Study of plane strain compression of composite sheets

In the plane strain compression of multi-layers metal, each layer of metal shows a different degree of deformation due to the differences in material properties. Also, the deformation in different positions of a metal layer is always inhomogeneous. In this study, the effects of material ratios, friction between the metal layers and the amount of compression on the deformation behaviors of a bi-layer metal strip under plane strain compression are investigated. 2D plane strain finite element simulation models of AISI-1008/AL6061-T6 bi-layer metal strips are used. The results indicate that the strips show different deformation behaviors under different conditions, and non-smooth interfaces caused by the inhomogeneous material flow during the deformation process are detected in most cases.


Introduction
The deformation behavior of multi-layered metals under compression is a complex phenomenon that depends on various factors, such as the material properties of each layer, the friction between layers, and the amount of compression applied [1].When a metal composite sheet is subjected to plane strain compression, each layer experiences a different degree of deformation due to the differences in material properties, resulting in non-uniform deformation behavior.Moreover, the deformation in different positions of a metal layer is always inhomogeneous due to the non-uniform distribution of stresses and strains.These factors can lead to the formation of non-smooth interfaces between the layers, which can affect the mechanical properties of the composite material.Some authors have studied the plane strain compression of the multi-layer metal strip from different aspects., for example, Alexandrov et al. [2] suggested a theoretical analysis of the plane-strain compression for a multi-layer strip of rigid perfectly/plastic materials with Tresca friction conditions at the platen surfaces and bi-material interfaces.The author specialized the closed-form solution to twolayer and three-layer strips and identifies domains corresponding to sticking conditions at all bi-material interfaces, and demonstrated that the occurrence of the sticking regime at all bi-material interfaces leads to deformation with a proportional decrease in the thicknesses of all layers.On the other hand, Jia et al. [3] studied the co-deformation and shear localization in heterophase alloys using two-dimensional crystal plasticity finite element simulations on plane strain compressed Cu-Ag and Cu-Nb metal matrix composites.It was found that significant shear banding occurs in fcc and bcc crystals, triggered by stress concentrations at the interfaces, leading to highly localized strains within the bands.The predicted topology and nature of the cross-phase shear bands agreed well with experimental observations in cold-rolled composites, and the results provided essential information for understanding the micromechanical boundary conditions inside co-deformed composites and the associated shear-induced chemical mixing.Besides, Uscinowicz [4] studied the hardening process of Ti/Cu bimetal during compression testing.The author obtained the bimetal by permanently connecting a copper core with a circular cross-section with a layer of titanium deposited on its circumference.The study evaluated the influence of the thickness of the titanium layer and the ratios of the outer diameter to the height of the cylindrical samples on the hardening process of the bimetal.The results showed that the geometrical dimensions of the specimens significantly affect the values of mechanical properties determined from the compression test.
In this study, the effects of material ratios, friction between the metal layers, and the amount of compression on the deformation behaviors of a bi-layer metal strip under plane strain compression was investigated.2D plane strain finite element simulation models of AISI-1008/AL6061-T6 bi-layer metal strips were created, and the deformation behavior and the formation of non-smooth interfaces under different conditions were analyzed.

Materials and methods
Finite element software DEFORM-2D was used to simulate the plane strain compression of a steelaluminum bi-layer strip with a total height (y-direction) of 10 mm, width (z-direction) of 10 mm, and length (x-direction) of 20 mm.The simulation model is illustrated in Figure 1, while Tables 1 and 2 provide information on the mechanical properties of the materials and the forming parameters used, respectively.The simulation process involved placing the bi-layer strip on a fixed bottom die and compressing it along the -y direction at a speed of 1 mm/s using a top die.The compression continued until the height of the strip reached 5 mm, resulting in plane strain compression along the x and y directions only.The friction coefficient between the strip and the dies was set to 0.15, while the friction coefficient between the two layers of materials was varied at five different levels, which were 0, 0.02, 0.1, 0.2, and 0.3.The friction coefficient of 0.3 represents dry friction, while 0.02 represents the optimum coefficient under suitable lubrication conditions.In addition, three different material ratios, 3:7, 5:5, and 7:3, were used in different groups of simulations.The simulation results were analyzed to investigate the deformation behaviors of the bi-layer strip under different friction coefficients and material ratios.The effects of these parameters on the deformation behaviors were studied and compared.

Initial height of the bi-layer strip [mm] 10
Final height of the bi-layer strip [mm] 5 Material ratio of the bi-layer strip 3:7, 5:5, 7:3 Compression speed of the top die [mm/s] 1 Friction coefficient between the strip and the dies 0.15 Friction coefficient between the two layers 0, 0.02, 0.1, 0.2, 0.3

Effects of the friction coefficient between the two layers on the deformation behavior
Figure 2 shows the appearance of the bi-layer strips (with original material ratios of 5:5) after compression from a total height of 10 mm to 5 mm in the simulations.There are 5 strips in the figure with different friction coefficients between the two layers (µ), while other simulation conditions are all the same as mentioned in the material and method section.Two main observations were made: The first observation concerns the horizontal strain (strain in the x-direction).Since the aluminum strip has a lower yield strain than the steel strip, under the same compression force, aluminum tends to deform to a greater extent than steel.Thus, in Figure 2, the aluminum in all five cases elongates more than the steel.However, the friction between the two metal layers (µ) is also a resistance force to the deformation process, in addition to the friction between the dies and the strip.When µ is not equal to zero, the steel strip applies a frictional force to the aluminum strip, directed towards the center of the material, which resists the elongation of steel in the x-direction.Therefore, as µ increases, the aluminum strip experiences greater resistance from the steel strip, resulting in a decrease in horizontal strain.At the same time, the aluminum strip applies a relative frictional force on the steel strip in the opposite direction, pulling the steel strip to elongate more.When µ increases, this pulling force increases, and hence the horizontal strain of the steel increases.Therefore, as µ increases, the difference in the horizontal strain of the two layers becomes smaller.
The second observation concerns the vertical strain (strain in the y-direction) of the materials.The results show that the materials have non-uniform y-strain at different points, especially at lower values of µ, where a wave-like structure appears in the contact surface.At higher values of µ, the contact surface becomes flatter.The wave-like morphology observed in the contact surface of the bi-layer metal strip under low friction conditions is a well-known phenomenon in the field of tribology.It is commonly referred to as the "waviness" of the contact interface [5][6][7].The waviness of the contact interface arises from the interaction between the elastic and plastic deformations of the contacting bodies and the frictional forces that are generated at the interface.When the friction coefficient between the two materials is low, the frictional forces are not strong enough to overcome the elastic restoring forces that arise from the deformation of the materials during the compression process.As a result, the interface undergoes elastic deformation, which can lead to the formation of undulations or ripples on the surface.The formation of these undulations is also influenced by the ratio of the elastic moduli and the yield strengths of the two materials, as well as the thickness and geometries of the contacting bodies.These factors can affect the distribution of the stress and strain fields near the interface, which in turn can affect the development of the waviness.

Effects of the material ratios on the deformation behavior
To investigate the effects of the material ratio on the deformation behavior of the bi-layer metal strips, three different material ratios were simulated, which were 3:7, 5:5, and 7:3.The simulations were conducted under the same conditions as described in the materials and methods section.Figure 3 shows the appearance of the bi-layer strips after compression from a total height of 10 mm to 5 mm in the simulations under different conditions.It can be seen that when the steel content in the bilayer strip is higher, the contact surface between the two layers becomes flatter, this is because steel has a higher yield strength and modulus of elasticity than aluminum, which means it can resist deformation better and provide more stable support to the aluminum layer.

Strain distribution of the materials under different simulation conditions and compression amounts
Figure 4 shows the strain distribution of a bi-layer strip under different compression amounts.It can be seen that the deformation was inhomogeneous from the distribution of effective strain.Figure 5a-c show the compressive strain of the center points of the materials in different strokes with an initial material ratio of 3:7, 5:5, and 7:3, respectively.There are three curves in each graph, the blue one denotes the compressive strain of steel, the orange one denotes the compressive strain of aluminum and

Figure 1 .
Figure 1.Simulation model of the compression process.

Figure 2 .
Figure 2. The appearance of the bi-layer strips after compression.

Figure 3 .
Figure 3.The appearance of the bi-layer strips after compression under different conditions.

Table 1 .
Mechanical properties of the materials.

Table 2 .
Forming parameters used in the simulations.