Separated Energy Release Rates Research Articles

Nonlinear crack opening integral: Mode mixity for finite cracks

In this work the incremental energy release rate is analyzed for single-lap adhesive joints by means of the crack closure/opening integral. To this aim, geometrically nonlinear numerical analyses are performed. For nonlinear elastic analyses the relationship between nodal forces and displacements during nodal load reduction generally cannot be approximated linearly. In the case of a nonlinear relation the forces must be integrated over the displacements in order to calculate the incremental energy release rates. Additionally for a nonlinear analysis the nodal forces and displacements must be transformed into a local nodal coordinate system to separate individual modes and calculate mode mixity. As an alternative, the mode mixity for a finite crack is estimated on basis of the stress state just before or after crack initiation. The mixity values and the resulting critical energy release rates needed for an energy criterion are finally compared to the direct evaluation of the mode separated energy release rates.

3D-Modeling and Numerical Analysis of Fracture Behavior in AFM-Specimen on Mixed-Mode I-II Loading Condition

The computational analysis of a three-dimensional (3D) finite element model of all fracture modes (AFM) specimen on mixed-mode I-II fracture was presented in this paper. The separated energy release rates (SERRs) along the crack front of the AFM-model were calculated by the modified virtual crack closure integral (MVCCI)-method and commercially available software ANSYS. The influence of finite geometry and loading angles on mixed mode I-II fracture was investigated.

Computational Analysis of the AFM Specimen on Mixed-Mode I+II+III Fracture

The computational analysis of an all fracture modes (AFM) specimen on mixed-mode I+II+III fracture is presented in this paper. The separated energy release rates (SERRs) along the crack front of the AFM-model are calculated by the modified virtual crack closure integral (MVCCI)-method and the commercially available software ANSYS. A transition model is built by adopting several 3D elements of SOLID45 and one point element of MASS21 in the ANSYS program. Under the related constraint conditions, the separate force and moments are respectively applied on the point element of the transition model, so the corresponding desired reaction forces can be obtained. When the desired loads are superimposed and applied on the AFM-model, the mixed-mode I+II+III fracture can then be achieved. Thereby, the SERR results are calculated. The calculation results show that the facture behavior of GII and GIII appears complex due to the global deformation and Poisson’s ratio, although the distribution of SEERs GI is symmetrical with respect to the middle point along the crack front. The total SERRs, GTn-values increase along the crack front with the minim value at one corner and the maxim value at the other corner. It can therefore be predicted that the fracture will occur initially at one corner on the crack front of the AFM-specimen in this case.

Finite Element Analyses of Modified Compact Tension Shear (MCTS)-Specimens under Mixed-Mode Loading Conditions

In this paper a detailed 3D-finite element analyses results of modified compact tension shear (MCTS)-specimens with an inclined crack plane or crack front under mixed-mode loading conditions are presented. It is found that under mixed-mode loading, a superposition of all fracture modes I, II and III can be generated along the straight crack front of MCTS-specimens, and the maximum of the total SERR along the crack front of two different MCTS-specimens is found at right hand side of crack front corner，where the risk of crack initial growth is highest. The computational fracture analysis is based on the calculation of separated energy release rates GI, GII and GIII along the crack front by the numerically highly effective modified virtual crack closure integral(MVCCI)-method.

Computational Fracture Analyses of a Compact Tension Shear (CTS) Specimen with an Inclined Crack Front

In this paper some results of 3D-finite element analyses of a modified CTS-specimen(MCTS) with an inclined crack front are presented. It will be shown, that through the inclination of the crack front, even under pure in-plane shear loading of the specimen, mixed-mode II and III loading conditions can be generated along the straight inclined crack front. Furthermore a superposition of all fracture modes I, II and III can be generated, if this MCTS-specimen is subject to an in-plane tension/shear loading. The computational fracture analysis is based on the calculation of separated energy release rates GI, GII and GIII along the crack front by the numerically highly effective modified virtual crack closure integral(MVCCI)-method and for the finite element(FE)-modelling the commercially available FE-code ANSYS is utilized.

Computational Fracture Analyses of a Compact Tension Shear (CTS) Specimen with an Inclined Crack Plane

In this paper some results of 3D-finite element analyses of a modified CTS-specimen with an inclined crack plane are presented. It will be shown, that through the inclination of the crack plane, even under pure tension loading of the specimen, a superposition of all fracture modes I, II and III can be generated along the straight crack front of the inclined crack plane. Furthermore, mixed-mode I, II and III loading conditions can also be generated if this modified CTS-specimen is subject to an in-plane tension/shear loading. The computational fracture analysis is based on the calculation of separated energy release rates GI, GII and GIII along the crack front by the numerically highly effective modified virtual crack closure integral(MVCCI)-method and for the finite element(FE)-modelling the commercially available FE-code ANSYS is utilized.

Concepts of Separated J-Integrals, Separated Energy Release Rates, and the Component Separation Method of the J-Integral for Interfacial Fracture Mechanics

First, this paper presents the concepts of separated J-integrals and separated energy release rates. The path-independent separated J-integrals have the physical significance of energy flows into an interfacial crack tip from adjacent individual material sides or, equivalently, separated energy release rates. Thus, the J-integral and the energy release rate can be evaluated by the sum of the path-independent separated J-integrals. Second, the relations between the separated J-integrals and the stress intensity factors are derived. Third, the component separation method of the J-integral is extended for interfacial crack problems to allow accurate evaluation of the stress intensity factors. Finally, pertinent numerical analyses are carried out to demonstrate the usefulness of the separated J-integrals and the component separation method.

Fracture analyses and experimental results of crack growth under general mixed mode loading conditions

In this paper detailed results of 3D finite element (FE) and mixed mode analyses of different fracture specimens are presented and discussed. Special interest is taken in 3D and mode coupling effects to be found in strain energy release rate (SERR) results along crack fronts, in particular adjacent to corners, where a crack front intersects a free surface of a specimen. It will be shown that these effects stay small if they are related to Poisson’s ratio but that they can also be considerably pronounced if they are related to the global deformation behaviour of the specimen. The computational fracture analysis is based on the calculation of separated energy release rates (SERRs) by the aid of the modified virtual crack closure integral (MVCCI)-method in order to calculate the local SERR-distributions along the crack front. Furthermore some qualitative experimental results will show the influence of these variable mixed mode I, II and III loading conditions along the crack front on crack initiation and on the further development of 3D crack growth in the specimens.

Measurements of Near-Tip Displacement Fields, Separated J Integrals and Separated Energy Release Rates for Interfacial Cracks Using Phase-Shifting Moire Interfrometry.

In this paper, first, the concepts of the separated J integrals and the separated energy release rates, which have the physical significance of the energy release rates from corresponding material sides of a bimaterial are briefly presented. Phase-shifting moire interferometry is used to investigate interfacial crack-tip behavior of a bimaterial specimen, which is fabricated of epoxy and aluminum. The loading angle to the interfacial crack is systematically changed. The inplane displacement fields near the interface crack are recorded by the phase-shifting moire interferometry. Using the measured displacement fields, the stress intensity factors and the separated energy release rates are evaluated. From the theoretical and experimental results, it is found that the compliant material (epoxy) side provides considerably larger fracture energy to the interfacial crack tip.

Computation analysis of interlaminar fracture of laminated composites

The interlaminar fracture behavior of laminated composites has been investigated. Contact and friction along the crack surfaces is taken into account in the finite element modeling of the delamination crack growth. Mode I, mode II and mixed mode loading conditions at the crack tip have been analyzed. For the cracks with contact and friction along the crack surfaces the virtual crack closure integral method is used in order to calculate separated energy release rates. Computational modeling and analysis of cross-ply laminates in three-point bending has been performed. Contact elements were used in order to prevent the material interpenetration along the crack surfaces. Comparison of the results obtained with and without using contact elements has been carried out and significant differences between the correlated values of the energy release rates have been found. The influence of the coefficient of friction on the energy release rates was found to be significant for short delamination crack lengths but insignificant for long cracks. Numerical analyses of experimental data obtained for unidirectionally reinforced glass fibre composites by double cantilever beam tests and by end notched flexure tests have been carried out. For the double cantilever beam test geometric linear and nonlinear finite element analyses have been performed and critical energy release rates were calculated. For the end notched flexure test the contact problem has been solved taking into account that adjacent to the support contact and friction will occur. For the double cantilever beam test the critical energy release rates obtained by linear and nonlinear finite element solution has been compared with those from four different analytical data reduction methods (the area method, the Berry method, the modified beam analysis, the compliance method). For the end notched flexure test the critical energy release rates, calculated by the finite element analysis and taking into account contact and friction along the crack surfaces, have been compared with those obtained by conventional beam analysis.