A simple indentation device and method for measuring thin layer young's modulus and adhesion energy

Abstract

This invention relates to a simple indentation device for measuring the Young's modulus and adhesion energy of thin films, belonging to the field of material mechanical property testing and surface and interface physical characterization technology. It includes a test platform, an XYZ three-axis cantilever linear module, a Z-axis electric slider moving platform, an analytical balance, a clamp, and a spherical indenter with a handle. The analytical balance and the XYZ three-axis cantilever linear module are mounted on the test platform. The XYZ three-axis cantilever linear module consists of two columns, an X-axis linear module, a Y-axis linear module, and a Z-axis linear module. The Z-axis electric slider moving platform is located at the lower end of the moving slider of the Z-axis linear module, directly facing the analytical balance. The clamp is located on the Z-axis electric slider moving platform and is used to hold the spherical indenter with a handle. The analytical balance has a tray for placing the thin film sample attached to a silicon wafer, and the tray is surrounded by a glass cover. The analytical balance outputs the normal contact force between the indenter and the thin film based on an electromagnetic force balance compensation system.

Description

Technical Field

[0001] This invention belongs to the field of material mechanical property testing and surface and interface physical characterization technology, and relates to a simple indentation device for measuring the Young's modulus and adhesion energy of thin layers. Background Technology

[0002] With the rapid development of biomedical engineering, flexible wearable electronic devices, and advanced polymer materials science, the surface mechanical properties and elastic properties of compliant materials with low Young's modulus are attracting significant attention from academia and industry. Accurate measurement of the Young's modulus and surface adhesion energy of these soft matter thin films plays an irreplaceable fundamental role in material design, service life assessment, and microscopic mechanism analysis. However, traditional uniaxial tensile testing is difficult to directly apply to micron- or nanometer-scale thin materials attached to rigid substrates, making instrumented indentation testing (IIT) the most mainstream characterization method.

[0003] In the current field of mechanical testing of thin film materials, existing technical solutions and commercial instruments reveal a severe dilemma: both the complexity of hardware operation and the applicability of underlying theories are limited.

[0004] Currently, the industry heavily relies on highly integrated commercial nanoindentation instruments for microscale indentation testing of materials. The NanoTest Vantage nanoindentation system produced by Micro Materials Ltd (MML) in the UK is a typical example in this field. Although these instruments exhibit certain versatility in complex environments such as high and low temperatures and liquids, they reveal significant drawbacks when routinely applied to measuring the fundamental elastic parameters and adhesion properties of soft thin film materials: First, for thin layers with low Young's modulus, due to van der Waals forces, adhesive tension will be generated between the indenter and the thin layer before and during contact. Traditional commercial nanoindenters cannot measure the adhesive force during the loading process of the indenter pressing down, so they cannot accurately measure the adhesion energy between the indenter and the thin layer and the Young's modulus of the thin layer.

[0005] Secondly, the complex instrument structure leads to extremely cumbersome operation and calibration procedures. The core loading mechanism of the NanoTest Vantage system employs a pendulum system based on a frictionless pivot. Its working principle involves a coil mounted on the top of the pendulum; when current is applied, it generates an electromagnetic attraction with a permanent magnet, thereby driving the diamond indenter at the end to move towards the sample surface. Simultaneously, the displacement of the indenter is indirectly measured through a parallel-plate capacitor and a capacitor bridge circuit mounted behind the indenter support. This indirect force and distance measurement mechanism based on pendulum and electromagnetic drive requires operators to strictly adhere to the ISO 14577 standard for extremely tedious iterative calibration before each indenter change or new batch of tests. Operators typically need to first perform large-load indentations on extremely hard standard samples (such as tungsten or sapphire) to calculate and subtract the instrument's own frame compliance; subsequently, a series of low-load tests must be performed on fused silica to fit the area function of the indenter tip. For researchers who only need to obtain the elasticity and adhesion parameters of the soft film, this calibration process is not only extremely time-consuming, but any minor misoperation in any step can lead to huge cumulative errors.

[0006] Furthermore, system drift and dynamic instability are significant challenges in soft material testing. Pendulum-type electromagnetic loading systems are extremely sensitive to environmental vibrations and thermal drift. When testing extremely soft polymer films, the required contact loads are very low, typically in the micronewton to millinenewton range, making the instrument's signal-to-noise ratio inadequate. Even with vibration isolation tables and temperature chambers, thermal drift severely contaminates displacement data during low-frequency loading or long-term load holding tests. Moreover, insufficient mechanical stiffness of the pendulum system often leads to dynamic instability phenomena such as "jump-out" when the indenter is pulled off the surface of a highly adhesive soft material, making the adhesion energy measurement results highly unreliable.

[0007] Finally, the high cost and low adoption rate of hardware are significant drawbacks. The complex capacitance bridge measurement circuit, electromagnetic feedback drive module, and precision three-axis DC motor platform mean that the purchase cost of commercial equipment like the NanoTest Vantage can easily reach hundreds of thousands to millions of RMB. Furthermore, subsequent maintenance and consumable materials such as diamond indenters are often extremely expensive. This severely restricts the promotion and application of this type of indentation testing technology in general university laboratories and small and medium-sized enterprises.

[0008] Regarding the choice of indenter shape, standard nanoindenters are typically equipped with sharp, pyramidal indenters such as the Berkovich or Vickers indenters. However, due to stress concentration at the tip, these indenters are prone to directly piercing the surface of soft films under extremely low loads, inducing plastic yielding and completely masking the material's purely elastic contact response and interfacial adhesion characteristics. Therefore, the use of a spherical indenter has become the choice for most researchers testing the elastic modulus and adhesion energy of soft material films. A large-radius spherical indenter can keep the thin layer in a low-stress, low-strain state within the contact area, thus greatly reducing or avoiding plastic deformation and damage to the material.

[0009] Furthermore, in nanoindentation experiments, if there is no adhesive force, d The initial reference state of 0 can be determined experimentally based on the indentation force. F The indentation depth is determined when the indentation depth is 0. However, under the influence of adhesive force, the indentation depth... d The initial reference state of 0 cannot be accurately determined. That is, only the relative indentation depth can be accurately measured in indentation experiments. Therefore, theoretically, it is necessary to propose a theoretical prediction formula for the thin-layer Young's modulus and adhesion energy for the relative indentation depth.

[0010] In the asymptotic solution analysis of classical contact mechanics, theoretically, the accuracy of the asymptotic solution increases with the radius of the indenter contact area. a With film thickness t ratio a / t The accuracy gradually increases with the increase of the indentation radius. However, a large indentation radius will cause high contact pressure, which may lead to the failure of linear elasticity theory. Therefore, the applicability of the first-order solution is relatively narrow, and the second-order solution must be used to simultaneously improve the accuracy and applicability of the asymptotic solution.

[0011] To avoid the aforementioned theoretical failure and maintain the linear elastic range, experimental operations are often forced to limit the indenter radius or control the indentation depth to an extremely shallow depth. a / t The ratio cannot be made large enough. However, existing theories, such as the first-order asymptotic solution models obtained by Yang et al. based on the Hankel transform or Argatov et al. based on the boundary layer solution assuming no stress at the contact zone boundary, can achieve a sufficiently large ratio. a / t Even when the ratio is not large enough, the performance is still poor. Quantitative studies in existing literature clearly indicate that for non-adhesive film indentations, even when the ratio of contact radius to film thickness is 10 (i.e., ... a / tWhen the coefficient of friction is 10, the relative error between the numerical solution and the first-order asymptotic solution can be as high as 50%, while the second-order solution can effectively reduce the error to about 10%. As the indenter radius and indentation depth increase, the deformation stress field penetrates the film and is strongly constrained by the underlying rigid substrate. If the hardening effect of the substrate cannot be accurately decoupled in the theoretical model, the experimentally measured modulus will be much higher than the true Young's modulus of the film.

[0012] For materials with low Young's modulus, such as compliant polymers and gels, they are generally assumed to be incompressible (Poisson's ratio). n = 0.5). In the indentation process of such materials, the surface adhesion effect is extremely significant and cannot be simply ignored as in testing metals or ceramics. While the classic Johnson-Kendall-Roberts (JKR) model was initially proposed to solve the adhesion problem in Hertz contacts, it only applies to contacts between two semi-infinite elastic bodies. When the model is transformed into a thin film with a rigid substrate, the boundary conditions, such as displacement constraints at the bottom, change fundamentally, resulting in a completely different form of the partial differential equation for the contact pressure compared to the compressible half-space case. The classic JKR formula cannot be directly applied. Finding an analytical solution that simultaneously considers incompressibility, the finite thickness substrate effect, and the surface adhesion energy, and that is simple enough for direct use by experimenters, is a core technical problem that urgently needs to be solved in this field.

[0013] In summary, existing commercial nanoindentation instruments cannot measure tensile force during loading, are cumbersome to operate, are prone to drift errors, and are extremely expensive. Furthermore, theoretically, they lack a simple, explicit formula for measuring Young's modulus and adhesion energy with high precision and universality for relative indentation depth. To address these dual shortcomings, there is an urgent need in this field for a novel indentation device and testing method that features extremely simplified hardware structure and high-order compensation in theoretical algorithms. Summary of the Invention

[0014] In view of this, the purpose of this invention is to provide a hardware device specifically for spherical indentation mechanical testing of incompressible soft thin film materials (such as polydimethylsiloxane PDMS, hydrogels, biological soft tissues, polymer coatings, and elastomers), and a matching analytical method based on second-order asymptotic solution contact mechanics. This invention is mainly used for high-precision and high-efficiency extraction of Young's modulus and interfacial adhesion energy of thin-film materials.

[0015] To achieve the above objectives, the present invention provides the following technical solution: On one hand, the present invention provides a simple indentation device for measuring the Young's modulus and adhesion energy of thin layers, including a test platform, an XYZ three-axis cantilever linear module, a Z-axis electric slider moving platform, an analytical balance, a fixture, and a ball-shaped indenter with a handle; the analytical balance and the XYZ three-axis cantilever linear module are mounted on the test platform; the XYZ three-axis cantilever linear module consists of two columns, an X-axis linear module, a Y-axis linear module, and a Z-axis linear module; the two columns are mounted on the test platform and located on one side of the analytical balance, with their tops supporting and fixing the X-axis linear module; the Y-axis linear module is vertically mounted. A cantilever structure extends outward from the slider of the X-axis linear module; the Z-axis linear module is vertically mounted on the slider at the cantilever end of the Y-axis linear module and is suspended directly above the analytical balance; the Z-axis electric slider moving platform is located at the lower end of the moving slider of the Z-axis linear module, directly facing the analytical balance; the clamp is located on the Z-axis electric slider moving platform and is used to clamp the spherical indenter with a handle; the analytical balance is provided with a tray for placing the thin film sample attached to the silicon wafer, and the tray is surrounded by a glass cover; the analytical balance outputs the normal contact force between the indenter and the thin film based on the electromagnetic force balance compensation system.

[0016] Furthermore, the Z-axis electric slider moving platform is equipped with a stepper motor, the guide bearing mechanism includes 8 sets of cross roller guides, the drive mechanism uses precision ground ball screws for transmission, and contains 2 limit sensors and 1 origin limit sensor. The bottom surface and the table surface are both designed with standard countersunk connection holes for controlling the fixture to drive the spherical pressure head with handle to move up and down slightly.

[0017] Furthermore, the fixture is provided with a shank through hole and a side set screw. The shank of the spherical press head passes through the shank through hole and is fixed by the side set screw. The end of the spherical press head is provided with a disc step, and the bottom of the shank through hole of the fixture is provided with a disc step expansion groove that cooperates with the disc step.

[0018] Furthermore, the radius of curvature of the spherical indenter with a handle is 40 mm.

[0019] On the other hand, the present invention provides a simple indentation method for measuring the Young's modulus and adhesion energy of a thin layer, comprising the following steps: S1: Place the incompressible elastic film to be tested, attached to a rigid substrate, on the analytical balance, and start the Z-axis electric slider movement platform controller to drive the film with a known geometric radius of curvature. R A rigid spherical indenter is pressed into the thin film layer to be tested at a uniform speed; S2: During the dynamic contact mechanics response of the system, capture and determine the state characteristic coordinates of the zero-load point when the internal and external forces of the system reach instantaneous equilibrium; S3: During the stage where the pressure head is lifted and removed from the film by the reverse unloading of the drive displacement stage, locate and capture the critical pull-off point state characteristic coordinates at the moment when the interface completely separates. S4: Obtain the indentation force during the dynamic process. F With indentation depth d The interfacial adhesion energy of the tested material is obtained by directly calculating using a first-order asymptotic solution formula or by data fitting. c Young's modulus E .

[0020] Furthermore, step S2 specifically includes the following steps: During the dynamic process of the indenter gradually pressing into or retracting from the film, the indentation force at the contact interface... F When the load reaches zero, it is the zero load point; Record the absolute physical coordinates of the Z-axis corresponding to the zero-load point, and obtain the indentation depth corresponding to this zero-load point, denoted as . d 0; in, F For indentation force, d 0 represents the initial reference indentation depth corresponding to the zero load point.

[0021] Furthermore, step S3 specifically includes the following steps: During the unloading and lifting process, at the instant the interface breaks and the indenter separates from the film, the system records the minimum indentation force. This force is the pull-out force, denoted as . F c ; Simultaneously record the critical indentation depth corresponding to this moment of pull-out, denoted as . d c ; Based on the data from the zero-load point and the critical pull-out point, the relative displacement of the interface is obtained. d 0 d c .

[0022] Furthermore, step S4, calculating the adhesion energy and Young's modulus of the thin film material, specifically includes the following steps: Minimum indentation force during loading F Equal to the pull-out force required to separate the pressure head from the layer. F c ; According to the first-order pull-out force formula:

[0023] In the formula l It is the elastic capillary length. R Let be the geometric radius of curvature of the rigid spherical indenter. E The Young's modulus of the material to be tested. c The interfacial adhesion energy of the tested material is determined by the measured pull-out force. F c The adhesion energy of the film was calculated. c ; According to the formula for elastic capillary length:

[0024] In the formula B To be comparable to Poisson n The relevant constants of the elasticity for incompressible layers n = 0.5:

[0025] Combining the above formula with relative displacement d 0 d c The slenderness of the elastic hair was calculated. l ; Through relational formulas E = g / l Young's modulus was calculated E .

[0026] Furthermore, step S4, which involves fitting to obtain the adhesion energy and Young's modulus of the thin film material, specifically includes the following steps: First order d - F The relationship is:

[0027] In the formula d Indentation depth B To be comparable to Poisson n The relevant constants of the elasticity for incompressible layers n =0.5, l To quantify the elastic capillary length of the adhesion effect, F For indentation force, R The radius of curvature of the pressure head is... t The thickness of the incompressible elastic film. E Young's modulus; when F When <0, d and a It is about F A two-valued function; According to the first order d - F The relationship is used to fit the data, and the known rigid indenter radius is used. R Thin layer thickness t The obtained indentation force F and the corresponding indentation depth dSubstitute into the formula; then fit Young's modulus using curve fitting method. E and the fineness of the elastic fibers l .

[0028] The beneficial effects of this invention are as follows: Compared with existing commercial nanoindentation instruments such as the NanotestVantage from MML in the UK and the traditional first-order asymptotic solution of indenter-film contact, the device of this invention has significant substantial progress and outstanding beneficial effects. These effects strictly correspond to the technical pain points in the mechanical testing of soft matter thin layers and the purpose of this invention, and are specifically reflected in the following four core dimensions: The hardware structure of this invention enables "power-on" operation, significantly reducing testing complexity and cost. This device employs a high-rigidity cantilever structure design with a dual-column supported XYZ three-axis cantilever linear module, coupled with a high-precision electric slider platform on the Z-axis at the end, providing near-infinite system rigidity. This direct-drive mechanical circuit minimizes deformation, eliminating the complex frame flexibility calibration steps found in commercial instruments from the hardware source. Thanks to the ultra-high rigidity of the mechanical circuit, testers do not need to perform lengthy probe area function calibrations, achieving "power-on" operation after sample placement, significantly reducing the technical operation threshold and manpower and time costs, and greatly simplifying the testing process. By optimizing the combination of commercially available standard high-precision analytical balances, stepper motor slides, and simple machined parts, the manufacturing cost of the device has been drastically reduced, greatly promoting the popularization of this technology in ordinary laboratories and quality inspection departments of small and medium-sized enterprises, demonstrating a significant cost advantage.

[0029] This invention employs an analytical balance based on an electromagnetic force balance compensation system as a mechanical sensor. Its fully mechanical rigid transmission and absence of heating coil interference completely solve the thermal drift contamination problem in long-term creep testing of electromagnetic loading systems. The analytical balance provides an ultra-high mechanical resolution of 0.1 mg, combined with micron-level displacement control of the high-precision Z-axis slider, and an external windproof cover, ensuring stable and accurate capture of the weak adhesion responses of soft material films under extremely low loads ranging from micronewtons to millinewtons.

[0030] Compared to traditional first-order asymptotic theory methods in thin film contact mechanics, the method of this invention derives and introduces a second-order asymptotic solution relationship based on the Kerr model. Quantitative studies show that under conditions where the ratio of indenter radius to film thickness is large (e.g., a ratio of 10), the second-order formula can effectively reduce the theoretical calculation error from over 50% of the first-order solution to about 10%, achieving a significant leap in accuracy. Through the intrinsic geometric coupling logic of the formula, the large ball indentation ensures that the deformation field is concentrated inside the film, enabling accurate extraction of the intrinsic Young's modulus of the film and effectively eliminating hardening interference caused by the rigid substrate effect.

[0031] In terms of data post-processing logic, traditional Oliver-Pharr methods or continuous stiffness methods require precise fitting of the initial slope of the unloading curve. For soft, thin-film materials with strong adhesion, uncontrollable surface jump contact occurs at the moment the indenter approaches, making it difficult to find the true zero point of indentation in absolute coordinates. d Reaching 0 becomes extremely difficult, and even a tiny deviation at the zero point can lead to several times the error in the final modulus calculation. The method of this invention incorporates parameter extraction logic based on feature point dimensionality reduction. By utilizing the extreme features of the pull-off point and the equilibrium features of the zero-force point, this method no longer requires tracing a continuous force curve, but instead relies solely on the relative distance difference between two physical extreme points. d 0 d c This fundamentally avoids the contamination of modulus calculation results by the absolute coordinate zero-point calibration error, ensuring extremely high test reproducibility and accuracy.

[0032] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0033] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 (a) is a schematic diagram of the overall structure of the simple indentation device, (b) is a top view of the simple indentation device, (c) is a side view of the simple indentation device, (d) is a front view of the simple indentation device, and (e) is a detailed diagram of the connection between the Z-axis high-precision electric slider moving platform, fixture, spherical indenter with handle, and thin film sample attached to the silicon wafer. Figure 2 Schematic diagram of a self-made rigid fixture; Figure 3 This is a model of the adhesive contact between a rigid spherical indenter and an incompressible elastic thin layer. Figure 4 Modeling and design drawings for a spherical cubic boron nitride indenter; Figure 5 Indentation force given for different models F With contact radius a Changes; Figure 6 For different models, predictions of adhesion a - F relation.

[0034] Figure labels: 1-Analytical balance; 2-Silicon wafer; 3-Sample film to be tested; 4-Spherical indenter; 5-Side set screw; 6-Indenter clamp; 7-Z-axis electric slider moving platform; 8-Glass windproof cover; 9-Z-axis linear module; 10-Y-axis linear module; 11-X-axis linear module; 12-Column; 13-Stepper motor; 14-Through hole in the handle; 15-Disc stepped enlarged slot; 16-Side set screw through hole; 17-Bolt hole; 18-Disc step. Detailed Implementation

[0035] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0036] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0037] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0038] Example 1: This invention provides a simple indentation device for measuring the Young's modulus and adhesion energy of thin layers, completely eliminating the complex pendulum-type electromagnetic loading system and capacitive bridge ranging structure of traditional commercial nanoindenters (such as the MML Nanotest Vantage). This invention aims to construct a testing platform with ultra-high frame stiffness, zero thermal drift, and low cost through an innovative mechanical combination of an "XYZ three-axis cantilever linear module + Z-axis high-precision electric slider moving platform + high-precision analytical balance." This design eliminates the need for cumbersome frame flexibility and indenter area function calibration, achieving highly efficient "power-on" operation.

[0039] Unlike commercial nanoindentation instruments that use flexible cantilever or pendulum systems, the testing device of this invention pursues absolute "frame rigidity" and "directness" in its design philosophy. For example... Figure 1-Figure 4 As shown, the structural composition of this simple indentation device and the connection relationships between its components are as follows: The mechanical load-bearing system of this simple indentation device adopts an XYZ three-axis cantilever layout. The XYZ three-axis cantilever linear module consists of three linear modules, which are mounted on the test platform via two columns and located on the side of the analytical balance 1. The top supports and fixes the X-axis linear module. The Y-axis linear module is vertically mounted on the slider of the X-axis linear module, extending outward to form a cantilever structure. This structure supported by two columns provides near-infinite system mechanical stiffness, and its own elastic deformation is negligible within the soft material test load range. This design completely eliminates the "frame flexibility" calibration step that must be performed in the system from a physical perspective, greatly simplifying the pre-test preparation work. In the XYZ three-axis cantilever linear module, the Z-axis linear module is positioned directly above the analytical balance, and the Z-axis high-precision electric slider moving platform is located at the lower end of the Z-axis linear module, facing the analytical balance. This Z-axis high-precision electric slider moving platform is equipped with a Japanese Orient Motor 42 stepper motor. The guiding and bearing mechanism includes 8 sets of crossed roller guides, and the drive mechanism uses precision-ground ball screws for transmission, featuring high precision and low vibration. Compared to electromagnetic coil drive, the motor-driven slider platform operates in a displacement control mode, significantly improving the fidelity of displacement data during long-term load testing.

[0040] Directly beneath the Z-axis high-precision electric slider moving platform, a self-made rigid aluminum alloy fixture block, precision CNC machined, is securely suspended and mounted via four high-strength internal hexagonal bolts. To ensure that the pressure head does not experience any lateral displacement or longitudinal misalignment during extremely small indentation and pull-out processes, the fixture is equipped with a shank through-hole and side set screws. This embodiment uses a specially designed spherical cubic boron nitride pressure head with a disc step at its end. The bottom of the fixture's shank through-hole has a disc step expansion groove that mates with the disc step. During assembly, the shank of the spherical pressure head passes through the fixture's shank through-hole and is fixed by the side set screws, while the disc step is perfectly fitted into the expansion groove. The axial limiting of the expansion groove and the disc step, combined with the radial locking of the side set screws, ensures absolute rigid coupling between the pressure head and the slider. This design ensures that the indenter will never slip axially during the unloading and pulling-off stage of the film, even with huge surface adhesion tension, thus guaranteeing the absolute accuracy of the measurement of the critical pull-off point state characteristic coordinates.

[0041] The radius of curvature of the spherical indenter with handle used in this invention RThe radius is extremely large, reaching 40 mm in this embodiment. Compared to the sharp, pyramidal indenters or small-radius ball heads used in conventional nanoindentation, this is an ultra-large radius. The large-radius ball head allows the thin layer to maintain a low-stress, low-strain state in the contact area, effectively preventing the indenter from piercing the soft film. At the same time, the huge contact area can significantly amplify the weak surface adhesion force signal, making it easier for the balance to capture the normal contact force.

[0042] A high-precision analytical balance with an accuracy of 0.1 mg, equivalent to a resolution of approximately 1 μN, is placed on a shock-resistant test bench directly below the pressure head. A tray is provided on the analytical balance, and the PDMS thin film sample to be tested is attached to a rigid silicon wafer and placed flat in the center of the tray.

[0043] To avoid the influence of airflow disturbances on micro-Newton level mechanical measurements, the analytical balance is equipped with a windproof glass cover. During testing, simply open the top window, allowing the spherical indenter connected to the Z-axis slider to pass through the window from top to bottom and contact the thin film surface located inside the cover. The analytical balance utilizes its internal, mature electromagnetic force balance compensation system to directly and in real-time output the normal contact force between the indenter and the thin film, displaying it on the computer acquisition software. This mechanical sensing solution completely eliminates the need for complex microelectromechanical system force sensors, achieving calibration-free, plug-and-play functionality.

[0044] In summary, this simple indentation device includes a test platform, an XYZ three-axis cantilever linear module, a Z-axis electric slider moving platform 7, an analytical balance 1, an indenter clamp 6, and a spherical indenter with a handle 4. In this embodiment, the spherical indenter with a handle 4 is made of cubic boron nitride. The analytical balance 1 and the XYZ three-axis cantilever linear module are set on the test platform. The XYZ three-axis cantilever linear module consists of two columns 12, an X-axis linear module 11, a Y-axis linear module 10, and a Z-axis linear module 9. The two columns 12 are set on the test platform and located on one side of the analytical balance 1, with the top supporting and fixing the X-axis linear module 11. The Y-axis linear module 10 is vertically mounted... The slider mounted on the X-axis linear module 11 extends outward to form a cantilever structure; the Z-axis linear module 9 is vertically mounted on the slider at the cantilever end of the Y-axis linear module 10, and is suspended directly above the analytical balance 1; the Z-axis electric slider moving platform 7 is set at the lower end of the moving slider of the Z-axis linear module 9, facing the analytical balance 1; the pressure head clamp 6 is set on the Z-axis electric slider moving platform 7 and is used to clamp the spherical pressure head 4 with a handle; the analytical balance 1 is provided with a tray for placing the thin film sample 3 attached to the silicon wafer 2, and the tray is surrounded by a glass windproof cover 8; the analytical balance 1 outputs the normal contact force between the pressure head and the thin film based on the electromagnetic force balance compensation system.

[0045] The Z-axis high-precision electric slider moving platform is equipped with a Japanese Oriental Motor 42 stepper motor 13. The guide bearing mechanism includes 8 sets of cross roller guides. The drive mechanism uses precision ground ball screws for transmission and includes 2 limit sensors and 1 origin limit sensor. The bottom and table surfaces are designed with standard countersunk connection holes for easy connection and fixation, and it has strong applicability. It features high precision and low vibration, and is used to control the pressure head clamp 6 to drive the spherical pressure head 4 with handle to move up and down with high precision micro-motion.

[0046] The pressure head clamp 6 has a handle through hole 14 and a side set screw 5. The handle of the ball pressure head 4 passes through the handle through hole 14 and is fixed by the side set screw 5. The end of the ball pressure head 4 has a disc step. The bottom of the handle through hole 14 of the pressure head clamp 6 has a disc step expansion groove 15 that mates with the disc step 18. The side of the handle has a side set screw through hole 16 for installing the side set screw 5. The upper end of the handle is connected to the Z-axis electric slider moving platform through four bolt holes 17.

[0047] Example 2: This embodiment provides a simple indentation method for measuring the Young's modulus and adhesion energy of a thin layer, including the following steps: S1: Place the incompressible elastic film to be tested, which is attached and firmly bonded to the rigid substrate, onto the analytical balance system, and activate the Z-axis high-precision electric slider moving platform controller to drive the film with a known geometric radius of curvature. R A rigid spherical indenter is pressed into the thin film layer to be tested at a uniform speed; S2: In the subsequent dynamic contact mechanics response of the system, capture and determine the zero-load point state characteristic coordinates when the internal and external forces of the system reach instantaneous equilibrium; S3: During the stage where the pressure head is lifted and removed from the film by the reverse unloading of the drive displacement stage, locate and capture the critical pull-off point state characteristic coordinates at the moment when the interface completely separates. S4: Obtain the indentation force during the dynamic process. F With indentation depth d The interfacial adhesion energy of the tested material is obtained by directly calculating using a first-order asymptotic solution formula or by data fitting. c Young's modulus E In this study, the minimum indentation force during the loading process is assumed. F Equal to the pull-out force required to separate the pressure head from the layer. F c .

[0048] One of the first-order pull-out forces F c for

[0049] Elastic capillary length l for

[0050]

[0051] In the above formula: F c For pull-off force ，l Elastic capillary length ，R Let be the geometric radius of curvature of the rigid spherical indenter. E The Young's modulus of the material to be tested. c The interfacial adhesion energy of the tested material. d 0 d c This is relative displacement. B To be comparable to Poisson n The relevant constants of the elasticity for incompressible layers n = 0.5; Optionally, step S2 specifically includes the following steps: During the dynamic process of the indenter gradually pressing into or retracting from the film, the indentation force at the contact interface... F When it reaches zero, it is the zero load point. F = 0); Record the absolute physical coordinates of the Z-axis corresponding to the zero-load point, and obtain the indentation depth corresponding to this zero-load point, denoted as . d 0; in, For indentation force, d 0 is the zero load point ( F = 0) corresponds to the initial reference indentation depth.

[0052] Optionally, step S3 specifically includes the following steps: During the unloading and lifting process, at the instant the interface breaks and the indenter separates from the film, the system records the minimum indentation force (i.e., the maximum negative force). This force is the pull-out force, denoted as . F c ; Simultaneously record the critical indentation depth corresponding to this moment of pull-out, denoted as . d c ; Based on the data from the zero-load point and the critical pull-out point, the relative displacement of the interface is obtained. d 0 d c ; in, F c For pull-out force, d c This represents the critical indentation depth. d 0 d c This represents relative displacement.

[0053] Optionally, the calculation of Young's modulus and adhesion energy in step S4 specifically includes the following steps: According to the first-order pull-out force formula, the measured pull-out force... F c The adhesion energy of the film was calculated. c ; Based on the formula for elastic capillary length and relative displacement d 0 d c The slenderness of the elastic capillary was calculated by measuring two specific experimental data points. l ; The calculated adhesion energy c Divide by the slenderness of the elastic fibers l That is, through relational formulas E = g / l Calculate and determine Young's modulus E ; in, F c For pull-out force, c For adhesion energy, d 0 represents the indentation depth at the zero-load point. d c This represents the critical indentation depth. l To quantify the elastic capillary length of the adhesion effect, E It is Young's modulus.

[0054] Optionally, the fitting of Young's modulus and adhesion energy in step S4 specifically includes the following steps: First order d - F The relationship is

[0055] In the above formula: d Indentation depth B To be comparable to Poisson n The relevant constants of the elasticity for incompressible layers n = 0.5, l To quantify the elastic capillary length of the adhesion effect, F For indentation force, R The radius of curvature of the pressure head is... t The thickness of the incompressible elastic film. E It is Young's modulus.

[0056] when F When <0, δ and a It is about F A two-valued function.

[0057] According to the first order d - F Data fitting using relational formulas; using the known rigid indenter radius R Thin layer thickness t The obtained indentation force F and the corresponding indentation depth d Substitute the data into the formula; based on the above formula, directly fit Young's modulus using curve fitting method. E and the fineness of the elastic fibers l .

[0058] The specific derivation process of the formula used to measure the Young's modulus and adhesion energy of the thin layer in step S4 is as follows.

[0059] Consider a component bonded to a rigid substrate with a thickness of... t A flat, adhesive, incompressible, elastic thin layer. This layer is bounded by a radius of... R A rigid spherical indenter is pressed in, forming an indentation with a radius of [missing value] in the axisymmetric coordinate system (r, z). a Indentation depth is d Contact area, see appendix Figure 3 The solution is based on asymptotic conditions. t << a << R The total potential energy of the thin-layer-indenter system is derived as follows: (1) in U e It is the strain energy of the layer. c = c 1+ c 2 c 12 It is the adhesion energy (per unit area). Here c 1, c 2 represents the surface energy (per unit area) of the pressure head and the layer, respectively. c 12 This indicates the interface's capabilities. (Item) Fδ It is the indentation force after deformation. F The potential energy change. Next, the Kerr model is used to determine... U e The model gives the contact pressure p ( r ) and downward deflection of the upper surface of the layer w ( r The linear differential relationship between them: (2) inA and B It is compared with Poisson n The relevant constants of the elasticity for incompressible layers n = 0.5 (3) Next, equation (2) is solved based on the displacement boundary conditions within the contact zone and the surface force-free boundary conditions outside the contact zone.

[0060] Pressure within the contact area ( 0<r<a The deflection of the upper surface of the inner layer in the contact area. w ( r ) can be made by Figure 1 The geometry of the indenter shown is determined (4) Substituting equation (4) into (2), we get... r = Bounded contact pressure solution at 0 (5) in c 2 and c 3 terms are particular solutions (6) In equation (6), based on d = O ( a 2 / R The fact that) c 2 has been simplified, in which O The symbol represents the order of magnitude. Constant. c 1 will be determined later using Betti's interchange theorem.

[0061] Surface deflection outside the contact area ( r>a Outside the contact zone, similar to the JKR model, Laplace pressure is neglected. Assumptions p ( r ) = 0, based on equation (2) and w exist r = a By applying the continuity condition at infinity, we obtain a bounded torsion solution at infinity. (7) in d 1. Due to the continuity condition w ( r = a ) = d a 2 / (2 R) Sure, K 0 represents the zeroth-order modified Bessel function. At this point, only the coefficients are known. c 1. Not yet determined.

[0062] The solution for the non-adhesive case is discussed below. This is to determine the solution using Betti's theorem. c 1. A known reference solution is required ( w 0, p 0). Here we utilize the solution for non-adhesive contact. Assume the layer is surrounded by a radius of... R A non-adhesive rigid spherical indenter is used for pressing, and the indentation depth is... d 0, radius is a 0, the surface deflection is given by the following formula. (8) The contact pressure is obtained from equation (2). p 0 (9) in (10) here e 1. Stress continuity condition of non-adhesive contact p ( r = a ) = 0 OK. d 0 and a The relationship between 0 and 0 can be obtained from the incompressibility condition. (11) Substitute equation (8) into equation (11), and note (12) Obtain the second order d 0 -a 0 relationships (13) Therefore, it is arbitrary. a 0. A known solution was constructed ( w 0, p 0).

[0063] Next, determine c 1. Using a reference solution ( w 0, p 0) Confirm c 1. Apply Betti's interchange theorem and assume... a 0 = (1 + Δ) a , Δ>> t / a We got (14) Note (15) Substituting equations (4)-(10) into (14) yields (16) Substituting equations (6), (10), and (13) into (16), we obtain... (17) Equation (17) is derived to second-order terms and arranged in ascending order. For a given... a 0 can be obtained from equation (17). c 1. Here we assume t / a <<Δ<<1, for example, Δ = ( t / a ) 1 / 2 Then the first-order solution is (18) Please note that the choice of Δ will have a slight impact. c The expression for 1 and the final d - a and F - a The relationship. We set Δ << 1 for two reasons: first, the solution becomes independent of the specific value of Δ; second, it allows for a more concise derivation in subsequent steps. d - a Relationship. Substituting equation (18) back into (17) yields the second-order solution. (19) At this point, the contact pressure within the contact area has been completely determined.

[0064] Next, several explicit asymptotic formulas are derived based on the principle of equilibrium potential energy. First, the elastic strain energy of the layer is equal to the elastic work done by the indentation pressure on the layer surface: (20) Substituting equations (4)-(6) and (18) into (19), we get: (twenty one) Therefore, the total potential energy (up to second order) of this layer-head system is: (twenty two) Based on the steady-state equilibrium condition of total energy, the explicit relationship between indentation force, indentation depth, and contact radius was derived. U / a= 0, thus obtaining the first order d - a The relationship is (twenty three) The second-order relation is given by the following equation. (twenty four) in l = c / E This is the elastic capillary length that quantifies the adhesion effect. Based on the physical requirement that adhesion reduces indentation depth, one root in equation (23) is ignored. First order d - a Relation (23) is identical to existing solutions based on the Hankel transform (Yang 2002) (see equation (50) in (Yang 2002)) and the boundary layer solution (Argatov et al. 2016) (see equation (4.22) in (Argatov et al. 2016)). By setting l = 0, equation (24) degenerates into a second-order non-adhesive system. d - a Relationship (13). Furthermore, by U / d = 0 (25) Substituting equation (24) into (25) yields the first order... F - a relation (26) and second-order relations (27) First order F - a Solution (25) is identical to the existing results (Yang 2002, Argatov et al. 2016) (see equation (49) in (Yang 2002) and equation (4.23) in (Argatov et al. 2016)). For example... Figure 5-Figure 6 As shown, the first-order solution and the second-order solution are in F - a The differences in relationships are quite significant; however, when a >5 t At that time, they were F - d The differences in the relationships are very small. Therefore, we provide an explicit solution based on the first-order solution. d - FThe relationship is complex because simple explicit second-order solutions are difficult to obtain. For a given indentation force... F The contact radius can be solved from equation (26). a This is about a 3 The quadratic polynomial. By... a Substituting the solution into equation (23), we obtain the first order. d - F relation (28) According to relevant literature, this first-order... d - F The relationship has not yet been reported in the literature. Note that when... F When <0, d and a It is about F A two-valued function.

[0065] The pull-out force is then calculated, assuming the minimum indentation force during loading is equal to the pull-out force required to separate the indenter from the layer. Based on the first-order solution above, the explicit pull-out force is calculated using the formula shown above. a c >5 t At that time, it approaches the second-order pull-out force, where a c It is the relevant first-order critical indentation radius, which is obtained by differentiating equation (26). F / a = 0 obtained (29) By substituting equation (29) into (26), the first-order pull-out force is obtained as follows: (30) This result is consistent with the existing solution reported in (Yang 2002). The adhesion energy can be directly obtained from the measured pull-off force in equation (29). c Furthermore, the relevant first-order critical indentation depth is obtained by combining equations (23) and (29). (31) In addition, when F When = 0, equation (28) yields (32) Therefore, the slenderness of the elastic hair is obtained from equations (31) and (32). (33) In equation (33), relative displacement is used. d0 d c Because of the presence of adhesion, it is difficult to determine the zero indentation depth in experiments. d The initial reference state is (= 0). Therefore, based on the first-order solution, two specific experimental data points can be used: the pull-out point ( F = F c , d = d c ) and zero load point ( F = 0, d = d 0), the adhesion energy and Young's modulus are uniquely determined by equations (30) and (33).

[0066] At this point, the derivation of the formulas used in step S4 is complete. The formulas (30), (33), (3), and (28) in the above specific derivation process correspond to the four formulas derived in step S4, respectively.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A simple indentation device for measuring the Young's modulus and adhesion energy of a thin layer, characterized in that: The system includes a test platform, an XYZ three-axis cantilever linear module, a Z-axis electric slider moving platform, an analytical balance, fixtures, and a ball-shaped pressure head with a handle. The analytical balance and the XYZ three-axis cantilever linear module are mounted on the test platform. The XYZ three-axis cantilever linear module consists of two columns, an X-axis linear module, a Y-axis linear module, and a Z-axis linear module. The two columns are mounted on the test platform and located on one side of the analytical balance, with their tops supporting and fixing the X-axis linear module. The Y-axis linear module is vertically mounted on the slider of the X-axis linear module and extends outwards. A cantilever structure is formed; the Z-axis linear module is vertically mounted on the slider at the cantilever end of the Y-axis linear module, and is suspended directly above the analytical balance; the Z-axis electric slider moving platform is located at the lower end of the moving slider of the Z-axis linear module, facing the analytical balance; the clamp is located on the Z-axis electric slider moving platform and is used to clamp the spherical indenter with a handle; the analytical balance is provided with a tray for placing the thin film sample attached to the silicon wafer, and the tray is surrounded by a glass cover; the analytical balance outputs the normal contact force between the indenter and the thin film based on the electromagnetic force balance compensation system.

2. The simple indentation device for measuring the Young's modulus and adhesion energy of a thin layer according to claim 1, characterized in that: The Z-axis electric slider moving platform is equipped with a stepper motor, the guide bearing mechanism includes 8 sets of cross roller guides, the drive mechanism uses precision ground ball screws for transmission, and contains 2 limit sensors and 1 origin limit sensor. The bottom surface and the table surface are both designed with standard countersunk head connection holes for controlling the fixture to drive the spherical pressure head with handle to move up and down slightly.

3. The simple indentation device for measuring the Young's modulus and adhesion energy of a thin layer according to claim 1, characterized in that: The fixture has a handle through hole and a side set screw. The handle of the spherical press head passes through the handle through hole and is fixed by the side set screw. The end of the spherical press head has a disc step. The bottom of the handle through hole of the fixture has a disc step expansion groove that cooperates with the disc step.

4. The simple indentation device for measuring the Young's modulus and adhesion energy of a thin layer according to claim 1, characterized in that: The radius of curvature of the spherical indenter with a handle is 40 mm.

5. A simplified indentation method for measuring the Young's modulus and adhesion energy of a thin layer, characterized in that: Includes the following steps: S1: Place the incompressible elastic film to be tested, attached to a rigid substrate, on the analytical balance, and start the Z-axis electric slider movement platform controller to drive the film with a known geometric radius of curvature. R A rigid spherical indenter is pressed into the thin film layer to be tested at a uniform speed; S2: During the dynamic contact mechanics response of the system, capture and determine the state characteristic coordinates of the zero-load point when the internal and external forces of the system reach instantaneous equilibrium; S3: During the stage where the pressure head is lifted and removed from the film by the reverse unloading of the drive displacement stage, locate and capture the critical pull-off point state characteristic coordinates at the moment when the interface completely separates. S4: Obtain the indentation force during the dynamic process. F With indentation depth δ The interfacial adhesion energy of the tested material is obtained by directly calculating using a first-order asymptotic solution formula or by data fitting. γ Young's modulus E .

6. The simplified indentation method for measuring the Young's modulus and adhesion energy of a thin layer according to claim 5, characterized in that: Step S2 specifically includes the following steps: During the dynamic process of the indenter gradually pressing into or retracting from the film, the indentation force at the contact interface... F When the load reaches zero, it is the zero load point; Record the value corresponding to the balance reading being zero. Z Obtain the indentation depth corresponding to the zero-load point by using the absolute physical coordinates of the axis, denoted as . δ 0; in, For indentation force, δ 0 represents the initial reference indentation depth corresponding to the zero load point.

7. The simplified indentation method for measuring the Young's modulus and adhesion energy of a thin layer according to claim 6, characterized in that: Step S3 specifically includes the following steps: During the unloading and lifting process, at the instant the interface breaks and the indenter separates from the film, the system records the minimum indentation force. This force is the pull-out force, denoted as . F c ; Simultaneously record the critical indentation depth corresponding to this moment of pull-out, denoted as . δ c ; Based on the data from the zero-load point and the critical pull-out point, the relative displacement of the interface is obtained. δ 0 δ c .

8. The simplified indentation method for measuring the Young's modulus and adhesion energy of a thin layer according to claim 7, characterized in that: Step S4, calculating the adhesion energy and Young's modulus of the thin film material, specifically includes the following steps: Minimum indentation force during loading F Equal to the pull-out force required to separate the pressure head from the layer. F c ; According to the first-order pull-out force formula: In the formula l It is the elastic capillary length. R Let be the geometric radius of curvature of the rigid spherical indenter. E The Young's modulus of the material to be tested. γ The interfacial adhesion energy of the tested material is determined by the measured pull-out force. F c The adhesion energy of the film was calculated. γ ; According to the formula for elastic capillary length: In the formula B To be comparable to Poisson ν The relevant constants of the elasticity for incompressible layers ν = 0.5: Combining the above formula with relative displacement δ 0 δ c The slenderness of the elastic hair was calculated. l ; Through relational formulas E = γ / l Young's modulus was calculated E .

9. The simplified indentation method for measuring the Young's modulus and adhesion energy of a thin layer according to claim 7, characterized in that: Step S4, which involves fitting to obtain the adhesion energy and Young's modulus of the thin film material, specifically includes the following steps: First order δ - F The relationship is: In the formula δ Indentation depth B To be comparable to Poisson ν The relevant positive constant elasticity, for the incompressible layer ν = 0.5, l To quantify the elastic capillary length of the adhesion effect, F For indentation force, R The radius of curvature of the pressure head is... t The thickness of the incompressible elastic film. E Young's modulus; when F When <0, δ and a It is about F A two-valued function; According to the first order δ - F The relationship is used to fit the data, and the known rigid indenter radius is used. R Thin layer thickness t The obtained indentation force F and the corresponding indentation depth δ Substitute into the formula; then fit Young's modulus using curve fitting method. E and the fineness of the elastic fibers l .

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