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 1 2 3 / p f D H d        D Author name / Structural Integrity Procedia 00 (2018) 000 – 000 Author name / Structural Integrity Procedia 00 (2018) 000 – 000 1 2 3 / p f D H d      D Author name / Structural Integrity Procedia 00 (2018) 000 – 000   1 2 3 / p f D H d        D Author name / Structural Integrity Procedia 00 (2018) 000 – 000

5 5 5 5 5 5 5 5

      

      

(9) (9) (9) (9) (9) (9) (9) (9)

130

          

f f f f f H d   H d    H d    H d    H d          

2 3 / p D 2 3 / p D 2 3 / p D 2 3 / p D 2 3 / p D

D D D D D

    

1 1 1 1 1

The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion requires the calibration of five constants, one less than the modified Lemaitre’s criterion. The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion requires the calibration of five constants, one less than the modified Lemaitre’s criterion. The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion requires the calibration of five constants, one less than the modified Lemaitre’s criterion. The work in this paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and numerical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S model were implemented via user subroutine for the commercial code Abaqus (ver. 6.14-4) and used in the FEA. The modified Lemaitre and modified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on the sample, alternatively. In the graphs of the section 3.2 the criteria will be indicated with L for the Lemaitre’s approach and with MC for the Mohr- Coulomb’s theory. The elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of samples: round notches bars and flat grooved plates. This choice is functional to the evaluation of the Lode angle influence on the degradation of the mechanical parameters since different experimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilkins et al., 1980; Zhang et al., 2001) pointed out a different ductility under different loading conditions (i.e. uniaxial extension, plane strain, pure shear, etc.). Moreover, each sample is characterized by a different notch/groove radius, in order to highlight the role of the stress triaxiality. The geometry of the specimens is reported in the following Figure 3a. For sake of simplicity the notched bars were modeled with a 2D geometry under the assumption of axial symmetry (see Figure 3b), whereas only one-eighth of the flat grooved plates were considered, applying symmetric boundary conditions as shown in Figure 3c. a b The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion requires the calibration of five constants, one less than the modified Lemaitre’s criterion. 3. Nume ical analyses The work i thi paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and numerical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S model were implemented via user subroutine for the c mmercial od Abaqus (ver. 6.14-4) and used in the FEA. Th modified Lemaitre and m dified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on th sample, alt rnatively. In the graphs of the section 3.2 the criteria will be indicated with L for the Lemaitre’s approach and with MC for the Mohr- C ulomb’s theory. 3.1. Geometry of the samples Th elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of samples: round notches bars and flat grooved plates. This choice is functional to the evaluation of the Lode angle inf uence on the egradation of the mechanical parame ers since different experimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilk ns et al., 1980; Zhang et al., 2001) pointed out a differ t ductility under different loading co ditions (i.e. uniaxial extension, plane strain, pure shear, etc.). Moreover, each sample is characterized by a different notch/groove radius, in order to highlight the role f he stress triaxiality. The geomet y o the specimens is rep rted in the following F gure 3a. For sake of simplicity the notched bars were modeled with a 2D geometry under the assumption of axial ymmetry (see Figure 3b), whereas only o e-eighth of the flat grooved plates were considered, applying symmetric boundary condi ions as shown in Figure 3c. a b The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion requires the calibration of five constants, one less than the mo ified Lemaitre’s criterion. 3. Nume ical analyses The work i t i paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and numerical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S mod l were implemented via user subroutine for the commercial code Abaqus (ver. 6.14-4) and used in the FEA. Th modified Lemaitre and modified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on th sample, alternatively. In the graphs of the section 3.2 the criteria will b indicated with L for the Lemaitre’s approach and with MC for the Mohr- Coulomb’s theory. 3.1. Geometry of the samples Th elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of samples: round notches bars and flat grooved plates. This choice is functional to the evaluation of the Lode angle influence on the degradation of the mechanical parameters since different experimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilkins et al., 1980; Zhang et l., 2001) pointed out a different ductility under differ nt loading conditions (i.e. uniaxial extension, plane strain, pure shear, etc.). Moreover, each sample is characterized by a different notch/groove radius, in order to highlight the role of the stress triaxiality. The geomet y of the speci ns is rep rted in the following Figure 3a. For sa e of simplicity the notched bars were modeled with a 2D geometry under the assumption of axial symmetry (see Figure 3b), whereas only one-eighth of the flat grooved plates were considered, applying symmetric boundary conditions as shown in Figure 3c. a b The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion equires th calibration of five constants, one less than th m dified Lemaitre’s criterion. 3. Numerical analyses The work in this paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and num rical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S model were implemented via user sub outine for the commercial cod Abaqus ( r. 6.14-4) and us d in the FEA. The modified Lemaitre and modified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on the sampl , alterna ively. In the graphs of the section 3.2 th rit ri will be indicated with L for the Lemaitre’s approach and with MC for the Mohr- Coulomb’s theory. 3.1. Geometry of the samples The elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of sampl s: round not hes bars nd flat gr oved plates. This choi e is functional to the eval ation of the Lode angle influence on th deg adation of the mechanical parameters since different experimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilk ns et al., 1980; Zhang et al., 2001) pointe out a different ductility u der different loading conditions (i.e. uniaxial xtension, plane strain, pure shear, etc.). Moreover, ach sample is characterized by a different notch/groove radius, in order to highlight the role of the stress triaxiality. The g ometry of the specimens is r ported in the following Figure 3a. For s ke of simplicity the n tc d bars were modeled wit a 2D geometry under the assumption of axial symmetry (see Figure 3b), whereas only one-eighth of the fl t grooved plates were considered, applying symmetric boundary conditions as shown in Figure 3c. a b The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion equires th calibration of five constants, one less than th modified Lemaitre’s criterion. 3. Num r cal n lys s The work i thi paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and num rical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S model were implemented via user subroutine for the commercial code Abaqus (ver. 6.14-4) and used in the FEA. The modified Lemaitre and modified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on the sample, alternatively. In the graphs of the section 3.2 the criteria will be indicated with L for the Lemaitre’s approach and with MC for the Mohr- Coulomb’s theory. 3.1. Geometry of the samples The elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of sampl s: round notches bars and flat grooved plates. This choice is functional to the evaluation of the Lode angle influence on the egradation of the mechanical parameters si ce differe t xperimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilkins et al., 1980; Zhang et l., 2001) pointed out a differe t ductility under different loading conditions (i.e. uniaxial xtensio , plan strain, pure shear, etc.). Moreover, each sample is charact rized by a different notch/groove radius, in rd r to highlight the role of the stress triaxiality. The geometry of the specimens is reported in the following Figure 3a. For s ke of simplicity the n tc d bars were modeled with a 2D geometry under the assumption of axial sy etry (see Figure 3b), whereas only one-eighth of the flat grooved plates were considered, applying ic b undary conditions as shown in Figure 3c. a b The material parameter d 1 has exactly the same meaning of the previous constant s 3 of Eq. (6). The M-C failure criterion requires th calibration of five constants, one less than the modified Lemaitre’s criterion. 3. Nume ical analyses The work i thi paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and num rical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S model were implemented via user subroutine for the commercial code Abaqus (ver. 6.14-4) and used in the FEA. The modified Lemaitre and modified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on the sample, alternatively. In the graphs of the section 3.2 the criteria will be in icated with L for the Lemaitre’s approach and with MC for the Mohr- Coulomb’s theory. 3.1. Geometry of the samples The elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of samples: round notches bars nd flat grooved plates. This choice is functional to the evaluation of the Lode angle influence on t eg adation of the mechanical parameters since different xperimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilkins et al., 1980; Zhang et l., 2001) pointe out a differe t ductility u der different loading conditions (i.e. uniaxial extension, plane strain, pure shear, etc.). Moreover, each sample is characterized by a different notch/groove radius, in rder to hi hlight the role of the stress triaxiality. The g ometry o the specimens is reported in the following Figure 3a. For s ke of simplicity the n tc d bars were modeled with a 2D geometry under the assumption of axial symmetry (see Figure 3b), whereas only one-eighth of the flat grooved plates were considered, applying t ic b undary conditions as shown in Figure 3c. a b 3. Numerical analyses 3. Numerical analyses 3. Numerical analyses The work in this paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and numerical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S model were implemented via user subroutine for the commercial code Abaqus (ver. 6.14-4) and used in the FEA. The modified Lemaitre and modified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on the sample, alternatively. In the graphs of the section 3.2 the criteria will be indicated with L for the Lemaitre’s approach and with MC for the Mohr- Coulomb’s theory. The elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of samples: round notches bars and flat grooved plates. This choice is functional to the evaluation of the Lode angle influence on the degradation of the mechanical parameters since different experimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilkins et al., 1980; Zhang et al., 2001) pointed out a different ductility under different loading conditions (i.e. uniaxial extension, plane strain, pure shear, etc.). Moreover, each sample is characterized by a different notch/groove radius, in order to highlight the role of the stress triaxiality. The geometry of the specimens is reported in the following Figure 3a. For sake of simplicity the notched bars were modeled with a 2D geometry under the assumption of axial symmetry (see Figure 3b), whereas only one-eighth of the flat grooved plates were considered, applying symmetric boundary conditions as shown in Figure 3c. a b The work in this paper aims to evaluate the ductile behavior of six specimens made of Q460 steel, reproducing the experimental and numerical works carried out by Li et al. (2016). The constitutive equations of the Damage S-S model were implemented via user subroutine for the commercial code Abaqus (ver. 6.14-4) and used in the FEA. The modified Lemaitre and modified Mohr- Coulomb’s failure criteria are adopted to model the crack initiation on the sample, alternatively. In the graphs of the section 3.2 the criteria will be indicated with L for the Lemaitre’s approach and with MC for the Mohr- Coulomb’s theory. 3.1. Geometry of the samples The elastoplastic and damage behavior of the Q460 construction steel is investigated using two types of samples: round notches bars and flat grooved plates. This choice is functional to the evaluation of the Lode angle influence on the degradation of the mechanical parameters since different experimental works (Bai and Wierzbicki, 2008; Clausing, 1970; Wierzbicki and Xue, 2005; Wilkins et al., 1980; Zhang et al., 2001) pointed out a different ductility under different loading conditions (i.e. uniaxial extension, plane strain, pure shear, etc.). Moreover, each sample is characterized by a different notch/groove radius, in order to highlight the role of the stress triaxiality. The geometry of the specimens is reported in the following Figure 3a. For sake of simplicity the notched bars were modeled with a 2D geometry under the assumption of axial symmetry (see Figure 3b), whereas only one-eighth of the flat grooved plates were considered, applying sy etric boundary conditions as shown in Figure 3c. a b 3.1. Geometry of the samples 3.1. Geometry of the samples

c c c c c c c c

d d d d d d d d

Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) uniaxial nominal stress-nominal strain curve. Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) uniaxial nominal stress-nominal strain curve. All the simulations were carried out applying a monotonic extension by means of an imposed displacement boundary condition. The information regarding the total number of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elastoplastic and damage parameters was carried out reproducing the experimental uniaxial extension nominal stress- nominal strain on a Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) uniaxial nominal stress-nominal strain curve. All the simulations were carried out applying a monotonic extension by means of an imposed displacement boundary condition. The information regarding the total number of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elastoplastic and damage parameters was carried out reproducing the experimental uniaxial extension nominal stress- nominal strain on a smooth bar by means of a single cubic element with reduced integration. The numerical results are reported in Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) uniaxial nominal stress-nominal strain curve. All the simulations were carried out applying a monotonic extension by means of an imposed displacement boundary condition. The information regarding the total number of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elastopla tic and damage parameters was carried out rep oduci g the experimental uniaxial extension nominal stress- nominal strain on a smooth bar by means of a s gle cubic element with reduced integration. The num ric l results are reported in Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) uniaxial nominal stress-nominal strain curve. All the simulations w re carried out applying a monotonic extension by eans of an imposed displacem nt boundary condition. The information regarding the total number of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elastopla tic and damage parameters was carried out reproducing the experi ental uniaxial extension nominal stress- nominal strain on a smooth bar by means of a si gle cubic element with reduced int gration. Th numeric l results are reported in Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) uniaxial nominal stress-nominal strain curve. All the simulations were carried out applying a monotonic extension by means of an imposed displacement boundary condition. Th information regarding the to al number of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elas oplastic and damage parameters was carried out reproducing the experimental uniaxial extension nominal stress- nominal strain on a smooth bar by means of a single cubic element with reduced integration. The numerical results are reported in Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) niaxi l nominal stress-nominal strain curve. All the simula ions w re carried out applying a monoto ic extension by ans of an imposed displacem nt boundary condition. The information regarding the total number of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elastoplastic and damage parameters was carried out reproducing the experimental u iaxial extension nominal stress- nominal strain on a smooth bar by means of a single cubic lement with reduced integration. The numeric l results are reported in Figure 3 a) Geometries of the samples, b) numerical modelling of the round notched bars, c) numerical modelling of the flat grooved plates, d) uniaxial nominal stress-nominal strain curve. All the simula ions were carried out applying a monot ic ext nsion by ans of an imposed displacem nt boundary condition. Th information regarding the total numb r of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elastoplastic and damage parameters was carried out reproduci g the experi ental uniaxial extension n minal stress- nomin l strain on a smo th bar by means of a si gle cubic element with reduced integration. The numerical results are reported in All the simulations were carried out applying a monotonic extension by means of an imposed displacement boundary condition. The information regarding the total number of nodes and elements are reported in the authors’ previous work (Fincato and Tsutsumi, 2017a). The calibration of the elastoplastic and damage