A crystalline material processing method comprising: providing a rigid carrier (72, 72A, 148, 176, 186, 196) and a substrate (60, 60A, 142, 172, 182, 190), whereby a lateral length and width dimension of the rigid carrier exceeds a lateral length and width dimension of the substrate, the exceeding lateral length and width dimension of the rigid carrier forming at least one portion; then temporarily bonding the rigid carrier (72, 72A, 148, 176, 186, 196) to a first surface (62, 191) of a crystalline material with an intervening adhesive material (68, 68A, 174, 184, 194), wherein the crystalline material comprises the substrate (60, 60A, 142, 172, 182, 190) having a subsurface laser damage region (66, 66A', 143, 183, 193) at a depth relative to the first surface (62, 191), and the adhesive material (68, 68A, 174, 184, 194) has a glass transition temperature T g of greater than 25°C; and fracturing the crystalline material along or proximate to the subsurface laser damage region (66, 66A', 143, 183, 193) to yield a bonded assembly (85, 168B, 178) comprising the rigid carrier, the adhesive material (68, 68A, 174, 184, 194), and the portion (80,192) of the crystalline material, whereby the bonded assembly is removed from the substrate (60, 60A, 142, 172, 182, 190); wherein the at least a portion of the rigid carrier (72, 72A, 148, 176, 186, 196) extends laterally beyond the substrate (60, 60A, 142, 172, 182, 190) to form a laterally protruding lip, the fracturing comprises applying a mechanical force proximate to at least one edge of the rigid carrier (72, 72A, 148, 176, 186, 196), and the mechanical force is configured to impart a bending moment in the at least a portion of the rigid carrier (72, 72A 148, 176, 186, 196). providing a rigid carrier (72, 72A, 148, 176, 186, 196) and a substrate (60, 60A, 142, 172, 182, 190), whereby a lateral length and width dimension of the rigid carrier exceeds a lateral length and width dimension of the substrate, the exceeding lateral length and width dimension of the rigid carrier forming at least one portion; then temporarily bonding the rigid carrier (72, 72A, 148, 176, 186, 196) to a first surface (62, 191) of a crystalline material with an intervening adhesive material (68, 68A, 174, 184, 194), wherein the crystalline material comprises the substrate (60, 60A, 142, 172, 182, 190) having a subsurface laser damage region (66, 66A', 143, 183, 193) at a depth relative to the first surface (62, 191), and the adhesive material (68, 68A, 174, 184, 194) has a glass transition temperature T g of greater than 25°C; and fracturing the crystalline material along or proximate to the subsurface laser damage region (66, 66A', 143, 183, 193) to yield a bonded assembly (85, 168B, 178) comprising the rigid carrier, the adhesive material (68, 68A, 174, 184, 194), and the portion (80,192) of the crystalline material, whereby the bonded assembly is removed from the substrate (60, 60A, 142, 172, 182, 190); wherein the at least a portion of the rigid carrier (72, 72A, 148, 176, 186, 196) extends laterally beyond the substrate (60, 60A, 142, 172, 182, 190) to form a laterally protruding lip, the fracturing comprises applying a mechanical force proximate to at least one edge of the rigid carrier (72, 72A, 148, 176, 186, 196), and the mechanical force is configured to impart a bending moment in the at least a portion of the rigid carrier (72, 72A 148, 176, 186, 196).