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The ASTM dicates a plain rectangular shape. I understand that the material necks pretty quickly but I frequently get breaks in the grips, particularly with films of thickness less than 0.002."

Dog bone samples seem as though they would help, so why not use those?

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ASTM D882 is for plastic films. For thins films of many other materials, dog-bone specimens are more commonly used.

The deformation of dog-bone specimens is not homogeneous through the length of the full specimen. That means that the cross-head displacement of the testing machine is not necessarily equal to the displacement of the gage region. As a result, you will need some sort of extensometer to measure the change in length of the specimen which makes the test a bit more complicated.

Of course, it can be argued that the deformation is not homogeneous in a rectangular specimen either - which is why you run into breaks at the grips.

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