An energy release rate criterion for mixed mode fracture

The initial energy release rate for a branch crack propagating at an arbitrary angle from an existing crack tip is obtained in a simple fashion and in closed form by using a continuity assumption. It is then postulated that the branch crack propagates in the direction which causes the energy release rate to be a maximum and that initiation occurs when the value of this release rate reaches a critical value. It is shown that these postulates yield results identical to the maximum stress theory, since the direction in which the maximum circumferential stress occurs is also the direction causing the maximum energy release rate.     

An end-notched beam test for specific fracture energy in mixed mode in timber

A simple method for achieving stable crack propagation in a beam notched at a support is presented. The method allows the measurement of fracture energy in mixed modeG _f,mix. Results from a small number of laminated veneer lumber specimens suggest that there is a relationship betweenG _f,mix and density and that the ratioG _f,mix/(G _f,I+G _f,II) is about 0.35. Calculations of fracture energy in mode IG _f,I and mode, IIG _f,II did not coincide with values from mode-specific tests, indicating that an adjustment is necessary to take account of the interaction between the modes.     

Strain energy density fracture criterion in elastodynamic mixed mode crack propagation

Sih's fracture criterion based on strain energy density, S, for mixed mode crack extension under static loading is extended to dynamic mixed mode, K_I and K_II, crack propagation. Influence of the second order term, σ_ox, which represents the non-singular constant stress acting parallel to the direction of crack propagation, on the S distribution surrounding the crack tip, is demonstrated. Numerical studies show that positive σ_ox enhances the fracture angle and negative σ_oxreduces the fracture angle irrespective of the sign of K_II/K_I, when S is measured at a critical distance r_c from the crack tip. This fracture criterion is verified by the crack curving results of dynamic photoelastic fracture specimens. Omission of σ_ox term leads to predicted fracture angles which are at variance with experimental data.     

A mixed mode fracture specimen for mode II dominant deformation

Several theories have been proposed for the failure of metals, as well as for the angle of crack propagation in mixed mode loading. In order to demonstrate the validity of these theories, the majority of tests have been carried out with an oblique crack placed in a uniaxial stress field. Better testing conditions may be achieved by placing a crack in a uniform bidimensional stress field. A specimen which was recently developed for $\text{K}{}_{\mathrm{IIC}}$ measurement may be readily adapted to achieve a bidimensional stress field and be used for mixed mode testing for the case in which shear deformation is dominant. The main aims of this study are to examine both the cracked and uncracked specimen by means of photoelasticity and finite elements in order to analyze the capabilities and limitations of this specimen for mixed mode testing. It will be demonstrated that there exists a nearly uniform biaxial field in the uncracked specimen. Moreover, calibration formulas will be presented for $\text{K}{}_{\mathrm{I}}$ and $\text{K}{}_{\mathrm{II}}$.     

The mixed mode fracture of unidirectional fibrous composites

With explicit restriction, the energy release rate principle in homogeneous anisotropic bodies is used to predict fracture strength of cracked unidirectional fibrous composite in mixed mode I and mode II loading. The range to which such prediction is valid in terms of the loading parameters (k₁ and K₂) is shown to depend on a certain ratio between the stress transverse to fibers to that along the fibers, in the vicinity of the crack tip. Some experimental data on oriented notches confirm the suggested approach and its range of validity reasonably well. A very good agreement with the strain energy density concept (“S” theory) is demonstrated on variety of composite materials. The operational simplicity of the energy release rate criterion is thus emerged.     

Development of a test method for measuring the mixed mode fracture resistance of bimaterial interfaces

Measurements of the mixed mode fracture resistance of bimaterial interface have been shown to be appreciably influenced by the presence of loading point friction and by residual strain. Analyses of the effect of these phenomena on the strain energy release rate and on the phase angle of loading are presented. The analyses are used to interpret experimental measurements obtained on several bimaterial models.     

The effect of specimen dimensions on mixed mode ductile fracture

The results from a series of experiments are presented to determine the effect of specimen dimensions on the ductile tearing resistance of A508 Class 3 forged steel at ambient temperature. Single edge notch tension specimens were subjected to Mode I, Mode II and combination of Modes I and II. Mode I tests on various specimen sizes reveal characteristic features found in earlier work, such as decreasing slope of the tearing resistance with increasing constraint (or specimen size). In contrast, for Mode II the tearing resistance is shown to be independent of specimen size, although dependent on initial crack length. The tests show that there is a competition between void growth and shear localisation as mechanisms for ductile crack extension. The dominance of one mechanism over the other is shown to be related to the local Mode I and Mode II components of the J-integral.     

Incipient fracture angle,fracture loci and critical stress for mixed mode loading

A prediction of the direction of incipient crack growth in brittle-like materials and the associated fracture loci under mixed mode loading is proposed. It is postulated that the direction of unstable crack propagation is determined by the “weakest” near-tip element defined as the one which would relax maximum potential energy upon prospective crack extension. Starting from the energy rate principle of crack extension (Eshelby energy-momentum tensor and Rice $\text{J-}\text{internal}$ vector) it is deduced that a crack will extent in the direction along which the following stress criterion is satisfied, $\text{(δ}{}_{\mathrm{\theta \theta }}{}^2\text{? δ}{}_{\mathrm{rr}}{}^2\text{) →}\text{maximum (for}\text{δ}{}_{\mathrm{\theta \theta \; >\; 0)}}$ The fracture angle in pure Mode II (70.4° away from the original straight path) is shown to be unstable in the sense that any slight tension along the crack (non-singular at the crack tip) affects considerably (up to 22%) the directionality of crack extension. It appears to be sensitive to the extent of the near-tip zone ($\text{r}{}_0$) in which linear elasticity does not hold and the non-singular stress term (squared).The fracture loci in mixed mode loading (generated by projecting the $\text{J-}\text{integral}$ vector along the prospective fracture path and letting this scalar function attain a critical value) is quadratic in $\text{K}{}_1$ and $\text{K}{}_2$ with an interactive cross product term $\text{K}{}_1\text{× K}{}_2$.The suggested criterion with its implication in predicting critical fracture load, exhibits behavior which is consistent with experimental observations collected from several sources. The common and uncommon features with respect to other known criteria are compared and discussed.     

Mixed mode fracture energy of sprucewood

The characterization of Mixed Mode (Mode I and Mode II) behaviour of wood was concentrated on concepts of linear fracture mechanics in the past. Using an adopted version of the splitting test it was possible to obtain complete load displacement curves under different Mixed Mode loading cases for crack propagation along the grain. Therefore fracture energy concepts (specific fracture energy) could be used to characterize the material behaviour. Additionally strength parameters were used in order to describe crack initation in two crack propagation systems. The values for specific fracture energies as well as the strength values were compared with pure Mode I fracture tests. Moreover, the size effect under Mixed Mode loading was investigated to guarantee size independent material characterizing values for the specific fracture energies.     

A strain energy criterion for mixed mode crack propagation

The strain energy criterion for crack propagation proposed in the paper is based on the principle that the direction of crack propagation takes place along the direction where the distance from the crack tip to a certain contour line of constant distortional strain energy density is minimum, and the crack will begin to propagate when the total strain energy in the region surrounded by the contour line reaches a critical value. In the paper, predicted was compared with the measured results.     

Cohesive crack model for mixed mode fracture of brick masonry

This paper presents a numerical procedure for mixed mode fracture of brickwork masonry. The model is an extension of the cohesive model prepared by the authors for concrete, and takes into account the anisotropy of the material. After the crack path is obtained, an interface finite element (using the cohesive fracture model) is incorporated into the trajectory. Such a model is then implemented into a commercial code by means of a user subroutine, consequently being contrasted with experimental results. Fracture properties of masonry are independently measured for two directions on the composed masonry, and then input in the numerical model. This numerical procedure accurately predicts the experimental mixed mode fracture records for different orientations of the brick layers and two homothetic sizes on masonry panels.     

Mode I and mixed mode fracture of polysilicon for MEMS

An experimental study was carried out to investigate the local and effective fracture behaviour of polycrystalline silicon for microelectromechanical systems (MEMS). The apparent mode I critical stress intensity factor was determined from MEMS‐scale tension specimens containing atomically sharp edge pre‐cracks, while local deformation fields were recorded near the crack tip, with high resolution by the in situ Atomic Force Microscopy (AFM)/Digital Image Correlation (DIC) method previously developed by this group. The effective mode I critical stress intensity factor varied in the range 0.843–1.225 MPa√m. This distribution of values was attributed to local (in grain) cleavage anisotropy and to enhanced grain boundary toughening. The same sources resulted in very different local and macroscopic (apparent) stress intensity factors, which, combined with the small grain size of polysilicon (0.3 μm,) were the reason for subcritical crack growth that was evidenced experimentally by AFM topographic and AFM/DIC displacement measurements. The effect of local in‐grain anisotropy and granular inhomogeneity was stronger under mixed mode loading of edge cracks inclined at angles up to 55° with respect to the applied far‐field load. The K_I–K_II locus was characterized by scatter in the K_Ic values but on average it followed the curves calculated by the maximum tensile stress and the maximum energy release rate criteria calculated assuming isotropy.