3-D stamp forming of thermoplastic matrix composites

In this investigation a mould with hemispherical cavity and 80 kN hydraulic press, allowing variable stamping speeds, are employed for experimentally studying of the 3-D stamp forming process of continuous fiber reinforced thermoplastic laminates. In particular, glass fiber (GF) reinforced polyetherimide (PEI) woven fabric made of sheath surrounded, polymer powder impregnated fiber bundles manufactured by Enichem, Italy, is used. Pre-consolidated laminates are heated by contact heating in an external heater up to about 120°C above the glass transition temperature (T _g) of the polymer matrix; they are then stamp formed in a cold matched metal tool. Typical cycle times (including preheating time of the preconsolidated laminates) are in the range of 3 min. Useful processing conditions, such as stamping temperature, stamping velocity and hold-down pressure required for stamp forming of this composite are determined. In addition the effect of die geometries (deformation radian) and original laminate dimensions are studied. The results describe the correlations between processing parameters and fiber buckling. Finally the thickness distribution in stamped parts are investigated in relation to different directions of fiber orientation.     

Localised blast loading of fibre–metal laminates with a polyamide matrix

This paper presents the results of localised blast tests on fully clamped square fibre–metal laminate panels, manufactured using sheets of 2024-O aluminium alloy, woven glass–fibre reinforced polyamide and a polypropylene adhesive. The fracture properties of the composite–metal interface were determined using the single cantilever beam geometry and the measured interfacial fracture toughness was between values in the literature for thermosetting composites and aluminium/glass fibre polypropylene. Observations from blast experiments performed on panels with different stacking configurations are reported. Diamond and circular back face damage were observed, along with pitting, global displacement and tearing of the front face. Examinations of sectioned panels are presented and multiple debonding, plastic deformation and fibre fracture were identified within the panels.     

A finite element model for thermomechanical analysis of sheet metal forming

A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin‐walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature‐dependent elastic–plastic model with a non‐linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one‐sided forming and quenching experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Non-linear characterization of PP/Twaron laminates based on a model of plasticity with damage

The non-linear stress–strain response of thermoplastic laminates was investigated for a polypropylene matrix composite reinforced with continuous Twaron fibers. Tensile tests were performed on unidirectional composites with a fiber orientation of [0]₅, [24]₅, [33]₅, [45]₅ and [90]₅ and also on a [±45]_2S laminate. The inelastic strains of these materials were described with a modification made to a model of plasticity with damage, originally proposed by Ladeveze (1992). This approach considers the longitudinal plasticity and stiffening behavior of a thermoplastic composite, and models the damaged elastoplastic stress–strain response of the material. The theoretical stress–strain curves and experimental results from the model composites [0]₅, [90]₅ and [±45]_2S were compared, demonstrating that the model can be used as a designing tool for laminated thermoplastic composites.     

Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.     

Optimal process design in non-isothermal,non-steady metal forming by the finite element method

A new approach to process optimal design in non-isothermal, non-steady-state metal forming is presented. In this approach, the optimal design problem is formulated on the basis of the integrated thermo-mechanical finite element process model so as to cover diverse objective functions and design variables, and a derivative-based approach is adopted for conducting optimization. The process model, the formulation for process optimal design, and the schemes for the evaluation of the design sensitivity, and an iterative procedure for optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach to deal with diverse process parameters and objective functions is demonstrated through applications to some selected process design problems. © 1998 John Wiley & Sons, Ltd.     

Analysis of superplastic metal forming by a finite element method

A finite element velocity method for analysing the superplastic sheet metal forming process is presented. This method is developed from the principle of virtual work and is based on the use of isoparametric continuum elements. The large inelastic deformation of the superplastic material is modelled as the behaviour of an incompressible non-linear viscous flow material. The contact and friction problem is solved by using the compatibility load step method, which is an extension of an earlier work. The finite element method is applied to selected problems to illustrate the applicability of the solution procedure.     

Process optimal design in non‐isothermal,steady‐state metal forming by the finite element method

A new approach to process optimal design in non‐isothermal, steady‐state metal forming is presented. In this approach, the optimal design problem is formulated on the basis of the integrated thermo‐mechanical finite element process model so as to cover a wide class of the objective functions and to accept diverse process parameters as design variables, and a derivative‐based approach is adopted as a solution technique. The process model, the formulation for process optimal design, and the schemes for the evaluation of the design sensitivity, and an iterative procedure for design optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach is demonstrated through applications to some selected process design problems. Copyright © 1999 John Wiley & Sons, Ltd.     

The inside–outside contact search algorithm for finite element analysis

A new contact search algorithm (Inside–Outside Algorithm) for the sheet forming simulation has been developed and implemented in the dynamic explicit FE code: ‘DYNAMIC’. The inside–outside algorithm is derived based on the feature of the inside–outside status of a nodal ‘mesh normal vector’ in respect to a surface segment for the judgment of the contact of FE nodes with the tool surface. This new algorithm includes local search, local track and penetration calculation processes. Almost no additional CPU time is required for the local search process, because the calculations for both global and local search are combined. Moreover, the problems of conventional contact searching algorithms, such as iterations for local search and the deadzone problem, are resolved. Therefore, the quick, robust contact searching and accurate evaluation of penetration have been achieved. The numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones. © 1997 John Wiley & Sons, Ltd.     

Fatigue damage development in new fibre metal laminates made by the VARTM process

This paper investigates the tensile and fatigue properties of a newly developed fibre metal laminate (FML) manufactured using the vacuum assisted resin transfer moulding (VARTM) method. This manufacturing method allows the glass fibre reinforced epoxy and 2024‐T3 aluminium FML to be prepared at lower cost than conventionally manufactured FMLs. However, in order for the resin to infiltrate the FML, the metal sheets need to be perforated. These perforation holes act as crack initiators and reduce the FML's performance. Tension and fatigue test results of three different designs are reported and compared to mechanical property predictions. Additionally, single sheet Al alloy specimens were tested in order to analyse the influence of the drilling method.     

A semi‐discrete shell finite element for textile composite reinforcement forming simulation

A triangular shell element for the simulation of textile composite reinforcements forming is proposed. This element is made up of unit woven cells. The internal virtual works are added on all woven cells of the element. They depend on tensions, in‐plane shear and bending moments that are directly those given by the experimental tests that are specific to textile composite reinforcement. The element has only displacement degrees of freedom; the bending curvatures are obtained from the displacement of the neighbouring elements. A set of example shows the efficiency of the approach and the relative roles of the tensile, in‐plane shear and bending rigidities. Especially their influence on the appearance and the development of wrinkles in draping and forming tests is analysed. Copyright © 2009 John Wiley & Sons, Ltd.     

The s-version of the finite element method for multilayer laminates

A methodology has been developed to accurately resolve the stress field in the vicinity of free edges as well as the overall response of laminated plates without significantly affecting the computational cost. This is accomplished by enriching a set of classical smooth interpolants throughout the thickness direction with C° continuous displacement interpolants (piecewise continuous strain field) in the regions where the most critical behaviour is anticipated. C° continuity of the displacement field is maintained by imposing homogeneous boundary conditions on the superimposed field in the portion of the boundary which is not contained within the boundary of the problem. Numerical experiments for both cylindrical bending and uniform extension of cross-ply laminates are presented to validate the present formulation.     

Efficient implicit finite element analysis of sheet forming processes

The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time‐savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton–Raphson iterations. This also applies to quasi‐static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd.     

A simple integration algorithm for a non‐associated anisotropic plasticity model for sheet metal forming

In this paper, an anisotropic material model based on a non‐associated flow rule and nonlinear mixed isotropic‐kinematic hardening is developed. The quadratic Hill48 yield criterion is considered in the non‐associated model for both yield function and plastic potential to account for anisotropic behavior. The developed model is integrated based on fully implicit backward Euler's method. The resulting problem is reduced to only two simple scalar equations. The consistent local tangent modulus is obtained by exact linearization of the algorithm. All numerical development was implemented into user‐defined material subroutine for the commercial finite element code ABAQUS/Standard. The performance of the present algorithm is demonstrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Applications of linear inverse finite element method in prediction of the optimum blank in sheet metal forming

A linear inverse finite element method has been developed and investigated to predict the optimum blank. To reduce the computation time, the part is unfolded properly on the flat sheet and treated as a 2D problem. This approach is employed primarily to design the optimum blank shape from the desired final shape with the linear formulations. The procedure is based on the minimization of energy for the unfolded elements. Two solution methods, Direct and Newton–Raphson methods have been examined for the solution of nodal displacements in the equilibrium equations. The convergence show high sensitivity to the initial guess for the strain path when assumed to be linear at the first step. Two applied examples are implemented to show the efficiency of this method. In S rail example, the thickness distributions have been compared with experimental analysis after obtaining the optimum blank with Linear IFEM. In circular cup example, the results have been compared with conventional forward incremental method. New calculation of the external forces vector has been displayed. In this calculation, both blank holder force (BHF) vector and in-plane force vector have been shown. Finally, in this approach good agreement was found between the forward incremental and Linear IFEM results.     

A new rigid‐viscoplastic model for simulating thermal strain effects in metal‐forming processes

A new rigid‐viscoplastic model that includes the effect of thermal strains when modelling steady‐state metal‐forming processes was developed. A symmetric approximation to the resulting non‐symmetric stiffness matrix was derived. The thermo‐mechanical flow formulation was implemented using the pseudo‐concentrations technique. The new formulation was numerically tested showing that it provides reliable results. Copyright © 2003 John Wiley & Sons, Ltd.     

A mesh re-zoning technique for finite element simulations of metal forming processes

Based on some fundamental properties of finite element approximations, a mesh re-zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analysing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.     

Adaptive generation of hexahedral element meshes for finite element analysis of metal plastic forming process

A method for the adaptive generation of hexahedral element mesh based on the geometric features of solid model is proposed. The first step is to construct the refinement information fields of source points and the corresponding ones of elements according to the surface curvature of the analyzed solid model. A thickness refinement criterion is then used to construct the thickness-based refinement information field of elements from digital topology. The second step is to generate a core mesh through removing all the undesired elements using even and odd parity rules. Then the core mesh is magnified in an inside–out manner method through a surface node projection process using the closest position approach. Finally, in order to match the mesh to the characteristic boundary of the solid model, a threading method is proposed and applied. The present method was applied in the mesh construction of different engineering problems. The resulting meshes are well-shaped and capture all the geometric features of the original solid models.