Indentation of pressurized viscoplastic polymer spherical shells

The indentation response of polymer spherical shells is investigated. Finite deformation analyses are carried out with the polymer characterized as a viscoelastic/viscoplastic solid. Both pressurized and unpressurized shells are considered. Attention is restricted to axisymmetric deformations with a conical indenter. The response is analyzed for various values of the shell thickness to radius ratio and various values of the internal pressure. Two sets of material parameters are considered: one set having network stiffening at a moderate strain and the other having no network stiffening until very large strains are attained. The transition from an indentation type mode of deformation to a structural mode of deformation involving bending that occurs as the indentation depth increases is studied. The results show the effects of shell thickness, internal pressure and polymer constitutive characterization on this transition and on the deformation modes in each of these regimes.     

A Finite Element Method for the Determination of Optimal Viscoelastic Material Properties from Indentation Tests of Polymer Film and Wire with Polymer Insulation

The time-dependent behavior of bulk polymer film and wire with polymer insulation is studied using indentation. The indenter is displaced into the material at a constant rate and then held at a fixed indentation depth to monitor load relaxation. A finite element simulation of the experiment is performed; this analysis is parameterized in terms of the unknown shear compliance modeled as a Prony series. An optimization method is then presented to determine the unknown material parameters by minimizing the RMS error between the model and the experimental data. The method is demonstrated with poly (vinyl chloride) (PVC) films after thermal aging and pristine polyethylene sheet; excellent agreement between the model and the data is demonstrated. The method is also demonstrated to successfully characterize the material properties for the compression of a wire with PVC insulation; the resulting properties are then shown to adequately predict the crossed-cylinder indentation behavior of the same wire using a 3D finite element model. The chief benefit of the method is that an analytical solution method is not required for its implementation; as such, the optimization approach can be readily applied to the determination of material properties from arbitrarily complex experimental geometries.

The plastic zone size in indentation experiments: The analogy with the expansion of a spherical cavity

This paper provides in-depth examinations of the well-known analogy between indentation experiments and the expansion of a spherical cavity. Closed-form solutions are derived for the extension of the plastic zone in perfectly plastic and strain hardening solids. The theoretical analysis takes into account the role of elastic and plastic deformations in the overall contact response, leading to accurate solutions for cavity inflation. Presently proposed analogy is based on comprehensive finite element simulations of conical, spherical and pyramidal indentation, which allow us to find a correspondence between the parameters describing the contact response and those in expanding cavity formulations. Such parametrical identification has the advantage to hold true both in expanding cavity formulations for perfectly plastic solids and in those derived herein for strain hardening solids. Attention is given to the assessment of the plastic zone along the indented surface, as well as to quantify the influence of further plastic flow induced upon load removal on the plastic zone size.     

Orientation effect on the Boussinesq indentation of a transversely isotropic piezoelectric material

Three-dimensional finite element analysis was used to study the effect of the angle between the loading direction and the axisymmetric direction on the indentation behavior of a transversely isotropic piezoelectric half-space by a cylindrical indenter of flat end. Two cases were considered in the analysis, which included (a) the indentation by an insulating indenter, and (b) the indentation by a conducting indenter. Both the indentation load and the indentation-induced potential were found to be proportional to the indentation depth. Using the simulation results and the analytical relationship for the indentation by a rigid, insulating indenter, semi-analytical relationships were developed between the indentation load and the indentation depth and between the indentation-induced potential on the indenter and the indentation depth for the conducting indenter, respectively. The proportionality between the indentation-induced potential and the indentation depth is only a function of the angle between the loading direction and the poling direction, independent of the type of indenters, which may be used to measure the relative direction of the loading axis to the axisymmetric axis of transversely piezoelectric materials from the indentation test.     

Neural networks for tip correction of spherical indentation curves from bulk metals and thin metal films

Spherical indentation is widely used to determine a variety of important mechanical properties from small volumes. However, the available nanoindenter tips mostly deviate from the perfect spherical shape making the application of analysis methods developed for perfect spheres uncertain. In this paper, neural network-based methods are presented that are used to correct force-depth curves measured with such indenter tips. Finite element simulations for imperfect and perfect spherical tips with varying material behaviour are used to train the neural networks, which solve the inverse problem of mapping the true tip shape and the measured force-depth curve to one that corresponds to a perfect spherical indenter. Solutions are provided for bulk materials and thin films. The method has been verified experimentally on nanocrystalline nickel and a copper film on a titanium substrate for different spherical tips.     

The effect of indentation sequence on rock breakages: A study based on laboratory and numerical tests

Rock may response differently to external loads applied in different sequences. Thus, we conducted indentation tests to investigate the effect of the indentation sequence on rock breakages. Sequential indentations, consuming less indentation energy, usually resulted in larger and deeper grooves and then led to lower specific energies. Thus, we conclude that sequential indentations occur instead of simultaneous indentations form larger grooves with the same indentation energy. To further validate this conclusion, we performed a series of numerical tests. The numerical analysis of stress evolution shows that, for simultaneous indentations, the propagation of an internal crack from an inner rim restrained the propagation of the other internal crack from the other inner rim. However, the chipping pattern varied for sequential indentations. In the first indentation process, an internal crack, initiating from an inner rim, is usually connected with an internal crack caused by the second indentation. The deflection angles of the internal cracks for the sequential indentations were smaller because of the lower compressive stress in the horizontal direction. Then, these smaller deflection angles led to larger chips.     

泡沫金属压痕试验的数值模拟及其反演

在理论研究的基础上,将泡 沫金属压痕试验的有限元数值模拟结果与用无量纲分析法构造出的一系列无量纲函数相结 合,建立了泡沫金属压痕试验中载荷-压痕深度关系曲线与泡沫金属的弹塑性材料参数之 间的联系. 利用这种联系,就可以实现用压痕试验通过反演分析来确定泡沫金属的材料参数. 研究结果表明,泡沫金属材料的杨氏模量,屈服强度及塑性可压缩因子等参数均可由其压痕 试验唯一的确定,但其塑性平台区终点应变的确定还需进一步的研究.     

球形装药爆腔预测的准静态模型

炸药土中爆炸形成爆腔的特征尺寸会影响远场地震波的幅频特征。为了准确预测爆腔的特征尺寸,本文建立了爆腔膨胀的准静态模型,该模型给出了无限均匀不可压缩的弹性介质中球形装药爆炸形成的粉碎区、裂隙区半径的解析表达式,并利用该模型计算讨论了不同条件下各分区尺度的变化。最后将该模型与现场实验、动力模型所得到的结果进行对比后表明,该模型与以上两者之间的误差约为5.4%~16.0%,能够较为准确地预测爆腔尺寸。     

Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity

A study of the indentation size effect (ISE) in aluminum and alpha brass is presented. The study employs rate effects to examine the fundamental mechanisms responsible for the ISE. These rate effects are characterized in terms of the rate sensitivity of the hardness, , where H is the hardness and is an effective strain rate in the plastic volume beneath the indenter. can be measured using indentation creep, load relaxation, or rate change experiments. The activation volume V∗, calculated based on which can traditionally be used to compare rate sensitivity data from a hardness test to conventional uniaxial testing, is calculated. Using materials with different stacking fault energy and specimens with different levels of work hardening, we demonstrate how increasing the dislocation density affects V∗; these effects may be taken as a kinetic signature of dislocation strengthening mechanisms. We noticed both H and exhibit an ISE. The course of V∗ vs. H as a result of the ISE is consistent with the course of testing specimens with different level of work hardening. This result was observed in both materials. This suggests that a dislocation mechanism is responsible for the ISE. When the results are fitted to a strain gradient plasticity model, the data at deep indents (microhardness and large nanoindentation) exhibit a straight-line behavior closely identical to literature data. However, for shallow indents (nanoindentation data), the slope of the line severely changes, decreasing by a factor of 10, resulting in a “bilinear behavior”.     

湍流模型对空泡形态影响的数值研究

为研究湍流模型对空泡尾部气体泄漏方式和空泡外形的影响,基于 FLUENT6.2的 VOF 多相流模型,对考虑重力作用下的三维通气空泡流进行了数值计算,比较了大涡模拟 LES 和 RNG k-ε两种湍流模型下的空泡形态和模型表面压力系数分布。结果显示,RNG k-ε模型计算的空泡内压力较大,空泡长度更长,而 LES 的瞬态计算结果更符合通气空泡的特性,相对而言更适用于通气空泡流的模拟。     

Sensitivity analysis,calibration and validation of a snow indentation model

Quantification of the mechanical behavior of snow in response to loading is of importance in vehicle-terrain interaction studies. Snow, like other engineering materials, may be studied using indentation tests. However, unlike engineered materials with targeted and repeatable material properties, snow is a naturally-occurring, heterogeneous material whose mechanical properties display a statistical distribution. This study accounts for the statistical nature of snow behavior that is calculated from the pressure-sinkage curves from indentation tests. Recent developments in the field of statistics were used in conjunction with experimental results to calibrate, validate, and study the sensitivity of the plasticity-based snow indentation model. It was found that for material properties, in the semi-infinite zone of indentation, the cohesion has the largest influence on indentation pressure, followed by one of the the hardening coefficients. In the finite depth zone, the friction angle has the largest influence on the indentation pressure. A Bayesian metamodel was developed, and model parameters were calibrated by maximizing a Gaussian likelihood function. The calibrated model was validated using three local and global confidence-interval based metrics with good results.     

Application of a kinematic hardening viscoplasticity model with thresholds to the residual stress relaxation

The life analysis of engine components needs to take into account the residual stress relaxation induced by cyclic service loads. The paper recalls a new class of constitutive equations for cyclic viscoplasticity, using a series of kinematic hardening models with thresholds. The equations are introduced within a recently enlarged thermodynamic framework. Some attention is focused to the relations with multisurface approaches and to a specific determination procedure of the model parameters. The new model is applied to the calculation of the near surface residual stress relaxation after shot peening, when the structure is submitted to cyclic service loads. The simulated stabilized residual stresses are in good accordance with experimental results obtained on an N18 disk alloy at 650°C. In comparison, the classical model without threshold predicts the complete vanishing of the residual stresses, which is not satisfactory.     

High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: Geometrically necessary dislocation densities

Experimental studies on indentation into face-centered cubic (FCC) single crystals such as copper and aluminum were performed to reveal the spatially resolved variation in crystal lattice rotation induced due to wedge indentation. The crystal lattice curvature tensors of the indented crystals were calculated from the in-plane lattice rotation results as measured by electron backscatter diffraction (EBSD). Nye's dislocation density tensors for plane strain deformation of both crystals were determined from the lattice curvature tensors. The least L²-norm solutions to the geometrically necessary dislocation densities for the case in which three effective in-plane slip systems were activated in the single crystals associated with the indentation were determined. Results show the formation of lattice rotation discontinuities along with a very high density of geometrically necessary dislocations.     

Numerical study of buoyancy- and thermocapillary-driven flows in a cavity

Thermocapillary- and buoyancy-driven convection in open cavities with differentially heated endwalls is investigated by numerical solutions of the two-dimensional Navier-Stokes equations coupled with the energy equation. We studied the thermocapillary and buoyancy convection in the cavities, filled with low-Prandtl-number fluids, with two aspect-ratiosA=1 and 4, Grashof number up to 10⁵ and Reynolds number ⋎Re⋎≤10⁴. Our results show that thermocapillary can have a quite significant effect on the stability of a primarily buoyancy-driven flow, as well as on the flow structures and dynamic behavior for both additive effect (i.e., positiveRe) and opposing effect (i.e., negativeRe).     

Uncoupled magnetoelastic problem for a ferromagnetic body with a spherical cavity

An uncoupled stress problem for an unbounded elastic soft ferromagnetic body with a spherical cavity in a magnetic field uniform at infinity is solved. The stresses, displacements, and magnetic quantities in the body are determined. The features of stress distribution over the body and its boundary surface are studied __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 42–48, October 2007.     

Numerical analysis of thermosolutal flows in a cavity with gravity modulation effects

 In this work, a two-dimensional thermosolutal convection flow under a sinusoidal gravity modulation (g-jitter) field is studied to understand the effects of the periodic source on flow field, as well as heat and mass transfer mechanisms. A semi-implicit projection finite element method is adopted to solve the transient Navier–Stokes, energy and species concentration equations. The fingering regime and the diffusive regime are explored for a series of gravity modulation frequencies. Two types of flow evolution, synchronous and subharmonic responses, are obtained for different frequencies. Distribution of unstable responses for the singly unstable condition is in agreement with the literature predict. The results show that heat and mass transfer rates are affected by the response type. For a subharmonic variation flow field, the overall Nusellt number and Sherwood number exhibit larger values. In addition, the augmenting condition in combining thermally driving force and solutally driving force is analyzed for a practical crystal material and displays a different response distribution from those in the fingering regime and the diffusive regime. Received on 19 February 2001 / Published online: 29 November 2001     

Mechanics of indentation of plastically graded materials—II: Experiments on nanocrystalline alloys with grain size gradients

A systematic study of depth-sensing indentation was performed on nanocrystalline (nc) Ni-W alloys specially synthesized with controlled unidirectional gradients in plastic properties. A yield strength gradient and a roughly constant Young's modulus were achieved in the nc alloys, using electrodeposition techniques. The force vs. displacement response from instrumented indentation experiments matched very well with that predicted from the analysis of Part I of this paper. The experiments also revealed that the pile-up of the graded alloy around the indenter is noticeably higher than that for the two homogeneous reference alloys that constitute the bounding conditions for the graded material. These trends are also consistent with the predictions of the indentation analysis.     

Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: Applications to probing nanoelectromechanical properties of materials

Stiffness relations for voltage-dependent contact mechanics of piezoelectric material are derived for an indenter of arbitrary planform under normal force, centrally or non-centrally applied, and electric charge distribution at the base. Relations between indentation depth, indentation force, electric potential and electric charge are explicitly given in terms of indenter's geometry and piezoelectric material constants. The analysis covers indenters with non-flat base approximated by a second-order surface; elliptic paraboloid is considered as an example. In the case of the elliptic non-flat planform, the derived stiffness relations are exact; otherwise, they are approximate and are shown to have good accuracy. The stiffness relations are given in elementary functions and are obtained by utilizing the recently established principle of correspondence between the piezoelectric and purely elastic problems. Besides contributing to extension of Hertzian mechanics to piezoelectric materials, these results are essential for quantitative interpretation of the scanning probe microscopy and piezoelectric nanoindentation data on piezoelectric, ferroelectric, and multiferroic materials.