Multi-scale Mechanical Response And Damage Analysis Of3-d Orthogonal Woven Composite Under Quasi-static/Low Cyclic Fatigue Loadings

Compared with interlaminar delamination resistance composite,3-D orthogonal woven composite (3DOWC) has higher fracture toughness, higher in-plane strength properties, and significantly enhanced damage tolerance with potential applications in fields of aircraft, ship, high speed vehicles, and naval vessels et al. This paper is mainly focused on the quasi-static and low cyclic tensile mechanical responses and damage mechanisms of3DOWCs using multi-scale finite element method (FEM).The3-D orthogonal woven composite was prepared from3-D orthogonal woven G-glass fabric (3DOWF) and unsaturated polyester of AROPOLTM INF80501using vacuum assisted resin transfer molding (VARTM) technique at room temperature. The micro/meso/macro-scale geometric repeating unit cells models (RUCs) were established respectively based on periodic boundary conditions (PBCs), fiber bundles (warp yarns, weft yarns and Z-bindles) architecture in3DOWC and principle of equivalent fiber volume fraction, The multi-scale materials models with damage evolution and switch rule were developed by user-defined material subroutine (UMAT) in Fortran90code corresponding to above-mentioned multi-scale RUCs and their components. The quasi-static and low cyclic tensile-tensile mechanical responses and damage evolution of3DOWC were simulated with UMAT incorporated into commercial finite element software ABAQUS/Standard. Simultaneously, the experimental data and damaged morphology were also provided and compared with the predicted results in good agreement. Furthermore, the versatility and reliability of the code need to be further verified by comparison with more experimental results and applied in terms of mechanical responses and damage analysis for the complicated composite under multi-axial loadings.The main contents are as follows.(1) The quasi-static tensile and3-point bending tests:The dog-bone and beam shaped specimens were manufactured respectively in length along warp yarns direction using water jet cutter. The quasi-tensile tests were conducted with done-bone shaped samples on MTS810machine. And the3-point bending tests were also operated with beam shaped samples. The mechanical responses with ultimate strengths and final damage morphology of3DOWC were obtained. Correspondingly, their damage mechanisms for quasi-tensile and3-point bending cases were determined approximately.(2) Low cyclic tensile fatigue tests:The dog-bone shaped specimens were performed by above MTS-810machine under strain control equipped with an electro-mechanical sensor to record the longitudinal strains in the middle fields of samples. The low cyclic mechanical responses and local damaged locations were obtained. The initial fatigue damage mechanisms were analyzed according to different loading paths.(3) Multi-scale geometric repeating unit cells (RUCs) models:Due to periodic array of3DOWC in in-plane directions, the meso-RUC was established firstly based on the real architecture of matrix impregnated fiber bundles (such as in-plane weaving density, fiber bundler layers, and thickness size in3DOWC). Then a micro-RUC was introduced to analyze the mechanical properties of fiber yarns (warp yarns, weft yarns and Z-binder yarns) with hexagonal distribution of fiber in matrix. To reveal the essential distinction of surface and interior fields of3DOWC, the inner meso-RUC and surface meso-RUC were further constructed because of an array of inner meso-RUC in interior fields of3DOWC. Finally the macro-scale beam for tested samples was established based on sizes of inner meso-RUC and surface meso-RUC and layers of weft and warp fiber bundles in3DOWC in thickness direction. For micro/meso-scale RUCs and sub-meso-RUCs, the periodic boundary conditions (PBCs) were applied correctly with master node to slave nodes technology. Finally the macro-scale beam was established based on the sub-meso-RUCs above-mentioned.(4) Multi-scale quasi-static material models with user-defined subroutines (UMAT):For multi-scale geometric RUCs, the elastic and nonlinear viscoelastic constitutive models with post-damage relation on the concept of smear crack and switch rule to represent a loading/unloading case were defined in Fortran90by user-defined subroutines (UMAT) respectively. In micro-RUC consisting of fiber and matrix, the isotropic elastic and nonlinear viscoelastic models with maximum principle theory failure criteria for glass fiber and polyester resin were coded. The mechanical parameters and ultimate failure strengths of micro-RUC were calculated by application of normal and shear strain loadings on master nodes. Then in the meso-RUC and inner/surface meso-RUCs including the matrix impregnated fiber bundles (micro-RUC) and pure matrix around the fiber bundles with matrix, a transversely isotropic materials models with maximum strengths failure independent on the concept of smear cracks in three principal directions (the failure criterions were transferred from ultimate strengths of micro-RUC in fiber direction and transverse directions) was proposed for matrix impregnated fiber bundles and an elastic isotropic or nonlinear viscoelastic models were used for pure matrix in meso-RUCs and sub-meso-RUCs respectively. The macro-scale beams of3DOWC in principal directions were modeled respectively with orthotropic anisotropic material model with maximum stress failure criteria separately in three principal directions. The in-plane and delaminated strengths for interior and surfacal elements of macro-scale beam were got from analysis of above-mentioned inner meso-RUC and surface meso-RUC.(5) Multi-scale low cyclic fatigue model by user-defined subroutines (UMAT):Based on above-mentioned multi-scale quasi-static user-defined material models (UMAT), a switch rule to represent the loading/unloading case was incorporated into the nonlinear viscoelastic model. With similar transferred mechanism of mechanical parameters and failure strengths from fiber/matrix to micro-RUC, meso-RUC and macro-scale beam, the low cyclic fatigue behaviors including damage locations of multi-scale RUCs and their components were obtained separately.(6) Applications of above multi-scale user-defined subroutines (UMATs) to multi-scale RUCs:To evaluate the versatility and reliability of current UMATs, the quasi-static and cyclic loading mechanical responses and damage mechanism of micro/meso/macro-RUCs were simulated respectively with UMATs incorporated into finite element software ABAQUS/Standard. The predicted results are verified well with the experimental data and observations.The multi-scale finite element analysis provided in current paper can be successively extended to predict mechanical responses, damage analysis, and low cyclic fatigue behavior of other complex textile composites. We hope such an effect could be applied to design and optimization of aircrafts, high speed vehicles and ballistic protections et al in which the3-D orthogonal woven composites are often used.