Probing of Micromechanical Properties of Compliant Polymeric Materials

Scanning force microscopy (SFM) was used for probing nanomechanical properties of compliant polymeric materials with lateral resolution from 20 to 140 nm and indentation depths from 2 to 200 nm. Sneddon's, Hertzian, and Johnson–Kendall–Roberts theories of elastic contacts were tested for a variety of polymeric materials with Young's modulus ranging from 1 MPa to 5 GPa. Results of these calculations were compared with a Sneddon's slope analysis widely used for hard materials. It was demonstrated that the Sneddon's slope analysis was ambiguous for polymeric materials. On the other hand, all models of elastic contact allowed probing depth profile of elastic properties with nanometre scale resolutions. The models gave consistent values of elastic moduli for indentation depth up to 200 nm with lateral resolution better 100 nm for most polymeric materials.     

Measurement of mechanical properties of 1045 steel with significant pile-up by sharp indentation

The Oliver–Pharr method has extensively been adopted for measuring hardness and elastic modulus by indentation techniques. However, the method assumes that the contact periphery sinks in, which limits the applicability to the materials pile up. This study proposed an improved methodology to calculate the real contact area of 1045 steel with significant pile-up. The contact boundary between indenter and specimen was assumed to overlap with the top points on the residual surface profile, and the real contact depth was defined by a sum of the indentation depth at maximum load, h _max, and average pile-up height, h_{\textpile - up}^\textave h_{\text{pile - up}}^{\text{ave}} , measured from the analysis on the residual indent morphology with atomic force microscope (AFM). The mechanical properties calculated by the newly proposed method were compared with those by the Oliver–Pharr method.     

A New Model Developed to Evaluate the Contact Area Arising During Nano-indentation Tests With Pileup Behavior of Metal Materials

A new mechanical model is developed in this paper for metal materials to investigate the behavior arising during the loading/unloading process of an indentation test. Two governing differential equations are derived for the depth solution of the indenter tip and the depth solution formed at the separation point, expressed in a power form. All spring/block and damping coefficients shown in these governing differential equations associated with the elastic/plastic and viscous behaviors are determined by the real-coded genetic algorithm. With the aid of experimental results of the depth at the indenter tip shown at large and small indentation depths, aluminum and steel were used as two examples of soft materials in this paper. The pileup behavior is implicitly included in the evaluation of the contact projected area (A) in the present model. A significant difference in is caused if the pileup is not considered in the model. Under a constant maximum load, the contact area is slightly increased by decreasing the loading/unloading rate.     

Conditions of applying Oliver–Pharr method to the nanoindentation of particles in composites

The indentation test is a popular experimental method to measure a material’s mechanical properties such as elastic modulus and hardness, and the Oliver–Pharr method is commonly used in commercial indentation instruments to obtain these two quantities. To apply the Oliver–Pharr method correctly in all of these cases, it is essential to know the limitations of this method. The present study focuses on the applicability of the Oliver–Pharr method to measure the mechanical properties of particles in composites. The finite element method is used to undertake virtual indentation tests on a particle embedded in a matrix. In our numerical studies, the indentation “pile-up” phenomenon is generally observed in our numerical case studies, which indicates that the contact area used for predicting the elastic modulus should be measured directly, not be estimated from the indentation curve. The Oliver–Pharr method based on the real contact area is applied to estimate the elastic modulus of the particles by using the indentation curve from the numerical simulation, with the estimated elastic modulus being compared with the input value. Applying the real contact area value (not the one predicted from the indentation curve) we show that the Oliver–Pharr method can still be applied to measure the elastic modulus of the particle with sufficient accuracy if the indentation depth is smaller than the particle-dominated depth, a value defined in this work. The influences of the matrix and particle properties on the particle-dominated depth are studied using a dimensional analysis and parametric study. Our results provide guidelines to allow the practical application of the Oliver–Pharr method to measure the elastic modulus of particles in composites. This could be particularly important where particles are formed in situ in a matrix (as opposed to being preformed and subsequently incorporated in a matrix), or when the modulus of individual performed particles is required such as for subsequent modelling, but the modulus of individual material particles (or its material) cannot readily be determined.     

Challenges and Progress in High‐Throughput Screening of Polymer Mechanical Properties by Indentation

Depth‐sensing or instrumented indentation is an experimental characterization approach well‐suited for high‐throughput investigation of mechanical properties of polymeric materials. This is due to both the precision of force and displacement, and to the small material volumes required for quantitative analysis. Recently, considerable progress in the throughput (number of distinct material samples analyzed per unit time) of indentation experiments has been achieved, particularly for studies of elastic properties. Future challenges include improving the agreement between various macroscopic properties (elastic modulus, creep compliance, loss tangent, onset of nonlinear elasticity, energy dissipation, etc.) and their counterpart properties obtained by indentation. Sample preparation constitutes a major factor for both the accuracy of the results and the speed and efficiency of experimental throughput. It is important to appreciate how this processing step may influence the mechanical properties, in particular the onset of nonlinear elastic or plastic deformation, and how the processing may affect the agreement between the indentation results and their macroscopic analogues.     

Grid indentation analysis of composite microstructure and mechanics: Principles and validation

Several composites comprise material phases that cannot be recapitulated ex situ, including calcium silicate hydrates in cementitous materials, hydroxyapatite in bone, and clay agglomerates in geomaterials. This requirement for in situ synthesis and characterization of chemically complex phases obviates conventional mechanical testing of large specimens representative of these material components. Current advances in experimental micro and nanomechanics have afforded new opportunities to explore and understand the effect of thermochemical environments on the microstructural and mechanical characteristics of naturally occurring material composites. Here, we propose a straightforward application of instrumented indentation to extract the in situ elastic properties of individual components and to image the connectivity among these phases in composites. This approach relies on a large array of nano to microscale contact experiments and the statistical analysis of the resulting data. Provided that the maximum indentation depth is chosen carefully, this method has the potential of extracting elastic properties of the indented phase which are minimally affected by the surrounding medium. An estimate of the limiting indentation depth is provided by asssuming a layered, thin film geometry. The proposed methodology is tested on a “model” composite material, a titanium-titanium monoboride (Ti–TiB) of various volumetric proportions. The elastic properties, volume fractions, and morphological arrangement of the two phases are recovered. These results demonstrate the information required for any micromechanical model that would predict composition-based mechanical performance of a given composite material.     

Examination of local variations in viscous,elastic, and plastic indentation responses in healing bone

A viscous-elastic-plastic indentation model was used to assess the local variability of properties in healing porcine bone. Constant loading- and unloading-rate depth-sensing indentation tests were performed and properties were computed from nonlinear curve-fits of the unloading displacement-time data. Three properties were obtained from the fit: modulus (the coefficient of an elastic reversible process), hardness (the coefficient of a nonreversible, time-independent process) and viscosity (the coefficient of a nonreversible, time-dependent process). The region adjacent to the dental implant interface demonstrated a slightly depressed elastic modulus along with an increase in local time-dependence (smaller viscosity); there was no clear trend in bone hardness with respect to the implant interface. Values of the elastic modulus and calculated contact hardness were comparable to those obtained in studies utilizing traditional elastic-plastic analysis techniques. The current approach to indentation data analysis shows promise for materials with time-dependent indentation responses.     

一种钠钙硅酸盐玻璃的纳米压痕测试分析

采用纳米压痕测试技术对一种钠钙硅酸盐玻璃进行微观力学性能的测试分析.测得加载-卸载过程载荷与压入深度曲线,发现被测玻璃的最大压深、残余深度和弹性回复量随最大加载力的增加而增大,但其相对弹性回复率系数基本稳定,平均值为58.2%.通过电子显微镜观察了不同最大载荷下的压痕形貌,发现压痕区域出现了边界沉陷现象.当最大加载力为1 000 mN左右时,三棱锥工具头测试的压痕区域出现了较明显的微裂纹;采用四棱锥工具头时出现微裂纹的最大加载力要小于该值,且裂纹取向均与金刚石工具头的棱角取向一致.利用非线性有限元软件MSC.Marc对纳米压痕过程进行了仿真分析,得到载荷与压入深度的仿真曲线,该曲线与试验结果基本相符;分析了载荷作用下材料内部的应力分布.利用Oliver-Pharr模型得到不同压入深度下被测玻璃的接触刚度值,该值随压入深度的增加而增大.     

圆锥压头递增载荷对材料的划痕行为

用Rockwell C金刚石压头对16种材料(2种玻璃、2种聚合物、4种陶瓷、4种金属和4种金属玻璃)进行微米划痕测试。结果表明,这些材料都存在与弹性恢复相关的最大划痕保持率(残余深度与压入深度之比),可作为表观摩擦系数变化曲线的分段过渡点。划痕的表观摩擦系数由黏着摩擦系数和犁沟摩擦系数组成,使用三维力学接触模型可较为准确地表征除金属玻璃外的摩擦系数。材料的初始摩擦系数与泊松比有一定的关系。聚合物(PC和PMMA)因堆积和下沉效应出现独有的双划痕沟槽现象。16种材料的划痕硬度与压痕硬度的比值为0.33~2.5,划痕硬度与体积模量呈线性关系。使用线弹性断裂力学(LEFM)模型和微观能量尺寸效应(MESEL)模型计算了材料的断裂韧性。结果表明,LEFM模型、Akono's MESEL和Hubler's MESEL模型都能较为准确地表征断裂韧性较低材料(玻璃、陶瓷和高分子)的断裂韧性,而对断裂韧性较大的金属材料其表征结果偏差较大。用Liu's MESEL模型可表征断裂韧性较大材料(金属材料和部分金属玻璃)的断裂韧性。材料的断裂韧性,与泊松比呈分段线性相关。     

Nanomechanical Characterisation of Graded NiTi Films Fabricated Through Diffusion Modification

Abstract:  Ni₄₇Ti₅₃ films of varying thickness were deposited onto Ni₅₆Ti₄₄ substrates. Annealing the films produced compositional gradients through diffusion modification. Nanoindentation measurements were used to probe the mechanical properties at various depths into the film. The films exhibited a variation in elastic modulus as a function of indentation depth that depended on the thickness of the film. A self-similarity principle permitted the mechanical properties of the graded NiTi films to be resolved further into substrate, beyond the contact depth of the tip. The observed variation of elastic modulus with indentation depth in the graded NiTi films was considered to be a combined response from changes in microstructure, substrate effects, and mechanically-induced phase transformations. This variation was predicted using an analysis that accounted for the transformation effects occurring under the tip during loading and the graded distribution of martensite volume fraction obtained from diffusion modification.     

试样倾斜对熔融石英硅三棱锥纳米压痕测试的影响

使用三棱锥压头对不同倾斜角下的熔融石英硅进行纳米压痕实验。结果表明,试样倾斜会影响加载曲线的形状。在相同的载荷下,随着试样倾斜角的增加,压痕最大深度、残余深度及接触深度逐渐减小,但卸载曲线不受影响,彼此保持平行,卸载曲线的拟合参数m及接触刚度值保持恒定。另外,试样倾斜将导致测量的压痕接触面积偏小,从而使得测量的硬度和弹性模量偏大。     

Numerical Study on the Effects of Equi-biaxial Residual Stress on Mechanical Properties of Nickel Film by Means of Nanoindentation

In this paper,mechanical properties of Nickel film under residual stress have been systematically examined by finite element method in nanoindentation.It was found that load-displacement curves shifted under elastic residual stress and residual stress exceeded the yield stress for fixed indentation depth.Indentation profiles changed monotonously with compressive and tensile stresses at peak force which determinates contact area observed directly by finite element modeling (FEM).The elastic residual stress h...     

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.     

Finite element analysis of deep indentation by a spherical indenter

Using the finite element analysis, the deep indentation of strain-hardening elastoplastic materials by a rigid, spherical indenter has been studied. The simulation results clearly show that the ratio of the indentation load to the maximum indentation depth increases with the increase of the strain-hardening index and reaches a maximum value at the maximum indentation depth being about 10% of the indenter radius. The power law relation between the indentation load and the indentation depth for shallow indentation becomes invalid for deep indentation. However, the ratio of the plastic energy to the total mechanical work is a linear function of the ratio of the residual indentation depth to the maximum indentation depth, independent of the strain-hardening index and the indentation depth.     

Mechanical and thermal properties of physical vapour deposited alumina films Part II Elastic, plastic, fracture, and adhesive behaviour

Two mechanical characterization techniques were used to deduce the elastic, plastic, fracture, and adhesive properties of non-reactive physical vapour deposited alumina films of varying thickness on Al₂O₃-TiC substrates deposited at two different substrate biases. Depth-sensing indentation at both nano- and macroscopic load scales was used to determine the elastic and plastic properties of the films. Gravity-loaded Vickers indentation was performed to examine the fracture properties of the film and of the interface. Novel fracture mechanics models were developed to describe indentation-induced film fracture by channel cracks and indentation-induced interface delamination. The former model was used to determine the film toughness and the latter model was used to deduce the interfacial fracture resistance of the films and correctly predicted the effect of changing film thickness. Both models described the measured crack lengths with indentation load well and were used to identify the transition from radial and lateral cracking to channel and interfacial cracking.     

Stress states and nonlinear mechanical behavior associated with nanoindentation testing of polymers

Interest in determining material properties on the nanoscale has promoted use of nanoindentation testing as a measurement technique. Classical elasticity solution of indentation geometry has provided values of the mechanical properties for linear elastic materials. Recent attempts to apply this test technique to polymers have given indications of time dependent response in the early relaxation period. There is corresponding interest in the possibility of obtaining their nonlinear viscoelastic behavior. As a preliminary to analytical study providing a basis for such testing, the first part of this paper examines the initial stress and strain condition in the vicinity of the indenter. Data from recent tests on poly(vinyl acetate) material at load levels typical of current testing indicate that stress magnitudes in the nonlinear and possibly plastic-like range are present near the specimen surface. The second part of this study pursues the examination of how the heavily nonlinear region may be characterized for polymers in analogy with the treatment utilized for metals and other elastic-plastic materials. As an example, analysis of data on PVAc indicates that its behavior in nanoindentation should in several respects correspond to materials exhibiting a relatively low value of the ratio of elastic modulus to yield stress.     

确定纳米压入面积函数的改进方法

针对薄膜等微小结构材料力学性能测试面积函数测量问题,提出了一种改善微小压入深度下压头面积函数准确性的方法.该方法将压头与被测样品之间的投影接触面积与压头针尖曲率半径和角度相关联,解决常用的面积函数确定方法在50 nm以下浅压痕测量中不可靠的问题.经实验验证,该面积函数确定方法可以提高微小接触深度下压入硬度和折合模量的测...     

An analytical assessment of the influence of skin imperfections on the indentation collapse mechanism in composite sandwich beams

The influence of skin imperfections, in the form of delamination damage or thickness variations, on the indentation collapse mechanism in composite sandwich beams with compressive yielding cores is studied using the models of non-prismatic beam and beam-column resting on a nonlinear Winkler foundation. Upper and lower threshold solutions are derived for the indentation response and collapse load and the transition between the two limits is defined as a function of size, magnitude and position of the imperfections. In beams where global bending effects are not negligible, the collapse load is limited from above by the indentation collapse load of beams with rigid-plastic cores and the face wrinkling collapse load of beams with elastic cores; the transition between the two limits is controlled by material/structure properties and the magnitude of the imperfections. Characteristic lengths, which depend on material and geometrical properties, define the minimum size of the imperfections with the strongest effect on the solution and the minimum distance between load and imperfections with no effect on the solution.     

Evaluation of mechanical properties using spherical ball indentation and coupled finite element–element-free galerkin approach

In the present work, the mechanical properties of pressure tube material (Zr-Nb2.5) are evaluated using the coupled finite element–element-free Galerkin approach. Penalty approach is used to impose contact constraints and non-penetration condition at the interface. An efficient node-to-segment algorithm is employed to model the contact behavior. An updated Lagrangian approach is used to model the large deformation. Loading and unloading response of the indentation process is analyzed using von-Mises and Gurson-Tvergaard-Needleman (GTN) plasticity models. In multiple indentations, the indentation depth is progressively increased up to a maximum specified limit with partial unloading. Load-indentation depth curves are used to extract the flow properties of the material.     

In situ nanomechanical behaviour of coexisting insulating and metallic domains in VO<Subscript>2</Subscript> microbeams

Measuring the electrical and mechanical responses of coexisting phases at nanoscale provides a platform to engineer micro-/nanoscale pattern of metallic and insulating domains with control over properties to make novel devices. Here, we employ several in situ characterization techniques, namely Raman, optical imaging and electrical measurements, to identify the phase coexistence of metallic and insulating domains. Further, we performed site-specific in situ nanoindentation to address the spatial variation in nanomechanical properties in vanadium dioxide (VO₂) single-crystal microbeams in proximity to metal–insulator transition temperature. We also investigated load or contact depth dependence on elastic modulus at various temperatures to avoid the interference of indentation size effect on nanomechanical properties across the phase transition. The obtained results confirm the abrupt increase in elastic modulus (~17 GPa) and nanohardness (1 GPa) across the transition from monoclinic (insulator) to rutile (metal) phase.