The boundary-value problem for a constrained elastic cylinder under axial load is solved for the correct boundary conditions, in terms of set of infinite orthogonal Bessel and trigonometric functions. The orthogonality conditions are chosen on the basis of surface deformations noted during the experiments. Analysis is used in predicting apparent modulus for materials and compared with available experimental data. The agreement is found to be extremely good. The influence of Poisson’s ratio on apparent modulus is discussed.

A short review of the current knowledge about machining induced texture states is given. The applied methods for the determination of texture and residual stress states are outlined. The surface textures and residual stress states present after grinding, milling and shot peening of initially residual stress-and texture-free as well as of 78% cold-rolled plain carbon steel are presented. Texture and residual stress states are represented by texture and lattice deformation pole figures. In the initially texture-free specimens, machining by grinding and milling gives rise to weak, but typical asymmetric textures. The appertaining principal residual stress systems do not coincide with the specimen system. Shot peening causes a centrosymmetric texture and residal stress state. The cold-rolling texture and residual stress state is significantly changed due to machining. Milling and grinding introduce an asymmetry into the symmetric rolling texture and residual stress state. After shot peening of cold-rolled specimens, a centrosymmetric residual stress state is found.

The experimental results and the widely used empirical formula (E/EApp)=(1+βS2)−1+(E/B) for the compression modulus are compared with analytical solutions obtained by Moghe and Neff. It is shown that the empirical formula does not represent the data adequately, particularly for large and small shape factors. It is also shown that the variation in β in the empirical formula arises due to the inadequacy of the representation rather than the thixotropic behavior as claimed.