Dear Che

If the  constant stroke-rate uniaxial tensile test  was assumed  in term of a strain rate  to be 10-6 /sec. and the uniaxial tensile test for instance took 20 minutes for the uniaxial sample to fracture, so called the actual loading time.  

So when you plot  values of the  obtained uniaxial stress (which correspond to the instantaneous strain rate of the uniaxial test) versus the duration time of the loading until fracture, i.e., 20minutes , therefore, the yield stress of the uniaxial sample can be obtained  from such plot (stress Versus Time) within the first 4 minutes of the test as the following:

the (20/100) X 20 minutes=4 minutes.

The KIc test is performed using a specific specimen having an initial crack.

In this case, it really refer to the same uniaxial test used to test the yield stress

You say that "the yield stress, σy, is to be taken from the maximum

load in a uniaxial tensile test."

Be sure to apply the correct definition of yield stress, which is different from the stress at maximum load.

The calculations related with the plain strain fracture thougness are referred to the yield strength. This test is applyed on material wich mechanical behavior is not ductile.

 Thanks for all your kind suggest !!  But I'm still wondering what if I can't get a yield stress that the time to yielding is less than 20% of the actual loading time .Does it means I have to try many different loading rates(0.5, 1, 5... mm/min) for my uniaxial tensile test to get a correct yield stress that the time to yielding is less than the time while the testing sample fracture? Thanks again !!

Dear Khaled 

But it seems that the time to yielding isn't possible to be less than 20% of time to the sample fracture? 

Dear Che

But I quote what you provided from the ASTM D5045-14 standard "the loading time to yield is within +-20 % of the actual loading time observed in the fracture test".   So, this statement is the same as the  time to yielding is possible to be less than 20% of time to the sample fracture.

Dear Khaled 

Thanks for answering back sir! The attached file is the result of the uniaxial  tensile test of the epoxy I test. Because according to the result, the stress-strain curve shows a non-ductile behavior but also not a classic brittle behavior. Yielding is able to observe for a really short segment but after that, fracture happened. And the time to yielding is very close to fracture.So I was wondering how could the time to yielding is less than 20% of time to fracture? Thanks a lot again !!