CTOD test is used to measure the materials resistance to crack propagation. CTOD is mainly used for ductile materials.
Fatigue crack growth tests (da/dN) are used for the measurement of crack growth rate (assuming a pre-existing crack) and for the determination of fatigue life and the Paris' constants.
A CTOD test is usually done on materials that undergoes plastic deformation (ductile or quasi brittle materials) prior to failure. In CTOD the specimen is placed on the work table and a notch is created exactly at the centre. The crack should be generated such that the defect length is about half the depth. this kind of test is generally performed on the fracture toughness testing geometry like- 3-point bending test and Compact tension specimen. A strain gauge is used to measure the crack opening. Crack tip plastically deforms until a critical point after which a cleavage crack is initiated that may lead to either partial or complete failure. The critical load and strain gauge measurements at the load are noted and a graph is plotted. The crack tip opening can be calculated from the length of the crack and opening at the mouth of the notch. According to the material used, the fracture can be brittle or ductile which can be concluded from the graph.
and in Fatigue crack growth behavior test we generally find the fatigue life corresponds to the dynamic or variable loading with respect to the change in crack length. fatigue analysis generally performed to know the variation in the fracture toughness (in terms of stress intensity factor )with the variation in the crack length.
There are three modes of fracture viz. Mode I, Mode II and Mode III. CTOD i.e. Crack Tip Opening Displacement is related to Mode I type of fracture. In Mode I, the load (tensile) is applied on a sample having a pre-existing crack which is perpendicular to crack surface.This tensile load is not a dynamic load and fatigue relates to dynamic loading condition. Fatigue crack nucleates and then propagates and one measures either endurance strength or endurance cycle to study the fatigue behaviour.They are very different fields.