### Filtern

#### Schlagworte

- Constitutive relations (1)
- FEA (1)
- Inverse analysis (1)
- Inverse method (1)
- Material equations (1)
- Nanoindentation (1)
- Nonlinear rheology (1)
- Simple-shear rheometer (1)
- Stress-strain curves (1)
- Tensile tests (1)

#### Organisationseinheit der BAM

An energy-based method to determine material constants in nonlinear rheology with applications
(2016)

Many polymer-type materials show a rate-dependent and nonlinear rheological behavior. Such a response may be modeled by using a series of spring-dashpot systems. However, in order to cover different time scales the number of systems may become unreasonably large. A more appropriate treatment based on continuum mechanics will be presented herein. This approach uses representation theorems for deriving material equations and allows for a systematic increase in modeling complexity. Moreover, we propose an approach based on energy to determine thematerial parameters.This method results in a simple linear regression problemeven for highly nonlinearmaterial equations. Therefore, the inverse problem leads to a unique solution. The significance of the proposed method is that the stored and dissipated energies necessary for the procedure are measurable quantities. We apply the proposed method to a 'semi-solid' material and measure its material parameters by using a simple-shear rheometer.

Fabrication of modern microelectronic components requires miscellaneous solder materials for joining. In order to guarantee the quality of the manufacturing process and the reliability of the resulting solder joint it is necessary to know the material properties of the joining parts and of the solder materials. In particular Youngs modulus, yield stress, and the hardness are of great interest. Moreover, a complete stress-strain curve is important for a detailed material characterization and simulation of a component, e.g., by Finite Elements (FE). The miniaturization of modern electronic products with small solder joints allows only fabrication of very small-sized specimens. Because of this miniature tests are used for measuring the mechanical properties of the solders in the experimental investigations of this paper. More specifically two miniature tests are presented and discussed, a mini-uniaxial-tension-test and a nanoindenter experiment. In the tensile test the axial loading is prescribed, the corresponding extension of the specimen length is recorded, both of which determines the stress-strain- curve directly. The stress-strain curves are then mathematically analyzed by assuming a non-linear relationship between stress and strain of the Ramberg-Osgood type and fitting the corresponding parameters to the experimental data by means of an optimization routine. For a detailed analysis of very local mechanical properties nanoindentation is used, resulting primarily in load vs. indentation-depth data. According to the procedure of Pharr and Oliver this data can be used to obtain hardness and Youngs modulus but not a complete stress-strain curve, at least not directly. In order to obtain such a stress-strain-curve, the nanoindentation experiment is combined with FE and the coefficients involved in the corresponding constitutive equation for stress and strain are obtained by means of the inverse method. Finally in this paper, the stress-strain curves from nanoindentation and tensile tests are compared for two materials, namely aluminum and steel and differences are explained in terms of the locality of the measured properties.