Asstr Straining Bulge
💣 👉🏻👉🏻👉🏻 ALL INFORMATION CLICK HERE 👈🏻👈🏻👈🏻
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 31 January 2011
College of Engineering, Koc University, Rumeli Feneri Yolu 34450 Sariyer, Istanbul, Turkey
College of Engineering, Koc University, Rumeli Feneri Yolu 34450 Sariyer, Istanbul, Turkey
Electrical and Electronics Engineering Department, Middle East Technical University, 06531 Ankara, Turkey
Electrical and Electronics Engineering Department, Middle East Technical University, 06531 Ankara, Turkey
A closed-loop approach is adopted to implement strain rate control during the bulge test. Due to the difficulty of measuring strains directly, the technique is based on the conversion of displacement measurements to the corresponding strains using the plane-strain formulation. The necessary temporal evolution of the midpoint displacement of a rectangular diaphragm is derived under the condition of constant strain rate and is imposed as a control criterion. The technique is demonstrated on 500-nm-thick Au diaphragms by applying strain rates ranging from 2 × 10−6 to 2 × 10−4 s–1. By measuring the corresponding yield strength values, a strain rate sensitivity of 0.11 is obtained, which is close to what was previously reported on similar specimens using the microbending test.
Copyright © Materials Research Society 2008
Institutional login
Log in with Open Athens, Shibboleth, or your institutional credentials
Personal login
Log in with your Cambridge Core account or society details.
If you should have access and can't see this content please contact technical support.
1Beams, J.W.: Mechanical properties of thin films of gold and silver in Proceedings of International Conference on Structure and Properties of Thin Films edited by C.A. Neugebauer, J.B. Newkirk, and D.A. Vermilya John Wiley NY 1959 183–192Google Scholar
2Bromley, E.I.: A technique for the determination of stress in thin films. J. Vac. Sci. Technol., B 1, 1364 1983CrossRefGoogle Scholar
3Vlassak, J.J., Nix, W.D.: A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J. Mater. Res. 7, 3242 1992CrossRefGoogle Scholar
4Edwards, R.L., Coles, G., Sharpe, W.N. Jr.: Comparison of tensile and bulge tests for thin-film silicon nitride. Exp. Mech. 44, 49 2004CrossRefGoogle Scholar
5Xiang, Y., Chen, X., Vlassak, J.J.: Plane-strain bulge test for thin films. J. Mater. Res. 20, 2360 2005CrossRefGoogle Scholar
6Kalkman, A.J., Verbruggen, A.H., Janssen, G.C.A.M.: Young’s modulus measurements and grain boundary sliding in free-standing thin metal films. Appl. Phys. Lett. 78, 2673 2001CrossRefGoogle Scholar
7Hall, J.D., Apperson, N.E., Crozier, B.T., Xu, C., Richards, R.F., Bahr, D.F., Richards, C.D.: A facility for characterizing the dynamic mechanical behavior of thin membranes for microelectromechanical systems. Rev. Sci. Instrum. 73, 2067 2002CrossRefGoogle Scholar
8Alaca, B.E., Selby, J.C., Saif, M.T.A., Sehitoglu, H.: Biaxial testing of nanoscale films on compliant substrates: Fatigue and fracture. Rev. Sci. Instrum. 73(8), 2963 2002CrossRefGoogle Scholar
9Kalkman, A.J., Verbruggen, A.H., Janssen, G.C.A.M., Radelaar, S.: Transient creep in free-standing thin polycrystalline aluminum films. J. Appl. Phys. 92, 4968 2002CrossRefGoogle Scholar
10Hyun, S., Hooghan, T.K., Brown, W.L., Vinci, R.P.: Linear viscoelasticity in aluminum films. Appl. Phys. Lett. 87, 061902 2005CrossRefGoogle Scholar
11Cieslar, M., Oliva, V., Karimi, A., Martin, J-L.: Plasticity of thin Al films as a function of temperature. Mater. Sci. Eng., A 387–389, 734 2004CrossRefGoogle Scholar
12Dieter, G.E.: Mechanical Metallurgy,SI Metric ed. (McGraw-Hill Book Company,Singapore, 1988 295–301Google Scholar
13Emery, R.D., Povirk, G.L.: Tensile behavior of free-standing gold films. Part I. Coarse-grained films. Acta Mater. 51, 2067 2003CrossRefGoogle Scholar
14Emery, R.D., Povirk, G.L.: Tensile behavior of free-standing gold films. Part II. Fine-grained films. Acta Mater. 51, 2079 2003CrossRefGoogle Scholar
15Chasiotis, I., Bateson, C., Timpano, K., McCarty, A.S., Barker, N.S., Stanec, J.R.: Strain rate effects on the mechanical behavior of nanocrystalline Au films. Thin Solid Films 515, 3183 2007CrossRefGoogle Scholar
16Wang, L., Prorok, B.C.: Characterization of the strain rate dependent behavior of nanocrystalline gold films. J. Mater. Res. 23, 55 2008CrossRefGoogle Scholar
17Zamiri, A., Porboghrat, F., Jiang, H., Bieler, T.R., Barlat, F., Brem, J., Compton, C., Grimm, T.L.: On mechanical properties of the superconducting niobium. Mater. Sci. Eng., A 435–436, 658 2006CrossRefGoogle Scholar
18Broomhead, P., Grieve, R.J.: The effect of strain rate on the strain to fracture of a sheet steel under biaxial tensile stress conditions. J. Eng. Mater. Technol. Trans. ASME 104, 102 1982CrossRefGoogle Scholar
19Montay, G., François, M., Tourneix, M., Guelorget, B., Vial-Edwards, C., Lira, I.: Strain and strain-rate measurement during the bulge test by electronic speckle pattern interferometry. J. Mater. Process. Technol. 184, 428 2007CrossRefGoogle Scholar
20Atkinson, M.: An investigation of hydraulic bulging as a biaxial straining test for sheet metal. J. Test. Eval. 33, 537 2005CrossRefGoogle Scholar
21Espinosa, H.D., Prorok, B.C., Peng, B.: Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension. J. Mech. Phys. Solids 52, 667 2004CrossRefGoogle Scholar
22Renault, P-O., Bourhis, E. Le, Villain, P., Goudeau, Ph., Badawi, K.F., Faurie, D.: Measurement of the elastic constants of textured anisotropic thin films from x-ray diffraction data. Appl. Phys. Lett. 83, 473 2003CrossRefGoogle Scholar
23Vinci, R.P., Vlassak, J.J.: Mechanical behavior of thin films. Annu. Rev. Mater. Sci. 26, 431 1996CrossRefGoogle Scholar
24Nix, W.D.: Mechanical properties of thin films. Metall. Trans. A 20, 2217 1989CrossRefGoogle Scholar
Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.
* Views captured on Cambridge Core between September 2016 - 6th April 2021. This data will be updated every 24 hours.
To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
@free.kindle.com @kindle.com (service fees apply)
By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services.
To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.
By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services.
To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.
By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services.
Title * Please enter a title for your response.
- No HTML tags allowed
- Web page URLs will display as text only
- Lines and paragraphs break automatically
- Attachments, images or tables are not permitted
First name * Please enter your first name.
Last name * Please enter your last name.
Your email address will be used in order to notify you when your comment has been reviewed by the moderator and in case the author(s) of the article or the moderator need to contact you directly.
Occupation Please enter your occupation.
Affiliation Please enter any affiliation.
Do you have any conflicting interests? *
Please list any fees and grants from, employment by, consultancy for, shared ownership in or any close relationship with, at any time over the preceding 36 months, any organisation whose interests may be affected by the publication of the response. Please also list any non-financial associations or interests (personal, professional, political, institutional, religious or other) that a reasonable reader would want to know about in relation to the submitted work. This pertains to all the authors of the piece, their spouses or partners.
More information * Please enter details of the conflict of interest or select 'No'.
Please tick the box to confirm you agree to our Terms of use. *
Please accept terms of use.
Please tick the box to confirm you agree that your name, comment and conflicts of interest (if accepted) will be visible on the website and your comment may be printed in the journal at the Editor’s discretion. *
Please confirm you agree that your details will be displayed.
Anyone you share the following link with will be able to freely read this content. Copy and paste the link or use the option below to share it via email. Alternatively you can download a PDF containing the link which can be freely shared online. For more information, please view our content sharing policy.
Copy and paste a formatted citation or use one of the options to export in your chosen format
A closed-loop approach is adopted to implement strain rate control during the bulge test. Due to the difficulty of measuring strains directly, the technique is based on the conversion of displacement measurements to the corresponding strains using the plane-strain formulation. The necessary temporal evolution of the midpoint displacement of a rectangular diaphragm is derived under the condition of constant strain rate and is imposed as a control criterion. The technique is demonstrated on 500-nm-thick Au diaphragms by applying strain rates ranging from 2 × 10 −6 to 2 × 10 −4 s –1 . By measuring the corresponding yield strength values, a strain rate sensitivity of 0.11 is obtained, which is close to what was previously reported on similar specimens using the microbending test.
Schematic illustration of the bulge test setup.
Alignment of the specimen with respect to the displacement sensor. (a) Out-of-plane alignment is carried out by utilizing rotation around x and y axes. As a result of this procedure, all points on the specimen become equally distant from the sensor head. (b) Close-up of the bulging diaphragm. In-plane alignment is carried out by rotating the sample around the z axis such that the long axis of the diaphragm, designated by , coincides with the plane . Hence, the bulging diaphragm acts as a perfectly horizontal plane moving toward the sensor head. This eliminates the disadvantage of point measurement associated with the triangulation principle.
(a) Total deflection at the center of the diaphragm is the sum of the substrate deflection and the actual deflection of the diaphragm. (b) Higher deflection reading can also result from a delamination of the thin film from the substrate. (c) The effect of delamination can be evaluated by testing the sample upside down.
Pressure versus deflection graph of a 320- m-wide diaphragm showing the effect of substrate deflection.
All figure content in this area was uploaded by Orhan Akar
Content may be subject to copyright.
Content may be subject to copyright.
College of Engineering, Koc University, Rumeli Feneri Yolu 34450 Sariyer, Istanbul, Turkey
Electrical and Electronics Engineering Department, Middle East Technical University,
(Received 26 March 2008; accepted 4 August 2008)
A closed-loop approach is adopted to implement strain rate control during the bulge
test. Due to the difficulty of measuring strains directly, the technique is based on the
conversion of displacement measurements to the corresponding strains using the
plane-strain formulation. The necessary temporal evolution of the midpoint
displacement of a rectangular diaphragm is derived under the condition of constant
strain rate and is imposed as a control criterion. The technique is demonstrated on
500-nm-thick Au diaphragms by applying strain rates ranging from2×10
. By measuring the corresponding yield strength values, a strain rate
sensitivity of 0.11 is obtained, which is close to what was previously reported on
similar specimens using the microbending test.
Bulge test is a versatile characterization method capa-
ble of determining a complete set of material properties
of thin films under various thermodynamic conditions. It
is based on measuring the deflection of a membrane un-
der an applied pressure. The obtained pressure-deflection
behavior is then utilized to extract a variety of properties
using the membrane theory. Following the original work
the technique was adapted to intrinsic stress
measurements of thin metal films on silicon nitride mem-
The method was extended to measure the Pois-
son’s ratio of thin films utilizing rectangular samples
become a fairly well-characterized and widely accepted
Two major advantages associated with bulge test are
the ease of specimen handling and the capability of im-
posing loading conditions. These advantages are unpar-
alleled by other thin film testing methods such as nanoin-
dentation, substrate-curvature technique, and microten-
sile testing. It is therefore not surprising that bulge test
found many applications in the field of materials testing,
ported. All these techniques require a more involved ap-
proach than that in a monotonic loading scenario, and
bulge test is capable of providing a suitable platform in
this regard. It is, of course, to be noted that even the case
of monotonic loading is not straightforward and requires
a considerable amount of attention for issues such as the
displacement of the testing equipment under applied
loads and the constancy of the applied strain rate.
The need for a constant strain rate is based on its effect
on the strength measurement. It is well known that in-
creasing the applied strain rate increases the flow stress
of the specimen under testing. This effect becomes more
pronounced at elevated temperatures. Strain rates utilized
in mechanical testing cover a wide spectrum ranging
The relation between flow stress and
applied strain rate ⑀˙ at any given strain and temperature
is described by the following relation:
where mis the strain-rate sensitivity. Although strain-rate
sensitivity is usually low for metals at room tempera-
there is a general consensus that for Au thin films
it increases with decreasing grain size.
It is to be noted that although bulge test provides
the capability for testing thin films under a constant
strain-rate condition, reported use of it in a strain-rate-
dependent material property measurement study is rare.
Reports are usually limited to the testing of bulk mate-
sheets. An extensometer can be utilized together with a
closed-loop servocontrol of the strain to increase the pre-
cision regarding the study of strain hardening.
Address all correspondence to this author.
J. Mater. Res., Vol. 23, No. 12, Dec 2008 © 2008 Materials Research Society 3295
in contrast to thin films testing, where the measurement
of strain has traditionally been a challenging task. Hence,
imposing a constant strain rate does not constitute a
straightforward task. A certain level of strain rate control
for thin films is implemented through techniques includ-
constant cross-head and probe displacement rate, respec-
tively. These techniques provide a nearly constant strain
rate as the true-strain rate decreases with increasing strain
if the cross-head velocity is kept constant. Therefore in
the absence of a direct strain measurement technique
such as the use of an extensometer, an open-loop ap-
proach is usually utilized where the cross-head displace-
ment rate is adjusted according to the specimen length.
The imposed condition is maintained until the onset of
non-uniformity of the plastic deformation.
In this work a similar approach was adopted for the
bulge test. We demonstrate the use of a closed-loop bulge
test for strain-controlled testing of submicron Au films,
where a pronounced strain-rate dependency of the yield
strength is observed. In the next section the condition for
constant strain rate is discussed for high-aspect ratio,
rectangular test samples. The description of the testing
setup and sample preparation are followed by a dis-
cussion of the experimental procedure, where already
established conditions are implemented as the con-
trol criterion. The paper is concluded by the validation of
the proposed technique using test results obtained on
500-nm-thick, sputtered Au films, whose properties are
fairly well documented in the literature.
II. CONDITION FOR CONSTANT STRAIN RATE
Specimens utilized in this work consist of rectangular
membranes. The deflection hat the center of the mem-
brane increases as a result of the applied pressure during
the bulge test. The deflection is not only dependent on
the applied pressure but it is also a function of the sample
geometry and material parameters. In the elastic regime,
for a linear elastic membrane, the relationship between
the pressure Pand the deflection his given in a polyno-
is the in-plane biaxial residual stress, Eis the
elastic modulus, is the Poisson’s ratio, dis the mem-
brane thickness, and ais the half-width of the membrane.
This model is a good approximation for membranes of
depends on both the geometry of the mem-
brane and the Poisson’s ratio. For rectangular membranes
with aspect ratios greater than 4, Eq. (2) can be further
simplified to the following relation:
In this case the stress state in the diaphragm can be
approximated by the plane strain assumption. Equation
(3) is used widely to extract residual stresses and elastic
Stresses and strains ⑀in the specimen can also be
calculated using the relations given in Eqs. (4) and (5)
under the condition that the diaphragm width is much
larger than the amount of deflections.
is the residual plane strain. Taking the first
derivative of strain with respect to time t, the strain rate
For a flat membrane exposed to gauge pressure, the ini-
is taken as zero. This is a condition that
can easily be cross-checked prior to testing. Hence, the
center displacement of a rectangular membrane at con-
stant strain rate, ⑀˙has a square-root time dependence as
Implementation of this condition in a bulge test setup
is possible using a control algorithm. To evaluate hcor-
rectly, we utilize point measurements of displacements
both at the center of the deforming diaphragm and the
edge of the diaphragm where the substrate deflection is
measured and eliminated from the readings. Compared to
the interferometric method of measuring deflections,
point measurement requires a considerable amount of
alignment of the specimen with respect to the optical
head. However, since obtain
4 ADVANCE Core Strengthening Exercises | L4 L5 Disc Bulge... - YouTube
Strain -controlled bulge test | Journal of Materials... | Cambridge Core
(PDF) Strain -controlled bulge test
An Investigation of Hydraulic Bulging as a Biaxial Straining Test for...
Hamstring Strain - Physiopedia
Lily Lane Porn
Pound Her Ass
Annie Body Porn
Asstr Straining Bulge
