Elsevier

Composite Structures

Volume 238, 15 April 2020, 111926
Composite Structures

A micromechanical-based finite element simulation of process-induced residual stresses in metal-CFRP-hybrid structures

https://doi.org/10.1016/j.compstruct.2020.111926Get rights and content

Abstract

Automotive lightweight design is a considerable measure to meet the worldwide need for reducing CO2 emissions. However, the lightweight potential of common materials like high strength steels or aluminium is limited. Hybrid materials allow to combine metals and CFRP in a manner to offset the drawbacks of every single material and reach an optimum of mechanical properties (Wang et al., 2016). Nonetheless, an essential shortcoming of hybrids are thermally induced residual stresses after cooling down from moulding temperature, driven by varying coefficients of thermal expansion and chemical shrinkage of the FRP.

For a reliable prediction of the residual stress evolution in hybrid-structures during curing and after cooling down, a numerical homogenization technique of representative unit cells is proposed to calculate effective cure-dependent properties. Starting from a heterogeneous microstructure, a thermo-chemical-mechanical constitutive model for the curing process of the epoxy resin is presented and applied to two representative volume elements (RVE). The transition between the micro- and macro-scale is done by using a numerical homogenization framework. The effective cure-dependent properties predicted by the homogenization are used to simulate the curing-process and analyses the residual stresses of a metal-CFRP plate. The results are compared with experimental data obtained by the incremental hole drilling measurement.

Introduction

Time- and cost-efficient production of metal-CFRP hybrids can be achieved if the bonding between the components and the actual component production are integrated into a single process step [1], [2], [3], [4]. Such intrinsic hybridization offers the advantage that the process steps required for component production can be reduced in total. Nonetheless, an essential shortcoming of intrinsic hybrid materials are thermally induced residual stresses after cooling down from the moulding temperature to ambient temperature, driven by varying coefficients of thermal expansion and chemically induced shrinkage of the CFRP.

The classification of residual stresses is made in [5] according to their origin in three main groups. This is first of all the microscopic level on which residual stresses are caused by varying coefficients of thermal expansion of fiber and matrix, as well as the chemical shrinkage of the matrix. On the next higher laminate level, the residual stresses result from the different orientation of adjacent laminates, which show a transverse isotropy of thermal expansion due to microscopic heterogeneity. On the macroscopic component level, the formation of residual stresses as a result of inhomogeneous temperature fields across the component domain is described. Different cooling rates between the inner and outer laminate layers lead to ”skin core stresses”, which are typically parabolic in the thickness direction [5]. A holistic assessment of the development of residual stresses therefore requires a multiscale approach. Numerical simulation methods are excellently suited to analyze and optimize influencing parameters such as fiber volume content, laminate structure or process parameters. For microscopic simulation of fiber matrix structures, numerous efforts have been made to describe the complex behavior of curing adhesives. The complexity here consists in the coupling of the chemical, thermal and mechanical behaviour, which has to be considered due to the phase transformation from viscous fluid to cured solid. The curing kinematics is usually modelled with a phenomenological model of Kamal and Sourour [6]. Numerous studies confirm the high quality of the model by showing the good agreement with experimentally measured results [7], [8], [9], [10]. The modeling of the viscous, cure-dependent behavior is treated with varying complexity, which can be categorized into three approaches [8]. In [7], simplified analytical approaches based on the classical laminate theory that take into account the cooling from the curing temperature have been presented. A major disadvantage is that the method is limited to flat, two-dimensional plates and that the ability to predict asymmetric layer structures and varying laminate thicknesses is significantly reduced. Residual stresses that arise during the curing process cannot be recorded with this method. In [11], an extension by means of viscoelasticity was developed to capture the hardening process. The classical laminate theory continues to serve as the basis for this model. Studies show that the predictive capability of this model is limited. More advanced constitutive models are based on incremental elasticity [12], [11], [13], [14]. The elasticity constants are stored as a function of temperature and degree of cure and are thus able to describe the development of residual stresses during the curing process. In numerous studies the model is used for micro- and macroscopic process simulation of fiber-plastic composites [15], [16], [17], [18], [19]. The relaxation of stresses during and after curing due to viscoelasticity is neglected. Thus, relaxation, temperature and strain rate dependencies are ignored. Approaches for modeling viscoelasticity are based on the integral form. The description of the shear modulus uses the Prony series approach. The changes of the equilibrium modulus and Prony coefficients caused by curing are described by phenomenological models. The viscoelasticity of the bulk modulus is neglected in numerous studies and only an incremental elasticity is considered for the development of the elastic bulk modulus. The work of [20] illustrates on the one hand the efficiency of such models. On the other hand the application of these models is limited due to the high experimental effort, which is necessary for a complete characterization.

Microscopic analyses of representative volume elements of a fibre-plastic composites to determine residual stresses during curing have been performed in [17], [18], [21], among others. Furthermore, in these work the influence on the initiation and evolution of damage caused by the curing stress were also investigated. The simulation of subsequent transversal loads was performed to predict the global macroscopic deformation behavior and was compared with experimental data.

A holistic investigation from the heterogeneous microstructure to the component domain requires the application of multiscale methods. In [22], [10] a multi-scale approach for the calculation of effective, cure-dependent elastic properties was presented. The mixture theory has been used in [15] for the calculation of effective elasticity parameters. However, analytical homogenization methods cannot be used to investigate influence of the morphology of microstructures.

In order to get a proper knowledge of process induced residual stresses across diffrent length scales a numerical simulation approach is presented. For this purpose, first a material model o simulate the curing of the epoxy resin of the CFRP at the microscale is presented. For this purpose different unit cells were used to predict the residual stress state at the microscale during curing and after cooling down to ambient temperature. With the help of the numerical homogenization method, microscopic unit cells were used to determine effective cure dependent material properties. These analyses forms the basis for the third section. Here, the curing and simultaneous hybridization of a metal CFRP composite is simulated and residual stresses are determined. The results of the analyse are compared with and validated by experimental results obtained with the hole drilling-method.

Section snippets

Constitutive modelling of epoxy resin during curing

The following section presents the implemented material model for modeling the curing process of epoxy resin. The model can be divided into three main parts. These are the temperature-driven curing kinematics, the cross-linking dependent viscoelasticity, as well as the thermal expansion and the chemical shrinkage. The implementation was carried out as a user material subroutine (UMAT) in the finite element software Abaqus/Standard. The prepreg system SGL Sigapreg E320 was used for the

Microscopic residual stress analysis

As representative volume element (RVE) a three-dimensional hexagonal packed unit cell as well as a unit cell with real microstructure distribution, derived from images of a light microscope, is used. Plasticity, pores and damage have not been considered in these models. The fiber volume content for the idealized unit cell is 50%. The fibers are modelled as transversal isotropic solids and have a diameter of 8 μm. Accordingly, the dimension of the unit cell is 18.661 μm × 10.774 μm × 1 μm. The

Simulation of an intrinsic hybridization process of a steel-CFRP-plate

In the following section, the homogenized material is applied for the curing and simultaneous hybridization simulation of a flat steel CFRP hybrid. The CFRP is modelled as a transversally isotropic, unidirectional laminate. The steel plate is modelled as a linear elastic solid (See Table 5). The constituents are ideally bonded from t=0 by a tie-constraint. An uncoupled temperature displacement analysis was selected for the simulation. The temperature field is homogeneous and prescribed over the

Summary and conclusions

In this paper a numerical homogenization framework for residual stress analysis in metal-CFRP-hybrids across different length scales is presented. Taking the manufacturing process into account, a coupled thermo-chemical-mechanical material model was implemented and used for the prediction of residual stress during curing and after cooling down from moulding temperature at the microscale of the CFRP. Stresses up to approximately 30 MPa are reached after the manufacturing process at the

Acknowledgements

This research was supported by the Deutsche Forschungsgemeinschaft (DFG), projectnumber 399304816. The authors gratefully acknowledge for the financial support. The authors gratefully acknowledge the funding of this project by computing time provided by the Paderborn Center for Parallel Computing (PC2).

References (42)

  • N. Rabearison et al.

    A fem coupling model for properties prediction during the curing of an epoxy matrix

    Comput Mater Sci

    (2009)
  • R. Hill

    Elastic properties of reinforced solids: some theoretical principles

    J Mech Phys Solids

    (1963)
  • R. Hill

    Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour

    J Mech Phys Solids

    (1964)
  • R. Hill

    Theory of mechanical properties of fibre-strengthened materials: Ii. Inelastic behaviour

    J Mech Phys Solids

    (1964)
  • R. Hill

    A self-consistent mechanics of composite materials

    J Mech Phys Solids

    (1965)
  • R. Hill

    Theory of mechanical properties of fibre-strengthened materialsiii. Self-consistent model

    J Mech Phys Solids

    (1965)
  • A. Tran et al.

    A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials

    Comput Methods Appl Mech Eng

    (2011)
  • E. Barbero et al.

    Micromechanical formulas for the relaxation tensor of linear viscoelastic composites with transversely isotropic fibers

    Int J Solids Struct

    (1995)
  • Wang Z, Lauter C, Sanitther B, Camberg A. Manufacturing and investigation of steel-cfrp hybrid pillar structures for...
  • Wang Z, Riemer M, Koch S-F, Barfuss D, Grtzner R, Augenthaler F, Schwennen J. Intrinsic hybrid composites for...
  • R. Kießling et al.

    On the development of an intrinsic hybrid composite

    Conf Ser: Mater Sci Eng

    (2016)
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