Prediction of Strain Hardening and Fatigue Life of Cyclically Unstable Materials

Abstract

The data on cyclic deformation of materials with different cyclic properties are analyzed. The relationship between the level of additional strain hardening and the mechanical characteristics of a material is established. The proposed models take into account the influence of the form of stressed state on strain hardening and durability under conditions of nonproportional cyclic deformation. The models are constructed on the basis of the analysis of the experimental data on cyclic deformation of 304 stainless steel. The prediction of strain hardening and durability is performed with separate analysis of the influence of shape of the cycle and the form of stressed state. To take into account the influence of shape of the cycle, we use the coefficient of disproportionality of the cycle and the parameter of sensitivity to disproportionality. To take into account the form of stressed state, we use the coefficient of the form of stressed state and the corresponding parameter of sensitivity to the form of stressed state. The results of prediction of both strain hardening and durability of materials on the basis of the proposed phenomenological models reveal their fairly high efficiency.Keywords: fatigue, nonproportional deformation, strain hardening, the coefficient of disproportionality of a cycle, durability. Notation Δε-strain range in a cycle Δε nr -reduced strain range in a cycle Δε 1 -range of the principal stain in the direction of maximum strain range in a cycle Δε 1max -maximum possible range of the principal strain σ npr -maximum level of the strain hardening under nonproportional loading σ pr -maximum level of the strain hardening under proportional loading σ Y -yield strength of the material σ u -ultimate strength of the material ϕ -minimum angle between the maximum strain range in a cycle and the direction of maximum possible principal strain Φ -coefficient of disproportionality of a cycle L cyc -length of the path in a cycle p -coefficient of influence of the form of stressed state 0039-2316/05/3705-0525 α α , 1 -parameters of sensitivity to disproportionality determined according to the data on strain hardening and durability, respectively k k , 1 -parameters of sensitivity of the material to the form of stressed state determined according to the data on strain hardening and durability, respectively n B , -parameters of linear approximation of the experimental data on low-cycle fatigue in uniaxial tension-compression N -number of cycles to failureIntroduction. The phenomena of strain hardening and softening are typical of cyclically unstable materials under low-cycle strain-controlled loading. As shown in [1], this group of materials includes materials for which the ratio of the yield strength to the ultimate strength is smaller than 0.75. Note that this is true for the major part of structural steels and alloys. In the case where the cycles of deformation are nonproportional, the degree of strain hardening of materials of this sort can be several times (or even by an order of magnitude) higher than unde...