Dear Xu Wenlong ,

This document might be useful for you: https://www.tainstruments.com/applications-notes/introduction-to-dynamic-mechanical-analysis-and-its-application-to-testing-of-polymer-solids/

Tan delta is a mathematical relation between both the storage (or elastic) and loss (or viscous) modulus of a material. Tan δ indicates the relative degree of energy dissipation or damping of the material. For example, a material with a tan δ > 1 will exhibit more damping than a material with a tan δ < 1, because the loss modulus is greater than the storage modulus in the former, which means the energy dissipating, viscous mechanisms will have a greater influence on the final properties of the material.

Normally, tan delta is measured as a function of temperature, mainly because the materials suffer transitions when being heated or cooled. This transitions, which essentially are changes either in loss or storage modulus, are related to the structure of the material. In the case of your DMA results, the maximum of the tan delta peak is related to the glass transition temperature of your material. Physically speaking, it is related with the temperature in which a transition in the material is ocurring: stops behaving like a glass, to soften. This temperature is extremely useful to know when thinking of applications, when looking for a very hard material, or rubber, at ambient temperature for example.

Hope it helps!

PS: in your case, your rubber has a maximum in tan delta (Tg) in -50C. This means that your rubber is soft above that temperature, which is why you can elongate it. But, if your application is at a temperature lower than -50C (let's say -70C), your rubber will no longer be a rubber-like. It will be hard as a glass, meaning it can break easily during an impact for example.