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The paper presents a theoretical study on the compression of a two-layer strip of strain-hardening rigid-plastic materials between rigid platens. Semianalytical solutions are obtained for stress and velocity fields in each layer. Special attention is devoted to the conditions corresponding to the beginning of cold bond formation between the layers. Depending on input parameters various general deformation patterns are possible. In particular, there exists such a range of process parameters that the soft metal layer yields while the hard metal layer is rigid at the beginning of the process. As the deformation proceeds, yielding also starts in the hard metal layer and the entire strip becomes plastic. This is a typical deformation pattern adopted in describing the process of joining by rolling. However, at a certain range of input parameters plastic deformation of the entire strip begins at the initial instant. Moreover, it is possible that only the hard metal layer yields while the soft metal layer does not. This deformation pattern takes place when the thickness of the soft metal layer is much smaller than that of the hard metal layer.

For many years rolling has been recognized as being an important process for joining by forming ([

A recent finite element solution for the roll-bonding process has been given in [

The progressive plane-strain compression of a two-layer strip between parallel, rough plates is considered. The Cartesian coordinate system

Compression of a two-layer strip between rough rigid plates.

It will be shown later that the bimaterial interface is a straight line parallel to the

for layers 1 and 2, respectively. Here

An exact solution of (

Compression of a single layer between rough rigid plates.

Here

The solution described in the previous section can be adopted to find a solution for the boundary value problem formulated in Section

for layers 1 and 2, respectively. It is also convenient to introduce new coordinates

Boundary conditions and coordinate systems for each layer.

To apply the solution (

To apply the solution (

The stress

respectively. In the range

Layer 1 is rigid when

Layer 2 is rigid when

Replacing

Each of these expressions involves four independent input parameters. Therefore, it is impossible to provide a clear geometric illustration of this solution in its generality. In order to give some insights into qualitative features of the solution, it is assumed that

Domain of sticking at the initial instant.

where

Since the hard layer is rigid during an initial stage of the process of compression,

Here

Variation of

Variation of

Variation of

A semianalytical solution for the compression of a two-layer strip of strain-hardening materials has been given. Numerical treatment has been reduced to solving a transcendental equation (

The process of bonding by rolling can be simulated using the approach proposed in [

The solution found reduces to the rigid perfectly plastic solution given in [

The authors declare that there is no conflict of interests regarding the publication of this paper.

The research described in this paper was supported by Grants RFBR-13-08-00969 and NSH-1275.2014.1 (Russia).