Use of the efficiency factor to account for previous straining on the tensile behavior of paper

Abstract The presented results suggest that the concept of efficiency factor previously used to demonstrate that changes in inter-fiber bonding in paper do not change the shape of the stress-strain curve can be extended to describe the changes that are observed in the tensile response of paper subjected to previous straining. It is found that the pre-yielding response for samples that have fully recovered from previous straining scales with changes in maximum tangent modulus. This deformation is mainly recoverable. When the scaling holds, one can extract a reasonable approximation of the initial recoverable deformation, which is separate from the plastic deformation. In essence, the efficiency factor acts as a stress magnification factor that easily can be incorporated into a constitutive equation. Tracking the change in efficiency factor with straining allows one to account for the loss of observed compliance for the entire range of recoverable deformation.