Nicht-lokale mikromechanische Schädigungsmodellierung für metallische Werkstoffe mittels netzfreien Verfahren

• Applicant: Professor Dr.-Ing. Huang Yuan
• Subject Area: Materials Engineering
• Term: from 2007 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 45037629

• Final Report Year: 2011

Final Report Abstract

Most published works on modeling of ductile material failure are based on the finite element methods. Under large deformations and distortions the FEM computation often fails to convergence. The problem becomes more severe if the material model depends on higher order of strain gradients. In the present project the nonlocal material failure is considered by using the element-free Galerkin method (EFG). The nonlocal damage model based on the known GTN model is reformulated within the frame of the strain gradient plasticity. Implementations of the gradient plasticity as well as the nonlocal damage model into EFG under plane strain and axisymmetric loading conditions are realized with the commercial FEM code ABAQUS by using the User-Element Interface. Following problems have been studied systematically: • Application of the nonlocal damage model to predict size effects agrees experimental data of tensile specimens. The computational convergence is more robust than the FEM algorithms. The EFG provides a more stable algorithm for complex material models. The investigation confirms that the nonlocal damage model with the element-free Galerkin method is suitable for computing damage problems and predicting size effects. • Effects of different strain-gradient dependent regulators have been considered analytically and numerically. It is found that the first order of strain gradient in the conventional form cannot eliminate the mesh-independence, while the second-order strain gradient will remove effects of discretization in numerical results. However, the second-order of strain gradient is generally too strong in crack tip fields to converge. A modified regulator based on the first-order of strain gradient has been introduced and generated mesh-independent results in shear band analysis. • Analysis of crack tip fields in gradient plasticity confirms that under the infinitesimal strain formulation, the crack field consists of three zones: The elastic K-field, the known plastic HRR-field and the hyper-singular stress field related to the gradient plasticity. The stress singularity from the gradient plasticity is significantly higher than the HRR and numerically equals 0.78, independently of plastic strain-hardening exponent. The HRR-zone is described by the known fracture parameters, e.g. the energy release rate G, whereas the hyper-singular zone seems not scalable. The finite strains do not change characterization of the crack tip fields. The hyper-singular zone under gradient plasticity with finite strains is the same as that under infinitesimal deformation theory. Generally, the finite strain affected zone is in the size of the hyper-singular zone, so that the known HRR concept can be applied for controlling the crack. The strain-gradient term in the strain-gradient plasticity does not affect characterization of cracks. The known elastic-plastic fracture mechanics parameters, G and δt , can be directly applied to the crack assessment under strain-gradient plasticity for l ≤ 0.1%L0 . • Based on the background mesh concept in meshless methods, a new efficient averaging algorithm for the damage variable is introduced for the GTN model and verified. The new algorithm can be easily implemented into the FEM, e.g. ABAQUS, or other numerical methods. The results confirm that the damage simulation using the present algorithm is mesh-independent. The algorithm can be directly extended to 3D specimens. The main aim of the present project is introducing the meshless method into simulation of nonlocal damage modeling. The meshless method can be combined with the commercial FEM codes, such as ABAQUS, directly, which makes the meshless method generally flexible in further development, especially for engineering applications. Furthermore, computations confirm that the EFG is more robust than the FEM, but less efficient. It can be used for more complex material models, but is generally more time-consuming. It could be difficult to use the EFG for 3D structure analysis. The gradient plasticity can be well embedded into the EFG and show reasonable convergence. The present works show that the crack assessment can follow the conventional fracture mechanics methodology which makes the structural integrity more easier. The nonlocal modeling for material failure based on both strain gradients and integration averaging method can be integrated into ABAQUS. The computations confirm the known size effects in material failure. For engineering application more experimental data are necessary. The research work in this field will be continued in a new project dealing with damage modeling in sintered metals. The results from the present project can be applied to the new research work.

Publications

• Meshless methods for micromechanical damage modelling. Modelling Simulation Material Science and Engineering. 17 (2009) 045005 (19pp)
  X. Pan, H. Yuan
  
• Nonlocal damage modelling using the element-free Galerkin method in the frame of finite strains. Computational Material Sciences. 46 (2009) 660-666
  X. Pan, H. Yuan
  
• Computational algorithms and applications of element-free Galerkin methods for nonlocal damage models. Engineering Fracture Mechanics. 77 (2010), 2640- 2653
  X. Pan, H. Yuan
  
• Applications of the element-free Galerkin method for singular stress analysis under strain gradient plasticity theories. Engineering Fracture Mechanics 78 (2011), 452-461
  X. Pan, H. Yuan
  
• Computational assessment of cracks under strain-gradient plasticity. International Journal of Fracture 167 (2011), 235-248
  X. Pan, H. Yuan