A method for joining component bodies of material over bonding regions of large dimensions by disposing a plurality of substantially contiguous sheets of reactive composite materials between the bodies and adjacent sheets of fusible material. The contiguous sheets of the reactive composite material are operatively connected by an ignitable bridging material so that an igniting reaction in one sheet will cause an igniting reaction in the other. An application of uniform pressure and an ignition of one or more of the contiguous sheets of reactive composite material causes an exothermic thermal reaction to propagate through the bonding region, fusing any adjacent sheets of fusible material and forming a bond between the component bodies.