On imposing a constant strain rate over time on a polymer melt sample, the transient elongational viscosity will increase until the sample breaks. Some investigators argue that the breaking of the sample coincides with steady state, however that is not at all sure. One can speak of a quasi-steady state. The figure on the left shows this for various constant strain rates.
The figure on the right shows the quasi-steady state elongational viscosity curve as a function of the strain rate.
In elongation, the polymer chains will completely and almost immediately be oriented in the flow direction. Due to entanglements, the molecules will be stretched. It will be difficult for the chains to slip, since they are so strongly oriented in the direction of the applied force. Therefore, viscosity will rise constantly until a quasi-steady state is reached and the sample breaks.