CHAPTER 4 DESIGN AND OPTIMISATION OF CRUCIFORM SPECIMENS
4.3 Optimisation of cruciform specimens
4.3.2 Dimension optimisation of cruciform specimen for testing under plane strain
(a) Geometry E-1 (0.047, 0.293) (b) Geometry E-2 (0.093, 0.303) Figure 4.18 Fracture of specimens E-1 and E-2 and the corresponding value of the ratio
minor to major strain
4.3.2 Dimension optimisation of cruciform specimen for testing under plane strain path
4.3.2.1 Modified cruciform specimens
Two opposite clamping regions of a cruciform specimen are fixed to the specimen carriages in the apparatus so that the overall deformation in that direction is close to zero for testing under the strain path of plane strain. When the same dimensions of cruciform specimen as that for equi-biaxial testing was used experimentally, failure always occurred in the arms of the specimen due to the fact that slots reduce the stiffness of the arms, which is even lower than that of the central recesses region. Therefore, a cruciform specimen modified in geometry from that used for biaxial testing under plane strain path needs to be used.
It would be possible to increase the width of the two loaded arms but that would increase the stiffness of the specimen significantly. Figure 4.19 shows the dimensions of geometry F-1 and F-2 used to investigate the effect of the number of slots on tests under the strain path of
Major strain Major strain
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plane strain. Only one slot is introduced in two loaded arms for geometry F-1 and the middle slot is 1.5 mm shorter than others in two fixed arms for geometry F-2.
(a) Geometry F-1 (b) Geometry F-2
Figure 4.19 Modified cruciform specimens for plane strain testing
4.3.2.2 Thermo-electrical and thermo-mechanical FE models
Figure 4.20 Locations of thermocouples welded on geometry F-1
Thermocouples were welded to 4 locations on the specimen, identified in Figure 4.20, of geometry F-1 to monitor temperature change during the heating and cooling process, marked in Figure 4.20. The specimen was heated up to 535°C at the centre point and soaked for 1min,
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then quenched to 440°C and soaked for 15 seconds. The average values at soaking temperatures were calculated.
Thermo-electrical and thermo-mechanical FE models coupled with the UAMP and VUMAT subroutines in ABAQUS were used to obtain the full-field temperature and strain distribution respectively on specimens of geometry shown in Figure 4.21. The sink temperature is defined as 180°C measured experimentally. Two opposite clamping regions are fixed and the other two undergo the displacement of stretching. The same relationship of time-displacement as in the experimental work was input to the FE model in each direction. The simulated results of temperature were compared with the measured results to validate the FE model, as shown in Table 4.5. Good agreement was observed for each thermocouple location. The simulation of deforming specimens was performed for geometry E-1, F-1 and F-2.
Figure 4.21 FE model coupled with thermo-electrical and thermo-mechanical boundary conditions for plane strain testing
Tensile displacements
Current flow Sink temperatures of 180°C
on each clamping region
Conduction heat transfer on surface
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Table 4.5 Comparison of experimental and simulated results of temperatures at different locations on geometry F-1
Temperature results (°C) T1 T2 T3 T4
Experiment 535.02 540.78 505.24 503.53
FE 535.99 537.07 507.55 502.31
Experiment 439.42 444.12 422.64 423.70
FE 439.34 441.39 422.21 418.71
4.3.2.3 Results and discussion
(a) Geometry E-1
(b) Geometry F-1 (c) Geometry F-2
Figure 4.22 Simulated results of the first principal strain for geometries E-1, F-1 and F-2
Figure 4.22 shows the FE results of the first principal strain for different geometries. For geometry E-1, the strain level in the arms is higher than the gauge zone from the beginning of
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the deformation, which could cause failure to occur in the arms. The number of slots is reduced to one in two opposite arms for geometry F-1 so that the central zone has higher strain values than that in the arms. However, failure may start from the middle slot since it is the closest one to the milled zone. The length of the middle slot is reduced for geometry F-2, which can avoid failure to start out of the central zone.
Figure 4.23 shows the simulated results of shear strain for geometries E-1, F-1 and F-2. The in-plane shear strains around the corner fillet regions are higher than the geometry before modification of corner fillets. It still remains a lower value in the gauge section for geometry F-1 and F-2, which is acceptable for the testing.
The changes of the cruciform specimen for testing under plane strain state just have a slight effect on the uniformity of strain distribution, as shown in Figure 4.24. Both geometry F-1 and geometry F-2 have a good uniformity of the first principal strain distribution.
(a) Geometry E-1
(b) Geometry F-1 (c) Geometry F-2
Figure 4.23 Simulated results of shear strain for geometries E-1, F-1 and F-2
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Figure 4.24 Variation of normalised the first principal strain over the milled zone for geometries E-1, F-1 and F-2
Figure 4.25 Ratio of minor strain to major strain under the plane strain path for different geometries
The evolution of the ratio values of strain path at the central point for different geometries changes little with change in geometry, as shown in Figure 4.25. The value is nonzero because of the absence of shear strain in the central zone so that the strains measured in the
0 0.4 0.8 1.2 1.6
-1.5 -1 -0.5 0 0.5 1 1.5
Normalised strain
Relative position in gauge section
Geometry E-1 Geometry F-1 Geometry F-2
-0.5 -0.2 0.1
0 1.5 3
Ratio of minor strain to major strain Time (s) Geometry E-1 Geometry F-2Geometry F-1
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two loading directions are not the principal strains. This could be improved potentially by applying a small tensile displacement in the two fixed arms to eliminate the shrink of the material so that the second principal strain is zero or by improving the uniformity of temperature distribution on the entire specimen.
4.3.2.4 Experimental validation
(-0.032, 0.243)
Figure 4.26 Fracture of specimen F-2 and the corresponding value of minor to major strain ratio
The biaxial tensile test under plane strain state was conducted by using geometry F-2 at the deformation temperature of 440°C and strain rate of 0.1 /s. Figure 4.26 shows the facture location, which was in the central zone. The uniformity of major strain distribution is good and the ratio of strain path is 0.132, which is close to plane strain state. Failure did occur in the arms of the geometry F-1 experimentally. In conclusion, geometry F-2 was the determined design of the cruciform specimen for plane strain testing.