The simplified method called Inverse Approach (I.A.) has been developed by Batoz, Guo et al.[1] for the sheet forming modelling. They are less accurate but much faster than classical incremental approaches. The main aim of the present work is to study the feasibility of the I.A. for the axi-symmetric forging process modelling. In contrast to the classical incremental methods, the I.A. exploits the known shape of the final part and executes the calculation from the final part to the initial billet. Two assumptions are used in this study: the assumption of proportional loading for cold forging gives an integrated constitutive law without considering the strain path and the viscoplasticity, the assumption of contact between the part and tools allows to replace the tool actions by nodal forces without contact treatment. The comparison with Abaqus shows that the I.A. can obtain a good strain distribution and it will be a good tool for the preliminary preform design.
A simplified method called “Pseudo Inverse Approach” (PIA) has been developed for the axi-symmetrical cold forging modeling in this paper. The traditional “Inverse Approach” (IA) based on the assumptions of the proportional loading and simplified tool actions may quickly give a fairly good strain distribution, but poor stress estimation. Meanwhile the PIA proposed in this paper not only keeps the advantages of the Inverse Approach but also gives good stress estimation by taking into account the loading history. To fulfill this aim, some kinematically admissible intermediate configurations represented by the free surface are used to consider the deformation paths without classical contact treatment. A new direct algorithm of plasticity integration has been used by using the notion of equivalent stress and the tensile curve, leading to a very fast and robust plastic integration procedure. An axi-symmetrical forging has been taken as an example to validate the PIA.
This paper presents a fast plastic integration algorithm and compares it with other algorithms for forming process simulations. The iterative Return Mapping Algorithm (RMA) is widely used owing to its accuracy and efficiency, but it is still time consuming and may cause divergence problems. Another algorithm based on the Incremental Deformation Theory (IDT) was proposed, using the deformation theory of plasticity by piecewise; it is very fast but could not well consider the loading history, leading to notable errors. The new Direct Scalar Algorithm (DSA) based on the flow theory of plasticity is proposed in this paper. The basic idea is to transform the constitutive equations in terms of the unknown stress vectors into a scalar equation in terms of the equivalent stresses which can be determined by using the experimental tensile curve; thus, the plastic multiplier λ can be directly calculated without iterative solution. The DSA is a fast and robust plastic integration algorithm. The comparison of the results obtained by using the three algorithms shows the accuracy and efficiency of the DSA.
Numerical modeling of honeycomb structures is too tedious and time consuming. The homogenization of these structures enables to obtain an equivalent homogeneous solid and its elastic stiffness thus to make very efficient simulations. In the present study, the skin effect is taken into consideration for the in-plane shear and torsion problems, in which the two skins are much more rigid than the honeycomb core. An analytic homogenization method, using trigonometric function series and based on the membrane plate theories, is proposed to study the influence of the honeycomb height on these properties, and the upper and lower bounds of the equivalent elastic stiffness of their curves are analyzed. A numerical H-model is established for the in-plane shear and torsion problems.
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