A comparison of electromigration failure of metal lines with fracture mechanics

Atoms constructing an interconnecting metal line in a semiconductor device are transported by electron flow in high density. This phenomenon is called electromigration, which may cause the line failure. In order to characterize the electromigration failure, a comparison study is carded out with some typical phenomena treated by fracture mechanics for thin and large structures. An example of thin structures, which have been treated by fracture mechanics, is silica opti- cal fibers for communication systems. The damage growth in a metal line by electromigration is characterized in compar- ison with the crack growth in a silica optical fiber subjected to static fatigue. Also a brief comparison is made between the electromigration failure and some fracture phenomena in large structures.

Modelling fracture propagation and failure in a rock pillar under mechanical and thermal loadings

The Aspoe Pillar Stability Experiment （APSE） was conducted to study the rock mass response in a heated rock pillar between two large boreholes. This paper summarizes the back calculations of the APSE using a two-dimensional （2D） fracture propagation code FRACOD. To be able to model all the loading phases of the APSE, including the thermal loading, the code was improved in several ways. A sequential excavation function was developed to model promptly the stepwise changing loading geometry. Prior to the mod- elling, short-term compressive strength test models were set up aiming to reproduce the stress-strain behaviour observed for the Aspoe diorite in laboratory. These models simulate both the axial and lateral strains of radial-controlled laboratory tests, The volumetric strain was calculated from the simulations and compared with the laboratory results, The pillar models include vertical and horizontal 2D models from where the stress in the pillar wall was investigated, The vertical model assesses the stability of the experimental rock volume and suggests the resultant stress below the tunnel floor in the pillar area. The horizontal model considers cross-sections of the pillar between the two large boreholes. The horizon- tal model is used to simulate the evolution of the stress in the rock mass during the excavation of the boreholes and during and the heating phase to give an estimation of the spalling strength. The modelling results suggest that the excavation-induced stresses will cause slight fracturing in the pillar walls, if the strength of the APSE pillar is set to about 123 MPa. Fracture propagation driven by thermal loading leads to minor spalling. The thermal evolution, elastic behaviour and brittle failure observed in the experiment are well reflected by the models.

Mechanical properties and failure characteristics of fractured sandstone with grouting and anchorage

Based on uniaxial compression experimental results on fractured sandstone with grouting and anchorage, we studied the strength and deformation properties, the failure model, crack formation and evolution laws of fractured sandstone under different conditions of anchorage. The experimental results show that the strength and elastic modulus of fractured sandstone with different fracture angles are significantly lower than those of intact sandstone. Compared with the fractured samples without anchorage,the peak strength, residual strength, peak and ultimate axial strain of fractured sandstone under different anchorage increase by 64.5–320.0%, 62.8–493.0%, and 31.6–181.4%, respectively. The number of bolts and degree of pre-stress has certain effects on the peak strength and failure model of fractured sandstone. The peak strength of fractured sandstone under different anchorage increases to some extent, and the failure model of fractured sandstone also transforms from tensile failure to tensile–shear mixed failure with the number of bolts. The pre-stress can restrain the formation and evolution process of tensile cracks, delay the failure process of fractured sandstone under anchorage and impel the transformation of failure model from brittle failure to plastic failure.

Parameters Calibration of the GISSMO Failure Model for SUS301L-MT

With the development of the rail transit industry,more attention has been paid to the passive safety of rail vehicles.Structural damage is one of the main failure behaviors in a rail vehicle collision,but it has been paid little attention to in past research.In this paper,the quasi-static fracture experiments of SUS301L-MT under different stress states were carried out.The mechanical fracture properties of this material were studied,and the corresponding finite element simulation accuracy was improved to guide the design of vehicle crashworthiness.Through the tests,the fracture behavior of materials with wide stress triaxiality was obtained,and each specimen’s fracture locations and fracture strains were determined.Parameters of a generalized incremental stress state dependent damage model(GISSMO)of the material were calibrated,and the model’s accuracy was verified with test results from a 45°shear specimen.The GISSMO failure model accurately reflected the fracture characteristics of the material.The mesh dependency of this model was modified and discussed.The results show that the simulation agrees well with experimental data for the force-displacement curve after correction,but the strain distribution needs to be further studied and improved.

Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the compressive strengths for all tested numerical models. Parameters of the elastic deformability of fractured models during elastic deformation stages were also evaluated, and represented as equivalent Young’s modulus and Poisson’s ratio as functions of lateral confning pressure. It is the frst time that such systematic numerical predicting for strength of fractured rocks was performed considering different loading conditions, with important fndings for different behaviors of fractured rock masses, compared with testing intact rock samples under similar loading conditions.

Limestone mechanical deformation behavior and failure mechanisms： a review

In this paper, several mechanical deformation curves of limestone are reviewed, and the effects of temperature, confining pressure, and fluid are discussed. Generally, Mohr–Coulomb is used for limestone brittle fracture. The characteristic of low temperature cataclastic flow and the conditions and constitutive equations of intracrystal plastic deformation such as dislocation creep,diffusion creep, and superplastic flow are discussed in detail. Specifically, from the macroscopic and microscopic view, inelastic compression deformation(shear-enhanced compaction) of large porosity limestone is elaborated.Compared with other mechanics models and strength equations, the dual porosity(macroporosity and microporosity) model is superior and more consistent with experimental data. Previous research has suffered from a shortage of high temperature and high pressure limestone research; we propose several suggestions to avoid this problem in the future:(1) fluid-rock interaction research;(2) mutual transition between natural conditions and laboratory research;(3) the uniform strength criterion forshear-enhanced compaction deformation;(4) test equipment; and(5) superplastic flow mechanism research.

Preliminary investigation of seismic damage to two steel space structures during the 2013 Lushan earthquake

Severe damage to steel space structures is rarely reported when compared to other structural systems damaged during past major earthquakes around the world. Two gymnasiums of steel space structures in downtown Lushan County that were damaged during the 2013 M7.0 Lushan earthquake in China were investigated and the observations are summarized in this paper. Typical damage to these two steel space structures ranges from moderate to severe. Moderate damage includes global buckling and dislocation of bolted connections of truss members, and inelastic elongation of anchor bolts and sliding of pedestal plates of supports. Severe damage includes member fracture caused by local buckling, and fracture failure of anchor bolts and welds. The distribution of structural damage to these two structures is described in detail and future research opportunities are suggested.

Effect of structural parameters on the setting performance of plug slips during hydraulic fracturing

Slip is one of the most critical components for the frac plug,which would lodge into the casing and lock the frac plug in place during the setting and anchoring process.However,fracture failure of slip significantly affects the hydraulic fracturing effects and has attracted tremendous attention.In this paper,a three-dimensional contact model is applied to explore the setting process of slip.The effects of key structural parameters such as apex angle,inclination angle,and wedge angle on the contact characteristics of slip are systematically investigated.Numerical results indicate that the maximum contact stress appears at the contact area between slip tooth and the casing’s inner wall.Besides,the maximum contact stress generally increases with the increase of apex angle and inclination angle,while decrease linearly with the rise in the wedge angle.Experimental results show that the slip teeth get blunt and appear severe plastic deformation,which arises from stress concentration.Comparison of biting area indicates that the experimental results are about 21.3%larger,which still have a reasonable agreement with the numerical results.These obtained results can guide the parametric selection of plug slip and other similar components.

Microstructure characterization and HCF fracture mode transition for modified 9Cr-1Mo dissimilarly welded joint at different elevated temperatures

The high cycle fatigue（HCF） tests of modified 9 Cr-1 Mo dissimilarly welded joint were carried out at different elevated temperatures and the fracture mechanism was systematically revealed. The fatigue strength at 108 cycles based on S-N curve can be estimated as a half of weld joint＇s yield strength for all conducted temperatures, which can be a reliable criterion in predicting the fatigue life. The results show that the inter-critical heat affected zones（IC-HAZs） of both sides are the weak zones due to their low hardness and inferior fatigue resistance property. HAZ of COST-FB2（BM2） is the weakest zone at room temperature due to the existence of numerously distributed defects and the initiation of cracks, either in the surface or interior zone, impacting a crucial effect on the fatigue life of the joint. While at elevated temperatures, fatigue life was controlled mostly by the intrusion-extrusion mechanism at the specimen surface under high stress level and subsurface non-defect fatigue crack origin（SNDFCO） from the interior material under low stress amplitude. With increasing temperature, more and more fatigue failures began to occur at the HAZ of COST-E（BM1） due to its higher susceptibility of temperature. Besides, it is found that the-ferrite in the BM1 has no harm to the HCF behavior of the joint at the conducted temperatures.

A toughness based deformation limit for X- and K-joints under brace axial tension

This study reports a deformation limit for the initiation of ductile fracture failure in fatigue-cracked circular hollow section （CHS） X- and K-joints subjected to brace axial tension. The proposed approach sets the deformation limit as the numerically computed crack driving force in a fatigue crack at the hot-spot location in the tubular joint reaches the material fracture toughness measured from standard fracture specimens. The calibration of the numerical procedure predicates on reported numerical computations on the crack driving force and previously published verification study against large-scale CHS X-joints with fatigue generated surface cracks. The development of the deformation limit includes a normalization procedure, which covers a wide range of the geometric parameters and material toughness levels. The lower-bound deformation limits thus developed follow a linear relationship with respect to the crack-depth ratio for both X- and K-joints. Comparison of the predicated deformation limit against experimental on cracked tubular X- and K- joints demonstrates the conservative nature of the proposed deformation limit. The proposed deformation limit, when extrapolated to a zero crack depth, provides an estimate on the deformation limits for intact X- and K-joints under brace axial loads.