硅晶体纳米压痕试验与应力场分析

采用纳米压入法测量了4种硅晶体的微压痕特性,讨论了加载过程与卸载过程的特征,分析了硅晶体的纳米压入测量结果,同时计算了硅晶体中的应力分布,计算结果表明,剪应力为硅晶体微薄片剥落失效的原因。     

Viscoelastic solutions for conical indentation

The aim of indentation analysis is to link indentation data, typically an indentation force vs. indentation depth curve, P–h, to meaningful mechanical properties of the indented material. While well established for time independent behavior, the presence of a time dependent behavior can strongly affect both the loading and the unloading responses. The paper presents a framework of viscoelastic indentation analysis based on the method of functional equations, developed by Lee and Radok [1960, The contact problem for viscoelastic bodies, J. Appl. Mech. 27, 438–444]. While the method is restricted to monotonically increasing contact areas, we show that it remains valid at the very beginning of the unloading phase as well. Based on this result, it is possible to derive closed form solutions following the classical procedure of functional formulations of viscoelasticity: (1) the identification of the indentation creep function, which is the indentation response to a Heaviside load; and (2) a convolution integral of the load history over the indentation creep function. This is shown here for a trapezoidal loading by a conical indenter on three linear isotropic viscoelastic materials with deviator creep: the 3-parameter Maxwell model, the 4-parameter Kelvin–Voigt model and the 5-parameter combined Kelvin–Voigt–Maxwell model. For these models, we derive closed form solutions that can be employed for the back-analysis of indentation results from the loading and holding period and for the definition of unloading time criteria that ensure that viscous effects are negligible in the unloading response.     

Determination of mechanical properties by instrumented indentation

The paper reviews the current state of the depth-sensing indentation (sometimes called nanoindentation), where the information on material behaviour and properties is obtained from the indenter load and depth, measured continuously during loading and unloading. It is shown how the contact parameters and principal characteristics are determined using pointed or spherical indenters. Indentation tests can be used for the measurement of hardness and elastic modulus, and also of the yield stress and for the construction of stress–strain diagrams, for the determination of the work of indentation and its components. Most devices use monotonic loading and unloading, but some also enable measurement under a small harmonic signal added to the basic monotonously increasing load. This makes possible continuous measurement of contact stiffness and the study of dynamic properties and the determination of properties of coatings. One section is devoted to the measurement on viscoelastic-plastic materials, where the delayed deforming must be considered during the measurement as well as in data evaluation. Instrumented indentation can also be used for the study of creep under high temperatures. The paper also discusses the errors arising in depth-sensing measurements and informs briefly about some other possibilities of the method.     

Effects of matrix inelasticity on the overall hysteretic behavior of TiNi-SMA fiber composites

The effects of the inelastic deformation of the matrix on the overall hysteretic behavior of a unidirectional titanium–nickel shape-memory alloy (TiNi-SMA) fiber composite and on the local pseudoelastic response of the embedded SMA fibers are studied under the isothermal loading and unloading condition. The multiaxial phase transformation of the SMA fibers is predicted using the phenomenological constitutive equations which can describe the two-step deformation due to the rhombohedral and martensitic transformations, and the inelastic behavior of the matrix material using the standard nonlinear viscoplastic model. The average behavior of the SMA composite is evaluated with the micromechanical method of cells. It is observed that the inelastic deformation of the matrix due to prior tension results in a compressive stress in the matrix after unloading of the SMA composite and this residual stress impedes the complete recovery of the pseudoelastic strain of the SMA fibers. This explains that a closed hysteresis behavior of the SMA composite is no longer observed in contrast with the case that an elastic behavior of matrix is assumed. The predicted local stress–strain behavior indicates that the cyclic response of matrix is crucial to the design of the hysteretic performance of the SMA composite under the repeated loading conditions.     

Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.     

TiNi合金冲击相变过程中温度变化规律的实验研究

针对初始SME(shape memory effect)和PE(pseudo-elastic)状态TiNi合金试样,采用带有红外测温系统的SHPB冲击压缩装置,实时测量了冲击相变过程中两种材料试样表面瞬态温度,并根据实验结果计算了相应的温度变化。实验结果表明,冲击加载相变过程中,温度随相变应变的增大而升高,当应变最大时,温度最高;卸载过程中,对初始PE状态试样,温度降低,对初始SME状态试样,温度保持最高温度不变或降低,这同加载最高温度有关;卸载完成后,两种试样温度均高于其初始温度。计算温度结果表明,相变耗散功对加、卸载相变过程中温度变化的作用不可忽略。     

TiNi相变悬臂梁的横向冲击特性实验研究

利用改装的霍普金森压杆装置对TiNi形状记忆合金圆截面悬臂梁进行了横向冲击实验研究,并与45#钢悬臂梁的实验结果进行了对比,目的是探索相变对结构动态响应的影响。结果表明:在同样冲击条件下,TiNi悬臂梁的吸能效率优于钢悬臂梁;发现冲击过程中,TiNi试件根部内侧可能形成局部相变铰,使阻力曲线的斜率发生变化;卸载后相变铰消失,TiNi悬臂梁试件基本回复原状,钢试件则留下显著的残余变形。TiNi悬臂梁的冲击特性受热弹性马氏体相变和逆相变的支配,不同于传统的弹塑性机制。     

冲击下宏观相边界的传播

研究了具有CdS型相变本构材料的宏观相边界传播规律。相边界包括纯新相和混合相两段。纯新相段可用逐步近似法,混合相段则必须用数值方法求解。给出了三种加卸载应力边界条件下的算例。在突加突卸的应力边界条件下,给出了相边界传播的解析解。在算例中,各种解法得到的结果彼此很好符合。     

Dynamic analysis of single and cyclic indentation of an elastic-plastic multi-layered medium by a rigid fractal surface

Dynamic indentation of an elastic-plastic multi-layered medium by a rigid rough surface that exhibits fractal behavior was analyzed with the finite element method. A sufficiently large mesh was used to avoid the effects of the faster propagating dilatation waves after they were reflected from the artificial mesh boundaries. Single-indentation results illustrate the significance of the thickness of the surface layer and the indentation speed on the contact pressure distribution and subsurface stresses and strains. The initiation of yielding and the development of plasticity are interpreted in the context of results for the von Mises equivalent stress and equivalent plastic strain obtained during the loading and unloading phases of an indentation cycle. Cumulative plasticity and elastic shakedown are discussed in light of results revealing the evolution of deformation in the multi-layered medium due to cyclic indentation. The analysis provides insight into the importance of indentation speed, layer thickness, surface topography, and indentation cycle on the mechanical response of a multi-layered medium in dynamic contact with a rough surface exhibiting multi-scale (fractal) roughness.     

A Load-Based Multiple-Partial Unloading Micro-Indentation Technique for Mechanical Property Evaluation

A load-based multiple-partial unloading micro-indentation technique has been developed for evaluating mechanical properties of materials. Comparing to the current prevailing nano/micro-indentation methods, which require precise measurements of the indentation depth and load, the proposed technique only measures indentation load and the overall indentation displacement (i.e. including displacement of the loading apparatus). Coupled with a multiple-partial unloading procedure during the indentation process, this technique results in a load-depth sensing indentation system capable of determining Young’s modulus of metallic alloys with flat, tubular, or curved architectures. Test results show consistent and correct elastic modulus values when performing indentation tests on standard alloys such as steel, aluminum, bronze, and single crystal superalloys. The proposed micro-indentation technique has led to the development of a portable load-depth sensing indentation system capable of on-site, in-situ material property measurement.     

Internal loops in superelastic shape memory alloy wires under torsion – Experiments and simulations/predictions

Understanding torsional responses of shape memory alloy (SMA) specimens under partial or fully transformed cases with internal loops is of particular importance as the entire response might not be always utilized and only a portion of the entire response (internal loop) might be of significance to designers. In this work, we present experimental results of large complex loading and unloading torsional cycles which were conducted on superelastic SMA wires, under isothermal conditions with the purpose of elucidating the torsional internal loop response during loading and unloading. Such data hereto has not been available in open literature. Utilizing this data, we model the torsional response of superelastic SMA wires subjected to various loading and unloading situations that can result in different extents of transformation.A thermodynamically consistent Preisach model (Rao and Srinivasa, 2013) captures such complex internal loops with a high degree of precision by modeling driving force for phase transformation vs. volume fraction of martensite relationships. This approach is different from capturing purely phenomenological stress–strain or stress–temperature Preisach models. The thermodynamic approach utilized here has broader predictive capability. The model predictions indicate good agreement with the internal loop structures even though only the outer loop information was used for model calibration. The addition of a single inner loop information for model calibration greatly improves the predictions.     

Effect of Varying Test Parameters on Elastic–plastic Properties Extracted by Nanoindentation Tests

A systematic experiment was performed in an effort to investigate how the levels of certain test parameters affect the values of elastic modulus, hardness, yield stress, and strain hardening constant obtained using nanoindentation test. Maximum applied load, loading (unloading) rate, and hold time at maximum load were varied at three levels. The effects of these testing parameters were investigated through a three-level, full factorial design of experiment. The experiments were conducted on ultrafine Al-Mg specimens that were mechanically extruded. Both longitudinal and transverse extrusion directions were examined to investigate effects of anisotropy on mechanical properties and evaluate the persistence of observed variations due to test parameters on different materials orientations. An indentation size effect (ISE) was observed demonstrating that maximum load—and thereby maximum indentation depth—can have a significant effect on values of hardness and elastic modulus. Hardness values decreased with higher loading rates, and higher rates of unloading resulted in higher values of elastic modulus (5–10 GPa increases). Strain-hardening exponent showed a decreasing trend with increasing loading rate while yield stress exhibited a consistent correlation to hardness across all studied parameters. The material exhibited very little creep during the hold period, and values of the calculated properties were not significantly altered by varying the length of the hold time. Anisotropy effect was observed, particularly in the values of yield strength. This is attributed to the preferred grain orientation due to extrusion.     

Martensite Strain Memory in the Shape Memory Alloy Nickel-Titanium Under Mechanical Cycling

This paper describes an experimental study of stress-induced martensitic phase transformation in the SMA Nickel-Titanium. The rich local thermo-mechanical interactions that underlie transformation are examined using three-dimensional Digital Image Correlation (strain fields) and infrared imaging (thermal fields). We quantify the complex local interactions between released/absorbed latent heat and the extent of transformation, and explore the characteristics of the phase fronts and the evolution of martensitic volume fraction. We also quantify a strong strain memory in the martensite that forms in the wake of the phase transformation front. The accommodated strain in the martensite will remain constant during loading, even as the existing phase front propagates. There also exists a remarkable strain memory in the martensite that persists from cycle to cycle, indicating that the local elastic stress fields in the martensite are driven by a dislocation structure and martensitic nuclei that largely stabilize during the first loading cycle.     

Localization in NiTi tubes under bending

Nearly equiatomic NiTi can exhibit pseudoelastic behavior due to reversible solid-to-solid stress induced phase transformation at room level temperatures. In tension, the transformation leads to localized deformation of several percent that tends to spread at nearly constant stress. The deformation is recovered upon unloading while again localized deformation is exhibited. Under compression, while still pseudoelastic, the transformation strains are smaller, the stress is higher, the response is monotonic, and the deformation is essentially homogeneous. This study examines how this texture-driven, complex material asymmetry affects a simple structure: the bending of a tube. To this end, NiTi tubes are bent in a custom four-point bending facility under rotation control and isothermal conditions. The phase transformations lead to a closed moment-rotation hysteresis comprised of loading and unloading moment plateaus. During loading, localized nucleation of martensite results in a high curvature for the transformed sections of the tube and low curvature for the untransformed. Martensite, which corresponds to the higher curvature regime, spreads gradually while the moment remains nearly constant. The nucleation of martensite is in the form of bands inclined to the axis of the tube that organize themselves into diamond shaped deformation patterns on the tensioned side of the structure. The patterns are similar to those observed in bending of steel tubes with Lüders bands, however, for NiTi they develop only on the tensioned side due to the material asymmetry. A lower moment plateau is traced upon unloading with similar localized bending and the erasure of the diamond deformation patterns. This complex behavior was found to repeat for a number of temperatures in the pseudoelastic regime of NiTi with the moment-rotation hysteresis moving to higher or lower moment levels depending on the temperature.     

Stress measurement of SS400 steel beam using the continuous indentation technique

An analytical model is presented for determining surface residual stress using continuous indentation. The elastic residual stress is assumed to have no influence on contact area or hardness and to be uniform over a volume that is several times larger than the indentation mark. A step-by-step analysis for the residual-stress-induced load difference at a given depth is outlined here and such concepts as stress interaction, stress-sensitive contact morphology, and reversible contact recoveries during a stress relaxation are described. Finally, the proposed method is applied to the interpretation of the continuous indentation results obtained from an SS400 steel beam in which controlled bending stresses are generated. The stress estimated, however, showed a high scatter due to plastic pile-up deformation. When the optically measured contact area is used as an alternative of the contact area calculated from the unloading curve, the re-evaluated stress agrees well with the already known applied stress.     

Nanoindentation and Microindentation of CuAlNi Shape Memory Alloy

Nanoindentation and microindentation studies were conducted within individual grains of a CuAlNi shape memory alloy. Linear surface features were observed near the indentations after unloading, many of which were responsive to heating. Crystallographic orientation information was obtained from electron backscattering diffraction in order to compare the orientation of observed surface features to predicted austenite–martensite interfaces, slip planes, and possible fracture planes in this alloy. Most of the features observed can be attributed to austenite–martensite interfaces, which remain in the material after unloading due to the constraints of the plastic deformation created by indentation. Due to the temperature dependence of the transformation stress in shape memory alloys, these stress-induced martensites are observed to diminish with heating and to reappear with cooling. Plastic deformation is observed in the form of pile-up near the indentation.     

Damage evolution in particulate composite materials

Damage evolution in heterogeneous solids is modeled using transformation field analysis and imperfect interface model. Stress changes caused by local debonding are simulated by residual stresses generated by equivalent transformation strains or eigenstrains. Decohesion and both overall and local stress and strain rates are derived from thermodynamics of irreversible processes, which provide an excellent framework for the development of constitutive equations. Both tangent and unloading secant stiffness tensors are found along any prescribed mechanical loading path. Numerical simulation of debonding evolution in glass/elastomer composites is compared with experimental data and provides good agreement between the model and experiments.     

Oliver–Pharr indentation method in determining elastic moduli of shape memory alloys—A phase transformable material

Instrumented indentation test has been extensively applied to study the mechanical properties such as elastic modulus of different materials. The Oliver–Pharr method to measure the elastic modulus from an indentation test was originally developed for single phase materials. During a spherical indentation test on shape memory alloys (SMAs), both austenite and martensite phases exist and evolve in the specimen due to stress-induced phase transformation. The question, “What is the measured indentation modulus by using the Oliver–Pharr method from a spherical indentation test on SMAs?” is answered in this paper. The finite element method, combined with dimensional analysis, was applied to simulate a series of spherical indentation tests on SMAs. Our numerical results indicate that the measured indentation modulus strongly depends on the elastic moduli of the two phases, the indentation depth, the forward transformation stress, the transformation hardening coefficient and the maximum transformation strain. Furthermore, a method based on theoretical analysis and numerical simulation was established to determine the elastic moduli of austenite and martensite by using the spherical indentation test and the Oliver–Pharr method. Our numerical experiments confirmed that the proposed method can be applied in practice with satisfactory accuracy. The research approach and findings can also be applied to the indentation of other types of phase transformable materials.     

On modelling phase propagation in SMAs by a Maxwellian thermo-viscoelastic approach

In this paper we propose a Maxwellian thermo-viscoelastic approach to the problem of phase transformation in shape memory alloys. An explicit temperature-dependent non-monotone piecewise linear stress–strain relation is considered and the corresponding free energy function is used to establish the heat propagation equation. The heat exchange between the material and its environment is also taken into account. The numerical simulations of three end-displacement rates lead to serrated hysteresis loops and result in inhomogeneous deformations and exothermic/endothermic behavior during loading/unloading tests. It is shown that the influence of the strain rate on the size and shape of the hysteresis loop is due in fact to the heat exchange between the bar and its environment. The predictions are compared qualitatively with experimental results.