Fracture behaviors of columnar jointed rock mass using interface mechanics theorem

For a special geological structure of columnar jointed rock mass(CJRM),its mechanical properties are strongly affected by the columnar joints.To describe the fracture behaviors of CJRM using the basic theories of interface mechanics for composite materials,the interface stresses of the vertical and horizontal joints,which are the two primary joints in the CJRM under triaxial compression,are studied,and their mathematical expressions are derived based on the superposition principle.Based on the obtained interface stresses of the vertical and horizontal joints in the CJRM,the crack initiation of the joint interface in the CJRM is studied using the maximum circumferential stress theory in fracture mechanics.Moreover,based on this investigation,the fracture behaviors of CJRM are analyzed.According to the results of similar material physical model tests for the CJRM,the theoretical study is verified.Finally,the influence of the mechanical parameters of the CJRM on the joint interface stress is discussed comprehensively.

Nonlinear Dynamic Modeling for Joint Interfaces by Combining Equivalent Linear Mechanics with Multi-objective Optimization

The nonlinear dynamic modeling by combining the equivalent linear mechanics with the multi-objective optimization algorithm is proposed to describe the nonlinear behaviors of the joint interfaces.The joint interfaces are simplified as the equivalent virtual material or linear spring damper element.The genetic algorithm for multi-objective optimization is then used to identify the mechanical properties of the equivalent joint by minimizing the error between the simulated dynamic characteristics and the experimental results,including the modal frequencies of the bolted joint beam and the frequency response functions(FRFs)of the rubber isolation system.The FRFs are divided into several subsections with frequency-varied dynamic properties of the joint to consider the nonlinear dynamic behaviors,and the effects of subsection number and excitation amplitudes on the FRFs are also investigated.The results show that the simulated dynamic characteristics of modal frequencies and FRFs agree well with the experimental results.With the increase in the subsection number,the simulated FRFs agree better with the experimental results,indicating a good performance of modeling the nonlinear dynamic behaviors of the joint interfaces forced by different excitation amplitudes.Larger excitation amplitudes will decrease the joint stiffness.

The Numerical Analysis of Strain Behavior at Solder Joint and Interface of Flip Chip Package

The flip chip package is a kind of advanced electri ca l packages. Due to the requirement of miniaturization, lower weight, higher dens ity and higher performance in the advanced electric package, it is expected that flip chip package will soon be a mainstream technology. The silicon chip is dir ectly connected to printing circuit substrate by SnPb solder joints. Also, the u nderfill, a composite of polymer and silica particles, is filled in the gap betw een the chip and substrate around the solder joints to improve the reliabili ty of solder joints. When flip chip package specimen is tested with thermal cycl ing, the cyclic stress/strain response that exists at the underfill interfaces and solder joints may result in interfacial crack initiation and propagation. Therefore, the chip cracking and the interfacial delamination between underfill and chip corner have been investigated in many studies. Also, most researches h ave focused on the effect of fatigue and creep properties of solder joint induce d by the plastic strain alternation and accumulation. The nuderfill must have lo w viscosity in the liquid state and good adhesion to the interface after solidif ying. Also, the mechanical behavior of such epoxy material has much dependen ce on temperature in its glass transition temperature range that is usually cove red by the temperature range of thermal cycling test. Therefore, the materia l behavior of underfill exists a significant non-linearity and the assumption o f linear elastic can lack for accuracy in numerical analysis. Through numerical analysis, this study had some comparisons about the effect of linear and non -linear properties of underfill on strain behaviors around the interface of fli p chip assembly. Especially, the deformation tendency inside solder bumps could be predicted. Also, it is worthily mentioned that we have pointed out which comp onent of plastic strain, thus, either normal or shear, has dominant influence to the fatigue and creep of solder bump, which have not brought up before. About the numerical analysis to the thermal plastic strain occurs in flip chip i nterconnection during thermal cycling test, a commercial finite element software , namely, ANSYS, was employed to simulate the thermal cycling test obeyed by MIL-STD-883C. The temperatures of thermal cycling ranged from -55 ℃ to 125 ℃ with ramp rate of 36 ℃/min and a dwell time of 25 min at peak temperature. T he schematic drawing of diagonal cross-section of flip chip package composed of FR-4 substrate, silicon chip, underfill and solder bump was shown as Fig.1. Th e numerical model was two-dimensional (2-D) with plane strain assumption and o nly one half of the cross-section was modeled due to geometry symmetry. The dim ensions and boundary conditions of numerical model were shown in Fig.2. The symm etric boundary conditions were applied along the left edge of the model, and the left bottom corner was additional constrained in vertical direction to prevent body motion. The finite element meshes of overall and local numerical model was shown as Fig.3. In this study, two cases of material model were used to describe the material behavior of the underfill: the case1 was linear elastic model that assumed Young’s Modulus (E) and thermal expansion coefficient (CTE) were consta nt during thermal cycling; the case2 was MKIN model (in ANSYS) that had nonlinea r temperature-dependent stress-strain relationship and temperature-dependent CTE. The material model applied to the solder bump was ANAND model (in ANSYS) th at described time-dependent plasticity phenomenon of viscoplastic material. Bot h the FR-4 substrate and silicon chip were assumed as temperature-independent elastic material; moreover, FR-4 substrate is orthotropic while silicon chip is isotropic. From the comparison between numerical results of linear and nonlinear material a ssumption of underfill, (i.e. case1 and case2), the quantities of plastic strain around the interconnection from case1 are higher than that in case2. Thus, the linear

COMPLEX VARIABLE-VARIATIONALMETHOD OF SOLUTION FOR BI-METALLAMINATES WITH INTERFACE CRACKSAND ITS APPLICATION IN GLUED JOINTS

In this paper, the eigen function expansions of displacements and stresses of bi-metal laminates with interface cracks are obtained. Furthermore, the stress intensity factors are determined by the variational method to satisfy the boundary conditions and there are only line integrals in the variational equations due to the previous satisfaction of all basic equations. The computations show that this method of solution has the advantages of rapid convergency and time-saving. The results obtained by this method for homogeneous material agree with the known ones very well.

Microstructure and fracture behavior of SiO_2 glass ceramic and TC4 alloy joint brazed with TiZrNiCu alloy

Vacuum brazing of SiO2 glass ceramic and TC4 alloy using a commercially available TiZrNiCu foil was investigated. The interfacial microstructure and the fractures were examined with an optical microscope （OM） and an S-4700 scanning electron microscope （SEM） equipped with an energy dispersive spectrometer （EDS） and an electron probe X-ray microanalyzer （EPMA）. The structure of joint interface was identified by XRD （JDX-3530M）. Meanwhile, the fracture paths of the joints were comprehensively studied. The results show that processing parameters, especially the brazing temperature, have a significant effect on the microstructure and mechanical properties of joints. The typical interface structure is SiO2/Ti2O＋Zr3Si2＋Ti5Si3/（Ti,Zr）＋Ti2O＋ TiZrNiCu/Ti（s.s）/TiZrNiCu＋Ti（s.s）＋Ti2（Cu,Ni）/TC4 from SiO2 glass ceramic to TC4 alloy side. Based on the mechanical property tests, the joints brazed at 880 ℃ for 5 rain has the maximum shear strength of 23 MPa.

Multi-degree-of-freedom coupling dynamic characteristic of TBM disc cutter under shock excitation

When the tunneling boring machine(TBM) cutterhead tunnels, the excessive vibration and damage are a severe engineering problem, thereby the anti-vibration design is a key technology in the disc cutter system. The structure of disc cutter contains many joint interfaces among cutter ring, cutter body, bearings and cutter shaft. On account of the coupling for dynamic contact and the transfer path among joint interface, mechanical behavior of disc cutter becomes extremely complex under the impact of heavy-duty, which puts forward higher requirements for disc cutter design. A multi-degree-of-freedom coupling dynamic model, which contains a cutter ring, a cutter body, two bearings and cutter shaft, is established, considering the external stochastic excitations, bearing nonlinear contact force, multidirectional mutual coupling vibration, etc. Based on the parameters of an actual project and the strong impact external excitations, the modal properties and dynamic responses are analyzed, as well as the cutter shaft and bearings' loads and load transmission law are obtained. Numerical results indicate the maximum radial and axial cutter ring amplitudes of dynamic responses are 0.568 mm and 0.112 mm; the maximum radial and axial vibration velocities are 41.1 mm/s and 38.9 mm/s; the maximum radial and axial vibration accelerations are 94.7 m/s2 and 58.6 m/s2; the maximum swing angle and angular velocity of cutter ring are 0.007° and 0.0074 rad/s, respectively. Finally, the maximum load of bearing roller is 40.3 k N. The proposed research lays a foundation for structure optimization design of disc cutter and cutter base, as well as model selection, modification and fatigue life of the cutter bearing.

Investigation on dynamic characteristics of a rod fastening rotor-bearing coupling system with fixed-point rubbing

The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine.First,a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed,where the fractal theory and the finite element method are utilized.For contact analysis,a novel contact force model is introduced in this paper.Meanwhile,the Coulomb model is adopted to expound the friction characteristics.Second,the governing equations of motion of the rotor system are numerically solved,and the nonlinear dynamic characteristics are analyzed in terms of the bifurcation diagram,Poincarémap,and time history.Third,the potential effects provided by contact degree of joint interface,distribution position,and amount of contact layer are discussed in detail.Finally,the contrast analysis between the integral rotor and the rod fastening rotor is conducted under the condition of fixed-point rubbing.

Effect of Heat Input on Microstructure and Mechanical Properties of Joints Made by Bypass-Current MIG Welding–Brazing of Magnesium Alloy to Galvanized Steel

Experiments were carried out with bypass-current MIG welding–brazing of magnesium alloy to galvanized steel to investigate the effect of heat input on the microstructure and mechanical properties of lap joints. Experimental results indicated that the joint efficiency tended to increase at first and then to reduce with the increase of heat input. The joint efficiency reached its maximum of about 70% when the heat input was 155 J/mm. The metallurgical bonding between magnesium alloy and steel was a thin continuous reaction layer, and the intermetallic compound layer consisted of Mg–Zn and slight Fe–Al phases. It is concluded that bypass-current MIG welding–brazing is a stable welding process, which can be used to achieve defect-free joining of magnesium alloy to steel with good weld appearances.

Latest advances in discontinuous deformation analysis method

Discontinuous deformation analysis （DDA） method, proposed firstly by Shi [1] in 1988, is a novel numerical approach to simulate the discontinuous deformation behaviors of blocky rock structures. In DDA, the domain of interest is represented as an assemblage of discrete blocks and the joints are treated as interfaces between blocks. The governing equations of DDA are derived from Newton’s Second Law of Motion and the Principle of Minimum Potential Energy.

Design and verification of on-chip debug circuit based on JTAG

An on-chip debug circuit based on Joint Test Action Group(JTAG)interface for L-digital signal processor(L-DSP)is proposed,which has debug functions such as storage resource access,central processing unit(CPU)pipeline control,hardware breakpoint/observation point,and parameter statistics.Compared with traditional debug mode,the proposed debug circuit completes direct transmission of data between peripherals and memory by adding data test-direct memory access(DT-DMA)module,which improves debug efficiency greatly.The proposed circuit was designed in a 0.18μm complementary metal-oxide-semiconductor(CMOS)process with an area of 167234.76μm~2 and a power consumption of 8.89 mW.And the proposed debug circuit and L-DSP were verified under a field programmable gate array(FPGA).Experimental results show that the proposed circuit has complete debug functions and the rate of DT-DMA for transferring debug data is three times faster than the CPU.