I did displacement controlled testing (0.05mm/min) of 40x40x160 mm mortar bar and the flexural strength result seems to be between 11-14 MPa, while other studies report only between 7-10 MPa for similar mortar composition.
I've been doing a lot of mechanical testing for the past 4 years on Servo Hydroulic MTS 810 system. Displacement control and force control are just two control parameters to carry out the test. If the speed of deformation(properties of some materials change with that) in both types of controls is same, the peak load in flexural test should be the same.
We can also discuss the problem in detail if you would like to.
My test samples are mainly cement mortar, 40(b)x40(h)x160 (L) mm dimension, made with water-cement ratio of 0.40. I tried both load controlled and displacement control flexural testing for samples of same composition and same batch. I observed a difference of 30% between the two test methods. Usually, for displacement control tests, my results do not vary by more than 10%.
The rate of displacement can influence crack initiation and propagation in cement composite. Therefore, I tried 0.05 mm/min and 0.5 mm/min displacement rate and found no statistically significant difference between peak strength.