Papers by Keyword: Stress Singularity

Abstract: The aim of this paper is to estimate a value of the critical applied force for a crack initiation from the sharp V-notch tip. The classical approach of the linear elastic fracture mechanics (LELM) was generalized, because the stress singularity exponent differs from 0.5 in studied case. The value of the stress singularity exponent depends on the V-notch opening angle. The finite element method was used for a determination of stress distribution in the vicinity of the sharp V-notch tip and for the estimation of the generalized stress intensity factor depending on the V-notch opening angle. Critical value of generalized stress intensity factor was obtained by using stability criterion based on the tangential stress component averaged over a critical distance d from the V-notch tip. Calculated values of the critical applied force were compared with experimental data taken from the literature.

Abstract: Slip localization is widely observed in metallic polycrystals after tensile deformation, cyclic deformation or pre-irradiation followed by tensile deformation. Such strong deformation localized in thin slip bands induces local stress concentrations in the quasi-elastic matrix around, at the intersections between slip bands (SBs) and grain boundaries (GBs) where microcrack initiation is often observed. Since the work of Stroh, such stress fields have been mostly modeled using the dislocation pile-up theory which leads to stress singularities similar to the LEFM ones. The Griffith criterion has then been widely applied, leading usually to strong underestimations of the macroscopic stress to GB crack initiation. In fact, slip band thickness is finite: 20nm-1000nm depending on material, temperature and loading conditions. Then, many slip planes are plastically activated through the thickness, and not only one single atomic plane. To evaluate more realistic stress fields, numerous crystalline finite element (FE) computations have been carried out using microstructure inputs (slip band aspect ratio, crystal and GB orientation...). A strong influence of slip band thickness close to the slip band corner has been highlighted, which is not accounted for by the pile-up theory. But far away, the thickness has a negligible effect and the predicted stress fields are close to the one predicted by the pile-up theory. Closed-form expressions are deduced from the numerous FE computation results allowing a straightforward prediction of GB stress fields. Slip band plasticity parameters, such as length and thickness, as well as crystal orientation, GB plane and remote stress are taken into account. The dependence with respect to the various parameters can be understood in the framework of matching expansions usually applied to cracks with V notches of finite thickness. As the exponent of the GB stress close-field is only about one-half of the pile-up or LEFM crack one, the Griffith criterion may not be used for GB microcrack prediction in case of finite thickness. That is why finite crack fracture mechanics is used together with both energy and stress criteria. Taking into account SB finite thickness, t>0, leads to predicted remote stresses to GB microcrack initiation three to six times lower than the ones predicted using the to pile-up theory, in agreement with experimental data.

Abstract: The contribution is focused on estimation of a critical value of generalized stress intensity factor for crack propagation from sharp V-notches. Stress distribution around the tip of the V-notch is described on the base of generalized linear elastic fracture mechanics, because V-notch is a singular stress concentrator with stress singularity exponent different from 0.5 (depending on V-notch opening angle). Then also stability criteria based on strain energy density factor and average critical stress are generalized for the stress singularity different from 0.5. Using FE analysis the critical stresses for crack initiation was estimated and compared with experimental data from the literature.

Abstract: The stress singularities are obtained by two methods in elastic-viscoelastic joints, one is extending the corresponding solutions for elastic-elastic joints by using elastic-viscoelastic correspondence principles and the other is replacing the elastic material parameters with viscoelastic ones in Dundurs parameters directly. The difference between the two methods and the validity are discussed.

Abstract: The stresses near the free edge of the interface of a joint of dissimilar materials after a change of the temperature can be described as the sum of one or two singular terms and a regular term which is independent of the distance and the geometry angles and . The regular stress terms are important for the stress distribution near the singular point. The emphasis in this paper is placed on giving an explicit form of the regular term by using a concept of equivalent edge load.

Abstract: Stress singularities exist on the interface endpoint or internal point, consisting of dissimilar linear elastic bonded wedges. The eigenvalue λ is an important parameter to represent the stress singularity on the interface singular point. And smaller eigenvalue represent stronger stress singularities on the interface singular points. The angular function is another parameter to represent stress singularities around singular points. It is known that the eigenvalue is influenced by the Young’s modulus, Poisson’s ratio and interface angles. The Airy stress eigenfunction method has been used to solve the eigenvalue on the bi- and tri-material junctions by verifying the Young’s modulus. And then talk about angular functions around the bi- and tri-material junctions’ singularity point. At last discuss the feasibility of enhancing the interfacial bonding strength in engineering practice.

Abstract: Numerical method is proposed for construction of singular solutions for spatial crossing wedge-and cone-shaped cracks. The results of numerical simulations made in the study allowed us to estimate the stress singularity indices at the tip of wedge-shaped cracks for different boundary conditions on the crack faces and at the tip of crossing cone cracks. The stress singularity at the tips of cone-shaped cracks is investigated.

Abstract: A generalized expression of the stress-singularity function at the tip of artificial crack is proposed, and a formula to calculate the stress intensity factor of artificial crack is obtained in the paper. The solutions of stress singularity of a cracked bi-materials beam under uniform tension and bending were computed. The results show that the degree of stress-singularity is determined by the exponent λ at the tip of artificial crack, and the exponent λ is, not only determined by materials parameter of artificial crack but also by angle. Key words: artificial crack; bi-material; stress singularity; eigen value; stress extrapolation method

Abstract: Fretting-fatigue often occurs at the contact area between two materials. There exist strong stress singularity exist at the contact edge, crack usually initiation at here. In this paper, the singular stress fields near the contact edge is obtained by using commercial code ABAQUS, then, the curve fitting method is used to determine the stress-singularity order and stress-strength parameter. Finally, the criterion of fretting-fatigue crack initiation in LZ50 steel is determined by using stress-strength parameters.

Abstract: An asymptotic analysis for singular stress fields around an interface-edge of dissimilar power-law hardening materials joint has been presented under plane strain condition and J2 deformation plasticity theory. Both the balance of force and the continuity of displacement are satisfied on the interface. In the higher order approximation, the nonlinear effective stress term was expanded by Taylor series. An iteration method is proposed for the determination of singular fields around interface edge. Multiple stress singular terms exist for in the higher order approximation. The order of stress singularity has a dependency with the combination of hardening exponents, .