Study of the geometrical inaccuracy on a SPIF two-slope pyramid by finite element simulations

in International Journal of Solids and Structures (2012)

Single Point Incremental Forming (SPIF) is a recent manufacturing process which can give a symmetrical or asymmetrical shape to an undeformed metal sheet by using a relative small tool. In this article, a ... [more ▼]

Single Point Incremental Forming (SPIF) is a recent manufacturing process which can give a symmetrical or asymmetrical shape to an undeformed metal sheet by using a relative small tool. In this article, a two-slope SPIF pyramid with two different depths, which suffers from large geometric deviations when comparing the intended and final shapes, is studied. The article goal is to detect if these divergences are due to new plastic strain while forming the second angle pyramid by using finite elements simulations. To validate the numerical results, both the shape and the forces are compared with experimental measurements. Then, an analysis of the material state is carried out taking the equivalent plastic strain, von Mises effective stress and yield stress distribution through a cut in the mesh. It is noticed that there is plastic deformation in the center of the pyramid, far from the tool neighbourhood. Also, high values of stresses are observed under the yield stress in other parts of the sheet. As a strong bending behaviour plus membrane tension is found in some sheet elements, these elastic stresses are due to a bending action of the tool. It is concluded that the main shape deviations come from elastic strains due to structural elastic bending, plus a minor contribution of localized springback, as no plastic deformation is observed in the angle change zone. Future developments in toolpath designs should eventually consider these elastic strains in order to achieve the intended geometry. [less ▲]

A two-scale model for subcritical damage propagation

in International Journal of Solids and Structures (2010), 47(3-4), 493-502

The failure behaviour of quasi-brittle materials is often time-dependent. This dependence is due to physical processes taking place at the level of the micro-structure. For a rigorous modeling of the time ... [more ▼]

The failure behaviour of quasi-brittle materials is often time-dependent. This dependence is due to physical processes taking place at the level of the micro-structure. For a rigorous modeling of the time-dependent behaviour of that kind of solids, a two-scale approach is well suited. This paper investigates time-dependent damage which microscopic origin is the subcritical micro-crack growth. We present a two-scale time-dependent damage model completely deduced from small-scale descriptions of subcritical micro-crack propagation, without any macroscopic assumptions. The passage from the micro-scale to the macro-scale is done through an asymptotic homogenization approach. At the micro-scale, the tensile failure due to the subcritical propagation of cracks is the dominant mechanism of creep observed at the macro-scale. We consider microstructures with cracks evolving in different subcritical regimes. We assume a complex propagation law that considers three characteristic regimes of subcritical crack growth, corresponding to different physical processes at the crack tip level. Numerical simulations of constant strain rate, relaxation and creep tests illustrate the ability of the developed model to reproduce different regimes of time-dependent damage response. [less ▲]

Thermomechanical modeling of metals at finite strains: First and mixed order finite elements

in International Journal of Solids and Structures (2005), 42(21-22), 5615-5655

The aim of this paper is to describe an updated EAS (Enhanced Assumed Strain) finite element formalism developed to model the thermomechanical behavior of metals submitted to large strains. We will also ... [more ▼]

The aim of this paper is to describe an updated EAS (Enhanced Assumed Strain) finite element formalism developed to model the thermomechanical behavior of metals submitted to large strains. We will also expose the use of mixed order elements (first order mechanical elements strongly coupled with quadratic thermal elements) which, as we will show, is of particular interest for modeling fast processes inducing important temperature gradients. The features of this formalism, used jointly with an Updated Lagrangian approach and an hypoelastic anisothermal constitutive formulation, will be described. Three applications involving finite strains and important thermomechanical couplings will be studied. The results obtained will be compared with the results given by the now classical SRI (Selective Reduced Integration) formalism. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲]

An equilibrium model for plate bending

in International Journal of Solids and Structures (1968), 4

A conforming displacement model for plate bending was presented earlier. It is of intyerest to have also an equilibrium moàdel available in order to generate both upper and lower bounds to plate ... [more ▼]

A conforming displacement model for plate bending was presented earlier. It is of intyerest to have also an equilibrium moàdel available in order to generate both upper and lower bounds to plate deflections. The theory of the triangular equilibriium model, which is presented here, takes advantage of oblique coordinates. Il allows to cover transvers loading modes. Because the numerical investigations required adaptibility of the model to a stiffness computer-program, only the elaboration of the stiffness matrix was aimed at. The element can nevertheless be recognised as the Southwell analogue of the plane stress model with quadratic displacement field. As such it can be handled efficiently by a force program. Numerical results show the monotonic convergence of deflections from above for the equilibrium model and from below for the conforming model. The convergence rate, in terms of generalized coordinates, is compâred with that of other plate bending elements. [less ▲]