In Fatigue Crack growth study We should keep stress ratio always positive or we can keep it negative as well (stress ratio (R)= Min Stress/Max Stress).
Note: Specimen is compact tension one, having side notch.
As in negative there will be compressive stress.
Fatigue crack growth rate expressed as a function of crack-tip stress intensity factor range, d a/dN versus ΔK, characterizes a material's resistance to stable crack extension under cyclic loading. Background information on the rationale for employing linear elastic fracture mechanics to analyze fatigue crack growth rate as according to ASTM E647
For crack growth, stress near crack tip should be always +ve. If min force is -ve is taken as 0 to calculate delta K.
There is no reason why R should always be positive in a crack growth test, but you should realize that maybe this experiment would be unfeasible if, for example buckling happens in your sample or if the sample deforms in a way that the solution for K is not valid anymore. With positive R this will never happen, and this is why most tests are done in this region.
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