The following technique is sometimes used to connect tubular components down oil wells. As manufactured, the smaller of the two tubes has inner and outer radii (b, c), while the larger has inner and outer radii (c, a), so that the end of the smaller tube can simply be inserted into the larger tube. An over-sized die is then pulled through the bore of the inner of the two tubes. The radius of the die is chosen so that both cylinders are fully plastically deformed as the die passes through the region where the two cylinders overlap. As a result, a state of residual stress is developed at the coupling, which clamps the two tubes together. For a / b = 2, calculate the value of c that gives the strongest coupling. The inner pipe has yield stress of 250 MPa, the yield stress for the outer pipe y = 500 MPa. Young's modulus and Poisson's ratio for both pipes can be assumed as having the same values. y = 250 MPa y = 500 MPa Undeformed Deformed