Enriched Finite Element Method For Typical Defects In Linear Viscoelastic Media

Starting by problems about structure integrity analysis of Solid Rocket Motor(SRM) containing defects such as cracks, drop pieces, cohesive cavities, and cut soltsexisting in the propellant grain, the theories including the formulation of enrichedelements for typical defects in viscoelastic media and the evaluation of fracturalparameters for defects in viscoelastic media, are studied. The main work andachievements are summaried as follows:1. The enriched finite method for2-D crack problems in a linear viscoelasticmedium is established.According to the classical elastic-viscoelastic correspondence principle, theasymptotic displacement field at a2-D crack tip in an isotropic viscoelastic medium isobtained. By enriching the viscoelastic asymptotic displacement field into the regular2-D element, the2-D enriched crack element is established. The viscoelasticincremental constitution relationship is formulated by using the Boltzmannsuperposition principle. With these treatments, the incremental enriched finite elementmethod formulations in time domain are derived by applying the incremental form ofthe principle of virtual work. The strain energy release rate with an arbitary direction atthe crack tip is finally presented by virtual crack closure principle for a2-D crack in aviscoelastic body.2. The enriched finite method for3-D crack problems in a linear viscoelasticmedium is established.Through combining the crack-tip asymptotic displacement field in a viscoelasticmedium under plane strain state and that under antiplane shear state, the asymptoticdisplacement field at an arbitary point of the3-D crack front is obtained. The3-Denriched crack element is established by enriching the viscoelastic asymptoticdisplacement field into the regular3-D element and the local prism coordinate systemfor some point inside an enriched element is definied. After deriving the viscoelasticincremental formulations of the3-D enriched finite element method in time domain, thestrain energy release rate for3-D crack at arbitary direction is presented.3. The enriched finite method for2-D V-shaped notch problems in a linearviscoelastic medium is established.Based on the asymptotic displacement field at the V-shaped notch tip, the2-Denriched notch element is formulated for a notched viscoelastic body by referring to the2-D enriched crack element. Then the incremental enriched FEM formulations in timedomain are also derived. A novel method for the strain energy release rate with anarbitary direction at the notch tip is presented by means of the relationship between thecrack-tip stress intensity factor at the notch tip and the generalized stress intensity factor of the corresponding notch without cracks.4. The enriched finite method for3-D V-shaped notch problems in a linearviscoelastic medium is established.By combining the notch-tip asymptotic displacement field in a viscoelastic mediumunder plane strain state and that under antiplane shear state, the3-D enriched notchelement is established and the corresponding viscoelastic incremental formulations ofthe3-D enriched finite element method in time domain are obtained. An exact formulato calculate mode-III stress intensity factor for a short crack emanating from a V-notchis supplemented based on the screw dislocation piles-up model, which are related to thethe mode-III generalized stress intensity factor of the uncracked notch. Further, thenovel method for evaluating the strain energy release rate of a2-D notch is extended for3-D notch problems.5. The enriched finite method for2-D blunt crack problems in a linearviscoelastic medium is established.The viscoelastic enriched finite element method is developed for2-D blunt crackproblems. The2-D enriched blunt-crack element is establiehed after the asymptoticdisplacement field at the blunt crack tip in a viscoelastic medium. Taking the strainenergy density factor as the fracture parameter, the formula for the blunt crack in aviscoelastic medium is presented.6. The enriched finite method for3-D blunt crack problems in a linearviscoelastic medium is established.The viscoelastic enriched finite element method is also developed for3-D bluntcrack problems. By combining the blunt-crack-tip asymptotic displacement field in aviscoelastic medium under plane strain state and that under antiplane shear state, the3-D enriched blunt-crack element is established. The strain energy density factor for the3-D blunt crack in a viscoelastic medium is presented based on the locally asymptoticstress field.To sum up, a numerical method, which is suitable for solving fracture problems inviscelastic media containing defects is systematically established based on the enrichedfinite element method. The method has great values for extending the applied range ofthe enriched finite element method and providing a technical support for structureintegrity analysis of SRM containing defects.