Strength of Materials

The article deals with the problem of constructing determining relations of the theory of plasticity for arbitrary complex processes of deformation. The point of departure are relations based on V. S. Lenskii's hypothesis of local determinability. It is suggested to generalize the equations of the hypothesis of local determinability to the scalar characteristics of the functional of plasticity. It is shown that analogous relations can be obtained in the endochronic theory of plasticity. The results of calculation are compared with the experiment entailing complex loading, and it is established that not only vector characteristics but also scalar characteristics of the functional of plasticity are perfectly satisfactorily described within the generalized variant of the hypothesis of local determinability suggested in the present work.

The δ c -model of a crack-containing elastoplastic body was used to specify parameters that influence the healing of crack-type defects by filling them with the other material. The relationships are derived, which can predict the extent of crack-containing body strength recovery with various fillings. The “characteristic distance” of crack (filled or free) growth is established, when the intensity of external loads reaches its limit. It is shown that this distance is the constant of the material for unfilled macrocracks and constitutes a certain portion of the plastic zone formed near the defect.

The article describes the working principle and design of an apparatus for quick control of damping capacity of materials in the amplitude-dependent region of internal friction with tension-compression loading of specimens in the ultrasonic range of frequencies (16–23 kHz). Amplitude dependences of energy dissipation parameters and modulus of elasticity defects of a series of metallic materials are presented as illustration.

A relationship between the threshold stress intensity factor ranges of the material is established for microstructurally short, physically small and long fatigue cracks depending on the microstructure at a symmetrical loading cycle. The threshold stress intensity factor ranges calculated by the proposed concept for titanium alloy VT3-1 in different structural states agree well with those determined experimentally. The criteria are proposed for the transition from a small to a long fatigue crack depending on the level of the applied load amplitude. In the whole range of the load amplitudes, the condition when a reversible plastic zone at the crack tip reaches the grain size is taken as a criterion for the transition from a physically small to a long fatigue crack. In the high cycle fatigue region, the physically small crack growth range is to be divided into two areas because of a change in the mechanisms of the physically small crack growth upon the attainment by the stress intensity factor range of the threshold value for the long crack.

The method of predicting thermal instability-initiated performance losses by nanocomposite structure elements is developed. It is based on the model of monoharmonic approximation of the material response to cyclic loading, amplitude ratios between main field variables, and concept of complex moduli. The methods of evaluating the moduli of accumulation and losses of nanocomposite components as well as the model allowing for the effect of the fiber-matrix contact surface were evolved. The modified homogenization procedure based on the Mori–Tanaka method was elaborated to obtain the complex moduli of a nanocomposite with random or unidirectional nanofiber orientation. Temperature- and amplitude-dependent complex moduli were used to study the effect of dissipative heating on the mechanical stability of a polymer nanocomposite bar under combined static and monoharmonic loadings. The effect of a load amplitude and volume content of nanofibers on the thermal instability of the bar was investigated.

An analysis of relationships used to define isotropic and kinematic hardening in a theory of flow previously proposed by the author is presented. Familiar hardening laws are obtained using appropriate simplifications of the relationships examined.