Further studies on dynamic crack branching

The newly derived dynamic-crack-branching criterion with its modifications is verified by the dynamicphotoelastic results of dynamic crack branchings in thinpolycarbonate, single-edged crack-tension specimens. Successful crack branching was observed in four specimens and unsuccessful branching in another. Crack branching consistently occurred when the necessary conditions ofK _I =K _{I b} =3.3 MPa \(\sqrt m\) and the sufficiency condition ofr _o =r _c =0.75 mm were satisfied simultaneously. In the unsuccessful branching test, the necessary condition was not satisfied sinceK _I was always less thanK _{I b} .     

Strain energy density prediction of crack initiation and direction in cracked T-beams and pipes

In this paper, the S-theory is applied to determine crack initiation and direction for cracked T-beams and circumferentially cracked pipes. It makes use of a parameter called strain energy density factor, S, which is a function of the stress intensity factors. The strain energy density theory provides a more general treatment of fracture mechanics problems by virtue of its ability in describing the multiscale feature of material damage and in dealing with mixed mode crack propagation problem. A simple method for obtaining approximate stress intensity factors is also applied. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. Some basic loading conditions in beams and pipes are studied.     

Dynamic fracture surface energy values and branching instabilities during rapid crack propagation in rubber toughened PMMA

An experimental device based on strip band geometry has been designed to explore the brittle behaviour of polymers during rapid crack propagation. The macroscopic crack speed is found to be quasi-constant along an entire RT-PMMA specimen, even in the case of crack branching and until arrest, if any. At the macroscopic branching velocity, the experimental fracture surface energy and the fracture surface roughness have no single values in RT-PMMA. In fact, the macroscopic fracture surface energy increases with the number of instabilities or frustrated micro-branches.     

Comparison of energy release rate and energy density criteria for a piezoelectric layered composite with a crack normal to interface

A critical comparison of the energy release rate and energy density criteria is made using the example of a piezoelectric layer bonded between two half-spaces of a different elastic solid containing a crack normal to the interfaces. Numerical values of stress intensity factor, energy release rate and energy density factor are presented to exhibit electroelastic interactions. Considered are the exact (permeable) and impermeable crack models. The energy release rate criterion led to negative values which are unphysical. This is consistent with previously published results that seem to contradict with experimental observation related to crack growth enhancement and retardation. The energy density factor always remains positive. This shows that a knowledge of the stress intensity factors alone is not sufficient to explain the behavior of fracture in piezoelectric materials.     

Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values minimum energy required for initiation of crack growth increases rapidly. Results received indicate a possibility to optimize energy consumption of different industrial processes connected with fracture. Much could be gained in for example drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e., frequency and amplitude of impacts, for industrial devices, e.g., bores, grinding machines, etc. and hence significantly reduce the process cost. The prediction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).     

Strain energy density prediction of fatigue crack growth from hole of aging aircraft structures

Fatigue crack growth rate depends not only on the load amplitude, but also on the morphology of crack path. The strain energy density theory has the ability to analyze crack growth rate. A strain energy density crack growth model is proposed. It can predict the lifetime of fatigue crack growth for mixed mode cracks while an equation for mode I crack is also obtained. The validity of the model is established with two cases: a center-crack panel and cracks emanating from the edge of a hole. The stress intensity factor expression for the former case is analytical while that of the latter is calculated numerically using finite elements. The results are compared with the testing data. Good agreement shows that the proposed model is useful.     

Effects of fillers on fracture performance of thermoplastics: Strain energy density criterion

This paper presents the experimental results on the fracture performance of filled thermoplastics. The emphasis is put on verification of the validity of different fracture criteria. The effects of two- and three-dimensional fillers on the fracture toughness of a representative thermoplastic, polypropylene, are analyzed. It has been found that classical fracture mechanics do not properly describe the fracture behavior of these composites. The strain energy density theory provides a more appropriate criterion for predicting fracture. On the macroscopic scale, the addition of fillers leads to a reduction in the critical strain energy density of thermoplastics. However, on the microscopic level fillers enhance a more wide spread crack-growth and failure by fracture becomes more stable. The material is therefore less prone to shatter in service. This effect of fillers is interpreted in terms of damage development, induced by the debonding at the matrix/fillers interface. A better interfacial adhesion reduces the microscopic damage and the critical increment of crack growth prior to instability. The results explain the negative effect of coupling agent on the impact resistance observed in practice.     

Strain energy density approach to stable crack extension under net section yielding of aircraft fuselage

In this paper, the incremental theory of plasticity is used in conjunction with the strain energy density criterion to determine the stress field in 4-in. wide test specimens containing 3 holes. These specimens, made from 0.04-in. thick sheets of 2024-T3 aluminum, also contained small collinear cracks emanating from the holes. The initial crack sizes varied from 0.15 to 0.26 in. Residual strength tests conducted with these specimens revealed that stable tearing occurred before failure. Analyses were performed to predict the stable crack extension and failure by plastic collapsed. Because of the complexities involved with nonlinear stress analysis combined with subcritical crack extension, the finite element method was used with the grid pattern adjusted for each increment of stable tearing. Reasonable correlation between the experimental data and predicted results was achieved.     

Strain energy density bounds for linear anisotropic elastic materials

Upper and lower bounds are presented for the magnitude of the strain energy density in linear anisotropic elastic materials. One set of bounds is given in terms of the magnitude of the stress field, another in terms of the magnitude of the strain field. Explicit algebraic formulas are given for the bounds in the case of cubic, transversely isotropic, hexagonal and tetragonal symmetry. In the case of orthotropic symmetry the explicit bounds depend upon the solution of a cubic equation, and in the case of the monoclinic and triclinic symmetries, on the solution of sixth order equations.     

Problems of dynamic fracture mechanics with allowance for contact of the crack edges

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine. Kharkov Institute of Highway Engineering. Translated from Prikladnaya Mekhanika, Vol. 31, No. 1, pp. 3–36, January, 1995.     

Mixed mode fatigue crack growth and the strain energy density factor

The strain energy density factor S was first proposed by Sih for the prediction of the critical of the load and failure direction under monotonic, mixed mode loading condition. It seems a natural extension to apply the same concept to fatigue crack propagation. However, a close examination of the existing theory indicates that the Strain Energy Density Factor cannot logically account for the phenomena of the R-ratio effect and crack arrest. Thus, modification is necessary before the concept can be applied successfully for the prediction of mixed mode fatigue crack propagation.Based on the concept of hysteresis energy dissipation, an effective strain energy density factor range, ΔS_p,eff, is proposed for the correlation of fatigue crack growth data. ΔS_p,eff is consistent with the concept of crack closure. Experimental investigation indicates that it could predict the crack growth rates and trajectories.     

Mode-I crack projection procedure using the strain energy density criterion

A practice used in linear elastic fracture mechanics is the projection of a crack onto a plane normal to the principal tensile stress axes for computing the stress intensity factor K_I. The minimum strain-energy criterion is applied for different crack configurations with the introduction of a safety factor S_i which is the ratio of the strain energy density factor of the projected crack and that of the original crack. Numerous crack configurations are investigated to illustrate the degree of conservativeness of the crack projection procedure.     

Stress multiaxiality factor for crack growth prediction using the strain energy density theory

The multiaxiality factor defined as the ratio of the von-Misses equivalent stress to the volumetric stress has been reported to be related to the initiation and progression of failure in structures. It is demonstrated in the present paper that the location around the crack tip where the multiaxiality factor obtains minimum value is an indicator of the direction of minimum material fracture resistance for crack propagation. It is also proposed that the location along the direction of crack propagation path where multiaxiality factor obtains minimum value is considered as the critical distance away from the crack tip, where the strain energy density should be evaluated and compared to its critical value. Theoretical predictions correlate well with the test results for the investigated cases.     

Problems of dynamic fracture mechanics without contact of the crack faces

Conclusion In this, the first part of the survey we have discussed only certain aspects of dynamic fracture mechanics. The surveyed material has been selected with a preference for the most highly developed parts of the theory, specifically those elements which have direct bearing on the second part of the survey. We have also included information on the dynamic fracture mechanics of initially stressed materials, in the development of which one of the authors has been a major contributor.Since many problems of dynamic fracture mechanics have been overlooked in the survey, we have added supplementary references to the literature. Various aspects of the strength and fracture of materials under dynamic loading are set forth in [11, 12, 40, 57, 60, 73, 80, 83]. Criteria of the initiation, motion, branching, and arrest of cracks are discussed in [7, 9, 60, 102, 111, 113, 124]. Among the most interesting elements of dynamic fracture mechanics are the problems of crack propagation. Certain analytical results pertinent to this topic have been obtained in [43–45, 47, 67–72, 78, 87, 92, 96, 97].S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Highway Engineering University, Kharkov. Translated from Prikladnaya Mekhanika, Vol. 30, No. 10, pp. 3–28, October, 1994.     

Modeling dynamic plasticity and spall fracture in high density polycrystalline alloys

The dynamic thermomechanical response of a tungsten heavy alloy is investigated via modeling and numerical simulation. The material of study consists of relatively stiff pure tungsten grains embedded within a more ductile matrix alloy comprised of tungsten, nickel, and iron. Constitutive models implemented for each phase account for finite deformation, heat conduction, plastic anisotropy, strain-rate dependence of flow stress, thermal softening, and thermoelastic coupling. The potentially nonlinear volumetric response in tungsten at large pressures is addressed by a pressure-dependent effective bulk modulus. Our framework also provides a quantitative prediction of the total dislocation density, associated with cumulative strain hardening in each phase, and enables calculation of the fraction of plastic dissipation converted into heat energy. Cohesive failure models are employed to represent intergranular fracture at grain and phase boundaries. Dynamic finite element simulations illustrate the response of realistic volume elements of the polycrystalline microstructure subjected to compressive impact loadings, ultimately resulting in spallation of the material. The relative effects of mixed-mode interfacial failure criteria, thermally-dependent fracture strengths, and grain shapes and orientations upon spall behavior are weighed, with interfacial properties exerting a somewhat larger influence on the average pressure supported by the volume element than grain shapes and initial lattice orientations within the bulk material. Spatially resolved profiles of particle velocities at the free surfaces of the volume elements indicate the degree to which the incident and reflected stress waves are altered by the heterogeneous microstructure.     

Dynamic crack curving and branching under biaxial loading

A 16-spark-gap camera was used to record the dynamic photoelastic patterns of ten centrally cracked, Homalite-100 specimens which fractured under ten initial biaxial-stress ratios ranging from 3.7 to 0, some of which do not exist in normal fracture specimens. The dynamic photoelastic patterns of curved cracks were used to verify the previously developed dynamic-crack-curving criterion. Cracks which immediately curved upon propagation in three specimens under abnormally high inital biaxial loading were used to verify the static counterpart of the dynamic-crack-curving criterion under these extreme loading conditions. A previously developed dynamic-crack-branching criterion was also verified by four dynamic photoelastic results involving cracks which eventually branched under the lower initial biaxial loading.     

Brittle fracture dynamics with arbitrary paths. II. Dynamic crack branching under general antiplane loading

The dynamic propagation of a bifurcated crack under antiplane loading is considered. The dependence of the stress intensity factor just after branching is given as a function of the stress intensity factor just before branching, the branching angle and the instantaneous velocity of the crack tip. The jump in the dynamic energy release rate due to the branching process is also computed. Similar to the single crack case, a growth criterion for a branched crack is applied. It is based on the equality between the energy flux into each propagating tip and the surface energy which is added as a result of this propagation. It is shown that the minimum speed of the initial single crack which allows branching is equal to 0.39c, where c is the shear wave speed. At the branching threshold, the corresponding bifurcated cracks start their propagation at a vanishing speed with a branching angle of approximately 40°.     

Stability analysis of crack path using the strain energy density theory

Prediction of crack growth path is a pre-requisite for estimating the final shape of broken solids and structures. Crack path in broken specimens provides information for the loading conditions just before fracture. Experiments on brittle materials, pre-cracked specimens of the same geometry under similar loading conditions, however, may yield different crack trajectories at times. The existing theories for the prediction of the crack path are based on the perturbation method combining the analytical and finite elements methods. They require a knowledge of the toughness equations. Moreover, they can only be applied to specimens with simple geometry and loadings.A different approach is used in the present work. The finite element technique is used to calculate the strain energy density (SED) contours. The predicted trajectory of the crack during unstable propagation is assumed to coincide with the minimum of the strain energy density function according to the SED criterion.The degree of crack path stability depends on the sharpness of the SED oscillations. This simple method offers a reliable prediction of the crack path stability for two as well as three-dimensional problems with complex geometry structures and arbitrary loadings. To be specific, both the TPB and DCB specimens are analysed. The findings are in good agreement with the theoretical and experimental results in the literature.