The effect of material anisotropy on the mechanics of a thin-film/substrate system under mechanical and thermal loads

2021 ◽  
pp. 108128652110312
Author(s):  
E. Nart ◽  
Y. Alinia ◽  
M. A. Güler
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Thermal Stresses ◽  
Stress Singularity ◽  
Film Stress ◽  
The Finite Element Method ◽  
Leading Role ◽  
Principal Directions ◽  
Soft Thin Film ◽  
Film Substrate

In this study, the stress analysis for an orthotropic thin film bonded to an orthotropic elastic substrate is addressed using both the analytical and finite element methods. The analytical method employs the integrodifferential formulation with the aid of membrane assumption. Utilizing the finite element method, the effect of orientation of the material principal directions are studied. The loading scenarios include a temperature gradient imposed on the film and a far-field uniaxial tension on the substrate. The results of current study indicate that the ratio of the film to the substrate stiffness plays a leading role in the film stress distribution. For the mechanical loading applied to the substrate, a soft thin film attached to a relatively stiffer substrate is preferred. The film can tolerate the induced thermal stresses as it is bonded to a softer host structure. The rotation angle of material orthotropy directions significantly affects the stress singularity near the film edges up to a certain extent.

Geometrically Nonlinear Stress-Deflection Relations for Thin Film/Substrate Systems With a Finite Element Comparison

1994 ◽  
Vol 61 (4) ◽  
pp. 872-878 ◽  
Author(s):  
C. B. Masters ◽  
N. J. Salamon
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Ritz Method ◽  
Spherical Shape ◽  
Free Edge ◽  
Boundary Region ◽  
Film Stress ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress ◽  
Film Substrate

A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film /substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixthorder polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

The Failure Investigations on the Thin Film Interface under the Dynamic Loading

2011 ◽  
Vol 464 ◽  
pp. 542-547
Author(s):  
He Jun Wang ◽  
Hui Xia Liu ◽  
Zong Bao Shen ◽  
Wei Li ◽  
Yuan Yuan Zheng ◽  
...  
Keyword(s):  
Thin Film ◽  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Dynamic Loading ◽  
Strong Impact ◽  
The Finite Element Method ◽  
Material Constitutive Model ◽  
Film Substrate ◽  
Film Interface

The film spallation, a typical film / substrate failure style, could be caused by many reasons. The strong impact on the film/substrate can also lead to this failure phenomenon. So the film spallation induced by the strong impact is explored in this paper. Here the strong impact comes from the laser-driven flyer loading. In the numerical simulating process, the Finite Element Method (FEM) and Johnson-Cook material constitutive model have been used, moreover, some ideal film spallation results were got, which are helpful for us to understand this failure phenomenon.

Stresses in a Multilayer Thin Film/Substrate System Subjected to Nonuniform Temperature

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
X. Feng ◽  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Field Measurements ◽  
Film Stress ◽  
Effect Of Temperature ◽  
Multilayer Thin Film ◽  
Nonuniform Temperature ◽  
Curvature Invariant ◽  
Full Field ◽  
Curvature Measurements ◽  
Film Substrate

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to uniform film stress and system curvature states over the entire system of a single thin film on a substrate. By considering a circular multilayer thin film/substrate system subjected to nonuniform temperature distributions, we derive relations between the stresses in each film and temperature, and between the system curvatures and temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part, which reflects the effect of temperature of other points on the location of scrutiny. We also derive relations between the film stresses in each film and the system curvatures, which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. The interfacial shear tractions between the films and between the film and substrate are proportional to the gradient of the first curvature invariant, and can also be inferred experimentally.

The Analyses and Calculation for Thermal Stresses of SBR Modified Asphalt Pavement

2011 ◽  
Vol 243-249 ◽  
pp. 4112-4118
Author(s):  
Min Jiang Zhang ◽  
Gang Chen ◽  
Li Xia Hou ◽  
Li Ping Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thermal Stresses ◽  
Asphalt Pavement ◽  
Asphalt Mixture ◽  
Asphalt Mixtures ◽  
The Finite Element Method ◽  
Temperature Stresses ◽  
Modified Asphalt ◽  
Temperature Performance

Based on the viscoelasticity theory and the data of creep test, Burgers model was established, which was used to study the viscoelastic property of SBR asphalt mixtures, and the viscoelastic constitutive relation was obtained. Using the finite element method, the temperature stresses field was calculated under the environmental conditions and the thermal stresses of SBR modified asphalt pavement was given at the last part of this paper. The study indicated that SBR modified asphalt mixtures have the advantage over common asphalt mixture in low-temperature performance.

scholarly journals The Effect of Stress on the Nanomechanical Properties of Au Surfaces

1996 ◽  
Vol 440 ◽  
Author(s):  
J. E. Houston
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Local Level ◽  
Maximum Shear Stress ◽  
Critical Role ◽  
Film Stress ◽  
Indentation Modulus ◽  
Nanomechanical Properties ◽  
Average Grain Size ◽  
Film Substrate

AbstractStress in thin films plays a critical role in many technologically important areas. The role is a beneficial one in strained layer superlattices where semiconductor electrical and optical properties can be tailored with film stress. On the negative side, residual stress in thin-film interconnects in microelectronics can lead to cracking and delamination. In spite of their importance, however, surface and thin-film stresses are difficult to measure and control, especially on a local level. In recent studies, we used the Interfacial Force Microscope (IFM) in a nanoindenter mode to survey the nanomechanical properties of Au films grown on various substrates. Quantitative tabulations of the indentation modulus and the maximum shear stress at the plastic threshold showed consistent values over individual samples but a wide variation from substrate to substrate. These values were compared with film properties such as surface roughness, average grain size and interfacial adhesion and no correlation was found. However, in a subsequent analysis of the results, we found consistencies which support the integrity of the data and point to the fact that the results are sensitive to some property of the various film/substrate combinations. In recent measurements on two of the original substrate materials we found a direct correlation between the nanomechanical values and the residual stress in the films, as measured globally by a wafer warping technique. In the present paper, we review these earlier results and show recent measurements dealing with stresses externally applied to the films which supports our earlier conclusion concerning the role of stress on our measurements. In addition, we present very recent results concerning morphological effects on nanomechanical properties which add additional support to the suggestion that near-threshold indentation holds promise of being able to measure stress on a very local level

Extension of Stoney’s Formula to Arbitrary Temperature Distributions in Thin Film/Substrate Systems

2006 ◽  
Vol 74 (6) ◽  
pp. 1225-1233 ◽  
Author(s):  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Field Measurements ◽  
Film Stress ◽  
Effect Of Temperature ◽  
Curvature Invariant ◽  
Full Field ◽  
Polar Components ◽  
Temperature Distributions ◽  
Curvature Measurements ◽  
Film Substrate

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to nonuniform and nonaxisymmetric temperature distributions, we derive relations between the film stresses and temperature, and between the plate system’s curvatures and the temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part that reflects the effect of temperature of other points on the location of scrutiny. Most notably, we also derive relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are related to the gradients of the first curvature invariant and can also be inferred experimentally.

Analysis of the accuracy of the bulge test in determining the mechanical properties of thin films

1992 ◽  
Vol 7 (6) ◽  
pp. 1553-1563 ◽  
Author(s):  
Martha K. Small ◽  
W.D. Nix
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Mechanical Properties ◽  
Finite Element ◽  
Material Properties ◽  
Deformation Behavior ◽  
Initial Conditions ◽  
Standard Technique ◽  
Bulge Test ◽  
The Finite Element Method

Since its first application to thin films in the 1950's the bulge test has become a standard technique for measuring thin film mechanical properties. While the apparatus required for the test is simple, interpretation of the data is not. Failure to recognize this fact has led to inconsistencies in the reported values of properties obtained using the bulge test. For this reason we have used the finite element method to model the deformation behavior of a thin film in a bulge test for a variety of initial conditions and material properties. In this paper we will review several of the existing models for describing the deformation behavior of a circular thin film in a bulge test, and then analyze these models in light of the finite element results. The product of this work is a set of equations and procedures for analyzing bulge test data that will improve the accuracy and reliability of this technique.

Finite element analysis of residual stress and interlayer in hard coating/interlayer/soft substrate system during nanoindentation

2008 ◽  
Vol 23 (5) ◽  
pp. 1358-1363 ◽  
Author(s):  
Liuhe Li ◽  
Lan Yin ◽  
Paul K. Chu
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Hard Coating ◽  
The Finite Element Method ◽  
Soft Substrate ◽  
Element Analysis ◽  
Load Displacement ◽  
Thin Interlayer ◽  
Film Substrate

The mechanical properties of thin films are frequently evaluated using nanoindentation. The finite element method (FEM) is very effective for investigating the stress and strain fields of the film–substrate system during nanoindentation. However, the role of residual stress and the thin interlayer between the film and substrate is not well known, especially when the hard coating/interlayer/soft substrate are considered together. In this work, the FEM is used to investigate the load-displacement behavior of the hardness of the hard coating/interlayer/soft substrate system. The load–displacement process is simulated, and the effects of different residual stresses and interlayer thicknesses are discussed.

A Finite Element Study on the Nanoindentation of Thin Films

2000 ◽  
Vol 649 ◽  
Author(s):  
Xi Chen ◽  
Joost J. Vlassak
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Finite Element ◽  
Film Thickness ◽  
Substrate Effect ◽  
The Finite Element Method ◽  
Effect Factor ◽  
Pile Up ◽  
Key Factor ◽  
Elastic Mismatch

ABSTRACTNanoindentation is a technique commonly used for measuring thin film mechanical properties such as hardness and stiffness. Typically, shallow indentations with contact depths less than 10-20% of the film thickness are used to ensure that measurements are not affected by the presence of the substrate. In this study, we have used the finite element method to investigate the effect of substrate and pile-up on hardness and stiffness measurements of thin film systems. We find that: i) for soft films on hard substrates, the hardness is independent of the substrate as long as the indentation depth is less than 50% of the film thickness; ii) as soon as the hardness exceeds that of the substrate, the substrate effect becomes significant, even for indentations as shallow as 5% of the film thickness; iii) if the film is at least 40 times harder than the substrate, the plastic zone is mostly confined to the substrate while the film conforms to the deformed substrate by bending. We define a substrate effect factor and construct a map that may be useful in the interpretation of indentation measurements on thin films. It is found that the yield stress mismatch is a key factor characterizing the hardness of thin film system, and the elastic mismatch is important when making stiffness measurements. The results obtained in this study are very useful when it is difficult to avoid the influence of the substrate on the measurements.

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