Plane-strain Bulge Test Research Articles

A study on thermo-mechanical behavior of MCD through bulge test analysis

The Micro circular diaphragm (MCD) is the mechanical actuator part used in the micro electro-mechanical sensors (MEMS) that combine electrical and mechanical components. These actuators are working under harsh mechanical and thermal conditions, so it is very important to study the mechanical and thermal behaviors of these actuators, in order to do with its function successfully. The objective of this paper is to determine the thermo-mechanical behavior of MCD by developing the traditional bulge test technique to achieve the aims of this work. The specimen is first pre-stressed to ensure that is no initial deflection before applied the loads on diaphragm and then clamped between two plates, a differential pressure (P) and temperature (Tb) is leading to a deformation of the MCD. Analytical formulation of developed bulge test technique for MCD thermo-mechanical characterization was established with taking in-to account effect of the residual strength from pre-stressed loading. These makes the plane-strain bulge test ideal for studying the mechanical and thermal behavior of diaphragm in both the elastic and plastic regimes. The differential specimen thickness due to bulge effect to describe the mechanical behavior, and the temperature effect on the MCD material properties to study the thermal behavior under deformation were discussed. A finite element model (FEM) can be extended to apply for investigating the reliability of the proposed bulge test of MCD and compare between the FEM results and another one from analytical calculus. The results show that, the good convergence between the finite element model and analytical model.

Experimental Investigation of Plastic Strain Recovery and Creep in Nanocrystalline Copper Thin Films

Nanocrystalline metals exhibit a phenomenon called plastic strain recovery whereby plastic strain introduced through a load cycle is gradually recovered under no external loading over a time period of hours and days. In this study, we experimentally explore the diffusive mechanisms and the strain rates for nanocrystalline thin films of copper with an average grain size of about 35 nm during plastic strain recovery and creep. The experiments are performed via the plane strain bulge test and the thin film samples are deposited using thermal evaporation and sputtering. The specimens recover their residual strain in a period of time with two characteristic strain rates, a transient strain recovery rate of the order of 10−7/s and a steady-state strain recovery rate of the order of 10−9/s and there is a characteristic time at which the transition occurs between the two rates. The results suggest that a diffusive mechanism in conjunction with voids within the nanocrystalline material can explain the two plastic strain recovery rates and the transition between the two.

A large-deformation thin plate theory with application to one-atom-thick layers

Nowadays, two-dimensional materials due to their vast engineering and biomedical applications have been the focus of many researches. The present paper proposes a large-deformation theory for thin plates with application to one-atom-thick layers (OATLs). The deformation is formulated exactly in the mathematical framework of Lagrangian description. In particular, an exact finite strain analysis is given – in addition to the usual strain tensor associated to the middle surface, the second and third fundamental forms of the middle surface of the deformed thin plate are also maintained in the analysis. Exact closed-form solutions for a uniaxially curved thin plate due to pure bending in one case and due to a combination of vertical and horizontal loading in another are obtained. As a special case of the latter problem, the exact solution for the plane-strain bulge test of thin plates is derived. Subsequently, the approximation of Vlassak and Nix [Vlassak, J.J., Nix, W.D., 1992. J. Mater. Res., 7(12), 3242–3249] for the load–deflection equation is recovered. The given numerical results are devoted to graphene as the most well-known OATL.

Time-dependent deformation behavior of freestanding and SiNx-supported gold thin films investigated by bulge tests

Abstract

Accuracy analysis of plane-strain bulge test for determining mechanical properties of thin films

The effect of a variety of geometrics, initial conditions and material properties on the deformation behavior of thin films in the plane-strain bulge test was systematically scrutinized by performing the finite element analysis, and then the accuracy of the plane-strain bulge test in determining the mechanical properties of thin films in terms of our finite element results was analyzed. The results indicate that although the determination of the plane-strain modulus in the light of the plane-strain bulge equation is fairly accurate, the calculation of the residual stress is not satisfied as expected, especially for low residual stress. Finally, an approach is proposed for analyzing bulge test data, which will improve the accuracy and reliability of this bulge test technique.

On the validity regime of the bulge equations

Abstract

Residual plastic strain recovery driven by grain boundary diffusion in nanocrystalline thin films

Residual strain in metals is typically considered to be irreversible. However, residual strain in nanocrystalline materials can be recovered over a period of time via diffusive mechanisms. In this study, free-standing copper films of submicron thickness with an average grain size of about 40 nm are mechanically loaded via a plane-strain bulge test, and residual strain recovery at room temperature is characterized after unloading. The specimens recover their residual strain in a period of time that can range from a few days to more than 1 month depending upon the surface conditions and heterogeneous residual strain distributions in multiple cycles of recoveries. A constant tensile stress of about 25 MPa is reached after each recovery finishes. Two characteristic strain rates occur during residual strain recovery, a transient strain recovery rate of the order of 10 −7 s −1 and a steady-state strain recovery rate of the order of 10 −9 s −1. A model of the plastic strain recovery is presented which demonstrates the plausibility that grain boundary diffusion driven by chemical potential gradients due to residual stresses and the presence of voids can rationalize the transient and steady-state plastic strain recovery rates, respectively.

Plane-strain bulge test for nanocrystalline copper thin films

Free-standing nanocrystalline Cu films with grain size around 39 nm are fabricated by thermal evaporation and characterized by the plane-strain bulge test. Young’s modulus and yield stress at a 0.2% offset are about 110–130 GPa and 400 MPa, respectively. Results show that the strength of the n-Cu films is largely independent of film thickness at a strain rate less than 10−5 s−1. No grain growth is observed and the predominant plastic deformation mechanism is grain boundary sliding accompanied by dislocation mechanisms.

Bauschinger and size effects in thin-film plasticity

We present an experimental investigation of the effects of surface passivation, film thickness and grain size on the plastic behavior of freestanding Cu thin films. The stress–strain curves of the films are measured using the plane–strain bulge test. Films with a passivation layer on one or both surfaces have an offset yield stress that increases significantly with decreasing film thickness; the yield stress of unpassivated films, by contrast, is relatively independent of film thickness and increases mainly as a result of grain-size strengthening. The stress–strain curves of passivated films show an unusual Bauschinger effect on unloading. This effect is not observed for unpassivated films. Our experimental results suggest that passivation layers prevent dislocations from exiting the films and that they block slip bands at the film–passivation interface. The back stresses associated with these blocked slip bands increase the resistance to forward plastic flow on loading and cause reverse plastic flow on unloading. The effect of the back stresses increases with decreasing film thickness and leads to the observed strengthening of the passivated films. The constraint of a passivating layer on dislocation motion and hence on plastic flow cannot be described by classical plasticity theories, but can be modeled with some strain–gradient plasticity theories. We evaluate the suitability of the strain–gradient plasticity theory developed by Fleck and Hutchinson to describe our experimental results in a continuum framework. Comparison between experimental results and calculations yields very good agreement for the effect of film thickness, but the strain–gradient plasticity model fails to describe the Bauschinger effect observed in passivated films.

Plastic deformation of freestanding thin films: Experiments and modeling

Experimental measurements and computational results for the evolution of plastic deformation in freestanding thin films are compared. In the experiments, the stress–strain response of two sets of Cu films is determined in the plane-strain bulge test. One set of samples consists of electroplated Cu films, while the other set is sputter-deposited. Unpassivated films, films passivated on one side and films passivated on both sides are considered. The calculations are carried out within a two-dimensional plane strain framework with the dislocations modeled as line singularities in an isotropic elastic solid. The film is modeled by a unit cell consisting of eight grains, each of which has three slip systems. The film is initially free of dislocations which then nucleate from a specified distribution of Frank–Read sources. The grain boundaries and any film-passivation layer interfaces are taken to be impenetrable to dislocations. Both the experiments and the computations show: (i) a flow strength for the passivated films that is greater than for the unpassivated films and (ii) hysteresis and a Bauschinger effect that increases with increasing pre-strain for passivated films, while for unpassivated films hysteresis and a Bauschinger effect are small or absent. Furthermore, the experimental measurements and computational results for the 0.2% offset yield strength stress, and the evolution of hysteresis and of the Bauschinger effect are in good quantitative agreement.

The mechanical properties of freestanding electroplated Cu thin films

The plane-strain bulge test is used to investigate the mechanical behavior of freestanding electroplated Cu thin films as a function of film thickness and microstructure. The stiffness of the films increases slightly with decreasing film thickness because of changes in the crystallographic texture and the elastic anisotropy of Cu. Experimental stiffness values agree well with values derived from single-crystal elastic constants and the appropriate orientation distribution functions. No modulus deficit is observed. The yield stress of the films varies with film thickness and heat treatment as a result of changes in the grain size of the films. The yield stress follows typical Hall-Petch behavior if twins are counted as distinct grains, indicating that twin boundaries are effective barriers to dislocation motion. The Hall-Petch coefficient is in good agreement with values reported for bulk Cu. Film thickness and crystallographic texture have a negligible effect on the yield stress of the films.

Novel technique for measuring the mechanical properties of porous materials by nanoindentation

A new technique for measuring the elastic-plastic properties of porous thin films by means of nanoindentation is proposed. The effects of porosity on indentation hardness and modulus are investigated through finite element analyses based on the Gurson model for plastic deformation of ductile porous materials. Intrinsic mechanical properties of the thin film are obtained by eliminating both substrate and densification effects. The technique is applied to the special case of a porous, low-permittivity dielectric thin film. The results are in good agreement with those obtained independently using the plane-strain bulge test.

Mechanical properties of porous and fully dense low-κ dielectric thin films measured by means of nanoindentation and the plane-strain bulge test technique

We report on the results of a comparative study in which the mechanical response of both fully dense and porous low-κ dielectric thin films was evaluated using two different techniques: nanoindentation and the plane-strain bulge test. Stiffness values measured by nanoindentation are systematically higher than those obtained using the bulge test technique. The difference between the measurements is caused by the Si substrate, which adds significantly to the contact stiffness in the indentation measurements. Depending on the properties of the coatings, the effect can be as large as 20%, even if the indentation depth is less than 5% of the film thickness. After correction of the nanoindentation results for the substrate effect using existing models, good agreement is achieved between both techniques. The results further show that densification of porous material under the indenter does not affect stiffness measurements significantly. By contrast, nanoindentation hardness values of porous thin films are affected by both substrate and densification effects. It is possible to eliminate the effect of densification and to extract the yield stress of the film using a model for the indentation of porous materials proposed by the authors. After correcting for substrate and densification effects, the nanoindentation results are in close agreement with the bulge test measurements. The results of this comparative study validate the numerical models proposed by Chen and Vlassak for the substrate effect and by Chen et al. for the densification effect.

Plane-strain Bulge Test for Thin Films

The plane-strain bulge test is a powerful new technique for measuring the mechanical properties of thin films. In this technique, the stress–strain curve of a thin film is determined from the pressure-deflection behavior of a long rectangular membrane made of the film of interest. For a thin membrane in a state of plane strain, film stress and stain are distributed uniformly across the membrane width, and simple analytical formulae for stress and strain can be established. This makes the plane-strain bulge test ideal for studying the mechanical behavior of thin films in both the elastic and plastic regimes. Finite element analysis confirms that the plane-strain condition holds for rectangular membranes with aspect ratios greater than 4 and that the simple formulae are highly accurate for materials with strain-hardening exponents ranging from 0 to 0.5. The residual stress in the film mainly affects the elastic deflection of the membrane and changes the initial point of yield in the plane-strain stress–strain curve, but has little or no effect on further plastic deformation. The effect of the residual stress can be eliminated by converting the plane-strain curve into the equivalent uniaxial stress–strain relationship using effective stress and strain. As an example, the technique was applied to an electroplated Cu film. Si micromachining was used to fabricate freestanding Cu membranes. Typical experimental results for the Cu film are presented. The data analysis is in good agreement with finite element calculations.