Andrzej Seweryn

Brittle fracture criterion for structures with sharp notches

Abstract A brittle fracture criterion for structures with sharp notches is proposed. It is based on Irwins and Novozhilovs criteria and states that a crack will propagate from a tip of a notch when the actual value of the stress intensity factor KI,II,III reaches a critical value. The considerations were carried out within the limits of linear elastic analysis and based on the general expressions for the stress distribution in the vicinity of the notch-tip. The parameters required to estimate the brittle fracture hazard can be easily obtained from experiments.

Verification of brittle fracture criteria for elements with V-shaped notches

Abstract In this paper an analysis of crack initiation in plane elements with V-shaped notches under biaxial loading (mode I and II) was presented. The following fracture criteria were used to evaluate the critical loads and directions of crack initiation: strain energy release rate criterion; strain energy density criterion; modified McClintocks stress criterion; non-local stress criterion. Results of numerical analysis obtained using the boundary element method and path independent H and J integrals were compared with experimental data.

Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions

Abstract The present paper deals with an analytical description of the stress and displacement fields around a sharp angular comer subjected to various loading and displacement boundary conditions, in plane problems of elasticity. The goal has been gained using a general solution of differential equations of equilibrium in terms of displacements and asymptotic stress function near the notch tip, expressed in polar coordinates. All possible combinations of the boundary conditions applied to the notch faces, such as: free, clamped and for a roller support, have been analyzed as well as symmetric and anti-symmetric loading modes being distinguished. Each case is accompanied by the corresponding characteristic equation of the complex eigenvalues λ and by its numerical solution presented in graphical form, showing the leading and the higher order terms of the series. Next, the solution to the similar problem for anti-plane shear has been given. Finally, the possibility of application of the generalized stress intensity factors to practical problems of fracture mechanics in all the cases mentioned above is discussed. A numerical method developed to solve the characteristic equations is also described.

A non-local stress failure condition for structural elements under multiaxial loading

Abstract A non-local stress condition for crack initiation and propagation is proposed and applied to several particular cases, such as plate with wedge-shaped notch, elliptical hole and hyperbolic notch. Brittle failure initiation for notched elements under complex loading (Modes I and II) is studied in detail. A value of critical load and crack orientation is predicted from the non-local condition, which is applicable to both regular and singular stress concentrations.

A NON-LOCAL STRESS AND STRAIN ENERGY RELEASE RATE MIXED MODE FRACTURE INITIATION AND PROPAGATION CRITERIA

Abstract A non-local stress condition for crack initiation and propagation in brittle materials is presented. This condition is expressed in terms of normal and tangential traction components acting on a physical plane segment (damage zone) of specified length. Next, a non-local strain energy release rate criterion is proposed. This condition is based on the assumption that initiation or propagation of cracking occurs when the maximal value of the function of opening and sliding energy release rates reaches a critical value. The value of energy release rates is determined for finite elementary crack growth. Mixed mode conditions are considered, for which both the critical load value and the crack orientation are predicted from the non-local stress and energy criteria, which are applicable to both regular and singular stress concentrations. The effect of non-singular second order term (Tσ-stress) on the crack propagation is discussed.

Modeling of singular stress fields using finite element method

The paper discusses methods of modeling of singular stress fields in problems with angular corners. A novel method of analytical constraints has been proposed. In this method the relations between the displacements of the finite element nodes are assumed to conform to the analytical solution. The method of analytical constraints has been used for calculations of the stress intensity factors and of the coefficients of the two consecutive terms of the asymptotic solution in the case of elements with cracks and V-notches under uniaxial and biaxial loading. Singular finite elements have been applied and various mesh discretisations have been used.

On the criterion of damage evolution for variable multiaxial stress states

The damage accumulation condition expressed in terms of traction components on a physical plane is discussed for both monotonic and cyclic loading conditions. The crack initiation is assumed to correspond to a critical value of damage reached on the physical plane. For singular stress distribution in the front of sharp notch or crack the non-local condition is formulated. The proposed condition is applied to predict damage distribution within the representative element for cyclic loading conditions. The rosette diagrams are constructed for visualization of damage distribution. The prediction of crack initiation for multiaxial fatigue loading is provided. The second- and fourth-order damage tensors in order to describe damage distribution within the element, and the associated compliance variation are introduced.

Solution for the stress and displacement fields in the vicinity of a V-notch of negative wedge angle in plane problems of elasticity

Abstract The method is presented of modeling displacement, strain and stress fields in the two-dimensional problems of elasticity considering the presence of V-shaped notches with any positive or negative angle. The analytical expressions for stress and strain states at the tip of a V-notch were obtained for two cases of deformation: opening (mode I) and sliding (mode II). This was achieved assuming the appropriate Airy function in polar coordinates with an origin at the notch tip. A new definition of the stress intensity factors was proposed. The analytical predictions were compared with the numerical results obtained using the finite element method. Finite elements with linear-stress distribution and finite elements with asymptotic-stress distribution were used in the mesh idealization.

MODELING OF THE TENSION AND COMPRESSION BEHAVIOR OF SINTERED 316L USING MICRO COMPUTED TOMOGRAPHY

Abstract This paper describes the method of numerical modeling of the tension and compression behavior of sintered 316L. In order to take into account the shape of the mesostructures of materials in the numerical modeling, X-ray microtomography was used. Based on the micro-CT images, three-dimensional geometrical models mapped shapes of the porosity were generated. To the numerical calculations was used finite element method. Based on the received stress and strain fields was described the mechanism of deformation of the materials until fracture. The influence of material discontinuities at the mesoscopic scale on macromechanical properties of the porous materials was investigated.

Fatigue and Fracture of Plane Elements with Sharp Notches under Biaxial Loading

ABSTRACT Theoretical, numerical and experimental investigations on fatigue and fracture of plane rectangular elements with opposite V-notches of various opening angles are presented. Two materials - a ductile aluminium alloy and brittle PMMA - were used to analyse damage processes under biaxial loading conditions, as tension and shear. Experiments have shown that material properties strongly affect the damage process in both monotonic and variable loading. Fracture mode, fatigue crack direction and shape depend on material properties, notch angle and tension/shear ratio. The explanation of this behaviour is based on an elastic-plastic FEM analysis for the aluminium alloy and a non-local damage accumulation criterion for the PMMA.