Measurement of Residual Stresses Using Nanoindentation Method

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Critical Reviews in Solid State and Materials Sciences

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Measurement of Residual Stresses Using Nanoindentation Method

Li-Na Zhu, Bin-Shi Xu, Hai-Dou Wang & Cheng-Biao Wang

To cite this article: Li-Na Zhu, Bin-Shi Xu, Hai-Dou Wang & Cheng-Biao Wang (2015)

Measurement of Residual Stresses Using Nanoindentation Method, Critical Reviews in Solid State and Materials Sciences, 40:2, 77-89, DOI: 10.1080/10408436.2014.940442To link to this article:

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Measurement of Residual Stresses Using Nanoindentation Method

Li-Na Zhu,1Bin-Shi Xu,2Hai-Dou Wang,1,2,*and Cheng-Biao Wang 1

1School of Engineering and Technology,China University of Geosciences,Beijing 100083,China

2

National Key Lab for Remanufacturing,Academy of Armored Forces Engineering,Beijing 100072,China

Instrumented indentation,which is also known as nanoindentation or depth-sensing indentation,is increasingly being used to probe the residual stresses of materials including bulk solids,thin ?lms,and coatings.The residual stresses are proved to have signi?cant effects on various nanoindentation parameters such as hardness,loading curve,unloading curve,pile-up amount around indentation,and true contact area.By analyzing these parameters,numerous methods are developed to evaluate the residual stresses of materials in recent years.This article reviews six commonly used models which determine residual stresses from analyzing load-depth curves,as well as indentation fracture technique which is based on the classical fracture mechanics.Emphasis is placed on the principle,application and limitation of each nanoindentation method.Keywords

nanoindentation,residual stress,non-destructive testing

Table of Contents

1.INTRODUCTION ...........................................................................................................................................2

2.BASIC PRINCIPLES OF NANOINDENTATION METHOD .............................................................................2

3.

EFFECT OF RESIDUAL STRESSES ON NANOINDENTATION RESPONSE ...................................................43.1.Effect on Mechanical Properties..................................................................................................................43.2.Effect on Load-Depth Curves .....................................................................................................................43.3.Effect on Pile-Up......................................................................................................................................43.4.Effect on True Contact Area.......................................................................................................................54.

NANOINDENTATION MODELS FOR THE DETERMINATION OF RESIDUAL STRESS ...............................54.1.Suresh Model...........................................................................................................................................54.2.Lee Models. (7)

4.2.1.Lee Model I....................................................................................................................................74.2.2.Lee Model II...................................................................................................................................84.2.3.Application of Lee Models................................................................................................................84.3.Xu Model................................................................................................................................................84.4.Swadener Models . (9)

4.4.1.Swadener Model I...........................................................................................................................94.4.2.Swadener Model II..........................................................................................................................94.4.3.Limitation of Swadener Models.........................................................................................................9

5.

INDENTATION FRACTURE TECHNIQUE FOR THE DETERMINATION OF RESIDUAL STRESS (10)

*E-mail:wanghaidou@https://www.wendangku.net/doc/593718660.html,

Color versions of one or more of the ?gures in this article can be found online at https://www.wendangku.net/doc/593718660.html,/bsms.

77

Critical Reviews in Solid State and Materials Sciences,40:77–89,2015Copyright óTaylor &Francis Group,LLC ISSN:1040-8436print /1547-6561online DOI:

10.1080/10408436.2014.940442

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6.CONCLUSIONS (11)

FUNDING .............................................................................................................................................................11REFERENCES (11)

1.INTRODUCTION

Residual stresses are readily generated by inhomogeneous heat treatment or local plastic deformation involving bulk sol-ids,1–3thin ?lms,4–6and coatings 7–9used in various industrial components.The existing residual stress ?eld in these compo-nents has a signi?cant effect on their performance such as mechanical properties,10fatigue strength,11wear and fracture properties,12,13etc.The existence of residual stress may be bene-?cial or detrimental,depending upon its value and the potential application.For instance,compressive residual stresses in the coatings can improve the adhesion and fatigue strength of the system,while high tensile stresses may cause cracking and fatigue failure.Thus,to measure and control accurately residual stresses is very important in both scienti?c and technological perspectives.

Various experimental techniques have been developed to measure the residual stresses in materials,such as X-ray dif-fraction,14hole-drilling,15layer removal,16neutron diffrac-tion,17synchrotron,18Raman spectroscopy,19ultrasonic method,20and magnetic method.21However,these methods all have some problems.For example,X-ray diffraction method is con?ned to crystals and inapplicable to amorphous materials.As the penetration depth of X ray is very shallow,the measurement depth is only about 30m m.Hole-drilling method is destructive to materials,and the measurement accu-racy is easily in?uenced by many factors such as aperture,hole depth,and bonding quality of strain gauges.Raman spec-troscopy and magnetic method are inapplicable to metals and non magnetics,respectively.Neutron diffraction and synchro-tron equipment are expensive and scanty,which are dif?cult to apply to actual production.The limitation of these methods drives the development of new measuring technology.

Nanoindentation is an instrumented indentation method,which is often used to extract the mechanical properties of bulk solids,thin ?lms,and coatings.22–28In addition,nanoindentation also can be used to estimate residual stresses in materials.In past decades,numerous studies have been conducted to determine residual stresses by nanoindentation.The in?uence of residual stress on various nanoindentation parameters such as hard-ness,29–31loading behavior,32–34unloading behavior,35–37con-tact area,34,37–39and pile-up,37,39–41has been investigated both experimentally and with ?nite element simulations.

The experiment carried out by Tsui et al.30showed that hardness calculated by standard methods decreased with ten-sile stress and increased with compressive stress.However,

the ?nite element analysis by Bolshakov et al.31revealed that the hardness was not always dependent of residual stress.For materials that are prone to pileup,the hardness is not signi?-cantly affected by residual stress when proper contact area is used.Based on that hardness is invariant regardless of the residual stress,Suresh et al.proposed a methodology to deter-mine the equibiaxial residual stress from the difference in con-tact area of stressed and stress-free materials indented to the same depth.42Lee et al.1developed a new model to evaluate the equibiaxial residual stress by combining stress relaxation with a shear plastic-deformation concept.This model ?tted the contact area as an equation of the third degree in the indenta-tion load to make the residual stress be only related to the indentation load.To overcome the limitation of the model to equibiaxial or uniaxial residual stress,Lee et al.43proposed a new indentation model,which can evaluate an arbitrary biaxial stress.Through ?nite element simulations,Xu et al.35,36pro-posed an empirical model,which is based on the effect of residual stress on the unloading curve of nanoindentation.It was found that the elastic recovery parameter h e /h max has a lin-ear relationship with the ratio of residual stress to yield stress s r /s y .Subsequently,the empirical model was applied to deter-mine the residual stress in a mechanically fused quartz beam.Swadener et al.44suggested that spherical indentation is more sensitive to stress effects than sharp indentation,and then developed two methods to measure biaxial residual stress.An alternative way to measure the residual stress is using indentation fracture technique,which is based on the classical fracture mechanics.45The residual stress can be estimated by comparing the crack lengths of indentations on stressed surfa-ces with those on stress-free surface.

This article reports on a brief description of different nano-indentation models to determine residual stress.The prerequi-site and limitation of these models are discussed.

2.BASIC PRINCIPLES OF NANOINDENTATION METHOD

Figure 1shows a typical load-depth curve consisting of load-ing and unloading.During loading,both elastic and plastic defor-mations occur as the permanent impression is generated.During unloading,only the elastic formation is assumed to be recovered,and reverse plastic deformation is usually negligible.46

Figure 2illustrates the unloading process and important parameters characterizing the contact geometry.At present,the Oliver method is commonly used to characterize the

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hardness and elastic modulus based on the analysis of the load-depth curves.47,48The hardness H and reduced modulus E r are de?ned by

H D

P max c

(1)

E r D S ???p p 2b ?????A c

p ;

(2)

where P max is the maximum load,A c is the contact area,S D d P /d h is the contact stiffness at the initial unloading,and b is a constant which depends on the geometry of the indenter.The

reduced modulus E r is de?ned by

1r D 1?n 2C 1?n 2i

i

;

(3)

where E and E i are the elastic modulus of the specimen and the

indenter,respectively and v and v i are the Poisson’s ratio of the specimen and the indenter,respectively.

A crucial step in calculating the hardness and elastic modu-lus is the determination of the contact stiffness at the initial unloading and the projected contact area at the peak load.The unloading curve is usually well approximated by the power law relation:

P D a h ?h r eTm ;

(4)

where a and m are power law ?tting constants and h r is the residual depth after unloading.

The contact stiffness at the initial unloading can be obtained by differentiating Eq.(4)at the maximum depth h max :

S D

dP dh

h D h max

D a m h max ?h r eTm ?1:

(5)

The projected contact area can be calculated from the relation

A c D f h c eT;

(6)

where h c is the contact depth.Since the Oliver method assumes that the contact periphery sinks in,h c is always smaller than h max :

h c D h max ?e

P max

S

;(7)

where e is a constant that depends on the geometry of the indenter.

As the indenter generally deviations from perfect geometry,the area function is usually ?tted by

A c D X 8n D 0

C n h c eT2?n

D C 0h 2c C C 1h c C L C C 8h 1=128

c

;(8)

where C 0...C 8are constants determined by curve-?tting procedures.

Once the contact stiffness and contact area are determined,the hardness and elastic modulus can be calculated by Eqs.(1)–(3).

Work-of-indentation methods can also be used to measure a material’s hardness.49The hardness can be determined

based

FIG.1.A typical load-depth

curve.

FIG.2.Schematic illustration of the unloading process show-ing parameters characterizing the contact geometry.(óCam-bridge University Press.Reproduced with permission of

Oliver and Pharr.47Permission to reuse must be obtained from the rightsholder.)

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on the total work and plastic work:

H W t D kP 3

max

9W 2t (9)H W p D

kP 3max

9W p

;(10)

where W t is the total work,W p is the plastic work,and k is a

constant equal to 0.0408for the Berkovich indenter.The total work and elastic work can be obtained by integrating the load-ing curve and unloading curve,respectively.The plastic work is the difference between the total work and elastic work.

Note that the Oliver method does not account for the pile-up of material at the contact periphery that occurs in some elastic-plastic materials.For pile-up,many correction methods have been proposed based on imaging the contact impres-sion.50–55

3.EFFECT OF RESIDUAL STRESSES

ON NANOINDENTATION RESPONSE 3.1.Effect on Mechanical Properties

Both experiments and ?nite element simulations were used to investigate the effect of residual stresses on nanoindentation response.Both hardness and elastic modulus were found to increase with compressive stress and decrease with tensile stress,30when the nanoindentation data were analyzed by stan-dard methods.However,the elastic modulus which is an intrinsic property of the material should not be affected by stresses.Subsequently,both experiments and simulations show that the properties measured according to standard meth-ods are inaccurate because pileup around the indentation is not accounted for in the contact area determination.Once the proper contact area is used,the hardness and elastic modulus are signi?cantly independent of stress.

3.2.Effect on Load-Depth Curves

The residual stresses signi?cantly affect load-depth curves.For a ?xed penetration depth,the loading curves for compres-sive stresses are higher than those for stress-free state,and conversely for tensile stresses.31,32,34,37,39,56–59Figure 3shows the effect of residual stress on loading curves.The compres-sive stress can constrain the indentation plasticity,thus leading to a higher indentation load than that for stress-free state.Sim-ilarly,the effect of tensile stress is opposite to that in compres-sive stress state by enhancing the indentation plasticity.

A similar behavior was found for the unloading curves which shifted to the left for compressive residual stress and right for tensile residual stress when compared with that of stress-free state.31,37,39Figure 4shows the ending part of unloading curves for indents made to a maximum depth of 700nm of copper single crystal with different residual stress states.Since the unloading process of nanoindentation is a

pure elastic process and the compressive stress in the material tends to push the indenter up more,more elastic recovery and smaller residual depth are induced.35While the tensile stress gives an opposite effect,thus leading to less elastic recovery and larger residual depth.

3.3.Effect on Pile-Up

It is well known that materials exhibiting low strain harden-ing tend to pile up around indents due to the

incompressibility

FIG.3.Loading curves for indents made to a maximum depth of 700nm of copper single crystal with different residual stress states.(óElsevier.Reproduced with permission of Zhu et al.39Permission to reuse must be obtained from the

rightsholder.)

FIG.4.The ending part of unloading curves for indents made to a maximum depth of 700nm of copper single crystal with different residual stress states.(óElsevier.Reproduced with permission of Zhu et al.39Permission to reuse must be obtained from the rightsholder.)

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of plastic deformation.60The amount of pile-up can be charac-terized by the height of the pile-up relative to the undeformed surface.It is shown that pileup is large when there are large compressive stresses in the materials,but relatively small for large tensile stresses.31,37-39For compressive stresses,the materials are pushed out to the surface of indenter,which results in more pile-up;whilst tensile stresses tend to pull the materials away from the surface of indenter to decrease the amount of pile-up.In addition to residual stress,pileup defor-mation behavior is related with the ratio h f /h max and work-hardening behavior.61The pile-up amount is large when h f /h max is close to 1and the degree of work hardening is small.When h f /h max is less than 0.7,very little pile-up occurs no matter what the work-hardening behavior of materials.3.4.Effect on True Contact Area

The residual stresses also have a signi?cant effect on the true contact area of indentation in pile-up materials.Numerous studies have shown that the true contact area has an almost lin-ear relationship with the residual stress and increases with increasing compressive stress,while it decreases with increas-ing tensile stress.31,35,37,62The different variation of true con-tact area with residual stresses is due to the fact that compressive stresses tend to increase the pile-up amount,thus increasing the true contact area,while tensile stresses gives an opposite effect to decrease the true contact area.

Determination of true contact area for pile-up material has been a hot and dif?cult research topic in recent years.Atomic force microscope is usually used to determine the true contact area.Kese et al.51proposed a semi-ellipse model to correct the contact area.Each pileup contact perimeter was approximated as projecting a semi-ellipse with major axis b and minor axis a i .Then the true contact area can be obtained as

A D A O-P C 5:915h c X

a i ;(11)

where A O-P is the contact area from the Oliver-Pharr method and a i (i D 1,2,3)is the width for 3pileup lobes.

Saha et al.53assumed that the piled-up material forms an arc around the edge of the indentation (three-arc model).Based on this assumption,Zhu et al.proposed a model to determine the true contact area.50The projected contact area can be modeled as an equilateral triangle bounded by three arcs,as shown in Fig.5.The true contact area A can be obtained as

A D 14:175

up

120sin u

2

?3cot u C ???3p

!h max C h ave

p 2:(12)

The pile-up width x can be de?ned as

x D R ?Rcos u 2D a 2sin u 21?cos

u

2

D 3:7651?cos u 2sin u

2

h max C h ave

p ;(13)

where h p and x can be determined from the pro?le of indents,as shown in Figures 6and 7.

Equating Eqs.(12)and (13),the true projected contact area A can be calculated.

Maybe there are other methods that can be used to measure the area of pile-up deformation,the above two models (semi-ellipse model and three-arc model)both have been used by other researchers.63,64However,a uni?ed method has not yet been formed.

In summary,residual stresses have signi?cant effect on load-depth curve,pile-up height,and true contact area.Thus,the state (tensile or compressive)of residual stress can be determined by comparing the load-depth curve,pile-up height,and true contact area of stressed material with those of stress-free reference material.Among the three parameters,it is easiest to obtain load-depth curve from nanoindentation data.However,only residual stress state can be qualitatively determined by simple comparison of load-depth curves for stressed and stress-free materials.To determine quantitatively the magnitude of residual stress in the materials,speci?c relationship between residual stress and nanoindentation parameters should be extracted from analyzing load-depth

curves.

FIG.5.Schematic representation of the projected contact area considering pile-up.(óElsevier.Reproduced with permission of Zhu et al.50Permission to reuse must be obtained from the rightsholder.)

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4.NANOINDENTATION MODELS FOR THE DETERMINATION OF RESIDUAL STRESS

At present,there is no one set method that can be applied to the calculation of residual stress for all materials.In this sec-tion,six typical models usually used to quantitatively deter-mine residual stress from analyzing load-depth curves are discussed,including Suresh model,Lee models,Xu model,and Swadener models.

4.1.Suresh Model

The residual stresses (tensile or compressive)are assumed to be equibiaxial and the magnitude is uniform over a depth which is at least several times larger than the indentation con-tact diameter.The prerequisite of the model is that the material hardness H is unaffected by any pre-existing residual stresses.The relation between the residual stress s and the ratio of the real contact area A of material with residual stress to that of stress-free material A 0can be written as

s D H A 0

A ?1 for tensile stress (14)s D H 1?A 0

for compressive stress :(15)This model is based on the difference of contact area

between a stress-free material and the same material with residual stress.When indented to the same depth,the contact area of material with compressive stress is larger than that of stress-free material,while smaller for tensile stress.

Note that there is a coef?cient difference (sin a )between the calculation formulae for tensile stress and compressive stress.Because the effects of tensile stress and compressive stress on the indentation process are different,as shown in Figures 8and 9.It is obvious that s A is the difference of load in the z direction between the materials with and without tensile stress,while s A sin a is the difference of load in the z direction between the materials with and without compressive stress.Before calculating the magnitude of residual stress using the Suresh model,the residual stress state (tensile or compressive)should be determined from the loading curves for the stressed and stress-free specimens.Figure 10shows the loading curves for the stressed and stress-free 1045steels at a ?xed depth of 230nm.It is concluded that the residual stress in the stressed steel is compressive,because the material with compressive residual stress requires larger force to be indented to the same depth as the one without residual stress.65According to Eq.(15),the residual stress in the stressed steel was ?117§20MPa,which was in good agreement with that by the

traditional

FIG.6.Pile-up height h p

.

FIG.7.Pile-up width x.

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XRD method (?114§32MPa).As the measuring depths for the indentation and XRD methods are different,the XRD results cannot provide a calibration standard for indentation testing,and only can be used as a reference.

Considerable efforts have been made to determine the resid-ual stresses introduced during the preparation of thermal spray-ing coatings.66–69The Suresh model has been con?rmed to be an attractive method,since it allows such residual stresses to be quickly measured in a small region with non-destructive man-ner and to be mapped across the coating thickness.29Note that the Suresh model is only valid for homogeneous coatings,and the calculated value is only an approximation for unhomogene-ous coatings containing micropores and microcracks,or

complicated phase structures.If the indentation location is close to micropores or microcracks,the indentation depth will increase.This will lead to the increase of contact area and decrease of hardness.As the contact area and hardness are char-acteristic parameters for the Suresh model,errors for the calcu-lated value of residual stress are bound to be produced.Therefore,in order to increase the accuracy of measurement,the location of indents should be selected through optical microscope or atomic force microscope to keep away from micropores or microcracks as far as possible.

The Suresh model also provides an accurate measure of residual stress in thin ?lms with unknown material properties.The study by Taylor et al.70showed that the residual stresses in the thin carbon ?lms calculated using the Suresh model agree well with the theoretical analysis.The Suresh model and classi-cal XRD technique were used by Atar 71to determine the resid-ual stresses in ceramic thin ?lms.The residual stresses obtained by the indentation method have been found to be three times higher than those of the XRD technique.As the XRD technique has certain errors in measuring residual stresses,thus it cannot be used to con?rm the accuracy of the Suresh model.

Although the Suresh model can be applied to various mate-rials,it has obvious disadvantages.The model is speci?c for sharp indenters,such as Berkovich or Vickers indenters,and is limited to equi-biaxial residual stresses.Moreover,the model requires a stress-free reference sample such as free-standing ?lm or coating,which is often dif?cult to produce.On the other hand,the residual stresses in free-standing ?lm or coat-ing cannot be completely released;the hardness values of the stressed sample or stress-free reference sample are not identi-cal.Thus,unavoidable errors cannot be diminished from an experimental

standpoint.

FIG.10.Loading curves for the stressed and stress-free 1045steels at a ?xed depth of 230nm.(óElsevier.Reproduced with permission of Zhu et al.34Permission to reuse must be obtained from the

rightsholder.)

FIG.8.Schematic of the role of tensile stress at the indented surface.(óElsevier.Reproduced with permission of Suresh and Giannakopoulos.42Permission to reuse must be obtained from the

rightsholder.)

FIG.9.Schematic of the role of compressive stress at the indented surface.(óElsevier.Reproduced with permission of Suresh and Giannakopoulos.42Permission to reuse must be obtained from the rightsholder.)

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4.2.Lee Models 4.2.1.Lee Model I

In 2003,Lee et al.proposed a new model based on stress relaxation theory to determine equibiaxial residual stresses.Keeping the penetration depth constant,relax the residual stress from the initial value s r to zero.

The residual stress can be calculated from the stress-induced normal load and load difference between the materials with and without residual stress:s r D

3

2P 0?P 1eT2R 3P 41C R 2?R 3P 0eTP 31

C R 1?R 2P 0eTP 21C R 0?R 1P 0eTP 1?R 0P 0

;(16)

where P 0and P 1are the peak loads for the stress-free material

and the material with residual stress.R 0,R 1,R 2,and R 3are ?t-ting constants between the contact area and peak load.

4.2.2.Lee Model II

In 2004,Lee et al.proposed another model to calculate non-equibiaxial surface stresses.Six different stresses were applied to the specimens using a special apparatus and divided into four categories (see Table 1):uniaxial stress

(s r x ?0;s r y D 0,3#and 5#),equibiaxial stress (s r x D s r

y ?0,1#

and 6#),biaxial stress (s r x ?s r

y ?0,2#),and pure shear stress

(s r x D ?s r y ?0;4#).s r y can be expressed as k s r

x using a stress

ratio k ,i.e.k D s r y =s r

x ,where k ranges from ?1.0to 1.0.

The biaxial stress can be separated into an equibiaxial stress and a pure shear stress.As the pure shear stress has no effect on the indentation load,the measurement of biaxial stress can be simpli?ed as an equibiaxial problem.The biaxial stress can be calculated as

s r x D

3P 0?P 1eT

1C k eTA c

;

(17)

where P 0and P 1are the peak loads for the stress-free material and the material with residual stress.A c is the contact area of stressed material.Actually,Lee model I is the same as Lee model II when the stress ratio k D 1,namely,equibiaxial stress state.

4.2.3.Application of Lee Models

The nanoindentation tests were performed on the cross-sec-tions of stressed and unstressed thermal barrier coating (TBC)samples.72The unstressed sample was obtained by immersing the stressed sample in hydrochloric acid to dissolve the 304stainless steel substrate.The residual stress in the TBC was compressive since the coef?cient of thermal expansion of the TBC is less than that of metal substrate.As the indentations were performed on the cross-section of the TBC,the compres-sive stress applied on the indenter can be considered as a uni-axial stress.Thus,the residual stress in the TBC was calculated using Eq.(17),k D 0.The results showed that the compressive stresses in the top coat (TBC)decrease from the bonding coat (BC)/TBC interface to the top surface of TBC.It is obvious that the Lee model can evaluate the distribution of the residual stress in micro scales.

X.Zhao et al.57investigated the residual stresses in TBCs by photoluminescence piezospectroscopy (PLPS)and nanoin-dentation.The residual stresses obtained by nanoindentation have similar trend with those calculated from PLPS measure-ments.However,X.Zhao et al pointed out that the Lee model is only valid for a homogeneous material.As the TBC is far from homogeneous,the residual stresses calculated by nanoin-dentation are only approximation.

M.K.Khan et al.37determined the residual stresses in Al-cladding and Al 2024-T351by the Suresh and Lee models.The residual stresses from both of the Suresh and Lee models agree well with those from ?nite element simulation.The divergence of the residual stresses on the far ends of the com-pressive and tensile regions is due to that the Suresh model describes a nonlinear relationship and the Lee model considers linearity in these regions.

Like the Suresh model,the Lee models also require a stress-free reference sample,although non-equi-biaxial surface stress can be determined.In addition,the models are based on a stress-relaxation theory,i.e.,the residual stresses are deter-mined from the changes in applied load during stress relaxa-tion at ?xed indentation depth.However,the indentation process is often considered as an elasto-plastic problem and residual stress cannot be relaxed alone when keeping the depth invariable,because the stress-relaxation process can lead to a simultaneous change in the indentation load and depth.654.3.Xu Model

In 2006,Xu et al investigated the effect of equibiaxial residual stress on the elastic recovery of nanoindentation using ?nite element simulations.The results showed that the residual stress affects not only the real contact area but also the elastic recovery parameter,i.e.the ratio of elastic recovery to the maximum penetration depth,h e /h max .The h e /h max ratio has a

TABLE 1

Unstressed reference and six different stressed states.(óElsevier.Reproduced with permission of Lee and Kwon.43Permission to reuse must be obtained from the rightsholder)Stress state s r x (MPa)s r y (MPa)k D s r y =s r

x Reference 00Unstressed

1#?415?414 1.0(equibiaxial)2#?375?2480.66(biaxial)3#?40800(uniaxial)

4#?239231?1.0(pure shear)5#41400(uniaxial)6#

428

427

1.0(equibiaxial)

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linear relationship with the ratio of residual stress to yield stress,s r /s y ,as shown in Figure.11.In addition,the slope of the h e /h max vs.s r /s y depends only on the E /s y ratio.The fol-lowing equation can be used to relate the h e /h max ratio with the s r /s y ratio:

h e h max D ?a s r

s y

C b ;(18)

where a and b are ?tting constants,a is the slope of h e /h max vs.s r /s y curves,and b is the intercept of h e /h max vs.s r /s y curves at s r D 0.a depends only on the E /s y ratio,and the relation-ship between them follows a power law relationship:

a D 10:53

E

y

?1:25:(19)

Equations (18)and (19)are the empirical model to determine equibiaxial residual stresses.

In order to verify the above model,Xu et al.estimated the residual stress in the mechanically polished fused quartz beam.The fused quartz beam was ?rmly held in a three-point bending device.The obtained residual stress in the mechani-cally polished fused quartz beam is a compressive stress with the magnitude of 30MPa.

The Xu model does not require any reference sample with known stress state,such as stress-free sample,or any particular mechanical properties.However,it requires a special three-point bending device,which limits the practical applications of this method.Moreover,as the method relies on an accurate determination of the ratio of h e /h max ,experimental factors such as surface roughness will result in a great error in

determination of h e /h max ratio from the unloading curve of indentation.Besides,the Xu model may be just suitable for the determination of residual stress in very hard materials with low E /s y ratios and limits the application to very soft materials with high E /s y ratios,since the sensitivity of the h e /h max ratio to the residual stress is inversely proportional to the E /s y ratio of the material.4.4.Swadener Models 4.4.1.Swadener Model I

In 2001,Swadener et al presented two methods for making measurements of biaxial residual stress using spherical inden-tation.The model based on the fact that the indentation depth or contact radius at the onset of yielding is affected by the residual stress in a way that can be analyzed by Hertzian con-tact mechanics.The residual stress can be calculated by

s R s y

D 1?3:723p

E r a s y R

0;

(20)

where R is the indenter radius;a the contact radius;s y the

yield stress.Obviously,if s y is available,the residual stress can be determined by Eq.(20)with experimental measurement of (E r a /s y R )0,which can be determined using least squares regression curve ?ts of h r /h max D A 1C A 2log(E r a /s y R ),as shown in Figure 12.4.4.2.Swadener Model II

Swadener model II is based on the empirical Tabor relation-ship between hardness and yield stress,

H D C s y ;

(21)

FIG.11.Effect of residual stress on elastic recovery parame-ter h e /h max .(óTaylor &Francis.Reproduced with permission

of Xu and Li.36Permission to reuse must be obtained from the

rightsholder.)

FIG.12.Relationships between h r /h max and E r a /s y R at differ-ent residual stresses.(óCambridge University Press.Repro-duced with permission of Swadener et al.44Permission to reuse must be obtained from the rightsholder.)

RESIDUAL STRESS MEASUREMENT

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where C is the constrain factor.For stressed materials,Eq.(21)should be rewritten as

H C s R D C s y :(22)

By establishing the variation of C s y with E r a /s y R through experiments in a reference material in a known stress state,then the residual stress can be calculated from measurements of hardness.

4.4.3.Limitation of Swadener Models

Swadener model I has an advantage that the measured depth at which yielding occurs is affected by the stress in a manner that can be analyzed by Hertzian contact mechanics.However,this model requires that the yield stress of materials be known in advance and that data be extrapolated outside the range of experimental accessibility.73

Swadener model II can be used to measure residual stresses in bulk materials to within 10–20%,but it cannot be easily applied to thin ?lms.73The stress-free reference specimen must be structurally identical to the tested speci-men if accurate residual stress measurements are to be made.Unfortunately,this is often dif?cult to achieve in practice.For bulk materials,there is no substrate in?uen-ces.However,the substrate greatly affects the measure-ment of thin ?lm residual stresses.The substrate effects can be alleviated when the indenter radius is on the order of or less than the ?lm thickness.

Table 2gives a comparison of the above six models.It is obvious that the models can characterize only equibiaxial stress or biaxial stress,while the stress along specimen depth cannot be obtained.Moreover,the six models all have limita-tions.Except Swadener model I,the other models requires a reference specimen,which is often dif?cult to obtain.For Swadener model I,although a reference specimen is not required,the yield stress must be determined by extra experiment.

5.INDENTATION FRACTURE TECHNIQUE FOR THE DETERMINATION OF RESIDUAL STRESS

When a brittle material is indented using a moderate force,a permanent impression is often formed with radially oriented cracks at the indent corner,as shown in Figure 13.74Based on the classic indentation fracture mechanics,the fracture tough-ness K c of elastic-plastic brittle materials is directly related to the indentation load P and the length of the radial cracks at the surface,c 0.For stress-free materials,the fracture toughness can be determined using the following expression:

K c D x P

c 3=20

;(23)

where x is the dimensionless residual stress factor which is related to the ratio of elastic modulus to hardness (E /H ).It is given by

x D ξ0cot u eT2=3E =H eT1=2;

(24)

where ξ0is a dimensionless constant,and u is the indenter half-angle.

For materials with preexisting residual stress s ,the fracture toughness is

K c D x P c §cs c 1=2;(25)

where c is a dimensionless constant which can be obtained from the crack shape,and c is the crack length for the stressed material.The ?rst term on the right hand of Eq.(25)is the stress intensity factor due to the indentation load,while the second term is the stress intensity factor due to the residual stress.Note that the second term is added to the ?rst term for tensile stress and subtracted for compressive stress.

TABLE 2

Comparison of six commonly used models to characterize residual stress

Models

Indenter type Characteristic parameters

Scope of application Limitations

Suresh model Sharp A Equibiaxial stress Require a stress-free reference sample Lee model I Sharp P Equibiaxial stress Require a stress-free reference sample Lee model II Sharp A Biaxial stress Require a stress-free reference sample

Xu model

Sharp h e /h max ratio Equibiaxial stress Requires a special three-point bending device Swadener model I Spherical E r a /s y R Biaxial stress Require known yield stress Swadener model II

Spherical

H

Biaxial stress

Require reference sample

86L.-N.ZHU ET AL.

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For a given indentation load P ,the residual stresses can be determined by combining Eqs.(23)and (25):

s D K c 1?c 0=c eT

3=2

1=2"#

for tensile stress

(26)

s D ?K c 1?c 0=c eT

3=2

c c "#

for compressive stress :

(27)

The residual stress state can be de?ned by comparing c 0and c .The tensile stress can extend the cracks of the stress-free mate-rial (c 0>c ),while the compressive stress can shorten them.T.-Y.Zhang 75et al.proposed a semi-empirical formula to assess residual stresses in SiO 2and Cr thin ?lms deposited on Si wafers using indentation fracture technique.The residual stresses in the SiO 2and Cr ?lms were evaluated to be ?358and 1095MPa,respectively,which agree well with the theo-retical prediction.W.G.Mao 76et al.characterized the residual stress in a thermal barrier coating system by indentation frac-ture technique.The residual stress on the top coating varies from ?36.8to ?243MPa.

For the interface region between the coating and bond coat,the residual stress varies from ?5to ?30MPa.These results are in agreement with available data.

Indentation fracture technique can be used to determine residual stresses in bulk materials,thin ?lms and coatings.However,it is only applicable to brittle materials.Moreover,the dif?culty in measuring the crack length at nanoscale severely limits the accuracy of determination of residual stress using indentation fracture technique.

6.CONCLUSIONS

Residual stresses are increasingly desired to be measured using a nanoindentation technique.There is no one set method that appears to work for all materials.Six major models from analyzing load-depth curves and indentation fracture tech-nique have been developed.Unfortunately,the six models involving Suresh model,Lee model I,Lee model II,Xu model,Swadener model I,and Swadener model II all have limitations.The Suresh model and Lee model I are restricted to equi-biax-ial residual stress.Lee model II accounts for a general residual stress state but cannot describe the well-known nonlinearity.Xu model requires a special three-point bending device and limits the application to very soft materials with high E /s y ratios.Swadener model I requires that the yield stress of mate-rials be known.Swadener model II cannot be applied to thin ?lms.The indentation fracture technique is destructive and only applicable to brittle materials.Therefore,in order to eval-uate residual stresses accurately,new methods should be developed in the future.The methods with non-destructive and universal characteristic should be the research direction.

FUNDING

This article was ?nancially supported by NSF of Beijing (3120001),NSFC (51275105),and Distinguished Young Scholars of NSFC (51125023).

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不必太在意童安格原唱【不必太在意的歌词】 是不是在找这首不必太在意的相关歌词?我这里有哦!下面是!就让小编来我来和你们一起去了解一下相关的资料吧，希望能对你有用哦! 不必太在意的歌词 歌曲：不必太在意 歌手：童安格专辑：一世情缘 别再徘徊沉寂的心灵 别再留恋破碎的回忆 大地迎春雷 抛弃你满腹的忧虑 缤纷的彩虹等着你 别再犹豫等待的心湖 别再沉迷过去的旧梦 暖暖的春风 走向那灿烂的天涯路

耀眼的阳光迎着你你不必太在意 也不必隐瞒自己 你要寻觅亮丽的彩云你不必太在意 也不必隐瞒自己 你要寻觅亮丽的彩云亮丽的彩云 别再犹豫等待的心湖别再沉迷过去的旧梦暖暖的春风 走向那灿烂的天涯路耀眼的阳光迎着你你不必太在意

也不必隐瞒自己 你要寻觅亮丽的彩云 你不必太在意 也不必隐瞒自己 你要寻觅亮丽的彩云 亮丽的彩云 你不必太在意 也不必隐瞒自己 你要寻觅亮丽的彩云 你不必太在意 也不必隐瞒自己 你要寻觅亮丽的彩云 亮丽的彩云 不必太在意的演唱者的信息 童安格，著名歌手、音乐人，1959年7月26日生于台湾高雄，是华语乐坛较早的实力派歌手。集作曲、作词、演唱于一身，是典型的浪漫主义爱情故事的发言人。他于1987

年获台湾最受欢迎男歌星奖。他1996年参加中央电视台春节联欢晚会，演唱歌曲《畅饮回忆》，是国内较早深受欢迎的实力歌手。与王杰、周华健、齐秦并称台湾四大天王(9194年)。童安格演唱过《把根留住》、《耶利亚女郎》、《其实你不懂我的心》等经典歌曲，2011年底，童安格以全新形象与著名的经纪公司点时唱片签约，并成为旗下主推艺人。目前，童安格在内地发展。2012年底，发行他的全新大碟。 感谢您的阅读！

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3. 考试面前一般都有一张白纸和一只笔。因此允许短时间的思考和列提纲（不过建议不要思考时间太长，15-20秒则ok） 4. 面试着装：自己穿着觉着舒服的正装。现在夏天，男生适合短袖衬衣+西裤，建议不打领带；女生适合套裙或者短袖衬衣+西裤 5. 面试之后，一般会要求到其他办公室回避一下，大概过几分钟，就会把面试成绩当场宣布给你。等面试人员基本结束后，就可以大致算出各自排名了。 三、体检 1. 体检一般是面试后两三天就开始，广州市考有几个定点体检医院，一般是各单位就近选择 2. 体检每个项目由医生填写具体记录和项目结论“合格”或“不合格”。如果有单项不合格，一般是不会录用的。医院也是根据公务员录用的要求来填写是否合格 3. 体检一般第二天或第三天招考单位即可知道结果。不联系考生则为通过了，如果联系考生可能就是要复检

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从你的全世界路过 From your world through 2019-03-05 我希望有个如你一般的人 如山间清爽的风 如古城温暖的光 从清晨到夜晚 由山野到书房 只要最后是你 就好 …………①………… 词：何星烁/刘流 曲：何星烁/刘流 女：让我从何提起 日子充实空虚 空气弥漫孤寂 美好时光与你 相遇在意和伤害成正比 逞强太无底气 为爱改变自己 为你与世为敌

生命重拾意义 不甘我的世界 和你阴差阳错轻描淡写只成一道风景 念白：从你的全世界路过你就只路过了一次 却成了我的全部世界RapStar—— 男：每晚坐在电台 用熟悉的声音陪伴 你坐在我的身旁 却无暇我的呐喊 是你的离开让我成为 全台的笑柄 你说你想爬的更高 去看看那的风景 我放你走 忍痛撒开了你的双手 我举牌上街游走 我甘愿为你出糗 我为你付出一切 因为我曾对你承诺

没错我叫陈沫 最后却只能选择沉默你抱着我说 你把爱情献给了青春你说合适大于爱情结束了这段缘分 怪我太过幼稚 是我不够成熟 以后的路陪不了了小容你要幸福 我的猪头兄弟 你丫差不多就回来吧我明白你的绝望 我也明白你很爱她做她爱吃的食物 去看她看过的风景她已经走了兄弟 拜托你要醒醒 你给了他你的一切那不是她想要的 你说没她你不活了你这不开玩笑嘛

她和你相爱因为感动和你的陪伴 但她因为现实走了 请不要再去遗憾 女：为爱改变自己 为你与世为敌 生命重拾意义 不甘我的世界和你 阴差阳错轻描淡写 只成一道风景 男：荔枝姑娘不要难过要相信十八还在 那小子真的命大 他很快就会回来 我真的羡慕你们那 童话般的爱情 祝你们永远幸福平安仪器不再报警 抱歉了幺鸡 让你等了我太久太久我不会再让你路过 我会占为己有

公务员计算机岗位类专业考试

操作系统 1、计算机的硬件基本上由哪五大部分组成？ 答：运算器、控制器、存储器、输入设备、输出设备。 2、运算器都可对数据进行哪两种运算？ 答：算术运算和逻辑运算。 3、CAD、CAM、CAT、CAI都代表什么？ 答：1、计算机辅助设计（CAD） 2、计算机辅助制造（CAM） 3、计算机辅助测试（CAT） 4、计算机辅助教学（CAI） 4、数据处理是指对数据的（收集）、（存储）、（加工）、（分析）、（传送）的全过程。 5、程序性语言分为（机器语言）、（汇编语言）、（高级语言）三类。 6、能举出哪些是高级语言、哪些是低级语言？ 低级语言：汇编语言 高级语言：basic . cobol . c. foxbase等 7、操作系统可分为（批处理操作系统）、（分时操作系统）、（实时操作系统）三种操作系统。 8、解释型程序和编译型程序有什么不同？哪种程序产生目标程序？编译程序产生目标程序 9、DBMS是什么的？

答：DBMS 是数据库管理系统。 10、计算机系统由（硬件）系统、（软件）系统两部份组成。 11、软件系统分为（系统）软件、（应用）软件两部分。 12、操作系统的特征：（并发）、（资源共享）、（虚拟）、（异步）。 13、没有任何软件支持的计算机称为（裸机）。 14、操作系统的五大功能（处理机管理）、（设备管理）、（存储器管理）、（文件管理）、（提供友好的用户接口）。 15、操作系统发展的过程：（无操作系统）、（单道批处理系统）、（多道批处理系统）、（分时系统）、（实时系统）、（网络操作系统）、（分布式系统）。 16、Spooling系统是（批处理）系统。 17、批处理系统有两大特点（自动性）、（顺序性）。 18、批处理系统追求的目标是什么？不断提高系统资源利用率，提高系统吞吐量。 19、分时系统的特点（多路性）、（独立性）、（及时性）、（交互性）。 20、分时系统的主要目标？系统对用户的响应时间。 21、实时系统分为哪两类？并能举出这两类的例子。飞机飞行、弹道发射、预定飞机票、查询航班都是什么系统？ 22、实时系统的主要特点是什么？（可靠性）、（多路性）、（独立性）、（及时性）、（交互性）。 23、个人计算机上的操作系统是（单用户多任务）操作系统。 24、计算机的应用领域包括什么？