Ciśnienie zredukowane jako jeden z parametrów wytężenia (przyrost właściwej energii swobodnej jako miara wytężenia)

Reduced pressure as a strength parameter (the increase of unit free energy as a measure of effective strew)

This strength theory belongs to the group of energy theories. The object of this paper is to establish a strength theory which can be applied in practice and which is based on the fundamental assumptions and laws of the theory of solid bodies. The theory proposed here call be applied directly in connection with many materials, including a number of technically important. metals. After some improvements, taking entropy changes into consideration, it can also be used for plastics.

If a body is loaded, the elastic strain energy increases in consequence of the change of the distances between the atoms or molecules in the nodes of the crystal net. In other words, the distortion energy and the volume energy change. This is not the only change, however, since the energy of atom vibration about the neutral position also increases. The increase of vibration energy favourizes the appearance of permanent set, in other words, the phenomenon of crossing an energy barrier and taking another position of transient equilibrium, stable or unstable, depending on the process of further plastic deformation.

Analysing the equations of the theory of a solid body for the model assumed, we take it that the increase in the vibration energy can be represented as a function of pressure or, in other words, as a function of the mean normal stress, in the form

Λ_d =π f (σ_n).

Here a is the coefficient of limit energy capacity depending on the properties of the material for various state parameters: T₀ (initial temperature), p₀ (initial pressure), v (.strain rate) and the local non-homogeneity of the state of stress; f(a_n) is a function assumed for the model under consideration.

A detailed analysis of the problem led to the establishment of the following alternative forms of the function f(a_n): (1) the vibration energy is a linear function of the stress a_n; (2) the vibration energy is a quadratic function of the stress a_n.

The first alternative concerns bodies characterized by small volume changes and small compressibility coefficients even for considerable loads, the second can be applied to quasi-isotropic bodies crystallizing in regular systems (and also in face and space-centred systems() and subjected to Hooke's law.

Thus, the final form of the basic equation of the theory is

A π²_n + Bσ²_n      – πf (σ_n) = K²_e

where A = 3G/4 and B = 1/2K are material constants, at is the coefficient of limit energy capacity, f (a_n) a function of normal octahedral stress and K²_e, limit energy capacity for one of the fundamental states (simple tension, for instance).