RESEARCH FOR THE STRAIN ENERGY RELEASE RATE OF COMPLEX CRACKS BY USING POINT-BY-POINT CLOSED EXTRAPOLATION APPROACH

A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point_by_point closed method was used to calculate the closed energy, thus the disadvantage of self_inconsistency in some published papers can be avoided. The disadvantage is that the closed energy is repeatedly calculated: when closed nodal number along radial direction is more than two, the displacement of nodes behind the crack tip that is multiplied by nodal forces, the closed energy has been calculated and the crack surfaces have been closed, and that closed energy of middle point is calculated repeatedly. A DCB (double cantilever beam) specimen was calculated and compared with other theoretical results, it is shown that a better coincidence is obtained. In addition the same results are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen. In comparison with theoretical results,the error can be limited within 1 per cent. This method can be extended to analyze the fracture of composite laminates with various delamination cracks.

ON CRACK-TIP STRAIA ENERGY RELEASE RATE IN NON-PRINCIPAL DIRECTIONS OF ELASTICITY FOR SIMPLE LAYER PLATE OF COMPOSITE MATERIALS

In this paper, the fracture problem in non-principal directions of elasticity for a simple layer plate of linear-elastic orthotropic composite materials is studied. The formulae of transformation between characteristic roots, coefficients of elastic compliances in non-principal directions of elasticity and corresponding parameters in principal directions of elasticity are derived. Then, the computing formulae of strain energy release rate under skew-symmetric loading in terms of engineering parameters for principal directions of elasticity are obtained by substituting crack-tip stresses and displacements into the basic formula of the strain energy release rate.

FRACTURE ANALYSIS OF A FUNCTIONALLY GRADED STRIP UNDER PLANE DEFORMATION

In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.

Anti-plane analysis of semi-infinite crack in piezoelectric strip

Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

Study of Debond Fracture Toughness of Sandwich Composites with Metal Foam Core

Two types of experiments were designed and performed to evaluate the adhesive bond in metal foam composite sandwich structures. The tensile bond strength of face/core was determined through the flatwise tensile test （FWT）. The test results show that the interfacial peel strength is lower than the interlaminar peel strength in FWT test. The mode I interracial fracture toughness （GIC） of sandwich structures containing a pre-crack on the upper face/core interface is determined by modified cracked sandwich beam （MCSB） experiment. It is found that the crack propagates unsynchronously on the two side of the specimen and the propagation of interfacial debonding always stays on the face/core interface during the MCSB tests. In order to simulate the failure of metal foam composite sandwich structures, a computational model based on the Tsai-Hill failure criterion and cohesive zone model is used. By comparing with experiment results, it can be concluded that the computational model can validly simulate the interracial failure of metal foam composite sandwich structures with reasonable accuracy.

A MODE-Ⅱ GRIFFITH CRACK IN DECAGONAL QUASICRYSTALS

By using the method of stress functions, the problem of mode-Ⅱ Griffith crack in decagonal quasicrystals was solved. First, the crack problem of two-dimensional quasi-crystals was decomposed into a plane strain state problem superposed on anti-plane state problem and secondly, by introducing stress functions, the 18 basic elasticity equations on coupling phonon-phason field of decagonal quasicrystals were reduced to a single higher- order partial differential equations. The solution of this equation under mixed boundary conditions of mode-Ⅱ Griffith crack was obtained in terms of Fourier transform and dual integral equations methods. All components of stresses and displacements can be expressed by elemental functions and the stress intensity factor and the strain energy release rate were determined.

PEELING-OFF PHENOMENON IN FRP STRENGTHENED CONCRETE BEAMS DUE TO THERMAL RESIDUAL STRESS

Peeling-off phenomena in FRP strengthened concrete beams are investigated in this paper. Based on the beam theory and the fracture mechanics, a new theoretical model is proposed to analyze the peeling-off behavior near FRP-concrete interfaces, which is governed by residual thermal stresses. Numerical examples are presented to provide a clear insight into the failure mechanism. Some suggestions are provided for the optimal design of FRP strengthened structures.

Mode Mixity for Orthotropic Interface Delamination in Laminated Composites

The mode mixity is defined based on nonoscillatory strain energy release rate components of delamination between two different orthotropic materials to evaluate the delamination behavior of laminated composites. The result showes that the relative location of the delamination through the thickness influences the mode mixity in a relatively well-regulated way, and that the reinforcement directions of the adjacent plies along the delamination front have a more complicated impact on the mode mixity. This is caused by the bending/twist coupling and bending/bending coupling in the stress field at the crack tip for delamination between multidirectional plies, which completely modifies the stress and strain fields ahead of the crack tip. These kinds of couplings account for the non- uniform distribution of mode mixity values along the delamination front. Application of appropriate mode mixity values is necessary for accurate prediction of delamination growth.

Phenomena and theoretical analysis for the failure of brittle rocks

Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulomb theory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena of rockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffith theory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensile failures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energy in the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) the understanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control, i.e. from keeping the reduction in initial compressive stress σ3 to restricting the creation of secondary tensile stress.