The phenomenon of the Portevin-LeChatelier effect is described on the basis of a constitutive model of dynamic strain ageing, which was implemented in three-dimensional finite element analysis. The simulation of the deformation behaviour of Al–Cu alloys is performed, using the constitutive parameters as required by the model. The simulations confirm the occurrence of propagative zones of localized deformation bands and provide insight into the strain rate distribution in the zones, characterized by a sharp strain rate peak. The influence of the applied strain rate on the localized deformation behaviour of a plane specimen is also analysed and the resulting stress–strain curves are calculated for each case. It is found, that the higher the applied strain rate, the faster the deformation band propagation and the smaller the amplitude of the stress–strain serrations. It is observed that macrosteps on the stress–strain curve match the reflection of the band at a specimen end. The propagative deformation bands in flat strip specimens are inclined with respect to the tensile axis from 45° to 53°, which is in good agreement with experimental findings.

The present study is devoted to the problem of enhancing fracture toughness of ZrO2 ceramic materials through the formation of composite structure by addition of Al2O3 and NiO particles. In this paper, we analyzed the general and distinguished features of microstructure of both composite materials and its effect on fracture toughness of materials. In this paper, we used the XRD, SEM, and EDS methods for determination of granulometric, phase, and chemical composition of sintered materials. The peculiarities of dependence of fracture toughness values from dopant concentration and changing the Y3+ amount in zirconia grains allow us to assume that at least two mechanisms can affect the fracture toughness of ZrO2 ceramics. Crack bridging/deflection processes with the “transformation toughening” affect the K1C values depending on the dopant concentration. Crack deflection mechanism affects the K1C values when the dopant concentrations are low, and transformation toughening affects the K1C values when the dopant concentrations begin to have an impact on microstructure reorganization–redistribution of Y3+ ions and formation of Y3+-depleted grains with high ability to phase transformation.

A combination of the phase‐field method for the simulation of the microstructure evolution during solidification with subsequent finite element simulation of fracture appearance in the final solidification structure is proposed for the prediction of the mechanical behavior of AlSi based casting alloys, including the effect of solidification porosity caused by hydrogen. Metallographic investigations and computer tomographic observations of the as cast microstructure of an Al7%Si0.3%Mg alloy together with the data obtained from mechanical tensile testing are used to compare and validate the simulation results to demonstrate the capabilities as well as current limitations in micromechanical modeling of void containing materials. In micromechanical simulations with the element elimination technique (EET) it is shown that porosity influences the crack path as well as crack propagation by connecting the pores. In the eutectic microstructure without porosity, failure starts to develop in silicon lamellae and proceeds in the ductile matrix. However, in the presence of pores fracture also initiates in silicon, and in the later stages of loading, porosity affects the path of the crack and results in additional crack nucleation, and thus, these pores also influence crack propagation in the matrix.

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Introduction. The principles and criteria of linear fracture mechanics [1][2][3][4][5] usually underlie the strength and durability calculations for the structural members. The criteria are calculated with allowance for the properties of the classical model of the Griffith crack despite its having significant two drawbacks. The first is the presence of a singular point at the end of a cut, an unbounded increase in the stress being observed as this point is approached. This explains the fact that the physical notion of the coefficient of stress concentration at the crack tip is not used in fracture mechanics, and the coefficient of stress intensity in the neighborhood of the singular point is used as the characteristic of the inhomogeneous stress field. To formulate the criterion for crack propagation, Griffith assumed that the formation of the crack surface is connected with the expenditure of energy. As the crack lengthens, the released elastic energy should be higher than the energy expended for the formation of the new surfaces. The additional energy 7 introduced by Griffith cannot be calculated from the elasticity equations for a solid body with a cut, which may be considered as the second drawback of the Griffith theory.The assnmptions of the nonlinear behavior of a material at the crack ends allowed one to employ a number of known models for calculations [2][3][4][5][6]. However, their application is restricted. They hold true in the case where the plastic-deformation zone is very small compared with the length of the crack. The description of the stress state near the crack tip with an extended plastic-deformation zone involves great mathematical and computing difficulties [2][3][4][5].This work suggests an improved model of the Griffith crack that is free from these drawbacks owing to the assumption that the effective moduli of elasticity in the immediate proximity of the real surface of a solid body differ from those in the volume of the material and owing to taking into account the relaxation effects (the stress decrease) in the plastic-deformation zone. This allowed us to characterize the crack in a solid body as a defect with the internal-stress field and to relate the formation of the free surface with work of the external forces.The method of relaxation elements was used to construct the model of a crack with the site of plastic deformation in a continuous medium and to calculate the stress state of this medium [7][8][9]. For the planestress state, analytical expressions were obtained which are applicable in engineering calculations of the stress concentration and in the formulation of the fracture criteria for cracked materials containing the plasticdeformation zones.