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2023 Vol. 44, No. 2
Published: 2023-04-28
133
On the Formulation of Isoparametric Triangular Thermal Inclusion for Numerical Determination of the Displacements
In material manufacturing and mechanical design, a key factor contributing to mechanical failure is due to the localized heat fluctuations. The thermal inclusion model has been widely applied in quantitatively exploring the underlying failure mechanisms. In previous works, Eshelby’s inclusion model considering uniform thermal eigenstrains has attracted considerable attention. However, due to the complexity of the theoretical derivations, thermal inclusion studies focusing on non-uniform eigenstrains have not been comprehensively documented in literature. In the present work, polygonal inclusion subjected to linearly distributed thermal eigenstrain is examined first through analytical approach. Based on the method of Green's function and contour integral formulation, closed-form solution of the displacements produced by a typical line element is presented. Consequently, the exact solution to an arbitrary polygonal inclusion subjected to linear thermal eigenstrains can be deduced directly, in light of the superposition principle. Inspired by the isoparametric element of the finite element method (FEM), an isoparametric triangular inclusion model is proposed for numerical determination of the displacements due to any two-dimensional Eshelby’s inclusion with arbitrarily distributed thermal eigenstrains. The present numerical scheme excels the traditional FEM in that the mesh generation is merely required inside the inclusion domain, leading to a significant enhancement of the computational efficiency. As confirmed by the benchmark examples, the novel isoparametric triangular inclusion model shows robust reliability and sufficient accuracy, even for problems involving complex thermal eigenstrains.
2023 Vol. 44 (2): 133-143 [
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144
Study on Dynamic Tensile Properties of Inorganic Glass Using Flattened Circular Ring Specimen
Inorganic glass has a lot of outstanding performances and is widely employed in various engineering applications. Apart from the quasi-static load, glass is usually subjected to the dynamic loading applied by different external objects, such as bird, stone and bullet. In addition, as a kind of brittle solid, glass features a much smaller tensile strength than the compressive strength. The fracture of glass in the service process also mostly occurs under the tensile type stress. As a result, the study on the tensile mechanical behavior and failure process of glass under various loading conditions is of great importance for the design of related engineering structures. In this paper, the tensile properties of soda-lime silicate glass were tested by flattened circular ring (FCR) specimens. The quasi-static, dynamic unidirectional and uniaxial-bidirectional tests were separately conducted on the servo-hydraulic controlled universal testing machine and the electromagnetic split Hopkinson pressure bar (ESHPB). The crack initiation and propagation process in the loaded specimens was observed by a high-speed photograph system. The recorded images were related to the stress curve to reveal the dynamic failure mechanism of tensile specimen. The testing results illustrated that the tensile strength of glass characterized a positive loading rate effect, namely it was apparently enhanced with the increase of loading rate. Different from the dynamic unidirectional loading, the uniaxial-bidirectional testing system is symmetric with respect to the middle section of specimen. Accordingly, the time from loading to achieving stress equilibrium is able to be greatly reduced. Contrary to the dynamic compressive strength, the dynamic tensile strength of glass material subjected to the above two stress wave loading modes was approximately the same. It was caused by the fact that the moment of crack generation in the specimens was synchronous with that of maximal stress. According to the finite element modelling results, a significant tensile stress gradient appears along the fracture route of flattened ring and semi-circular bend (SCB) specimens. It results in the tensile strength measured by these two specimens are not the same as that obtained by the flattened Brazilian disk (FBD) specimen. Specifically, the strength of FCR specimen is the highest, followed by SCB specimen and the strength of FBD specimen is the lowest. The conclusions obtained from the present work are beneficial to the efficient use of glass materials and the prevention of glass breakage disasters. In addition, the dynamic testing method (ESHPB and FCR specimen) utilized in this work can also be applicable to other brittle solids, such as ceramics, rocks and concrete.
2023 Vol. 44 (2): 144-156 [
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157
Study on shear properties of InSb thin film
InSb thin films are widely used in high-precision photoelectric storage and infrared detection, fine mechanical property is the key to guarantee their stability under working conditions. In order to improve the shear strength of InSb material, in this paper, the shear response and atomic-scale evolution of InSb films were analyzed from four aspects of different thicknesses, temperatures, slip system orientations and hole densities to further study the influencing factors of shear strength and toughness. In this paper, the molecular dynamics code of the large scale atomic and molecular parallelist (LAMMPS) is applied for atomic-scale simulations. Firstly, InSb model is established and appropriate potential function is selected. Secondly, the boundary conditions and environmental conditions in the relaxation and shear processes are determined, respectively. Finally, the relation of shear stress-strain, the atomic strain and the dislocation analysis were studied, and the shear performance of InSb films under various conditions were discussed. As for InSb films in different aspects, we conclude that thicker films have greater elastic modulus and ultimate strength. The increase of temperature will lead to the decrease of the ultimate strength and shear toughness of the material. It is also observed that the pore shape has an obvious effect on the shear property of the material at 10% pore density, while such effect is greatly weakened at 20% pore density. In addition, it is found that the influence of orientation on shear strength and toughness of materials is not synchronous, for instance, the material has better shear strength under the slip system (130)[-310], while has better shear toughness under the slip system (110)[1-10]. The above conclusions have guiding significance for improving the shear properties of InSb thin films and synthesizing InSb electro-optical and magnetic-sensitive materials with excellent mechanical properties.
2023 Vol. 44 (2): 157-171 [
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172
Molecular Dynamics Study on the Evolution of Hydrogen Ions, Crystal Defects and Stress in Single Crystal Silicon During the Annealing to Splitting Process of Smart-Cut?
The ion implantation process and the annealing to splitting process in Smart-Cut? technology were simulated using molecular dynamics method. The splitting behavior at micro/nano-scale of hydrogen implanted single crystal silicon was investigated, as well as the evolution of distributions along the implantation direction of hydrogen atoms, silicon defects and average normal stress. Firstly, the variations of silicon crystal structure and forms of implanted hydrogen atoms and the splitting position were examined through OVITO and chemical bond analysis. Dividing the silicon crystal into elements of equal size and calculating the numbers of hydrogen atoms and silicon defects in each element, the distributions and distribution ranges of implanted hydrogen atoms and silicon defects were obtained. Splitting characteristics were then analyzed in terms of the evolution of distributions of hydrogen atoms and silicon defects. Meanwhile, variation of the distribution ranges with the annealing time was adopted to quantify the influence of hydrogen diffusion, thermal deformation and stress deformation. Finally, average normal stress was applied to feature the stress distribution. Research results show that silicon lattice structure in the hydrogen atoms concentration area is severely damaged by the atom implantation and the annealing.Various silicon-hydrogen compounds are formed via chemical reaction between hydrogen and silicon atoms and will transform their forms during the annealing to splitting process. Splitting generally occurs at the hydrogen concentration peak after the implantation process. Splitting of hydrogen implanted silicon experiences three stages: nucleation and growth of vacancy point defects without considerable local expansion of platelets, continuous growth of vacancy defects leading to remarkable local expansion of platelets, and Ostwald growth of platelets. Due to the influence of hydrogen diffusion and deformation, distributions of hydrogen atoms, crystal defects and stress exhibit different evolution characteristics for three stages with the progress of annealing to splitting process. Moreover, Numerical method established in this work to systematically and quantitatively analyse the wafer splitting in Smart-Cut? technology can be further applied to improve and optimize Smart-Cut? technology, and can also be potentially extended to ion irradiation and other related fields.
2023 Vol. 44 (2): 172-184 [
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185
Equal peak optimization of landing gear semi-active control with Magnetorheological Damper
A method is proposed to reduce the amplitude by utilizing the time delay in the magnetorheological damper of the aircraft landing gear sway system.Firstly, considering the time delay generated in the process of using magnetorheological damper to control the roll angle, and the lateral displacement and roll angle in the landing gear system, the vibration differential equation of the landing gear sway system is established, and the characteristic equation is used to solve it.The relationship between the yaw angle and the external excitation frequency. Then, due to the large amplitude of the second formant, the amplitude difference between the two peaks is too large, an equal peak optimization method is designed, and an optimization criterion is designed, which effectively reduces the amplitude of the second formant, and The difference between the two peaks is controlled between 0.02. Finally, the designed optimization criterion is verified and analyzed in the time and frequency domains, which verifies the accuracy of the calculation process and the benefit of the time-delay system to reduce the difference between the two peaks.
2023 Vol. 44 (2): 185-196 [
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197
Research on the quasi-static lateral crushing of aluminum foam sandwich tubes with V-shaped constraint
Sandwich structure with lightweight cellular core shows high specific strength and excellent energy-absorption capacity. Tube is also widely used to dissipate energy. The combination of these two kinds of structures might exhibit better performance on load-carrying and energy-absorption capacity. In this paper, sandwich tube, which consists of two concentric aluminum tubes of different diameters separated by aluminum foam, is investigated. Experimental studies on the quasi-static lateral crushing of aluminum foam sandwich tubes with V-shaped constraint are carried out. The collapse history and load-displacement curves are obtained. Three different crushing patterns are observed in the experiments, including overall yield, core shear, and indentation. Deformation and failure mechanisms of aluminum foam sandwich tubes under lateral loading and constraint are revealed. The results show that, the thickness of the aluminum foam core of the sandwich tubes plays an important role on the competition of three crushing patterns. Different factors are considered, including the geometrical parameters of the aluminum foam sandwich tubes and the angle of the lateral V-shaped constraint, and their influences on load-carrying and energy-absorption capacity are analyzed. The results show that, the load-carrying and energy-absorption capacity of the aluminum foam sandwich tubes is higher than that of the corresponding empty tubes. The load-carrying and energy-absorption capacity of sandwich tubes increases with the increase of the outer tube diameter, but decreases with the increase of the inner tube diameter. The larger the angle of the lateral V-shaped constraint is，the better performance on load-carrying and energy-absorption capacity of aluminum foam sandwich tubes is. The present work is expected to provide some insights for researchers and engineers to design such structures for energy absorption applications.
2023 Vol. 44 (2): 197-208 [
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209
Study on Fracture of Pressure Vessel with Surface Crack Based on GABP
Surface cracks often exist in pressure vessels with long service. The safety assessment based on fracture analysis has a strong practical significance for the stable running of pressure vessels. The conventional method is to evaluate the safety of pressure vessels with surface cracks by using 2D J-integral, but there are two obvious problems in practice. One is the inapplicability of 2D J-integral for surface semi-elliptic cracks, the other is the numerical simulation is time-consuming for elastoplastic vessels. Aiming to solve these two problems, an artificial neural network safety evaluation method based on the three-dimensional J-integral is proposed in this paper. The 3D J-integral is applied to quantify the stress intensity at the crack tip of surface crack in pressure vessel and the trained neural network is to predict the 3D J-integral. By finite element method, 1200 cases of elastoplastic pressure vessels with surface cracks with different geometric sizes, crack sizes and internal pressures are calculated. The 3D J-integral results of semi-elliptical crack tip are analyzed. A correction factor F is constructed to characterize the material properties, the singularity of crack tip and the influence of vessel’s geometry on the 3D J-integral. Based on the generated machine learning data set from FEM calculation, the back propagation neural network (BPNN) model is built, and the GABPNN prediction model is formed by genetic algorithm optimization. The data set is randomly divided into training set(90%) and validation set(10%). The training process shows that genetic algorithm optimization can accelerate the convergence speed of neural network and improve the stability of training. The results show that the prediction accuracy of BPNN and GABPNN model is more than 96%, and relatively accurate results can be obtained on the unknown data. The 3D J-integral of crack tip can be predicted efficiently, which provides a new idea and method for the realization of the computer aided on-site safety assessment of pressure vessels with surface cracks.
2023 Vol. 44 (2): 209-221 [
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222
Enhanced Tensile Properties of Vulcanized Natural Rubber Composites by Applications of Carbon Nanotube: Molecular dynamics simulation
A molecular dynamics (MD) simulation model for carbon nanotube(CNT)/natural rubber composite system was established to simulate the tensile process of composites with different carbon nanotube contents. The basic microscopic properties of the material and the agglomeration mechanism of carbon nanotubes were investigated based on analysis of free volume fraction, mean square dis-placement and radius of gyration for the composite system. By calculating the interfacial energy between carbon nanotubes and natural rubber, it is found that the change of the total potential energy of the system during loading is mainly caused by the vulcanized natural rubber matrix, in which the non-bonding energy plays a leading role. Due to the good mechanical properties of carbon nanotubes and the interfacial energy generated by the interaction with natural rubber molecular chain, the mechanical properties of materials are improved, and the yield stress of materials increases significantly to the increase in carbon nanotube content.
2023 Vol. 44 (2): 222-231 [
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232
Hysteretic behavior of SMA laminated variable stiffness horizontal universal damper
A new type of SMA laminated variable stiffness horizontal universal damper was developed utilizing the superelastic properties of NiTi shape memory alloy (SMA) wires, and the essential configuration and working mechanism were introduced. The calculation model of damper restoring force-displacement hysteretic curve was established and the parameter analysis was carried out. Results shows that the restoring force-displacement hysteretic curve of the damper presented a full spindle shape, the damper possessed good energy dissipation capacity, self resetting function, large stroke and unique variable stiffness characteristics; the maximum stroke of the damper decreased continuously whereas the unit cycle energy dissipation increased at first and decreased afterwards with the pre-tension strain of SMA wire increasing from 0.03 to 0.06; with the increase of SMA wire diameter, the stiffness and energy dissipation capacity of the damper increased whereas the maximum stroke and equivalent damping coefficient remain unchanged; the maximum stroke and unit cycle energy consumption increased wheras the stiffness decreased continuously with the increase of the number of damper layer; with the number of SMA wires in each damper layer increasing from 8 to 16 and 32, the stiffness and unit cycle energy dissipation increased, however, the change of the maximum stroke and equivalent damping coefficient was not obvious.
2023 Vol. 44 (2): 232-248 [
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249
Application of smooth edge domain continuous-discontinuous cellular automaton in crack propagation
Aiming at the crack propagation problem of rock cracks, the strain smoothing technique is combined with the continuous-discontinuous cellular automaton method, and the smooth strain fields of the discontinuous crack penetration element and the crack tip element are constructed, and the fast adaptive smooth edge domain continuous-discontinuous cellular automaton is proposed. Using the Gaussian divergence theorem to solve the smooth strain matrix, the area integral of the element is converted into a smooth domain boundary line integral, and the calculation expression of the smooth boundary domain continuous-discontinuous cellular automaton strain matrix is deduced, and an adaptive acceleration algorithm is established in which the acceleration factor is updated synchronously with the cell update. Based on this, the optimal acceleration factor is automatically obtained with the updating, and the convergence speed is greatly improved compared with the traditional cellular automaton method. The analysis and calculation program are compiled with C++, and the multi-crack crack propagation process is simulated and compared with the conventional extended finite element method. It is found that the smooth edge domain continuous-discontinuous cellular automaton has significant advantages over the conventional finite element in the accuracy, stability and convergence of the solution.
2023 Vol. 44 (2): 249-263 [
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264
Study on the evolution law of tension fracture of diameter compression rock under internal driving force
Rock is a complex natural non-uniform brittle material. There is a big gap between tensile and compressive properties. Tensile failure often controls the overall stability of rock engineering. In this paper, the difference of internal forces acting on a certain point in rock within a certain scale is defined as internal driving force. Experiments on crack propagation of diametral compression rock are carried out. A high-speed camera was used to capture the transient tensile crack growth process and the first principal strain evolution process was analyzed by digital speckle software. The continuous-discontinuous method is used to simulate the tensile crack growth process of diametrically compressed rock. It can be seen from the experimental results that the crack propagation of tension fracture can be divided into three stages: the cumulative stage of tension fracture deformation (macro crack free), stable stage of tension fracture crack propagation and dynamic stage of tension fracture crack propagation. It compares the experimental and numerical results with the analytical solutions. The propagation law of experimental and numerical results is basically consistent, but different from the analytical solution of elasticity. The analytical solution is based on the assumption of homogeneity, while the external load and the rock itself are non-uniform. The external load and the inhomogeneity of the rock itself are the main reasons for the difference between the crack initiation point, propagation path and the analytical solution. Through comprehensive analysis, the law of tensile crack growth is given: the internal driving force is used to analyze the propagation law of tensile crack. When the internal driving force exceeds the connecting force of atom or molecule, the propagation direction is perpendicular to the direction of internal driving force. The study of crack propagation and evolution law of rock tension fracture can provide theoretical basis for the prevention and control of rock engineering tension failure.
2023 Vol. 44 (2): 264-272 [
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