How can we measure the toughness of mortar or concrete of unnotched section through load deflection method? any standard are available for measure the toughness of unnotched beam?
You can use your load-deflection curve to get your toughness by calculating the area under the load-deflection curve to a net deflection of L/150. Check ASTM C 1609 for details
Since concrete is generally considered a classically brittle material, no standards exist for the measurement of its toughness (i.e. fracture toughness stress intensity factor) without the use of notched sections. However, if you are simply interested in comparing different concrete samples, then the approach given by AA above (i.e. compare the area under the stress-strain curve) is adequate.
Are you interested in toughness up to the first crack, or are you interested in the descending portion of the stress-strain curve after peak stress as well? If the former, you can use the appearance of the first crack (i.e. first significant drop in stress without a reduction in strain) as the point to stop integrating under the curve. If you are interested in the latter, you will need to define an arbitrary maximum deflection based on the observed behaviour of the group.
A word of caution - if you are interested in the descending portion of the stress-strain curve, you need to make sure your tests are carried out under strain rate (i.e. displacement) control. Many concrete testing machines operate under load rate control, and these are not suitable as the descending portion of the curve is not reproducible under load control.
It sound like a fracture mechanics issue and crack-tip energy, K1c, and energy release rate. You might want to wade into that.
Material always have notches or cracks, even if at the micro-scale. So the crack is there just really small. You might be able to see them with some form of dye-penetrant material. Don't know how that works on concrete as the substrate is more absorptive than metals.
It's meant for use with metals but perhaps you can find something useful to adapt in ASTM E604. Since the crack tip moves at the speed of sound you'll have to be really quick. Applying an axial compressive strain may slow the fracture rate.