Project MagFest

"Fatigue analysis for lightweight structures made of wrought magnesium alloys"

Project content and result

The project objective was to determine and describe the quasi-static and cyclic mechanical properties of wrought magnesium alloys and to develop a service life model for a numerical fatigue analysis. Sheets of wrought magnesium alloys AM50, AZ31B and ME21 were used for most of the investigations. These are cast-rolled AM50 and AZ31B sheets with a sheet thickness of 1.2 mm, provided by Magnesium Flachprodukte GmbH, and extruded ME21 with a sheet thickness of 1.5 mm from Stolfig GmbH.

Microstructural examinations were performed on sheets made from the wrought magnesium alloys to characterize the microstructure and texture. In addition, optical microscope images were taken on plastically deformed AM50 specimens. The average grain size on the sample surface of the initial sheets is 5 µm for AM50 and AZ31B and 20 µm for ME21. The difference in grain size between the rolling or extrusion direction and across the rolling or extrusion direction is negligible. The grain size of AM50 was 5 µm in all three perpendicular spatial directions. All three alloys exhibit a strong basal texture with high intensity levels of the pole figure maxima. In the case of the alloys AM50 and AZ31B, at the point of highest intensity of the pole figure, the c-axis is tilted by an angle of about 5° with respect to the sheet normal direction in the rolling direction. In ME21 the tilt has an angle of approx. 20° with respect to the sheet normal direction in the extrusion direction.

All tests were carried out at room temperature. For all three alloys, quasi-static tests were carried out in the rolling or extrusion direction and transverse to these directions. In addition to the quasi-static tensile tests, quasi-static compression tests were also performed. For the compression tests, compression supports were used to avoid stability problems. Stress-controlled and strain-controlled cyclic tests under purely alternating loading in the rolling and extrusion directions, respectively, were performed on specimens from ME21 and AZ31B. Approximately 230 cyclic tests were performed on specimens made of AM50 under a wide range of test conditions. These test conditions are:

- tests at different stress and strain ratios

- Stress and strain controlled tests

- Tests with constant and variable load amplitude

- Tests in the rolling direction and transverse to the rolling direction

The strong basal texture of the three alloys is the cause of the anisotropic and asymmetric mechanical properties. The compressive yield strength is only 40-70% of the tensile yield strength. The existing polexcentricity of the {0002} plane also allows <a> prismatic sliding in the rolling or extrusion directions, but not transverse to these directions. Therefore, the tensile elongation at break transverse to the rolling or extrusion direction is also only 25-54% of the tensile elongation at break in the rolling or extrusion direction.

It was found that the quasi-static and cyclic properties of AM50 and AZ31B are very similar. Caused by the four times larger grain size of ME21, the tensile and compressive yield strengths of ME21 are significantly smaller than those of AM50 and AZ31B. In addition, specimens of ME21 show plastic deformation even at very small stresses just above 0 MPa. From this plastic deformation at very small stresses follows a lower stiffness of the ME21 alloy.

In the range of 5 - 10% plastic strain, the tensile plastic strain is caused by <a> base slip and additionally <a> prismatic slip in the rolling or extrusion direction. Plastic compressive strain results from {1012}<1011> twinning. After exceeding the compressive yield point, a strain hardening rate close to zero was observed for all three alloys until the entire test area exhibited high twinning density. In strain-controlled tests, the formation of twin bands was observed during plastic deformation in compression. These nearly parallel macroscopic bands extend over the entire specimen width and lead to a non-uniform strain distribution in the longitudinal direction of the specimen.

The directionality of twinning leads to asymmetric s-shaped hysteresis loops in cyclic tests in the elasto-plastic region. In addition, pseudoelastic deformation was observed in all three alloys. In alternating strain-controlled tests, the hysteresis shape depends only slightly on the strain ratio. In contrast, the hysteresis shape in alternating stress-controlled tests depends strongly on the selected stress ratio. In these tests, a very large mean strain immediately sets in after the compressive yield point is exceeded, which is caused by the abrupt twinning throughout the test area. For strain-controlled variable amplitude tests, it was found that the envelope hysteresis of a variable amplitude test is very similar to hystereses from constant and equal strain amplitude tests. The hysteresis shapes of the internal hystereses differ significantly from constant amplitude tests and depend strongly on the mean strain and mean stress. The measured hysteresis shapes are significantly different from hysteresis shapes that can be represented by the Masing model, which is why the Masing model is not suitable for representing the hysteresis of wrought magnesium alloys.

For numerical fatigue analysis, a description of the stress-strain hysteresis of wrought magnesium alloys is necessary. For this purpose, a uniaxial phenomenological material model was developed and tested in this project. The material model is based on an equation in which the total strain consists of an elastic, a pseudoelastic and a plastic strain component. For the measured hystereses of specimens made of AM50, AZ31B and ME21, as well as other hystereses of other alloys from the literature, the newly developed material model achieves high agreement. Eight material constants are required for the material model, which can be determined by experiments. The material model assumes a stabilized material state and therefore does not consider cyclic hardening, cyclic softening and cyclic stress relaxation. By emulating stress-strain hysteresis, the material model is able to provide quantities such as stresses, strains or strain energy densities for damage parameters.

Analogous to the quasi-static mechanical properties, the fatigue behavior of AM50 and AZ31B is very similar. Specimens from ME21 fatigue earlier than specimens from AM50 and AZ31B under the same external load. Based on cyclic tests on AM50 in the rolling direction and transverse to the rolling direction, it was found that the fatigue strength transverse to the rolling direction is significantly lower than the fatigue strength in the rolling direction.
Various well-known damage parameters based on stresses, strains and strain energy densities were tested for the service life calculation for AM50 in the rolling direction. Significant discrepancies were found between the service life calculation and the experimentally determined values, so a new damage parameter was defined for wrought magnesium alloys. This damage parameter is called "combined strain energy density per cycle" and is defined as the sum of the plastic and the weighted positive elastic strain energy density per cycle. Weighting the positive elastic strain energy density per cycle by 25% best represents the material-specific medium stress sensitivity. Using the "combined strain energy density per cycle", the values of most of the investigated specimens are within a ±2x scatter band. It was found that for all three alloys investigated, the fatigue life can be represented using the damage parameter "combined strain energy density per cycle" with only one bilinear compensation function. However, the service life for loading transverse to the rolling direction must be described with a further bilinear compensation function, since tests on AM50 transverse to the rolling direction showed that for this case the service life is significantly lower than for tests with loading in the rolling direction.

The damage parameters "Smith-Watson-Topper damage parameter", "combined strain energy density per cycle without weighting" and "combined strain energy density per cycle" were applied to the test results from 22 tests with variable amplitudes and mean values. The calculated lifetimes were determined using hystereses reproduced with the phenomenological material model. The best agreement between calculated and measured hystereses is obtained with the damage parameter "combined strain energy density per cycle". For this damage parameter, the parameters of the damage parameter Woehler lines for AM50, AZ31B and ME21 were determined in the rolling or extrusion direction and transverse to the rolling or extrusion direction. Using the damage parameter Woehler lines and the material constants for the developed phenomenological material model, the numerical fatigue analysis can be performed for uniaxial loading conditions at arbitrary load-time functions.

A Python program was developed and tested on unnotched as well as notched specimens and a component for the fatigue analysis according to the local concept considering variable amplitudes and mean values as well as Neuber's plasticity correction. Only a few tests with notched specimens were carried out as part of this project. The plasticity correction applied is therefore based on as yet little well-founded knowledge. Based on component tests, it was shown that a battery holder made of magnesium can be built 68.3% lighter than the non-optimized standard steel variant, with a simultaneous calculated increase in service life by a factor of 2.58. Thus, structural components made of wrought magnesium alloys offer high lightweighting potential. By comparing experimentally determined service life of a component and the corresponding service life calculation, it was demonstrated that the results from the developed calculation method are basically close to the actual service life and in the conservative range.

Further investigations are required to verify the use of the developed phenomenological material model in combination with a plasticity correction. In further work, the focus will be on the acquisition and description of the fatigue behavior considering stress gradients and multi-axial stress states via experiments. Notch sensitivity and the influence of twin bands at the notch base have to be analyzed to obtain more accurate results and to extend the range of applications.