A turbine rotor system, comprising: a rotor and at least one blade segment; the blade segment, comprising: a blade; and a mounting segment coupled to the blade, wherein at least a portion of the mounting segment is configured to insert within a slot of the rotor to form a joint, and the mounting segment comprises: a first contact face and a second contact face each having a proximal end and a distal end, wherein each proximal end is configured to be inserted within the slot and each distal end is configured to remain outside of the slot when the joint is formed, and the respective proximal ends of the first and second contact faces (94; 96) are curved outwardly with respect to a longitudinal axis of the blade segment; and a lower face coupling the respective proximal ends of the first and second contact faces (94; 96), wherein the lower face projects generally radially away from the blade characterized in that the blade segment is constructed from a composite material (106, 108, 114, 116, 118) which comprises a ceramic matrix composite, wherein the mounting segment of the blade segment is formed from a composite assembly of one or more laminated plies, which comprise a ceramic matrix composite. a rotor and at least one blade segment; the blade segment, comprising: a blade; and a mounting segment coupled to the blade, wherein at least a portion of the mounting segment is configured to insert within a slot of the rotor to form a joint, and the mounting segment comprises: a first contact face and a second contact face each having a proximal end and a distal end, wherein each proximal end is configured to be inserted within the slot and each distal end is configured to remain outside of the slot when the joint is formed, and the respective proximal ends of the first and second contact faces (94; 96) are curved outwardly with respect to a longitudinal axis of the blade segment; and a lower face coupling the respective proximal ends of the first and second contact faces (94; 96), wherein the lower face projects generally radially away from the blade characterized in that the blade segment is constructed from a composite material (106, 108, 114, 116, 118) which comprises a ceramic matrix composite, wherein the mounting segment of the blade segment is formed from a composite assembly of one or more laminated plies, which comprise a ceramic matrix composite. a blade; and a mounting segment coupled to the blade, wherein at least a portion of the mounting segment is configured to insert within a slot of the rotor to form a joint, and the mounting segment comprises: a first contact face and a second contact face each having a proximal end and a distal end, wherein each proximal end is configured to be inserted within the slot and each distal end is configured to remain outside of the slot when the joint is formed, and the respective proximal ends of the first and second contact faces (94; 96) are curved outwardly with respect to a longitudinal axis of the blade segment; and a lower face coupling the respective proximal ends of the first and second contact faces (94; 96), wherein the lower face projects generally radially away from the blade a first contact face and a second contact face each having a proximal end and a distal end, wherein each proximal end is configured to be inserted within the slot and each distal end is configured to remain outside of the slot when the joint is formed, and the respective proximal ends of the first and second contact faces (94; 96) are curved outwardly with respect to a longitudinal axis of the blade segment; and a lower face coupling the respective proximal ends of the first and second contact faces (94; 96), wherein the lower face projects generally radially away from the blade characterized in that the blade segment is constructed from a composite material (106, 108, 114, 116, 118) which comprises a ceramic matrix composite, wherein the mounting segment of the blade segment is formed from a composite assembly of one or more laminated plies, which comprise a ceramic matrix composite.