Indentation Curves Research Articles

Analysis of mechanical properties of single crystal copper under low-temperature indentation test

Abstract As a common superconducting material in the aerospace field, the mechanical properties of single-crystal copper at low temperatures have attracted much attention. Combined with the current low-temperature nanoindentation test technology and the research status of micromechanical properties of crystal copper at home and abroad, this paper puts forward the low-temperature nanoindentation test on single-crystal copper. It analyzes the changes in mechanical properties of the low-temperature environment by indentation curve. Before the formal test, we first analyzed the Oliver-Pharr micro and nanoindentation test theory and described briefly the advantages of using nanoindentation to test the mechanical properties. The final test results show that in the temperature range of 300K~150K, the hardness and elastic modulus of the single-crystal copper increase with the decrease in temperature. The lower the temperature is, the faster the increase of hardness and elastic modulus is. At the same temperature, the hardness and elastic modulus of single-crystal copper with three crystal faces are (111) > (110) > (100). The mechanical properties at low temperatures are effectively reflected by means of low-temperature nanoindentation, which can be used to guide the production of materials in real life.

A mechanical TiAl/TiAlN multinanolayer coating model based on microstructural analysis and nanoindentation

A finite element model reproducing the mechanical behaviour during nanoindentation tests on Ti0.67Al0.33/Ti0.54Al0.46N multilayer coatings was developed. Coatings with two different nanoperiods (10 and 50 nm) were deposited by radio-frequency magnetron sputtering from a single sintered titanium/aluminium target using the reactive gas pulsing process. X-ray diffraction and transmission electron microscopy confirmed the multilayer stacking of the coatings. The finite element models of coatings with these two stacking periods were built considering successive hypotheses: equal thicknesses for metal and nitride nanolayers stacked without transition layer, equal thicknesses stacking with a transition layer between each metal and nitride nanolayer and finally imbalanced thicknesses stacking with a transition layer. The elastic and plastic properties of the stacked nanolayers were determined on thick monolithic coatings of metal and nitride using indentation testing and the finite element model updating method respectively. The elastic-plastic properties of the interface were introduced in the multilayer model as a rule of mixtures of the metal and nitride properties using two hypotheses: parallel or serial. For 50 nm-period film, the interface has a negligible effect on the overall indentation response. On the other hand, for the 10 nm period, the imbalanced stacking model with precise knowledge of the transition layer thickness obtained by N K-edge electron energy loss spectroscopy is required to reproduce the experimental indentation curve. Compared to classical analytical models accounting for hardness, not only the hardnesses but also the indentation moduli appear to be well predicted and evaluated in this work.

Surface residual stress in H-section steel beams processed by quenching and self-tempering using instrumented indentation testing

Using instrumented indentation testing, we explore the measurement of surface residual stress in H-section steel beams produced through the quenching and self-tempering (QST) process. We establish a significant correlation between the plastic pile-up behavior observed during indentation and the magnitude of surface residual stress. We thoroughly clarify the distribution of plastic pile-up and residual stress, linking their variations to non-uniform phase transformation and changes in mechanical properties resulting from the QST process. Moreover, we employ an indentation curve analysis to evaluate surface residual stress, obviating the need for direct measurements of pile-up height. These findings facilitate the measurement of non-uniform surface residual stress in H-section beams, crucial for ensuring structural integrity, yet challenging to measure in situ.

Non-Destructive Hardness Indentation Measurement of Residual Stress on Large Aerospace Forged Components at the Engineering Site Based on Impact Hardness Tester.

Large forgings are crucial in aerospace applications; however, the residual stresses generated during their forming and heat treatment seriously affect their serviceability. Therefore, the non-destructive detection of residual stresses in large forgings is of far-reaching significance for ensuring the quality of forgings and realising precision machining. Although a variety of detection methods are available, there is still a lack of a programme that can comprehensively, accurately and non-destructively measure the residual stresses in large forgings. This study is dedicated to exploring the application of the bouncing impact indentation method in the non-destructive testing of residual stresses in large forgings. Through in-depth finite element simulations and orthogonal scheme analyses, we found that the elastic modulus, yield strength and work hardening indexes have significant effects on the impact indentation process. Further, we establish the dimensionless function of residual stress and indentation parameters, and successfully obtain the inversion algorithm of residual stress. The relative error of the calculated values of the indentation curves hm and hr in the simulation with reference values is not more than 3%, and the relative error of the corrected Pm inversion values for most virtual materials is not more than 5%. The folding elastic modulus and apparent elastic modulus obtained by inversion are controlled within 10%, which demonstrates a high value for engineering applications. In addition, we innovatively express the research results in the form of 3D stress diagrams, realising the digital expression of 3D residual stresses in large forgings based on feature point measurements and contour surface configurations, which provides intuitive and comprehensive data support for engineering practice.

Size Matters: Rethinking Hertz Model Interpretation for Cell Mechanics Using AFM.

Cell mechanics are a biophysical indicator of cell state, such as cancer metastasis, leukocyte activation, and cell cycle progression. Atomic force microscopy (AFM) is a widely used technique to measure cell mechanics, where the Young modulus of a cell is usually derived from the Hertz contact model. However, the Hertz model assumes that the cell is an elastic, isotropic, and homogeneous material and that the indentation is small compared to the cell size. These assumptions neglect the effects of the cytoskeleton, cell size and shape, and cell environment on cell deformation. In this study, we investigated the influence of cell size on the estimated Young's modulus using liposomes as cell models. Liposomes were prepared with different sizes and filled with phosphate buffered saline (PBS) or hyaluronic acid (HA) to mimic the cytoplasm. AFM was used to obtain the force indentation curves and fit them to the Hertz model. We found that the larger the liposome, the lower the estimated Young's modulus for both PBS-filled and HA-filled liposomes. This suggests that the Young modulus obtained from the Hertz model is not only a property of the cell material but also depends on the cell dimensions. Therefore, when comparing or interpreting cell mechanics using the Hertz model, it is essential to account for cell size.

Estimation of Mechanical Properties of Aluminum Alloy Based on Indentation Curve and Projection Area of Contact Zone

This study proposes a method for determining aluminum alloys’ yield stress and hardening index based on indentation experiments and finite element simulations. Firstly, the dimensionless analysis of indentation variables was performed on three different aluminum alloys using the same maximum indentation depth to obtain load-displacement curves. Then, laser confocal microscopy was used to observe the residual indentation morphology. And four dimensionless parameters were derived from the load-displacement curves while another dimensionless parameter was obtained from the projection area of the contact zone. Subsequently, a genetic algorithm was employed to solve these five dimensionless parameters and estimate the yield stress and hardening index. Finally, the predicted results are compared with uniaxial tensile experiments and the results obtained are essentially the same. The yield stress and hardening index can be predicted using this method. And an example is used to verify that this method enables predictions for unidentified “mysterious material” and the expected results agree with the experiments.

A Linear Fit for Atomic Force Microscopy Nanoindentation Experiments on Soft Samples

Atomic Force Microscopy (AFM) nanoindentation is a powerful technique for determining the mechanical properties of soft samples at the nanoscale. The Hertz model is typically used for data processing when employing spherical indenters for small indentation depths (h) compared to the radius of the tip (R). When dealing with larger indentation depths, Sneddon’s equations can be used instead. In such cases, the fitting procedure becomes more intricate. Nevertheless, as the h/R ratio increases, the force–indentation curves tend to become linear. In this paper the potential of using the linear segment of the curve (for h > R) to determine Young’s modulus is explored. Force–indentation data from mouse and human lung tissues were utilized, and Young’s modulus was calculated using both conventional and linear approximation methods. The linear approximation proved to be accurate in all cases. Gaussian functions were applied to the results obtained from both classic Sneddon’s equations and the simplified approach, resulting in identical distribution means. Moreover, the simplified approach was notably unaffected by contact point determination. The linear segment of the force–indentation curve in deep spherical indentations can accurately determine the Young’s modulus of soft materials at the nanoscale.

Deep Learning Regressors of Surface Properties from Atomic Force Microscopy Nanoindentations

Atomic force microscopy (AFM) is a powerful technique to study the nanomechanical properties of a wide range of materials at the piconewton level. AFM force–indentation curves can be fitted with appropriate contact models, enabling the determination of material properties for a given sample. However, the analysis of large datasets comprising thousands of curves using conventional methods presents a time-intensive challenge. As a result, there is an increasing interest in exploring alternative methodologies, such as integrating machine learning (ML) models to streamline and improve the efficiency of this process. In this work, two data-driven regressors were tuned to predict the Young’s modulus and adhesion energy from force–indentation curves of soft samples (Young’s modulus up to 10 kPa). Both models were trained exclusively on synthetic data derived from the contact theories developed by Hertz as well as Johnson, Kendall and Roberts (JKR). The PyTorch library was employed to build and train the models; then, the key hyperparameters were refined by implementing the optimization framework Optuna. The first model was successfully tested with synthetic and experimental curves from AFM nanoindentations, and the second presented promising results on the synthetic data. Our work suggests that experimental data may not be essential for training data-driven models to predict surface properties from AFM nanoindentations. By delivering accurate predictions in a computationally efficient way, our regressors validate the potential of a deep learning approach in exploring AFM nanoindentations and motivate further development of similar strategies to overcome current limitations in AFM postprocessing.

Profiling native pulmonary basement membrane stiffness using atomic force microscopy.

Mammalian cells sense and react to the mechanics of their immediate microenvironment. Therefore, the characterization of the biomechanical properties of tissues with high spatial resolution provides valuable insights into a broad variety of developmental, homeostatic and pathological processes within living organisms. The biomechanical properties of the basement membrane (BM), an extracellular matrix (ECM) substructure measuring only ∼100-400 nm across, are, among other things, pivotal to tumor progression and metastasis formation. Although the precise assignment of the Young's modulus E of such a thin ECM substructure especially in between two cell layers is still challenging, biomechanical data of the BM can provide information of eminent diagnostic potential. Here we present a detailed protocol to quantify the elastic modulus of the BM in murine and human lung tissue, which is one of the major organs prone to metastasis. This protocol describes a streamlined workflow to determine the Young's modulus E of the BM between the endothelial and epithelial cell layers shaping the alveolar wall in lung tissues using atomic force microscopy (AFM). Our step-by-step protocol provides instructions for murine and human lung tissue extraction, inflation of these tissues with cryogenic cutting medium, freezing and cryosectioning of the tissue samples, and AFM force-map recording. In addition, it guides the reader through a semi-automatic data analysis procedure to identify the pulmonary BM and extract its Young's modulus E using an in-house tailored user-friendly AFM data analysis software, the Center for Applied Tissue Engineering and Regenerative Medicine processing toolbox, which enables automatic loading of the recorded force maps, conversion of the force versus piezo-extension curves to force versus indentation curves, calculation of Young's moduli and generation of Young's modulus maps, where the pulmonary BM can be identified using a semi-automatic spatial filtering tool. The entire protocol takes 1-2 d.

Investigation of cracking in monocrystalline silicon induced by high- temperature indentation

A simulation model of the indentation process via Berkovich indenter with cohesive interface elements and changeable temperature condition was developed. The indentation curves and imprints obtained by simulation were compared with experimental results. Compared with room temperature, the hardness of monocrystalline silicon decreases by 7.2 % at 400 °C, while it decreases dramatically by 64.3 % at 600 ℃. The initiation and expansion process of monocrystalline silicon cracks are investigated through the evolution of the scalar degradation parameter (SDEG). The original location of the half-penny crack changes from beneath the center of the imprint at room temperature to the edge region at 400 °C. The half-penny cracks were replaced by radial cracks at 500 ℃, and no crack formation occurs at 600 ℃. Stresses S11 and S22 were examined to investigate the evolution of surface and internal cracks in monocrystalline silicon. This analysis revealed the phenomenon of median crack closure under compressive stresses and a reduced cracking threshold under elevated temperatures.

Mechanomics study of cardiomyocytes with filamin c truncations

Abstract Background Filamin C (FLNC) is expressed in cardiomyocytes, where it binds to actin and localizes to Z-discs, sarcolemma, and intercalated discs. Although FLNC truncation variants (FLNCtv) are an established cause of arrhythmias and heart failure (arrhythmogenic cardiomyopathy), the underlying mechanisms, in particular changes in mechanical properties of cardiomyocytes, are mostly unknown. Purpose In this study, we applied a biophysical approach to investigate the interaction between altered mechanical properties and biological response in human induced pluripotent stem cells–derived cardiomyocytes (hiPSC-CMs) carrying FLNCtv. Methods CRISPR/Cas9 genome-edited FLNC-/- hiPSC-CMs, a homozygous condition that is lethal in animal models, and FLNC+/- hiPSC-CMs, recapitulating the heterozygous human disease, were analyzed. Wild-type FLNC hiPSC-CMs were used as controls. Atomic Force microscopy (AFM) was used to perform single-cell force spectroscopy (SCFS) microindentation, to evaluate passive and dynamic mechanical properties. From the loading curves, two cell Young’s Moduli were calculated: E1, related to the compression of the plasma membrane and actin cortex, and E2, including the rest of the inner cell layers (cytoskeleton and nucleus). Cell adhesion was assessed using the retraction curve of the SCFS. Data were processed in terms of adhesion force (the highest value of the force exerted by the cell-surface contact to the cantilever during retraction) and work of adhesion (integrating the area under the retraction curve). Finally, FLNC-/- hiPSC-CMs were incubated with 1 µM Crenolanib (a PDGFRA signaling inhibitor) for 3 days, and the microindentation was performed again using DMSO-only-treated FLNC-/- cells as controls. Results The AFM indentation curve for the cells analyzed showed significant differences. Both elastic contributions (E1 and E2) show that wild-type FLNC iPSC-CMs are stiffer than both mutant FLNC+/- and FLNC-/- iPSC-CMs (see Figure upper panel). The adhesion showed the same trend as the elasticity: mutant FLNC iPSC-CMs showed a progressive decrease of work of adhesion as well as max adhesion force from the FLNC+/- to the FLNC-/- models. Rescue of the latter with Crenolanib showed to moderately increase their stiffness. Moreover, a qualitative analysis of the beating traces showed that FLNC+/- but mostly FLNC-/- display "irregular" small peaks, resembling those of delayed after depolarizations (see Figure lower panel). Conclusions We found that FLNCtv causes a decrease in cell stiffness which declines progressively from the heterozygous status, which is associated with FLNC haploinsufficiency, to the homozygous status, which lacks FLNC. This indicates a progressive softening of the cardiomyocytes, suggesting a damaged cytoskeleton. Crenolanib rescue suggests that the inhibition of PDGFRA signaling could partially restore such damage (see Figure upper panel - right corner).

Development of modular cryogenic indentation apparatus for investigating micro-region mechanical properties of materials

High-precision cryogenic micromechanical testing apparatuses are of significant importance in investigating the micro-region mechanical properties and deformation behaviors of materials at cryogenic temperatures. In this study, a modular cryogenic indentation apparatus was designed and developed utilizing a contact-atmosphere hybrid refrigeration technique with a minimum temperature of −150 °C. The temperature of both the indenter tip and the specimen was independently controlled through a dual-channel proportional–integral–derivative (PID) feedback loop to eliminate contact thermal drift to within 0.1 nm/s. The application of cryogenic nitrogen (N2) atmosphere refrigeration eliminated additional stiffness at the indenter tip completely. The feasibility of the apparatus was demonstrated through calibrations and tests conducted on standard fused silica and single crystal nickel. Highly accurate indentation curves and micro-region mechanical properties of single crystal nickel were obtained at variable cryogenic temperatures. With decreasing temperature, both slip bands and pile-up around residual indentation imprints were weakened. Notably, at −150 °C, the slip bands disappeared, and the phenomenon of pile-up was replaced by sink-in. This developed cryogenic indentation apparatus will be a powerful tool to reveal the effect of cryogenic temperatures on the evolution mechanisms of materials’ micro-region mechanical properties.

An indentation method for measuring welding residual stress: Estimation of stress-free indentation curve using BP neural network prediction model

The measurement of welding residual stress (WRS) is necessary to formulate the stress control strategies, in order to ensure the reliability of engineering structures during their service life. The instrumented indentation technique can detect surface residual stress nondestructively with an acceptable accuracy, making it a desirable option for in-situ applications. However, it is difficult to meet the requirement for stress-free samples, particularly in the case of welded joints with non-uniform mechanical properties. In this work, the impact of stress-free indentation curves on determining WRS is furtherly studied based on the previously proposed indentation energy difference method. The WRS in a mismatched welded plate is measured using single reference method and distributed reference method, respectively. The study suggests that using the single reference method can lead to significant errors in determining the sign and magnitude of WRS in the weld zone. A prediction model combining the continuous spherical indentation (CSI) method and Back Propagation (BP) neural network is proposed to obtain the stress-free indentation curves of local positions nondestructively. And the CSI-BP method is verified through reverse finite element analysis and experiments.

Effect of loading/unloading rate on instrumented indentation measurements in alloy Cu-2%Be

The influence of the loading/unloading rate on the indentation strain rate, hardness and elastic modulus in Cu-2wt%Be samples subjected to different aging treatments was analyzed. Homogenized samples were aged for 1 and 10 h at 400 °C to induce the formation of γ′ and γ precipitates, and instrumented indentation tests were performed at different loading rates between 0.15 and 1 mN s−1. The indentation curves of all the samples were influenced by the loading/unloading rate, but the behavior of the samples with precipitates was different from that of the homogenized samples. Strain rate levels during loading were also influenced by the loading rate. The strain rate increased almost linearly with the loading rate in the homogenized sample and the sample with γ′ nanoprecipitates, while it experienced a decelerated increase with the loading rate in the sample with γ phase. The hardness and reduced modulus were estimated from the indentation curves using the Oliver and Pharr method. Hardness remained almost constant at approximately 2.4 GPa as the rate was varied in the homogenized sample. On the other hand, the samples with γ′ and γ phase exhibited higher hardness values at 0.15 mN s−1, while it remained approximately constant for the other rates. The reduced modulus increased with the loading/unloading rate and this increase was more pronounced for the sample with γ precipitates, with a higher sensitivity of the reduced modulus increase.

Application of artificial neural networks in atomic force microscopy

The paper describes a method of artificial neural network application to build a computer database for numerical simulation of the process of indentation of an atomic force microscope probe into an elastomeric composite with a granular filler (nonlinear elastic medium with rigid spherical inclusions). The use of such a base makes it possible to significantly improve the speed and quality of interpretation of the results of nanoindentation for structurally inhomogeneous materials. In this case, information becomes available not only about what is done on the surface of the sample but also in the near-surface layer inside it. An algorithm has been developed with the help of which an artificial neural network was built and “trained,” designed to obtain indentation curves depending on the size of the filler particles and its localization in the near-surface layer of the composite (depth and horizontal distance from the top of the AFM probe). It is shown that the speed of constructing indentation curves increases by several orders of magnitude compared to conventional approaches based on the numerical solution of the corresponding boundary value problems for each specific case. Accordingly, computer costs are also significantly reduced, that is, in the presence of an already built and “trained” neural network, powerful and high-speed computers are not needed.

A New Elementary Method for Determining the Tip Radius and Young's Modulus in AFM Spherical Indentations.

Atomic force microscopy (AFM) is a powerful tool for characterizing biological materials at the nanoscale utilizing the AFM nanoindentation method. When testing biological materials, spherical indenters are typically employed to reduce the possibility of damaging the sample. The accuracy of determining Young's modulus depends, among other factors, on the calibration of the indenter, i.e., the determination of the tip radius. This paper demonstrates that the tip radius can be approximately calculated using a single force-indentation curve on an unknown, soft sample without performing any additional experimental calibration process. The proposed method is based on plotting a tangent line on the force indentation curve at the maximum indentation depth. Subsequently, using equations that relate the applied force, maximum indentation depth, and the tip radius, the calculation of the tip radius becomes trivial. It is significant to note that the method requires only a single force-indentation curve and does not necessitate knowledge of the sample's Young's modulus. Consequently, the determination of both the sample's Young's modulus and the tip radius can be performed simultaneously. Thus, the experimental effort is significantly reduced. The method was tested on 80 force-indentation curves obtained on an agarose gel, and the results were accurate.

Quantitative nanohistology of aging dermal collagen.

The skin is the largest organ in the body and is essential for protecting us from environmental stressors such as UV radiation, pollution, and pathogens. As we age, our skin undergoes complex changes that can affect its function, appearance, and health. These changes result from intrinsic (chronological) and extrinsic (environmental) factors that can cause damage to the skin's cells and extracellular matrix. As higher-resolution microscopical techniques, such as Atomic Force Microscopy (AFM), are being deployed to support histology, it is possible to explore the biophysical properties of the dermal scaffold's constituents, such as the collagen network. In this study, we demonstrate the use of our AFM-based quantitative nanohistology, performed directly on unfixed cryosections of 30 donors (female, Caucasian), to differentiate between dermal collagen from different age groups and anatomical sites. The initial 420 (10 × 10μm2) Atomic Force Microscopy images were segmented into 42,000 (1 × 1μm2) images before being classified according to four pre-defined empirical collagen structural biomarkers to quantify the structural heterogeneity of the dermal collagen. These markers include interfibrillar gap formation, undefined collagen structure, and registered or unregistered dense collagen fibrillar network with evident D-banding. The structural analysis was also complemented by extensive nanoindentation (∼1,000 curves) performed on individual fibrils from each section, yielding 30,000 indentation curves for this study. Principal Component Analysis was used to reduce the complexity of high-dimensional datasets. The % prevalence of the empirical collagen structural biomarkers between the papillary and reticular dermis for each section proves determinant in differentiating between the donors as a function of their age or the anatomical site (cheek or breast). A case of abnormal biological aging validated our markers and nanohistology approach. This case also highlighted the difference between chronological and biological aging regarding dermal collagen phenotyping. However, quantifying the impact of chronic and pathological conditions on the structure and function of collagen at the sub-micron level remains challenging and lengthy. By employing tools such as the Atomic Force Microscope as presented here, it is possible to start evaluating the complexity of the dermal matrix at the nanoscale and start identifying relevant collagen morphology which could be used toward histopathology standards.

Evaluation of anisotropy of yield stress using surface in-plane displacements around an indentation residual imprint

This study proposed a practical method to evaluate the anisotropy of yield stress using spherical indentation with in-plane surface radial displacements around residual imprint measured by the digital image correlation method for metallic material without indentation curve. The relation between the ratio of yield stresses and the in-plane displacements developed on the surface was analyzed using finite element method (FEM) simulations for the materials with various mechanical properties. The development of radial displacements depends on the anisotropy of the yield stresses, and the ratio between radial displacement values on principal directions has a strong relation with the anisotropy of the yield stresses. An analytical solution for predicting the ratio of yield stresses was developed and it was verified using experimental data with anisotropic materials. The results for various metallic materials showed the feasibility of the proposed model with good accuracy.

Research on Determining Elastic-Plastic Constitutive Parameters of Materials from Load Depth Curves Based on Nanoindentation Technology.

It is of great significance for structural design and engineering evaluation to obtain the elastic-plastic parameters of materials. The inverse estimation of elastic-plastic parameters of materials based on nanoindentation technology has been applied in many pieces of research, but it has proved to be difficult to determine the elastic-plastic properties of materials by only using a single indentation curve. A new optimal inversion strategy based on a spherical indentation curve was proposed to obtain the elastoplastic parameters (the Young's modulus E, yield strength σy, and hardening exponent n) of materials in this study. A high-precision finite element model of indentation with a spherical indenter (radius R = 20 µm) was established, and the relationship between the three parameters and indentation response was analyzed using the design of experiment (DOE) method. The well-posed problem of inverse estimation under different maximum indentation depths (hmax1 = 0.06 R, hmax2 = 0.1 R, hmax3 = 0.2 R, hmax4 = 0.3 R) was explored based on numerical simulations. The results show that the unique solution with high accuracy can be obtained under different maximum press-in depths (the minimum error was within 0.2% and the maximum error was up to 1.5%). Next, the load-depth curves of Q355 were obtained by a cyclic loading nanoindentation experiment, and the elastic-plastic parameters of Q355 were determined by the proposed inverse-estimation strategy based on the average indentation load-depth curve. The results showed that the optimized load-depth curve was in good agreement with the experimental curve, and the optimized stress-strain curve was slightly different from the tensile test, and the obtained parameters were basically consistent with the existing research.

Study on parameter measurement of elastic thin films with substrate effect based on contact mechanics

The development of contact theories for films is valuable for high-precision machining and measurement. Accordingly, accurate contact mechanics theories for films under common indenter loading are established based on the constitutive equations and potential theory method, Here, the film structures are “film with two free boundaries” and “film/rigid substrate.” The displacement and stress at arbitrary positions can be obtained using exact solutions represented by elementary functions. The application of the foregoing theories to resolve the contact problem encountered in films is convenient for engineers. The influences of substrate and film parameters on contact radius and indentation depth were analyzed. Indentation curves are slightly influenced by Poisson’s ratio, but primarily affected by the elastic modulus. An effective method for measuring of film material parameters is presented. Using numerical software platforms, the method’s analytic algorithm can be transformed into numerical codes and be integrated into special software.