Advanced friction modeling in sheet metal forming

The Coulomb friction model is frequently used for sheet metal forming simulations. This model incorporates a constant coefficient of friction and does not take the influence of important parameters such as contact pressure or deformation of the sheet material into account. This article presents a more advanced friction model for large-scale forming simulations based on the surface changes on the micro-scale. When two surfaces are in contact, the surface texture of a material changes due to the combination of normal loading and stretching. Consequently, shear stresses between contacting surfaces, caused by the adhesion and ploughing effect between contacting asperities, will change when the surface texture changes. A friction model has been developed which accounts for these microscopic dependencies and its influence on the friction behavior on the macro-scale. The friction model has been validated by means of finite element simulations on the micro-scale and has been implemented in a finite element code to run large scale sheet metal forming simulations. Results showed a realistic distribution of the coefficient of friction depending on the local process conditions

Multiscale analyses of fibre metal laminates

The advance of composites used in aerospace, civil and biomechanical engineering and other technology branches over the last decades has led to a substantial increase in the application of these materials. In addition, the search for new and improved materials in aerospace industry has stimulated the development of hybrid materials partly made out of composites, such as Fibre-Metal Laminates (FMLs). These materials are composed of alternatively stacked aluminium and fibre-reinforced composite layers such that the best features of both constituents are combined. FMLs also have additional advantages over conventional monolithic aluminium alloys and fibre-reinforced composites, such as an excellent fatigue and damage-tolerance behaviour. Furthermore, this class of materials possesses good fire, impact, damping, insulation and corrosion-resistance properties.To ensure a maximal reliability under service conditions, the failure mechanisms of FMLs must be well understood. The main mesoscale failure mechanisms that endanger their overall reliability are delamination between adjacent plies, cracking, and plasticity in individual metal layers. Important failure mechanisms at the microscale are debonding of fibres, fibre breakage, pull-out of broken fibres and crack growth in the epoxy matrix.Finite element simulations serve as an important tool for understanding the mechanical failure behaviour of FMLs in engineering applications. However, the performance of a direct numerical analysis of an engineering structure (e.g., an aircraft wing), where all features of the underlying heterogeneous microstructure are accounted for explicitly, requires an extremely fine finite element mesh and thus an impractical amount of computational time. A more efficient approach is to study engineering structures with the aid of mesoscale material models that account for the underlying microstructure in an average sense. The average properties in the mesoscale model can be computed using a numerical homogenization approach, where the microstructural stresses and deformations are averaged over a representative material volume. The present thesis comprises a detailed study of the failure behaviour of fibre-metal laminates at the meso- and microscale levels, and proposes a numerical homogenization framework that links specific failure mechanisms at these two levels of observation.Aerospace Engineerin

Transverse failure behavior of fiber-epoxy systems

The transverse failure response of unidirectional fiber-epoxy systems is studied by means of finite element simulations. An interface damage model is used for modeling fiber debonding and epoxy cracking. The convergence of the numerical results upon mesh refinement is analyzed. It is found that the failure response depends on the relative strength and relative toughness of the fiber-epoxy interface and the epoxy matrix. The tensile failure response of epoxy systems containing multiple fibers is also analyzed. In addition, the simulations demonstrate the influence on the failure response by the relative strength of the fiber-epoxy interface and the epoxy matrix, and by the fiber volume fraction and fiber distribution. The simulated fracture patterns are shown to be in good agreement with experimental observations reported in the literature

Multiscale modelling of the failure behaviour of fibre-reinforced laminates

The static failure behaviour of fibre-reinforced laminates is examined at the mesoscale and microscale levels of observation using finite element simulations. The actual cracking and delamination processes are simulated with interface elements equipped with a mixedmode damage model. The mesoscale simulations consider a fibre-metal laminate GLARE that is subjected to uniaxial tension. The effect of plasticity in the metal layers on the cracking and delamination processes in the laminate is analysed. The results for a brittle laminate are compared against a closed-form expression derived from energy considerations. In the microscale simulations the transverse failure response is studied of unidirectional fibre-epoxy systems subjected to uniaxial tension. The influence on the failure response by the relative strength of the fibre-epoxy interface and the epoxy matrix is demonstrated for single-fibre epoxy systems. For multiple-fibre epoxy systems the effect of the volume fraction on the failure response is assessed. Finally, the discrete, microscale fracture processes in thin fibre-epoxy layers are coupled to a mesoscale traction-separation law by means of a numerical homogenization approach. It is demonstrated how the effective traction-separation response and the corresponding microscale fracture patterns under mesoscale tensile conditions depend on the presence of microscale imperfections

A Multi-scale Friction Model for Sheet Metal Forming Simulations

This paper presents a multi-scale friction model for large-scale forming simulations based on the surface changes on the micro-scale. The surface texture of a material changes when it is subjected to normal loading and stretching. Consequently, the frictional behavior between contacting surfaces, caused by the adhesion and ploughing effect between contacting asperities, will change when the surface texture changes. A friction model has been developed which accounts for the change of the surface texture on the micro-scale. Statistical parameters have been introduced to make a fast and efficient translation from micro to macro modeling. The flattening models are validated by means of FE simulations on micro-scale and the implementation of the advanced macroscopic friction model in FE codes is discussed

Computational homogenization of discrete fracture in fibre-epoxy systems

In the present paper the effective mesoscale failure response of a ¿bre-epoxy sample is computed from its complex microscale fracture behaviour. The mesoscale failure response is represented by a traction-separation curve derived from numerically homogenizing the fracture response of a periodic ¿bre-epoxy microstructure loaded under uniaxial tension. The traction-separation curve can be applied in material points of interface elements that are used for simulating mode I mesoscopic fracture in macroscopic laminate failure problems. The size of the microscopic ¿bre-epoxy sample on the mesoscale failure response is examined, as well as the effect of local imperfections at ¿bre-epoxy interfaces

Analysis of fracture and delamination in laminates using 3D numerical modelling

The static failure behaviour of the fibre–metal laminate GLARE is examined using 3D finite element simulations. The configuration analysed is a centre-cracked tensile specimen composed of two aluminium layers sandwiching a cross-plied, fibre-epoxy layer. The crack and delamination growths are simulated by means of interface elements equipped with a mixed-mode damage model. The mode-mixity is derived from an energy criterion typically used in linear elastic fracture mechanics studies. The damage kinetic law is rate-dependent, in order to simulate rate effects during interfacial delamination and to avoid numerical convergence problems due to crack bifurcations. The numerical implementation of the interface damage model is based on a backward Euler approach. In the boundary value problem studied, the failure responses of GLARE specimens containing elastic aluminium layers and elasto-plastic aluminium layers are compared. The development of plastic deformations in the aluminium layers stabilizes the effective failure response, and increases the residual strength of the laminate. For a ‘quasi-brittle’ GLARE specimen with elastic aluminium layers, the residual strength is governed by the toughness for interfacial delamination, and is in close correspondence with the residual strength obtained from a closed-form expression derived from energy considerations. Conversely, for a ‘ductile’ GLARE specimen with elasto-plastic aluminium layers, the residual strength is also determined by the relation between the fracture strength and the yield strength of the aluminium. The amount of constraint by the horizontal displacements at the vertical specimen edges has a moderate to small influence on the residual strength. Furthermore, the ultimate laminate strength is lower for a larger initial crack length, and shows to be in good correspondence with experimental values