TW200909792A - Process for determining viscous, elastic, plastic, and adhesive (VEPA) properties of materials using AFM-based or conventional nano-indentation - Google Patents

Abstract

A process is described for determining elastic modulus, plastic yield strain, and viscosity of a material, and the work of adhesion between the material and an indenter tip, using Atomic Force Microscopy-based or conventional nanoindentation. Specifically, the process includes a measurement method whereby a sequence of load-unload quasistatic indentations are performed in the vicinity of each chosen point on a sample. The loading-unloading curves are analyzed using a specific modeling algorithm to calculate multiple mechanical properties of the sample.

Description

200909792 IX. DESCRIPTION OF THE INVENTION: TECHNICAL FIELD The present invention relates to a method for determining the properties of materials by atomic force microscopy (AFM) and/or a nanoindenter; in particular, the present invention relates to the simultaneous determination of the viscosity of materials. Devices, systems, and methods for the properties of hysteresis, elasticity, plasticity, and adhesions, which include test protocols and related data analysis models. This study was supported by the National Institute of Standards and Technology NIST-ATP Grant 588 70NANB4H3055, so the US government has certain rights in the present invention. [Prior Art] Nano-grade materials, which have a structure based on nanometer (<1〇〇 _), provide revolutionary capabilities and performance based on the unique advantages of ultra-small structures. However, until the relationship between structure and physical properties is understood at the nanometer level, the expectations of such nanomaterials can be fully realized. Atomic force microscopy (AFM) and nanoindenters have been used to determine the mechanical properties of materials by applying a load force to the tip of the probe to create an indentation on the surface of the material and then releasing (unloading) the force from the tip. Therefore, by loading and unloading the tip of the needle tip, the relationship between the displacement of the negative (four) indenter can be obtained. This curve allows the determination of the plasticity (persistence) and elasticity (rebound) of the tested material. Both of the deformation properties. The N-indentation method and the X-gate of the AFM method are directly introduced to the probe tip β ^ Wan method. The former uses the vertical force to the probe "the force of the probe to vertically lead the probe tip into the substrate, and 200909792 The AFM uses a substantially slightly inclined cantilever to direct force to the tip and the sample to introduce the tip vertically. However, each of the dust marks methods can be used in the systems and methods of the present invention. Currently, 'in nanoindentation or The current method based on the Afm nanoindentation method only evaluates various subsets of mechanical properties (for example, the modulus and hardness of the elastoplastic material model, or the elastic modulus and viscosity of the linear point elastic material model). The existence of such limitations is due to the fact that current methods often involve the analysis of load-displacement data by eliminating plasticity (time-independent) or viscous (interstitial-related) components in the load or unloading procedure. Fully characterizing polymers and polymer composites, it is important to understand the elastic hysteresis and plasticity characteristics. In the case of composite materials, it is often necessary to analyze their properties at the nanometer level. Therefore, development is required. At the same time: 疋: stagnation, elasticity and plastic properties (for example, elastic modulus, yield should =, the overall modulus of the array as a function of frequency, and the tip _ sample adhesion:) = quantitative nanometer The mechanical measurement provides engineering materials (ie, material design) @tools and capitals that are suitable for the treatment of specific stresses, which will greatly accelerate the discovery and development of materials. [Invention] The invention is provided by - The prior art method is allowed to be solved by a test procedure in which a plurality of nanoindentation methods are used: and the obtained data set is fitted according to a nonlinear method, and the material is tested for the sex and plastic properties. The data from the collected test program takes the relevant analytical model of the material property information. 200909792 In the '匕, sample, the present invention provides a method for determining the properties of a sample via an indentation method, comprising: selecting to perform an indentation Sample area; use the indenter tip and use at least two locations, load rate and penetration depth to indent the sample; obtain load-displacement relationships from each indentation; and use load-displacement relationships Determining at least two physical properties of the sample. In another aspect, the invention provides a system comprising: an indenter tip 'for starring a sample; a controller for controlling the indenter a tip-to-sample trace and thereby obtaining a plurality of load-displacement relationships, wherein the plurality of load-displacement relationships represent a plurality of sample locations, a plurality of load rates, and a plurality of penetration depths; and - a resource (four) system for A plurality of load-displacement relationships determine at least two physical properties of the sample. :: It is possible to determine the elastic, viscous, plastic and adhesive parameters of the material within the same test procedure. The method of the present invention allows for the resolution of mechanical properties over a conventional "overall level" (e.g., based on a resolution of about two plants\100, and the conventional nanodust method has a resolution of about 1000 nm). In the first aspect, the present invention provides a wire such as a bite that is too much to be pressed by an AFM, and is determined by an indentation test (eg, a method of not indentation) comprising the following steps: (1) Select the sample area where the indentation will be performed, (8) use the indenter tip to select the sample in the selected area, more than one load, more than one position, and one or more penetration depths, and 200909792 The indentation obtains a load-displacement relationship; and (in) uses a load edge shift relationship to determine at least two physical properties of the sample, which method is hereinafter referred to as Method A. In the first-specific example of the first aspect, the present invention The method of method A is provided, wherein (Π) comprises the following steps: at a position, with a first negative

Using the first load rate and the first penetration depth of the indenter tip in the selected area, the tip of the indenter is at the second position in the selected area,

And wherein the first load rate is different from the second load rate and the load-displacement relationship obtained from the greater of the first load rate and the second load rate is analyzed to determine at least one property of the material; Called Method B.

The load-displacement relationship performs the analysis.

Method [wherein (ii) comprises the steps of: a) using an indenter tip at a first location in the selected region, at a first load rate and at a first location, in a first shift relationship; penetration depth to indent the sample Obtaining a first load bit 9 200909792 less one (b) analyzing a first load_displacement relationship to determine material properties; and (c) using a tip of the grime gauge at a second location within the selected region at a second load rate And the second penetration depth indents the sample to obtain a second negative shift relationship, wherein the first load rate is greater than the second load rate, the method is hereinafter referred to as Method B-1.

The present invention provides a method of method A in place of one of the first aspects, wherein (Π) comprises the following steps: (a) using the indenter tip at a first position in the selected region at a first load rate And the first penetration depth indents the sample to obtain a first displacement relationship; ' (b) pressing the sample at a second position in the selected region with the indenter tip at a second load rate and a second penetration depth The trace obtains a second load-displacement relationship, wherein the first load rate is greater than the second load rate, and (〇 analyzing the first load-displacement relationship to determine at least one property of the material; the method is hereinafter referred to as Method B-2. In a first aspect - instead of a specific real money, the present invention provides a method of method A, wherein (ii) comprises the steps of: (a) using the indenter tip at a first location within the selected region, at a first load The rate and the first penetration depth will indent the sample to obtain a first-shift relationship; '200909792 (b) with the indenter tip at a second position in the selected region, at a second load rate and a second penetration depth Sample indentation to obtain a second load-displacement relationship, Wherein the second load rate is greater than the first load rate, and (c) analyzing the second load-displacement relationship to determine at least one property of the material; the method is hereinafter referred to as Method B-3. Another specific aspect of the first aspect In an embodiment, the invention provides a method of method B, B-1, B-2 or B-3, wherein (η) further comprises the following steps: (d) hysteresis of the second load-displacement relationship The first predetermined value is compared. The method is hereinafter referred to as method C. In another specific example of the first aspect, the present invention provides a method of method, wherein (ii) further comprises: (e) using an indenter The tip indents the sample at a third location in the selected region at a second load rate and a third penetration depth to obtain a third load-displacement relationship, wherein the third load rate is greater than the second load rate; and the third wear The penetration depth is greater than both the first and second penetration depths, the method is hereinafter referred to as method D. In another specific example of the first aspect, the present invention provides a method of method d, wherein the second load_displacement The hysteresis of the relationship is less than or equal to the first reservation The value of the temple is then repeated, the method is hereinafter referred to as the method e. The present invention provides a method of the method D in another specific example of the first aspect of the method of 200909792, wherein when the first -, #, then (8) In: step, package:, the hysteresis of the shift relationship is greater than the first-predetermined value (〇 the third load_bit according to the & value phase warfare displacement relationship hysteresis and the second pre-comparison, the method is hereinafter referred to as Method F. In a specific example of the first aspect of the first aspect, the present invention provides a method and method, wherein when the hysteresis of the '戟 displacement relationship of the third load I is less than a predetermined value, then (ϋ) further Including:, brother one (g) with the indenter tip in the selected ring office, the fourth position in the region, with the flute four load rate and the fourth penetration deep production will engage in σ ° indentation to obtain the fourth a load-displacement relationship, wherein the fourth load rate is greater than the second load rate and less than the first load rate; and - the negative fourth penetration depth is greater than the first and second penetration depths and the small penetration depth, the second method is Hereinafter referred to as method G. In another specific example of the first sadness, the present invention provides a method, wherein when the hysteresis of the third load-displacement relationship is predetermined, then (ii) further comprises: a value (g) Using the indenter tip at a fourth position in the selected area, the four load rate, and the fourth penetration depth to obtain a fourth shift relationship, wherein the fourth load rate is less than the first and the fourth a third load rate; and 12 200909792 a fourth penetration depth greater than both the first and second penetration depths; and (h) using the indenter tip at a fifth position within the selected region, at a fifth load rate and Five penetration depths indenting the sample to obtain a fifth load-displacement relationship, wherein the fifth load rate is greater than the second and fourth load rates and less than the first and third load rates; and the fifth penetration depth is greater than the first The second penetration depth is less than the third and fourth penetration depths, wherein (g) and (h) can be performed in any order; the method is hereinafter referred to as method Η. In a preferred embodiment, '(g) is performed before (h). In a preferred embodiment of method C-H, the first and second predetermined values (i.e., for maximum allowable hysteresis) are independently less than or equal to 〇_〗. In a preferred embodiment of the methods A-Η and B-1 to B-3, the first and second penetration depths are each independently about 〇1 to 01 times the tip of the indenter half, first The loading rate is about 1 nm/s to 100, 〇〇〇nm/s, and the JL second negative cutting rate is about 0.1 nm/s to 1 〇, 〇〇〇nm/s. In a preferred embodiment of method D-Η, wherein the third penetration depth is from about 0.5 to 1.0 times the indenter tip radius and the third loading rate is from about 1 nm/s to 100,000 nm/s. In a preferred embodiment of the method G, the fourth penetration depth is about 〇2 to 0.5 times the indenter tip radius, and the fourth negative growth rate is about nm/s to 3 〇, 〇〇〇nm/ s 〇13 200909792 In one preferred embodiment of the method, the fourth penetration depth is about 〇.5 to 1. 〇 times the indenter tip radius, and the fourth load rate is about ^ nm/s to 10,000 nm. /s, the fifth penetration depth is about 〇2 to 〇5 times the indenter tip radius, and the fifth load rate is about 〇3 nm/s to 3 〇, 〇〇〇nm/s. In a more preferred embodiment of the methods A-Η and B-1 to B-3, the first and second penetration depths are each independently from about G G1 to Q1 times the indenter tip radius, first and third The three load rates are independently from about i nm/s to 1 〇〇, and the first load rate of 〇〇〇nm/s ' is about nm1 nm/s to i〇, 〇〇〇, and the third penetration depth is about 0.5 to 1. 〇 times the radius of the indenter tip. In a more preferred embodiment of the method G, the first and second penetration depths are each independently about Ο. Η to 〇" times the indenter tip radius, the first and second loading rates are independently about i nm /s to 1〇〇, 〇〇〇, the second loading rate is about 0.1 nm/s to 10,000 nm/s, the third penetration depth is about 0.5 to 1.OL at the indenter tip radius, the fourth penetration The depth is about 0.2 to Ο" times the tip radius of the indenter, and the fourth load rate is about 〇·3 η - to 30, 〇〇〇nm / s 更 in one of the methods 更 better, in the specific example, the first And the second penetration depth is independently about 〇〇1 s μ1 μ ·〇ι to ο·ι times the indenter tip radius, the first and third load rates are independent of the rabbit, and the ground is about 1 nm/ s to 100,000 nm/s, the second and fourth load rates are independent of the rabbit έΛ> Λ1 Ώ von from about 0.1 nm/s to 10,000 nm/s, and the third and fourth penetration depths are independent & π, - also 0.5 to ι·〇 times the tip radius of the indenter, the fifth penetration depth is about s 0·2 to 0.5 times the tip radius of the indenter, and the fifth load rate is about 〇.3 s to 30 , _nm/s. The measured rut is 'in any of the previous specific examples (丨丨)(b) 14 200909792 The at least one physical property of the material is the adhesion work between the tips of the reduced-profile indenter (^). , 〃 and / or sample and ruler, at least one physical property of the material, is a reduced b). The adhesion work (γ) between the crucible and the tip of the indenter. , and even better, the material ΜM r ρ V of the measured material is a physical property of the number of torsion reduction wheels (4) and the adhesion work between the sample and the tip of the tracer (7), 2 the load (ρ) % is made into h3/ 2 r in 丨l and although ^ r臬 is h (for example, equation 3, shell order, number, reduced modulus (5) and σ σ numb) (4) number (4) and sample - with the sharpener tip The adhesion work (y) between the two is determined by the slope of the load-displacement relationship of (π) fa, eve 6, and (). The present invention provides a method of any of the preceding specific examples, wherein the first location is the same as the second location. In a preferred embodiment, the invention provides a method of any of the preceding embodiments wherein each location within the region of the indented sample is at least 5 times the center-to-center distance of the highest penetration depth from any other indentation locations. In a more preferred embodiment of one of methods A-Η and B-1 to B-3, when an AFM tip is used, the first and second penetration depths are each independently about $10 to 10 nm 'first load rate It is about 1 nm/s to 1 〇〇, 〇〇〇nm/s, and the second loading rate is about 〇·1 nm/s to 1 〇, 〇〇〇nm/s. In a preferred embodiment of the method D-Η, when the afM tip is used, the depth of the second tooth is about 60 nm to 100 nm, and the third load rate is about 1 nm/s to 1 〇〇, 〇〇〇nm/s. In a preferred embodiment of the method G, when afjv [tip] is used, the fourth penetration depth is about 20 ηιη to 40 nm, and the fourth load rate is 15 200909792 about 3 nm/s to 30, 〇〇〇nm/s. In a preferred embodiment of the method, when the AFM tip is used, the fourth penetration depth is about 60 nm to 100 nm, and the fourth loading rate is about 0.1 nm/s to 1 〇, 〇〇〇nm /s and the fifth penetration depth is about 2 〇 nm to nm ' and the fifth loading rate is about nm3 nm/s to 3 〇, 〇〇〇nm/s. In a more specific example of the methods A-Η and B-1 to B-3, when the AFM tip is used, the first and second penetration depths are each independently about 5 to 10 nm, first And the third load rate is independently from about 1 nm/s to ιοο, οοο ws, the second load rate is from about 01 nm/s to 1 〇〇〇〇nm/s, and the third penetration depth is about 60 nrn to 100 nm. In a more preferred embodiment of the method G, when the afm tip is used, the first and second penetration depths are each independently about 5 nm to 10 nm, and the first and third loading rates are independently about i nm. /s to (10), _ the first load rate is about oi nm / s to 10,000 nm / s 'the third penetration depth is about 60 (10) to 100 nm, the fourth penetration depth is about 20 nm to 40 nm, and the fourth load The rate is about 〇3 nm / ^ 3MQQnm / s. In a preferred embodiment of the method, when the tip is used, the first and second penetration depths are each independently from about 5 (10) to 1 〇·, and the first and third: carrier rates are independently from about one to one. 1〇. ,. First, the rate is independently about 〇. One to _. -, the first and fourth penetration, the degree of independence of the Zhudu is about 20 nm to 4 〇 n (10) to 1 〇〇 nm, the fifth penetration ^ 30,000 nm / s 〇 ' ' and the fifth load rate is about 〇 3 nm/s In a preferred embodiment the invention provides the method of any preceding embodiment 16 200909792, wherein the first and/or third load rate is from about 1 nm/s to about 1 00,000 nm/s ° in one In a preferred embodiment, 'the invention provides a method of any of the preceding specific examples' wherein the second and/or fourth loading rate is from about 〇_丨nm/s to about 10,000 nm/s. In a preferred embodiment, the invention provides a method of any of the previous embodiments wherein the fifth loading rate is from about 0.3 nm/s to about 30,0 〇〇 nm/s. In a preferred embodiment, the invention provides a method of any of the preceding embodiments, wherein the indenter tip comprises a material selected from the group consisting of: Shi Xi, Carbonized Stone, Nitride, Diamond, Sapphire or Coated with carbonized hair, tantalum nitride, diamond and sapphire. In a preferred embodiment, the invention provides a method of any of the preceding specific examples, wherein the indenter tip is spherical or parabolic. In a preferred embodiment, the invention provides a method of any of the preceding specific examples, wherein the indenter tip is spherical or parabolic, and the indenter tip comprises a material selected from the group consisting of: Carbonized carbide, nitrogen cut, diamond, sapphire or coated with carbon cut, nitrogen cut, diamond, and in a preferred embodiment, the present invention is as illustrated for any of the previous specific examples, wherein the indenter tip is a ball The makeup is wavy or parabolic and has a radius of about 10 main 10,000 nm. In a more preferred embodiment, the ancient, +^ & alum of the present invention is for any of the preceding specific examples <RTI ID=0.0>>>>>> The half-press of nm is preferably from about 20 to about 50. 200909792 In a more preferred embodiment, the invention provides a method of any of the preceding specific examples, wherein the indenter tip is a spherical or parabolic traditional nanometer. The indenter is known to have 'a radius of about 1 〇〇 to 1 〇, 〇〇〇 nm; the radius is preferably 100 nm to 1 〇〇〇 nrn. In a preferred embodiment, the invention provides a method of any of the preceding embodiments, wherein the sample has a thickness that is at least 10 times the penetration depth of all of the indentations performed. More preferably, the sample has a thickness that is at least 2 times the highest penetration depth of all indentations performed. In a preferred embodiment, the invention provides a method of any of the preceding specific examples wherein at least two of the material properties are selected from the group consisting of Young's modulus, adhesion work, yield strain, viscosity, and A group of relaxation time. In a preferred embodiment, the invention provides a method of any of the preceding specific examples, further comprising non-dimensioning the load-displacement relationship obtained from each indentation by dividing the load data by the final load value for each indentation. A step of. In a preferred embodiment, the present invention provides a method H of any of the previous specific examples of the load-displacement relationship (4) as an effective stress-strain (σ-ε) curve via the following transformation: 200909792 where the load is the lowest load (), The penetration depth' is the radius of the indenter tip. In a preferred embodiment, the invention provides a method of any of the preceding specific examples, wherein the effective stress-strain curve is fitted to a particular micromechanical karyotype (such as Hookean, MaxweU, Kelvin ( Kelvin) model, obtaining the reduced modulus, Young's modulus, relaxation time and yield strength. In a preferred embodiment, the invention provides a method of any of the preceding specific examples' wherein in (iii) the resulting load-displacement correlation model is fitted to a model, the pest is non-linear

Er

VMST 1 - exp·}

ST

ΧΒ{ε)ε + [l - Xe(e)s^Y

1-expJ where l + c (\ ε 1/3 4 卜D 「 "'1 KSY y > ^^load _R- 3/2 Ο): (4/3π)(/2/Λ)3/2 ; σ = _ pmiJ/7tR2 = (p +2nyR)/nR2 . The middle ~ and ~ represent the relative contributions of Maxwell and Hooke elements, respectively, from + V" = 1 ; and the deep sound kρ for the indenter tip疋 疋 负载 Α Α Α Α Α Α Α Α Α 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透 穿透y is the indenter tip and sample between 19 200909792 and the viscosity of the work, ~ is the yield strain ·, and c and d are empirically determined constants, the indenter tip is the ball HH This method is hereinafter referred to as the method In another preferred embodiment, the present invention provides a method of method, wherein the data is fitted by nonlinear model optimization with respect to 7 and ρ2t. In a preferred embodiment, the present invention provides a method of method ,, ===2 for 'and s, and via a nonlinear model to optimize the data between the data and the model Χ2 minimized and optimized The λ monument owner dares to use another method, and the present invention provides a method ^ method, wherein when the hysteresis in (ii) (d) Φ - Μ m w- r ) is less than or equal to a predetermined value, the poor material is to be In the case of synthesizing the previous model, in another preferred embodiment, the present invention provides a method for the Hi Μ (1) towel to be cut or equal to the use of 〇〇 when the bead is fitted to the previous model. ' In any of the previous examples - Preferably, the specific value is 0.10. The predetermined value is preferably 0.05. The value is one of the methods A-Ι and B-1~B-3, and the value is determined by the method. A-UB-b B_3 - preferably has a specific load rate. τ top is measured in the methods A-Ι and B-Uj - better, in the body example, pre-measured 20 200909792 to determine the penetration depth and load Rate system. The method comprising: > indentation of a sample and in a second aspect, the present invention provides an indenter tip for indenting a sample, a controller for controlling pressure The tip of the tracer obtains a plurality of load-displacement relationships, wherein the plurality of load-displacement relationships represent a plurality of sample positions, Multiple rates and multiple penetration depths, and - data sub-systems determine the at least two physical properties of the sample based on a plurality of load-displacement relationships. In the first aspect - a preferred embodiment, control The device is an atomic force microscope or a nanoindenter. In one preferred embodiment of the second aspect, a plurality of load-displacement relationships are collected according to any of the specific examples of the first aspect. In a second aspect - a more preferred embodiment, the #man is an atomic force microscopy or a nanoindenter' and a plurality of load-displacement relationships are collected according to any of the specific examples of (4). In one or even more preferred embodiment of the second aspect, the controller is an atomic force microscope and a plurality of load-displacement relationships are collected according to any of the specific examples of the first aspect. In one or even more preferred embodiment of the second aspect, the controller is a nanoindenter and a plurality of load-displacement relationships are collected according to any of the specific examples of the first aspect. In another preferred embodiment of the second aspect, the indenter tip comprises a material selected from the group consisting of: tantalum, tantalum carbide, tantalum nitride, 21 200909792 diamond, sapphire or tantalum carbide coated, Barium nitride, diamond and sapphire. In another preferred embodiment of the second aspect, the indenter tip is spherical or parabolic and has a radius of from about 10 to about 1 〇 11111. In a more preferred embodiment of the second aspect, the indenter tip is spherical or parabolic AFM missing and has a radius of about 5 to 2 Å; the radius is preferably from about 20 to about 50 nm. In a second aspect - a more preferred embodiment, the indenter tip is a spherical or parabolic conventional nanoindenter tip and has a length of about 1 to 1 〇, half of the 〇〇〇nm, Semi-administration is preferably from 1 〇〇 to 1 〇〇〇 nm. In another preferred embodiment of the second aspect, the indenter tip comprises a material selected from the group consisting of: carbon cut, nitride nitride, diamond, sapphire or coated with carbon carbide, nitrogen. Fossils, diamonds and sapphire's and the indenter tip is spherical or parabolic and has a radius of from about W to about 1 〇 nm. In another preferred embodiment of the second aspect of the Z, the data analysis system package "knows the software to analyze the resulting load-displacement relationship and thereby determines at least two material properties." In another preferred embodiment, the indenter tip is spherical or parabolic, and the data analysis includes the step of transitioning to an effective stress-strain (σ_ε) curve via the following transformation relationship: shift 22 200909792 on 3π r The micromachine is used to obtain a reduction in the specific example, wherein the corpse is the load, which is the lowest, the depth 'and the radius of the indenter tip. In a preferred embodiment A, the present invention provides any prior method by Fitting the effective stress-strain curve to a special model (such as Hooke, Maxwell, or Kelvin model), modulus, Young's modulus, relaxation time, and yield strength. In another preferred embodiment of the second aspect, The indenter tip is spherical or parabolic, and the data analysis system is based on a plurality of load-displacement relationships, and the sample is determined by fitting the load_displacement relationship to the following model. At least two physical properties,

r r r λ\ / Er 1 - exp j--1 - ^ 1 s^)j \ ^e(£)S + [! - ^e{£)£^Y 1 - exp]

A where 0)=——l-_ Γ π3/2 ί ε V,3 η 4 h, UJ , ε = (4/3Ti)(h/R)3/2 ; σ = (p _ Pmin)/7cR2 = (p +2πγΚ_)/πκ2 ; vm and respectively represent the relative contributions of Maxwell and Hooke elements, where + vH = 1 ; R is the radius of the indenter tip; P is the measured load; h is the penetration depth; Ht is the final penetration depth; tiQad is the total time of the indenter to reach ht; 23 200909792 ^ reduced modulus; τ is loose (four); γ is the adhesion between the tip of the indenter and the sample, S is the yield strain And c and D are constants determined empirically. Not only is the month fa enough for the nose to reduce the modulus (if you can use 〇iiver_ Ρ1ΐ3ΓΓ [see 〇llver and Pharr, J. Mater. Res. 7:1564; 〇liver and pw, j. Mater Res 19:3 (2〇 Quzhou or similar methods), and ', sentence summarization slack time and yield strain. The appropriate algorithm for calculation is given below. Familiar with the load of the spherical tip indentation to the linear elastic material _ displacement curve Described by Hertz, equation [see Sneddon, Int. J. g Sci. 3.47 (1965); Hertz, On the Contact of Two Elastic Solids, MacMillan (1882)]: 4 P=:Zp ¢^2/ , 3/2 h (1) where P is the load (in N) and the tip radius (in m) '々 is the penetration depth (in m) and is the sample's reduced-fold mode Number, which is given by:

Where £ is the Young's modulus of the sample (in p a), 曰 ', which is the Poisson's ratio (s ratio). When the equation (1) is derived, the modulus of the indenter tip is much higher than the sample 24 200909792 modulus. If there is adhesion between the sample and the tip, modify the Hertz equation. Can be used in a wide range, shallow tip-sample adhesion interaction

Derjaguin-Toporov-Muller (DMT) [see Maugis, J. Co//oM / price r/αα 150: 243 (1992); Derjaguin et al., J. / «ier/acia/Scz·· 53:3 14 ( 1975)] Approximate method: P = ^ErRmhvl-2nRY (3) where γ (in N/m) is the adhesion work. It is also known that in the case of a linear viscoelastic material, the load-displacement characteristic can be estimated by the following expression (see Lee and Rad〇k, J. Price: c/2 27:438 (196〇)): (4) where /(1) is compliance, defined as ... 1/Er. Note that equation (4) applies in the case of a specified load history (load control pressure rather than displacement control indentation). Right, use ε = (4/3π)(_3/2, σ = (p _ p_)^r2 = (p W(10)(4)) to write the dependence of σ on ε under general elastic and viscoelastic conditions. Approximate solution: : foot 1-exp Ε, 1-expf--

ST

+ VHS (5) Equation (5) is written for the simplest condition of "minimum solid state model" or "one-element Prony series" (see Lu 荨人, Mec/? 77 from aier. 7:189 (2003)), in which the Maxwell element is connected in parallel with the Hooke element, and % represents the relative contribution of the two elements, where Va/ + %=1 〇 is a description of plasticity, which can be assumed to be a Hooke element. Becomes elastic - perfect plastic element. In this case, equation (5) is modified as follows:

+ VH ^e(e)e + [l~Xe(s)e],Y

(6) where Χ6(ε) describes the portion of the Tiger element that remains elastic and does not yield under a given deformation ε. The approximate expression of χβ(ε) is given by: 1 (7) i+c -1 , εΥ j In the test, the indentation is performed using a constant indentation velocity mu. In the following relationship, the indentation speed is related to the deformation rate,

(8) . Equation (1) Arbitrary viscosity of the instrument - (8) constitutes the property · elastic-plastic constant C and j) empirically determines the equation definition required to use the load curve of a spherical or parabolic indentation material 26 200909792 As used herein, "empty,,,, ητ πσ penetration ice" & means that when the load is applied by the indenter tip to the sample σ facet (relative to the free surface) table, the end penetration The distance to the sample is broad:: As used herein, the term "load rate" means that the tip penetrates the surface of the sample or the cantilever when it is loaded by a conventional nanometer tip, .... &&& The load of the sample as a function of time to maintain a constant load rate. As used herein, the term "unloading rate" means the rate at which the tip is removed from the sample when the load applied by the indented end is reduced; the adjustment is applied to the sample by the tip & The load of the 4th functional relationship is maintained at a constant rate. , π As used herein, the term "°. hysteresis" means the ratio of the area between the measured load to the load-displacement relationship of the unloading and the total area under the load curve (limited to the area under which the load is positive). . As used herein, the term "final load value" λ means the load applied to the sample by the tip when the tip of the house gauge has reached the desired penetration depth for measurement. The final load value is measured for each wear scar depth and catch rate and δ is unique — and used to make the resulting data dimensionless. As used herein, the term "minimum load value" U refers to the minimum value of the load applied to the sample by the tip of the grime. This minimum can be zero (no adhesion) or negative (existing adhesion). The term reduced modulus Μ is the ratio of Young's modulus r to (/ ν0 (complex ν is Poisson's ratio)'. The constraint condition is that the modulus of the relocation tester is significantly higher than the sample modulus. Yong 27 200909792 The term 'χ2' used in the term means the sum of the least squares of the observed data points and the model as defined above (above). As used herein, the term "load-bit shift relationship" means a self-indentation indenter. The relationship between the large & load and unloading samples. Off, each load-displacement relationship defines the associated hysteresis as defined herein. In this paper, (4) the radius of the tip of the indenter is not placed in contact with the sample. The radius of curvature of the tip portion of the indenter. For any shape of the tip two, the radius is the radius closest to the parabolic tip. The closest parabolic tip is the parabola whose cross section is closest to the cross section of the tip of the present invention. Example Tips - Finite Element Analysis - Viscous - Elastic-Plastic Modeling Materials Simulated Nano Dust Marking Method In the following examples, the kit software ABAQUS/Standard (Providence, Rhode Island, USA; 6.5) was used. Version -7) produces a load-indentation curve. The terms viscosity, '*elasticity, and '*plasticity' are the material characterization symbols for the packaged soft body. Use finite element analysis (FEA) computer model software to simulate the load _ Indentation curve. For FEA simulation, use ABAQUS/Standard (Providence, Rhode Island; 6.5-7). The indenter tip is represented as a hard sphere with a radius of R = 100 nm. The indented material model is constructed as a sticky滞 _ elastic-plastic half space, where Young's modulus E = 2.69 GPa, Poisson's ratio v = 0.3 5 ' yield strain sy = 0.05 and relaxation time τ = 50 sec. Used to represent the elements of the 28 200909792 material The viscous-elasticity/plasticity model is shown in circle 2. The following assumptions are used in the simulation: (a) completely smooth surface '·((8) frictionless contact; (〇 homogeneous viscous_elastic_plastic half space 丨(d Adhesive interface with less adhesion. Use a two-dimensional analysis of rigid surfaces to create a spherical (four) tracer model. Axial symmetric 4-node bilinear and 4-node bilinear reduced-order integral solid elements are used to create a half-space model. Under the I tracer In the small area, the extremely fine mesh of the fully integrated element is used. The grid becomes sparse (in four stages) away from the indenter; in these areas, the reduced-order integral element M is used to establish the infinite axisymmetric element. Half*: Far: Regional model 'Constrained boundary... Upper node: Excludes genus 2: 2: Γ) Displacement in *x direction. Boundary conditions do not need to impose a limit on the edge of the element in the infinite direction. The use is called "hardness". The preset contact pressure-clearance relationship in the ABAQUS of the type, the contact model between the pressure, the device and the + space is constructed as a frictionless contact. A two-layer viscoplastic method is used to model the behavior of a viscoplastic material. The method uses a *viscosity selection and *elastic and *plastic selection: a non-linear step to apply a specified displacement to the indenter reference node: the test cycle. At each step, the *viscosity procedure was used to perform a quasi-static analysis of the instantaneous response to temporal, material behavior. Move at the specified displacement of the desired maximum penetration so that the indenter is moved down to the original position step, applying a zero specified displacement to return the indenter to its degree, h, 5 nm; (2) Tt = 2〇 〇sec,\ performs five simulations: (1) load time, Tt = 2 sec, penetration depth nm (3) Tt = 20 29 200909792 sec > ht = 3〇nm . ( 4 ) T =9 200 sec,h,6 〇n .; C', = 6〇nm; and (5) Tt = t 6〇_. A load-penetration curve for all five cases is generated. = material fitting (viscosity of material. Determination of elastic and plastic parameters). If the load curve of case (1) is used, load/displacement (Μ) is private: force-strain (σ_ε), and Μ-"selecting the distance ^ Suppressing the linear fit of the singularity gives the reduced modulus vector—(Comparatively accurate value 3 to Gpa). To determine the other two (loose time τ and yield strain S), by dividing P by Pt All five load curves are dimensionless. Then all dimensionless loads are input into the statistical analysis software mP6.0; the "non-linear" model features are used to fit the cause without the parameter τ and optimization. Secondary load. The results of the fitting are shown in Figures 3 and 4 'which shows that the model and the muscle material are very close to each other. The fitting parameters as well as the exact values (input FEA parameters) are summarized in Table 1. For reduced modulus, estimates from the existing method (Oliver Pharr) are also provided to show that the new program provides equal or better accuracy. The exact value of the material parameters is used to fit the model. v v^r.PVi iirr Er (Gpa) 3.066 3.1 2 07 z ( sec ) 50 55 εγ 0.05 0.049 Table 1 Reduced modulus, relaxation time and yield The calculated value of the strain (third row) is compared to the exact value (second row). For the purpose of comparison 'in the fourth line, give the reduction modulus - (OIiver-pharr method does not provide another! The estimated value of the material parameters) 〇30 200909792 Example 2 - PMMA nanoindentation A poly(meth) methacrylate (pMMA) (part number ME303020) in sheet form (2 mm thick) was obtained from Goodfellow Cambridge Ltd., Huntingdon, England. This PMMA is Mw=l,810, 〇〇〇 g/m〇1 and

Rep 〇l YPF acrylic acid having Mn = 261, 〇〇〇 g / mol, as determined by size exclusion chromatography (corrected using linear polystyrene). Sample Preparation and Monolithic Pulling. Using a Nanchang Round Mine, the tensile specimen was cut from a 2 mm sheet into 25 mm long and 0.25 inch wide rods. Tensile testing was performed on Instr〇n 42〇1 using a priced (10) Bluehill software. The specimen was attached using a gas clamp pressurized to 8 psi. The 1 吋 gauge Instr〇n mechanical extensometer was reset to zero and attached to the specimen prior to testing to measure tensile strain. The tensile test was performed at 0.05, 0.5 and 5 mm/s. The indentation method of the nano indentation method uses a jade saw (sewer) to manually cut several pmma sheets. The sheets were embedded in a Buehler Epoxicure resin and cured therein, and an internal 1.25 inch diameter hardened material was formed for metallographic polishing. Polishing was achieved using Struers R〇top〇l and following a series of five grinding steps under 7 〇N applied force: i) uoo particle size Sic paper, using DI water lubricant for 2 sec; ii) 2400 grit SiC paper, using water-repellent full-slip agent, lasting 〇sec; iii) 4000 grit sic paper, using m water lubricant for 10 sec; 3 micron diamond in Tex fine cloth, using diamond 31 200909792 paste incremental lubricant, duration 3 min ; v) 0.25 micron diamond in Texmet cloth, using Lec 〇 diamond paste incremental lubricant for 4 min. Final polishing was achieved on a Buehler Vibromet using a 0.25 μηι diamond on a LeCloth surface under a load of 300 gm and using Leco Diamond Paste to increase the lubricant for 2 hours. Nanoindentation method - constant should be performed on a MTS nanoindenter equipped with a DCM head and a Berkovich diamond Accutip indenter (MTS Ν&η〇Instruments in 〇ak Ridge, Tennessee) Trace experiment. The area function of the tip of the positive indenter is determined by the manufacturer using molten yttria. The test was controlled via an MTS Testworks software computer using a continuous stiffness measurement (CSM) method that provides accurate detection of the surface of the indented material. Set the CSM parameter to a frequency of 75 Hz and an amplitude of 1 nm. Surface detection is caused by an increase in the stiffness of the harmonic contact above 100 N/m. The strain rate target of the load curve is set to 〇.〇5/s and the constant unloading rate is between 0 7 and 0 8 mN/s. The traditional 〇liver_Pharr calculation of the reduced modulus Er and the hardness [ [see 〇Uver and pharr, 乂M_U: 1564; 〇liver and Pharr, implementation (10) fine 19:3 (2〇〇4)], automatically by Testworks software Execution, its Poisson's ratio is set to 〇·35, and the unloading curve part for automatic calculation is set to nanoindentation method - the constant displacement rate will be given to MTS DCM Nai equipped with DCM head and Berkovich diamond Accutip indenter The nanoindentation test was performed on a meter indenter. The area function of the tip of the indenter by the manufacturer. The test was controlled by a MTS TeStworks software computer using a continuous stiffness measurement (csm) method that provides accurate detection of the surface of the trace material. Set the csm parameter

The frequency of Hz and the amplitude of 〖nm. Surface detection is triggered by an increase in the stiffness of the harmonic contact above 100 N/m. Standard (4) Ding _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ The output function of the Test Cream software was used to output the load-displacement curve data for viscous_elasticity-plasticity-adhesion analysis. The load displacement curve of PMMA is transferred to 5 towels. The load and unloading measurements of the five displacement controls are shown, wherein the maximum penetration depth and average velocity for each measurement are summarized in Table 2. Since the hysteresis between the curves corresponding to different indentation velocities is significant, it is determined that the material has viscosity, elasticity, and plasticity.

Table 2. Measurement parameters for the nanoindentation method. Here, for maximum penetration, for maximum load, v is the indentation velocity, and 5 is the rate of change of the deformation variable s. In order to analyze the data and evaluate the viscous-elastic-plastic properties of the polymer, it is useful to describe the (p_h) description into (σ-ε) according to the following equation.

Fhf2 UJ 4 3π 33 200909792

The load-displacement curve in the P a + lanthanum (stress-strain) is plotted in Fig. 藉 by fitting the load portion of the σ_ε curve with a straight line to fit the effective reduction modulus of the rate (^ 3 and low). The results are summarized in the table i " by the quasi-expression of the five = do " convert the reduced modulus to ^ where Poisson's ratio v = 0.35. For the purpose of comparison, 7 can perform the overall tensile loading of the same polymer at different strain rates. In the figure, the calculated value of the modulus and the calculated value of the overall modulus are plotted as a function of the effective speed ratio ^; the results are very consistent. ______ mark ~-two-_I s, sec'1 --- _ Er, GPa E, GPa ri? ' —- — 2.18E-01 6.53 5.73 4.80E-02 3.86 3.39 —Low ------ 5.00 E-03 5.30 4.65 • The calculated values of the reduced modulus and Young's modulus are a function of the average strain rate. The viscoelastic effect is manifested in the dependence of the modulus on the rate of deformation. To approximate the out-of-symmetry relaxation time τ, or more precisely, the dependence of compliance on $ can be fitted to the following function: E \s) = JQ+j] exp(-ir) is the value of τ, and τ Summarized in Table 4. 34 200909792 J〇, GPa-' J1, GPa*1 -—~~_ T, S G Γ: 0.174 ～----- 0.13 25 Table 4· Calculation of the parameters and characteristic relaxation time. (d) 塑性, the plastic properties, such as yield stress or yielding, are useful in considering both the load and the unloading portion of the curve. For the case of measurement, the plasticity measure can be defined as: H = Er{s^t~ef\ where the heart is the maximum deformation and e/ is the final deformation (related to the material plasticity). // The higher the material behavior, the more "elastic" the material is (for a given ^). In particular, // can be correlated with the stress at which plastic deformation begins (i.e., material hardness). Then, the yield stress ~ can be calculated based on the Tab〇r formula [see D. Tabor, TTze o/Meia/s, 〇xfor(j

Clarendon Press, 1951] (where Tabor constant 9):

The calculated values of H = kaY are given in Table 5. H, GPa σν, GPa 0.5 0.172 Table 5 · Calculation of hardness and yield stress of PMMA. Since the typical literature value for the yield stress of PMMA is in the range of 5 〇 to 15 MPa ‘, the estimate given by this method is slightly higher than expected. This 35 200909792 difference may be due to strain hardening in compression. The standard Oliver-Pharr analysis yields the following estimates for E, Η and: Er = 5.46 Gpa; E = 4.79 Gpa; Η = 0.31 Gpa; oy = 0.107

Gpa. Example 3 - PC Nanoindentation Method A polycarbonate (pc) (part number CT303100) in sheet form (2 mm thick) was obtained from Goodfellow Cambridge Co., Ltd., Huntingdon, England. This is a Bayer Makrolon type pc with Mw=49 〇〇() g/m〇1 and Mn=13 000 g/m〇i, as determined by size exclusion chromatography (corrected using linear polystyrene) . The sample preparation and the overall extension were measured by using a round-trip error. The tensile specimen was cut from a 2 mm sheet into a 2.5-inch long rod of 忖·25吋 width. The tensile test was performed on the Instr〇n 42〇1 using the instr〇n Bliiehill software. The sample was attached using a gas clamp that was pressurized to 8 Torr. The Instr〇n mechanical extensometer with a gauge length of i吋 was reset to zero and attached to the specimen prior to testing to measure the tensile strain. The tensile test was performed under 0.05, 0.5 and 5 claws. Several pieces of PC sheets were manually cut using a jade saw. The pieces were embedded in

The Buehh Epoxicure tree is solidified in and cured, and forms an internal (a 吋 diameter hardened material for metallographic polishing. Using Struers _〇ρ〇ι and according to the 7 0 N applied force, the rod w | Add one of the following 歹丨 five grinding steps to polish: 1) 1200 grit SiC paper, using DI water lubricant, lasting 2 〇 coffee; 36 200909792 ii) 2400 grit SiC paper, using DI water lubricant, duration I〇sec ; iii) 4000 grit SiC paper, using DI water lubricant for 1 sec; iv) 3 micron diamond in Texmet cloth, using Leco diamond paste incremental lubricant for 3 min; v) Texmet cloth After the 25 micron diamond, the Leco diamond paste incremental lubricant was used for 4 minutes. The final polishing was achieved on a Buehler Vibromet using 0. 25 μηι diamond on the LeCloth surface under a load of 300 gm and using Leco diamond paste to lubricate the lubricant for 2 hours. Nanoindentation Method - Constant Response The nanoindentation test was performed on a MTS Nanoindenter (MTS Nano Instruments, 〇ak Ridge, Tennessee) equipped with a DCM head and a Berkovich diamond Accutip indenter. The area function of the indenter tip is corrected by the manufacturer using molten silica. The test was controlled via an MTS Testworks software computer using a continuous stiffness measurement (CSM) method that provides accurate detection of the surface of the indented material. Set the CSM parameter to a frequency of 75 Hz and an amplitude of 1 nm. Surface detection is caused by an increase in the stiffness of the harmonic contact above 100 N/m. The strain rate target for the load curve was set at 0.05/s and the constant unloading rate was between 0.7 and 0.8 mN/s. The traditional Oliver-Pharr calculation of the reduced modulus Er and the hardness [ [see 〇Hver and pharr, J. Mater. Res. 7:1564; Oliver and Pharr, 如施如心心! 9:3 (2004)] is automatically executed by Testworks software with a Poisson's ratio set to 0.35' and the unloading curve portion for automatic metering is set to 5〇%. Nai indentation method - constant displacement rate camp 37 200909792 Performed a nanoindentation test on a DCM head and a Berkovich diamond Accutip indenter _ S DCM nanoindenter. The area function of the indenter tip is corrected by the manufacturer using molten cerium oxide. The test is controlled by a MTS Testw〇rks software computer using a continuous stiffness measurement (CSM) method that provides accurate detection of the surface of the indented material. Set the csm parameter to a frequency of 75 Hz and an amplitude of i nm. Surface indifference is triggered by an increase in the stiffness of the harmonic contact above (10) N/m. The standard MTS^~^(4) method is modified by replacing the strange strain rate standard with the recorded displacement rate standard in the method. The load-displacement curve data was output using the output function of the Testw〇rks software for viscosity_elasticity_plasticity_adhesion analysis. The load-displacement curve of pc is plotted in Figure 8. The load and unloading measurements for five displacements are shown, with the maximum penetration depth and average for each measurement: ^ summarized in Table 6. The material has viscous, elastic and plastic characteristics because of the obvious lateness of the curves corresponding to different indentation velocities.

----————L^iOE^ Households. The parameters are determined by the indentation method. Here, for maximum penetration, (10) is the maximum load, V is the indentation velocity, and 5 is the average of the deformation variables ε 38 200909792 rate of change. To analyze the data and evaluate the viscosity of the polymer, transform the (Ph) description into ((y- nature, ;refer to useful: 4 3π ^γ/2 p πΚ2 new coordinate system (stress-strain) according to the following formula In the middle of the evening, the load-displacement curve of Lashizheng 1 ώ 绘制 is plotted in Figure 9. By dividing the negative σ_ε curve by Qiu Ba Tianshi, one bell warping * knife is used to calculate the opening, rate The effective reduced modulus of (shang, medium and low) 乂.f 仏. The results are summarized in Table 7. (via the standard expression £ = # Λ _ V; convert the reduced modulus to Young's modulus' Among them, the Poisson's ratio V = er f, , · ) is used for the purpose of comparison, and the same polymer is measured at different strain rates of 1 〇φ ^ 仃1. In Figure 10, the modulus is calculated. The overall magnetic quotation, + rate "T k and the measured value of the normal body modulus are plotted as a function of the effective shift half-^; the visible results are very consistent

S, sec'1 — Er, CJPg 3.72 1LIAEi〇2 1 ---------- 3.64 Ll^OE-os_|_ 2.35. The calculated value of the reduced modulus and Young's modulus is the average strain rate ‘ E, GPa 27 19 2.06. When calculating the characteristic relaxation, the rotation should be expressed in the dependence of the modulus on the deformation rate. To approximate Γ'厶C or more precisely, the dependence of compliance on j 39 200909792 can be fitted to the following function·· ^ (^) = Λ + ^ exp(-ir) The values of Λ, ..., and τ are summarized in In Table 8. _ ~~— ---_ Jn, GPa-1 J 1 〇p - -1 ~~SS, s ----^ 1 ? 1 0.3 _ 0.25 « · * Calculated value of human pine to 〇 is analysis The plasticity of the PC, & , + wang properties, such as the yield stress or the case, the plasticity measure Η can be defined as: Η = Ελ^){ει-εί\ Considering both the load and the unloading part of the curve is useful . For the second highest, ε is the maximum deformation and e/ is the final deformation (related to the material plasticity). //The higher the material behavior, the more "elastic" (for a given ^). The foreign language's can relate the enthalpy to the stress at which plastic deformation begins (ie, material hardness). Next, the yield stress ~ can be calculated based on the Tabor formula [see D. Tabor, TTze ifardness anc/Sirewgi/io/Meia, s, Oxford Clarendon Press, 1951] (where Tabor constant #2.9): H - Ic^y // and The calculated values of q are given in Table 9. 200909792 H, GPa rr ΠΡη 0.2 -----υ γ-, α -0.069 Table 9· pc hardness and yield stress calculated. The results were in good agreement with the overall tensile values of the polycarbonate at room temperature in the manufacturer's specifications (0_06_0.07 GPa, E = 2.3-2.4 GPa). The standard Oliver-Pharr analysis yields the following estimates of Er, e, Η and σ: Er = 3.9 〇 GPa; E = 3.42 GPa; Η = 〇·2ι Gpa; 〇广 〇 〇 72 GPa. Example 4 - PS Nanoindentation Method Polystyrene (PS X PS 1683) in the form of extruded pellets was obtained from The Dow Chemical Company, Midland, Michigan. This Ps is a general-purpose random ps of Mw = 269, 〇〇〇 g / mol and Mn = 96,300 g / mol, as determined by size exclusion chromatography (corrected using linear polystyrene). Preparation and bulk tensile test Tensile test specimens were prepared by compression molding at 255 C using the following sequential compression: 7 min at 1,000 psi; 7 min at 40 000 psi; and 40 min Slowly cool to room temperature. The drawn specimen was cut into a 2 mm long and 0.25 inch wide rod from the formed form using a high speed circular saw. Tensile testing was performed on an Instron 4201 using an Instron BluehU1 software. The sample was attached using an instron gas clamp pressurized to 80 psi. The Instron mechanical extensometer was reset to zero and the specimen was attached before the test to measure the tensile strain. Tensile testing is performed at 〇 〇 5, 〇 5 and 5. 41 200909792 PS pellets were embedded in a Buehler Epoxicure resin and cured therein, and an internal 1.25 inch diameter hardened material was formed for metallographic polishing. Polishing was achieved using Struers Rotopol and performing one of the following five grinding steps under 7 〇N applied force: i) 1200 grit SiC paper with DI water lubricant for 2 ; coffee; ii) 2400 grit SiC paper, Using DI water lubricant, lasting 1 〇 coffee; Hi) 4000 granule SiC paper 'using DI water lubricant, lasting 1 〇 coffee; iv) 3 micron diamond in Texmet cloth, using Leeo diamond paste incremental lubricant, lasting 3 Min ; v) 0.25 micron diamond in Texmet cloth, using Lec 〇 diamond paste incremental lubricant for 4 min. The final polishing was achieved on a Buehler Vibromet using a 〇25 μηι diamond on a LeCloth surface under a load of 300 gm and using a Lec(R) diamond paste to increase the lubricant for 2 hours. Nanoindentation Method - Constant Strain Farness The nanoindentation test was performed on a MTS Nanoindenter (MTS Instruments in 〇ak Ridge, Tennessee) equipped with a DCM head and a Berkovich diamond Accutip indenter. The area function of the tip of the reticle is corrected by the manufacturer using molten oxidized silica. The test is controlled via a MTs Testworks software computer using a continuous stiffness measurement (CSM) method that provides accurate detection of the surface of the indented material. Set the CSM parameter to a frequency of 75 ^ and an amplitude of 1 nm. The surface detection is caused by an increase in the stiffness of the harmonic contact of more than 100 N/m. The strain rate target of the load curve is set to 〇_〇5/s and the constant unloading rate is between 0.7 and 〇8 mN/s. Reduced bending mode 42 200909792 Number Er and hardness Η traditional 〇liver_Pharr calculation [see 〇liver and pharr, J. Mater. Res. 7:1564; Oliver and Pharr,··. steal (10). and 仏1 9:3 (2 〇〇4)] is automatically executed by Testworks software, its Poisson's ratio is set to 0.3 5, and the unloading curve portion for automatic calculation is set to 5〇%. Nanoindentation Method - 惶 Positioning Transfer Rate Age The nanoindentation test was performed on an MTS DCM nanoindenter equipped with a DCJV [head and Berk〇vich diamond Accutip indenter. The area function of the tip of the indenter is corrected by the manufacturer. The test was controlled by a MTS TeStw〇rks software computer using a continuous stiffness measurement (csm) method that provides accurate detection of the surface of the indented material. Set the csm parameter to a frequency of 75 Hz and an amplitude of 1 nm. The increase in stiffness is higher than 100 N/m and the surface detection is caused by harmonic contact.

The MTS Testworks CSM method is modified by replacing the set strain 2 standard with the displacement rate standard in this method. The load-displacement curve is output using the output function of the Testw〇rks software for viscosity, elasticity, plasticity, and adhesion analysis. The load-displacement curve of ps is plotted on the graph. The system is not the five displacement controls. The load-unloading measurement, in which the maximum degree of each measurement is at 矣 eight buds and the average speed ~ is shown in Table 10. Since the curves correspond to the lunar surface of the hysteresis H H 座 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 43 200909792 Marking hmnr, nm P..., mN v, nm/sec 121.79 0.13 94.13 South · Low 102.84 0.07 2.59 Medium - Medium 59.82 0.03 29.62 Low - South 24.71 0.013 76.48 Low - Low 11.82 0.0028 3.94 -l^sec'1 -- ---- -1λ〇7Ε-01 -U0E-03 ^6〇E-02

r Table 10. Determination of parameters by the nanoindentation method. Here ';!OTa;c is the maximum penetration, the maximum load, V is the indentation speed, and?? For the deformation variable < thousand mean rate of change. In order to analyze the data and evaluate the viscous-elastic-plastic properties of the polymer, it is useful to transform the (Ph) description into (σ_ε) according to the following formula: , 3/2 Ρ in the new coordinate system (stress-strain) The load_displacement curve is plotted in Figure 。. The effective reduced modulus of each deformation rate (high, medium, and low) is calculated by fitting the load portion of the σ-ε curve with a straight line. The results are summarized in Table 。. (via the standard expression five = do " _ convert the reduced modulus to Yang, the number 'which takes the Poisson's ratio ν = 〇 · 35.) For the purpose of comparison, the same polymer can be used at different strain rates The overall tensile measurement was performed. In Fig. 13 11, ^ τ ', the calculated value of the modulus and the measured value of the overall modulus are plotted as a function of the effective strain 44 44 200909792 rate;

The function i^l〇E-03 is always consistent Er, GPa E, GPa L 5.50 4.83 1 4.34 3.81 1 3.59 3.15 --------I-/_ IJ · Upper J_ reduced modulus and Young's mode The calculated value of the number is the average strain rate... 135 should be expressed in the dependence of the modulus on the deformation rate. To approximate the heterogeneous characteristics between loose or more precisely, the dependence of compliance π) on s can be fitted to the following function: V CO = J〇 + { exp(_5,) A, and the values of τ are summarized in the table 12 in.

Table 1 2. Calculated values of compliance parameters and characteristic relaxation times. To analyze the plastic properties of PS, such as yield stress or yield strain, it is useful to consider both the loading and unloading portions of the curve. For the case of high-low measurement, the plasticity measure is defined as: where ~ is the maximum deformation and ^ is the final deformation (closed to the material plastic phase 45 200909792). The better the higher the material behavior, the more "elastic" (for a given e,). In detail, the opening can be correlated with the stress at which plastic deformation begins (i.e., material hardness). Then, the yield stress ~ can be calculated based on the Tab〇r formula [see D_ Tabor, 27ie — &<<other oil, such as ^

Clarendon Press, ι951] (where Tab〇r constant 9):

The calculated values of H = kaY ugly and ~ are given in Table 13. The estimation of the yield strain is based on the assumption that the material can be considered as viscous_elastic_plastic. In the case of p S , it is known that brittle fracture takes precedence over plasticity, so the hardness observed in the overall test can be lower than the estimate obtained by the nanoindentation method. H, GPa σγ. GPa 0.45 0.155 Table 13. Calculated values of hardness and yield stress of PS. Standard Oliver-Pharr calculation: Er = 5.13 GPa; E GPa. The analysis yields the following estimates for Er, E, Η and Gy = 4.50 GPa; Η = 0.25 GPa; ay = 0.085 Conclusion It should be understood that the above examples are intended to be illustrative examples of materials that can be studied and procedures that can be used, rather than Detailed embodiment. Similar procedures can be used to characterize the viscous, elastic and/or plastic properties of other materials. 46 200909792 [Simple description of the diagram] Figure 1 (a) is a schematic diagram of an exemplary configuration. Figure 1 (b) is a typical load-displacement curve representing the nanoindentation method for viscous_elastic. The model based on the model 1 ") is a function that can be used to determine the mechanical properties of the material and the load rate and penetration depth (8). - The viscous viscosity of the results of the plastic % nanoindentation method - elasticity - Figure of the plastic 杈 type. Figure 3 is the (P/Pt) fitting (solid line) versus (P/Pt) FEA data (point: scatter plot; the trend line indicates that the two groups are very close. Figure 4 ( a) FEA (symbol) and model fit (line) for load-displacement relationship (P_h) for small penetration depth and large load rate and small load rate. ^ Figure 4(b) is for large penetration depth and FEA (symbol) and model fit (line) of load-displacement relationship (P_h) for large load rate and small load rate. Figure 5 shows PMMA load-displacement curve for nanoindentation. Figure 6 shows calculation of pMMA Stress-strain curve Figure 7 compares the modulus-dependent rate of change for PMMA. Figure 8 shows the pc load-displacement curve for the nanoindentation method. Figure 9 shows the calculated stress-strain curve for PC. Figure 10 compares the modulus of PC. For strain rate, Figure 11 shows the PS load-displacement curve for the nanoindentation method. Figure 12 shows the calculated stress-strain for PS. Figure 13 compares the modulus corresponding to the rate of change of PS. Figure 14 is a flow chart illustrating a specific example of the method of the present invention, when the hysteresis of the linear elastic characteristic of the 47th 200909792 load-displacement relationship is less than or equal to a predetermined value. Corresponding to the flowchart of the main figure 15 is #+一奋', 5 is a specific example of the method of the present invention, when the second: ^ is large _ value and the first - off elastic characteristic. Viscosity diagram 16 is an illustration A flow chart of a specific example of the method of the present invention, when the hysteresis of the first load displacement relationship is greater than a predetermined value and the hysteresis of the third load-displacement relationship is greater than a predetermined value, corresponding to the main viscosity_elastic-plastic [mainly Component Symbol Description] Benefit 48

Claims (1)

200909792 X. Patent Application Range: 1. A method for determining the properties of a sample by indentation, comprising the steps of: (I) selecting the region of the sample that will perform the indentation; (II) using the indenter tip Indenting the sample at more than one load rate and one or more penetration depths in the selected region at more than one location to obtain a plurality of load-displacement relationships; (111) The load-displacement relationship is used to determine at least two physical properties of the sample. 2. As in the method of claim 帛i, |(ii) comprises the steps of: using the indenter tip at a first position in the selected region at a first load rate and a first penetration depth Sample indentation to obtain a first load-displacement relationship; at a second location within the second indentation to obtain a second load-bit indenter tip at a selected region load rate and a second penetration depth Moving the sample relationship, wherein the first load rate is different from the second load rate, and analyzing a load-displacement relationship obtained from the larger of the first load rate and the second load rate to determine the material At least one property. - 3. If the second step of the patent application scope is: , , (1) contains - the first position in the selected area 49 200909792 :: load rate and first penetration depth a sample indentation-displacement relationship; and a first load-shift relationship to determine at least a second tracer tip of the material at a second location within the selected region, And... the penetration depth of the sample is indented to obtain a first load-displacement relationship, wherein the first load rate is greater than the second load rate. Ii) further comprising the following steps: 4. The method of claim 3, wherein (d) comparing the hysteresis 盥筮 of the second load-bit predetermined value to the Bellows displacement relationship. ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Wherein the third load rate is greater than the first and the third penetration depth is greater than the third location within the selected region, the sample is indented to obtain a third load rate; 6. For example, in the scope of claim 5, the penetration odour and the second penetration depth are no longer indented when the second load-displacement relationship is fixed. The hysteresis is less than or equal to the first pre-50 200909792 7: The method of claim 5, wherein when the second load-bit, the (π)-step packet: the hysteresis of the relationship is greater than the - The predetermined value is read. The second load_displacement relationship has a hysteresis and a second predetermined value. The method of claim 7, wherein when the third load is shifted, the fourth load is further divided into four (4) and further comprises: 11 A (g) indenting the sample with the indenter tip at a fourth position in the selected region at a fourth load rate and a fourth penetration deep edging edge to obtain a fourth load-displacement relationship Wherein the fourth load rate is greater than the second load rate and less than the first load rate and the third load rate; and the penetration depth and the second penetration depth the fourth penetration depth is greater than the first degree And less than the third penetration depth. 9. The method of claim 7, wherein when the hysteresis of the third load_displacement relationship is greater than the second predetermined value, then (^) into the step comprises: '(g) using an indenter tip Pressing the sample at a fourth load rate and a fourth penetration depth at a fourth and fourth position in the selected region to obtain a fourth load-displacement relationship, wherein the fourth load rate is less than the a first load rate A the third load rate; 51 200909792 and the fourth penetration depth is greater than both the first penetration depth and the second penetration depth; and (h) using the indenter tip in the selected area The sample is indented at a fifth position within the domain at a fifth load capture rate and a fifth penetration depth to obtain a fifth load-displacement relationship, wherein '^ the fifth load rate is greater than the second load rate and the first a fourth load rate and less than the first load rate and the third load rate; and the fifth penetration depth is greater than the first penetration depth and the second penetration depth and less than the third penetration depth and the fourth Penetration depth, where (g) and (h) Performed in any order. The method of any one of claims 2-9, wherein the first penetration depth and the second penetration depth are each independently about 1 to ι·ι times the indenter Tip radius, the load rate is about 1 nm/sJ_100 000 nm/s, and the second load rate is about oi nm/s to 1 〇, _ nm/s. The method of any one of claims 5-9, wherein the X-penetration twist is about 0.5 to 1.0 times the tip radius of the indenter' and the first loading rate is about 1 nm. /s to 1〇〇, 〇〇〇nm/s 〇j2. The method of claim 8 wherein the fourth penetration depth of X is about 〇2 to 〇5 times the tip of the indenter half 52 200909792 The diameter, and the fourth load rate is about 13. As described in the patent application, the fourth penetration depth is about 〇3 nm/s to 3 〇, _nm/s. The method of item 9, wherein 〇·5 to 1.〇 times the tip of the indenter half the fourth load rate is about (M nm/s to 1 〇, 〇〇〇nm/s, the fifth penetration depth For about 〇2 to 〇5 pull, the main υ.5 times the tip radius of the indenter, and the fifth load rate is about 〇·3 nm/s to 30, 〇〇〇nm/s. The method of any one of clauses 5-9, wherein the first penetration depth and the second penetration depth are each independently selected to be about 0.01 to 0.1 times the radius of the indenter tip, the first The load rate and the third load rate are independently from about 1 nm/s to 100,000 nm/s, and the second load rate is about 〇.lnm/sm〇〇〇nm/sq. The third penetration depth is about 〇.5. To U times the tip radius of the indenter. The method of claim 8, wherein the first penetration depth and the first penetration depth of the flute X are each independently about 0.01 to 0.1 times At the tip radius of the indenter, the first load rate and the third load month rate are independently from about 1 nm/s to 100,000 nm/s, and the load rate is about 〇彳nm/ s 勹] ul nm / s to 10 〇〇〇 nm / s, the third penetration depth is about 〇 • to 1.0 times the tip of the indenter half 53 200909792 diameter, the fourth penetration depth is the diameter, and the first The fourth load rate is about 0.3 nm/s to 3 〇, _ nm/s. The method of claim 9, wherein the first penetration depth and the second penetration depth are each independently about 0.01. Up to 0.1 times the tip radius of the indenter, the first load rate and the third load rate are independently about "m/s to 100,000 nm/s, and the second load rate and the fourth load rate are independently about _ to 10,000 nm/s, the third penetration depth and the fourth penetration depth are independently about 5 to 1.0 times the indenter tip radius, and the fifth penetration depth is about 0.2 to 0.5 times The indenter has a tip diameter, and the fifth load rate is about 〇.3 nm/s to 3 〇, 〇〇〇(10)^. 17. The method of any one of clauses 2-9, wherein the A position is the same as the second position. K is the method of any one of the items in the scope of the patent application, wherein the sample passes through each of the regions Positioning at least five times the center of the highest of the penetration depths from the other indentation positions - in the method of any of the items in the item μ of the scope of the application, the fourth item of the history of the indentation is selected from the following Material composition group: Shi Xi, carbonized stone, nitrogen cut, diamond, blue f stone or coated with carbon cut, nitrided stone, 54 200909792 diamond and sapphire. 2. The method of any one of claims 1 to 9 wherein the tip is spherical or parabolic and has a method of any one of items 1-9 Where ν is 10 times the thickness of the highest penetration depth. To: The method of any of the above-mentioned items, wherein the physical property is selected from the group consisting of Young's modulus, adhesive work, yield strain, viscosity, and __. Yield strain 23_If the load-displacement relationship of any of the 申请_9 items in the patent application scope is changed to the effective stress-strain 3π (W, 3/2 among the households via the following change, 'the two (σ_ε) curve) For the load, the household _ is the lowest load (p depth...the radius of the tip of the repeater.), 4 is the penetration of the patent range of the patents _9 items _ folding modulus, Young's modulus, relaxation time And the yield strength:: 'where: by applying the effective stress to the >, one of the Wei effect force-strain curves is fitted to the microcomputer 25. If the application is for the _9 shot, it is obtained. The tip of the tracer is a spherical or parabolic method, where 55 200909792 (iii) includes fitting the resulting load-displacement relationship to the following model E. where 1 - expi sr Xe{s)e + [\-Xe{£ )s], Y expi : εγ 1 + C / \ ε 1/3 9 s = D—~ (5) \εΥ y ^load [r_ 3/2 ε = (4/3π)(_'σ = (Ρ·ρ ')/πΙι2=(ρ+2πγΚ)/πΚ2; νΜ and νΗ represent the relative contributions of Maxweiuan and Hookean elements, respectively, where ~+vh= !; R is the The radius of the tip of the indenter; p is the measured load; h is the penetration depth; ht is the final penetration depth; and the total time for the indenter to reach & Er is the reduced modulus' τ is loose Time; 丫 is the adhesion work between the tip of the waste meter and the sample; s is the yield strain; 1 〇 and D are empirically determined constants. 26. The method of claim 25, wherein (8)(1) When the hysteresis is less than or equal to the predetermined value, it is used when fitting the data. 27. If the patented ribs are used, the method of the 25th item is used, wherein the hysteresis in (ii) (d) is less than or When it is equal to the predetermined I and the pre-value, the ε 28· system is used when fitting the data, which includes: 56 200909792 Indenter tip for indenting the sample; controller for controlling the pressure The indentation of the sample at the tip of the tracer can obtain a plurality of load-displacement relationships, wherein the plurality of load-displacement relationships represent a plurality of sample positions, a plurality of load rates, and a plurality of penetration depths; and a bedding analysis system , which is determined based on the plurality of load-displacement relationships At least two physical properties of the sample. 29. The system of claim 28, wherein the plurality of load-displacement relationships are collected according to the method of any one of the following claims. For example, the system of claim 28, wherein the indenter tip is selected from the group consisting of bismuth, tantalum carbide, nitriding: diamond, sapphire or coated with carbon carbide, nitrite Diamond, sapphire and magic. Instrumentation 31. If the big end of the 28th or 3rd item of the patent application is spherical or parabolic, and has a system of about 50, the indentation is 5 to about 200 nm, and the system is 29, wherein The indenter tip is spherical or parabolic, and the data analysis system is configured to convert the negative displacement relationship into an effective stress _ strain via the following transformation nR2 57 200909792 4 hY2 /, for the load 'household one for the lowest load (household one), /2 for the penetrating ice and 'and the radius of the tip of the indenter. #中专利的范围范围(4), the indenter is spherical or parabolic, and (iv) the rt material analysis system is configured to form the micromechanical model by the effective stress-strain curve & To calculate at least one of the Young's modulus, relaxation time, and yield strength. 34. The system of claim 29, wherein the tip of the oscillating indenter is spherical or parabolic, and the ... 4 bunker analysis system is based on the plurality of load-displacement relationships, by loading -H The displacement relationship is fitted to the following model to determine at least two physical properties of the sample, Ε. 1 - expJ -- ^e(s)s + [l-Xe(e)sh 1 - expJ where / \1/3 1 + C ε ' s^d 4 K_ J ^load R_ 3/2 Field): :(4/37l)(h/R)3/2 : σ = (P - Pmin)^R2 = (ρ +2πγΚ)/πΚ2 And νΗ respectively represent the relative contributions of Maxwell and Hooke elements, respectively, in VM 2009 V V V = 1 in 2009 200979; R is the radius of the indenter tip; P is the measured load; h is the penetration depth; ht is the final wear Penetration depth; t1 (5ad is the total time of the indenter reaching ht; is the reduced modulus; τ is the relaxation time; γ is the adhesion between the tip of the indenter and the sample; is the yield strain; and C And D is a constant determined by experience. 35. The system of claim 34, wherein the at least two physical properties are selected from the group consisting of Young's modulus, adhesive work, yield strain, and viscosity. And the group consisting of eleven relaxation time, the drawings: such as hypophosphorous Page 59