Tension testing can be conducted on ceramics similar to other material.  You are correct that ceramics are elastic, so the stress-strain response will be a positive-slope line from the origin to the maximum stress-strain point.  Since ceramics are brittle and difficult to fixture, they normally are bend tested.  For equipment, you can look at Instron:

http://www.instron.com

For testing procedures, try ASTM International:

http://www.astm.org

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

Also as an aside.

Since the results obtained in the uniaxial tensile test are highly scattered for ceramics it is usual to use the Weibull method or similar to determine different estimated values of properties.

Nick
I love materials science!

ASTM has a standard coupon for conducting tensile test on brazed ceramics.  The test requires special fixturing to capture and load the coupons in a non-damaging way.  It would seem practical to make a ceramic test coupon with geometry resembling the final geometry of the brazed version.

Sorry I don't know the ASTM reference.

Jesus is THE life,
Leonard

This subject is covered in ceramics engineering books, e.g., ‘Chapter 3. Mechanical Properties and Their Measurement,’ in Modern Ceramic Engineering, D. W. Richardson (1982).
As CoryPad said, ceramics can be tensile tested by the same methods as used for metals.  However, such testing is much more sensitive to mis-alignment and the cost of machining specimens is high.

On-line sources for equipment, information and test methods, from a search ‘tensile testing ceramics:’
 
Tensile tester grips rubber test machines equipment gripper Lloyd Instruments is an established manufacturer of materials testing ...
 http://www.tensile-tester-grips.co.uk  ;

Tensile Testing - Learn ways to predict material behavior through tensile testing. ... Chapter 7: Tensile Testing of Ceramics and Ceramic-Matrix Composites 147 ...
http://www.engineeringbookstore.com/smeb/MaterialsTesting/Tensile  ;

ASTM C1359-96(2000) Standard Test Method for Monotonic Tensile Strength Tes - ... Method for Monotonic Tensile Strength Testing of Continuous Fiber-Reinforced Advanced Ceramics With Solid Rectangular ...
http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/PAGES/C135  ;

ASTM C1366-97 Standard Test Method for Tensile Strength of Monolithic Advan - ... Ceramics. Index Terms. advanced ceramic; elevated temperatures; percent bending; tensile strength; tensile testing ...
http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/PAGES/C136  ;

Testing ceramics for creep - Testing ceramics for creep by Michael G. Jenkins Before advanced ceramics can be seriously considered for use in heat engines, they must pass stringent long-term tests at high temperatures ...
http://www.memagazine.org/backissues/february97/features/ceramics  ;

Tensile Testers - Universal Testing Machines - from Benz - Designs and manufactures tensile testers (universal testing machines) and other material testing instruments, systems and software for plastics, rubber, ceramics, composites, paper, ...
http://www.benztesters.com/tt2100.htm  ;

Applications by Material - Ceramics Testing Materials and Systems - ... materials testing. The nature of ceramics makes it extremely difficult to perform a conventional tensile test. ...
http://www.dynatup.com/applications/ceramics/testing.asp  ;

High Temperature Creep Testing Machine for Ceramics - High Temperature Creep Testing Machine for Ceramics This machine is designed to evaluate the creep strength of refractory metals and ceramics under the higher temperature range more than ...
http://www.toshinkogyo.com/hctte.html  ;

Tensile Testing
Edited by: P. Han; Hardbound; Publisher: ASM; Publication Date: 1992; ISBN 0-87170-440-4; 207 pages ... methodology and data analysis. Tensile testing of metals and alloys, plastics, elastomers, ceramics and composites
http://www.normas.com/ASM/pages/6373.html  ;

GPG No. 7 Flexural Strength Testing of Ceramics and Hardmetals - Good Practice Guide No 7: Flexural Strength Testing of Ceramic and Hardmetals ... Figure B.1 Changes in tensile surface stress distribution due to lateral misalignment ...
http://midas.npl.co.uk/midas/content/gpg07.html  ;

CMMT(MN)048 Room Temperature Tensile Testing: A Method for Estimating - ... Room Temperature Tensile Testing: A Method for Estimating ... Tensile testing, together with hardness and Charpy impact ... undertaking Room Temperature Tensile Testing in accordance ...
http://midas.npl.co.uk/midas/content/mn048.html  ;

MTI -- Universal Testing Machines - MTI offers New Universal Testing Machines and can Reconstruct and Automate your own Antiquated Instron, Tinius Olsen, or similar Electromechanical Load Frame
[http://www.mti-atlanta.com  ;

Ceramics: Industrial Processing & Testing - ... CERAMICS: INDUSTRIAL PROCESSING AND TESTING (ISBN 0813802911) by J. T. Jones ... of Rupture, Compressive Strength, Tensile Strength, Modulus of Elasticity, Hardness, Impact Testing, ...
http://www.tjbooks.com/ceram.htm  ;

Benz materials testing instruments - ceramics - ... TT2100 Series Tensile Testers. Grips & Fixtures. Clicker presses. Molds & Dies. Adhesives Ceramics Composites Metals ...
http://www.benztesters.com/ceramics.htm  ;