A mathematical modelling of preheated accumulative roll bonded Al-Al2O3 composite sheet

Accumulative roll bonding (ARB) technique is used in this paper to produce aluminum/alumina composite sheets. Alumina content was added as 1,3 and 5wt%. The produced Al/Al2O3 composite sheets are piled up and processed by accumulative roll bonding (50% reduction) after preheating at 280 °C with different regimes (2–8 cycles). Statistical design analysis was applied to examine the effects of alumina content and no. of accumulative roll bonding cycles on the ultimate tensile strength for aluminum/alumina composite sheets. Empirical formulas were deduced to recognize key parameters that controlling tensile behavior. XRD detection was carried out to explore dominant planes controlling plasticity Al/Al2O3 composites. In general, addition of alumina and proceeding different cycles increases strength. FE-SEM microstructure showed that alumina plays important roll on the aluminum sheets during ARB process where the metal of aluminum flow among them producing highly sheared matrix.


Introduction
Aluminum/alumina (Al/Al 2 O 3 ) composite are considered new advanced materials in industries because of their light weight, good wear and corrosion resistance, high strength and high modulus of elasticity and low coefficient of thermal expansion. Several methods are used to fabricate Al/Al 2 O 3 composite such as powder metallurgy [1], squeeze casting and spray forming [2,3] accumulative roll bonding (ARB) [4] equal channel angular pressing (ECAP) [5] and multi-axial free forging. ARB is known as kind of severe plastic deformation (SPD) methods [6]. The ARB method is considered as easy production and based on cold rolling process [7]. ARB technique is one kind of the (SPD) mechanism in which large plastic strain is enacted into the material [8].
In order to attain an ultra-fine-grained metal with excellent mechanical properties. In Al/Al 2 O 3 composite, fine particles of Alumina (<50 μm) is utilized to produce Al/Al 2 O 3 composite. Fabricating of Al/Al 2 O 3 composite using ARB process cold at room temperature exhibits Al/Al 2 O 3 sheets of very weak bonding strength due to severe strain hardening of metal layers. For example, large number of cracks begin to nucleate and propagate during cold rolling passes [9]. Reduction in thickness and preheating temperatures are key parameters that control the preconditioning for successful bonding of Al/Al 2 O 3 layers. At higher reduction of thickness, the bonding strength between two layers of composite rises [10]. Very few papers demonstrate the ARB at higher temperature. It was found that the peeling force (Adhesive Bonding Force) of composite layers enhances [11]. The target of this research is to manufacture Al/Al 2 O 3 composite sheet containing different Alumina using preheating ARB Process (at 280°C). Also, to correlate the relationship between Alumina content and number of cycles on the ultimate tensile strength (UTS) using Experimental Design Technique (Statistical design analysis).

Experimental work
The aluminum sheets dimensions were of length, width and thickness 330 mm×150 mm×1.5 mm strips, respectively. The direction of the cutting of strip was parallel to the sheet rolling direction. The quality of surface preparation is important in ARB. Surface preparation was carried out to increase the adhesion aluminum (AA1050) sheets. It can be done chemically and mechanically. Chemical cleaning (degreasing) entails the removal of dirt, oil, grease and other external materials with organic solvents as acetone solution. Al sheets were subjected to mechanical cleaning (wire brushing). Specification of scratch brush used in this study with a 90 mm diameter stainless-steel circumferential brush with 0.27 mm wire diameter, 35 mm wire length and peripheral speed of 2000 rpm. After surface preparation, Al 2 O 3 particles were uniformly diffused between the two strips of aluminum sheets with different content of alumina (1,3 and 5wt%). Al/Al 2 O 3 sheets were then stacked over each other and fastened at both ends by steel wires. The experiment pays minute attention to proper alignment of the two strip surfaces before rolling. Assembled Al/Al 2 O 3 sheets containing different Al 2 O 3 content (1,3 and 5wt%) were preheated at 300°C for 5 min and then rolled for single pass with 67% reduction in thickness (without any lubrication) to 1mm strip thickness and air cooled. This produced sandwiches of Al/Al 2 O 3 composite (containing different concentration of alumina) is called (Cycle 0). To remove work hardening from previous steps and to improve bonding strength of the cycle 0 sandwich, Al/Al 2 O 3 composites sheets then (1, 3 and 5wt% Al 2 O 3 ) were fully annealed at 400°C for 60 min, and then cooled in the furnace. The fully annealed sandwiches were cut in perpendicular to the ARB direction. According to the number of assembled sandwiches together (1, 2, the sandwiches were called as demonstrated in figure 1 and listed below in table 1. The sandwiches were preheated at 280°C for 7 min followed by ARB equals to 50%. The ARB experiments were executed, without lubricant, by using rolling machine. The rolling machine is a two-high rolling mill with 300 mm roll diameter, 600 mm width and a rolling speed of 0.40 m s −1 it. The experimental steps are shown in figure 1. The most complex problem in the roll bonding step was small edge cracks. Tensile specimens were cut according to ASTM E8M shows in figure 2. Tensile testing was performed at room temperature with initial strain rate 1.1×10 −4 s −1 [12]. The different planes after ARB were identified by x-ray diffraction method (XRD, Bruker D8) using Cu Kα radiation (λ=1.541 8 Å) with a scanning angle (2θ) of 10°-100°at a scan speed of 4 (°)/min, a voltage of 40 KV and a current of 300 mA [13].

Microstructure preparation
Microstructure characterization studies were conducted on a metallographically polished specimens to investigate the morphology of grains. The metallographic samples after different cycles were cut with  Table 4 describes run, factors A, B and the UTS response.
According to this design, the optimal conditions were assessed using a second order polynomial function by which a correlation between examined factors and response (UTS) was generated. The overall form of this equation is: according to this design, the optimal conditions were estimated using a second order polynomial function by which a correlation between studied factors and response (UTS) was created. The general form of this equation is: where y is the estimate of the response variable and Xi's are the independent variables (Alumina content, and number of cycles) that are known for each experimental run. The parameters β0, βi, and βij are the regression parameters. Software package, Design-Expert 11 was used for regression analysis of experimental data and to plot response surface. Analysis of variance (ANOVA) was used to assess the statistical parameters. The extent of fitting the experimental results to the polynomial model equation was stated by the determination coefficient, R 2 . F-test was used to estimate the significance of all terms in the polynomial equation within 95% confidence interval [15,16].  where boundaries of Al sheets layers disappeared. It can also be noticed that the thickness of alumina dense clusters decreases and consequently their size diminishes too. Figure 5 demonstrates that after the cycle 8, the uniformity of alumina clusters considerably increases. In other words, during the ARB process, the Al matrix flows between the alumina clusters, and consequently, the distance between the layers of Alumina particles increases. Cycle 8 (FE-SEM micrograph in figure 5) shows diffused interfaces with a good continuity. On the other hand, after the cycle 8, the porosities in the clusters are eliminated (well sound due good surface welding).   At early stages of ARB (Cycle 3), alumina layers are still apparent for 3wt% alumina sandwich. While in the late stages of ARB (Cycle 8), alumina layers disappeared, due to increase the aluminum layers. As it can be observed from figures 6 and 7, the behavior of Al/Al 2 O 3 (3wt%) is similar as in Al/Al 2 O 3 (1wt%). In addition, the thickness of alumina (3wt%) layers is larger than Al/Al 2 O 3 (1wt%).   Alumina particles cannot deform plastically due to its ceramic nature; hence they create free space between them (horizontally or vertically). Adhesion between particles is not sufficient, so micro-cracks appear in these areas. On macroscale level, this is shown as weak bonding between the sheets, as demonstrated in figure 8.

Mechanism of dispersion of alumina particles
The FE-SEM micrographs at longitudinal sections of Al/1wt% Al 2 O 3 composite were produced by ARB process in various cycles. It is observed that by increasing the number of ARB cycles, the laminate structure (the  aluminum sheets and powder layers) changed to a particle reinforced composite. There are several efficient mechanisms for changing the lamination structure to uniform dispersion of alumina particles in the Al matrix. At the initial cycles (early stages of ARB), during ARB the powder layers break up to small fragments and metal matrix of Al is extruded or squeezed through the fragments. Evidences of extrusion of the base metal through the powder layer fragments are detected in FE-SEM micrographs. As deformation of the harder agglomerates is considerably less than the matrix, the matrix flows past the fragments during the ARB, causing shear flow. The particles adjoining to the interface of fragments and matrix are less constrained than those in the interior of the fragments, and because of matrix shearing effect.
They flow by tumbling along the fragment's borders. By intensifying the strain (more ARB), the fragments continue to change their shape and their size as more particles are eliminated from the borders of the fragments (or Alumina agglomerates) and transferred to the end of the elongated clusters and/or agglomerations. FE-SEM shows elongated agglomeration with removed particles around it. By more deformations, the clusters or agglomerates show a preference orientation and gradually string themselves out along the rolling direction and finally, particles are regularly dispersed in the matrix. The fragments of the powder layer are completely disappeared at the last cycles of ARB process (late stages). Figure 9 shows the XRD of Al pure (annealed). The maximum peak is Plane (111) (closest plane). The second dominant plane is (200). The background is so smooth due to annealed structure. Figures 10, 11 and 12 show XRD plateau which explain synergetic effect of both ARB process and alumina particles content on the different peaks of aluminum/Al 2 O 3 composite sheets. Generally, it is apparent that main plane (highest peak) of Plasticity for ARB sheet is (220) plane (dominant). Therefore, the elongation is sharply decreased than that of annealed one (main peak of aluminum annealed is (111)). Moreover, sheets containing 3 and 5wt% alumina, have dominant planes (111) and (200) after cycle 8 for 3wt% and after cycle 7 for 5wt% alumina. In addition, for sheets containing 3wt% alumina after cycle 3 and cycle 0, the main planes (dominants) are (200) and (311), respectively. It is also clear that the background is rough due to high angle grain boundaries.

Mathematical modeling for Al/Al 2 O 3 composite
The mathematical model boundary conditions are very important to avoid any irregularities of data response (UTS) and to choose the proper empirical equation which completely represents the whole data at different zones with very low errors. At first, cycle 0 data is excluded due to different preheating temperature (300°C, 5 min), time and ARB ratio 67% while the rest of ARB experiments are carried out at 280°C for 7 min having 50% reduction in thickness. Figures 13 and 14 shows the contour behavior of alumina content (1, 3 and 5wt%) at number of cycles (ARB) on the ultimate tensile strength (UTS). At low, moderate or high cycle and 1wt% alumina, it is found that UTS slightly decreases till cycle 5 (142-136MPa) and then slightly increases again (136-143MPa).   More than 3wt% alumina, on increasing the cycle, UTS gradually decreases.
The empirical equation that describes the mathematical relationship between alumina content and number of cycles on UTS is listed below. In general, it is obvious that both alumina and number of cycles decrease the UTS as indicated in the terms of alumina (91%) and number of cycles (667%). However, the number of cycles has more effect.   The interaction between alumina content (wt%) and number of cycles is demonstrated in figure 15. Addition of 1wt% alumina increases UTS than cycle 0 of composite Al/Al 2 O 3 . Furthermore, increasing the alumina content gradually decreases the UTS at low number of cycles. On the contrary, at high number of cycles, the UTS steeply decreases with increasing the alumina content. When the Alumina content increases, it agglomerates in the Aluminum matrix, weakens Al/Al 2 O 3 composite and works as non-metallic inclusions according to Orowan concept [17]. Moreover, aluminum after severe plastic deformation exhibits to self-dynamic softening which decreases Al strength. Figure 16 describes the relationship between the actual UTS from experiments and the predicted UTS from the empirical formula (deduced by Design Expert). This relationship can determine the error between actual and predicted values of UTS via correlation factor (R). It is found that the maximum error value is less than 2%.