Studies On Fracture Behaviors Of Heterogeneous Materials Using Peridynamic Theory

Due to its good designability,heterogeneous materials are one of the most important potential materials for aerospace and other large-scale structures.The fracture behaviors of heterogeneous materials are very complicated.Because of its theoretical limitation,numerical methods based on classical local mechanics often meet difficults when they are used to study fracture behaviors of heterogeneous material structures.As a new non-local mechanics,peridynamic(PD)theory has inherent advantages to be used to calculate fracture behaviors of materials.In this paper,the modified peridynamic calculation formations and algorithms are proposed.The fracture behaviors and crack propagation mechanism of heterogeneous materials under quasi-static load,fatigue load and thermal shock are studied.The main content and the innovation of this paper are:(1)A discrete bond-based PD model is developed.The calculation formation of material micro-modulus is derived and the enengy proportion strategy of bond constants for heterogeneous materials is proposed.The numerical algorithms of peridynamics to solve dynamic and static problems are presented.Dyanmic displacement,static displacement,thermally-induced deformation,stress intensity factor and peridynamic J-integral are calculated.Compared numerical results of original PD model,discrete PD model and analytical solution,the result predicted by discrete PD model is verified and the accuracy is improved.It can be found that the surface correction can be avoided in the modified model;the calculation accuracies of deformation and fracture parameters predicted by discrete PD model are increased.(2)Mixed-mode crack propagation behavior of heterogeneous materials under quasi-static load is studied based on discrete PD model.A modified PD J-integral formula of heterogeneous materials in displacement format is derived.Its integral path independency in heterogeneous materials is proved.The complicated calculation of original PD J-integral domain is simplified.Effects of the material heterogeneousity and the load level on mixed-mode crack propagation paths and contour integral of functionally graded materials are studied.Compared with published experimental and numerical results,the modified PD model can preferably capture the mixed-mode crack path.When the material orientation is not perpendicular to pre-crack,the crack propagation angle is deviated by the material heterogeneousity and the load level.The contour integral result is also affected by them significantly.(3)Plastic fracture behavior is calculated by discrete PD model and fatigue fracture model algorithm is modified.Crack turning and fatigue crack growth in heterogeneous materials are studied.In order to verify numerical results of crack turning and fatigue crack growth,friction stir welded joint samples are designed and tensile fracture and fatigue crack growth experiments are performed.Effects of the material heterogeneousity caused by the welding direction and a hole on crack turning and fatigue crack growth are calculated and investigated.It can be seen that the crack turning and fatigue crack growth rates of experiment can be predicted by the modified PD model and its algorithm.When the material orientation is perpendicular to pre-crack,the crack preferably propagates and turns to the soft side of materials.Effect of the material heterogeneousity on fatigue crack growth rates is slight.When a hole presents in structure,the crack propagation direction is mainly controlled by the hole position and the material heterogeneousity has a slight effect on the crack direction.(4)Discrete PD thermo-mechanical model and algorithm are developed.The modified model can validly decrease surface effect.The calculation accuracy of heat conduction is improved.Thermally-induced crack propagation of a ceramic plate under quenching is calculated.Compared with published experimental and numerical results,the thermally-induced crack initiation and propagation predicted by the modified PD model are better.The crack initiation number and the crack path are more similar to experimental results.Functionally graded materials are taken as an example.Effects of material features,defects and temperature loads on transient heat conduction and thermally-induced crack propagation behaviors of heterogeneous materials are studied.It is shown that material features,defects and boundary temperatures have important effects on temperature fields of heterogeneous materials;the effects of material heterogeneousity and iniatial temperature of structure on thermally-induced crack initiation number and crack propagation length are significant as well.This work can provide the peridynamic theory,formulations and algorithms to calculate fracture behaviors of heterogeneous materials and it is helpful to understand its crack propagation mechanism.