Testing methods for fracture modelling

Transcription

1 Testing methods for fracture modelling Authors C.H.L.J. ten Horn, Corus Technology, IJmuiden (NL) M.P.J. Lambriks, Corus Strip Products IJmuiden, IJmuiden (NL) K. Unruh, Faurecia Autositze GmbH, Stadthagen (D) Please Note Care has been taken to ensure that the information herein is accurate, but Tata Steel and its subsidiary companies do not accept responsibility for errors or for information which is found to be misleading. Suggestions for or descriptions of the end use or applications of products or methods of working are for information only and Tata Steel and its subsidiaries accept no liability in respect thereof. Before using products supplied or manufactured by Tata Steel the customer should satisfy themselves of their suitability All drawings, calculations and advisory services are provided subject to Tata Steel Standard Conditions available on request.

2 Testing methods for fracture modelling C.H.L.J. ten Horn, Corus Technology, IJmuiden (NL) M.P.J. Lambriks, Corus Strip Products IJmuiden, IJmuiden (NL) K. Unruh, Faurecia Autositze GmbH, Stadthagen (D) Summary For Advanced High Strength Steels (AHSS) the point at which the material starts necking (FLC forming limit) is no longer the only failure mechanism. The increased use of these materials makes fracture prediction (other than through forming limit curve) an important topic. In an initial investigation 5 damage and fracture models were evaluated using 8 test cases. From this study it was concluded that our future research will focus on two commercially available fracture models: CrachFEM and EWK. Important aspects to commission such fracture models in finite element simulations, are accuracy and predictiveness of the results and the effort it takes to obtain the fracture input data. This study has also highlighted that different tests and specimens are being recommended for determining the parameters of the different models. When several fracture models are being used, it would be ideal to have one set of tests that can be used for all models. In order to find that set of tests, this paper compares several fracture tests, some are specific for fracture characterisation while others are adaptations of general tests. The most important aspect of these tests is how the strain and strain state at fracture can be determined. However, there does not seem to be a unified procedure for this. Therefore, it was concluded that further standardisation will be required. Keywords: Fracture, Modelling, Measurement, Forming 1 Introduction For Advance High Strength Steels (AHSS) the conventional methods of predicting failure (e.g. using a FLC) do not always work. When fracture can not be predicted it can be a real showstopper. For example, it limits the design freedom by limiting the stamping, bending or hemming capacity or by limiting the energy absorption in crash. In order to overcome problems with fracture, Finite Element (FE) simulations can be performed using damage and fracture models. Currently a large number of models are available in commercial FE packages. Several models are compared in the next chapter. As the predictions can only be as good as the measurements they are based on, the key to unlocking the real potential of the models is whether accurate measurements can be made. This will also be covered in this paper and it will be shown that different tests are recommended for the different models. 2 Modelling Damage and Fracture In the past, many different models have been developed to predict fracture in different applications. Some of the models that are available in commercial FE codes [1, 2], are shown in Figure 1. The models have been split in Fracture models vs. Damage models and in Local models vs. Non-local models. The difference between Fracture and Damage models is that the former only predicts when fracture takes place while the latter also couples the developed damage back to the workhardening, see Figure 1b. Non-local models distinguish themselves from local models in the fact that they evaluate the damage or fracture criterion not just in one point but over a larger area (making them less mesh-size sensitive). Not all models in Figure 1 were evaluated, but only the 5 highlighted models. These models were chosen based on: required element size, general applicability, predictiveness and simplicity both in the model and in their parameter identification procedure. For evaluation, their implementation in PAM-STAMP, PAM-CRASH and LS-Dyna was used and the models

3 Local Non local were validated against: a number of standard application tests like: FLC tests, shear tests, a plane strain test, 3-point bending and the crushing of a closed-top-hat box. A. Fracture models EWK Wilkins RcDc CrachFEM max, max Marc FAIL DATA Kolmogorov-Dell Dyna NON-LOCAL Damage models Gurson R C D C Mediavilla Johnson-Cook Goijaerts Lemaitre Oyane Rice-Tracey Gurson Marc CRACK DATA Linear softening B. Fracture modelx fracture Damage model x Figure 1. A. Overview of damage and fracture models. B. Stress-strain response for Damage models and Fracture models. The results of the simulations for the closed-top-hat are shown in Figure 2; also a typical result for experiments is shown. From this figure it is clear that in reality, fracture occurs in the inner folds of the box. Contrary to the experiments, the Lemaitre model predicts that the corners of the box will fracture and that no stable folding collapse mode will occur. Gurson on the other hand predicts that no fracture will occur while the EWK and CrachFEM models predict high fracture risks and they also occur in the correct areas. Based on these results combined with the results from the other test cases, the EWK and CrachFEM models were chosen for further study. Figure 2. Fracture risk for 4 damage or fracture models for crushing of the closed-top-hat box. Deformations for EWK, CrachFEM and Gurson scaled by Requirements and tests for EWK The EWK model is based on the Wilkins model and is modified by Kamoulakos [3]. In this model, a damage value is calculated based on the equivalent plastic strain rate, the mean tensile stress and the asymmetric stress distribution. Fracture is predicted when a critical level of the damage over a critical area is exceeded. The tests that are recommended by ESI to obtain the parameters of the EWK model are: a tensile test, a shear test and a notched tensile test. The first two tests will provide the local fracture strains in tension and shear, while the last test will provide the length scale (that defines the critical area). 2.2 Requirements and tests for CrachFEM CrachFEM [4] was developed by MATFEM and defines 3 failure modes: Plastic Instability, Ductile Normal Fracture and Ductile Shear fracture; see also Figure 3. Plastic Instability represents necking of the material, Ductile Normal fracture represents void formation and growth and Ductile Shear fracture represents the development of shear band localisation. For each failure mode a failure curve (similar to FLC) is defined as a function of the strain ratio. As a result several tests are recommended to trigger a specific fracture mode at a specific strain ratio; the tests will be discussed in more detail in the next chapter.

4 Plastic Instability Ductile Normal Fracture Ductile Shear Fracture Figure 3. Failure modes used in CrachFEM (Schematic). 2.3 Summary of recommended tests The tests recommended by MATFEM and ESI are summarised in Table 1; the tests used at Corus are also shown. As can be seen from this table, they have only a few tests in common. Also most recommended tests are not standard and will probably need some development before they can be done at different labs. As different models recommend different tests, it would be very beneficial to have one set of tests that can be used for all models. The testing effort can also be reduced if tests that are already common practice can be re-interpreted to provide local fracture strains. However, it is usually not very clear how the local fracture strain should be measured; the next chapter explains several measurement techniques. Table 1. Tests recommended for CrachFEM and EWK and those used by Corus. Ductile Normal fracture Ductile Shear fracture CrachFEM ESI - EWK Corus Biaxial Erichsen, FLC specimens, plane 2 waisted tensile tests Tensile, shear and strain test Shear & tensile-shear, notched tensile test Shear & tensile-shear, bulge test equibiaxial FLC test 3 Measurements for fracture models From Table 1 it was seen that different specimens are being recommended for different models. However, even using the same specimens is not a guarantee that the results will be similar. Most models need the local fracture strain at different strain states as input, and those strains are difficult to measure. Techniques that are being used are: local thickness and shear angle measurements and optical strain measurements. Thickness and shear angle measurements seem very straight forward; however, measuring the thickness of a sheet at the point of fracture is difficult. Mechanical thickness gauges easily slip off the specimen when measuring very close to the fracture surface or are too conservative when measuring further from the edge. Optical techniques like microscopes could be used here but that does not make the measurement any quicker or easier. Optical strain measurements that are done on the surface of the sheet come in two forms: measuring during the test or measuring only at the end of the test. Measurements done at the end of the test, like GOM Argus, have the advantage that they can be done outside the test machine; however, in some cases measuring the local fracture strain on broken specimens may be virtually impossible. On-line strain measurement system, like GOM Aramis, record the strains during the test enabling the determination of strain that occur just before fracture. As CrachFEM needs more tests than the EWK model, the next paragraphs will focus on the strain measurements for CrachFEM. Those tests should also provide enough information to determine the EWK parameters. 3.1 Ductile normal fracture As the specimens that are recommended for determining the Ductile Normal Fracture curve, were not available at Corus, it was investigated whether existing tests could provide the same

5 Failure strain [-] shear uniaxial plane strain equibiaxial Fracture strain [-] information. In FLC testing, that is routinely done, specimens at different strain states are tested until necking and fracture. When off-line strain measurements are done, the points closest to the fracture are discarded as the necking point needs to be determined and not the fracture point. The discarded points meanwhile can give information about the local strains at fracture if the crack opening is accounted for. In Figure 4 two FLC specimens are shown together with the recommended specimens. The plane strain specimen (left most specimen) is also shown; it provides the uniaxial fracture point as fracture starts at the edge of the specimen (uniaxial stress) and not at the centre (plane strain). Corus CrachFEM Figure 4. Overview of specimens used to determine the Ductile Normal Fracture curve. As different tests are used, a comparison of the results using the different approaches was needed and is shown in Figure 5. In this figure it can be clearly seen that the measurements of MATFEM and Corus are close together and that at Corus the tests were performed in rolling direction and in transverse direction. Although there is scatter in the Corus measurements, it is still clear that the material fractures in the rolling direction at a slightly higher strain level than in the transverse direction. Therefore, if measurements are only done in one direction, the transverse direction should give the more conservative results. The standard way of testing the FLC for steel is also in the transverse direction as it is the lower of the two Lab 1 - rolling direction 0.4 Lab 1 - rolling direction fit Lab 2 - rolling direction Lab 2 - rolling direction fit 0.2 Lab 2 - transverse direction Lab 2 - transverse direction fit Figure 5. Comparison of results for Ductile Normal Fracture measurements. 3.2 Ductile shear fracture The recommended specimens for determination of the Ductile Shear Fracture curve are shown in Figure 6. The tensile-shear specimens (strain ratios: -0.7, -0.2 and 0) have a groove at specific angles to the loading direction to give specific ratios of tensile and shear loading. For measuring the local fracture strains in the in-plane shear test (strain ratio of -1), several options exist: using an optical system with a grid or angle measurement using scribed lines. The disadvantage of the first method is that only the average shear strain can be measured as the minimum grid size is 0.5 mm while the shear zone is 1.5 mm wide. When angle measurements using scribed lines are used, localised shear bands can be observed as

6 Fracture strain [-] shear uniaxial plane strain equibiaxial schematically shown in Figure 7. As the bands are very narrow, they are difficult or impossible to capture with other techniques. Corus CrachFEM Figure 6. Overview of the specimens used to determine the Ductile Shear Fracture curve. max avr Figure 7. Shear angle measurement on a simple shear test. For the tensile-shear specimens, three options for measuring the local fracture strain exist: thickness and angle measurements, off-line grid systems or an on-line strain measurement system. Thickness measurement have the same difficulties as described before. Off-line strain measurement systems are not ideal either as they can only be used on specimen that are not broken; otherwise the strains cannot be measured anymore. Specimens that are not broken yet can be measured but will always be on the conservative side and it is not clear how far they are from the fracture point. This is where the on-line systems have an advantage in that specimens can be tested until fracture. Because an on-line system measures during the test, the last measurement before fracture can be retrieved to provide the local fracture strain. An on-line system is not without its difficulties. An initial test showed that the white paint layer of the speckle pattern delaminated from the specimen before the fracture strains were reached making determination of the fracture strain impossible, see Figure 8. This problem was solved by etching the specimens black before applying white speckles. An example of results that can be obtained are shown in Figure 9. It can be seen from this figure that the equivalent strain is very constant over the width of the specimen and that it can be measured without much scatter in the data even at strains of over 0.4. A. B. Figure 8. A. Initial problem with delamination of speckle pattern. B. The pattern applied by etching the specimen and applying white speckles, remains intact even at necking.

7 Equivalent strain [-] Equivalent strain [-] section line Y Coord X [mm] X Figure 9. Example of results of tensile-shear test using GOM Aramis. Fracture occurred between step 12 and 13 (not shown). In order to compare the different specimens and measurement techniques, the same material was measured at four different labs; the results can be seen in Figure 10. Large differences seen between labs are partly due to the way local fracture strains are measured. These differences in testing results will lead to large differences in fracture predictions when they are used in simulations. Further study and standardisation is needed to get more reliable results Lab 1 Fit Lab 1 Lab 2 Fit Lab 2 Lab 3 Fit Lab 3 Lab 4 Fit Lab Figure 10. Comparison of shear fracture results for different labs. 4 Conclusion Predictive modelling of fracture is an important tool to unlock the full potential of AHSS. Many different damage and fracture models have been developed; however, not all of them are equally applicable to sheet metal forming or crash. Most models need local fracture strain data to obtain the parameters. Different tests and different strain measurement techniques are being recommended for the different models. Using several fracture model would mean that a large number of tests need to be performed. It would be very beneficial if all damage and fracture models could use the same tests and if those tests would be more standardised. 5 Acknowledgements We are pleased to acknowledge the support of Faurecia for the on-line strain measurements. 6 References [1] ESI Group, PAM-STAMP 2G & PAM-TUBE 2G 2008 User s Guide, [2] Livermore Software Technology Corporation, LS-Dyna User s manual, v971. [3] Kamoulakos, A; EuroPAM2005. [4] Dell, H; Gese, H; Oberhofer, G; Numiform 07, p165