Path of the honed fist

Some warriors feel the most alive when threading the line between life and death, their hearts beat like the pounding drums of war, and their battle cries echo like the sounding horns of war. Those who choose this path have been to the doors of death and back, and taunt death until it takes them. These barbarians forsake all weaponry, leaping into battle with their bare fists. they forsake beauty and peace, seeking power, and more seeking a good fight. They may even spare their foes from death so that they may become more powerful and offer a more thrilling fight.

abandon all

When select this path at 3rd level, you forsake all weapons. you are no longer able to wield weapons, or use shields.

As you gain levels you become more adapted to this style of fighting, while raging and not wearing armor, you gain a bonus to you AC equal to half your proficiency bonus, rounded down, that and your strength modifier halved, rounded down as well.

your fists are now your weapons. when you make an unarmed attack you may roll a d6 in place of the normal damage. this damage increases your brutal critical feature at higher levels, becoming a d8 at 9th level, a S10 at 13th level, and a D12 at 17th  level

momentous blow

at 3rd level you've freed yourself to move quick and pack momentum in your fists, like falling hammers. Once per turn you can spend an additional 5 feet of a movement to add an additional die of damage to all unarmed strikes in your next attack action.

While you are raging you can add your rage damage to one of these blows on your turn,

Using the adrenaline of these blows, you keep yourself fighting. As a bonus action on your turn, you may gain temporary hit points equal to the highest damage dealt by a single one of your attacks this turn. You can gain temporary hit points to this way a number of times equal to your constitution modifier, and you regain all uses on a long rest.

bloody counter

at 6th level, you can focus your mind in a split second, forcing your rage to subside only to explode in a vicious counter attack against your foe. As a reaction, if you take physical damage, you can reduce the damage by a d10 + your strength modifier + your barbarian level. If you reduce the damage to 0 you can make an unarmed strike against the creature who attacked you if they are in range, and without the strength modifier on the damage roll. Your rage continues at the start of your next turn. If you were raging, your rage starts the next start of your turn. If you were not raging, you automatically enter into a rage. it does this without using a bonus action.

improved boxing

at the 10th level your fighting style has been honed to the point that all your strikes are made with precision and strength befitting a master while raging if you use your bonus action to make an unarmed strike, you can add your strength modifier  + your rage damage roll additionally, you can impose disadvantage on any check made to a contest grapple, throw or shove from your barbaric boxing ability. you must finish a short or long rest before using this ability again

Vicious combo

by the 14th level your strikes have become faster then the normal eye can perceive When you use your bonus action to make an unarmed strike from your barbaric boxing ability, you can attack twice instead of once, rolling separate attack roll for each strike.