15 mm on each end.

Laser forming experiments were conducted using a PRC CO₂ laser with a laser power of 180 W at scanning speed of 10 mm/s and a laser spot size of 12 mm (Fig. 3(b)). Transversely scanned specimens were scanned with 15 parallel scans, and axially scanned specimens were scanned with three parallel scans. Each scan is repeated 10 times and 6 mm apart from each other, and the parallel scans were conducted within the gauge length on both sides of the dogbone specimens. Repeated parallel scans were used to make sure that the entire specimen is affected by laser forming, and scanning on both sides was to counter the bending effect from laser forming in order to conduct stable fatigue testing. Specimens were flipped after each scan to avoid excessive bending from laser forming and were flooded with cold air during forming to prevent excessive heat accumulation. The laser treated specimen was also initially coated with graphite paint to increase laser absorption.

Fatigue testing of metal foam was conducted on an MTS 858 table top universal testing machine. Customized fixture was made to secure the specimen during the fatigue loading, as seen in Fig. 3(c). This arrangement makes it possible not to clamp foam specimens so tightly that their cellular structure may distort or crush. Tension-to-tension cyclic loading was applied at 20 Hz with load ratio of 0.1, at 0.2–2 MPa (40–400 N), 0.225–2.25 MPa (45–450 N), 0.25–2.5 MPa (50–500 N), and 0.275–2.75 MPa (55–550 N), respectively. Uniaxial tensile testing at 0.5 mm/min showed an average fracture stress at 3.25 MPa (650 N). Both as-received and laser formed specimens were subjected to fatigue testing under these four conditions (Fig. 4).

Strain gauges were also attached within the gauge length to monitor the deformation of the specimen during fatigue loading, with the data being recorded continuously with a data-acquisition system. These data were used to construct the strain versus load cycle diagram.

Shown in Fig. 5 are fatigue test specimens subjected to laser forming treatment prior to testing. The specimen on top was scanned on the top surface only and bending towards the laser is visible. The bottom specimen was additionally scanned on the opposite surface as well and the initial bending was reversed to be more suited for stable fatigue testing.

While laser forming has proven to be a viable method to bend metal foam, the process does induce residual stress and strain, which can significantly affect the fatigue performance of the material and is thus worth investigating.

During laser forming, the material is plastically compressed at the laser scanned area due to the temperature gradient developed in the process. When laser is removed, the material would experience compressive plastic strain at the laser scanned surface and slightly tensile strain on the opposite surface, resulting in the bending of the material. For metal foam, since the material cannot go through large tensile deformation, the laser bending of metal foam is mainly achieved through compressive plastic deformation of the cell structure at the laser scanned region, and cell wall bending and crushing at high bending angle. When the material is further subjected to tension-to-tension fatigue loading, this compressive deformation can offset the tensile deformation experienced by the material and effectively extend the material’s fatigue life. Furthermore, the slight densification resulted from laser forming can increase the material’s strength, making it more resistant to fatigue loading.

Simulation results demonstrated the distribution of the compressive strain resulted from laser forming. An uncoupled thermal–mechanical analysis was conducted on an equivalent dogbone foam specimen with same dimension as the experiment. A laser scan of 90 W with scan speed of 5 mm/s was applied transversely across the gauge length. After the material was cooled down, another laser scan was applied on the opposite side to counter the bending from the first scan. The model and material data used in this study are adopted from Ref. [7], in which the strain result was validated with digital image correlation, and the bending angle was validated with experiments. Figure 6 shows the plastic strain distribution after the first laser scan. As can be seen in Figs. 6(a) and 6(c), the resulted tensile plastic strain along the axial direction (PE22) was much smaller than the compressive strain. The region affected by compressive strain was also much larger than the tensile region. Even though the tensile strain can possibly hamper the material’s fatigue performance, in practice, tensile cracks do not occur until high bending angle due to the heat-softening effect during the laser forming process, therefore laser forming is mainly beneficial to the fatigue performance of the material.

In this study, laser scans were applied on both sides of the specimen and allow more stable fatigue testing. As can be seen in Figs. 6(b) and 6(d), after laser scanning on both sides, the material only experienced compressive residual strain and the bending effect was countered. In addition, the compressive plastic strain was localized at the laser scanning path. Figure 7 shows the plastic strain distribution along the gauge length. Tensile strain is small compared to compressive strain after the first scan, and after the second scan on the back side, both sides have similar compressive strain. The size of the plastic compressed region is comparable to the laser spot size, while the rest of the material was unaffected.

Similar results were observed when the specimen was axially scanned. As can be seen in Fig. 8, for a dogbone specimen axially scanned at the center axis, the plastic compressive strain was also located at the laser scanned area and the bending is countered after scanning on both sides. The compressive strain in the transverse direction is higher than the previous case due to more material in the axial direction to prevent the heat expansion in the transverse direction. In addition, the principal strain direction is changed to be perpendicular to the axial direction. However, plastic strain in the axial direction also exists, and it is comparable to the transversely scanned specimen. The existence of compressive strain in the axial direction and densification from the compressive deformation should still be beneficial to the material’s fatigue performance.

In addition to compressive strain, laser forming may also apply undesirable effects such as micro-cracks and surface degradation at the laser scanned surface. Due to the cell surface being non-flat, surface under the laser may undergo uneven heating which can lead to surface degradation. The repeated air quenching during laser forming also may cause local micro-cracks. These defects, however, remain only at the surface of the laser scanned path and stopped developing at repeated scans.

In this study, metal foam subjected to tension–tension fatigue testing demonstrated typical cyclic ratching. Figure 9 shows typical strain history during the fatigue test for the three different loading conditions, which resulted in a fatigue life over 10⁵. The material underwent slight elongation as the number of cycle increases, which is then followed by a rapid increase in strain near fracture. The mean strain increase before fracture ranged from 0.05% to 0.2%, with higher loading resulted in faster and larger increase in mean strain. This elongation was less obvious than results from the literature. However, the strain increase was consistently observed among the tested specimens, and the strain increase was linear until near fracture.

Although the strain increase during the fatigue cycles was not as manifest as seen in other works, evidence from the fracture surfaces still proved that the specimens fail under ductile fractures. As seen in Fig. 10(a), cell walls undergo large deformation before fracture, indicated by highlighted cell wall bending and tearing. In addition, Fig. 10(b) shows that specimen sometimes have multiple crack locations; this further proves that fracture did not happen abruptly. Figure 10(c) shows an SEM image of the factured surface. Dimple rupture pattern can be seen on the cell wall and no excessive tearing was found, indicating a ductile fracture of the material.

During the fatigue testing, a number of specimens fractured during the initial load ramping or endured significant less cycles within the same loading condition. Even though metal foams have scattered material properties and may thus have some specimen with reduced strength, the loads selected in this study were small compared to the ultimate strength of the material. Therefore, such pheonomenon needs to be studied to reduce uncertainty in actual industry applications.

One factor that can cause the early fracture of specimen is flaws in the foam structure. During the manufacturing and processing of metal foam, cell walls may have initial fractures or even large holes. The fatigue performance of the material is sensitive to such defects and thus the inclusion of initial cell flaws can significantly reduce the fatigue life. Figure 11 shows two specimens with the same loading condition. The specimen with large cell wall cracks had much smaller fatigue life. Such flawed specimens may not be fully eliminated before testing due to hidden cell fractures within the foam. On the other hand, some specimen with overall thicker cell walls and less flaws can have much longer fatigue life. Figure 11(b), for example, has fatigue life two order higher than its counterparts due to its thick cell walls. In industry applications, the existence of cell flaws and inconsistency in material can be alleviated with improved metal foam manufacturing technology. When subjected to laser forming, some foam material may induce additional defects such as micro-cracks and cell surface degradation as explained in previous section. However, such induced defects can be alleviated by improved laser forming parameter and adding protective facesheet to the foam.

Another pheonomenon that contributes to the reduced fatigue life is stress concentrations in the foam. The irregularity of the foam structure inevitably leads to stress concentration under fatigue loading. In addition, the existence of large cells can also reduce the local relative density and lead to higher stresses near the large cells. The stress concentration can lower the fatigue life of the material, but not as detrimental as the cell flaws. This point can also be seen in the simulation of fatigue of metal foam. Figure 12(a) shows the fatigue life distribution of a Kelvin dogbone specimen under the loading 55–550 N. As the Kelvin model uses the same Kelvin cell to approximate the foam structure, the irregularity in the foam structure is limited, which resulted in a fatigue life much higher than the experimental value at the regular structure. However, at the edge of the dogbone, thin-walled structure existed due to dimensional constraints, as can be seen in Fig. 12(b). At such location, the foam has lower relative density and thus the thin-walled structure experience higher local stresses, which lead to much smaller fatigue life comparable to the experimental value.

Laser forming, on the other hand, increases the local relative density of the foam by plastic compressive deformation. Even though the densification is usually minor at low to medium bending angle, the increased relative density still plays a beneficial role to the material’s fatigue performance.

The S–N curve for laser formed and as-received specimen is shown in Fig. 13. The laser forming results were based on transverse scanning. The axially scanned specimens show a similar trend at 45–450 and 50–550 N. Specimens fractured early during the linear ramping of the load or before the cyclic load amplitude reaches the target load amplitude were considered as outliners and were not included in the fatigue life comparison. Specimens that did not fail for at least 10⁷ cycles are visually confirmed to have overall thicker cell walls as described in previous section and were not included in the fatigue life data as well. As-received material was also simulated with the Kelvin model to predict the shortest fatigue life in the dogbone specimen. The S–N curve followed the general fatigue behavior. The log fatigue life increases linearly with reducing maximum stress. The simulation result showed a trend agreeable with the experimental result and had a slight lower predicted fatigue life than the experiment due to the thin-walled structure in the model. In ideal cases, simulation results should have improved fatigue life due to the elimination of irregularities in the foam structure, thus reducing stress concentration. But the thin-walled structure in the model may not be a perfect representation of experimental specimens. This is because in such a model, after one specifies the cell pitch (size), there is little control over cell wall thickness and thickness distribution.

When comparing the laser formed specimen with the as-received specimen, laser treated specimen showed significant improvement in fatigue life at the lowest loading level, and the improvement in fatigue life is reduced when stress levels increase. At the highest loading level, laser forming shortens specimen fatigue life. As explained in previous sections, the improvement in fatigue life can mainly be attributed to the plastic compressive strain from laser forming. The compressive strain can effectively offset the tensile deformation during the fatigue testing and resulted in extended fatigue lives. The improvement of fatigue life of laser formed specimens is more pronnounced at lower loading levels, even makes the material to not fail at the lowest load setting. This is because that when the load is low, the compressive strain can more effectively offset the tensile deformation. While at higher loading, the tensile deformation overshadowed the compressive strain of laser forming. At the highest load level, where the tensile deformaion is so large that the deterimental effect of laser forming induced minor defects was amplified to overtake the benefitial effect of laser forming induced compressive strain. Testing on axially scanned specimen at the two lower stress levels shows a similar trend in fatigue life improvement.

While the trends are very clear, scatter of fatigue data is seen due to the reasons given in the previsous section. As-received specimen showed similar scatter at different loading levels. However, laser forming shows a larger scatter at lower loading. This is likely due to the fact that the laser forming process has introduced additional variations to foam properties because of its interactions with original structural variation. Such an additional effect becomes more pronounced at the lower loading levels, where loading plays a relatively minor role in foam fatigue behavior and thus larger scatter. At the higher loading levels, the loading plays a more significant role and such an effect is somewhat suppressed and so is the scatter.

Laser forming process generates compressive residual strain at the laser scanned surface and very minor tensile strain on the opposite side. After the opposite side is also laser scanned, both surfaces have compressive residual strain. This is the case for both the transverse and axial scanning patterns. This compressive strain offsets tensile deformation and effectively improves the fatigue life under tension-to-tension cyclic loading at low loading levels. The effect of fatigue life improvement is very effective at lower fatigue loading, where the compressive strain can sufficiently offset the tensile strain experienced by the material. In addition, laser forming also alters the material property of metal foam, which is more pronounced at lower loading, yielding a large variance in fatigue data. When subjected to higher tensile fatigue loading, the amplitude of the tensile deformation started overshadowing the effect of laser forming induced compressive strain, thus the performance of laser formed specimen started falling behind that of the as-received metal foam. Overall, laser forming has a beneficial effect to the tensile fatigue performance of metal foam at low stress levels, but the improvement of fatigue life is reduced at higher loading level and may even cause shortened fatigue life due to laser-induced defects. Initial fractures in cell wall and thin-walled structure have been found to hamper the fatigue performance of metal foam and should be avoided during manufacturing and handling of the material.

This work was supported by a grant 1725980 from NSF and by Columbia University.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.