平头压痕试验确定薄膜弹塑性参数的研究

本文研究用平头压痕试验确定薄膜-基体材料中薄膜材料弹塑性参数的可行性,重点研究了薄膜材料的屈服强度和硬化模量的确定方法.利用有限元(FEM)进行了模拟计算,给出了平头压痕下典型的等应力分布,以及载荷-压入深度的曲线.通过对载荷-压入深度曲线的研究,给出了通过平头压痕试验确定薄膜屈服强度和薄膜硬化模量的方法.     

Numerical Study of Creep Damage Behavior of Thin Film/Substrate Systems under Indentation

A numerical study has been performed on the creep damage development of the thin film/substrate systems by the Kachanov‐Rabothov damage law. The emphasis was to study the influence of the modulus ratio of the substrate to the thin film, the size of the indenter and the indentation stress. Results show that two obvious damage zones are found ahead of the indenter. One is at the edge of the indenter, the other is at the interface ahead of the indenter edge. The influence of the modulus ratio of the substrate to the thin film on the indentation damage is not obvious before a certain creep time, and later, the greater modulus ratio of the substrate to the thin film has the smaller damage rate. And the indentation depth rate and the damage rate are also affected by the size of the indenter and indentation stress.     

Prediction of stress–strain relation using cone indentation: effect of friction

Atkins and Tabor's approach (J. Mech. Phys. Solids 1965; 13 : 149) for predicting uniaxial stress–strain relation of metals from cone indentation tests has been studied using numerical (finite element) simulation of cone indentation. Two indentation parameters, namely representative strain and constraint factor, which are central to the prediction approach, have been estimated using the simulation for cone indenters of different apical angles. The effect of specimen–indenter interface friction on these parameters has been characterized. It is shown that uncertainty in our knowledge of this friction condition has an important bearing on the prediction of the stress–strain curve. However, a good estimate of the stress–strain curve can be obtained by making reasonable assumptions about the nature of the friction at the specimen–indenter interface. The simulation results are found to agree well with those reported in the experimental study of Atkins and Tabor, when a coefficient of friction value typical for the specimen–indenter interface is used. Copyright © 2004 John Wiley & Sons, Ltd.     

An investigation on the onset of plastic deformation of nanocrystalline solid solution Ti-Al-N films

The nanoscale deformation behavior of the solid solution Ti_0.5Al_0.5N thin film was systematically investigated by nanoindentation measurements. The effect of the tip radius of the indenter on the behavior of elastic-plastic deformation was also evaluated. The Hertzian stress analysis was used to determine the distribution of resolved shear stress at the initiate plastic deformation, and the obtained critical resolved shear stress was compared to the theoretical shear strength to establish correlations and differences. Comparison of the calculated critical shear stress and theoretical shear strength also indicated that new complete dislocation nucleation during nanoindentation was not the prerequisite of the onset of plastic deformation, even at very shallow indentation depth.     

Elastic-plastic characterization of thin films with spherical indentation

Indentation characterization of thin films has most recently been investigated with currently available ultramicroindentation hardness instruments that use a pyramidal diamond tipped indenter. With these instruments determination of the hardness at depths of penetration as shallow as 5–10 nm is possible. However, the problems associated with such indenters are the inability to characterize the indenter tip radius and the fact that pointed indenters essentially perform tests at constant plastic strain. An alternative approach to measuring the mechanical properties of thin films is to use spherically tipped indenters of known tip radius and to follow the transition from elastic to plastic deformation. The Hertzian analysis provides the basis for determining the elastic behaviour and it may be modified to examine the elastic-plastic transition. From such observations it is possible to determine the variation in the mean indentation pressure with depth of penetration and to construct an equivalent stress-strain response of a material. Examples of this approach are given for bulk materials and metallic and polymeric thin films. Data have been collected with a UMIS-2000 instrument and have been analysed and simulated on the basis of the approach outlined above.     

Elastic/plastic indentation hardness and indentation fracture toughness: The inclusion core model

A new model for determining elastic/plastic indentation is presented. This model generalizes Johnson's incompressible core model to a compressible material and allows the indentation pressure to be transmitted via a misfitted inclusion core beneath the indenter which is surrounded by a hemispherical plastic zone. The internal stress field inside the core is obtained by applying Eshelby's spherical inclusion problem together with Hill's spherical-cavity expansion analysis. The plastic deformation considered here exactly ensures compatibility between the volume of a material displaced by the indenter and that accommodated by expansion. The analysis explains the essential relationships between the dimensions of the indentation and plastic zone and the dominant material properties; yield stress, hardness and elastic modulus. The solution is extended to evaluate the indentation fracture toughness by taking into account the reduced half-space constraint by the image force.     

A numerical fracture analysis of indentation into thin hard films on soft substrates

In this paper, finite element simulations of spherical indentation of a thin hard film deposited on a soft substrate are carried out. The primary objective of this work is to understand the mechanics of fracture of the film due to formation of cylindrical or circumferential cracks extending inwards from the film surface. Also, the role of plastic yielding in the substrate on the above mechanics is studied. To this end, the plastic zone development in the substrate and its influence on the load versus indentation depth characteristics and the stress distribution in the film are first examined. Next, the energy release rate J associated with cylindrical cracks is computed. The variation of J with indentation depth and crack length is investigated. The results show that for cracks located near the indenter axis and at small indentation depth, J decreases over a range of crack lengths, which implies stability of crack growth. This regime vanishes as the location of the crack from the axis increases, particularly for a substrate with low yield strength. Finally, a method for combining experimental load versus indentation depth data with simulation results in order to obtain the fracture energy of the film is proposed.     

Finite Element Analysis of Ceramic Coatings under Spherical Indentation with Metallic Interlayer： Part Ⅰ Uncracked Coatings

Spherical indentation of ceramic coatings with metallic interlayer was performed by means of axisymmetric finite element analysis （FEA）. Two typical ceramic coatings with relatively high and low elastic modulus deposited on aluminum alloy and carbon steel were considered. Various combinations of indenter radius-coating thickness ratios and interlayer thickness-coating thickness ratios were used in the modeling. The effects of the interlayer, the coating and the substrate on the indentation behavior, such as the radial stress distribution along the coating surface as well as the coating interface, and the plastic deformation zone evolution in the substrate were investigated in connection with the above mentioned ratios. The coating cracking dominant modes were also discussed within the context of the peak tensile stresses on the coating surface and on the coating interface.     

A three-dimensional finite element analysis of interface delamination in a ductile film/hard substrate system induced by wedge indentation

Interface delamination and arching of a ductile thin film on a hard substrate subject to microwedge indentation were investigated systematically using a three-dimensional finite element method. A traction-separation law was introduced to simulate the cohesion and failure behavior of the interface between the film and the substrate. The effects of the interface strength and the length of the microwedge indenter on the onset and growth of interface delamination and film arching were analyzed. It was shown that a two-dimensional to three-dimensional transition of stress state occurs during indentation, depending on the indenter length and indentation depth. Conditions for using two-dimensional and three-dimensional models were suggested.     

Finite Element Analysis of Ceramic Coatings under Spherical Indentation with Metallic Interlayer: Part Ⅰ Uncracked Coatings

Spherical indentation of ceramic coatings with metallic interlayer was performed by means of axisymmetric finite element analysis (FEA). Two typical ceramic coatings with relatively high and low elastic modulus deposited on aluminum alloy and carbon steel were considered. Various combinations of indenter radius-coating thickness ratios and interlayer thickness-coating thickness ratios were used in the modeling. The effects of the interlayer, the coating and the substrate on the indentation behavior, such as the radial stress distribution along the coating surface as well as the coating interface, and the plastic deformation zone evolution in the substrate were investigated in connection with the above mentioned ratios. The coating cracking dominant modes were also discussed within the context of the peak tensile stresses on the coating surface and on the coating interface.     

Mechanical properties of multilayered films using different nanoindenters

The effects of interface, contact hardness, deformation, and adhesion of Al/Ni multilayered films under nanoindentation were investigated using molecular dynamics (MD) simulations. The results show that the indentation force of the sphere indenter is the largest among nanoindentations using sphere, cone, Vickers, or Berkovich type indenters at the same penetration depth. Force increasing, relaxation and adhesion took place during loading, holding depth and unloading, respectively. The interface occurred along the {111} (110) slip systems and the maximum width of the glide bands was about 1 nm. The reaction force and plastic energy of the indented films are also discussed.     

Three dimensional imaging of deformation modes in TiN-based thin film coatings

A TiN thin film coating, approximately 4 μm in thickness, deposited on a ductile steel substrate, was subject to surface deformation via nanoindentation using a spherical indenter, 5 μm in radius, with loads up to 500 mN. Pop-ins were observed during loading, which are characteristic of the onset of cracking and the formation of shear steps at the coating-substrate interface. Focused ion beam microscopy was used to prepare cross-sections through the indentation that revealed the presence of both intercolumnar and inclined cracks. Three-dimensional reconstructions of the deformation zone beneath the indentation were performed using a dual-beam focus ion beam instrument. These constructions provided more detailed images of the morphology of cracks, which were observed to be consistent with theoretical models of plastic deformation of such brittle coatings.     

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.     

Cyclic indentation in aluminum

Cyclic indentation was used to evaluate the dynamic deformation of aluminum. Under the load-controlled cyclic indentation, the indenter continuously penetrated into the material and reached a steady state at which the penetration speed (per cycle) was a constant. The amplitude of the cyclic indentation depth was basically controlled by the amplitude of the cyclic indentation load, independent of the mean indentation load and the indentation frequency. The steady state penetration speed decreased with increasing the amplitude of the cyclic indentation load due to the increase in the size of plastic zone. It also decreased with the increase in the mean indentation load due to local strain hardening, while it increased with the increase of the indentation frequency.     

闭孔铝泡沫在静压痕下的力学响应

采用球形压头对闭孔铝泡沫材料进行了准静态压痕实验,研究了不同直径、铝泡沫相对密度及边界条件对铝泡沫的压痕硬度、吸能能力及能量吸收率的影响。研究表明,铝泡沫在球形压头作用下的响应曲线可采用幂函数形式进行描述,幂函数指数随相对密度的增大而线性增加。铝泡沫压痕处的断面显示铝泡沫变形被严格限制在压头之下,铝泡沫的压痕变形是局部的不均匀变形。铝泡沫的压痕硬度及吸能能力均随压头直径的增大而线性减小,但它们却均随铝泡沫相对密度的增大而线性增大;能量吸收率不随压头直径和铝泡沫相对密度而变化。在一定压痕深度范围内,刚性基础和简支条件对铝泡沫的压痕响应影响可以忽略不计。最后基于实验数据分别建立了压痕硬度和吸能能力与压头直径及铝泡沫相对密度的关系。      

Influence of contact geometry on hardness behavior in nano-indentation

In this paper the influence of contact geometry, including the round tip of the indenter and the roughness of the specimen, on hardness behavior for elastic-plastic materials is studied by means of finite element simulation. We idealize the actual indenter by an equivalent rigid conic indenter fitted smoothly with a spherical tip and examine the interaction of this indenter with both a flat surface and a rough surface. In the latter case the rough surface is represented by either a single spherical asperity or a dent (cavity). Indented solids include elastic perfectly plastic materials and strain hardening elastic–plastic materials, and the effects of the yield stress and strain hardening index are explored. Our results show that due to the finite curvature of the indenter tip the hardness versus indentation depth curve rises or drops (depending on the material properties of the indented solids) as the indentation depth decreases, in qualitative agreement with experimental results. Surface asperities and dents of curvature comparable to that of the indenter tip can appreciably modify the hardness value at small indentation depth. Their effects would appear as random variation in hardness.     

Determination of Elastic and Creep Properties of Thin-film Systems from IndentationExperiments

(3) The exponent "INDENT is dependent not onlyon the creep parameters C..... (f) and "cREEP (f) andCo.... (f) and "cREEP ('), but also on the size of theindenter as well as the thickness of the film. All the"INDENT are between "cREEP (f) and ncRBEP (s). Thesubstrate has more influence on the bigger indenter.(4) The boundary between the film and substratehas great obvious influence on the indentation creepbehavior. There is a stress concentration along theboundary. And as the creep…     

Improved core model of indentation and its application to measure diamond hardness

A model of the indentation using conical and pyramidal indenters has been proposed, in which not only a sample but the indenter as well are elastoplastically deformed and their materials obey the Mises yield condition. These conditions are characteristic of the measuring of diamond hardness through a diamond indenter. The model that has been proposed generalizes and refines the known simplified Johnson’s model, which uses an elastically deformed indenter. The proposed model makes it possible to determine approximately the sizes of elastoplastic zones in the indenter and sample, the effective apex angle of the loaded indenter and effective angles of the indenter and imprint after unloading. Based on this model a procedure of the determination of the sample and indenter yield strengths (Y _s and Y _i , respectively) has been developed, in which the relations that use the experimental values of the effective angle of the sample imprint and measured values of the Meyer hardness, HM (mean contact pressure) are added to theoretical relations of the indentation model. The developed computational procedure was applied in indentation experiments on synthetic diamond at the temperature 900°C (at which diamond exhibits a noticeable plastic properties) using natural diamond pyramidal indenters having different apex angles. According to the proposed model, the stress-strain states of samples and indenters have been investigated and their yield strengths and plasticity characteristics were defined. The stress–strain curve of the diamond in the stress-total strain coordinates has been constructed. The strain hardening of diamond was also studied.     

Effect of surface roughness on nanoindentation test of thin films

By using the two-dimensional quasicontinuum method, the nanoindentation process on a single crystal copper thin film with surface roughness is simulated to study the effect of surface morphology on the measurements of mechanical parameters. The nanohardness and elastic modulus are calculated according to Oliver-Pharr’s method. The obtained results show a good agreement with relevant theoretical and experimental results. It is found that surface roughness has a significant influence on both the nanohardness and elastic modulus of thin films determined from nanoindentation tests. The effect of such factors as the indenter size, indentation depth and surface morphology are also examined. To rule out the influence of surface morphology, the indentation depth should be much greater than the characteristic size of surface roughness and a reasonable indenter size should be chosen. This study is helpful for identifying the mechanical parameters of rough thin films by nanoindentation test and designing nanoindentation experiments.     

平头压头下基体对压痕规律的影响研究

本文通过对软薄膜/硬基体两相材料体系的平头压痕弹塑性模拟.重点研究了平压头压入过程中,不同屈服强度比(软薄膜屈服强度与硬基体屈服强度之比)以及不同压头尺寸下硬基体对压痕规律的影响.研究发现硬基体对压痕规律的影响与屈服强度比近似满足线性关系,且这种线性关系不随压头尺寸的改变而改变,相同压头半径下,屈服强度比越大,影响就越明显;相同屈服强度比下,压头半径越大,影响就越小.研究还发现压头压入过程中,材料的堆积对压入深度没有影响.