Elastic-plastic characterization of thin films with spherical indentation

Indentation characterization of thin films has most recently been investigated with currently available ultramicroindentation hardness instruments that use a pyramidal diamond tipped indenter. With these instruments determination of the hardness at depths of penetration as shallow as 5–10 nm is possible. However, the problems associated with such indenters are the inability to characterize the indenter tip radius and the fact that pointed indenters essentially perform tests at constant plastic strain. An alternative approach to measuring the mechanical properties of thin films is to use spherically tipped indenters of known tip radius and to follow the transition from elastic to plastic deformation. The Hertzian analysis provides the basis for determining the elastic behaviour and it may be modified to examine the elastic-plastic transition. From such observations it is possible to determine the variation in the mean indentation pressure with depth of penetration and to construct an equivalent stress-strain response of a material. Examples of this approach are given for bulk materials and metallic and polymeric thin films. Data have been collected with a UMIS-2000 instrument and have been analysed and simulated on the basis of the approach outlined above.     

Elastic-plastic analysis of indentation damage: cyclic loading of copper

This is the second in a two-paper series examining the elastic-plastic deformation of a metallic target material under repeated impact. This paper examines the effect of statically cyclic loading on copper and numerical calculations have been performed up to ten cycles. The extent of the loading phase in each cycle is specified by a constant external work done by the indenter. The deformed configuration of the target material, the locus of material flow, and elastic-plastic boundaries due to cyclic loading are presented. There is a saturation of the stress field near the bottom of the indented crater after the first few cycles of loading. A residual tensile stress field in the direction normal to the target surface exists underneath the indenter in every cycle, which is responsible for the formation of subsurface layer cracks. Results of the coefficient of restitution obtained from the analysis and experiments are also presented.     

压痕应变法测量残余应力的不确定度分析

压痕应变法是近期出现的一种非常有价值的(焊接)残余应力测量技术,它具有无损、快捷、精确、成本低等特点。采用该技术测量残余应力时的误差大小或不确定度分析是人们关注的问题之一。应用B类评定法对采用该技术测量Q345低合金钢中焊接残余应力的不确定度进行了详尽分析,结果表明,应力相对不确定度的大小主要决定于应变的绝对值,低应变情况下的相对不确定度主要由重复性试验的应变不确定度决定。一般情况下,应力的标准不确定度数值为20～30MPa。     

Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finite-element method

A technique to evaluate the dynamic stress intensity factors and T-stress is developed by extending the scaled boundary finite-element method. Only the boundary of the problem domain is discretized. The inertial effect at high frequencies is modeled by a continued fraction solution of the dynamic stiffness matrix without introducing an internal mesh. Standard time-stepping scheme is applied to perform response history analyses directly in the time domain. The internal displacement field is obtained by numerical integration after removing the stress singularity. The dynamic stress intensity factors and the T-stress are evaluated directly based on their definitions. No asymptotic solution around the singular point is required. Numerical examples of cracks in homogeneous and bi-material plates demonstrate the simplicity and accuracy of this technique.     

Adaptive finite-element method for diffraction gratings

A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.     

Perturbation finite-element method for magnetic circuits

Accurate magnetic flux distributions are calculated in magnetic circuits via a subproblem finite-element (FE) method based on a perturbation technique. An approximate FE problem considering ideal flux tubes is first solved. It gives the source for FE perturbation problems considering the flux tubes with their exterior regions, accounting thus for leakage fluxes, as well as for changes of material properties and shapes. The proposed technique aims to accurately quantify the gain given by each model refinement on both local fields and global quantities and to justify the usefulness of this refinement. It is also well adapted to parameterised analyses on geometrical and material data.     

Stabilized finite-element method for the stationary Navier-Stokes equations

A stabilized finite-element method for the two-dimensional stationary incompressible Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation of the stationary Navier-Stokes equations. By satisfying this condition, the stability of the Q₁–P₀ quadrilateral element and the P₁–P₀ triangular element are established. Moreover, the well-posedness and the optimal error estimate of the stabilized finite-element method for the stationary Navier-Stokes equations are obtained. Finally, some numerical tests to confirm the theoretical results of the stabilized finite-element method are provided.     

A perturbation method for predicting the temperature and stress sensitivities of quartz vibrating structures simulated by finite-element analysis

Thermal and mechanical sensitivities of vibrating structures and wave guides are key parameters for the optimization of high stability resonant devices operating in the ultrasonic frequency range (from a few tenth of kilohertz to a few gigahertz). In this paper, the possibility to simulate and predict temperature coefficients of frequency (TCF) of quartz transducers of any shape as well as their stress sensitivity coefficients is addressed. The theoretical developments based on harmonic finite-element analysis coupled with a variational perturbation method are detailed, showing how to derive the regarded parameters. The proposed approach is validated using a two-dimensional (2-D) model of a plane face-bulk acoustic resonator for which an analytical model can give access to both TCF and stress sensitivity coefficients. It is then applied to a 2-D model of convex plane bulk acoustic resonator of singly rotated quartz and used to compute the first order TCF of a 3-D model of a tuning fork structure. In the latter case, the importance of considering the actual excitation of the device is demonstrated, allowing for the accurate definition of angular loci for which thermal compensation can be expected, in agreement with literature. Possible extensions and improvements of the proposed method is discussed in conclusion.     

Elastic-plastic fem calculations of the stress distribution of notches with different geometry

A two-dimensional elasto-plastic finite element analysis of double notched rectangular tensile specimens with different notch geometries has been performed. The maximum value of stress concentration below the notch is given as function of the applied stress for varying notch radius and notch angles. The results of the finite element method are compared with the predictions of the slip line theory.     

Determination of the critical stress intensity factor of glass under conditions of elastic contact by the dynamic indentation method

The possibility of determining the fracture toughness under conditions of elastic contact during dynamic indentation is analyzed. Procedures are proposed for estimating the critical stress intensity factor from the parameters of initiating cracks and directly from the contact force versus indentation depth curve during dynamic indentation.     

Radiative transfer in the atmosphere-ocean system: the finite-element method

The finite-element method has been applied to solving the radiative-transfer equation in a layered medium with a change in the refractive index, such as the atmosphere-ocean system. The physical processes that are included in the algorithm are multiple scattering, bottom-boundary bidirectional reflectivity, and refraction and reflection at the interface between the media with different refractive properties. The incident radiation is a parallel flux on the top boundary that is characteristic of illumination of the atmosphere by the Sun in the UV, visible, and near-IR regions of the electromagnetic spectrum. The necessary changes, compared with the case of a uniformly refracting layered medium, are described. An energy-conservation test has been performed on the model. The algorithm has also been validated through comparison with an equivalent backward Monte Carlo code and with data taken from the literature, and optimal agreement was shown. The results show that the model allows energy conservation independently of the adopted phase function, the number of grid points, and the relative refractive index. The radiative-transfer model can be applied to any other layered system with a change in the refractive index. The fortran code for this algorithm is documented and is available for applications.