Study on Crack Development of Concrete Lining with Insufficient Lining Thickness Based on CZM Method

The most common structural defect of a tunnel in the operation period is the cracking of concrete lining. The insufficient thickness of tunnel lining is one of the main reasons for its cracking. This study studied the cracking behavior of standard concrete specimens and the failure behavior of tunnel structures caused by insufficient lining thickness using Cohesive Zone Model (CZM). Firstly, zero-thickness cohesive elements were globally inserted between solid elements of the standard concrete specimen model, and the crack development process of different concrete grades was compared. On this basis, a three-dimensional numerical model of the tunnel in the operation period was established. The mechanism and characteristics of crack propagation under different lining thicknesses were discussed. In addition, the statistics of cracks were made to discuss the development rules of lining cracks quantitatively. The results show that the CZM can reasonably simulate the fracture behavior of concrete. With the increase in concrete strength grade, the number of cohesive damaged elements and crack area increases. The insufficient lining thickness changes the lining stress distribution characteristics, reduces the lining structure’s overall safety, and leads to the cracking of the diseased area more easily. When surrounding rock does not contact the insufficient lining thickness, its influence on the structure is more evident than when surrounding rock fills the entire lining thickness. The number of cohesive damaged elements and the size of the crack area increases significantly.

Distribution of Cracks in an Anchored Cavern Under Blast Load Based on Cohesive Elements

To explore the distribution of cracks in anchored caverns under the blast load, cohesive elements with zero thickness were employed to simulate crack propagation through numerical analysis based on a similar model test. Furthermore, the crack propagation process in anchored caverns under top explosion was analysed and the distribution and mode of propagation of cracks in anchored caverns when a fracture with different dip angles was present in the vault were discussed. With the propagation of the explosive stress waves, cracks successively occur at the boundary of the anchored zone of the vault, arch foot, and floor of the anchored caverns. Tensile cracks are preliminarily found in rocks surrounding the caverns. In the case that a pre-fabricated fracture is present in the upper part of the vault, the number of cracks at the boundary of the anchored zone of the vault decreases, then increases with increasing dip angle of the pre-fabricated fracture. The fewest cracks at the boundary of the anchored zone occur if the dip angle of the pre-fabricated fracture is 45º. The wing cracks deflected to the vault are formed at the tip of the pre-fabricated fracture, around which tensile and shear cracks are synchronously present. Under top explosion, both the peak displacement and peak particle velocity in surrounding rocks of anchored caverns reach their maximum values at the vault, successively followed by the side wall and the floor. In addition, they show asymmetry with the difference of the dip angle of the pre-fabricated fracture; the vault displacement of anchored caverns is mainly attributed to the formation of tensile cracks at the boundary of the anchored zone generated due to tensile waves reflected from the free face of the vault. When a fracture is present in the vault, the peak displacement of the vault decreases while the residual displacement increases.

Grain-Scale Anisotropic Analysis of Steady-State Creep in Oligocrystalline SAC Solder Joints

Heterogeneous integration is leading to unprecedented miniaturization of solder joints, often with thousands of joints within a single package. The thermomechanical behavior of such SAC solder joints is critically important to assembly performance and reliability, but can be difficult to predict due to the significant joint-to-joint variability caused by the stochastic variability of the arrangement of a few highly-anisotropic grains in each joint. This study relies on grain-scale testing to characterize the mechanical behavior of such oligocrystalline solder joints, while a grain-scale modeling approach has been developed to assess the effect of microstructure that lacks statistical homogeneity. The contribution of the grain boundaries is modeled with isotropic cohesive elements and identified by an inverse iterative method that extracts material properties by comparing simulation with experimental measurements. The properties are extracted from the results of one test and validated by verifying reasonable agreement with test results from a different specimen. Equivalent creep strain heterogeneity within the same specimen and between different specimens are compared to assess typical variability due to the variability of microstructure.

Numerical Simulation of Fracturing in Coals Using Water and Supercritical Carbon Dioxide with Potential-Based Cohesive Zone Models

The Park-Paulino-Roesler (PPR) cohesive zone model (CZM) for coal was established for analyzing mixed-mode I/II fractures using semicircular specimens under punch-through shear (PTS) and three-point bending (SCB) tests. In these methods, the main parameters of the fracture were obtained through SCB tests and PTS tests. And according to the experimental results, the coal specimens show obvious characteristics of ductile fracture under mode I and II loading. Moreover, hydraulic and supercritical carbon dioxide (ScCO2) fracture tests were conducted, and accordingly, it was found that the crack initiation pressure of coal specimens for hydraulic fracturing is 17.76 MPa, about 1.59 times that driven by ScCO2. And the crack initiation time of coal with ScCO2 fracturing is 123.73 s, which is 1.58 times that for hydraulic fracturing. A macrocrack eventually formed in the coal specimen due to the hydraulic drive, which penetrated through the entire specimen. Yet, there was no crack penetrating the whole fracture specimen and several widely distributed secondary cracks in the fractured coal specimens by ScCO2. Furthermore, zero-thickness pore pressure cohesive elements were utilized to investigate multicrack propagation in coals undergoing hydraulic and ScCO2 fracturing. The constitutive relationships of the established PPR CZM were introduced into the cohesive elements. The obtained results are consistent with the hydraulic and ScCO2 fracturing experiment results for the coal specimens. This indicates that the established PPR CZMs can accurately represent the crack propagation behavior in coals for hydraulic and ScCO2 fracturing.

A new progressive damage model for predicting the tensile behavior of the three-dimensional woven carbon/carbon composites using micromechanics method

A new progressive damage model for the three-dimensional (3 D) woven carbon/carbon (C/C) composites is developed at fiber-matrix level using the micromechanics method. A woven architecture based Representative Volume Element (RVE) model composed of yarns, matrix and yarn/matrix interface is constructed, in which the manufacturing void defects are accounted for. The fiber-matrix concentric cylinder model is employed as a repeating unit cell to represent the yarn, and the matrix micro strain field is computed analytically by the micromechanics method. The maximum stain criteria is utilized for fiber longitudinal breakage, and the Von-Mises criterion is applied for the damage initiation of matrix in both intra-yarns and inter-yarns. The damaged fiber and matrix are modeled by the stiffness degradation method combined with exponential damage evolution equations. The zero thickness cohesive elements governed by bilinear traction-separation constitutive are adopted for yarn/matrix interfacial debonding behavior. The micro progressive damage and failure behavior of the 3 D woven C/C composites subjected to tension is implemented through a developed user-defined material subroutine in commercial software ABAQUS. The predicted stress-strain response is in a good agreement with experimental results. In addition, the effect of manufacturing void defects is also examined by the developed model.