An Improved Support Domain Model of Smoothed Particle Hydrodynamics Method to Simulate Crack Propagation in Materials

Smoothed particle hydrodynamics (SPH) has its unique advantages in simulating large deformation. However, in its calculation, it is easy for some regional particles to break off. This paper puts forward the concept of virtual crack boundary to solve crack propagating problems in the framework of SPH. The parameters of virtual crack boundary are determined by the projection method of descending dimension, which improves the support domains of crack tip particles. Based on the principle of minimum strain energy density factor in fracture mechanics, the initiation and extended directions of cracks in materials are estimated. By simulating the generation and expansion of three modes of cracks in materials, the SPH calculation results of the three types of support domain forms are compared with the ABAQUS simulation results and experiment results. It indicates that the method of virtual crack boundary method is more stable than the one based on discontinuous medium. And it can generate more reasonable results than the method based on continuous medium. This paper proves the effectiveness of strain energy density factor based on fracture mechanics theory in searching the direction of crack expansion using SPH, and explores the application of new support domain model in SPH crack solution.

Thermoelastic analysis of a cracked orthotropic strip under heat conduction effect of crack interior

The problem of a Griffith crack embedded in an orthotropic strip is investigated under a combination of thermal and mechanical loadings. The extended thermal-medium crack model is used to address the effects of thermal conductivity of crack interior on the fracture parameters of concerns. Using the Fourier transform technique, the boundary-value problem is reduced to solving singular integral equations with Cauchy kernel. The closed-form solutions of temperature fields are determined. In solving the elastic fields, the Lobatto–Chebyshev integration formula is applied to discretize the obtained singular integral equations as a system of algebraic equations, which is solved by elaborating an algorithm. Numerical results are reported to illustrate the effects of the thermal conductivity inside crack and the thickness of orthotropic strip on the partial insulation coefficient, the thermal stress intensity factor, and the strain energy density factor. The crack initiation behavior is analyzed according to the normalized strain energy density factor. The observations reveal that the crack-tip thermoelastic fields in an orthotropic strip are dependent on the combined effects of the thermoelastic loadings, the physical and geometrical properties of the material and crack. Some comparisons with the existing works are offered to show the novelty and applicability of the obtained results.

The Influence of the Backfilling Roadway Driving Sequence on the Rockburst Risk of a Coal Pillar Based on an Energy Density Criterion

The rockburst hazard has always been an important issue affecting the safety production of coal mines in China. The unreasonable sequencing of roadway driving can lead to the dynamic instability of coal pillars, which subsequently causes rockburst accidents in roadway backfilling mining engineering and poses a serious threat to the safety of the mines. Roadway backfilling mining technology is an effective approach with which to mine corner residual coal resources under buildings, railways, and rivers. An energy density criterion is established and programmed with FISH language using numerical analysis software for the rockburst risk evaluation of coal pillars. On this basis, a numerical simulation model is established based on four scheme types, namely, the sequential mining, one-roadway interval mining, two-roadway interval mining, and three-roadway interval mining schemes. The influence of the backfilling roadway driving sequence on coal pillar stability is investigated, and the change law of vertical stress and energy density factor of coal pillars in different driving sequences in roadway backfilling mining technology are analyzed. According to the research results, the maximum energy density factor value of 21,172 J/m4 for coal pillars in one-roadway interval mining is the lowest among the different schemes. Therefore, the one-roadway interval mining scheme is the optimal choice in roadway backfilling mining technology. The results can be treated as an important basis for the prevention and treatment of coal pillar instability and rockburst in roadway backfilling mining technology.

Study of Influence of Residual Stresses on Crack Propagation in Particulate Ceramic Composites

The aim of the present work is to analyze the influence of residual stresses in the particulate ceramic composite on the crack propagation. The crack propagation direction was estimated using Sih’s criterion based on the strain energy density factor. A two-dimensional finite element model was developed for determination of crack path. The residual stresses resulting from the mismatch of coefficients of thermal expansion during the fabrication process of the composite were implemented to the computational model. The effect of the particles shape on the crack propagation was investigated. Conclusions of this paper can contribute to a better understanding of the propagation of micro-cracks in particulate composites in the field of residual stresses.