Forming limit diagram

A forming limit diagram, also known as a forming limit curve, is used in sheet metal forming for predicting forming behaviour of sheet metal. The diagram attempts to provide a graphical description of material failure tests, such as a punched dome test.

In order to determine whether a given region has failed, a mechanical test is performed. The mechanical test is performed by placing a circular mark on the workpiece prior to deformation, and then measuring the post-deformation ellipse that is generated from the action on this circle. By repeating the mechanical test to generate a range of stress states, the formability limit diagram can be generated as a line at which failure is onset (see also formability).

The semi-axes of the ellipse formed in this circle allow for the measurement of relative strain in two primary directions, known as the major and minor directions, which correspond to the major and minor semi-axes of the ellipse. Under the assumption of path independent strain, the relative strains will reach a critical value at which deformations occur. Through repeated measurements, the shape of the curve can be obtained experimentally. Alternately, a formability limit diagram can be generated by mapping the shape of a failure criterion into the formability limit domain. How ever the diagram is obtained, the resultant diagram provides a tool for the determination as to whether a given forming process will result in failure or not. Such information is critical in the design of forming processes, and is therefore fundamental to the design of sheet metal forming processes. Through the establishment of forming limit diagrams for a range of alloys, the forming process and alloy behavior can be matched at the metalworking design time by the process engineer.

With the availability and use of optical strain measurement system in combination with digital data processing forming limit curves can be acquired in a more automatic and productive way compared to the classic way as described above. This procedure has been standardized and is contained in an ISO document (12004).

In order to obtain a full forming limit curve, test pieces with different geometries are drawn by a punch (e. g. with a diameter of 100 mm) until fracture occurs. Friction is almost zero by using a complex tribo-system with foils and grease between sheet and tool. By use of an optical strain measurement system spatial strain paths are evaluated immediately before failure of the test piece. Using an interpolation method for the strain variation between the severely deformed and necked area – the limits of this area are computed by a sign change of the second derivative of the strain distribution – the major and minor strain values are obtained. Using an averaged value for several cross-section evaluations and 3 test samples for the same geometry a strain pair (one point in the forming limit diagram) as forming limit is identified.

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