Methods and machine tools for machine-cutting workpieces in plate form or bar form

A method for processing a plate-shaped workpiece or rod-shaped workpiece in a processing machine having a laser processing device, the method comprising:

• moving at least one of the workpiece and a processing head for a laser beam with respect to one another;
• directing the laser beam towards the workpiece using the processing head;
• forming a recess in the workpiece using the laser beam, wherein the recess is formed by the laser beam to have at least one of parallel, tapering, and widening wall sections bordering the recess, wherein the recess has at least one of a polygonal contour and a non-round contour;
• and
• widening the recess formed by the laser beam to an enlarged borehole using a flow drill.