Measurement of coatings' elastic properties by mechanical methods: Part 1. Consideration on experimental errors

A critical analysis of some mechanical methods employed for measuring the elastic properties of coatings is presented. A rational basis for properly choosing test methods, transducers and layer thicknesses is provided. The analyzed methods, usually applied to relatively thick coatings, include four-point bending tests and the resonance technique. General relationships for the evaluation of coatings' elastic properties, derived from the multilayer beam and plate theories, are discussed. On the basis of the error propagation theory, for different combinations of materials and layer thicknesses, the influence of typical experimental errors, test setup parameters and material properties is analyzed, and sensitivity coefficients for relative errors are discussed. The critical experimental variables and their effect on measurement accuracy are highlighted, suggesting suitable conditions for selecting specimen geometry and testing conditions. A procedure for measurement at high temperature is outlined.     

热障涂层弹性模量和残余应力测试研究

采用数字图像相关法实验研究了热喷涂制作的热障涂层的弹性模量和残余应力。首先,采用三点弯测试方法对热障涂层试件进行加载,并利用二维数字图像相关方法对热障涂层试件加装过程中的弯曲变形进行了精确的测量,进而获得了热障涂层在受拉和受压两种状态下的弹性模量,结果表明,受拉时热障涂层试件陶瓷层的弹性模量为31GPa,而受压时其弹性模量为34GPa。其次,基于内力平衡,推导了考虑曲率变化的涂层残余应力计算公式;利用三维数字图像相关法测量了喷涂前后基体曲率的变化,进而获得了涂层残余应力的大小,结果表明,热喷涂后的热障涂层残余应力为压应力,大小为-86^-70MPa。     

Boundary film shear elastic modulus effect in hydrodynamic contact. Part II: influence of operational parameters

The present paper is the subsequent research of the first part (Theor Comput Fluid Dyn, 2009). It investigates the boundary film shear elastic modulus effect in a hydrodynamic contact in different operating conditions. The hydrodynamic contact is one-dimensional, composed of two parallel plane surfaces, which are respectively rough rigid with rectangular micro projections in profile periodically distributed on the surface and ideally smooth rigid. The whole contact consists of cavitated area and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the contact. The hydrodynamic contact in a micro Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity of the film–contact interface large enough. In boundary film area, the viscosity, density, and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions, and their effective values are used in modeling which depends on the film thickness. In fluid film area, the film does not slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. It is found from the simulation results that the boundary film shear elastic modulus influences are normally negligible on the mass flow through the contact, the carried load of the contact and the overall film thickness of the contact, and the boundary film shear elastic modulus would normally influence the local film thickness in an elastic contact when the local film thickness is on the film molecule diameter scale. It is also found that the boundary film shear elastic modulus effect has the tendency of being increased with the reduction of the width of a micro contact. It is increased with the reduction of the boundary film–contact interfacial shear strength or with the increase of the critical boundary film thickness, while it is strongest at certain values of the contact surface roughness, the width ratio of fluid film area to boundary film area, and the lubricant film shear elastic modulus.

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Boundary film shear elastic modulus effect in hydrodynamic contact. Part I: theoretical analysis and typical solution

Boundary film shear elastic modulus effect is analyzed in a hydrodynamic contact. The contact is one-dimensional composed of two parallel plane surfaces, which are, respectively, rough rigid with rectangular micro projections in profile periodically distributed on the surface and ideally smooth rigid. The whole contact is consisted of cavitated area and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the contact. Analysis is thus carried out for a micro Raleigh bearing in this contact. The hydrodynamic contact in this micro Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity large enough at the film–contact interface. In boundary film area, the viscosity, density and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions, and their effective values are used in modeling, which depend on the film thickness. The analytical approach proposed by Zhang (J Mol Liq 128:60–64, 2006) and Zhang et al. (Int J Fluid Mech Res 30:542–557, 2003) is used for boundary film area. In fluid film area, the film does not slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. Conventional hydrodynamic analysis is used for fluid film area. The present paper presents the theoretical analysis and a typical solution. It is found that for the simulated case the boundary film shear elastic modulus effects on the mass flow through the contact, the overall film thickness of the contact and the carried load of the contact are negligible but the boundary film shear elastic modulus effect on the local film thickness of the contact may be significant when the boundary film thickness is on the 1 nm scale and the contact surfaces are elastic. In Part II will be presented detailed results showing boundary film shear elastic modulus effects in different operating conditions.

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Effect of dentin tubules to the mechanical properties of dentin. Part II: Experimental study

To verify the theoretical models of varying transversely isotropic stress-strain relations of dentin established in the preceding work (Part I), we perform a set of experiments. Because of the very fine tooth size, it usually seems to be difficult to directly measure the inhomogeneous and anisotropic parameters of dentin. In this paper, by the digital speckle correlation method, tensile experiments are made on the small dentin samples either parallel or perpendicular to the dentin tubules. With the theoretically predicted elastic stress-strain relations, an optimization method is proposed to fit the strain curve adapted to the experimental data. The results show that the theoretical elastic stress-strain relations coincides very well with the experimental observations. The determined Young's modulus and Poisson's ratio of dentin matrix are 29.5 GPa and 0.44, respectively, in the optimization sense. The project supported by the National Natural Science Foundation of China (19525207)     

钢质套筒被动围压下混凝土材料的冲击动态力学性能

为了研究混凝土材料在钢质套筒侧限约束下的动态力学性能参数和破坏规律,采用分离式大直径（75 mm）SHPB实验技术,测试了钢质套筒侧限约束下不同混凝土试件在不同载荷作用下轴向或径向的应力、应变峰值,平均应变率,计算了混凝土材料的损伤值,描述了加载破坏现象,对实验结果进行了分析。结果表明:混凝土材料在被动围压下,延性、抗破坏能力得到加强,具有明显的增强效应。被动围压下SHPB实验中混凝土材料的破坏应变为典型SHPB实验中破坏应变的1.8～2.8倍;破坏应力达到150 MPa以上,为静力学无围压条件下的2～5倍。     

Effect of dentin tubules on the mechanical properties of dentin. Part I: Stress-strain relations and strength criterion

As known, there is a large number of dentin tubules in dentin. These tubules have varying radii and are shaped into radially parallel pattern. The anisotropy of microstructure of dentin shows that dentin should be treated as a material of varying transverse isotropy. In this Part, the elastic stress-strain relations and the quadratic strength criterion are established in the form of having varying transverse isotropy, in the framework of micromechanics to take into account of the effect of the microstructures-dentin tubules. Simplified forms for isotropic and homogeneous cases, as well as the corresponding plane stress form of the stress-strain relations are also given. These theoretical models are very well supported by the experiments shown later in the continued paper (Part II). The project supported by the National Natural Science Foundation of China (19525207).     

Hysteresis loops predicted by isoenergy density theory for polycrystals. Part I: fundamentals of non-equilibrium thermal–mechanical coupling effects

When a polycrystal is stressed or strained at fifty percent of the corresponding yield value, damage will be inflicted non-homogeneously in the material due to the fact that the stress and/or strain distribution is non-uniform even if isotropy and homogeneity are assumed for the initial microstructure. This effect will be cumulated for each cycle of the load if the applied stress or strain is repeated continuously. Nucleation of microcracks can eventually lead to the propagation of a macrocrack.The process of damage accumulation in fatigue is defined to be sufficiently slow such that inhomogeneity of material behavior created by loading is a significant factor that can not be arbitrarily dismissed without a good reason. What this means specifically is that the difference of the stress and strain behavior at each point in a fatigue specimen must be accounted for in the analytical model in order to predict the correct cumulative effect. Such a requirement translates into a non-equilibrium formulation where the constitutive relations for each point and loading cycle must be determined separately. In this sense, the true problem of fatigue cannot be completely treated by the classical continuum mechanics approach that is limited to equilibrium mechanics for a closed system. Having said this, the isoenergy density theory will be applied to estimate the hysteresis loops of a hour-glass profile cylindrical bar specimen as recommended by the American Society for Testing and Materials (ASTM) for low-cycle fatigue.The work will be divided into two parts. Part I will cover the fundamentals of a non-equilibrium theory where the continuum elements are finite in size; they do not vanish in the limit. Therefore, size effects are immediately encountered as a function of time. General expressions for the rate change of volume of these elements with surface area are derived such that they can be computed from the nine displacement gradients. These elements can differ in size and must fit together without discontinuities or gaps to form the continuum. The condition of isoenergy energy density is invoked such that the size of these individual elements under large and finite deformation and rotation can be determined without loss in generality. The existence of such a space having the property of the same isoenergy density in all directions is thus proved. This enables the establishment of the one dimensional energy state with that in three dimensions without restriction, the absence of which has prevented the development of a complete non-linear theory of mechanics that can be solved in a direct fashion in contrast to the inverse method of assuming the displacement field. Illustration is provided for deriving the constitutive relation incrementally for a given location for the hour-glass specimen made of 6061-T6 aluminum. Once the specimen is loaded, each material point will follow a different stress and strain curve according to the local displacement rate. Hence, the method applies to material with non-homogeneous microstructure if their individual expressions can be assessed and fed into the computer.Part II computes for the non-equilibrium temperature and an entropy-like quantity that can be positive and negative. This implies that the system can absorb or dissipate energy with reference to the surrounding. Additional data for hysteresis loops are given for 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium. Accumulation of the local hysteresis energy per cycle is found to be the highest near the surface of the uniaxial specimen where load symmetry prevails. This is a consequence of the difference in accumulation of the energy density due to distortion in contrast to dilatation at the specimen center. This is why fatigue cracks tend to nucleate near the specimen surface, at a small distance towards the interior. Another distinct feature of fatigue is that the non-equilibrium temperature is found to oscillate about the ambient temperature while the local stress states fluctuate between tension and compression. This temperature reversal behavior is typical of non-equilibrium behavior and also occurs under monotonic loading. The space and time variations of the dissipated energy density for different materials are found to be related to the initial monotonic energy density or area under the true stress and true strain curve.What will be demonstrated is that no special consideration need to be made when applying the isoenergy density theory for analyzing the nucleation of micro and macrocracks in addition to failure of the specimen. Crack nucleation under fatigue is assumed to occur when the total hysteresis energy reaches a critical value. It is possible to establish a relation between the average hysteresis energy per cycle and the number of cycles to failure. The proposed method requires only a knowledge of the initial monotonic energy density curve for a given material. Predicted results for the fatigue of cylindrical bar specimens with hour-glass profile are given and they can be found in Part II of this work.     

Importance of unsteady contributions to force and heating for particles in compressible flows. Part 2: Application to particle dispersal by blast waves

Particle dispersal by blast waves is an interesting phenomenon. A model problem, i.e., a sudden release of a compressed gas–particle mixture contained in a spherical container, is employed to investigate the fundamental physics of particle dispersal. The problem is simulated by the multiphase flow models proposed in Part 1 of this article that include unsteady contributions in momentum and energy exchange between gas and particles. At early times, when particles are accelerated in the expansion fan, unsteady force and heating contributions are much larger than the corresponding quasi-steady contributions. Consequently, neglecting unsteady contributions leads to significant errors in particle front location (the boundary of the particle cloud). The complex wave interactions in the flow have strong influence on the particle motion. As a result, the particle motion is a non-monotonic function of particle density or diameter and the evolution of particle concentration is non-uniform and unsteady.     

Accurate heat transfer measurements using thermochromic liquid crystal. Part 2: Application to a rotating disc

Encapsulated thermochromic liquid crystal (TLC) can accurately measure surface temperature in a variety of heat transfer and fluid-flow experiments. In Part 1 of this two-part paper, two narrow-band liquid crystals were specifically calibrated for application to experiments on a disc rotating at high speed (5000 rpm). Part 2 describes how these crystals were used to measure the surface temperature on the disc in a transient experiment that models the flow of internal cooling air in a gas turbine. The TLC was viewed through the transparent polycarbonate disc using a digital video camera and strobe light synchronised to the disc frequency. The convective heat transfer coefficient, h, was subsequently calculated from the one-dimensional solution of Fourier’s conduction equation for a semi-infinite wall. The analysis accounted for the exponential rise in the air temperature driving the heat transfer, and for experimental uncertainties in the measured values of h. The paper focuses on the method used, and sample experimental results are provided to demonstrate the accuracy and potency of the technique.     

Actuation of the Kagome Double-Layer Grid. Part 2: Effect of imperfections on the measured and predicted actuation stiffness

The actuation stiffness of a set of steel Kagome Double-Layer Grid (KDLG) structures with brazed joints is measured experimentally and compared with predictions by the finite element method. The predicted actuation stiffnesses for the perfect KDLGs much exceed the measured values, and it is argued that the low values of observed actuation stiffness are due to the presence of geometric imperfections introduced during manufacture. In order to assess the significance of geometric defects upon actuation stiffness, finite element calculations are performed on structures with a stochastic dispersion in nodal position from the perfectly periodic arrangement, and on structures with wavy bars. It is found that bar waviness has the dominant effect upon the actuation stiffness. The predicted actuation stiffness for the imperfect structures are in satisfactory agreement with the measured values assuming the same level of imperfection between theory and experiment.     

The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations

A systematic study of failure initiation in small-scale specimens has been performed to assess the effect of size scale on “failure properties” by drawing on the classical analysis of elliptically perforated specimens. Limitations imposed by photolithography restricted the minimum radii of curvature of the specimen perforations to one micron. By varying the radius of curvature and the size of the ellipses, the effects of domain size and stress concentration amplitude could be assessed separately to the point where the size of individual grains becomes important. The measurements demonstrate a strong influence of the domain size under elevated stress on the “failure strength” of MEMS scale specimens, while the amplitude, or the variation, of the stress concentration factor is less significant. In agreement with probabilistic considerations of failure, the “local failure strength” at the root of a notch clearly increases as the radius of curvature becomes smaller. Accordingly, the statistical scatter also increases with decreasing size of the (super)stressed domain. When the notch radius becomes as small as the failure stress increases on average by a factor of two relative to the tension values derived from unnotched specimens. This effect becomes moderate for larger radii of curvature, up to a radius of (25 times the grain size), for which the failure stress at the notch tip closely approaches the value of the tensile strength for un-notched tensile configurations. We deduce that standard tests, performed on micron-sized, non-perforated, tension specimens, provide conservative strength values for design purposes. In addition, a Weibull analysis shows for surface-micromachined specimens a dependence of the strength on the specimen length, rather than the surface area or volume, which implies that the sidewall geometry, dimensions and surface conditions can dominate the failure process.