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1. Geometric and mechanic model of mold

Mold has higher rigidity than sheet. In general, mold is used as rigid body. When referring to frictional wear, mold also should be considered to be used as elastic plastic body. Geometrical shape of mold can be described by using finite element mesh. It also can be described by using analytical surface or CAD surface. CAD surface has high geometric accuracy, which requires particular processing algorithm of contact interface. Movement of punch is described as given displacement or velocity. Blank holder is usually only limited to move in stamping direction. Degree of freedom of fixed die is completely limited. 

 

2. Deformation pattern of sheet and shell element

At present, almost all of simulation software of covering parts stamping assume that deformation patterns of sheet conform to some shell theories, ignoring the influence thickness stress of sheet during forming. Stress in beading or region having relatively smaller bending radius is nearly close to three dimensional state. The impact of simulation result to forming under state of local three-dimensional stress has already begun to attract attention from researchers. Shell element is commonly used as low order bilinear unit including trigonal and quardrilateral elements. Low-order elements are not only convenient for calculation and processing on contact interface, but also are the most suitable for simulation algorithm.

 

3. Constitutive model of sheet

Sheet used for stamping auto covering parts has obvious orthotropy caused by work hardening during rolling. So, when structuring criterion of sheet and flow rule, anisotropism is important. Meanwhile, what should be noticed that stamping can change anisotropism of sheet. Barlat model, Hill model and their modifications are mostly used. In terms of simulation for sheet stamping, calculation of constitutive model is also critical. Stress in plastic deformation region cannot only meet yield criterion, but also meet assumption that thickness stress is zero in plate theory, which increasing difficulty for calculation of sheet plastic deformation. Research shows that return mapping algorithm under plane stress has high precision and few calculation effort.

 

4. Theory and algorithm of contact friction

Stamping of auto covering parts completely depends on contact force and friction of sheet. So, computational accuracy of contact force and friction has direct influence on computational of sheet deformation. Calculation of contact force and friction is firstly requested that can figure out actual contact in any given moments, which is called as contact searching. In finite element algorithm, calculating contact area is to find out all of contacting finite element nodes. Although contact searching is a process of geometric calculation in fact, it still has critical mechanical meanings.

 

Calculation of contact force has two basic algorithms: penalty function and lagrangian multiplier. Penalty function is an approximate algorithm which allows contacting boundary to cause penetration and contact contact force with boundary penetration. The algorithm is quite simple, suitable for explicit algorithm. However, it affects crash time in explicit algorithm and reversibility of coefficient matrix in computer in implicit algorithm. Quality of penalty factors also has impact on reliability of result. Lagrangian multiplier does not allow contact boundary to penetrate with each other, an accurate contact force algorithm. However, it cannot be consistent with explicit algorithm, requiring particular numerical treatment. Defense node is such an algorithm. 

 

Calculation of friction firstly requires a friction law suitable for friction features of two contact interfaces. Nowadays, traditional coulomb law of friction is the most commonly used. However, the law has the assumption of pure adhesion state, increasing difficulty on explicit algorithm. To overcome the difficulty, penalty function or defense node are adopted to figure friction force under state of pure adhesion. In implicit algorithm, frictional sliding can result in asymmetric coefficient matrix, growing difficulty on figuring out. In recent years, some scholars come up with nonlinear friction law instead of the assumption of pure adhesion in traditional friction law on the base of experiment and observation, providing convenience to explicit algorithm. Surface rigidity coefficient used for nonlinear friction law is chosen based on physical and chemical features of two contact surfaces. And there is no sufficient experimental data used for reference.