Improved corrosion behavior of nanocrystalline Cu–20Zr films in HCl solution

Both in-plane and through-thickness linear viscoelastic properties of the single-wall carbon nanotubes (SWNT)/polyelectrolyte multilayer nanocomposite film were characterized using nanoindentation. The SWNT nanocomposite films with a SWNT loading of 4.7% by weight was made by layer-by-layer assembly (LBL). The viscoelastic functions of materials were measured using two methods: (1) the direct differentiation method from the load–displacement data; and (2) the material parameter extraction method by fitting the analytical load–displacement relation to nanoindentation data. Results from both methods agree well. The in-plane Young's moduli of the films were also measured from small-scale tensile tests; the results agree well with nanoindentation data. This investigation indicates that the in-plane and through-thickness linear viscoelastic properties are almost identical for a SWNT nanocomposite made by LBL technique, despite the preferred orientation of the SWNT in a nanocomposite film.     

Indentation fatigue behaviour of polycrystalline copper

Conventional indentation experiments have been widely used to extract the mechanical properties of materials from a load–depth curve. However, most of them are focused on static loading conditions. In the present study, the detailed indentation fatigue behaviour of polycrystalline copper under cyclic loading was studied experimentally. The experimental work emphasized indentation depth propagation behaviour such as the influence of overloading and underloading. It was shown that an increase in the maximum load can accelerate indentation depth propagation, while a decrease in the maximum load can retard indentation depth propagation. Further experiments showed that a sudden increase in maximum load after achieving a steady state followed by cycling at normal loading conditions can also delay indentation depth propagation, while a sudden drop in maximum load had a contrary effect. Those experimental phenomena implied that there were some similarities in the behaviour of indentation fatigue depth propagation and conventional fatigue crack propagation. In the following analysis, optical microscopy (OM) and scanning electron microscopy (SEM) were used to investigate the microstructures of the indentation cross-sections. The results revealed that the nucleation and accumulation of cavities to develop cracks was promised to be the main damage mechanism during the indentation fatigue.     

A simple framework of spherical indentation for measuring elastoplastic properties

Based on the indentation load–displacement curve, spherical indentation may deduce material elastoplastic properties from the measurements at several depths (which mimics the dual/plural sharp indentation method). The previous approaches, however, have very complex formulations and involve many fitting parameters that lack theoretical backgrounds; moreover, studies based on shallow indentation may not lead to unique solution. To close these gaps, we propose a simple framework of spherical indentation based on a new limit analysis-based representative strain analysis, which contains minimum number of fitting parameters. Two simple equations of the normalized loading work (at two different depths) are proposed, which can determine the material plastic properties accurately from the loading curve. In addition, by using either the established Fischer-Cripps method or an extra equation based on the contact stiffness, both the elastic and plastic properties are determined with reasonable accuracy. The simple framework may be useful for guiding the measurement of elastoplastic properties via spherical indentation.     

Static indentation and unloading response of sandwich beams

This paper deals with analysis of foam core sandwich beams subject to static indentation and subsequent unloading (removal of load). Sandwich beams are assumed continuously supported by a rigid platen to eliminate global bending. An analytical model is presented assuming an elastic-perfectly plastic compressive behaviour of the foam core. An elastic part of indentation response is described using the Winkler foundation model. Upon removal of the load, an elastic unloading response of the foam core is assumed. Also, finite element (FE) analysis of static indentation and unloading of sandwich beams is performed using the FE code ABAQUS. The foam core is modelled using the crushable foam material model. To obtain input data for the analytical model and to calibrate the crushable foam model in FE analysis, the response of the foam core is experimentally characterized in uniaxial compression, up to densification, with subsequent unloading and tension until tensile fracture. Both models can predict load–displacement response of sandwich beams under static indentation and a residual dent magnitude in the face sheet after unloading along with residual strain levels in the foam core at the unloaded equilibrium state. The analytical and FE analyses are experimentally verified through static indentation tests of composite sandwich beams with two different foam cores. The load–displacement response, size of a crushed core zone and the depth of a residual dent are measured in the testing. A digital speckle photography technique is also used in the indentation tests in order to measure the strain levels in the crushed core zone. The experimental results are in good agreement with the analytical and FE analyses.     

Material characterization by instrumented spherical indentation

It was illustrated by the author in the previous work that combinations between material properties and indentation parameters can be used as mixed parameters in dimensionless functions to capture the sharp indentation response of materials. These issues are further extended for spherical indentation in the present study. Instrumented spherical indentation was performed by a parametric finite element analysis for a wide range of materials with maximum indentation depth-indenter radius ratios rising from 0.01 to 0.3 to investigate several fundamental features within the frame work of limit analysis. Frictional effects are taken into account. Regarding dimensional analyses and using a Taylor series expansion, a new set of dimensionless functions is constructed for spherical indentation parameters and hardness associated to a 70.3° conical indenter. Based on formulated functions, a reverse analysis procedure is suggested to extract material properties and hardness from spherical indentation force-depth curves with respect to two different indentation depth-indenter radius ratios. Effects of indenter compliance on indentation parameters and reverse results are considered. The accuracy of the proposed method is studied and discussed by carrying out reverse and sensitivity analyses for 22 representative materials with rigid and deformable indenters.     

弹塑性比例叠加的锥压入半解析模型与试验方法

基于能量密度等效,考虑圆锥压入(锥压入)过程中线性律纯弹性和幂律纯塑性的应变能比例叠加,提出了弹塑性应变能比例叠加的锥压入载荷-位移模型(Load vs. Displacement Model based on Proportional Superposition of elastoplastic-energy under conical indenting,LDM-PS),进而提出了获取材料Ramberg-Osgood律(R-O律)应力-应变关系的锥压入试验方法。针对80种设定材料,通过LDM-PS预测的载荷-位移曲线(正向预测)与有限元分析结果密切吻合,并且以有限元分析(Finite Element Analysis,FEA)所得载荷-位移曲线作为试验模拟曲线,采用两种锥角圆锥压头分别对平滑材料表面进行两次单锥压入加载(双锥压入),可通过对双锥压入的两个载荷-位移曲线的加载阶段按抛物律(Kick律)回归可实现R-O律参数的求解。由LDM-PS预测的R-O律应力-应变关系曲线(反向预测)与FEA的条件关系曲线密切吻合;针对8种金属材料完成了双锥压入试验,通过锥压入试验新方法预测的应力...     

Evaluation of bias-extension and picture-frame test methods for the measurement of intraply shear properties of PP/glass commingled fabrics

Efforts are currently devoted to the development of numerical tools for predicting the forming process of continuous fiber-reinforced thermoplastic composites. To ensure good predictions, reliable experimental measurements of the laminate properties must be performed at the processing temperature. This paper presents experimental results of the intraply shear properties measured on a polypropylene/glass fabric using two different methods known as the bias-extension and the picture-frame testing methods. Based on kinematic equations, both methods of measurement are discussed in regards to their respective weaknesses, mainly related to the difficulty to measure precise shear angles in the bias-extension method and the undesired fiber tension invalidating the load–displacement curve in the picture-frame test. To remove these difficulties, a modified version of the picture-frame test is proposed. This new method avoids fiber tensioning during testing and is considered more appropriate to capture the influence of the fabric architecture on the measured properties. Good correlations between the load–displacement curves and viscosities measured with the modified picture-frame and bias-extension methods were obtained compared to the standard picture-frame method.     

Coulomb friction controlled bridging stresses and crack resistance of ceramic matrix composites

Bridging stresses in ceramic matrix composites (CMC) are calculated taking into account the effect of Poisson contraction of fibre and matrix during loading and a two parameter Weibull distribution of fibre strength. A parameter study is performed in order to assess the influence of the constituent properties. The bridging stress curve provides the link from the micromechanical analysis to the prediction of macroscopic composite behaviour. The load–deflection behaviour of pre-notched CMC specimens is derived by application of the method of weight functions. The predictions are compared with experimental results giving information about the actual properties of the material.     

On the effect of substrate properties on the indentation behaviour of coated systems

The indentation behaviour of an elastoplastic coating–substrate system is investigated using a combination of dimensional and finite element analyses. Scaling functions relating the indentation load–depth curves to coating and substrate mechanical properties are given. Based on these scaling functions, the indentation behaviour of various coated systems is examined. The critical indentation depth to coating thickness ratio below which the substrate material has a negligible effect on the indentation response of the coated system is identified for various generic coating–substrate systems. Such ratio is given in terms of the yield strength and Young’s modulus of the coating and substrate, i.e. σ_yc/σ_ys and E_c/E_s. The results of parametric studies revealed that the commonly used rule that the maximum indentation depth should be less than 10% of the coating thickness, is applicable only when σ_yc/σ_ys<10. However, indentation experiments should be carried out up to a maximum depth of 5% of the film thickness to avoid any influence from the substrate when σ_yc/σ_ys≥10 and E_c/E_s>0.1.     

A dual conical indentation technique based on FEA solutions for property evaluation

The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity so that we can obtain only one parameter from an indentation loading curve, which makes different materials have the same load-displacement relation. Most studies to evaluate elastic-plastic properties by using the geometrical self-similar indenter have therefore tried to use dual/plural indentation techniques, on the basis of the concept of representative strain/stress varying with the indenter angle. However, any suggested representative concept is not universally operative for real materials. In this work, we suggest a method of material property evaluation without using the concept of representative strain. We begin the work by studying the characteristics of load-depth curves of conical indenters via finite element (FE) method. From FE analyses of dual-conical indentation, we investigate the relationships between indentation parameters and load-depth curves. The projected contact diameter is expressed as a function of the indenter angle, tip-radius, and material properties, which allows us to simply predict the elastic modulus. Two mapping functions for two indenter angles (45° and 70.3°) are presented to find the two unknowns (yield strain and strain-hardening exponent) via dual indentation technique. The method provides elastic modulus, yield strength and strain-hardening exponent with an average error of less than 5%. The method is valid for any elastically deforming indenters. We also discuss the sensitivity of measured properties to the load-displacement curve variation, and the difference between conical and Berkovich indenters.     

Impact and dynamic response of high-density structural foams used as filler inside circular steel tube

Structural foams have good energy absorption properties and are effective in reducing the vulnerability of sandwich structures. This research investigated the impact and dynamic response of three different high-density polymeric structural foams; designated A, B and C for proprietary reasons. Foam-C had the lowest density out of the three; density of foam-B was approximately twice the density of foam-C, while the density of foam-A was about three times the density of foam-C. The cylindrical foam samples were initially impacted at different velocities in a DYNATUP Model 8250 instrumented impact test machine and their energy absorption was characterized from the resulting load–deflection data. Each of the three foams was then modeled as filler inside a circular steel tube of 0.8 mm thickness. Non-linear finite element analysis was performed under displacement controlled quasi-static compressive monotonic loading using PATRAN as pre-processor and ABAQUS Standard commercial software. The area under the load–deflection curve was calculated to obtain the absorbed energy and the crush loads for the three foam fillers were compared. Results indicate that foam-A having the highest density was more effective as filler inside the circular steel tube, with the intermediate density foam-B performing equally well under uni-axial compressive loading. Foam-C, which had the lowest density, was found to be ineffective as filler in this application due to large differences in stiffness between this foam and the enclosed steel tube.

A TA Instruments Model 983 DMA (dynamic mechanical analyzer) was used for obtaining the storage and loss modulus along with the damping and glass transition properties of the different density structural foams. Frequency multiplexing was also used in conjunction with the time–temperature superposition principle for characterizing the long-term behavior of these viscoelastic foams.     

Measurement of Creep Compliance of Solid Polymers by Nanoindentation

Methods to measure the local surface creep compliance of time-dependent materials are proposedand validated in the regime of linear viscoelasticity using nanoindentation. Two different bulkpolymers, Polymethyl Methacrylate (PMMA) and Polycarbonate (PC), were employed in thevalidation study; though it is expected that the methods developed herein can be applied for verysmall amounts of materials and heterogeneous materials. Both Berkovich and sphericalnanoindenters were used to indent into the material in nanoindentation tests. Two loading historieswere used: (1) a ramp loading history, in which the indentation load and displacement wererecorded; and (2) a step loading history, in which the indentation displacement was recorded as afunction of time. Analysis of the linearly viscoelastic material response was performed to measurethe creep compliance functions for the two materials under two different loading histories. The limitof linearly viscoelastic behavior for each of the two materials was determined through theobservation of the indent impression recovery after complete unloading; it is postulated that linearityis achieved if indentation impression is fully recovered after unloading. Results fromnanoindentation tests generally agree well with data from conventional tension and shear tests. It hasthus validated the techniques of measuring linear creep compliance in the glassy state usingnanoindentation with the Berkovich and spherical indenter tips.     

Evaluation of the elastic modulus of thin film considering the substrate effect and geometry effect of indenter tip

A method using finite element method (FEM) is proposed to evaluate the geometry effect of indenter tip on indentation behavior of film/substrate system. For the nanoindentation of film/substrate system, the power function relationship is proposed to describe the loading curve of the thin film indentation process due to substrate effect. The exponent of the power function and the maximum indentation load can reflect the geometry effect of indenter and substrate effect. In the forward analysis, FEM is used to simulate the indentation behavior of thin film with different apex angles of numerical conical indenter tip, and maximum indentation load and loading curve exponent are obtained from the numerical loading curves. Meanwhile, the dimensionless equations between the loading curve exponent, the maximum load, elastic properties of film/substrate system and apex angle of indenter are established considering substrate effect. In the reverse analysis, a nanoindentation test was performed on thin film to obtain the maximum indentation load and the loading curve exponent, and then the experimental data is substituted into the dimensionless equations. The elastic modulus of thin film and the real apex angle of indenter can be obtained by solving the dimensionless equations. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.     

Element Analysis of Instrumented Sharp Indentations into Pressure-sensitive Materials

Finite element analysis was carried out to investigate the conical indentation response of elastic-plastic solids within the framework of the hydrostatic pressure dependence and the power law strain hardening. A large number of 40 difierent combinations of elasto-plastic properties with n ranging from 0 to 0.5 and σy/E ranging from 0.0014 to 0.03 were used in the computations. The loading curvature C and the average contact pressure Pave were considered within the concept of representative strains and the dimensional analysis.Dimensionless functions associated with these two parameters were formulated for each studied value of the pressure sensitivity. The results for pressure sensitive materials lie between those for Von Mises materials and the elastic model.     

Evaluation the effect of aspect ratio for Young’s modulus of nanobelt using finite element method

The traditional nanoindentation method provides experimental data for the calibrating mechanical parameters of nanobelt through semi-empirical formulae. In this paper, a technique to identify Young’s modulus of nanobelts with different aspect ratios is introduced combining finite element method (FEM) and nanoindentation test. For the nanobelt on the substrate, the power function relationship is used to describe the loading curve of the nanobelt indentation behavior. The loading curve exponent of the power function which is the fitting parameter can reflect the influence of aspect ratio of nanobelt on Young’s modulus of nanobelts as well as the maximum indentation load. In the forward analysis, considering the substrate effect and the size effect, the numerical loading responses are simulated at the appropriate penetration depth, and then the dimensionless equations between the parameters characterizing the indentation loading curve and the properties of nanobelt/substrate system can be established via extensive FEM simulation. In the reverse analysis, the nanoindentation tests were performed on ZnO and ZnS nanobelts, and the experimental indentation loading curves can be fitted as power function. The maximum indentation loads and the loading curve exponents are extracted from two experimental loading curves, and then they are substituted into the dimensionless equations to solve the Young’s moduli of ZnO and ZnS nanobelts. The results show the Young’s moduli solved are close to previous values, indicating that the Young’s moduli are reasonable. This developed method is effective to identify the Young’s modulus of nanobelt and it can be applied to identify the Young’s modulus of other nanobelts in practice.     

Step by step building of a model for the Berkovich indentation cycle

The indentation cycle obtained from hardness testing of material has two singular points. The first one is the right end of the definition interval of loading/unloading curves; it corresponds to the cycle tip and poses no difficulties for mathematical analysis. The second one is the latest contact point between the material and the indenter tip in phase of withdrawal, it is located inside the interval of definition, more towards the left- or the right-hand side depending on the elasticity degree of the material. This second point is impractical for the analytical modelling of the cycle as the unloading curve loses there all mathematical properties of derivability and differentiability.This difficulty induced a tendency for empirical models built from experimental results that are, like any empirical laws, affected by some lack of precision. It also led to an intense focusing on the unloading curve to which main nanomechanical and structural properties have been connected, forgetting sometimes the loading curve and the valuable information it can provides.In this article, we work out an analytical model to represent the two curves of the indentation cycle as accurately as possible. In this step by step modeling we use functional analysis and force the modelling curves to fit the interval of definition, the concavity direction and the materials energetic properties.     

Effect of different loading conditions on the mechanical behavior of [0/±45/90]s woven composites

The main objective of this paper is to investigate the behavior of [0/±45/90]_s woven FRP composites under tension, bending, and combined bending/tension loading conditions. First, the mechanical properties of the composite were determined experimentally using the ASTM testing standards. Bending properties were determined using 3-point and 4-point bending tests. The results showed that the woven composites performed better under bending loading than under tension loading. Finally, special test fixtures were designed to facilitate the study of the effect of the combined bending/tension loading. The bending moments were applied using offset shims of various thicknesses placed between the plane of the specimen and the loading axis. At the beginning, the load–strain diagrams at the specimen center showed the domination of bending strains, tension on one surface and compression on the other. With the advance of the loading process, the tension strain dominated and the strain on both sides were almost equal. The failure under combined bending/tension loading was due to the high stresses near the fixture. However, in pure bending, the material failed at the center because of the excessive delamination on the compressive side.     

Failure analysis of low velocity impact on thin composite laminates: Experimental and numerical approaches

The dynamic behavior of composite laminates is very complex because there are many concurrent phenomena during composite laminate failure under impact load. Fiber breakage, delaminations, matrix cracking, plastic deformations due to contact and large displacements are some effects which should be considered when a structure made from composite material is impacted by a foreign object. Thus, an investigation of the low velocity impact on laminated composite thin disks of epoxy resin reinforced by carbon fiber is presented. The influence of stacking sequence and energy impact was investigated using load–time histories, displacement–time histories and energy–time histories as well as images from NDE. Indentation tests results were compared to dynamic results, verifying the inertia effects when thin composite laminate was impacted by foreign object with low velocity. Finite element analysis (FEA) was developed, using Hill’s model and material models implemented by UMAT (User Material Subroutine) into software ABAQUS™, in order to simulate the failure mechanisms under indentation tests.     

Dynamic models for low-velocity impact damage of composite sandwich panels – Part A: Deformation

Equivalent single and multi degree-of-freedom systems are used to predict the low-velocity impact response of rigidly supported, two-sided clamped, simply supported and four-sided clamped composite sandwich panels. The composite sandwich panels have orthotropic facesheets and are symmetric. Analytical solutions for the transient deformation response of the sandwich panels are presented in this paper, and analytical predictions of impact damage initiation are given in a companion paper. Equivalent masses are derived by assuming velocity distributions and calculating average kinetic energies (KEs) in terms of the amplitude of the top facesheet indentation and the global panel deflection. Equivalent spring and dashpot resistances are derived from the static load–indentation response and adjusted with dynamic material properties of the facesheet and core. Analytical predictions of the impact force compare well with experimental values from three independent studies.     

基于70.3°圆锥形压头的材料压入测试方法研究

依据压入理论和弹塑性接触有限元分析,提出了采用70.3°锥形压头完成压入测试并基于能量方法获取金属材料本构关系的方法(Constitutiverelationshipbasedonenergymethodofindentation,CR-EMI)。该方法揭示锥形压入能量比与Hollomon屈服应力之间存在线性律,结合该线性律和载荷P-位移h曲线实现了材料Hollomon模型参数求取;同时,提出采用Hollomon模型参数并基于能量方法预测布氏硬度的方法(HardnessbasedonEnergyMethodofIndentation,H-EMI)。通过对多种金属材料进行压入试验和有限元分析,验证了CR-EMI方法和H-EMI方法的有效性与精确性。