To address the issue that the traditional A* algorithm has a long search time and the path obtained is not always the shortest path, this paper proposes an improved A* method that removes redundant child nodes based on the positional relationship between the current node and the target point and incorporates a bi-directional search to search for paths from both the starting and end points at the same time. According to the results of simulation experiments on raster maps of various sizes and complexity, the improved A* algorithm proposed in this paper significantly improves search speed, reduces search time by an order of magnitude, and shortens path length in some specific environments compared to the traditional A* algorithm.

Characterising the microstructure of foams is an important task for improving foam manufacturing processes and building foam numerical models. This study proposed a method for measuring the thickness of individual cell walls of closed-cell foams in micro-CT images. It comprises a distance transform on CT images to obtain thickness information of cell walls, a watershed transform on the distance matrix to locate the midlines of cell walls, identifying the intersections of midlines of cell walls by examining how many regions each pixel on the midlines of cell walls connects with, disconnecting and numbering the midlines of cell walls, extracting the distance values of the pixels on the midlines (or midplanes) of cell walls, and calculating the thickness of individual cell walls by multiplying the extracted distance values by two. Using this method, the thickness of cell walls of a polymeric closed-cell foam was measured. It was found that cell wall thickness measured in 2D images shows larger average values (around 1.5 times) and dispersion compared to that measured in volumetric images.

In this work, polymeric foam thermoforming, foam injection moulding, bead foaming and film foaming were reviewed in an effort to explore feasible processes to manufacture sandwich structures of complex geometry for automotive applications. Injection moulded foams generally suffer from high density, poor cell morphologies and unnecessary skin layers. Foamable films currently available are pressure-induced. In order for foamable films to produce foam, high uniformly-distributed pressure needs to be applied, which makes it difficult to manufacture foam parts of three-dimensional complex geometry with foamable films. The majority of commercial high-performance foam cores can be thermoformed. Ideally, thermoformed foam cores would have good mechanical properties if high-performance foam sheets are used. However, the mechanical properties of foams might be reduced during the process of thermoforming, especially around corners. Bead foaming offers a high level of freedom in foam geometry to be moulded, and inserts can be integrated into foam cores during the process of moulding. Moreover, foam cores with high density in high stressed areas and low density in low stressed areas can be manufactured with foam beads of different densities. However, due to nonhomogeneous degree of fusion and weak bonds and voids between beads, bead foams generally show mechanical properties lower than their block counterpart. Relatively speaking, thermoforming with high-performance foam sheets and moulding with high-performance foam beads hold great potentials for mass production of sandwich cores of complex geometry for automotive applications. However, further investigation on the mechanical properties of thermoformed foams and high-performance bead foams is still in need to confirm their suitability.

This paper studied the effect of sintering temperature on phase composition, microstructure, Mn sublimation and compressive properties of the Fe-Mn-Al-C powder compacts with high-Mn and high-Al content. The phase composition gradually transformed from heterogeneous phases at the temperature of <= 1100 degrees C to the dominant gamma-Fe at 1200 degrees C, while alpha-Fe was the main phase at 1300 degrees C due to the sublimation of Mn. The sublimation of Mn in the sintered compacts increased with elevated temperature. The porosity of the sintered samples peaked at 1200 degrees C, then reduced sharply to similar to 45% (open porosity) and similar to 50% (overall porosity) at 1300 degrees C. The porosity trend was affected by the combined factors of solid diffusion/reactions, transient liquid phases, Mn sublimation and the final densification. The compressive strength at the macroscopic crack initiation increased drastically from similar to 17 MPa at 800 degrees C to similar to 296 MPa at 1300 degrees C. The failure mode transformed from transgranular cleavage fracture at the temperature of <= 1100 degrees C to ductile fracture at 1200 degrees C, followed by quasi-cleavage fracture at 1300 degrees C.

In this study, the microstructure of a SAN foam was imaged using a micro-CT scanner. Through image processing and analysis, variations in density, cell wall thickness and cell size in the foam were quantitatively explored. It is found that cells in the foam are not elongated in the thickness (or rise) direction of foam sheets, but rather equiaxed. Cell walls in the foam are significantly straight. Density, cell size and cell wall thickness all vary along the thickness direction of foam sheets. The low density in the vicinity of one face of foam sheets leads to low compressive stiffness and strength, resulting in the strain localization observed in our previous compressive tests. For M80, large open cells on the top face of foam sheets are likely to buckle in compressive tests, therefore being another potential contributor to the strain localization as well. The average cell wall thickness measured from 2D slice images is around 1.4 times that measured from 3D images, and the average cell size measured from 2D slice images is about 13.8% smaller than that measured from 3D images. The dispersions of cell wall thickness measured from 2D slice images are 1.16–1.20 times those measured from 3D images. The dispersions of cell size measured from 2D slice images are 1.12–1.36 times those measured from 3D images.

Fifth wheel coupling is a key component of heavy duty semi-trailer tractor, providing the link between the semi-trailer and the towing tractor. In the present work, the failure of fifth wheel coupling utilized in heavy duty semi-trailer tractors was analyzed. Firstly, the chemical composition and metallographic microstructure of the material of the fifth wheel coupling were characterized using scanning electron microscopy with an energy dispersive spectrometer. Secondly, the mechanical properties of the material was investigated by tensile tests on specimens manufactured out from the failed fifth wheel couplings. Thirdly, the stress distributions of the fifth wheel coupling under typical loading conditions were obtained via multibody dynamics analysis and finite element analysis. Finally, crack morphology and fracture surface were examined. Results showed that the chemical composition, metallographic microstructure and mechanical properties of the matrix material were in accordance with standard requirements, which rules out the possibility that the failures were caused by casting defects in the matrix material. Stresses in the crack regions were in tensile stress state under different loading cases and were much smaller than both the mechanical strength and fatigue strength of the material. Therefore, the failure of the fifth wheel couplings was attributed to stress corrosion cracking induced by tensile stress and damp environment. Measures to prevent such failures were discussed in details as well.

The mechanism of bubble removal in a narrow viscous fluid by using ultrasonic vibration is analyzed in this study. Experimental studies were performed on the adhesive bonding between a carbon fiber reinforced plastic (CFRP) laminate and an aluminum plate. After applying ultrasonic vibration on the CFRP laminate, it was found that the high-frequency vibration could induce an oscillating flow of the adhesive in the narrow bonding layer. Such a flow caused the entrapped bubbles to move and break until all of them were eliminated from the viscous adhesive. A fluid–solid coupling simulation and fluid tracer analysis were performed to analyze the underlying principle of bubble motion. The results reveal that because of the internal pressure of the bubble and the asymmetric characteristic of the fluid resistance around the bubble, the oscillating fluid induced by ultrasonic vibration drove the bubble to move in the direction closest to the edge. The reduction of the gas volume fraction in the adhesive resulted in an improved bonding between the CFRP laminate and aluminum plate.

The compressive and shear responses of the closed-cell Kelvin and Weaire-Phelan foams along the lattice direction [100] were studied using explicit dynamic analyses in this work. Expressions describing the relationship of compressive and shear strengths to relative density were developed for these two foams. The compressive and shear strengths of the Kelvin and Weaire-Phelan foams are found to increase quadratically with relative density at low relative densities and linearly at high relative densities. This is because elastic buckling followed by material yielding cause the failure of low relative density foams, while large deformation and material yielding is the main cause of failure for high relative density foams. Cell wall buckling and local material yielding only cause reduction in global stiffness. Ductile foams fail globally when a certain amount of material has yielded, forming a plastic band across the foams. Shear buckling occurs in foams with very low relative density under shear.

Global properties of foams depend on foam base materials and microstructures. Characterisation of foam microstructures is important for developing numerical foam models. In this study, the microstructures of four polymeric structural foams were imaged using a micro-CT scanner. Image processing and analysis methods were proposed to quantify the relative density, cell wall thickness and cell size of these foams from the captured CT images. Overall, the cells in these foams are fairly isotropic, and cell walls are rather straight. The measured average relative densities are in good agreement with the actual values. Relative density, cell size and cell wall thickness in these foams are found to vary along the thickness of foam panel direction. Cell walls in two of these foams are found to be filled with secondary pores. In addition, it is found that the average cell wall thickness measured from 2D images is around 1.4 times of that measured from 3D images, and the average cell size measured from 3D images is 1.16 times of that measured from 2D images. The distributions of cell wall thickness and cell size measured from 2D images exhibit lager dispersion in comparison to those measured from 3D images.

Compared with regular honeycombs, irregular honeycombs are more representative of real foams, and thus more suitable for the study of foam mechanics. In this paper, the deformation and failure progression in the irregular honeycombs are investigated by analysing the images captured in order to gain an improved understanding on foam failure. Irregular honeycombs with varying cell wall thickness, cell size and cell shape were manufactured using a three-dimensional printer and tested under compression. The behaviour of irregular honeycombs is found to be different from that of regular honeycombs. In irregular honeycombs, cell walls start to fracture at some point, initially at a low speed from multiple locations. The global stress reaches its maximum value shortly after the first fracture of cell walls. Only a few cell walls buckle in the specimens with cells of irregular shape. Fracture is more likely to occur to thin and long cell walls aligned within a medium angle (around 30 to 60°) to the compressive load. However, the susceptibility of a cell wall is to fracture is also affected by its neighbouring cell walls. Strong and stiff neighbouring cell walls could shield load away and protect it from breaking. Because of this, it is better to think of a weak spot as a region, rather than an individual cell or cell wall. Overall, the more uniform cell wall size and thickness are, the better the mechanical performance of cellular solids is.

This paper aim to establish a framework for finite element modelling of the compressive and shear responses of closed-cell foams using computed tomography images, and to explore the deformation and failure mechanisms at cell level in closed-cell foams under compression and shear. Results show that quadratic tetrahedral mesh is more suited than cubic voxel mesh in modelling closed-cell foams. The mesh density with one quadratic tetrahedral element across the thickness of cell walls can yield results with good accuracy. Representative volume elements for closed-cell foams need contain at least 5.2 cells and 3.9 cells along each edge for compression and shear tests, respectively. Compressive buckling and shear buckling appear during the initial elastic regime of compression and shear, respectively. Buckling acts as a failure initiator, which changes the deformation modes of cell walls from in-plane compression, tension or shear to bending. Subsequent large deflection of cell walls and material yielding lead to further degradation in the global stiffness of foams. Shear buckling causes cell walls to lose load-carrying capacity along the direction of the compressive component of the shear load, therefore is less detrimental than compressive buckling in reducing the load-bearing capacity of cell walls. Consequently, the global stiffness of closed-cell foams degrades less rapidly in shear tests compared to compression tests. The Young’s modulus of foam base materials slightly affects foam strengths. This is because cell walls undergo bending after buckling, and the maximum bending load that the buckled cell walls can bear is determined by the yield strength of base materials.

Study on the response of honeycombs subjected to in-plane shear helps establish the constitutive relations for honeycombs and shed light on the mechanics of cellular materials. The present study explores the nonlinear elastic response of honeycombs under in-plane shear by analyzing the large deflection of cell walls in a unit cell. Governing equations are established which relate the macroscopic response of honeycombs to the deflection of cell walls. Solving these equations, the behavior of regular honeycombs under in-plane shear along horizontal (X) and vertical (Y) directions was investigated. It is found that the response of regular honeycombs under in-plane shear depends on the nondimensional shear stress which is a parameter combining the thickness-to-length ratio of cell walls, the Young's modulus of base materials, and macroscopic shear stress. Lateral shrinking is a distinctive characteristic for honeycombs under in-plane shear, which should be taken into account when establishing constitutive relations and performing simple shear experiments. Expressions for predicting the shear strength of honeycombs are formulated in this paper. It is noted that the normalized shear strength of regular honeycombs depends on two ratios: the thickness-to-length ratio of cell walls and the ratio of Young's modulus to yield strength of base materials, and the former has a dominant effect. By comparing honeycombs with cell walls of uniform thickness against honeycombs with vertical cell walls of double thickness, it is found that doubling the thickness of vertical cell walls of honeycombs increases their shear strength along horizontal (X) direction nearly twice, but does not improve the shear strength that much along the vertical (Y) direction.

In the present study, two irregular honeycombs are manufactured by a 3D printer and tested under compression. Experimental observation shows that the first fracture of cell walls is significantly critical, which is indeed the onset of global failure of honeycombs. To predict the onset of global failure of honeycombs, failure criteria based on stress or strain at integration point level need to be used, which is difficult to realize due to stress singularity at cell wall joints. To circumvent this issue, a mesh level, 40 elements within each cell wall, is chosen in FE analysis so that numerical results at cell wall joints are close to engineering solutions. Failure criteria based on von Mises stress, equivalent plastic strain, tensile plastic strain, surface tensile stress and bending moment are then employed to predict the first fracture of cell walls. It is found that failure criteria based on von Mises stress, equivalent plastic strain, tensile plastic strain yield the same predictions which are within 9% of experiment value for strength and within 24% for strain at failure. The cell walls which are predicted to be the most likely to fracture first in the honeycombs agree well with these cell walls that rupture first in experiments.

This paper concerns with the micromechanical modelling of closed-cell polymeric foams (M130) using Laguerre tessellation models incorporated with realistic foam cell size and cell wall thickness distributions. The cell size and cell wall thickness distributions of the foam were measured from microscope images. The Young’s modulus of cell wall material of the foam was characterised by nanoindentation tests. It is found that when the cell size and cell wall thickness are assumed to be uniform in the models, the Kelvin, Weaire–Phelan and Laguerre models overpredict the stiffness of the foam. However, the Young’s modulus and shear modulus predicted by the Laguerre models incorporating measured foam cell size and cell wall thickness distributions agree well with the experimental data. This emphasizes the fact that the integration of realistic cell wall and cell size variations is vital for foam modelling. Subsequently the effects of cell size and cell wall thickness variations on the stiffness of closed-cell foams were investigated using Laguerre models. It is found that the Young’s modulus and shear modulus decrease with increasing cell size and cell wall thickness variations. The degree of stiffness variation of closed-cell foams resulting from the cell size dispersion and cell wall thickness dispersion are comparable. There is little interaction between the cell size variation and cell wall thickness variation as far as their effects on foam moduli are concerned. Based on the simulation results, expressions incorporating cell size and cell wall thickness variations were formulated for predicting the stiffness of closed-cell foams. Lastly, a simple spring system model was proposed to explain the effects of cell size and cell wall thickness variations on the stiffness of cellular structures.