Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

Probabilistic analysis of linear elastic cracked structures

This paper presents a probabilistic methodology for linear fracture mechanics analysis of cracked structures. The main focus is on probabilistic aspect related to the nature of crack in material. The methodology involves finite element analysis; sta- tistical models for uncertainty in material properties, crack size, fracture toughness and loads; and standard reliability methods for evaluating probabilistic characteristics of linear elastic fracture parameter. The uncertainty in the crack size can have a significant effect on the probability of failure, particularly when the crack size has a large coefficient of variation. Numerical example is presented to show that probabilistic methodology based on Monte Carlo simulation provides accurate estimates of failure prob- ability for use in linear elastic fracture mechanics.

An adaptive finite element procedure for crack propagation analysis

This paper presents the adaptive mesh finite element estimation method for analyzing 2D linear elastic fracture problems. The mesh is generated by the advancing front method and the norm stress error is taken as a posteriori error estimator for the h-type adaptive refinement. The stress intensity factors are estimated by a displacement extrapolation technique. The near crack tip displacements used are obtained from specific nodes of natural six-noded quarter-point elements which are generated around the crack tip defined by the user. The crack growth and its direction are determined by the calculated stress intensity factors. The maximum circumference theory is used for the latter. In evaluating the accuracy of the estimated stress intensity factors, four cases are tested consisting of compact tension specimen, three-point bending specimen, central cracked plate and double edge notched plate. These were carried out and compared to the results from other studies. The crack trajectories of these specimen tests are also illustrated.

Microstructure and mechanical properties of lost foam cast 356 alloys

Microstructure and mechanical properties of lost foam cast aluminum alloys have been investigated in both primary A356(0.13% Fe) and secondary 356(0.47%). As expected, secondary 356 shows much higher content of Fe-rich intermetallic phases, and in particular the porosity in comparison with primary A356. The average area percent and size(length) of Fe-rich intermetallics change from about 0.5% and 6 μm in A356 to 2% and 25 μm in 356 alloy. The average area percent and maximum size of porosity also increase from about 0.4% and 420 μm to 1.4% and 600 μm, respectively. As a result, tensile ductility decreases about 60% and ultimate tensile strength declines about 8%. Lower fatigue strength was also experienced in the secondary 356 alloy. Low cycle fatigue(LCF) strength decreased from 187 MPa in A356 to 159 MPa in 356 and high cycle fatigue(HCF) strength also declined slightly from 68 MPa to 64 MPa.