PSI- Issue 9

Author name / Structural Integrity Procedia 00 (2018) 000 – 000 Author name / Structural Integrity Procedia 00 (2018) 000 – 000 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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Riccardo Fincato et al. / Procedia Structural Integrity 9 (2018) 126–135 Autho name / Structural Integrity Procedia 00 (2018) 000 – 000 Author name / Structural Integrity Procedia 00 (2018) 000 – 000 the definition of the failure envelope in both L and MC approaches. The decrease of the ductility with the stress triaxiality has to be investigated with two samples of different notch radii under the same loading conditions, wher as the dependency on the Lod angle has to be carried out with a third sample having approximatively the same stress triaxiality evolution of one of the previous two but under a different loading condition. The calibration of the damage parameter seemed to be easier using the MC criterion. The first reason is that it requires the calibration of 5 material param te s against the 6 mat ri l parameters of the modified L formula in Eq. (6). A second reason is that Eq. (8) gives directly an analytical expression of the failure envelope that can be easily fitted once the experimental failure points are k own in terms of equivalent strain to fracture (obtained for example through the Digital Imaging Correlation method). The fitting can be done using an optimization algorithm that calibrates the four mat rial parameters A , N , c 1 and c 2 by minimizing the distance of f  computed with Eq.(8), giving a range of possible stress triaxiality and Lode angle parameters (i.e. a first set can be selected for exampl using the Bridgman formula (Bridgman, 1952)) and the total strain measured in the experiments. The damage evolution obtained with the Lemaitre’s approach gives a slow evolution for lower stress triaxial stat s and sudden acceleration for increasing values of the stress triaxiality, as shown by the green dashed lines in Figure 4. On the contrary, the rate of the damage evolution with the MC criterion seems more uniform. This required to set a threshold on the cumul tive pl stic strain after which the damage ca evolve, in order to catch a realistic material behaviou . the definition of the failure envelope in both L and MC approaches. The decrease of the ductility with the stress triaxiality has to be investigated with two samples of different notch radii under the same loading conditions, whereas the dependency on the Lode angle has to be carried out with a third sample having approximatively the same stress triaxiality evolution of one of the previous two but under a diff rent loading condition. The calibrati n of the damage parameter seem d t be easier using the MC criterion. Th first reason is that it require calibration of 5 material parameters against the 6 material parameters of the modified L formula in Eq. (6). A second reason is hat Eq. (8) gives directly an analytic l expression of the failure envelope that can be easily fitted once the experi ental failure points are known in terms of equivalen strain to fractur (obta ned for xample thr ugh the Digital Imaging Correlation method). The fitting can be done using an optimizatio algorithm that calibrates the four material parameters A , N , c 1 and c 2 by minimizing the distance of f  computed with Eq.(8), giving a r nge of possible stress triaxiality and Lode ngle paramete s (i.e. a first s t can be selected for example using the Bridgman formula (Bridgman, 1952)) and the t tal strain measured in the experiments. The damage evolution obtained with the Lemai r ’ appro ch gives a slow evolution for low r stre s triaxial states and sudden cce ration for inc easing values of the stress triaxiality, as s own by the green dashed lines in Figur 4. On the contrary, the rate of the damage evolution with the MC criterion seems more uniform. This requir d to set a threshold on the cumula ive plast c strain after which the damage can evolve, in order to catch a re li tic materi l behaviour. In this paper the ductile fracture characteristic of the Q460 construction steel was evaluated by means of a novel unconventional elastoplastic and d mage model named Damage Subloading Surface mo el. Th authors c mpared the material description obtained using two different ductile damage approaches within the CDM framework. The concl sions can be summarized in the following points:  The original Lemaitre’s ductile damage approach is not suitable for the description of the damage evolution nder different loading paths since it cannot take into consideration the effect of the Lode angle. A modification of the damage law was suggested by the authors in Fincato and Tsutsumi (2017a) to overcome this issue.  The modified Mohr- Coulomb’s failure criterion (Bai and Wierzbicki, 2010) can be applied to metallic materials for the evaluation of the ductile fracture since it can catch the decay in ductility with the stress triaxiality and the different damage evolution und r different loading conditions.  The calibration of the damage parameters seems to be easier for the MC criterion due to the lower number of constants; five against th six in the Lemaitre’s criterion, and because it provides an analytical expression of the equivalent strain to failure that can be easily fitted against experimental data.  Both criteria are suitable for the description of monotonic loading tests, however a modification of the laws has to be considered in case of non-proportional (Cortese et al., 2016; Fincato and Tsutsumi, 2017e; Papasidero et al., 2015) or cyclic l adi g cases (Algarni et al., 2017; Bonora, 1997). Future works of the authors will focus attention on the formulation of a ductile damage law for low cycle and extremely low cycl fatigue problems. Algarni, M., Bai, Y., Choi, Y., 2015. A study of Inconel 718 dependency on stress triaxiality and Lode angle in plastic deformation and du tile fracture. Eng. Fract. Mech. 147, 140 – 157. https://doi.org/10.1016/j.engfracmech.2015.08.007 Algarni, M., Choi, Y., Bai, Y., 2017. A unified material model for multiaxial ductile fracture and extremely low cycle fatigue of Inconel 718 Int. J. Fatigue 96, 16 – 177. ht ps://doi.org/10.10 6/j.ijfatigue.2016.11.033 Bai, Y., Wierzbicki, T., 2010. Application of extended M hr – Coulomb criterion to ductile fracture. Int. J. Fract. 161, 1 – 20. https://doi.org/10.1007/s10704-009-9422-8 Bai, Y., Wierzbicki, T., 2008. A new model of metal plasticity and fract re with pressure and Lode dependence. Int. J. Plast. 24, 1071 – 1096. https://doi.org/10.1016/j.ijplas.2007.09.004 Bonora, N., 1997. A nonlinear CDM model for ductile failure. Eng. Fract. Mech. 58, 11 – 28. https://doi.org/10.1016/S0013-7944(97)00074 X the definition of the failure envelope in both L and MC approaches. The decrease of the ductility with the stress triaxiality has to be investigated with two samples of different notch ra ii under the same loading conditions, whereas the dependency on the Lode angle has to be carried out with a third sample having approximatively the same stress triaxiality evolution of one of the previous two but under a different loading condition. The calibration of the damage parameter seemed to be easier using the MC criterion. The first reason is that it requires the calibration of 5 material parameters against the 6 material parameters of the modified L formul in Eq. (6). A second reason is that Eq. (8) gives directly an analytic l expression of the failure envelope that can be easily fitted once the experimental failure points are known in terms of equivalent strain to fracture (obt ined for example thr ugh the Digital Imaging Correlation method). The fitting can be done using an optimizati n algorithm that calibrates the four material parameters A , N , c 1 and c 2 by minimizing the distance of f  computed with Eq.(8), giving a range of possible stress triaxiality and Lode angle parameters (i.e. a first set can be selected for example using the Bridgman formula (Bridgman, 1952)) and the total strain measured in the experiments. The damage evolution obtained with the Lemaitre’s approach gives a slow evolution for lower stress triaxial states and sudden acceleration for increasing values of the stress triaxiality, as shown by the green dashed lines in Figure 4. On the contrary, the rate of the damage evolution with the MC criterion seems more uniform. This required to set a threshold on the cumulative plastic strain after which the damage can evolve, in order to catc a realistic materi l behaviour. 4. Conclusions In this paper the ductile fracture characteristic of the Q460 construction steel was evaluated by means of a novel unconventional elastoplastic and damage model named Damage Subloading Surface mo el. Th authors compared the material description obtained using two different ductile damage approaches within the CDM framework. conclusions c n be summarized in the following points:  original Lem itre’s ductile damage approach is n t suitable for the description of the damage evolution under different loading paths since it cannot take into consideration the effect of the Lod angle. A modification of the damage law was suggested by the authors in Fincato and Tsutsumi (2017a) to overcome this issue.  The modified Mohr- Coulomb’s failure criterion (Bai and Wierzbicki, 2010) can be applied to metallic materials for the evaluation of the ductile fracture since it can catch the decay in ductility with the stress triaxiality and the different damage evolution u d r different loading conditions.  The calibration of the damage parameters seems to be easier for the MC criterion due to the lower number of constants; five against the six in the Lemaitre’s criterion, and because it provides an analytical expression of the equivalent strain to failure that can be easily fitted against experimental data.  Both criteria are suitable for the description of monotonic loading tests, however a modification of the laws has to be considered in case of non-proportional (Cortese et al., 2016; Fin to and Tsutsumi, 2017e; Papasidero et al., 2015) or cyclic loading cases (Algarni et al., 2017; Bonora, 1997). Future works of the authors will focus attention on the formulation of a ductile damage law for low cycle and extremely low cycl fatigue problems. References Algarni, M., Bai, Y., Choi, Y., 2015. A study of Inconel 718 dependency on stress triaxiality and Lode angle in plastic deformation and ductile fracture. Eng. Fract. Mech. 147, 140 – 157. https://doi.org/10.1016/j.engfracmech.2015.08.007 Algarni, M., Choi, Y., Bai, Y., 2017. A unified material model for multiaxial ductile fracture and extremely low cycle fatigue of Inconel 718. Int. J. Fatigue 96, 162 – 177. https://doi.org/10.1016/j.ijfatigue.2016.11.033 Bai, Y., Wierzbicki, T., 2010. Application of extended Mohr – Coulomb criterion to ductile fracture. Int. J. Fract. 161, 1 – 20. https://doi.org/10.1007/s10704-009-9422-8 Bai, Y., Wierzbicki, T., 2008. A new model of metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24, 1071 – 1096. https://doi.org/10.1016/j.ijplas.2007.09.004 Bonora, N., 1997. A nonlinear CDM model for ductile failure. Eng. Fract. Mech. 58, 11 – 28. https://doi.org/10.1016/S0013-7944(97)00074 X the definition of the failure envelope in both L and MC approaches. The decrease of the ductility with the stress triaxiality has to be investigated with two samples of different notch radii under the same loading conditions, whereas the dependency on the Lode angle has to be carried out with a third sample having approximatively the same stress triaxiality evolution of one of the previous two but under a different loading condition. The calibration of the damage parameter seemed to be easier using the MC criterion. The first reason is that it requires the calibration of 5 material parameters against the 6 material parameters of the modified L formula in Eq. (6). A second reason is that Eq. (8) gives directly an analytical expression of the failure envelope that can be easily fitted once the experimental failure points are known in terms of equivalent strain to fracture (obtained for example through the Digital Imaging Correlation method). The fitting can be done using an optimization algorithm that calibrates the four material parameters A , N , c 1 and c 2 by minimizing the distance of f  computed with Eq.(8), giving a range of possible stress triaxiality and Lode angle parameters (i.e. a first set can be selected for example using the Bridgman formula (Bridgman, 1952)) and the total strain measured in the experiments. The damage evolution obtained with the Lemaitre’s approach gives a slow evolution for lower stress triaxial states and sudden acceleration for increasing values of the stress triaxiality, as shown by the green dashed lines in Figure 4. On the contrary, the rate of the damage evolution with the MC criterion seems more uniform. This required to set a threshold on the cumulative plastic strain after which the damage can evolve, in order to catch a realistic material behaviour. the definition of the failure envelope in both L and MC approaches. The decrease of the ductility with the stress triaxiality has to be investigated with two samples of different notch radii under the same loading conditions, whereas the dependency on the Lode angle has to be carried out with a third sample having approximatively the same stress triaxiality evolution of one of the previous two but under a different loading condition. The calibration of the damage parameter seemed to be easier using the MC criterion. The first reason is that it requires the calibration of 5 material parameters against the 6 material parameters of the modified L formula in Eq. (6). A second reason is that Eq. (8) gives directly an analytical expression of the failure envelope that can be easily fitted once the experimental failure points are known in terms of equivalent strain to fracture (obtained for example through the Digital Imaging Correlation method). The fitting can be done using an optimization algorithm that calibrates the four material parameters A , N , c 1 and c 2 by minimizing the distance of f  computed with Eq.(8), giving a range of possible stress triaxiality and Lode angle parameters (i.e. a first set can be selected for example using the Bridgman formula (Bridgman, 1952)) and the total strain measured in the experiments. The damage evolution obtained with the Lemaitre’s approach gives a slow evolution for lower stress triaxial states and sudden acceleration for increasing values of the stress triaxiality, as shown by the green dashed lines in Figure 4. On the contrary, the rate of the damage evolution with the MC criterion seems more uniform. This required to set a threshold on the cumulative plastic strain after which the damage can evolve, in order to catch a realistic material behaviour. In this paper the ductile fracture characteristic of the Q460 construction steel was evaluated by means of a novel unconventional elastoplastic and damage model named Damage Subloading Surface model. The authors compared the material description obtained using two different ductile damage approaches within the CDM framework. The conclusions can be summarized in the following points:  The original Lemaitre’s ductile damage approach is not suitable for the description of the damage evolution under different loading paths since it cannot take into consideration the effect of the Lode angle. A modification of the damage law was suggested by the authors in Fincato and Tsutsumi (2017a) to overcome this issue.  The modified Mohr- Coulomb’s failure criterion (Bai and Wierzbicki, 2010) can be applied to metallic materials for the evaluation of the ductile fracture since it can catch the decay in ductility with the stress triaxiality and the different damage evolution under different loading conditions.  The calibration of the damage parameters seems to be easier for the MC criterion due to the lower number of constants; five against the six in the Lemaitre’s criterion, and because it provides an analytical expression of the equivalent strain to failure that can be easily fitted against experimental data.  Both criteria are suitable for the description of monotonic loading tests, however a modification of the laws has to be considered in case of non-proportional (Cortese et al., 2016; Fincato and Tsutsumi, 2017e; Papasidero et al., 2015) or cyclic loading cases (Algarni et al., 2017; Bonora, 1997). Future works of the authors will focus attention on the formulation of a ductile damage law for low cycle and extremely low cycle fatigue problems. Algarni, M., Bai, Y., Choi, Y., 2015. A study of Inconel 718 dependency on stress triaxiality and Lode angle in plastic deformation and ductile fracture. Eng. Fract. Mech. 147, 140 – 157. https://doi.org/10.1016/j.engfracmech.2015.08.007 Algarni, M., Choi, Y., Bai, Y., 2017. A unified material model for multiaxial ductile fracture and extremely low cycle fatigue of Inconel 718. Int. J. Fatigue 96, 162 – 177. https://doi.org/10.1016/j.ijfatigue.2016.11.033 Bai, Y., Wierzbicki, T., 2010. Application of extended Mohr – Coulomb criterion to ductile fracture. Int. J. Fract. 161, 1 – 20. https://doi.org/10.1007/s10704-009-9422-8 Bai, Y., Wierzbicki, T., 2008. A new model of metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24, 1071 – 1096. https://doi.org/10.1016/j.ijplas.2007.09.004 Bonora, N., 1997. A nonlinear CDM model for ductile failure. Eng. Fract. Mech. 58, 11 – 28. https://doi.org/10.1016/S0013-7944(97)00074- 4. Con lusions In this paper the ductile fracture characteristic of the Q460 construction steel was evaluated by means of a novel unconventional elastoplastic and damage model named Damage Subloading Surface model. The authors compared the mat rial description obtained using two different ductile damage approaches within the CDM framework. The c clusions c n be summarized in the following points:  h original Lemaitre’s ductile damage approach is n t suitable for the description of the damage evolution under different loading paths since it cannot take into consideration the effect of the Lode angle. A modification of the damage law was suggested by the authors in Fincato and Tsutsumi (2017a) to overcome this issue.  The modified Mohr- Coulomb’s failure criterion (Bai and Wierzbicki, 2010) can be applied to metallic materials for the evaluation of the ductile fracture since it can catch the decay in ductility with the stress triaxiality and the different damage evolution under different loading conditions.  The calibration of the damage parameters seems to be easier for the MC criterion due to the lower number of constants; five against the six in the Lemaitre’s criterion, and because it provides an analytical expression of the equivalent strain to failur that can be easily fitted against experimental data.  Both criteria are suitable for the description of monotonic loading tests, however a modification of the laws has to be considered in case of non-proportional (Cortese et al., 2016; Fincato and Tsutsumi, 2017e; Papasidero et al., 2015) or cyclic loading cases (Algarni et al., 2017; Bonora, 1997). Future works of the authors will focus attention on the formulation of a ductile damage law for low cycle and extremely low cycle fatigue problems. References Algarni, M., Bai, Y., Choi, Y., 2015. A study of Inconel 718 dependency on stress triaxiality and Lode angle in plastic deformation and ductile fracture. Eng. Fract. Mech. 147, 140 – 157. https://doi.org/10.1016/j.engfracmech.2015.08.007 Algarni, M., Choi, Y., Bai, Y., 2017. A unified material model for multiaxial ductile fracture and extremely low cycle fatigue of Inconel 718. Int. J. Fatigue 96, 162 – 177. https://doi.org/10.1016/j.ijfatigue.2016.11.033 Bai, Y., Wierzbicki, T., 2010. Application of extended Mohr – Coulomb criterion to ductile fracture. Int. J. Fract. 161, 1 – 20. https://doi.org/10.1007/s10704-009-9422-8 i, Y., Wierzbicki, T., 2008. A new model f metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24, 071 – 096. https://doi.org/10.1016/j.ijplas.2007.09.004 onora, N., 1997. A nonlinear CDM l for ductile failure. Eng. Fract. Mech. 58, 11 – 28. https://doi.org/10.1016/S0013-7944(9 )00 74 X 4. Conclusions Refe ences 4. Conclusions 4. Conclusions In this paper the ductile fracture characteristic of the Q460 construction steel was evaluated by means of a novel unconventional elastoplastic and damage model named Damage Subloading Surface model. The authors compared the material description obtained using two different ductile damage approaches within the CDM framework. The conclusions can be summarized in the following points:  The original Lemaitre’s ductile damage approach is not suitable for the description of the damage evolution under different loading paths since it cannot take into consideration the effect of the Lode angle. A modification of the damage law was suggested by the authors in Fincato and Tsutsumi (2017a) to overcome this issue.  The modified Mohr- Coulomb’s failure criterion (Bai and Wierzbicki, 2010) can be applied to metallic materials for the evaluation of the ductile fracture since it can catch the decay in ductility with the stress triaxiality and the different damage evolution under different loading conditions.  The calibration of the damage parameters seems to be easier for the MC criterion due to the lower number of constants; five against the six in the Lemaitre’s criterion, and because it provides an analytical expression of the equivalent strain to failure that can be easily fitted against experimental data.  Both criteria are suitable for the description of monotonic loading tests, however a modification of the laws has to be considered in case of non-proportional (Cortese et al., 2016; Fincato and Tsutsumi, 2017e; Papasidero et al., 2015) or cyclic loading cases (Algarni et al., 2017; Bonora, 1997). Future works of the authors will focus attention on the formulation of a ductile damage law for low cycle and extremely low cycle fatigue problems. Algarni, M., Bai, Y., Choi, Y., 2015. A study of Inconel 718 dependency on stress triaxiality and Lode angle in plastic deformation and ductile fracture. Eng. Fract. Mech. 147, 140 – 157. https://doi.org/10.1016/j.engfracmech.2015.08.007 Algarni, M., Choi, Y., Bai, Y., 2017. A unified material model for multiaxial ductile fracture and extremely low cycle fatigue of Inconel 718. Int. J. Fatigue 96, 162 – 177. https://doi.org/10.1016/j.ijfatigue.2016.11.033 Bai, Y., Wierzbicki, T., 2010. Application of extended Mohr – Coulomb criterion to ductile fracture. Int. J. Fract. 161, 1 – 20. https://doi.org/10.1007/s10704-009-9422-8 Bai, Y., Wierzbicki, T., 2008. A new model of metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24, 1071 – 1096. https://doi.org/10.1016/j.ijplas.2007.09.004 Bonora, N., 1997. A nonlinear CDM model for ductile failure. Eng. Fract. Mech. 58, 11 – 28. https://doi.org/10.1016/S0013-7944(97)00074- References References

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