PSI- Issue 9

Riccardo Fincato et al. / Procedia Structural Integrity 9 (2018) 126–135 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 Author name / Structural Integrity Procedia 00 (2018) 000 – 000 Author name / Structural Integrity Procedia 00 (2018) 000 – 000 equivalent strain to fracture. A similar representation of the failure envelope is more complicated to graphic for the Lemaitre’s criterion. a 8 8 8 8 8 equivalent strain to fracture. A similar representation of the failure envelope is more complicated to graphic for the Lemaitre’s criterion. a equivalent strain to fracture. A similar representation of the failure envelope is more complicated to graphic for the Lemaitre’s criterion. a equivalent strain to fracture. A similar representation of the failure envelope is more complicated to graphic for the Lemaitre’s criterion. a equivalent strain to fracture. A simil representation of the failure envelope is more complicated to graphic for the Lemaitre’s criterion. a

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Figure 5 a) Mohr- Coulomb’s failure envelope, b) stress triaxiality -equivalent strain to fracture graph for the samples, c) Lode angle parameter-equivalent strain to fracture for the samples. Figure 5 a) Mohr- Coulomb’s failure envelope, b) stress triaxiality -equivalent strain to fracture graph for the samples, c) Lode angle parameter-equivalent strain to fracture for the samples. It is clear that the round notched bars tend to fail under a pure uniaxial tensile condition,  = 1, whereas the flat grooved plates fail around a plane strain condition  ≈ 0. An easier representation of the paths to failure is offered in Figure 5b and c where the stress triaxiality-equivalent strain to fracture and the Lode angle parameter- equivalent strain to fracture are depicted for the MC solutions. In addition, the average stress triaxiality paths and average Lode angle parameter paths are also displayed by dotted lines in Figure 5b and c, respectively. The averages values are obtained using the integral formulation suggested by Bai and Wierzbicki in Bai and Wierzbicki (2010). The comparison with the numerical values obtained by Li et al. (2016) shows a good agreement with the average values obtained with the MC criterion. There is a general overestimation of the equivalent strain to failure in the curves obtained with the Damage S-S model, however, this may be due to the fact that in Li et al. (2016) the analyses were carried out with a simple elastoplastic model without a coupling with the ductile damage variable. The same graph of the failure paths in the stress triaxiality-equivalent strain to fracture plane is also reported in Fincato and Tsutsumi (2017a) for the Lemaitre’s ductile damage evolution law, showing the same tendency of overestimating the equivalent strain to fracture compared with the Li et al.’s numerical values. 3.3. Discussion The use of both the modified Lemaitre’s and modified Mohr - Coulomb’s criteria can produce excellent results in modeling the ductile f ailure under monotonic loading. The original Lemaitre’s formula is not suitable for the description of the damage evolution under different loading conditions since the effect of the Lode angle is not accounted for. The modification suggested by the authors in Fincato and Tsutsumi (2017a) overcome this issue but, at the same time, it introduces three additional material parameters that have to be calibrated by carrying an experimental campaign. In general, as mentioned already in section 3.1, one single tensile test is not enough for Figure 5 a) Mohr- Coulomb’s failure envelope, b) stress triaxiality -equivalent strain to fracture graph for the samples, c) Lode angle parameter-equivalent strain to fracture for the samples. It is clear that the round notched bars tend to fail under a pure uniaxial tensile condition,  = 1, whereas the flat grooved plates fail around a plane strain condition  ≈ 0. An easier representation of the paths to failure is offered in Figure 5b and c where the stress triaxial ty-equivalent strain to fracture and the Lode angle parameter- equivale t strain to fracture are depicted for the MC solutions. In addition, the average stress triaxiality paths and average Lode angle param ter aths are also displayed by dotted lines in Figure 5b and c, respectively. T e ver g s values are obtained using the integral formulation suggested by Bai and Wierzbicki in Bai and Wierzbicki (2010). The compar son with the numerical values obtained by Li et al. (2016) shows a goo agr ement with the average values obta ned with the MC crit rion. Th re is a g neral overestimation of the equival strain to f ilure in the curves obtained with the Damage S-S model, however, this may be due to fact that in Li et al. (2016) the analyses were carried out with simple elastoplastic model without a coupling with the ductil damage variable. The same graph of the failure paths in the stress triaxiality-equivalent strain to fractur plane is also reported in Fincato and Tsutsumi (2017a) for the Lemaitre’s ductile damage evolution law, showing the same tendency of overesti ating the equivalent strain to fracture compared with the Li et al.’s numerical values. 3.3. Discussion The use of both the modified Lemaitre’s and modified Mohr - Coulomb’s criteria can produce excellent results in modeling the ductile f ailur under monotonic loading. The original Lemaitr ’s formula is not suitable for the description of the damage evol tion under different loading c nditions since the effect of the Lode ngle is not accounted f r. The modification suggest d by th authors in Fi cat and Tsutsumi (2017a) overcome this issue but, at the same time, it introduces three additional material parameters that have to be calibrated by carrying an experimental campaign. I general, as mentioned already in section 3.1, one single tensile test is not enough for Figure 5 a) Mohr- Coulomb’s failure envelope, b) stress triaxiality -equivalent strain to fracture graph for the samples, c) Lode angle parameter-equivalent strain to fractur for th sampl . It is clear that the round notched bars tend to fail under a pure uniaxial tensile condition,  = 1, whereas the flat grooved plates fail around a plane strain condition  ≈ 0. An easier representation of the paths to failure is offered in Figure 5b and c where the stress triaxiality-equivalent strain to fracture and the Lode angle parameter- equivalent strain to fracture are depicted for the MC solutions. In addition, the average stress triaxiality path and average Lode angle parameter paths are also displayed by dotted lines in Figure 5b and c, respectively. The averag s values are ob ained using the integral formulati suggested by Bai and Wierzbicki in Bai and Wierzbicki (2010). The co parison with the numerical values obtained by Li et al. (2016) shows a goo agreement with the average values obtained with the MC criterion. There is a general overestimation of the equivale t strain to failure in the curves obtained with the D mage S-S model, however, this may be due to t e fact that in L et al. (2016) the analyses w re carried out with a simple elastoplastic model without a coupling with th ductile damage variabl . The same graph of the failure paths in the stress triaxiality-equival nt strain to fracture plane is also reported in Fincato and Tsutsumi (2017a) for the Lemai re’s du tile damage evoluti n law, showing the same tendency of over sti ating the equiv lent strain to fracture compared with the Li et al.’s nume ical values. 3.3. Discussion The use of both the modified Lemaitre’s and modified Mohr - Coulomb’s criteria can produce excellent results in modeling the ductile f ailure under monotonic loading. The original Lemaitre’s formula is not suitable for the description of the damage evolution under different loa ing conditions since the effect of the Lode angle is not accounted for. The modification suggested by the authors in Fincato and Tsutsumi (2017a) overcome this issue but, at the same time, it introduces three additional material parameters that have to be calibrated by carrying an experimental campaign. In general, as m ntioned already in section 3.1, one single tensile test is not enough for Figure 5 a) Mohr- Coulomb’s failure envelope, b) stress triaxiality -equivalent strain to fracture graph for the samples, c) Lode angle parameter-equivalent strain to fractur for th sampl . It is clear that the round notched bars tend to fail under a pure uniaxial tensile condition,  = 1, whereas the flat grooved p ate fail around a plane strain condition  ≈ 0. An easier representation of the paths to failure is offered in Figure 5b and c where the stress triaxiality-equivalent strain to fracture and the Lode angle parameter- equivale t strain to fracture are depicted for the MC solutions. In addition, the average stress triaxiality pat s and average Lode angle param ter aths are also displayed by dotted lines in Figure 5b and c, respectively. T e averag s values are obtained using the integral formulation suggested by Bai and Wierzbicki in Bai and Wierzbicki (2010). The comparison with the numerical values obtained by Li et al. (2016) shows a goo agr ement with the average values obtained with the MC criterion. There is a general overestimation of the equivalent strain to failure in the curves obtained with the Damage S-S model, however, this may be due to t fact that in Li et al. (2016) the analyses were carried out with a simple elastoplastic model without a coupling with the ductile damage variable. The same graph of the failure paths in the stress triaxiality-equivalent strain to fracture plane is also reported in Fincato and Tsutsumi (2017a) for the Lemaitre’s ductile damage evolution law, showing the same tendency of overestimating the equivalent strain to fracture compared with the Li et al.’s numerical values. 3.3. Discussion The use of both the modified Lemaitre’s and modified Mohr - Coulomb’s criteria can produce excellent results in modeling the ductile f ailur under monoto ic l ading. The original Lemaitre’s formula is not suitable for the descriptio of the damage evol tion under different loading c nditions since the effect of the Lode angle is not accounted f r. The modification suggest d by th authors in Fi cat and Tsutsumi (2017a) overcome this issue but, at the same time, it introduces thr e a ditional material parameters that have to be calibrated by carrying an experimental campaign. In general, as mentioned already in section 3.1, one single tensile test is not enough for It is clear that the round notched bars tend to fail under a pure uniaxial tensile condition,  = 1, whereas the flat grooved plates fail around a plane strain condition  ≈ 0. An easier representation of the paths to failure is offered in Figure 5b and c where the stress triaxiality-equivalent strain to fracture and the Lode angle parameter- equivalent strain to fracture are depicted for the MC solutions. In addition, the average stress triaxiality paths and average Lode angle parameter paths are also displayed by dotted lines in Figure 5b and c, respectively. The averages values are obtained using the integral formulation suggested by Bai and Wierzbicki in Bai and Wierzbicki (2010). The comparison with the numerical values obtained by Li et al. (2016) shows a good agreement with the average values obtained with the MC criterion. There is a general overestimation of the equivalent strain to failure in the curves obtained with the Damage S-S model, however, this may be due to the fact that in Li et al. (2016) the analyses were carried out with a simple elastoplastic model without a coupling with the ductile damage variable. The same graph of the failure paths in the stress triaxiality-equivalent strain to fracture plane is also reported in Fincato and Tsutsumi (2017a) for the Lemaitre’s ductile damage evolution law, showing the same tendency of overestimating the equivalent strain to fracture compared with the Li et al.’s numerical values. 3.3. Discussion The use of both the modified Lemaitre’s and modified Mohr - Coulomb’s criteria can produce excellent results in modeling the ductile f ailure under monotonic loading. The original Lemaitre’s formula is not suitable for the description of the damage evolution under different loading conditions since the effect of the Lode angle is not accounted for. The modification suggested by the authors in Fincato and Tsutsumi (2017a) overcome this issue but, at the same time, it introduces three additional material parameters that have to be calibrated by carrying an