Self-piercing rivet die, assembly, and method of joining materials with a self-piercing rivet

A method of joining a top substrate to a bottom substrate, the method comprising:

• positioning the bottom substrate on a top surface of a die;
• positioning the top substrate on the bottom substrate so that the bottom substrate is between the top substrate and the die in an axial direction of the die;
• and
• pressing a self-piercing rivet in the axial direction against the top substrate until the self-piercing rivet penetrates through the top substrate and into the bottom substrate, wherein pressing the self-piercing rivet deforms the bottom substrate into a relief defined by at least:
• a raised central portion of the die;
• an outer portion of the die disposed about a central axis of the die;
• a side surface of the die disposed about the central axis, the side surface being located radially between the outer portion and the top surface to connect the outer portion to the top surface;
• and
• an annular channel disposed about the central axis and disposed, in a radial direction, between the raised central portion and the outer portion, the annular channel being recessed in the axial direction from the raised central portion and at least a part of the outer portion that is adjacent to the annular channel,
• wherein the annular channel is radially inward of a toe of the self-piercing rivet after the self-piercing rivet deforms the bottom substrate into the relief,
• wherein the raised central portion is between the top surface and the outer portion in the axial direction.