T-stress For Cracks Research Articles

Determination of T-stress for thermal cracks in homogeneous and functionally graded materials with the numerical manifold method

T-stress plays an important role in the fracture of various materials, and is frequently adopted as a second fracture parameter in addition to the stress intensity factor. In this paper, the T-stresses for cracks in both homogeneous and functionally graded materials under thermal loadings are computed by the numerical manifold method (NMM), which is very suitable for crack modeling due to the use of bi-cover systems. After the calculation of temperature and displacement fields by the NMM solver, the T-stress is extracted through the domain-independent interaction integral. The proposed method is verified through two benchmark problems and then applied to study three more complex cases where the effects of material parameters and crack configurations on the T-stress are further examined.

Calculation of K-factor and T-stress for cracks in anisotropic bimaterials

The problem of a crack in a thin layer terminating perpendicular to a layer/substrate interface is analyzed for a general case of elastic anisotropy. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. A system of simultaneous functional equations is obtained that enables to find the singularity exponent λ. The reciprocal theorem ( ψ-integral) is used to compute the generalized stress intensity factor (GSIF) through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. The results obtained are compared with the evaluation of GSIF based upon the dislocation arrays technique. Existing semi-analytical solution for singularities in anisotropic trimaterials is applied and its validity for the specimen investigated is checked by FEM. The evaluation of T-stress using the dislocation arrays technique is performed.

Evaluation of T-stress for cracks in elastic sheets

The T-stress of cracks in elastic sheets is solved by using the fractal finite element method (FFEM). The FFEM, which had been developed to determine the stress intensity factors of cracks, is re-applied to evaluate the T-stress which is one of the important fracture parameters. The FFEM combines an exterior finite element model with a localized inner model near the crack tip. The mesh geometry of the latter is self-similar in radial layers around the tip. The higher order Williams series is used to condense the large numbers of nodal displacements at the inner model near the crack tip to a small set of unknown coefficients. Numerical examples revealed that the present approach is simple and accurate for calculating the T-stresses and the stress intensity factors. Some errors of the T-stress solutions shown in the previous literature are identified and the new solutions for the T-stress calculations are presented.