A Discontinuous Elastic Interface Transfer Model of Thin Film Nanoindentation

A new model of thin film indentation that accounted for an apparent discontinuity in elastic strain transfer at the film/substrate interface was developed. Finite element analysis suggested that numerical values of strain were not directly continuous across the interface; the values in the film were higher when a soft film was deposited on a hard substrate. The new model was constructed based on this discontinuity; whereby, separate weighting factors were applied to account for the influence of the substrate in strain developed in the film and vice-versa. By comparing the model to experimental data from thirteen different amorphous thin film materials on a silicon substrate, constants in each weighting factor were found to have physical significance in being numerically similar to the bulk scale Poisson’s ratios of the materials involved. When employing these material properties in the new model it was found to provide an improved match to the experimental data over the existing Doerner and Nix and Gao models. Finally, the model was found to be capable of assessing the Young’s modulus of thin films that do not exhibit a flat region as long as the bulk Poisson’s ratio is known.     

On Poisson’s Ratio in Linearly Viscoelastic Solids

Poisson’s ratio in viscoelastic solids is in general a time dependent (in the time domain) or a complex frequency dependent quantity (in the frequency domain). We show that the viscoelastic Poisson’s ratio has a different time dependence depending on the test modality chosen; interrelations are developed between Poisson’s ratios in creep and relaxation. The difference, for a moderate degree of viscoelasticity, is minor. Correspondence principles are derived for the Poisson’s ratio in transient and dynamic contexts. The viscoelastic Poisson’s ratio need not increase with time, and it need not be monotonic with time. Examples are given of material microstructures which give rise to designed time dependent Poisson’s ratios.     

Bending analysis of thin functionally graded plates using generalized differential quadrature method

In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson’s ratio and varying Young’s modulus in the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately thick FG plate with exponential Young’s modulus is used as the benchmark. Two examples, including a thin FG rectangular plate and a thin FGC rectangular plate with sigmoidal Young’s modulus, are investigated. The numerical results of PDQ and HDQ methods reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates are similar, except that the plane strain components of the middle surface in FG plates are not zero.     

Experimental investigation on surface deformation of soft half plane indented by rigid wedge

In this work, the mechanical behavior of a block of soft material subject to large deformation from a series of wedge-shaped indenters is evaluated. Data fields acquired from digital image correlation (DIC) are compared with the existing theoretical models. The slope angles of the wedges vary from 5° to 73.5°, and the minimum measurement uncertainties of the DIC system are established in advance to define the accuracy. It is concluded that the assumptions underpinning the analytical theory make it difficult to characterize large deformation of soft materials during contact. The strain fields are also obtained from the measured displacement field and verify the previously postulated existence of two deformation sectors, namely, a so-called shrinkage sector symmetric to the loading axis and an expansion sector, which become smaller with the increasing load and decreasing wedge angle.     

Specimen and Grain Size Effects of Al1100 on Strain and Strain Rate Hardening at Various Strain Rates for Al1100

This paper is concerned with comparison of the tensile properties of Al1100 thin film in a micro-scale to that of Al1100 sheet in a macro-scale. The material properties of Al1100 film and sheet with a thickness of 96 μm and 1 mm respectively have been investigated at strain rates ranging from 0.001 to 100 s^?1. The experiments were conducted with Static Micro-Material Testing Machine (SMMTM) and High Speed Micro-Material Testing Machine (HSMMTM) for micro-specimens and with Instron 5583 and high speed material testing machine (HSMTM) for macro-specimens. A reliable jig system for SMMTM and HSMMTM has been newly developed for easy installation of a specimen and accurate alignment between a specimen and the jig system to enhance the reproducibility of tests. The digital image correlation (DIC) method is employed to measure the axial strain of the specimens. In order to obtain a fine speckle pattern for the DIC method, a novel technique is employed to print the speckle pattern with fine particles by blowing sprayed particles before printing. The grain sizes of two Al1100 specimens have been compared and the number of grains in the gauge cross-section has been calculated to obtain the grain number which is related to the specimen size effect. Electron Back Scattered Diffraction (EBSD) images were obtained for both micro-specimens and macro-specimens and analyzed to measure the grain size. The Al1100 film with a smaller average grain size shows larger strain hardening than the Al1100 sheet with a larger average grain size.     

Stress analysis of a functional graded material plate with a circular hole

This paper is to study the two-dimensional stress distribution of a functional graded material plate (FGMP) with a circular hole under arbitrary constant loads. With using the method of piece-wise homogeneous layers, the stress distribution of the functional graded material plate having radial arbitrary elastic properties is derived based on the theory of the complex variable functions. As examples, numerical results are presented for the FGMPs having given radial Young’s modulus or Poisson’s ratio. It is shown that the stress is greatly reduced as the radial Young’s modulus increased, but it is less influenced by the variation of the Poisson’s ratio. Moreover, it is also found that the stress level varies when the radial Young’s modulus increased in different ways. Thus, it can be concluded that the stress around the circular hole in the FGMP can be effectively reduced by choosing the proper change ways of the radial elastic properties.     

Use of 3-D Digital Image Correlation to Characterize the Mechanical Behavior of a Fiber Reinforced Refractory Castable

Refractory castables exhibit very low fracture strain levels when subjected to tension or bending. The main objective of this work is to show that 3-D digital image correlation (3-D DIC) allows such low strain levels to be measured. Compared to mechanical extensometer measurements, 3-D DIC makes it possible to reach similar strain resolution levels and to avoid the problem of position dependance related to the heterogeneous nature of the strain and to strain localization phenomena. First, the 3-D DIC method and the experimental set-up are presented. Secondly, an analysis of the 3-D DIC method is performed in order to evaluate the resolution, the standard uncertainty and the spatial resolution for both displacement and strain measurements. An optimized compromise between strain spatial resolution and standard uncertainty is reached for the configuration of the experimental bending test. Finally, the macroscopic mechanical behavior of a fiber reinforced refractory castable (FRRC) is studied using mechanical extensometry and 3-D DIC in the case of tensile and four-point bending tests. It is shown that similar results are obtained with both methods. Furthermore, in the case of bending tests on damaged castable, 3-D DIC results demonstrate the ability to determine Young’s modulus from heterogeneous strain fields better than by using classical beam deflection measurements.     

Techniques and Applications of the Simulated Pattern Adaptation of Wilkinson’s Method for Advanced Microstructure Analysis and Characterization of Plastic Deformation

Electron Backscatter Diffraction (EBSD) based Orientation Imaging Microscopy (OIM) is used routinely at ~500 materials laboratories worldwide for the characterization and development of diverse crystalline materials. Statistically significant data sets (~10⁷ individual EBSD measurements) can be collected and analyzed within time periods of acceptable beam stability (~10⁵s). However, limitations in angular and spatial resolution have motivated a continued search for more robust EBSD-based methods. Herein is a gathered presentation of advanced techniques in use, intended as a guide to researchers in selecting the most appropriate method for their work. Wilkinson’s method has been shown to increase angular resolution nearly two orders of magnitude to ±0.006°, facilitating measurement of elastic strain, lattice curvature, and dislocation density. A simulated pattern adaptation of Wilkinson’s method extends these measurement capabilities to polycrystalline materials, by avoiding the need for an experimental strain free reference pattern. The angular resolution limit obtained is ~0.04°. Accurate pattern center calibration, essential to the high resolution methods, is accomplished by parallelization of band edges projected onto a sphere centered at the interaction volume. FFT powered cross-correlation functions improve the spatial resolution near grain boundaries and correct for measurement inaccuracies induced by overlapping patterns. To corroborate these claims, exemplary results taken from a wedge-indented nickel single crystal, cold-worked copper polycrystal, and rolled nickel polycrystal are shown.     

Effect of interfacial contact forces in radial contact wire strand

A new mathematical model has been developed to predict the behaviour of a stranded cable assembly under the influence of interfacial radial contact forces and radial contraction of the core. A single layered cable assembly with six helical wires and a straight cylindrical core, all made with the same material, Steel has been chosen to explain this phenomenon when the assembly is under the influence of core–wire radial contact. An attempt is made in this paper to model the strand with a radial (core–wire) contact and deduce its equations of equilibrium. Numerical analysis of strand force, twisting moment, strand stiffness, contact force and contact stresses is carriedout based on the equilibrium of thin rods, and the results are compared with the earlier research work. The importance of the inclusion of interfacial forces at the contact locations and their associated effects of axial and twist slip of the helical wires on the core, is highlighted. The behaviour of the stranded cable assembly due to the contact force in the radial direction and its associated effects on the axial strain of the core due to Poisson’s effect is one more additional feature incorporated in the present work.     

Characterization of mechanical properties of aluminum cast alloy at elevated temperature

The tensile response, the low cycle fatigue(LCF) resistance, and the creep behavior of an aluminum(Al) cast alloy are studied at ambient and elevated temperatures.A non-contact real-time optical extensometer based on the digital image correlation(DIC)is developed to achieve strain measurements without damage to the specimen. The optical extensometer is validated and used to monitor dynamic strains during the mechanical experiments. Results show that Young's modulus of the cast alloy decreases with the increasing temperature, and the percentage elongation to fracture at 100℃ is the lowest over the temperature range evaluated from 25℃ to 300℃. In the LCF test, the fatigue strength coefficient decreases, whereas the fatigue strength exponent increases with the rising temperature. The fatigue ductility coefficient and exponent reach maximum values at 100℃. As expected, the resistance to creep decreases with the increasing temperature and changes from 200℃ to 300℃.     

Fourier series based FE analysis of a disc under prescribed displacements–elastic stress study

This paper examines the numerical displacements and stresses developed around a disc under horizontal prescribed displacements and at the interface separating it from the surrounding elastic soil. Since the geometry of the problem exhibits axial symmetry and the loading is non-axisymmetric, the semi-analytical FE approach is used as it proves to be efficient and economical. First, both analytical and numerical expressions for soil reaction are established and compared. Results of comparison show a very good agreement. Then, for different values of the soil Poisson’s ratio, normal radial stresses, orthoradial stresses and shear stresses distributions along radial distance reaching 20r _d (r _d is the disc radius) are presented for a disc that has either perfectly smooth or perfectly rough interfaces with the elastic medium. The paper finishes by showing the effect of the soil Poisson’s ratio as well as the relative soil/interface stiffness on the stresses developed at the interface locations.     

Crystallization of an ethylene-based butene plastomer: the effect of uniaxial extension

In this paper, the effect of uniaxial extension on the crystallization of an ethylene-based butane plastomer is examined by using rheometry coupled with differential scanning calorimetry (DSC). Uniaxial extension experiments were performed at temperatures below and above the peak melting point of the polyethylene in order to characterize its flow-induced crystallization behavior at extensional rates relevant to processing. The degree of crystallinity of the stretched samples was quantified by DSC, i.e., by analyzing the thermal behavior of samples after stretching. Analysis of the tensile strain-hardening behavior very near the peak melt temperature revealed that crystallization depends on temperature, strain, and strain rate. In addition, it was revealed that a very small window of temperatures spanning just 1–2°C can have a dramatic effect on polymer crystallization. Finally, flow-induced crystallization experiments at temperatures close to the peak melting point have shown the recrystallization of multiple crystalline structures within a polymer matrix, witnessed by double peaks within a narrow window of 89–93°C in the DSC thermographs, with the most demonstrable double peak behavior occurring at a temperature of 91°C, a temperature that is just 1°C cooler than the peak melt temperature of the polymer.     

Large Strain Shear Compression Test of Sheet Metal Specimens

A hybrid experimental-computational procedure to establish accurate true stress-plastic strain curve of sheet metal specimen covering the large plastic strain region using shear compression test data is described. A new shear compression jig assembly with a machined gage slot inclined at 35° to the horizontal plane of the assembly is designed and fabricated. The novel design of the shear compression jig assembly fulfills the requirement to maintain a uniform volume of yielded material with characteristic maximum plastic strain level across the gage region of the Shear Compression Metal Sheet (SCMS) specimen. The approach relies on a one-to-one correlation between measured global load–displacement response of the shear compression jig assembly with SCMS specimen to the local stress-plastic strain behavior of the material. Such correlations have been demonstrated using finite element (FE) simulation of the shear compression test. Coefficients of the proposed correlations and their dependency on relative plastic modulus were determined. The procedure has been established for materials with relative plastic modulus in the range 5?×?10^?4?<?(E _p /E)?<?0.01. It can be readily extended to materials with relative plastic modulus values beyond the range considered in this study. Nonlinear characteristic hardening of the material could be established through piecewise linear consideration of the measured load–displacement curve. Validity of the procedure is established by close comparison of measured and FE-predicted load–displacement curve when the provisional hardening curve is employed as input material data in the simulation. The procedure has successfully been demonstrated in establishing the true stress-plastic strain curve of a demonstrator 0.0627C steel SCMS specimen to a plastic strain level of 49.2 pct.     

Surface Forces Driven Wrinkling of an Elastic Half-Space Coated with a Thin Stiff Surface Layer

This paper studies surface instability of a coated semi-infinite linear elastic body interacting with another flat rigid body through surface van der Waals (vdW) forces under plane strain conditions. The emphasis is on the effect of the surface coating layer on the wavelength of surface wrinkling. It is shown that the surface of the coated elastic half-plane is always unstable even in the presence of a very stiff coating layer. However, the numerical results show that the stiff coating layer has a significant effect on the wavelength of the surface instability mode and can effectively prevent the surface from short-wavelength wrinkling. In particular, the surface tangential displacement associated with the surface instability vanishes when the elastic half-plane is incompressible. In this case, the in-plane rigidity of the coating layer has no effect on surface instability while the bending stiffness of the coating layer has an effect on the wave-length of the surface instability mode. Furthermore, the Poisson’s ratio of elastic half-plane has a significant role in the surface instability and the associated wave-length. C. Q. Ru is on leave from the University of Alberta, Edmonton, T6G. 2G8, Canada.     

Full-Field Strain Measurement and Identification of Composites Moduli at High Strain Rate with the Virtual Fields Method

The present paper deals with full-field strain measurement on glass/epoxy composite tensile specimens submitted to high strain rate loading through a split Hopkinson pressure bar (SHPB) device and with the identification of their mechanical properties. First, the adopted methodology is presented: the device, including an Ultra-High Speed camera, and the experimental procedure to obtain relevant displacement maps are described. The different full-field results including displacement, strain and acceleration maps for two mechanical tests are then addressed. The last part of the paper deals with an original procedure to identify stiffnesses on this dynamic case only using the actual strain and acceleration maps (without the applied force) by using the Virtual Fields Method. The results provide very promising values of Young’s modulus and Poisson’s ratio on a quasi-isotropic glass-epoxy laminate. The load reconstructed from the moduli and strains compares favourably with that from the readings.     

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTHCRACK ON ELASTIC-ELASTIC POWER LAWCREEPING BIMATERIAL INTERFACE

A mechanical model was established for mode Ⅱ interfacial crack static growingalong an elastic-elastic power law creeping bimaterial interface. For two kinds of boundaryconditions on crack faces, traction free and frictional contact, asymptotic solutions of thestress and strain near tip-crack were given. Results derived indicate that the stress andstrain have the same singularity, there is not the oscillatory singularity in the field; thecreep power-hardening index n and the ratio of Young‘s module notably influence the crack-tip field in region of elastic power law creeping material and n only influences distribution ofstresses and strains in region of elastic material. When n is bigger, the creepingdeformation is dominant and stress fields become steady, which does not change with n.Poisson‘s ratio does not affect the distributing of the crack-tip field.     

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson’s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.