Strength,Fracture and Complexity

Based on the energy release rate criterion, the behavior of vertical fracture penetration/deflection at interface between coal seam and mudstone layers are investigated by finite element method (FEM) in this study. Considering its interfacial effect that is simulated by linear spring model (LSM), the energy release rates (ERRs) of vertical fracture penetration and deflection at the interface are calculated using virtual crack close technique (VCCT). Combined with the critical energy release rates (CERRs) of coal seam layer, mudstone layer, and sandstone layer as well as the interface between them were tested in a laboratory. The layers were gathered from the southern Qinshui Basin. The judging methods of vertical fracture penetration/deflection at interface are presented and the maximum penetration length which extends into the mudstone layer is calculated. The result is consistent with the analyses from the field monitoring results. Furthermore, the effects of interfacial stiffness, coal seam thickness, Young’s modulus of sandstone cap and in-situ differential stress on the propagation behavior are also evaluated. The results show that the interfacial stiffness of interface between coal seam and mudstone layers vary between 10⁹ Pa/m and 10¹² Pa/m, which is about 10¹⁰ Pa/m. The state of interface is separation or perfect when the interfacial stiffness is smaller than 10⁹ Pa/m or larger than 10¹² Pa/m. With the increase of coal seam thickness, the maximum penetration length gradually and faintly decreases. In contrast, the maximum penetration length obviously decreases when Young’s modulus of sandstone cap raises or the in-situ differential stress Δ𝜎 declines. In other words, Young’s modulus of sandstone cap and the in-situ differential stress Δ𝜎 are the main factors which influence the behavior of vertical fracture penetration/deflection at the interface between coal seam and mudstone layers.

Intergranular slow crack growth (SCG) in ceramic polycrystal is described with a cohesive zone model that mechanically simulates the reaction-rupture mechanism underlying stress and environmentally assisted failure. A 2D polycrystal is considered with cohesive surfaces inserted along the grain boundaries. The anisotropic elastic modulus and grain-to-grain misorientation are accounted for together with an initial stress state related to the processing. A minimum load threshold is shown to originate from the onset of the reaction-rupture mechanism to proceed where a minimum traction is reached locally and from the magnitude of the initial compression stresses. The cohesive model incorporates a characteristic length scale, so that size effects can be investigated. SCG is grain size dependent with the decrease of the crack velocity at a given load level and improvement of the load threshold with the grain size. Polycrystals of zirconia and alumina are both considered in the current study and a comparison between SCG resistance of alumina and zirconia is presented. This work aims at providing reliable predictions in long lasting applications of ceramics.

The present work aims to study the stress concentration factor (SCF) reduction using different functionally graded materials (FGMs) layer around the circular hole in an infinite homogeneous material panel for different load conditions. Young’s modulus of FGM layer has been considered to be varied along radial direction while Poisson’s ratio has been kept constant. The extended finite element method (XFEM) is used to find the effect of FGM layer properties i.e. Young’s modulus ratio, power law index and layer thickness on SCF. Four FGM models have been used in the present work out of which power law function based thicker FGM layer ensure the least value of SCF.

The combined theoretical-experimental technique to estimate high-tempered 65Γ steel resistance to rolling contact fatigue cracking is used. As a result of complex studies, the fatigue life data of high-tempered 65Γ steel is obtained. The dimensions of spall formed by pitting mechanism for deferent contact pressure values is determined. It is shown that the significant role in rolling contact fatigue estimation of similar steels has an initiation shear crack length. The influence of tempering temperature after quenching on rolling contact fatigue resistance of 65Γ steel is evaluated.