I came across 2 creep coefficient diagram. First one is from Eurocode, second one is from elsewhere. I think the second one make sense, As the time progress, the creep coefficient shall increase, hence, the effetive modulus of concrete shall decrese. Can someone explain it ? I am confused.
You are looking at a diagram for an infinite duration of loading, which is noted by the $\infty$-symbol. For a limited duration of loading, refer EN 1992-1-1 annex B.1.
Just for clarity, the time shown on the first diagram, $t_0$, is the concrete age when loading starts, which is why the creep coefficient decreases with increasing $t_0$.
Creep rate for steel does not change with time. That is the basis of ASME Boiler code allowable stresses. Most of the world uses boiler code ; often they rewrite it for national pride. Superalloys (gas turbine blades and vanes) also have constant creep rate at constant temperature. Depending on how it is measured , it may appear to change as the cross-section area of the test bar changes with strain and constant load. Footnote: Over 60 years ago , some creep test machines had curved load arms ( that changed the load) to compensate for the diameter reduction of test bars as the the tests progressed.