Recent advances and trends in roll bonding process and bonding model: A review

Zixun LI, Shhe REZAEI, To WANG,*, Jinho HAN, Xueo SHU,Zigniew PATER, Qingxue HUANG

aCollege of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030002, China

bInstitute of Materials Science, Technische Universit?t Darmstadt, Darmstadt 64287, Germany

cFaculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China

dFaculty of Mechanical Engineering, Lublin University of Technology, Lublin, 20618, Poland

KEYWORDSBimetallic;Bonding mechanism;Bonding model;Numerical simulation;Roll bonding process

AbstractThis review presents a thorough survey of the roll bonding process with a focus on the bimetallic bars/tubes as well as the bonding models and criteria.The review aims to provide insight into cold,hot and cryogenic bonding mechanisms at the micro and atomic scale and act as a guide for researchers working on roll bonding, other joining processes and bonding simulation.Meanwhile,the shortcomings of roll bonding processes are presented from the aspect of formable shapes,while bonding models are shown from the aspect of calculation time,convergence,interface behavior of dissimilar materials as well as hot bonding status prediction.Two well-accepted numerical methodologies of bonding models, namely the contact algorithm and cohesive zone model(CZM) of bonding models and in simulations of the bonding process are highlighted.Particularly,recent advances and trends in the application of the combination of mechanical interlocking and metallurgical bonding, special energy fields, gradient structure, novel materials, green technology and soft computing method in the roll bonding process are also discussed.The challenges for advancing and prospects of the roll bonding process and bonding model are presented in an attempt to shed some light on the future research direction.

1.Introduction

There is still a long way to achieve the Paris climate goals.As the data investigated by Ren et al.,1the iron and steel industry accounted for 22%of industrial energy use and 28%of industrial carbon emissions in 2019.Carbon neutrality and carbon peaking have become a goal all over the world.To improve this situation, the use of lightweight constructions and materials is an effective method to limit CO2emissions.As demonstrated by Cheah,2every 10% total weight reduction in a vehicle can bring 4.9%fuel economy improvement.Thus,more and more metal composites have been applied to replace the traditional mechanical parts.

Metallic composites, which consist of multi-material and hybrid structures, can increase both performance and functionality, as stated by Martinsen et al.3Except for the lightweight function, it can also save precious metals and achieve the effect of‘‘1+1>2”.Bay et al.4regarded that the regular welding process cannot meet the high requirement of dissimilar material bonding and alternative bonding methods must be applied.Generally,as Ji and Huang5introduced,the bimetallic bonding processes can be mainly divided into solid–solid bonding, solid–liquid bonding, and liquid–liquid bonding.Some typical solid–solid bonding processes are as follows: In explosive welding, the metallurgical bond can be generated with a wave interface.As Findik6introduced, sheets, pipes,tubes, and rods are common applications.In spin-bonding process, bimetallic tubes with ultra-fine grains can be obtained.7A similar phenomenon can also be found in the accumulative extrusion bonding process which was proposed by Standley and Knezevic.8Some complex geometry of parts can be produced by magnetic pulse welding because the size and shape are controlled by the coil or field shaper,as demonstrated by Kapil and Sharma.For solid–liquid bonding, Ji et al.9fabricated Cu/Al bimetallic pipes by the solid–liquid cast-rolling bonding process.The bonding shape of this process is usually simple and mainly determined by the roll pass design.As for liquid-phase bonding, the bond strength can be stronger than the explosive welding.Gre? et al.10adopted vertical continuous compound casting to produce Cu/Al bimetallic rods.But as Guo et al.11stated in the centrifugal casting process, the size of bimetallic products is limited by the molds.

Another division method stated by Chen et al.12is based on the different bonding materials.Thus, metal composites can also be divided into ferrous metal/ferrous metal (such as carbon steel/stainless steel),non-ferrous metal/ferrous metal(such as Mg/steel, Ti/steel), non-ferrous metal/non-ferrous metal(e.g.Al/Mg,Ti/Al,Cu/Al).As illustrated by Chen et al.,13division can also be according to functions as structural, thermal expansion management, thermomechanical control, electrical,magnetic, corrosion resistance, joining, and cosmetic applications.For example,carbon steel can be used as structural function material with a well-accepted economy, while stainless steel has excellent performance and high price.As investigated by Li et al.,14compared with traditional single stainless steel,the cost of carbon steel/stainless steel composite can be reduced by 42.5–54%.In addition,as stated by Li et al.,15precious alloy elements in stainless steel are also saved.Mg is the lightest available metal structural material with poor corrosion resistance and strength, while Al can overcome the disadvantages of Mg.Al/Mg/Al laminates show both advantages of Mg and Al.Thus, it can be applied in engine cylinder blocks and body sheets of new energy vehicles to reduce the weight and enhance buffering capacity.Huo et al.16proposed a hard plate rolling method to improve the bonding ability of Al/Mg/Al laminates.They found the interface layer thickness can be increased greatly which makes the laminates have more potential applications.Also, Danaie et al.17fabricated Mg/Ti and Mg/steel multilayer composites by accumulative roll bonding which can be used in hydrogen storage areas.Li et al.18produced Ti/steel bimetal plate by hot roll bonding which can be used for corrosion resistance.Ma et al.19thought the Ti/Al composites have great potential for industrial applications because of their high strength, corrosion resistance, and low density.Based on the effect of ‘‘complementing each other’s weakness”, metal composites can be widely applied in aerospace, nuclear power, shipbuilding, and military fields.

Currently, as overviewed by Jamaati and Toroghinejad,20roll bonding of metal composites can be mainly summarized as the bonding mechanism of different metals, the influence of different process parameters on the bonding quality, the microstructure evolution law of the substrate metal, and the properties of the interface.However, there are still only a few studies focusing on the bimetallic rod or tube bonding process.In addition, metal composites are formed by the longitudinal rolling process, while rods or tubes are formed by continuous rolling, skew rolling or pilger rolling processes.For metal composites rolling, the non-uniform deformation of heterogeneous metals is mainly reflected in the rolling direction, resulting in the inconsistent length of heterogeneous metal composites in the rolling direction.Different from metal composites rolling, the non-uniform deformation of tube or rod rolling is reflected in both axial and circumferential directions.The axial non-uniform deformation leads to length inconsistency, and the circumferential non-uniform deformation easily leads to the separation of heterogeneous metals at the roll gap, which affects the bonding effect.Moreover, the geometrical and mechanical properties of the circumferential and axial interface of the composite tube or rod are still not clear.In addition, the method of binding nodes or gluing the interface in the existing finite element model cannot truly characterize the roll bonding state,and a typical basic bonding criterion is the comparison of compressive stress in the contact surface and the material deformation resistance, as Tian and Huang21implemented in the simulation of bimetallic bushes roll bonding process and Gao et al.22demonstrated in the cladding rods rolling simulation.This kind of simple bonding criterion does however not consider other key parameters of bonding except the pressure.Moreover,research on the prediction model of the roll bonding process is still relatively sparse.

Therefore,this review first overviews some main solid–solid bonding,solid–liquid bonding,and liquid–liquid bonding processes.In addition, a thorough overview of the roll bonding processes for plates, rods and tubes is investigated; followed by the related bonding mechanisms and limitations of this process.Going a step further, the bonding models, bonding criteria in the joining processes and the limitations are highlighted.Finally,future development directions of the roll bonding process and bonding models are discussed in the future trends.

2.Brief overview of bonding methods

Previous reviews have divided and introduced the joining processes in detail.Mori et al.23mainly overviewed welding,riveting,and clinching,and some joining by forming processes and pointed out that plastic deformation in joining plays a more and more important role in high productivity, high dimensional accuracy, high strength, and low-cost solutions.Wohletz and Groche24presented the main mechanical bonding and metallurgical bonding processes.They regarded the accurate prediction of joint’s properties is impossible.There are still gaps between joining knowledge and industrial applications.Weber et al.25mainly overviewed some currently novel joining by forming processes,such as chip extrusion,incremental tube forming, and polymer injection forming.The division was based on geometries.In this chapter,some main processes of solid–solid bonding,solid–liquid bonding,and liquid–liquid bonding are overviewed.

2.1.Solid-solid bonding process

In the solid–solid bonding process, both metals are in solidstate.In general,the billets need to be assembled together first and then after several different hot/cold deformation processes to join them together.Based on Wohletz and Groche24′s division, the main solid-state bonding processes are clinching,welding(such as friction stir welding, impact welding process),forging, extrusion, hemming, hydroforming, riveting, rolling,spinning, swaging, and so on.However, in this section, only some typical solid–solid bonding processes with plastic deformation such as hydroforming, spin-bonding, extrusion bonding, impact welding are chosen to overview.

2.1.1.Hydroforming process

As stated by Yuan,26the hydroforming process is a kind of technology that uses a fluid medium to load and deform workpieces into complex shapes.For the hydroforming process,the complexity of the workpiece is determined by the shape of forming tools.For hydroforming of bimetal workpieces, two workpieces should be assembled first.After the workpieces are put into the forming tools,the cover layer is flooded.Next,axial and fluid pressure increases so that the cover layer can bond together with the parent workpiece.As Fig.1(a) shows,the special shape of a bi-layered tube(Alaswad et al.27)can be manufactured by hydroforming.In Fig.1(b), Weber et al.28extended the die-less hydroforming to join rectangular profiles.Hashemi et al.29produced bimetallic cup of Al1050/St 14 (see Fig.1(c)).But generally,the interface can only get mechanical bonding.

Based on the complex designed dies,the hydroforming process has the ability to create complex geometries with better surface quality and mechanical properties.As stated by Bell et al.,30the produced workpieces are closer to the final shape and rework is less required.However, one pair of dies for one type of product is the main limitation of this process which can induce high cost.In addition, strain hardening may cause less ductility and sharp radii are hard to obtain.

2.1.2.Spin-bonding process

Fig.1 Bimetallic hydroforming process.

Fig.2 Diagram of bimetal spin-bonding process.

The metal spinning process is a single-point high-pressure rotary forming process.31For both the conventional spinning and power spinning processes, the general application is to form the workpiece with a designed roller trace.32Mohebbi and Akbarzadeh7first proposed a novel spin-bonding process to manufacture bimetal tubes using the flow forming process.The mechanism of the spin-bonding process is shown in Fig.2(a).In order to get better bonding strength, Samandari et al.33eliminated the oxide film between the inner and outer tube interface by brushing before assembly and bonding.The bonding mechanism of the cold spin-bonding process is similar to that demonstrated in the cold welding process by Bay34(see Fig.2(b)).Furthermore,the hot spin-bonding process can also be used to manufacture bimetal tubes, as demonstrated in Xu et al.35′s work.The tensile shear test result shows that the interface bond strength exceeds the lower yield strength of the material36(see Fig.2(c)).Thus, for cold spin-bonding,mechanical bonding can be obtained on the interface.While for hot spin-bonding, the metallurgical bonding can be stronger than the weaker metal strength.

Spin-bonding has the advantages of low roller force, good dimensional accuracy, simple tooling and low cost, and high material utilization.The mechanical properties of the product can also be improved.However, the forming length is limited by the mandrel.Although Arai37produced spun parts with complex shapes by non-circular spinning, few reports have been found on non-circular spin-bonding process.Thus, current bonding geometry is limited to the circular shapes.

2.1.3.Extrusion bonding process

As Qamar et al.38stated,extrusion is a multi-faceted manufacturing process because of its versatility and net-shape ability.The metal flows in a closed space with high pressure,high friction, and other complex boundary conditions in the extrusion process.However, for the bimetal extrusion process, only when the two materials flow at the same velocity near the interface,can they bond together with compressive stress inside the tools, which has been demonstrated by Khosravifard and Ebrahimi.39

Currently, an accumulative extrusion bonding (AEB)method is adopted by Standley and Knezevic8to manufacture ultrafine microstructure multilayered bimetallic products because of the significantly improved strength, thermal stability, resistance to shock damage, and radiation damage (see Fig.3(a)).

Fan et al.40found that the traditional extrusion method cannot well remove the oxidation and impurities on the initial interface of the bimetal parts, thereby affecting its bonding performance.Based on this defect, some new methods are proposed such as the porthole die extrusion (PDE) process and semisolid extrusion bonding.For PDE bonding, as shown in Fig.3(b), two streams of fresh metal (without oxidation and impurities) are bonded together in the lower die with high temperature, high pressure, and almost vacuum atmosphere.

For the traditional solid–solid extrusion process, a large number of materials extrude through gaps among the cracked oxide layers to obtain metallurgical bonding.However, semisolid extrusion breaks the oxide film under temperature and pressure to achieve metallurgical bonding.The latter point verified by Zhao and Li41shows better tensile strength than solid–solid and solid–liquid extrusion bonding(see Fig.3(c)).

Extrusion bonding can form complex shapes with high dimensional accuracy.42Because of the high compressive stresses in the container and die,less ductile metals can be formed.However, short service life and high cost are the main limitations of extrusion tools.Unremoved oxidation and impurities on the interface may affect the bonding strength.

Fig.3 Novel extrusion bonding processes.

2.1.4.High velocity impact welding process

As stated by Wang HM and Wang YL,43the two typical characteristics of high-velocity impact welding are low bonding temperature and high bonding velocity.As a typical highvelocity impact welding process, explosive welding (EXW)has been widely used in the joining of tubes, bars, and plates(such as heat exchangers and pressure vessels, as shown in Crossland44′s work).In the First World War, people found that the fragments of shells can be bonded firmly with metal parts, while in the Second World War, many metal fragments were found on the armor of the tanks.The phenomenon of EXW was however not recognized until Carl45proposed this conception.As a kind of solid-state bonding process, EXW uses energy generated by explosives to impact the workpiece.Three critical conditions must exist for the welding to occur:jetting, sufficient impact pressure, and stand-off distance.The wave interface formation is a consequence of the Kelvin-Helmholtz mechanism.46The mechanism of EXW47is shown in Fig.4.

As stated by Findik,6high bond strength can be achieved because of the Kelvin-Helmholtz waves in explosive welding.However,because of the high-velocity impact effect,the metals must have enough thickness, impact resistance, and ductility.While complex geometries are hard to be welded together.Noise, pollution, and low production efficiency are the other drawbacks of this process.

Similar to explosive welding, magnetic pulse welding(MPW) is another kind of high-velocity impact welding process.The bonding in both processes is achieved by the jetting phenomenon.Different from explosives, the MPW is driven by electromagnetic forces, as stated by Kapil and Sharma.48The joining mechanism of MPW is shown in Fig.5(a).49As shown in Psyk et al.50′s work, in tube compression or tube bonding processes,a field shaper in Fig.5(a)is always adopted between the tool coil and workpiece to obtain higher current density and higher field strength.As demonstrated by Yan et al.,51for the field shaper with one slot, the defect occurs at the slot because of the different contact-free force in this area (see Fig.5(b)),52while multi-slot field shaper has better forming uniformity (see Fig.5(c)).51

Although MPW is also a kind of impact welding process,the driven force is contact-free.It can join not only metals but also members of glass and polymers.The bonding occurs without lubrication and heating.Meanwhile, a clean workpiece surface can be obtained.As studied by Psyk et al.,50springback is significantly reduced after MPW.However,MPW is only suitable for materials with high electrical conductivity and low flow stress.The bonding geometry and size are controlled by the coil or field shaper.Low energy efficiency and safety problems are the other drawbacks.

2.2.Solid-liquid bonding process

In the solid–liquid bonding process, one kind of metal is in solid-state,while another is in the liquid-state.Li et al.53fabricated Cu/Al composites by the solid–liquid compound casting(SLCC) method.They found that graded interfaces formed during the interdiffusion of Cu and Al.The reaction–diffusion of the interface is the dominant effect in SLCC (see Fig.6(a)).Huang et al.54found similar results when they adopted the solid–liquid cast-rolling bonding (SLCRB) process to produce Ti/Al strips(see Fig.6(b)).The solid–liquid or semisolid-liquid reaction can help get a better bonding effect.In addition,they fabricated Cu/Al bimetallic tubes with this SLCRB process(see Fig.6(c)).Compared with bimetallic strips produced by SLCRB,the deformation changes from 2D to 3D,the bonding mechanisms are also different.9During the SLCRB process,the metal state changes from solid-liquid, solid-semisolid to solid–solid, while the interface also goes through four stages:contact, cast-bonding, roll-bonding, and diffusion welding.

Fig.4 Mechanism of explosive welding with Kelvin-Helmholtz waves.47

Solid-liquid bonding processes have the advantage of sound bonding strength.But pores and cracks can always be found on the interface.53In addition, as stated by Zare et al.,55if the oxide layer of the solid part is not removed, only limited and local bonding can be obtained.

2.3.Liquid-liquid bonding process

In the liquid–liquid bonding process, both kinds of metals are in the liquid-state.In Fig.7(a), Wang et al.56produced Cu/Al bimetallic plates by horizontal continuous composite casting(HCCC) process.They found that inappropriate temperature causes the generation of intermetallic compounds on the interface which may cause crack during the following rolling process.While in Fig.7(b), Japanese company KUBOTA adopted multi-layer centrifugal casting to fabricate triplelayer composite roll to obtain better properties.57Guo et al.11introduced a centrifugal casting process to obtain composite billets, which has been adopted by Xinxing Ductile Iron Pipes Co.,Ltd.to produce various specifications of bimetallic tubes.But this technology may cause mixed melting, layering,nonuniform thickness, and other defects.

Strong metallurgical bonding can be generated during this process.But when two kinds of liquid metals combine together, mixed melting may occur.Different solidification temperatures can bring difficulties to the bonding quality.In addition, accurate dimensions and surface quality are hard to be controlled.In order to get the final product,the following processes such as cutting are needed.Thus,the recovery rate of the metal is not high.

2.4.Joining processes comparison

After the overview of different bonding processes.The comparison of the above-introduced bonding processes and roll bonding process together with their advantages, limitations and applications are summarized in Table 1.

3.Roll bonding process and bonding mechanisms

The roll bonding process is the most typical process of solid–solid bonding, which makes the two bimetallic plates break the oxide film on the contact surface of different metals under the high rolling pressure, and facilitates plastic flow in the whole contact surface.The fresh metal flows together through the surface crack and then produces a micro-scale atomic reaction.Finally, a certain strength of metallurgical bonding occurs at the contact interface between the metal layers to realize the welding effect.58According to the different bonding temperatures, it can be divided into cold roll bonding and hot roll bonding processes.In the cold roll bonding process,film theory is the main bonding mechanism.While in the hot roll bonding process,diffusion is the dominant bonding mechanism, intermetallic compounds layer may be generated.In this chapter, some main roll bonding processes and bonding mechanisms are overviewed.

Fig.5 Magnetic pulse welding of bimetallic tubes.

3.1.Roll bonding process

3.1.1.Roll bonding of bimetallic plates

Currently,the main focuses of the roll bonding process are on the composite plates.Thus,as stated by Yu et al.,59several different rolling processes have been developed, such as hot roll bonding,cold roll bonding,different temperature roll bonding,accumulative roll bonding, asymmetrical roll bonding,explosive-rolling, solid–liquid cast-rolling bonding, hot-pack rolling, brazing/hot-rolling, electrically-assisted roll bonding,electrochemical-assisted roll bonding, and some other processes.

Although the conventional roll bonding process can realize the metallurgical bonding of the composite plates,the interface line is linear,the carbide zone is generated on the stainless steel side,while the decarburized zone is formed on the carbon steel side.But the bond strength of the interface is still lower than those of the explosive welding process with wavy bonding interface (see Fig.8(a)–(c)).60,61In their work, before rolling,there is an obvious wavy interface, and the shear strength of the interface is the highest.After rolling, the thickness of the composite plates becomes thinner, the wavy interface changes to a less wavy type, and the shear strength of the interface decreases greatly.

Based on this defect, as shown in Fig.8(d), Huang et al.62proposed a corrugated flat rolling (CFR) process to obtain a corrugation bonding interface similar to explosive welding,which greatly improved the interfacial shear strength of composite plates.The schematic of CFR is shown in Fig.9, in the CFR process, there are more than two cross shear zones(depending on the roll profile).While only one cross shear zone in the general flat rolling process.Thus, CFR can increase the friction stress and the cross shear zones greatly.63In their another work64of Mg/Al composites manufactured by CFR,the micro bonding mechanism of CFR is illustrated.During corrugated rolling, the larger strain at the trough position will accelerate the breaking of the oxide film and work hardening layer on the interface, and realize metallurgical bonding.During flat rolling, the compounds at the wave peak and wave trough break, and the virgin metal is squeezed into the interface, which improves the interface bonding area.In addition,Wang et al.65adopted CFR to fabricate Cu/Al composites and found that under the same conditions (40% reduction),the shear strength of flat rolling is about 20 MPa, the shear strength of CFR is up to 70 MPa.Similar results also verified in work.66

Fig.6 Solid-liquid bonding processes.

3.1.2.Roll bonding of bimetallic rods/tubes

Unlike in the bimetallic plates, the thickness and deformation along the circumferential direction of the rods are not uniform under the roll bonding process, and the bonding interface is wavy and curved.Among all the bimetallic rods/tubes,carbon steel/stainless steel rods/tubes are commonly used in many fields such as oil gas pipeline, first loop pipe of the nuclear power plant, etc.For this kind of bonding, both Liu et al.67and Mujtaba et al.68found duplex structures (mainly martensite and ferrite) at the transition zone in the vicinity of the stainless steel.As can be seen in Fig.10(a) and (b), the interface microhardness shows a gradient distribution.The microstructure evolution in the vicinity of the bonding interface can be predicted through the Schaeffler diagram in Fig.10(c).

The continual mandrel rolling process is mainly used for continuous rolling, tube sizing and clad rods bonding.It is suitable for the roll bonding of soft materials such as copper,and aluminum, but it is difficult to ensure the roll bonding effect of hard materials such as stainless steel.For example,Cacace69proposed a method of rolling a heated hollow tube filled with the carbon steel swarf.Based on this method,NXInfrastructure Limited and Stelax Industries Ltd.can produce the clad rebars.However,as mentioned by Xiang et al.,70this method has the following defects: (i) there are cracks on the bonding interface, and the rib height is low which shows poor joining capacity with concrete (see Fig.11(a)); (ii) the thickness of the stainless steel layer is nonuniform (see Fig.11(b));(iii)the production process is complex and the cost is high (the product price can be 70–75% of the pure stainless steel rebars).

Fig.7 Liquid-liquid bonding processes.

Based on the defects of Fig.11,Wu et al.75adopted vacuum treatment and plasma welding to obtain the 316/HRB400 bimetallic billets and rolled through 18 passes.The yield strength of the produced bimetallic rebars can reach 470 MPa, the tensile strength is about 600 MPa and the elongation is larger than 25%,which shows better bonding properties than the previously produced rebars.

Except for the continuous rolling process, the skew rolling process can also be applied in the bonding process.The cold skew rolling process has the characteristics of large deformation, short process route, high efficiency, and low energy consumption.It has been proved that the small-diameter and thinwalled bimetallic tubes can be bonded successfully.However,in the cold rolling process,it is difficult to activate the interface atoms to achieve atomic diffusion and metallurgical bonding.As a result, Qin et al.76found that the metallic tube can only realize mechanical bonding, and the application place is greatly limited.

Given the shortcomings of the cold skew rolling process,the pilger hot rolling process came into being.However, He et al.77found that due to the periodic movement in a pilger rolling mill, the work hardening of stainless steel in the forming process is larger than that of carbon steel,and the deformation is more difficult, which leads to the more inconsistent thickness of inner and outer tube, and it is difficult to ensure the forming accuracy.The process of hot three skew rolling of a carbon steel/stainless steel rod can facilitate metallurgical bonding.78As introduced by Wang et al.,79the hot skew rolling process has the advantages of large deformation and high efficiency and avoids the technical shortcomings of the mechanical bonding in cold forming processes.However,Yamane et al.80found that internal fractures easily occurred during the skew rolling process because the tensile and shear stresses can induce voids to nucleate, grow and coalesce to macro fracture.

In addition, for the skew roll bonding process of different tubes or rods, the uncoordinated deformation in both axial and circumferential directions is obvious.The deformation can be divided into three stages (see Fig.12): (i) in the initial bite zone, only the diameters of the outer and inner tube are reduced; (ii) the diameter and wall thickness of the outer tube is reduced,while only the diameter of the inner tube is reduced;(iii) both the diameter and wall thickness of inner and outer tubes are reduced.As analyzed by Teterin,81in the axial direction, the uncoordinated deformation will cause the different elongation of the metal tubes or rods,while in the circumferen-tial direction,the triangle effect will occur,which will cause the gap between the inner and outer tubes at the triangle roll gap area under the effect of three-dimensional compressive stresses.Recent studies on different applications of bimetallic rods/tubes rolling methods are listed in Table 2.82–86

Table 1 Joining processes comparison.

Table 1 (continued)

Fig.8 Interface comparison of different processes.

Except for the above roll processes,the authors proposed a novel tube roll bonding process called ‘‘three-skew corrugated flat stagger rolling”(TSCFSR)(see Fig.13(a)).In this process,three rolls rotate in the same direction and drive the heated bimetal tube with a mandrel inside to rotate and feed.The two tubes are ends welded together.Among them,the corrugations of the three corrugated rolls are arranged in the wall thickness reducing section (Fig.13(b)).The stagger distance between corrugations is the same as the axial feeding distance of the tube, and the corrugation area can gradually increase along the rolling direction.The relationship between stagger distance and increasing corrugations are shown in Fig.13(c).Under the action of the thickness reducing section of the rolls,the bimetallic tube changes its diameter and wall thickness.Three kinds of increasing corrugations that are gradually deeper and wider are rolled on the surface of the outer tube, and the three kinds of corrugations are located on the same spiral line(see Fig.13(d)).Meanwhile,the corrugations are transmitted to the inner tube through the flattening section of the rolls.Corrugation occurs at the interface and the corrugations at the outer surface of the outer tube are flattened (see Fig.13(e)).

Fig.9 Schematic of CFR process and cross shear zone.63

Fig.10 Interface hardness and microstructure evolution.67

Fig.11 Section of stainless steel/carbon steel clad rebar.70

The advantages of the proposed three-skew corrugated flat stagger rolling process are as follows:

Fig.12 Axial and circumferential deformation of bimetallic tube.

(i) As a local loading and axial continuous forming process,skew rolling has the advantages of low rolling force,high production efficiency and energy saving.The production and manufacturing costs are significantly reduced.

(ii) Axial forming solves the difficulty that the size of bimetallic tube is constrained by the size of die and equipment in the traditional joining process.The rolled part is placed outside the equipment,which significantly saves the rolling space of the equipment,and reduces the size of the equipment body.

(iii) By setting corrugations in the thickness reducing section of the roll,the skew rolling process can realize the multipass rolling process in a single stand.The corrugation bonding interface can greatly improve the bonding strength.

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(iv) The corrugations at the outer surface of the bimetallic tube can be realized by arranging the increasing corrugations on the three rolls at a stagger distance.Finally, a single spiral corrugation bonding interface between the inner and outer tube is formed.The increasing corrugations can share the deformation and improve the biting quality, which not only avoids the biting difficulty and rolling seizing caused by too high corrugations,but also prevents the indentation caused by too low corrugation is too shallow,which affects the forming effect of corrugation bonding interface and significantly improves the bonding effect.

Fig.14(a)shows the whole process of TSCFSR.During the rolling process, corrugations first appeared on the outer surface of both outer and inner tube.After the flattening section,the outer surface of the outer tube changes to flat and the bonding interface is still corrugated shape.Fig.14(b) shows the 3D view of the corrugation interface.From the effective strain distribution of the inner tube’s outer surface, we can see, there is a threaded corrugation interface in the bimetallic tube.For the hot roll bonding process, this type of bonding interface can not only generate metallurgical bonding but also mechanical interlocking,which can increase both axial and circumferential bonding strength.However,if the corrugation on the roll is designed unreasonable,several defects such as corrugation on the outer surface cannot be flattened or corrugation malalignment may occur (see Fig.14(c)).Thus, the design criteria of corrugated roll and the TSCFSR process still need further studies.

3.2.Bonding mechanism

Li et al.87concluded the bonding mechanism as the film theory, energy barrier theory, diffusion bonding theory, and recrystallization theory.As stated by Mohamed and Washburn,88the film theory proposes that bonding will be created if two clean metal surfaces are in close contact.In the energy barrier theory,besides the contact of two clean metal surfaces,bonding can only occur when the existing energy barrier hasbeen overcome.This energy barrier was considered as recrystallization or diffusion, while Semenov89pointed out that the energy comes from the misorientation of the crystals at the interface.The reason is that metal can be bonded together at liquid nitrogen temperature where diffusion or recrystallization could not occur.Thus, diffusion or recrystallization can be considered as the energy to motivate the bonding.In this respect, the diffusion bonding theory and the recrystallization theory are parts of the energy barrier theory.

Table 2 Different rolling methods and treatment of bimetallic billets.

3.2.1.Cold bonding mechanism

Similar to the cold welding process,the mechanism of the cold roll bonding process can be well described by the ‘‘film theory”.In general, virgin metal is covered by a thin oxide layer and other contaminants, which will prevent metallic bonding.Compared with the metal substrate, the oxide layer is brittle.This cover layer may crack easily when the interface expands under pressure.As shown in Fig.15, when the composite plates contact with rolls,the oxide film breaks as the substrate metal stretches along the rolling direction.The virgin metal can extrude together in the oxide film crack channels within atomic distances.Thus,metallurgical bonding is established.90According to this mechanism,increasing cracked contact interface can increase bonding area.Processes such as CFR or asymmetric rolling can increase the shear deformation of the contact surface, help to break the surface oxide film and promote the exposure of fresh metal compared with flat roll bonding process.To enhance the bonding quality, as stated by Jamaati and Toroghinejad20in the solid-phase bonding process,the reduction,the type of bond materials(different material combinations were implemented in Bay et al.91′s work of cold welding process), surface roughness (Zhang et al.92studied the surface roughness effect in the hot isostatic pressing process of 304/Q235), pre-rolling and post-rolling annealing treatment, initial thickness, rolling speed, rolling direction,friction as well as particles should be considered carefully.

3.2.2.Hot bonding mechanism

For hot bonding,the bonding mechanism of the same and different materials are different.For bonding the same materials,the initial bond interface can be eliminated under the required temperature, contact time, pressure, and deformation.As Huang et al.93,94investigated, for a superplastic alloy, grain growth was the main reason to remove the initial bond interface;while for a hot-rolled alloy,the reason changed to recrystallization, Wang et al.95also demonstrated this view.Zhang et al.96found that at the initial bonding stage, heterogeneous strain inside the interfacial grains appeared because of the small plastic deformation.Hence, more and more different density dislocations in the vicinity of the interface appear in the deformed grains (see Fig.16(a)).With the continuous increase of the strain, bulging in the interfacial grain boundaries (IGB) occurs because the dislocation accumulation reaches a certain threshold (an energy barrier) (see Fig.16(b)).The driving force of under-developed dislocation accumulation cannot induce bulging or recrystallization at a low level of strain.This phenomenon is considered strain-induced grain boundary migration (SIBM).Generally, with the increasing strain, the stored energy of dislocations is also increasing,which causes the increasing stored energy difference.This can decrease the critical radius of the nucleus.The nucleus can be formed when this radius is smaller than the cells, as shown in Fig.16(c), because the cell may bulge into the near grains.Fig.16(d)–(f) show the bonding interface microstructures of the IN718 based on the above mechanism.With the increasing bulging and DRXed grains, the initial bonding line disappears (see Fig.16(g)), which results in higher bond strength.The two different mechanisms are shown in Fig.16(h)–(k).

The above mechanism has also been verified by Xu et al.97in their work on 2196 Al-Cu-Li alloy hot compression.However,Gao et al.98found that increasing temperature and reducing bonding strain rate can improve the bond strength of HCCI/LCS prepared by the hot compressive bonding process.The strain rate law for dissimilar materials is different from Zhou et al.99′s work of 14Cr ferrite steel.

Fig.13 Forming mechanism of three-skew corrugated flat stagger rolling.

For bonding of different materials, which are commonly adopted in the roll bonding process, the bonding mechanisms of different metals are quite different.For some metal combinations such as Ti/steel and steel/Cu, the bonding is hard to obtain.The following example shows the basic diffusion mechanism of the carbon steel/stainless steel in the hot roll bonding process:

When the oxide film on both sides of the interface is deformed and broken, the substrate metal diffuses to expose the atoms on the interface, and when the gap of the metallic plate is close to the atomic radius scale under the rolling force,C has larger mobility because the atomic radius of C(0.077 nm)is far smaller than other elements.C migrates from the carbon steel side to the interface and accumulates around the interface, forming a carbon layer, Cr, Ni, and other elements also migrate to various degrees from the stainless steel side to the interface and carbon steel side, which leads to the gradual disappearance of the original contact interface and the formation of the interface with gradient distribution of elements, similar results can be found in Xie et al.100and Dhib et al.101′s work.

However,hot rolling will inevitably leave oxygen atoms on the contact surface of the prefabricated composite plate, and then generate dispersed fine oxides on the contact surface during the heating process of the composite plate.102According to the WDS analysis,Feng et al.103showed that the oxides at the interface are Si-Mn composite oxide, MnCr2O4oxide, and MnS inclusion (see Fig.17(a)).They claimed that large deformation causes large fragmentation of interface inclusions,which is easier for the bonding.In addition, decarburization and diffusion of C elements on the carbon steel side may cause defects in the decarburized zone and reduce the strength of the composite plate, as demonstrated in Tomczak et al.104′s work of skew rolling.However, due to the Schaeffler diagram in Fig.10(c), Wang et al.105found that the martensite layer may be generated under a low rolling reduction ratio, which can cause interface delamination(see Fig.17(b)).With increasing rolling reduction ratio and over the diffusion of Cr, the thickness of the martensite layer decreased and finally disappeared (see Fig.17(c)–(d)).

Fig.14 Simulation of TSCFSR process.

Fig.15 Schematic illustration of oxide film and roll bonding process.90

As opposed to the cold roll bonding process, Mittelman et al.106enhanced that the dominant mechanism in the hot roll bonding process is solid-state diffusion.Diffusion leads to the mixing of atoms or molecules because of the Brownian motion.Studies have been done on the parameters that may affect the diffusion:

Hosseini et al.107adopted the roll bonded Cu/Cu strips to study the effect of thickness reduction, rolling temperature,and scratch brushed layer on the bond strength.Apart from the above parameters,Jamaati and Toroghinejad108also studied the effect of pre-rolling annealing, post-rolling annealing,rolling speed, and rolling direction on the bond strength of Al/Al strips.Sheng et al.109studied deeply the heat treatment of Cu/Al composites and found that low-temperature heat treatment can improve the bond strength.Different from the bimetallic plates, Manesh and Shahabi110studied a sandwich structure of Al/St/Al strips.They discussed the effect of internal layer thickness,yield strength,and the friction between roll and strips.

In addition, another interesting phenomenon is about the relationship between diffusion layer and bond strength.The bond strength increasing with the thicker diffusion layer first.But with the increasing interface thickness, the ductile diffusion layer transferred into brittle diffusion layer with massive pores, which will cause a huge decreasing of bond strength.

Fig.16 Mechanism of solid-state plastic deformation bonding process.96

Fig.17 Schematic diagram of bonding interface formation process of carbon steel/stainless steel plate.105

Thus, the temperature, bonding pressure, time of contact,forming velocity,annealing treatment,and initial surface quality are the key parameters that control the diffusion, which also determine the bond strength.As mentioned above, some of the parameters (e.g.temperature, pressure, and time) are also the key factors to overcome the energy barrier.Thus,one type of energy can be replaced by another89(e.g.if the temperature is higher, pressure and deformation can be smaller).To obtain a sound bonding quality in hot bonding process, not only the above parameters but also the composition of the interface layer should be considered.

Fig.18 Cryogenic bonding mechanism of Al/Ti/Al laminate plate.111

3.2.3.Cryogenic bonding mechanism

Only a few works focus on the cryogenic rolling bonding process.The bond mechanism has not been fully revealed.In Yu et al.111′s work,the bonding mechanism of Al/Ti at room temperature (RT) and cryogenic temperature are compared (see Fig.18).Soft layer (Al in this work) interfacial grain refinement is more easily to occur at cryogenic temperature because the temperature limits the dynamic recovery behavior(RT:186.3 nm/cryogenic:47.8 nm).With increasing pressure and thickness reduction, the grains grow to ultrafine grain,and nano grain and the soft layer bonded with the hard layer(RT:398.7 nm/cryogenic:386.8 nm).

3.2.4.Atomic level bonding mechanism

Extensive investigations have been done on micro-level bonding mechanisms, but the atomic-level bonding phenomena remains unclear.Czelej and Kurzyd?owski112proposed that brittle intermetallic phases at the interface region may promote failure and induce poor interface quality under low strain levels.To eliminate the inclusion on the interface, Hoppe et al.113promoted the interface cohesion of Cu and Al-based on ultra-thin mercapto-propyl (trimethoxy) silane film.The film helps to form stable Cu-S and Si-O-Al interfacial bonds at the atomic scale.

To understand the micro bonding mechanism,Peter et al.114investigated the steel/Al cold extrusion process at the atomic level,the process is shown in Fig.19(a).Micro asperities get in contact first under the pressure(see Fig.19(b)).With the increasing pressure, the oxide film cracked into brittles where virgin metals extruded into the gaps,as illustrated in Section 3.1.Zone 1 and 2 in Fig.19(c)are the oxygen-free and oxygen-rich zones.Fe ions are reduced to elemental Fe at the expense of the more reactive metallic Al.Meanwhile,oxygen ions play a charge carrier role in this process.In zone 1, elemental Fe and Al can obtain a closer bond by sharing their electrons under the oxygen-free and high-pressure conditions (see Fig.19(d)).The above phenomenon described the Bay theory at the atomic level.

In addition, Czelej and Kurzyd?owski112found the interfacial bonds formation and their impact on the bond strength based on the density functional theory.A thorough survey on the atomic level bonding mechanism can show the effect of alloying elements on the bond strength clearly (e.g.effects of residual stress,oxidation,and interface structure115).It also helps to provide suggestions on the selection of constituent alloys.

Fig.19 Schematic of the atomic level bonding mechanism.114

Fig.20 Bond formation at the atomistic scale.116

According to Fig.20 from Rezaei et al.116′work,as soon as the atomistic distance between the two neighboring aluminum grains is smaller than a certain value, new bonds will form.This critical distance can be related to the cut-off distance in the atomistic simulation which is a basic material property.Note that in the loading part, a crack is created at the grain boundary and all the bonds are fully damaged.Upon unloading, freshly created bonding is observed.

4.Modeling of bonding in joining process

4.1.Contact algorithm method

4.1.1.Zhang-Bay model

As earlier proposed in the extrusion process by Akeret,117the bonding occurs when the normal contact stress is larger than a certain limit.Later, Bay34defined the surface expansion Y in the cold welding process.In the rolling process, they also proposed that the surface expansion equals the thickness reduction r (see Eq.(1)).Only when a threshold Y is reached, the bonding occurs.Therefore, one can write:

Fig.21 Bond strength of different metal combinations in rolling as a function of surface expansion.91

where A0denotes the initial area of the surface and A1represents the final area of the surface.In addition,the local surface expansion in the roll gap is estimated by Bay et al.91:

Here h0is the initial and h1is the rolled thickness, R denotes the roll radius, while φ means the angular position in the roll gap.The surface expansion threshold and the relationship between surface expansion and bond strength of different metal combinations are given in Fig.21.Thus, surface expansion can be an index to reflect the bond status.Bonding can only occur when the surface expansion exceeds the threshold.

In fact, the surface status is more complex than they imagined.Based on their other work,118two cases of the true surface exposure are discussed because of the different types of surface film:(i)cover layer and(ii)contaminant films.For case(i):

where, ACdenotes the area remaining with the cover layer.

For case (ii) we have:

where A′means the threshold surface area to expose virgin surface.

Based on the investigation of Conrad and Rice,119the bond strength on the clean interface is approximately equal to the applied pressure.However, in the real roll bonding process,both types of surface film exist.Thus, the bond strength can be described as:

According to Bay34′s work, the fraction β0weighting the two mechanisms can be obtained by micro-observation.While pBdenotes the normal pressure, and pErepresents the extrusion pressure.However, as mentioned by Bambach et al.,120there is no true internal variable in Eq.(5) that can reflect the interface status.According to the balance of energy dissipation, pEincludes the following three terms:

Fig.22 Deformation zone of extrusion through cracks in interface layer.121

where piis the internal power dissipation in the deformation zone,pfdenotes the frictional power dissipation along the dead zone, and prrepresents the redundant power dissipation (see Fig.22).121The detailed parameters of Eq.(7) can be found in the model of Zhang and Bay.118

To estimate the bond strength in Eq.(5), two maximum limits must be applied, as discussed by Bay et al.91:

Here, σ0is the yield stress of the deformed material.First of Eq.(8)represents a condition that the maximum bond strength equals the yield strength of the bonding occurring in the cracks.Second of Eq.(8) shows that the maximum bond strength equals the yield stress of the weaker material.

In fact,σBshows the bond strength in the normal direction of the interface.The bond strength in tangential direction can be described as:

where C, B and n are material parameters of Swift hardening law.122

4.1.2.Cooper and Allwood model

In the general rolling process,perpendicular compressive strain is the reason for surface expansion.The film theory does not consider the shear effect.But for some special rolling processes(e.g.asynchronous rolling), the cross-shear zone appears because of the shear stress.The above model cannot well reflect the bonding in the situation with shear effect, temperature, and strain rate.Thus, Cooper and Allwood123derived a model considering key parameters (e.g.normal contact stress, temperature, strain rate,strain) of bonding to predict bond shear strength:

Here σFis the flow stress,τappmeans the nominal shear stress,v denotes the fraction of the final contact area that is exposed fresh metal without the oxide film and pBis normal contact stress as mentioned before, while pEXis the pressure that can extrude the substrate metal through the cracks(a typical value for aluminium is 95 MPa).Kolpak et al.124divided this model into three terms: (i) the first term considering the true contact micro-surface which is affected by normal pressure pBand nominal shear stress τapp; (ii) The second term (with variable v,a typical value is 0.3)contains the strain threshold to initiate crack of the oxide film;(iii)The third term determines the necessary pressure to start micro extrusion of fresh metal into x(see Fig.22).To verify this model, they designed a special device on the tensile test machine (see Fig.23(a)) to stretch two adjacent aluminium strips with crosshead 7 and simultaneously press in the horizontal direction with ceramic plates 6.The proposed Equation can predict the trends correctly, but for higher temperatures(see 473 Kelvin in Fig.23(b))it underestimates the bond strengths because the diffusion mechanism is not considered.

Based on Cooper’s model,to describe the less adverse effect of the oxides,Wang et al.95adopted a strain-amplifying factor in the Equation:

Here, Cm-mshows the material contact condition with the oxide fractures, the term e0/(e0+λl) represents the dispersion of the oxide fragments.The variable e0is the gap between brittle oxides while λldenotes the length of fragments (assumed as constant).The authors adopted three contact pairs in the model, which are oxide-oxide, oxide-metal, and metal–metal.The proposed model can predict the total bond ratio of above three contact pairs in a hot compressive bonding experiment.However, the experiments were only verified in the same material (Inconel 718) and the shear strain was not considered in this process.

4.1.3.Bambach et al.’model

To implement the bond strength model in a finite element model, Bambach et al.120adopted the normal bond strength model of Zhang and Bay118and also extended the tangential bond strength model in the ABAQUS UINTER subroutine.125They first modeled the normal contact with a gap function h.To avoid the penetration, the Karush-Kuhn-Tucker (KKT)conditions must be applied.

A linear pressure-gap relationship is used in Bambach et al.120′s model where kpis the stiffness parameter and h denotes the gap distance:

In general,the bond strength σBrepresents a uniaxial stress condition, but for multi-axial stresses or 3D conditions, the bond strength σBis compared with the von Mises stress when the contact surface is in tensile state.

For the tangential component, the critical tangential stress τcritand the equivalent frictional stress τeqcan be determined via:

where τi(i=1, 2) is the interface shear stress components,μ denotes the friction coefficient and τmaxrepresents the shear flow stress of the weaker metal.

The tangential displacements can be divided into two cases(as shown in Eq.(15)): (i) when τeq<τcrit, no slip occurs, the whole increment is elastic (ii) when τeq=τcrit, slip occurs, the additional new slip increments Δγislis needed.The relationship of the tangential displacements is shown in Fig.24(a)–(b).Once the two substrates can slip relative to each other,the classical Coulomb friction model can be adopted.When the shear stress is larger than the shear bond strength, as shown in Fig.24(c), the debonding occurs.

Fig.23 Solid-state aluminium bonding process.123

Fig.24 Constitutive relations.120

where i=1,2.Based on Eqs.(13)and(16),the interface stiffness matrix can be obtained.The Eq.(17) is necessary for the UINTER subroutine:

4.1.4.Hot bonding empirical model

However, diffusion effect and multi-pass roll bonding process are not considered in the above models.In addition, for the rotary part roll bonding process (such as rings, tubes and rods), attention should be paid on whether a previously bonded area ruptures under the axial and circumferential non-uniform deformation conditions.Thus,Mikloweit et al.126and Guenther et al.127adopted plastometer and specially designed samples to determine the bond strength with an empirical model (see Fig.25(a)–(d)) in the hot joining-byforming processes.Although many key factors may affect the bond strength in the hot bonding process, the empirical model in Fig.25(b) simplifies the complex coupling relationship into a linear relationship between surface expansion and bond strength (For stronger slope in this model, the turning point bond strength is 45 MPa).

Fig.25 Hot bonding empirical model and application in ring rolling process.

4.1.5.Bonding model applications

Bambach et al.120,128only verified the bond criterion in 2D implicit models.Thus, Pietryga et al.129modified this model to describe the bond formation and failure.Due to the above model not taking the temperature influence into account, Liu et al.130proposed a FE framework to simulate the 2D hot roll bonding process.They coupled UINTER and UHARD in the FE model and obtained both bond strength and interface temperature distributions (see Fig.26(a)–(b)).

Based on the Zhang-Bay model, Rahmati and Jodoin131adopted a VUINTER subroutine in ABAQUS/Explicit to predict the bonded area of the particles in the cold spray process.The authors developed a python script to extract the bond status (which is defined as a state variable in VUINTER) of the contact surface nodes from VUINTER and present it in the postprocessing result.Furthermore, Rahmati et al.132predicted the superficial oxide layer removal and the position of localized metallic bonding in the cold spray process with coupled VUINTERACTION and VUSLFD subroutine, the simulation and experimental results can be seen in Fig.27.

As concluded by Guenther et al.86in ABAQUS,for implicit UINTER, the subroutine is called for every node of the contacting surfaces separately, while for explicit VUINTER, the subroutine is only called once per increment.In addition, the stiffness matrix is not necessary for the VUINTER subroutine.They did the same calculation as Eq.(17)to obtain the normal and tangential stresses in the composite ring rolling process.Based on Bambach et al.’s model, Guenther et al.86changed the simulation from implicit to explicit as well as 2D–3D (see Fig.25(c)).If a strong bonding slope is adopted in the simulation, no debonding occurs during the ring rolling process.When the weak bonding slope is used,the established bonding cracks during the process (see Fig.25(d)).

Fig.26 Coupled thermal-stress FE model.130

Fig.27 Experimental and numerical bond status in cold spray process.131,132

In conclude, Zhang-Bay model is suitable for normal pressure dominated joining process.When considering the shear effect, Cooper, Bambach’s model will predict the bond strength more accurate.However, above models cannot predict the bond strength well in diffusion effect dominated joining process.Guenther et al.86provided a potential solution with empirical model, but it is not a general model (for different bonding metals, parameter calibration with plastometer is needed).

4.2.Bonding criteria and applications

Except for the above theories,some researchers adopted other criteria to predict the bonding.Zhang et al.133proposed a bond criterion for the hot roll bonding process:

where εtdenotes a threshold strain, σformedmeans the bond strength formed in the bonded interface forming period, and σris a critical bonding strength to avoid the interface ruptures in hot rolling.The proposed bond criterion does not consider the diffusion effect and key parameters such as temperature and the surface condition.Rezaii et al.134based on their work of the equal velocities of the different steel/Al composites to predict the bonding start point in ABAQUS with UVARM subroutine.Mittelman et al.106demonstrated that 2D FEM cannot describe the interface conditions compared with 3D FEM analysis.They also adopted a Q criterion proposed by Plata and Piwnik,135which is based on the energy barrier theory:

where P represents the welding pressure, σmisesis the Von mises effective stress of the material.The authors also claimed that the governing Equations of the roll bonding process can only be solved by numerical methods because of the strongly coupled mechanical-thermal fields.Based on this criterion, Ceretti et al.136determined the threshold value via the interpolated method in hot roll bonding experiments of AA6061 plates and predicted the bonding phenomena in the PDE process (see Fig.28(a)).To describe the diffusion effect on the void closure, Yu et al.137introduced a diffusion integration and proposed a J criterion in the PDE process as follows:

Here ksdenotes a coefficient related to material and the surface conditions of metal for bonding, σmshows the mean normal stress, ˙ε- is the effective strain rate, Rgrepresents the universal gas constant,T is the absolute temperature,and QDis the diffusion activation energy.The schematic diagram of the PDE process is shown in Fig.3(b).The prediction of the bonding status of five points and the critical line can be seen in Fig.28(b).

The above bonding criteria although can be used in both cold and hot bonding processes, only bond status (bonded and debonded) can be obtained.The bond strength of the bonding zone is hard to be predicted.In addition, the shear effect is not considered in these criteria.Thus, for processes with large interfacial shear stress or bonding of different yield stress metals, these criteria may not be suitable.

4.3.Cohesive zone model method

4.3.1.Bonding interface element model

In addition to the above-mentioned models which utilize the contact method to implement the roll bonding process, some researchers make use of a layer of interface elements between the two contact surfaces to describe the bonding and debonding process.This specific interface element is also known as the cohesive zone element.

Generally, as stated by Alfano and Crisfield,138CZM is applied to describe the nonlinear fracture process in engineering materials, while Park and Paulino139divided them into nonpotential-based and potential-based models.However,the focus of this paper is not on the traditional fracture behavior of the CZM, but on the modified CZM that considers the bonding process.

Fig.28 Application of Q criterion and J criterion.

Kebriaei et al.140developed a zero-thickness cohesive zone element which makes it possible to describe bonding and debonding behavior within the traction-separation law of Needleman.141The normal and tangential tractions σtnand σtτused in their model are:

Here δnand δτare the relative opening displacement, δn0and δτ0denote material parameters and w1, w2, w3and w4are the weighting parameters determined by experimental tests(w1=0.31, w2=0.69, w3=0.12 and w4=0.88 are adopted in their work of welding AA5754/AA1050).The index tmaxrepresents the maximum normal or tangential traction reached under loading.The tangential vector considering interface friction is computed based on Wriggers et al.142and Buczkowski and Kleiber.143

Then,Rezaei et al.116,144deduced the detail stiffness matrix Cmatrixfor the zero-thickness, two-dimensional cohesive zone element based on the positive and negative normal gap:

Here, gnand gsare the normal and tangential components of the gap vector along the interface (see Fig.29),145k0is the interface stiffness, the parameter β is a scalar that controls the contribution of the shear components in the traction vector(the presented Eq.(22) is slightly improved compared to the one in Rezaei et al.’s work.144For the details of the derivation see Appendix A).The relationship for the evolution of the damage parameter d is shown below:

where the effective separation λ considering the Macaulay brackets 〈?〉= （?+?）/2 is written as follows:

In addition,based on Khaledi et al.’s work,90they extended four cases of the stiffness matrix including initially separated,contact,bonding formed,and separation.They utilized a finite element analysis program (FEAP) to implement the model of the roll bonding process (see Eq.(25)):

Fig.29 Relationship between gap vector, traction vector and parameter β.145

Parameters in Eq.(25) have been explained in the above equations.

4.3.2.Cohesive zone model applications

Fig.30 Peel test and simulation showing debonding behavior of rolled structures.140

Fig.31 Interface traction-separation relation during roll bonding and debonding process.90,146

Fig.32 Metal flow direction of oxide-substrate interface under extrusion and bonded metal–metal substrates.145

Compared to the contact algorithm method,the cohesive zone model method has the advantage to present the debonding behavior.Based on the damage evolution relationship and the predicted bond strength, the debonding model matches the peel test very well in Kebriaei et al.’s work140(see Fig.30).Thus, the roll bonding process and the peel test can be described in Fig.31.146O-A is the initial stage 1 without contact,the normal gap reduces but the normal traction is still kept zero; in stage 2 (A–B), where contact occurs, the contact pressure is increasing to the peak value(bonding occurs in this stage).Compared to stage 1,bond strength keeps constant and the crack density is also high.90New cracks of the surface make more fresh metal extruded together to get the bonding;in stage 3 (B–A), the bimetal plates leave the roll bite zone which causes the contact pressure to reduce to zero; in stage 4 (A–C), peel test begins and the normal traction increases with the increasing gap (the threshold is the maximum bond strength); in stage 5 (C–D), damage evolution in Eq.(23) is intervened and the traction decreases; finally in stage 6 (D–E), the bimetal plates debonded.

Khaledi et al.145established the metallic bonding process at the microscale (see Fig.32).To describe the metal flow phenomenon at the contact interface, the authors established the model of oxide-oxide and substrate-oxide behavior during compression and separation processes.Only similar metals were verified in the simulation.

Fig.33 Roll bonding simulation with different materials.

Based on Eq.(25), the metal roll bonding process can be divided into three cases: (i) substrate 1 and substrate 2 are of the same material with equal yield stresses and elongations,as shown in Fig.33(a).Thus, the shape of the metal composite is straight and the flatness is good;(ii)substrate 1 and substrate 2 are similar materials with different yield stresses and elongations.In this case,the upper and lower rolls contact with different materials which causes different friction along upper and lower surfaces.Furthermore,due to the different temperatures of the two surfaces,warping may occur during the roll bonding process as verified by Yoshii et al.147The metal composite in Fig.33(b) is produced by continuous clad casting, while the warping is obvious in both simulation and experiment;148,149iii) when the yield stress and elongation of the two materials are significantly different (see Fig.33(c)), the interface elements such as CZM is not suitable for the roll bonding process anymore because of the heavy deformation.

As case iii illustrated,when the shear stress is too large to be neglected, the contribution of shear stress to the bonding cannot be well described by current models.Based on these shortcomings,Rezaei et al.116proposed a nonlocal method to model the interface.They introduced a new quantity measure called‘‘traction density”to capture the complex behavior of the interface (see Fig.34(a)).In this modeling approach, the traction vector for the CZM is obtained by integrating the traction density vector over a nonlocal region which constantly can be updated to capture the active contact or bonding area (see Fig.34(b)).Certainly, the computational effort, in this case,can get higher but it is shown that much interesting physics of the interface and bonding nature can be reproduced by using this methodology.

In conclude,the bonding theory behind the CZM method is similar as introduced in Section 4.1.And because it can be used to describe the fracture process well, CZM method can better describe the debonding process compared with contact algorithm method.General CZM method is only suitable for same and similar metals, while the nonlocal method with ‘‘traction density”is a potential solution for different metal bonding process.

5.Limitations and future trends

Based on the above overview, some main joining processes,different roll bonding processes,bonding mechanisms and different bonding models are presented.The brief points of main limitations of roll bonding process (Section 3.3), bonding model (Section 4.4) and future directions are shown in Fig.35.For traditional roll bonding process,only simple shape products (such as plate and tube) can be produced.For tube bonding, the axial and circumferential mechanical properties,microstructures and bond strengths are still hard to be consistent(temperature gradient has important effect on the product axial performance).Furthermore, the bond strength of line bonding interface generated by traditional roll bonding process is not as high as other joining processes such as explosive welding or centrifugal casting.Thus, future trends of roll bonding process should focus on how to manufacture high quality (mechanical interlocking/metallurgical bonding, cryogenic rolling, and rolling under special energy fields) and various products(novel materials,structures,ultra-thin composite strips, complex geometries) with low emission (green bonding process).As for bonding models, how to accurately predict the bond strength, especially in hot bonding processes is still unknown.The deep reasons behind this limitation are: (i)how to characterize the diffusion mechanism in theoretical bonding model is unknown, (ii) the complex various factors coupling relationship that may affect the bond strength is still unclear.A potential solution is using the data driven model or data combine physical model.Except for the above bonding model challenges,how to implement these models into simulations are still facing difficulties:the convergence problem in 3D complex bonding simulation, dissimilar materials bonding with big nodes displacements problem.In addition, the bonding mechanism at atomic level and cryogenic temperature also need further studies.

Fig.34 A nonlocal method for modeling interface.116

Fig.35 Limitations and future directions in roll bonding processes and bonding models.

5.1.Limitations of roll bonding process and bonding model

5.1.1.Limitations of roll bonding process

The main advantages of roll bonding processes are the high production efficiency and simple technological processing,which can bring more profit in industrial applications.However, as mentioned in Table 1, the biggest shortcoming of this technique is the limitation of forming shapes(only plates,rods or tubes can be produced).Forming more complex shapes requires more flexible forming processes.150In recent years,the flexible rolling process or the so-called flexible geometric variation by continuous operation has been used in rolling processes.151Landgrebe et al.152proposed a novel axial feed cross rolling process that can produce complex part geometries with simple tools (see Fig.36(a)).Based on this technique,Guilleaume and Brosius153,154adopted cross rolling to form circumferential grooves and join gear wheels between the grooves (see Fig.36(b)).The future trend may focus on the solutions to break through the limitation of forming shapes in the roll bonding process.For billets without rotation in the axial feeding direction (such as continuous rolling), the complex forming shapes can be realized by the design of complex tools.For billets with rotation in the axial feeding direction (such as skew rolling), the complex forming shapes can be realized by the design of complex tool paths.When the tools have special axial and radial feeding movements, non-circular shapes of the rotation billet can be obtained.Currently, for metal materials that are hard to be bonded in traditional rolling processes, special energy fields such as electricity, magnetism, and ultrasound have been applied to get better bonding quality.The mechanisms of these energies are still needed for further investigations.

Fig.36 Flexible roll bonding process.

Besides, some defects are still not figured out.For roll bonding of circular billets, as shown in Fig.12, the nonuniform deformation mechanism, especially in the circumferential direction,is a key problem that affects the bonding quality which is still not unclear yet.Moreover, in real production processes,there is temperature loss in two main stages:(i)after heating,the billet transfers to the rolling mill;(ii)the billet contacts with rolls.In the first stage,heat loss occurs when the billet leaves the heating device because of the convection to the surrounding room temperature air.The conduction also occurs when the billet is on the feeding device.106For the second stage, the heat is lost due to the conduction of the rolls.Thus, there is a temperature across the upper and lower surfaces of the billet (for rebars or tubes, that should be outer and inner surfaces).There also exists a temperature gradient in the rolling direction.These temperature differences can affect the microstructure evolution as well as the diffusion effect.The temperature gradient effects are still not clear.

5.1.2.Limitations of bonding model

At present, there are two main methods for the roll bonding simulation,one is to calibrate the bonding state of each surface node and calculate the bonding strength through the contact algorithm.The other is through the modified CZ element.Currently, debonding can be well characterized by CZM.To realize the accurate prediction of bond strength, the CZ element has been extended.However, most of the current research focuses on the cold bonding model,while less attention is paid to hot bonding processes.The models are mainly implemented in two-dimensional simulation, where the calculation time is short and convergence is easiest to obtain.Only few works refer to the three-dimensional bonding process of the cold gas dynamic spray process132and ring rolling process.86For complex large plastic deformation behavior in threedimensional simulation, the price for the convergence is unacceptable because of the extremely fine requirement of discretization and the long calculation time.Thus, the threedimensional bonding prediction model is difficult to be applied in complex bonding processes.

To conclude, for roll bonding of two members of the same metal, the interface is mainly subjected to normal pressure which is similar to cold welding.The bonding mechanism can be well described by the Zhang-Bay model.For similar metals, the interface has both normal and tangential stresses and the elongation difference in the rolling direction is small,so the shear stress on the interface is not large enough to affect the debonding process.For different metals,the shear stress on the interface may be larger than the shear bond strength,which will cause the initial bonded area to separate under the big difference in elongation along the rolling direction.In this condition, the Zhang-Bay model cannot be fitted very well.The nonlocal method for modeling the interface studied by Rezaei is an effective way to solve this problem.However, this technique is still in the early development stage.

As for the hot roll bonding process,the current models cannot predict the bond strength accurately.Although some work has been done at the atomic level cold bonding mechanism,the hot bonding mechanism in atomic scale is still unveiled.In addition,the bond strength is increasing first and then decreasing with the thicker diffusion layer because the ductile phase transfer to the brittle phase.Thus, solid diffusion is hard to describe in the model.Based on the X-ray155and molecular dynamic (MD)156methods, the element diffusion coefficients can be described by the Arrhenius Equation.Also, Yilmaz and C? elik157found the influence of the bonding parameters such as temperature, pressure, surface roughness, and time can be obtained in experiments.However, the accurate mathematical relationship between key factors and bond strength is still a‘‘black box”,so Yu et al.137only proposed a bonding criterion to judge the bond status in the extrusion process,but the prediction of bond strength is hard to achieve in this model.This is also the reason why Guenther et al.86implemented the empirical model in the numerical analysis of composite ring rolling process.Research on the bonding of nonmetallic materials can also be a reference for the evolution modeling of hot bimetallic bonding processes, such as Levy et al.158developed a multiphysical model to predict the evolution of the adhesion at the interface of CF/PEI composites.

Besides,Sun et al.159,160proposed an element concentration diffusion model that considers diffusion distance, strain, temperature and time to predict the concentrations of Fe, Cr and Ni.The model is verified by hot compression test and extrusion process with both 316L/X65 and Q235/316L (see Fig.37).Zhang et al.161proposed a diffusion layer thickness calculation formula of Al/Mg based on Fick’s second law and MD simulation in the explosive welding process.If the relationship among interface compounds, element concentration, diffusion layer thickness, and the bond strength can be found, the hot bonding model considering diffusion mechanism could be established.Thus, more attention should be focused on this area.

In conclusion, the analytical hot bonding models considering diffusion mechanism, the thickness prediction of the interface, and the accurate bond strength prediction need further development.

5.2.Future trends

5.2.1.Combination of mechanical interlocking and metallurgical bonding

To enhance the bond strength of bimetallic products,an effective solution is the combination of mechanical interlocking and metallurgical bonding on the interface.As shown in Fig.38,Chen et al.162proposed a method of prefabrication corrugation on the Al side of the steel/Al bimetallic plate, and then the bimetallic plate assembly with 5083 aluminum plate to get steel/Al/Al laminated plate with an average interface shear strength of 77.68 MPa(much higher than the Chinese standard 55 MPa).

The proposed TSCFSR process(see Fig.13)in this paper is also a kind of mechanical interlocking and metallurgical bonding combination process.But for bimetallic products that are used in heat transfer areas, such as pipeline transportation of high temperature corrosive gas.Corrugation interfaces may cause heat concentration in special areas, which will cause these areas more easily to get corrosion and crack.Thus, this combination process is limited by some special application areas.

5.2.2.Roll bonding process at special energy field

Fig.37 Element concentration diffusion model and its application in extrusion bonding process.160

Fig.38 Novel method of prefabricating corrugation by cold rolling and flat roller leveling by hot rolling.162

Fig.39 Cryogenic roll bonding process.

As Xu et al.163introduced, the special energy field forming technology is mainly adopted electric, electromagnetic and ultrasonic in the forming process.For the electric energy field,the mechanism of electroplastic effect is still not fully unveiled now.The electron wind effect,metallic bond dissolution,Joule heating, and magnetoplasticity are the four main existing theories.Perkins et al.164showed that current can reduce the material deformation resistance and enhance the forming limit.Thus, Ng et al.165adopted electrically-assisted roll bonding(EARB)to fabricate Cu/Al bimetallic strip.Two current levels of 50 and 150 A are applied in their experiments.The results show that the rolling force can be decreased when the same reduction is adopted in EARB and the bonding strength can be 3 times larger than the conventional roll bonding (CRB)process.Ren et al.166adopted EARB to manufacture TA1/304 bimetallic plate and obtained a highest bond strength of 356 MPa, which is much higher than CRB of 69 MPa.In this work, the relationship of reduction rate and current density on the bonding strength is studied.

However, as stated by Ruszkiewicz et al.,167the direct current(DC),alternating current(AC),the different levels of current density, the pulse frequency, pulse period, and duration,the waveform may all have effects on the material electroplastic.In addition, the combination of above key parameters,such as low and high-frequency pulse current can also be attempted in EARB.

Except for the EARB method, the electromagnetic and ultrasonic energy-field also have particular effects on the material properties.Li et al.168added electromagnetic field and ultrasonic in the cast-rolling of AZ31B.They found that DRX of a special energy field can be advanced by one rolling pass compared with conventional cast-rolling.The yield strength, tensile strength, and elongation are also higher.Liu et al.169studied the ultrasonic effect on the AZ91 solidification process and found that in the nucleation stage, grain refinement can be obtained because of the acoustic cavitation and flows.Besides, acoustic softening and stress superposition can also be found in the forming process under ultrasonic vibration fields.170Thus, to solve the problem of coordinated deformation of different metals, future research should focus on the roll bonding process under the special energy fields.

5.2.3.Cryogenic roll bonding process

Metals can enhance mechanical properties (such as yield strength,tensile strength)not only under different energy fields but also at cryogenic conditions.171Thus,cryorolling(CR)can also be adopted for bonding.The schematic of cryorolling is shown in Fig.39(a).The elongation property of typical Al alloys at room and cryogenic temperature are shown in Fig.39(b).172Yu et al.111used cryogenic roll bonding process to fabricate Al/Ti/Al laminate plate.In their work, the ultimate tensile strength of cryogenic roll bonding sample increased 36.7% compared with the room temperature bonding sample(see Fig.39(c)).Takagawa et al.173studied accumulative roll bonding (ARB) and CR of Cu-Ni-Si alloy.Besides CR condition,cycles and pre-aging are also significant to grain refinement.However, except for the above works, few studies focus on the cryogenic roll bonding process.

Fig.40 Producing gradient structure laminate plate of AZ31.176

5.2.4.Roll bonding of gradient structured materials

As studied by Lu,174metal with gradient nanograined structures can get both strength and ductility.Chen et al.175fabricated layered and nanostructured AISI 304 SS with surface mechanical attrition treatment (SMAT) and warm co-rolling.The gradient structure consists of nanocrystalline layer, ultrafine grained layer and micron grained layer.Yan et al.176also adopted SMAT and ARB to produce layered and gradient structured AZ31 (see Fig.40(a)).Results show that although the strength of layered and gradient structured materials decreased a little compared with ARB samples and SMAT samples, the fracture elongation increased a lot (see Fig.40(b)–(c)).The strength-ductility relationship has been improved a lot.

Roll bonding of metal composite can inherit advantages of different metals.These advantages are usually physical characteristics,such as corrosion resistance,lightweight,high temperature resistance, etc.Roll bonding of gradient structured materials provides a method to enhance mechanical properties.The metal composite can get both good strength and ductility and provides more possibilities for subsequent processing.

5.2.5.Roll bonding of novel materials

Currently, novel materials such as amorphous alloy, high entropy alloy (HEA) and shape memory alloy (SMA) have attracted more and more attentions.The amorphous alloy has the excellent properties of high strength, good corrosion,wear resistance, and so on because of its combination of short-range ordered and long-range disordered atomic arrangement as well as no grain boundaries and dislocations.177But poor plasticity and small size are the main limitations for industrial application.178Thus, bonding with other ductile materials can be an effective method to solve the plasticity problem.Wang et al.179fabricated an iron-based amorphous strip/Al bimetallic plate with ultrasonic consolidation method.The fracture mode was a combination of brittle and ductile fracture.Based on the same bonding materials, Zhou et al.180adopted the vacuum hot-pressing method to produce multilayer composites with a hardness gradient from 30 to 1120 HV.To break through the size limitation, Liu et al.181fabricated large size iron-based amorphous alloy via the twin-roll strip casting method.Therefore, we think the previously introduced SLCRB process can be adopted in the bonding of amorphous alloy/ductile metal.

HEA has the unique properties of high temperature strength, good corrosion, wear and oxidation resistance, good plasticity, etc, due to its multi principal element composition.Although HEA also has the size limitation problem.It can still be bonded with other materials.Yu et al.182adopted HEA particles to enhance the wear resistance of Cu matrix composites,the wear resistance can be improved by 30%.Tsai and Yeh183pointed out HEA claddings can be fabricated by bonding technologies.

For SMA,Inoue et al.184produced TiNi SMA sheets by the roll bonding process.Peltier et al.185fabricated Cu-based sandwich composite SMA by cold roll bonding process and heat treatment.Wang et al.186pointed out that the bonding materials with texture can be produced through the control of reaction diffusion in the hot roll bonding process.Except for the above-mentioned novel materials, roll bonding of thin strips can be another future research area.

5.2.6.Green technology in roll bonding processes

The greenhouse effect is more and more apparent in the world.Metals have a key role to play in changing for the better.Metals are perfectly suited for a sustainable economy as they are durable and can be infinitely recycled without degrading their quality or properties.Therefore, except for reducing the CO2emission in the production and processing of metals,green joining methods and metal composites recycling should also be paid attention to.To solve this problem, Silva et al.187proposed a green joining process to connect tubes by a‘‘tubular lap joint”.Kolpak et al.124used cold-compacted aluminium chips in hot extrusion to save energy and resources and to reduce CO2emission.Narayanan188regarded the roll bonding process as a surface-to-surface sustainable and green joining method.Soo et al.189performed a life cycle assessment to evaluate the environmental impact of recycling different aluminium scrap qualities.

Challenges still exist in developing green joining methods.As stated by the IEA,190high-temperature heat requirements,process emissions,long-lived capital assets,and trade considerations are the four main reasons for‘‘hard to abate emissions”in heavy industries.Allwood and Cullen191presented a case on manufacturing the steel car door panel, where the energy consumption of hot rolling is about 10%,while cold rolling is only 4%, and galvanizing and pickling together about 9%.As for the cold roll bonding process,bonding occurs under huge pressure of the roll without heating.Emissions and pollution may occur during the pre or post-heat treatment and surface cleaning processes (e.g.galvanizing and pickling).For the hot roll bonding process, high temperature heat is mostly provided by burning fossil fuels which cause carbon emission.Thus,novel techniques are needed to solve this problem.Qi et al.192manufactured Ti/Al bimetallic sheets with differential forming temperatures(see Fig.41).The multilayer blank was heated by a 2100A induction current for 20 s and roll bonded together.Heating by electricity for mass production is impractical and costly with today’s commercial technologies.Scheele et al.193applied flameless oxyfuel technology in the aluminum processing industry.Compared with the conventional oxyfuel method,the emission of NOxlevels decreased significantly, but industrial applications of this kind of hydrogen technology are still in early stages of development.Thus, as stated by Wang,194zero-CO2emission and carbon capture, utilization, and storage(CCUS) technologies should be developed for an‘‘ecological”roll bonding process in the future.

5.2.7.Use of soft computing method for prediction of bonding strength

Because of the complex mechanism of the multi-factor coupling effect in hot bonding process, the relationship between bond strength and bonding parameters is nonlinear.The bond strength and bond status based on physical modeling is therefore hard to obtain,and it is difficult to characterize the evolution of the bonding interface.One method to solve this problem is using a linear approximation to replace the nonlinear interactions (such as Cooper’s model123), but the errors may affect the prediction accuracy seriously.Another method is to adopt soft computing techniques, namely artificial neural networks(ANN),fuzzy logic,evolutionary computing,probabilistic computing, chaotic computing, machine learning, or the combination method to capture the complex interactions,which has been verified in Wang et al.195and Ferna′ndez et al.196′s work.The concept of soft computing was first proposed by Zadeh,197and when the different techniques blend,better results can be obtained because of the synergistic effect.

At present, the applications of soft computing methods in metal rolling processes are mainly in the three aspects:198(i)the evolutionary algorithm; (ii) artificial neural networks; (iii)the finite element method.Details of the application targets can be seen in Fig.42.

Only few studies are focused on the bond strength prediction of the metal bonding process.Gao et al.199predicted the bond strength of extrusion forming of AA6061/AZ31 bimetallic sheets based on the GA-BP neural network.The prediction accuracy can be achieved as high as 99.5%.In their work,three extrusion parameters are considered as the input layer,while the bond strength is set as the output layer (see Fig.43).As stated by Alizadeh et al.,200the bond strength among the concrete and reinforced bars can be more accurately obtained by Adaptive Neuro-Fuzzy Inference System(ANFIS) than regulation formulas.The bond, shear, torsion,flexure, and damage of reinforced concrete can also be predicted by soft computing methods.201Based on the above works, the soft computing method application in bonding modeling might be a future trend.It can be used to capture the complex bonding parameter interactions in the hot roll bonding process,which may get a better result than the empirical model86or regulation formula.123However, as mentioned by Datta and Chattopadhyay,202challenges also exist:

Fig.42 Metal rolling with soft computing methods.198

(i) The bond strength prediction accuracy is critically determined by the dataset (mainly factors are size, content,and structure).The small size of the dataset will cause low prediction accuracy and uncertainty, so the size should be large enough.The data which do not come from experiments(such as FEM data)may have a different internal relationship structure compared with experimental data because of some idealized assumptions and boundary conditions.Thus, the dataset for training should come from experiments and consider all possible variables that may affect the bonding (data-driven model).For the current studies of bonding processes,few works could satisfy this high requirement of the training datasets.

(ii) The combination of soft computing methods with physical models can be a novel method to capture the complex relationship between bonding parameters and bond strength (data combined physical model), but the prediction accuracy beyond the training dataset range is unknown.

Fig.43 Bond strength prediction of extrusion bonding process based on BP neural network model.199

6.Conclusions

A comprehensive study of the research works in bonding mechanisms, roll bonding processes, and bonding models are presented in this paper.

Roll bonding products have the characteristics of large output,various kinds and wide applications.The review of bonding mechanisms and novel roll bonding processes is more significant for industrial production.Initially, the characteristics of roll bonding processes are compared with some main joining processes.Except reviewing some novel roll bonding processes in bimetallic plates, roll bonding of bimetallic bars/-tubes are paid attention to in this paper.Further,the cold,hot and cryogenic bonding mechanisms are introduced.In addition, the bonding mechanism at the atomic scale is identified.The main limitations of roll bonding process and bonding model are concluded.Future works should focus on more flexible roll bonding processes to produce more complex products.Novel materials,gradient structure,special energy fields,cryogenic roll bonding, as well as bonding with mechanical interlocking and metallurgical bonding methods should also be paid attention to.In hot bonding processes, the traditional heating method should also be replaced by greener energy sources.

Numerical simulation is an effective way to guide the production process, but the application in bonding processes is immature.Thus, the bonding model, bonding criteria, and bond strength prediction methods are in focus in this paper.Two main modeling methods (contact algorithm and CZM)are overviewed.Currently, the hot bonding status and bond strength are still difficult to predict by analytical models.Future works should address the complex relationship among hot bonding process parameters.Black box methods such as soft computing and deep learning can be applied to predict the bond strength.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements:

This study is financially supported by the National Key R&D Program of China(No.:2018YFA0707300),National Natural Science Foundation of China(No.:51905372),Major Program of National Natural Science Foundation of China (No.:U1710254), Fundamental Research Program of Shanxi Province (No.: 20210302124115).

Special thanks are due to Dr.Chris Valentin Nielsen from Technical University of Denmark for reviewing and language assistance.

Appendix A.The normal and tangential tractions defined in Rezaei et al.’s model144are:

The tangent matrix is calculated for the positive and negative normal gap:

Based on the Macaulay brackets, two cases must be considered.

For the second term in Eq.(A2),based on Eqs.(21)–(22)we have:

Based on the Eqs.(A3)–(A6), Eq.(A2) can be written as:

Eqs.(A7) and (A12) are slightly improved compared with the version provided in Rezaei et al.’s model.144In addition,the fourth Equation of Eq.(25) is same as derived above,which is different from Khaledi et al.90