CHAPTER 4 Chosen Benchmark Test Cases
4.2 Non-Linear Static Structural Analysis test cases
4.2.2 Plastic Deformation of Tensile Test Specimen
This test case was created from results obtained through experimental testing done as part of this work using facilities available at the University of KwaZulu-Natal. Initially, the material used for this experiment was sent to an external material testing laboratory in order to obtain the mechanical material properties for the batch used during testing. This was done so that a trusted external source could be referenced for the actual material data used in the computational analysis. However the results provided by the laboratory deviated considerably within the test batch and it was financially impractical to commission more tests to be done. It was therefore considered acceptable that testing for the material data as well as the generation of a target solution for the computational testing be done internally.
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A standard tensile test piece geometry, shown in Figure 4-8, was created following guidelines specified in the document, βStandards for metallic materials tensile testingβ
published by the SABS standards division (South African Bureau of Standards, 2010). This specimen was used to obtain the mechanical properties of the material being used.
Dimensions are presented in millimetres.
Figure 4-8. Specimen geometry created following SABS standards for metallic material tensile testing.
Another geometry following the same guidelines was created, as seen in Figure 4-9. This specimen contained a custom-shaped cut-out along the gauge length. This was done to add complexity to the model. The cut-out also ensured that the fracture will occur within the narrowed portion along the gauge length. This portion is shorter than the minimum reach of the extensometer (a device used to measure strain). This was important as it ensured that the extensometer would be able to read the strain during the entire tensile test.
Figure 4-9. Custom tensile test specimen geometry
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The specimens were water-jet cut from 3 mm thick 1050 H14 aluminium sheet. Water-jet cutting was employed to eliminate the formation of heat-affected zones, associated with laser cutting metals. Testing was conducted on an Instron 5500R material testing machine. The extension was conducted at a constant strain rate of 2 mm/min. An extensometer with a 50 mm gauge length and a 10 mm extension was used. A 100 KN load cell was used to record the tensile force experienced by the specimens.
A lecturer from the Discipline of Statistics of the University of KwaZulu-Natal was consulted with regards to the handling of the data extracted from the Instron machine. It was advised that the way in which these curves were generated prevented the data from easily being averaged to find a best-fit curve. For small sample sizes such as this, the lecturer suggested that it was good practice to choose a median curve and ensure that the majority of result sets fell within one standard deviation of this curve. (Roberts, 2016)
Figure 4-10 shows the stress vs strain curves from the standard specimen geometry. The results were used to determine the flow curve and elastic modulus that was applied in the FEA packages when modelling this test case. A total of ten tests were done using the standard specimen geometry. Three data sets were omitted as they deviated excessively and were considered to be influenced by inconsistencies in geometry or experimental conditions.
The median curve can be seen with error bars indicated. It can be seen that the majority of the result sets fall within one standard deviation of the median. Curves 2, 5 and 8 appear to drop off suddenly, as the fracture occurred outside the bounds of the extensometer.
Figure 4-10. Seven result sets of stress (MPa) vs strain (%) for standard specimen geometry.
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Intuitively, the elastic limit of a material is the point at which plastic deformation first occurs i.e. the stress-strain curve begins to deviate from linearity. This is not a very useful definition as the ability to determine this point depends on how accurately the stress and strain can be measured. To avoid this problem, the onset of the plasticity is usually described by an offset yield strength (ASM International, 2004). It can be found by constructing a straight line parallel to the initial linear portion of the stress-strain curve, but offset by Ξ΅= 0.002 or 0.2 % (ASM International, 2004). The 0.2% offset line can be seen in Figure 4-11.
Figure 4-11. Median material curve showing 0.2% offset line.
Finite element analysis packages accept stress-strain data in the form of true stress and true strain. The following formulae found in (ASM International, 2004), were used to convert engineering stress and strain to true stress and strain.
πππ‘π‘π‘π‘π‘π‘π‘π‘= ππ(1 + ππ) (4.2)
πππ‘π‘π‘π‘π‘π‘π‘π‘= ππππ(1 + ππ) (4.3)
At lower strains, the differences between true and engineering stresses and strains are very small. It must be noted that these equations are only valid for uniform deformation. They are no longer valid once necking begins, thus only valid up to the ultimate tensile stress (UTS) (ASM International, 2004).
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Table 4-13 shows the mechanical material properties that are used for this test case.
Table 4-13. Model properties for Tensile test specimen analyses
Material Properties chosen
E= 63 GPa ( Measured from chosen curve) Ξ½ = 0.3 (From material specification sheet) Yield Stress= 91.44 MPa
Geometric properties chosen As seen in Figure 4-9 Boundary conditions chosen Fully fixed end on face A
Displacement face B
Figure 4-12 shows six of the twelve result sets obtained. These fell within one devition of the chosen median curve for most of the extension. The median curve was used as the target solution for this test case.
Figure 4-12. Six result sets of stress vs strain for custom specimen geometry
Material non-linearities are less frequently analysed, however it was decided that it was important that a package have the capabilities to perform this type of analysis nonetheless. It was also decided that this case be carried out experimentally so that results could be verified.
To successfully analyse this test case, the 3-D solid geometry representation of the specimen must be imported into the pre-processor. The pre-processor must be able to apply an appropriate material plasticity model to the finite element model and allow for the material properties to be entered. The required boundary conditions should be applied. It would be necessary for the incremental results could be recorded for each load step. Lastly, the post- processing module of the package must be able to represent the target solution on an appropriate plot.
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