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.     

Micro-scratch analysis and mechanical properties of plasma-deposited silicon-based coatings on polymer substrates

Advanced optical applications require multifunctional coatings with specific mechanical properties, such as resistance to damage and good adhesion to different types of substrates, including polymers. In the present study we deposited amorphous hydrogenated silicon nitride (SiN_1.3) and oxide (SiO₂) films on polycarbonate and on silicon substrates by plasma enhanced chemical vapor deposition (PECVD), using a dual-mode microwave/radio frequency plasma system. The film adhesion was determined by the micro-scratch test. Depth-sensing indentation and substrate curvature measurements were used to evaluate the microhardness. Young's modulus and residual stresses of the films. The adhesion strength, represented by the critical load, L_c, when the film starts to delaminate, was determined as a function of the substrate material and the energy of bombarding ions. A direct correlation between the L_c values and the mechanical properties of the films was found. The formation of different crack patterns in the coatings during the scratch procedure is explained in terms of stress release mechanism depending on the mechanical properties of the film, the substrate and the interface region. In addition, different models applicable to the evaluation of the work of adhesion in the case of hard coatings on soft substrates are critically reviewed.     

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…     

Wedge indentation of a thin film on a substrate based on micromorphic plasticity

In this article, we use the small strain micromorphic plasticity (MP) to study the wedge indentation of a thin film on a substrate and find qualitative agreement with experiments. A two-dimensional plane strain finite element formulation of the entire MP theory framework is outlined. The generalization of the radial return method for modeling the elasto-plastic deformation is presented. The numerical results show that the MP theory is capable of describing the initial fall in hardness at small depth of indentation and then the rise at larger depth for a soft film on a hard substrate. The indentation force and hardness increase with decreasing film thickness for a given depth. It is also shown that the hardness falls monotonically as the indentation depth increases and never approaches a constant for a hard film on a soft substrate. Contrary to the soft film/hard substrate system, the force and hardness diminish with decreasing film thickness for a given depth. Besides, the influences of internal length scale and hardening modulus of the film on hardness predictions are investigated.     

Nanoindentation technique for measuring residual stress field around a laser-induced crack in fused silica

A nanometre scale indentation technique using microprobe indentations to measure residual stresses at selected positions near u.v.-laser-induced cracks in fused silica is presented. The approach is based on the observation that the nanoindentations' penetration depths are affected by the residual stress field emanating from the laser-induced crack. A simple theoretical model based on the change of the nanoindentation penetration depth as well as the change in Young's modulus and hardness of the material is derived. The results show good agreement with the inclusion model [15] suggesting that the residual stress field around a laser-induced crack in fused silica is of shear nature. An exploratory test made on an unstressed sample (free of a laser-induced crack), yielding values for Young's modulus and hardness in accordance with handbook values, shows the high accuracy of this nanoindentation diagnostic.     

Two-step method to evaluate equibiaxial residual stress of metal surface based on micro-indentation tests

The present study proposed a method to evaluate the equibiaxial compressive residual stress of a metal surface by means of a depth-sensing indentation method using a spherical indenter. Inverse analysis using the elastic–plastic finite-element model for an indentation test was established to evaluate residual stress from the indentation load–depth curve. The proposed inverse analysis utilizes two indentation test results for a reference specimen whose residual stress is already known and for a target specimen whose residual stress is unknown, in order to exclude the effect of other unknown mechanical properties, such as Young’s modulus and yield stress. Residual stress estimated by using the indentation method is almost identical to that measured by X-ray diffraction for indentation loads of 0.49–0.98 N. Therefore, it can be concluded that the proposed method can effectively evaluate residual stress on metal surface.     

Extracting thin film hardness of extremely compliant films on stiff substrates

A previously reported method for extracting the thin film hardness from nanoindentation into a film on an elastically mismatched substrate was applied to four different cases of extreme mismatch in elastic properties: Parmax, Ultem, Polysulfone and Perfluorocyclobutyl polymer thin films on Si substrates. All of these cases represent extremely compliant films on a stiff substrate, where the ratio of film shear modulus to substrate shear modulus ranged from 0.008 to 0.036. Analyzing the nanoindentation data into these film/substrate systems poses a significant limitation when using the Oliver and Pharr method as the hardness increases rapidly with indentation depth. Therefore, a method involving the measured contact stiffnesses to more accurately determine the correct contact areas was used to extract the true hardness of the polymer thin films. The results indicate that our method is able to remove the substrate effects as well as the complications arising from pile-up and surface roughness to yield a wide plateau in hardness despite the extreme elastic mismatch conditions.     

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.     

Determination of creep parameters from indentation creep experiments: a parametric finite element study for single phase materials

Abstract

This paper explores the possibilities of determining creep parameters for a simple Norton law material from indentation creep testing. Using creep finite element analysis the creep indentation test technique is analysed in terms of indentation rates at constant loads. Emphasis is placed on the evolving stress distribution in front of the indenter during indentation creep. Moreover the role of indenter geometry, size effects and of macroscopic constraints is explicitly considered. A simple procedure is proposed to translate indentation creep results into constitutive creep equations for cases where the dimensions of the tested material are significantly larger than the indenter. The influence of macroscopic constraints becomes important when the size of the indenter is of the same order of magnitude as the size of the testing material. As a striking example for size effects and for macroscopic constraints the indentation creep process in a thin film is analyzed. The results contribute to a better mechanical understanding of indentation creep testing.     

The Analytical and Numerical Study on the Nanoindentation of Nonlinear Elastic Materials

In nanoindentation testing of materials, the analytical/numerical models to connect the indentation load, indentation depth and material properties are crucial for the extraction of mechanical properties. This paper studied the methods of extracting the mechanical properties of nonlinear elastic materials and built general relationships of the indentation load and depth of hyperelastic materials combined with the dimensional analysis and finite element method (FEM). Compared with the elastic contact models and other nonlinear elastic contact models, the proposed models can extract the mechanical properties of nonlinear elastic materials under large deformation simply and effectively.     

A Simple Method for Estimation of Residual Stresses by Depth‐Sensing Indentation

Abstract: The evaluation of residual stresses is an important aspect in many engineering applications, such as surfaces produced by mechanical or thermal treatment processes or even thin films deposited on substrates. Currently, there are several techniques for residual stress measurement. However, its application is limited by problems associated with the precision and simplicity of measurement, as well as their applicability to a wide variety of materials and situations. Indentation tests are widely used in determining the mechanical properties of materials, so it is very important to assess their sensitivity to the presence of residual stresses. In this context, recourse to numerical simulation of indentation testing proves to be an important tool to study the effect of residual stresses in the determination of hardness and modulus as well as the actual determination of residual stresses. This paper investigates the influence of the presence of equibiaxial residual stresses in the indentation test results. It proposes a methodology for reverse analysis to determine the sign and value of the equibiaxial residual stresses present in the surface of materials, from depth‐sensing indentation results. For applying this methodology, the elastic and plastic behaviour of the material must be previously determined.     

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.     

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.     

基于纳米压痕法的羟基磷灰石/聚乳酸复合材料力学性能表征

采用准静态和动态纳米压痕技术研究了羟基磷灰石/聚乳酸（HA/PLA）复合材料在微纳尺度的表面力学性能。在静态模式下研究了保载和卸载时间对模量和硬度测试结果的影响。结果发现,当保载时间小于45 s时,由于蠕变使保载和卸载时间对测试结果产生显著影响;保载时间短且卸载时间长时,在卸载段会形成"鼻子",为了避免"鼻子"选择保载时间为45 s。在动态模式下研究了材料的动态力学性能,结果表明,存储模量和硬度均随着压入深度的增加而减小。压痕和划痕实验结果均表明：HA显著提高了PLA的力学性能,与纯PLA相比,9wt% HA/PLA复合材料的模量增加了35.5%,硬度增加了44.7%,蠕变深度下降了9.5%,相同载荷下的最大划痕深度和残余深度均小于纯PLA,表现出良好的弹性恢复能力和抗变形能力。     

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.     

On the factors affecting the critical indenter penetration for measurement of coating hardness

The nanoindentation test is the only viable approach to assess the properties of very thin coatings (<1 μm) since it can operate at the required scale and provides a fingerprint of the indentation response of the coating/substrate system. To measure the hardness of the coating only it is traditionally assumed that, as a rule-of-thumb, when the relative indentation depth (RID, i.e. the penetration divided by the coating thickness) is less than 0.1, the substrate will not affect the measured hardness of the coating. However, it is found that this rule is too strict for some and too loose for other coated systems. In this paper we present a comprehensive investigation of the factors influencing the critical relative indentation depth (CRID) using finite element simulation. The CRID is very sensitive to tip radius for soft coatings on hard substrates. For most coating/substrate combinations at reasonable penetration depths the 0.1 rule-of-thumb is a safe estimate. It is shown that the elastic property mismatch between coating and substrate also has an important effect on the measured hardness and this means that the Oliver and Pharr method generally used to extract hardness from nanoindentation data may give inaccurate results in coating/substrate systems with significant elastic mismatch.     

Finite element analysis of the indentation stress characteristics of the thin film/substrate systems by flat cylindrical indenters

The indentation stress characteristics of thin film/substrate systems by the flat cylindrical indenters have been simulated by means of the finite element method (FEM). The emphasis was put on the stress distribution ahead of the indenters. The influences of the friction coefficient between the indenter and the thin film, the thickness and hardening modulus of the thin film have been considered. It is found that the stress distribution was not affected by the friction coefficient. But the influence of the thickness and hardening modulus of the thin film on the stress distribution was obvious. At small indentation depth, the plastic deformation occurs at the edge of the indenter only, and the zone will propagation both vertically and laterally with the indentation depth increasing. When the indentation depth reaches a certain value, the thin film at the interface will occur the deformation plastic zone for the case studied in this paper. At lager depths, the two plastic zones will connect, and then the plastic zone propagates along the lateral direction. Beside, it is also found that the maximum of the Mises stress and the shearing stress on the interface occur at 0.8r and r(r is the radius of the indenter), respectively.     

An Inverse Approach for Extracting Elastic-plastic Properties of Thin Films from Small Scale Sharp Indentation

An inverse method for extracting the elastic-plastic properties of metallic thin films from instrumented sharp indentation has been proposed in terms of dimensional analysis and finite element modeling.A wide range of materials with different elastic modulus,yield strength,and strain-hardening exponent were examined.Similar to the Nix-Gao model for the depth dependence of hardness H,(H/H0)2=1+h*Hh,the relationship between elastic modulus E and indentation depth h can be expressed as(E/E0)4=1+h*Eh.By combining these two formulas,we find that there is a relationship between yield stress σ y and indentation depth h:σy = σy0·(1+h*Hh)f(n)·(1+h*Eh)[0.25-0.54f(n)],where σ y0 is the yield strength associated with the strainhardening exponent n,the true hardness H0 and the true elastic modulus E0.f(n)= 1/2(1-n) is constant,which is only related to n,and h*H and h*E are characteristic lengths for hardness and elastic modulus.The results obtained from inverse analysis show that the elastic-plastic properties of thin films can be uniquely extracted from the solution of this relationship when the indentation size effect has to be taken into account.     

Computer Simulation of the Indentation Creep Tests on Particle-Reinforced Composites

A systematical simulation has been carried out on the indentation creep test on particle-reinforced composites.The deformation ,failure mechanisms and life are analyzed by three reasonable models.The following five factors have been considered simultaneously:creep property of the particle,creep property of the matrix,the shape of the particle, the volume faction of the particle and the size(relative size to the particle )of the indentation indenter.For all the cases,the power law respecting to the applied stress can be used to model the steady indentation creep depth rate of the indenter,and the detail expressions have been presented.The computer simulation is analyzed by the two-phase model and the three-phase model.Two places of the stress concentration are found in the composites.One is ahead of the indentation indenter, where the high stress state is deduced by the edge of theindenter and will decrease rapidly near to a steady value with the creep time The other one is at the interface,where the high stress state is deduced by the misfit of material properties between the particles and matrix.It has been found that the creep dissipation energy density other than a stress parameter can be used to be the criterion to model the debonding of the interfaces.With the criterion of the critical creep dissipation energy density, a power law to the applied stress with negative exponent can be used to model the failure life deduced by the debonding of interfaces.The influences of the shape of the particles and the matching of creep properties of particle and matrix can be discussed for the failure.With a crack model,the further growthe of interface crack is analyzed, and some important experimental phenomena can be predicted.The failure mechanism which the particle will be punched into matrix has been also discussed.The critical differences between the creep properties of the particles and matrix have been calculated, after a parameter has been defined.In the view of competition of failure mechanisms, the best matching of the creep properties of the two phases and the best shape of the particles are discussed for the composite design.     

A Reverse Numerical Approach to Determine Elastic-plastic Properties of Multi-layer Material Systems with Flat Cylindrical Indenters

In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extracting the yield stresses and strain-hardening modulus of upper and middle-layers of three-layer material systems from the indentation testing. The slope of the indentation depth to the applied indentation stress curve was found to have a turning point, which can be used to determine the yield stress of the upper-layer. Then, a different method was also presented to determine the yield stress of the middle-layer. This method was based on a set of assumed applied indentation stresses which were to be intersected by the experimental results in order to meet the requirement of having the experimental indentation depth. At last, a reverse numerical algorithm was explored to determine the yield stresses of upper and middle-layers simultaneously by using the indentation testing with two different size indenters. This method assumed two ranges of yield stresses to simulate the indentation behavior. The experimental depth behavior was used to intersect the simulated indentation behavior. And the intersection corresponded to the values of yield stresses of upper and middle-layers. This method was also used further to determine the strain-hardening modulus of upper and middle-layers simultaneously.