Crack propagation simulation in brittle elastic materials by a phase field method

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1]to characterize discontinuous cracks in brittle materials.This method can well describe the crack initiation and propagation without assuming the shape,size and orientation of the initial crack in advance.In this paper,a phase field method based on Miehe's approach[Miehe et al.,Comp.Meth.App.Mech.Eng.(2010)]is applied to simulate different crack propagation problems in twodimensional(2D),isotropic and linear elastic materials.The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM).The validity,accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature.Several numerical examples are presented to show the effects of the loading type(tension and shear),boundary conditions,and initial crack location and orientation on the crack propagation path and force-displacement curve.Furthermore,for a single edge-cracked bi-material specimen,the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed.It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials,and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.

Mechanical characteristics of composite honeycomb sandwichstructures under oblique impact

Carbon fiber reinforced polymer(CFRP)and CFRP-based composite honeycomb sandwich structures are particularly sensitive to impact.The mechanical characteristics of composite honeycomb sandwich structures under oblique impact are studied by numerical simulation and experiment.The oblique impact model is established,and the reliability of the model is verified by the oblique impact test.To further analyze the influence of structural parameters on energy absorption under oblique impact,the influence of impact angle,face sheet thickness and wall thickness of the honeycomb is numerically studied.The results show that the impact angle has an important effect on energy distribution.The structural parameters also have an effect on the peak contact force,contact time,and energy absorption,and the effect is different from normal impact due to the presence of frictional dissipation energy.Compared with normal impact,the debonding of oblique impact will be reduced,but the buckling range of the honeycomb core will be expanded.

Isolation and Characterization of Endophytic Fungi from Purslane and the Effects of Isolates on the Growth of the Host

Purslane, a common weed, has been used as food or folk medicine in many countries. The growth, medicinal components and nutrient contents of the plant are closely associated with endophytes, especially endophytic fungi. In this study, the endophytic fungi associated with purslane were isolated, and the effects of the isolates on the host were investigated to lay a foundation for further research and development of purslane resources. The results showed that a total of eight endophytic fungi were isolated from purslane (collected from Hohhot, Inner Mongolia, China), and they belonged to the genera Penicillium (isolates K, N, P, M and I), Chaetomium (isolate J), Fusarium (isolate H) and Petriella (isolate O). Moreover, the growth of purslane was significantly influenced by its endophytic fungi. Isolate M can significantly decrease the germination rate, while J can significantly increase the germination rate of purslane. In addition, H, J and M can significantly increase the bud length of purslane, and the fermentation broth of P has a negative influence on the bud length of purslane. M and I can significantly increase the height, fresh weight and chlorophyll content of purslane due, in part, to the lower pH of the fermentation broth of I and M.

Tensile properties analysis of CFRP-titanium plate multi-bolt hybrid joints

Hybrid joints have better tensile properties than pure bonded and bolted bolts,and are increasingly used in the aerospace field.Tensile tests are carried out for the Hybrid Bonded/Bolted(HBB)joints of Carbon Fiber Reinforced Polymer(CFRP)laminate and titanium alloy plate under different bolt numbers,and the corresponding load–displacement curves are obtained.At the same time,based on Continuum Damage Mechanics(CDM)theory,which is derived from 3D Hashin failure criteria,and a Cohesive Zone Model(CZM),the tensile strength prediction model of the composite laminate-titanium alloy plate multi-bolted HBB joint was established,and the numerical simulation results were in good agreement with the experimental height,which validate the feasibility of the model.The difference in the bearing capacity of HBB joints under different numbers of bolts is compared and analyzed.On this basis,the influence of inter-bolt distance on the tensile properties of the HBB joints is explored.The results show that the double-nail HBB joints can effectively improve the end warpage and low bearing capacity of the single-nail HBB joints.The tensile failure load of the double-nail HBB joints under the standard lap width(30 mm)is 82.6%higher than that of the single nail,the tensile failure load of the three-bolt HBB joints is 34.1%higher than that of the double nail.For the three-bolt HBB joint,the joint strength is controlled by the adhesive and the external bolt,while the internal bolt is redundant,the hybrid joint can be simplified by reducing the middle bolt.The inter-bolt distance has a great influence on the failure load of the hybrid joint.Increasing the inter-bolt distance can effectively improve the bearing capacity of the structure.

Crack nucleation and propagation simulation in brittle two-phase perforated/particulate composites by a phase field model

Fracture is a very common failure mode of the composite materials,which seriously affects the reliability and service-life of composite materials.Therefore,the study of the fracture behavior of the composite materials is of great significance and necessity,which demands an accurate and efficient numerical tool in general cases because of the complexity of the arising boundary-value or initial-boundary value problems.In this paper,a phase field model is adopted and applied for the numerical simulation of the crack nucleation and propagation in brittle linear elastic two-phase perforated/particulate composites under a quasi-static tensile loading.The phase field model can well describe the initiation,propagation and coalescence of the cracks without assuming the existence and the geometry of the initial cracks in advance.Its numerical implementation is realized within the framework of the finite element method(FEM).The accuracy and the efficiency of the present phase field model are verified by the available reference results in literature.In the numerical examples,we first study and discuss the influences of the hole/particle size on the crack propagation trajectory and the force-displacement curve.Then,the effects of the hole/particle shape on the crack initiation and propagation are investigated.Furthermore,numerical examples are presented and discussed to show the influences of the hole/particle location on the crack initiation and propagation characteristics.It will be demonstrated that the present phase field model is an efficient tool for the numerical simulation of the crack initiation and propagation problems in brittle two-phase composite materials,and the corresponding results may play an important role in predicting and preventing possible hazardous crack initiation and propagation in engineering applications.