Fulin Shang

Thermal stresses analysis of a three-dimensional crack in a thermopiezoelectric solid

Abstract Thermopiezoelectric materials have attracted considerable attention because of their potential use in the smart structural systems. Due to the intrinsic coupling effects that take place among thermal, mechanical and electrical fields, the governing equations of a three-dimensional thermopiezoelectric medium are much more complex; relatively few solutions to such coupled problems are available in the literature. In this paper, we propose a method for three-dimensional axisymmetric problems of transversely isotropic thermopiezoelectric materials by means of potential functions and Fourier—Hankel transformations. As an illustrative example, a thermopiezoelectric problem of a penny-shaped crack whose surface is uniformly covered with a constant temperature different from that of the surrounding material is analyzed; the analytical expressions of stress field and electric displacement in the vicinity of the crack are obtained. The results show the characteristic 1 √ r singular behaviour of the crack-tip stress field and electric displacement.

Analysis of thermally induced cylindrical flexure of laminated plates with piezoelectric layers

Abstract The problem of thermally induced cylindrical flexure of laminated plates with piezoelectric layers is analyzed in this paper. The exact solutions are obtained in the context of the mathematical theory of elasticity. The deformation of laminated plates is considered under exponential distributions of temperature through the thickness. Different from the theory of classical laminated plates, our solutions not only satisfy governing equations and boundary conditions, but also interface continuity conditions of thermal, mechanical and electric components. Numerical results for plates with the simply supported boundary conditions are presented. It is shown that the assumption of classical lamination theory may give errors to some extent in assessing deformation. Additionally, the ‘smart’ property of structures can be reached through proper design of piezoelectric laminated plates.

Determination of high temperature mechanical properties of thermal barrier coatings by nanoindentation

Abstract A nanoindentation method is employed to measure the high temperature mechanical properties, including hardness H, Young’s modulus E and fracture toughness Kc, of 8YSZ (ZrO2+8 wt-%Y2O3) thermal barrier coatings (TBCs) under as sprayed condition and after subjecting them to thermal oxidation. The tests are conducted on the surfaces of YSZ coatings at temperatures of 250 and 450°C. The expressions for indentation H and E are deduced analytically, and the influence of testing temperature and thermal oxidation on them is discussed. An expression for estimating the fracture toughness of the coatings is also derived. The estimated fracture toughness values for the as sprayed YSZ coatings in terms of stress intensity factor at 250 and 450°C are determined to be 1·58 and 0·84 MPa m1/2 respectively. For the oxidised YSZ coatings, these values are 1·35 and 1·10 MPa m1/2 respectively. This study proves that nanoindentation tests can be performed at elevated temperatures for YSZ based TBCs.

Scale-free behavior of displacement bursts: Lower limit and scaling exponent

Plastic flow of micro-samples proceeds in an intermittent displacement bursts, showing a scale-free power-law distribution. Using maximum likelihood estimator and the Kolmogorov-Smirnov statistic, we investigate the statistics of displacement bursts such as lower limit and scaling exponent, for selected micro-samples from previous researches. The results of lower limit indicate that all the crystals considered share a common lower limit, the magnitude of which is found to be comparable to the largest burst size governed by short-range interactions (i.e., junctions). Additionally, the calculated results of the scaling exponents challenge those observed in many previous studies where other statistical techniques are employed. We demonstrate that our results are consistently manifested in the experimental data.

Effect of dislocation pile-up on size-dependent yield strength in finite single-crystal micro-samples

Recent research has explained that the steeply increasing yield strength in metals depends on decreasing sample size. In this work, we derive a statistical physical model of the yield strength of finite single-crystal micro-pillars that depends on single-ended dislocation pile-up inside the micro-pillars. We show that this size effect can be explained almost completely by considering the stochastic lengths of the dislocation source and the dislocation pile-up length in the single-crystal micro-pillars. The Hall–Petch-type relation holds even in a microscale single-crystal, which is characterized by its dislocation source lengths. Our quantitative conclusions suggest that the number of dislocation sources and pile-ups are significant factors for the size effect. They also indicate that starvation of dislocation sources is another reason for the size effect. Moreover, we investigated the explicit relationship between the stacking fault energy and the dislocation “pile-up” effect inside the sample: materials with low stacking fault energy exhibit an obvious dislocation pile-up effect. Our proposed physical model predicts a sample strength that agrees well with experimental data, and our model can give a more precise prediction than the current single arm source model, especially for materials with low stacking fault energy.

Compression-induced phase transition of GaN bulk from wurtzite phase to five-fold coordination hexagonal phase

The phase transformation of GaN bulk from the Wurtzite phase (WZ) to the hexagonal phase (HX) is studied by molecular dynamics simulation. The mechanical response and atomic structural evolution of transition are analyzed in detail. In addition, the loading rate effect on the phase transition is determined, that is, the phase transition ratio declines with a decrease of the strain rate. The WZ GaN bulk completely transforms into the HX phase in the case of compression at an ultrahigh strain rate. However, at a relatively slower strain rate, the HX phase of GaN partly nucleates and the untransformed regions are proved to be elastic deformed regions. Combined with an energy analysis, two atomic movement modes are recognized as the inducements for the phase transition and formation of elastic deformed regions. The first mode, which is responsible for the formation of elastic deformed regions, is an atomic sliding motion along the c {0001} planes. The second mode is a radial stretching atomic motion. The radi...

A molecular dynamics study on indentation response of single crystalline wurtzite GaN

A series of molecular dynamics simulations are carried out to investigate the plastic deformation in wurtzite GaN. Besides the formation of an amorphous zone under the contact region, plastic slips nucleated on the m plane (10-10), c plane (0001), r plane (10-12), and s plane (10-11) are observed in the indentation. Combined with a close analysis of critical stress that induces a specific slip on different crystalline planes, the defect evolution is discussed in detail. Slip systems of [10-1-1](10-12) and 1/3[2-1-1-3](10-11) on the pyramidal planes are not supposed to nucleate easily since higher stress is required to activate them. However, a significant decrease in the shear stress that induces a pyramidal slip could be expected if the slip evolves gradually following a two-step procedure. The gradual slips on both the r plane (10-12) and s plane (10-11) are observed in our indentation simulation; the mechanism is studied by the calculation of generalized stacking fault energy.A series of molecular dynamics simulations are carried out to investigate the plastic deformation in wurtzite GaN. Besides the formation of an amorphous zone under the contact region, plastic slips nucleated on the m plane (10-10), c plane (0001), r plane (10-12), and s plane (10-11) are observed in the indentation. Combined with a close analysis of critical stress that induces a specific slip on different crystalline planes, the defect evolution is discussed in detail. Slip systems of [10-1-1](10-12) and 1/3[2-1-1-3](10-11) on the pyramidal planes are not supposed to nucleate easily since higher stress is required to activate them. However, a significant decrease in the shear stress that induces a pyramidal slip could be expected if the slip evolves gradually following a two-step procedure. The gradual slips on both the r plane (10-12) and s plane (10-11) are observed in our indentation simulation; the mechanism is studied by the calculation of generalized stacking fault energy.

Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

Here we present a theoretical analysis on the nonlinear free vibration of a tri-cross string system, which is an element of space net-antennas. We derived the governing equations from Hamilton’s principle and obtained a linearized solution by the standard perturbation method. The semi-analytical solutions of the governing equations have not been provided referring to the solution of plate vibrating problem. This analysis revealed that natural frequencies of the tri-cross string depend on the vibration amplitude due to the geometrical nonlinearity in the constitutive equation. The geometric parameters, such as the diameters and the lengths of the constituent strings, also affect the frequency through the nonlinearity of the tri-cross string. The nonlinear natural frequency shows coupled characteristic; that is, the natural frequency of the tri-cross string varies with that of the constituent strings, but the contribution of each constituent string to the natural frequency is in different proportions.

Strain Avalanches in Microsized Single Crystals: A Theoretical Study of the Relation between the Avalanche Size and Duration*

Single crystal micropillars deform via a sequence of discrete strain avalanches, observed as displacement jumps or stress drops. Here we develop a simple crystal plasticity model to provide a quantitative expression of the relation between avalanche duration and avalanche size. It is found that the avalanche durations in scale with the averaged avalanche sizes only hold for those larger magnitudes. We show that the theoretical predictions are capable of capturing the essential aspects of scaling behaviors from micro-compression tests.

Strain Avalanches in Microsized Single Crystals: Avalanche Size Predicted by a Continuum Crystal Plasticity Model

Plastic deformation of small crystals occurs by power-law distributed strain avalanches whose universality is still debated. In this work we introduce a continuum crystal plasticity model for the deformation of microsized single crystals, which is able to reproduce the main experimental observations such as flow intermittency and statistics of strain avalanches. We report exact predictions for scaling exponents and scaling functions associated with random distribution of avalanche sizes. In this way, the developed model provides a routine for a quantitative characterization of the statistical aspects of strain avalanches in microsized single crystals.