Chemical explosives are not a must for explosive effect. Like hollow point bullet, dumdum bullet or FAPDS round, all of them greatly expand (explosion like) after impact. The more fragments or deformation, the more they act like chemical explosions.
However, for this non-explosive round to work like explosives, the hardness of the target must be considered unlike in case of chemical explosives. The round must be hard enough to penetrate, also soft enough to deform and fragment once inside. This requires a good design of the shell with differentiated layered density and hardness and density center. Even so, if the outer shell is so hard that it fully penetrate the target without fragmentation, the damage would be too small, just a small hole. One example is the 6.5mm bullet of type 38 rifle of Japan in WWII, while highly accurate, it usually just punch a hole of the victim if not through critical organ, the victim would be able to continue fighting. But if that bullet travels slower, and being made of softer material, it would have stayed inside the body and tumbled around to create much bigger damage.
However, for this non-explosive round to work like explosives, the hardness of the target must be considered unlike in case of chemical explosives. The round must be hard enough to penetrate, also soft enough to deform and fragment once inside. This requires a good design of the shell with differentiated layered density and hardness and density center. Even so, if the outer shell is so hard that it fully penetrate the target without fragmentation, the damage would be too small, just a small hole. One example is the 6.5mm bullet of type 38 rifle of Japan in WWII, while highly accurate, it usually just punch a hole of the victim if not through critical organ, the victim would be able to continue fighting. But if that bullet travels slower, and being made of softer material, it would have stayed inside the body and tumbled around to create much bigger damage.