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2019 Vol. 40, No. 3
Published: 2019-06-28
193
Progress in Mechanical Properties, Deformation Mechanisms and Multiscale Simulations of Gradient Nanostructured Metals
Gradient nanostructured metals are increasingly being investigated due to their unique mechanical properties and deformation mechanisms, and are emerging as a new research frontier in mechanical science and mechanics. This review summarizes strength, ductility, fatigue resistance and other mechanical properties of gradient nanostructured metals, followed by a discussion about plastic deformation mechanisms of gradient nanostructured metals, including grain growth, plastic strain gradient and geometrically necessary dislocations. Multiscale modeling and simulations of gradient nanostructured metals are introduced with a focus on finite element method and molecular dynamics simulation method. A range of challenges to the research of mechanics of gradient nanostructured metals are proposed in the end.
2019 Vol. 40 (3): 193-212 [
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213
Strain Burst Criteria for Microscale Metal Based on Energy Change
Significant strain burst phenomenon is observed during the plastic deformation of microscale metal. This work aims to develop the strain burst criteria and judging conditions for different deformation stages of microscale metal, taking single-crystal Ni micro-pillar under force loading and Au nano-pillar under displacement loading as examples. Based on the classical Hill’s stability condition in continuum plasticity theory, the criteria for the occurrence and termination of the strain burst are proposed according to the variations of kinetic energy during the deformation process of small pillars. Furthermore, the internal energy evolution of pillars during the deformation process is analyzed. Based on the simultaneous changes of kinetic energy and internal energy, the judging conditions for different deformation stages of pillars are established. Then, these theoretical developments are verified by comparing their finite element outputs with the experimental and theoretical results in literature. It is found that the proposed strain burst criteria using kinetic energy increment can effectively identify the occurrence and termination of the strain burst events, and the judging conditions based on energy changes are capable of distinguishing different deformation stages of micro- and nano-pillars. The applicability and merits of the newly proposed criteria are discussed at the end of the paper.
2019 Vol. 40 (3): 213-224 [
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218
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225
Second-order Sensitivity Dynamic Optimization Design of Structural Element Size with Frequency- prohibited Band
Adjusting structural dynamic characteristics by searching reasonable structural design parameters to avoid the predominant frequencies or high energy bands corresponding to the external excitation for structures subjected to wind, earthquake or vehicle-borne excitation, which can inevitably improve the safety of structures during service. In this paper, an optimal method of structural dynamic design with dimension constraints, single frequency-prohibited band constraint and structural weight minimization is studied. A single factor iteration algorithm of second-order sensitivity of structural frequency to variables based on the Kuhn-Tucker condition and the sensitivity of frequency to variables is deduced and established by Taylor's second-order expansion formulation. The first-order and second-order sensitivity computing programs in terms of the same example are developed based on the platform of MATLAB. The example shows that the optimization results of both algorithms are identical, but the second-order sensitivity algorithm is more efficient and convergent than the first-order algorithm, and the correction factor doesn’t need to be adjusted in the whole process of optimization, which is more convenient for operators. The reasonable range of the single factor is given. It is found and preliminarily demonstrated that" no weight reduction", when all design variables do not reach the upper and lower bounds of the constraints, can only be regarded as the necessary condition for optimum, while "higher-order frequency converges to the upper limit of the frequency-prohibited band " should be a sufficient and necessary condition, which is more suitable as a convergence criterion. The conclusion can effectively discriminate the "pseudo-optimal" situation. Based on data representation in the example, it is preliminarily revealed that the modification of optimization variables is mainly dominated by frequency gradient, and the magnitude of frequency gradient is inversely proportional to the magnitude of variable modification. The work done here has important theoretical guiding value and practical significance for the design of wind resistance, earthquake resistance, dynamic reinforcement or reconstruction of structures in service.
2019 Vol. 40 (3): 225-237 [
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188
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238
Crack growth simulation in heterogeneous material using the adaptively refined XFEM
An adaptive mesh refinement method based on the quadtree structure is proposed to model the fracture problem of heterogeneous material. By introducing the shape functions of the virtual node polygonal elements into the approximation of standard extended finite element method (XFEM), a regulatable multi-level refined mesh in the vicinity of the discontinuities can be created. Especially for the cracks, the dynamic mesh refinement and coarsening near the crack tips can be realized by the proposed method. According to above schemes, a novel crack growth computational method is thus formulated as VP-XFEM in the framework of linear elastic fracture mechanics. To verify the computational accuracy and efficiency of VP-XFEM, two fracture problems of structures containing cracks and holes are simulated using this method. The results show that the VP-XFEM can achieve better accuracy and efficiency compared with the standard XFEM.
2019 Vol. 40 (3): 238-247 [
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375
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248
Experimental study on in-plane nonlinear vibration of a cable-stayed bridge subjected to a hamonic excitation
The vibration problem of cable-stayed bridge cables has always been a research hotspot in the field of bridge engineering. In order to reveal mechanical mechanism of the large vibration of cables, our group established a full-bridge refined model of cable-stayed bridge. The possible nonlinear vibration behaviors of cable-stayed bridges under single-frequency excitation are studied in the paper. Firstly, modal parameters of this model are examined by free vibration test, which is compared with two types of finite element models (OECS model and MECS model). The results are in good agreement with each other. Secondly, the non-linear response of cable-stayed bridge model under a single vertical harmonic excitation is studied. The research shows that when the excitation frequency is close to the global modal frequency of the cable-stayed bridge, the phenomenon of primary resonance is observed on the beam, which causes great amplitude parametric and forced vibrations of some long cables; when the ratio of excitation frequency to the first-order in-plane frequency of the cable is 1:2 or 2:1, the Superharmonic resonance or Subharmonic resonance phenomenon have also been observed in the cable.
2019 Vol. 40 (3): 248-259 [
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231
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260
《Fatigue life prediction under multiaxial loading using energy-based models》
Abstract: For engineering components under multiaxial loadings, fatigue life prediction is significant for guaranteeing their structural safety. A new energy-based model for fatigue life prediction is proposed based on the critical plane approach. The proposed model takes the different energy parameters acting on critical plane as the damage parameters to distinguish different failure modes. These damage parameters can reflect not only the mean stress effect but also the influences of normal and shear components on fatigue damage. The proposed model and three other classical energy-based models were used to evaluate the fatigue life of six kinds of materials under multiaxial loading. Results show that the proposed model has better prediction accuracy and engineering applicability.
2019 Vol. 40 (3): 260-268 [
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383
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269
Fracture characteristics of cracked hole in piezoelectric solids considering surface effect
When defects (holes and cracks) in the piezoelectric material are on the order of nanometers, the surface properties of the defects have great influences on the distributions of the stress fields and the electric displacement fields, and the surface effects are not negligible. In this paper, the surface electroelastic constants of the defects are introduced to extend the size of the cracked circular hole in the piezoelectric solids to nanoscale. The fracture characteristics of piezoelectric solids containing two edge cracks emanating from a circular hole with surface under antiplane mechanical loads and inplane electric displacement loads was investigated theoretically. Based on the Gurtin-Murdoch surface model, the closed solutions of the stress field and electric displacement field of the problem are obtained using the complex potential function electroelastic theory via constructing a conformal mapping function. Analytical s of the stress intensity factor, electric displacement field factor and energy release rate at the crack tip are presented. The influences of the geometric parameters of the cracked hole, the applied mechanical load and electrical load on the electroelastic fields intensity factors and the energy release rate are discussed. The major results are as follows: The dimensionless stress intensity factor and the dimensionless electric displacement field factor of the nanoscale cracked hole are different, and both have significant size dependence. The dimensionless electroelastic field factors increase monotonously with the increase of the relative length of the crack to a fixed value. The dimensionless energy release rate of the nanoscale cracked hole has a significant size effect. The larger the hole and the longer the crack are, the greater the normalized energy release rate is. The effect of the mechanical loads on the normalized energy release rate is affected by the applied electrical loads. The normalized energy release rate increases first and then decreases with the increase of the electrical loads.
2019 Vol. 40 (3): 269-276 [
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164
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277
Study on quasi-static loading velocity in explicit calculation of elastic and elastic-plastic materials
Abstract: The dynamic explicit algorithm is based on the principle of time integration. It is more applicable to nonlinear problems than the static implicit algorithm. In order to use this method to calculate nonlinear materials including rock and soil, it is extremely necessary to analyze selection of quasi-static loading speed of the dynamic explicit algorithm in simulation calculation, because the kinetic energy influences in the explicit algorithm will result in fluctuation of results. How to look for balance as reducing simulated consumption time and result accuracy is the research emphasis in this thesis. The fluctuation ratio of the load-displacement curve is proposed in this research to evaluate the effect of quasi-static calculation. First of all, the plane strain simulation test of elastic materials is conducted to analyze the effect of the elastic modulus, density, Poisson’s ratio and confining pressure on the value of quasi-static load speed. The findings indicate that the increase of elastic modulus, Poisson’s ratio and confining pressure will increase quasi-static load speed, while the increase of density will reduce the quasi-static load speed. Correlation analysis between each influence factor and quasi-static load speed gives the empirical formula of quasi-static load speed. At last, the elastic-plastic constitutive model that can reveal complicated mechanical property of sandy soil is selected to develop the plane strain simulation test. The applicability difference in the empirical formula of quasi-static load speed between elastic materials and elastic-plastic materials is conducted contrastive analysis, and the application suggestion formula is proposed.
2019 Vol. 40 (3): 277-286 [
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372
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