268 J Fail. Anal and Preven.(2012)12: 267-272 problems in FEM. SPH (smoothed particle hydrodynamics) Table 1 Material constants and Johnson-Cook parameters in the [19, 20], DEM(diffuse element method) [21], EFG model (element-free Galerkin)[22], RKPM(reproducing kernel Materials E GPa D A MPa B MPa n particle method)[23]. MLSRKM(moving least-square reproducing kernel method)(24, 25), etc are all the rep- 2024-T3Al 710.34 369 6840730. I7 resentative models in MMs. However, such MMs usually PU coatin 2.30.151461500.4980.097 ost more computation times than FEM. Consequently, E and D denote the elastic modulus and Poisson,s ratio several algorithms coupled with both FEM and MM have been put forward to utilize the respective advantages of each of them [26-31. In this article, a coupled simulation method between FEM and the meshfree model (MM) SPH was employed via the impact effect on ductile metal pipe with polymer coating [32]. Specifically, the impacted area(involving both the coating and the substrate) with large deformation was dis- cretized by SPH particles while the other section with les deformation was still modeled by FEM meshes. Two dif- ferent impact angles of 90 and 45(representing the normal and the oblique impacts, respectively) were imposed, and their functions on energy evolution, plastic strain, and stresses distribution of the targets during the impact process ere systematically analyzed. Finally, results of the normal impact with this coupled method were also compared with that of the sole FEm and the sole SPh method to discuss their Fig. 1 Schematic diagram of the impact model individual advantages and disadvantages Fig. 1. Specifically, the impacted area was modeled as SPH particles including 1, 350 for polymer coating and 3, 600 for metal substrate, and their uniform masses were, respectively, Modeling 3.733 10 and 1.385 x 10 kg per particle. The other section of the target was still modeled by FEM meshes with The impact process was simulated by means of 3D explicit element of SOLID 164. The impact velocity was 80 m/s, and dynamic analysis in ANSYS/LS-DYNA I0.0. The Johnson- two impact angles of 90 and 45 were exerted, respectively, Cook(-C)(33, 34 ]viscoplastic material model was applied representing the normal and the oblique impacts. The solu- for the flow stress behavior of the target materials and the tion time was set 1.5 x t. where t was the time that the von Mises flow stress was accordingly expressed in Eq 1: erodent particle needed to contact the target surface Gr=A+B(py 1+cIn(p As for the constrained conditions, the tied-nodes-to- surface contact was established between the sph scheme (Eg 1) and the FEM meshes to couple the two sections. Besides, the where A and B are the yield stress constant and the strain dent particle and the SPH section. In order to simplify the hardening constant; n,C, and m are constants; EP is the simulation, only a half-model was evaluated, and hence, the equivalent plastic strain; aP is the plastic strain rate, and Eo is constraints and SPH symmetry planes were set for the FEM the reference strain rate. T and Tm are the temperature and and SPH sections at the boundaries to achieve the symmetry the melting point of the target material, while T is the room conditions. Also, all of the bottom and outside nodes of the temperature. Aluminum alloy 2024-T3 Al and polyurethane target materials were defined to non-reflecting boundaries (PU) were chosen as the metal substrate and the polymer coating, respectively, material constants as well as J-C parameters of which are listed in Table 1 [9, 35]. The ero- Results and Discussion dent was 2 mm(diameter)aluminum spherical particle with density of 2, 770 kg/mand elastic modulus of 71 GPa. oupled Method In terms of the model geometry, thicknesses of the Al substrate and PU coating were 1. 4 and 0. I mm, respectively. During the simulation process, the internal and the kinetic The size of the whole target was 1.5 66 mm, as shownin energies evolutions of the normal (90%)and the obliqueproblems in FEM. SPH (smoothed particle hydrodynamics) [19, 20], DEM (diffuse element method) [21], EFG (element-free Galerkin) [22], RKPM (reproducing kernel particle method) [23], MLSRKM (moving least-square reproducing kernel method) [24, 25], etc. are all the rep￾resentative models in MMs. However, such MMs usually cost more computation times than FEM. Consequently, several algorithms coupled with both FEM and MM have been put forward to utilize the respective advantages of each of them [26–31]. In this article, a coupled simulation method between FEM and the meshfree model (MM) SPH was employed via the commercial software ANSYS/LS-DYNA to study the impact effect on ductile metal pipe with polymer coating [32]. Specifically, the impacted area (involving both the coating and the substrate) with large deformation was dis￾cretized by SPH particles while the other section with less deformation was still modeled by FEM meshes. Two dif￾ferent impact angles of 90 and 45(representing the normal and the oblique impacts, respectively) were imposed, and their functions on energy evolution, plastic strain, and stresses distribution of the targets during the impact process were systematically analyzed. Finally, results of the normal impact with this coupled method were also compared with that of the sole FEM and the sole SPH method to discuss their individual advantages and disadvantages. Modeling The impact process was simulated by means of 3D explicit dynamic analysis in ANSYS/LS-DYNA 10.0. The Johnson– Cook (J–C) [33, 34] viscoplastic material model was applied for the flow stress behavior of the target materials, and the von Mises flow stress was accordingly expressed in Eq 1: rf ¼ A þ Bðe p Þ n ½ 1 þ c ln e_ p e_0   1  T  Tr Tm  Tr   m ðEq 1Þ where A and B are the yield stress constant and the strain hardening constant; n, c, and m are constants; ep is the equivalent plastic strain; e_ p is the plastic strain rate, and e_0 is the reference strain rate. T and Tm are the temperature and the melting point of the target material, while Tr is the room temperature. Aluminum alloy 2024-T3 Al and polyurethane (PU) were chosen as the metal substrate and the polymer coating, respectively, material constants as well as J–C parameters of which are listed in Table 1 [9, 35]. The ero￾dent was 2 mm (diameter) aluminum spherical particle with density of 2,770 kg/m3 and elastic modulus of 71 GPa. In terms of the model geometry, thicknesses of the Al substrate and PU coating were 1.4 and 0.1 mm, respectively. The size of the whole target was 1.5 9 696 mm, as shown in Fig. 1. Specifically, the impacted area was modeled as SPH particles including 1,350 for polymer coating and 3,600 for metal substrate, and their uniform masses were, respectively, 3.733 9 107 and 1.385 9 106 kg per particle. The other section of the target was still modeled by FEM meshes with element of SOLID 164. The impact velocity was 80 m/s, and two impact angles of 90 and 45 were exerted, respectively, representing the normal and the oblique impacts. The solu￾tion time was set 1.5 9 t, where t was the time that the erodent particle needed to contact the target surface. As for the constrained conditions, the tied-nodes-to￾surface contact was established between the SPH scheme and the FEM meshes to couple the two sections. Besides, the eroding-nodes-to-surface contact was defined between ero￾dent particle and the SPH section. In order to simplify the simulation, only a half-model was evaluated, and hence, the constraints and SPH symmetry planes were set for the FEM and SPH sections at the boundaries to achieve the symmetry conditions. Also, all of the bottom and outside nodes of the target materials were defined to non-reflecting boundaries. Results and Discussion Coupled Method During the simulation process, the internal and the kinetic energies evolutions of the normal (90) and the oblique Table 1 Material constants and Johnson-Cook parameters in the model Materials E, GPa t A, MPa B, MPa n cm 2024-T3 Al 71 0.34 369 684 0.73 0.0083 1.7 PU coating 2.3 0.15 146 150 0.498 0.097 … E and t denote the elastic modulus and Poisson’s ratio Fig. 1 Schematic diagram of the impact model 268 J Fail. Anal. and Preven. (2012) 12:267–272 123