Forming limit diagram
Encyclopedia
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
).
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 occurs. Through repeated experimental 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.
However 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 range of alloys, the forming process and alloy behaviour can be matched at the metalworking design time by the process engineer.
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.
, n, the initial sheet thickness, t0 and the strain rate hardening coefficient, m. The lankford coefficient
, r, which defines the plastic anisotropy
of the material, has two effects on the forming limit curve. On the left side there is no influence except that the curve extends to larger values, on the right hand side increasing r values reduce the forming limits.
as a simulation tool which is widely used in a production environment.
Sheet metal
Sheet metal is simply metal formed into thin and flat pieces. It is one of the fundamental forms used in metalworking, and can be cut and bent into a variety of different shapes. Countless everyday objects are constructed of the material...
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
Formability
Formability is the ability of a given metal workpiece to undergo plastic deformation without being damaged. The plastic deformation capacity of metallic materials, however, is limited to a certain extent....
).
Description
The semi-axes of the ellipse formed in this circle allow for the measurement of relative strainDeformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...
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 occurs. Through repeated experimental 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.
However the diagram is obtained, the resultant diagram provides a tool for the determination as to whether a given forming
Work hardening
Work hardening, also known as strain hardening or cold working, is the strengthening of a metal by plastic deformation. This strengthening occurs because of dislocation movements within the crystal structure of the material. Any material with a reasonably high melting point such as metals and...
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 range of alloys, the forming process and alloy behaviour can be matched at the metalworking design time by the process engineer.
Modern determination
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.
Influence parameters
Forming limit curves (FLC) for four steel sheet grades are displayed in the attached figure. All forming limit curves have essentially the same shape. A minimum of the curve exists at the intercept with the major strain axis or close thereby, the plane strain forming limit. With the definition of the onset of local necking (e. g. membrane force reaches an extreme value) and the assumption of a hardening law according to Hollomon (σ = K εn) it can be shown that the corresponding theoretical plane strain forming limit is identical with the strain hardening coefficient, n. There is no thickness effect. Taking into account the strain rate sensitivity of the material, which is obvious in steel, along with the sheet thickness, the fact can be explained that practical forming limits, obtained by the use of the above described method, lie well above theoretical forming limits. Thus the basic influence parameters for the forming limits are, the strain hardening exponentStrain hardening exponent
The strain hardening exponent , noted as n, is a materials constant which is used in calculations for stress-strain behaviour in work hardening....
, n, the initial sheet thickness, t0 and the strain rate hardening coefficient, m. The lankford coefficient
Lankford coefficient
The Lankford coefficient is a measure of the plastic anisotropy of a rolled sheet metal. This scalar quantity is used extensively as an indicator of the formability of recrystallized low-carbon steel sheets....
, r, which defines the plastic anisotropy
Anisotropy
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...
of the material, has two effects on the forming limit curve. On the left side there is no influence except that the curve extends to larger values, on the right hand side increasing r values reduce the forming limits.
M-K method
There is a widely used method for computation of FLCs, introduced by Marciniak in 1967. It assumes an inclined band in the investigated plane sheet piece with smaller thickness which denotes an imperfection. With this model limit strains can be calculated numerically. The advantage of this method is that any material model can be used and limits can also be obtained for nonproportional forming. However there is one drawback. Calculated forming limits are sensitive to the imperfection value. With the assumption of a strain rate sensitive material model realistic forming limits may be obtained which lie above theoretical limit strains. Basically with this calculation method smooth forming limit curves are generated for materials for which only one experimental value exists. A good overview of state of the art about FLC calculation methods is given in the proceedings of a conference held in Zurich in 2006 and the Numisheet conference in 2008.Use of FLCs
For many years forming limit curves have been used in order to assess the sheet material formability. They have been applied in the design stage of tools using the finite element methodFinite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
as a simulation tool which is widely used in a production environment.