T-stress based fracture model for cracks in isotropic materials

A modified version of the T-stress based fracture model, developed by Cotterell and Rice, is proposed. In this version an experimentally determined T_crit value is included in the model. The model is then applied to a branched crack in an isotropic material, and the direction of growth of the crack is predicted qualitatively. The branched crack problem is solved using the method of dislocations and a singular integral equation is obtained. The singular integral equation is solved using three different numerical techniques and their respective merits are discussed. The stress intensity factors and the T-stress in front of the branched crack tip are evaluated numerically. It is shown that the T-stress and the stress intensity factors are insensitive to the order of the singularity assumed at the reentrant wedge corner of the branched crack. For an uniaxial load and short kink length it is demonstrated that the kink will turn from its initial direction and realign with the main crack. However if the loading is biaxial then the direction of kink growth depends strongly on the applied transverse stress σ_xx. For a longer initial kink length the direction of kink growth depends on both the kink angle and loading.     

Criteria for brittle fracture in biaxial tension

The criteria of maximum tangential stress, maximum tangential principal stress, maximum tangential strain and strain energy density are applied to the problems of slit and elliptical cracks under remote uniform biaxial tension. The predicted direction of crack extension and the critical load are compared with experimental results reported by other investigators. The unstable crack paths are determined. The four criteria differ in the case of unequal tension; the strain energy density criterion is the least satisfactory. The criteria of maximum tangential strain and strain energy density can be modified to give a good prediction of critical load.     

Further studies on elastic-plastic stable fracture utilizing the T integral

Herein, the T^* fracture parameter is shown to have relevance to the mechanics of elastic-plastic fracture. Specifically, it is shown to have certain advantages over the currently established plastic fracture parameters such as J and CTOA. Finite element analyses of experimental data were carried out as a means to obtain a comparison of the effectiveness of the plastic fracture parameters. T^* is clearly superior. A note on problems associated with satisfying the plastic incompressibility constraint is also included.     

Phenomenological fracture model for biaxial fibre reinforced composites

This paper proposes a new mathematical fracture model (FM) applicable to a biaxial reinforced composite material. The mathematical model provides predictions about the limit state of composite material. It is applicable both in uniaxial and biaxial requests. The mathematical model is validated by comparing its predictions with the experimental data obtained by authors. The studied composite material is composed by carbon fibre in epoxy matrix. The process used for obtaining the composite materials plates is vacuum forming.     

Fracture criterion based on the higher-order asymptotic fields

A complete development for the higher-order asymptotic solutions of the crack tip fields and finite element calculations for mode I loading of hardening materials in plane strain are performed. The results show that in the higher-order asymptotic solution (to the twentieth order), only three coefficients are independent. These coefficients are determined by matching with the finite element solutions carried out in the present paper (our attention is focused on the first five terms of the higher-order asymptotic solution). We obtain an analytic characterization of crack tip fields, which conform very well to the finite element solutions over wide range.A modified two parameter criterion based on the asymptotic solution of five terms is presented. The upper bound and lower bound fracture toughness curves predicted by modified two parameter criterion are given. These two curves agree with most of the experimental data and fully capture the proper trend.     

Invariant formulation of the strain dependence of the critical temperature Tc of Nb3Sn in a three term approximation

It has been shown previously in a full detailed analysis that the strain dependence of the critical temperature may be obtained from a general strain invariant formulation of T_c in strong superconductivity. A physical model was presented in which the phonon frequency spectrum is represented through generalized elastic stiffness coefficients that include strain dependence. The primary purpose of the present work is to achieve a simplification of the analysis in order to facilitate calculation and reveal the essential physical content. The formulation in wave vector space of the equations for T_c in strong superconductivity is reviewed. The method of simplification employs a succession of approximations to the effective elastic constants that enter the relation between phonon frequency and wave number. It is found that the effective elastic constants in the crystal symmetry directions may be grouped into sets having similar form, and this form includes terms in common among the sets and difference terms. The difference terms are found to be in the nature of gradients and may be eliminated to good approximation. The common terms include the strain dependence in a form identified as a deformation strain parameter. The analysis treats spherical (hydrostatic) and deformation strain dependence under longitudinal and transverse applied strain for wire and tape conductor. The analysis is applicable over a full range of applied strain, including small strains often described by a power law strain dependence, and larger strains often described by a deviatoric strain approach. A comparison is provided between the results of the full detailed analysis and the results of the approximate treatment showing the degree of agreement in the various applied strain orientations.     

Energy release rate approximation for edge cracks using higher-order topological derivatives

Sub-micron films deposited on a flexible substrate are now commonly used in electronic industry. The main damaging mode of these systems is a multi-cracking of the film under the action of thermal and mechanical stresses. This multi-cracking phenomenon is described using the coupled criterion based on the simultaneous fulfilment of an energy and a stress criteria. The coupled criterion is implemented in a representative volume element and it allows to decide whether the stress or the energy condition governs the cracking mechanism. It is found that the energy conditions predominates for very thin films whereas the stress condition can take place for thicker films. The initial density of cracks is determined and is in good agreement with the experimental measures. Further subdivisions, when increasing the load, are also predicted. Moreover, under some conditions, a master curve can rule the density of cracks function of the applied strain, showing a good agreement between predictions and experiments for a wide range of film thicknesses.     

A non-singular boundary integral formula for determining the T-stress for cracks of arbitrary geometry

A simple, yet accurate 2-D boundary integral equation (BIE) for determining the T-stress for cracks of arbitrarily geometry is introduced in this paper. The formulation is based upon the asymptotic expansion for the stress field in the vicinity of a crack tip. It can be conveniently implemented in the post-processing stage of a boundary element fracture analysis. As demonstrated in this work, the proposed BIE is non-singular, and thus it can directly be collocated at the crack tip under consideration. The technique requires a similar computational effort as that used in calculating the stress components at an interior point of a domain. Consequently, this new approach is very computationally effective and accurate for evaluating the elastic T-stress. Five test examples, involving straight, kink and curved cracks, are studied to validate the proposed technique and to assess its accuracy.     

Uniaxial and biaxial fracture behaviour of refractory materials

Mechanical fracture properties of specimens taken from refractory materials of different brittleness are described using the wedge splitting method according to Tschegg in uniaxial and biaxial load cases. Notch-tensile strength, fracture energy and the characteristic length were determined. Fracture energy under a uniaxial load is more or less the same for all materials; if a load becomes biaxial, values fall to approx. 70% in materials with reduced brittleness and to 40% in brittle materials, compared to uniaxial values. The sensitivity against crack propagation (l_ch) changes insignificantly under both uniaxial and biaxial loading of brittle and brittleness-reduced materials.     

Higher-order crack-tip creep stress fields in materials under biaxial loading

We have developed and implemented a method for calculating the fields of parameters of the crack-tip creep stress-strain state by taking direct account of the higher-order terms. The paper presents some calculated data on the fields of crack-tip stresses, creep strain rates, and amplitude ratios in the creep case. The influence of loading biaxiality on redistribution of stresses between the creep stages and on the constraint parameters in failure is assessed. Translated from Problemy Prochnosti, No. 6, pp. 25–43, November–December, 2008.     

Tcenhancement in superconductor-semiconductor arrays

Subsequent to our observation that the Tl- and Bi-based cuprate high-T _c superconductors are built of superconductor-semiconductor arrays (P. C. W. Fung and W. Y. Kwok,J. Superconduct., this issue), we investigate in this paper the possibility ofT _c enhancement arising from the effect of change of phonon spectrum and the effect of size quantization when one or more semiconductor blocks is attached to the basic superconductor in the unit cell.     

A review of multiaxial/biaxial loading tests for composite materials

Multiaxial/biaxial loading tests of fibre-reinforced polymer-matrix composite materials are reviewed, and results of these experimental investigations under both monotonic and cyclic loadings are discussed. It is noted that composite materials could exhibit complicated behaviour in the biaxial loading conditions which often exist in engineering practice. The importance of biaxial loading tests of composites is indicated by this assessment.     

Mode I fracture behaviour of concrete under biaxial loading

Most concrete structures are biaxially loaded when cracking occurs and propagates. A test equipment was developed to evaluate fracture mechanic parameters of concrete, based on the principle of wedge splitting. Notched cubic specimens are tested under stable crack propagation. An additional compressive load application device simulates a homogeneous biaxial state of stress. A force-crack opening displacement diagram is obtained from which the specific fracture energy is calculated. The strain softening behaviour is then evaluated by means of numerical modelling. The approach was applied for biaxially loaded concrete samples with 8, 16 and 32 mm maximum size aggregate (MSA). Based on the experimental data a model is developed and discussed. It is found that the fracture energy changes non-uniformly with increasing compressive stress level, and that interaction of microcracking and aggregate interlocking influences the fracture mechanism.