CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

Material Models for Metallic Materials

Metals are the dominant material group for the body-in- white. A CAE based development includes the metal forming simulation of the different parts and the simulation of misuse and crashworthiness of subcomponents and the whole body- in-white. The phenomenological models for the elastovisco- plastic behaviour and failure initiation of metals are discussed in general. The implementation of those models can differ between the commercial FEA codes. A comprehensive material model must cover the following effects: „ „ Description of elastic material behaviour „ „ Stress state dependent criterion for the onset of a plastic deformation (stress yield locus) and criterion for derivation of plastic strain components (plastic potential) „ „ Model for strain hardening and strain rate sensitivity (in case of pronounced viscoplastic behaviour) „ „ Criteria for onset of material failure (mainly strain-based for metallic materials) Elastic Behaviour The elastic behaviour of metals is assumed to be linear. For most technical alloys the elastic properties are assumed to be isotropic on a macroscopic scale (single grains can exhibit a pronounced orthotropy of the elastic properties). Isotropic linear-elastic behaviour can be described by 2 independent values, for example by the „ „ Young’s modulus E with σ = ε Ε and the „ „ shear modulus G with τ = γ G „ „ From these values two further dependent elastic constants may be derived: Yield Locus and Plastic Potential The proportional limit R p or the technical 0.2% yield strength of a tensile test indicates the onset of plastic deformation in metallic materials. In a finite element analysis a criterion for the onset of plastic deformation is needed for general multiaxial stress states. The yield locus is used for this purpose. Figure 1 shows the yield locus according to von Mises in the stress space. Stress states inside the cylinder are still elastic. Stress states on the cylinder shell indicate the onset of plastic flow. The body diagonal in Figure 1 represents the hydrostatic stress p. As volume constancy is assumed for the plastic „ „ bulk modulus K: „ „ Possion’s ratio ν:

deformation of metals the onset of plastic deformation is not influenced by the level of hydrostatic stress. In case of a plane stress condition (σ 3 =0) for shell elements the yield locus reduces to an ellipse in the σ 1 -σ 2 -plane. Typically an associated flow rule is applied for metallic ma- terials. This means that the yield surface or yield locus is also used as a plastic potential. The plastic potential defines the components of the plastic strain rates by the direction of the normal on the surface.

Figure 1: Yield surface according to von Mises If the vonMises plasticity is used the only user input is the yield stress from uniaxial tension. The yield stress and the corresponding hardening curve defines the initial size of the cylinder and its increase during strain hardening. Sheet metals typically exhibit an orthotropy of the plastic be- haviour due to the rolling process. In this case an orthotropic yield locus should be used. Hill-1948 offers an orthotropic extension of the vonMises yield locus. This locus is available in nearly all commercial FEA codes. The orthotropy parame- ters are typically defined via three Lankford coefficients r 0 , r 45 and r 90 which are derived from tensile tests in 3 orientations to rolling direction. The Lankford coefficient is defined as follows: Here b 0 and b are the initial and current width of the tensile specimen. t 0 and t are the initial and current thickness of the tensile specimen. The Lankford coefficient is typically evaluat- ed between 2% and uniform elongation. The Hill-1948 locus based on Lankford coefficients is appropriate for mild and high strength steel sheets. However advanced high strength steel sheets and aluminium sheets are not represented adequately by this model. More complex yield loci should be used.

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