MATHEMATICAL MODEL OF THE DEVELOPMENT OF A SINGLE TWIN LAYER IN METAL CRYSTALS

By analyzing the experimental data available in the scientific literature, a mathematical model of the development of a single twin layer in metal crystals has been obtained. The model has the form of a differential equation, the order of which is determined by the required accuracy of obtaining the results associated with the solution of this equation. Even in the linear approximation of one of the main parameters of the phenomenological model, the latter gives qualitatively the same dependences of the development of single twins under different loading conditions compared to the experiment. Despite a large number of experimental works devoted to twinning, there is still no rigorous quantitative theory of the development of twinning layers in different media and under different conditions. However, in these works, the mathematical approach was demonstrated only in relation to elastic twins. This work is an introduction to the creation of a quantitative theory of twinning in metal crystals. Comparisons with the experimental results of the proposed phenomenological model were limited in this work to the task of demonstrating the performance of the model in the sense of predicting the most specific effects of the development of twins under various conditions and loading modes. In particular, the model implies the effect of loss and subsequent restoration of hardening by twin boundaries during stress pulsations, the Bauschinger effect upon a change in the sign of the applied voltage, and a number of other effects observed experimentally on a number of different metal crystals.

A Study on Residual Stresses on Autofrettaged LDPE Tubing Including the Bauschinger Effect and Strain Aging

This paper compares and discusses the change to the residual stresses and strains on four tubes of SA-723 Gr 1 Cl 2 (Timken HS 220) tubing material that were autofrettaged at different Overstrain ratios (20% and 40%). The four tubes were autofrettaged with strain gages to obtain actual OD strain. The effect on the residual stress and strain of the material is reviewed after a single autofrettage and after a low temperature heat treat followed by a second autofrettage. The low temperature heat treat was performed on two of the four tubes to create comparable data. Any strain aging effect from the low temperature heat treat is examined on the measured residual stress and strains. The effect and possible benefits of strain aging and re-autofrettage on tubes with different Overstrain ratios is discussed. To obtain the residual stress values in the tube wall after the autofrettage cycles, the sample tube pieces were tested by X-ray diffraction. The actual residual stresses after autofrettage were then compared with the calculated theoretical residual stresses including Bauschinger effect correction factors from ASME Section VIII Div. 3 KD-5. The residual stress and strain data between one and two rounds of autofrettage is also studied to see if the Bauschinger effect is present.