Analysis of elastoplastic sharp notches

Abstract

In this paper the elastoplastic solutions with higher-order terms for apex V-notches in power-law hardening materials have been discussed. Two-term expansions of the plane strain and the plane stress solutions have been obtained. It has been shown that the leading-order singularity approaches the value for a crack when the notch angle is not too large. In plane strain cases the elasticity does not enter the second-order solutions when the notch opening angle is too small. For a large notch angle, the two-term expansions of the plane strain near-tip fields are described by a single amplitude parameter. The plane stress solutions generally contain the elasticity terms. The boundary layer formulations based on the small-strain plasticity theory confirm that a dominance zone exists ahead of the notch tip. Finite element results give good agreement to the asymptotic solutions under both plane strain and plane stress conditions. The second-order terms cannot improve the predictions significantly. The near-tip fields are dominated by a single parameter. Finite element calculations under the finite strain J2-flow plasticity theory revealed that the finite strains can only affect local characterization of the asymptotic solution.The asymptotic solution has a large dominance zone around the notch tip. For an apex notch bounded to a rigid substrate the leading-order singularity falls with the notch angle significantly more slowly than in the homogeneous material. It vanishes at the notch angle about 135 ° for all power-hardening exponents. The elasticity effects enter the second-order solutions when the notch angle becomes large enough. The tip fields are characterized by the hydrostatic stress and the shear stress ahead of the notch.

The Equivalent Strain Energy Density approach re‐formulated and applied to sharp V‐shaped notches under localized and generalized plasticity

“…The determination of the angular function σ̄ ij ( θ ), σ̄ e ( θ ) requires a numerical solution (generally based on shooting techniques) of the differential equations system that controls the problem. 19, 20 …”

“…The determination of the angular functions s ij (y), s s e (y) requires a numerical solution (generally based on shooting techniques) of the differential equations system that controls the problem. 19,20 Since angular stress components are defined within a constant value, an unambiguous definition of the plastic N-SIF requires that angular stress components always be normalized in the same manner. In the present paper, the maximum value ofs s e (y) over the entire domain was set to unity.…”

“…In the presence of a certain amount of plasticity, at the failure point we have again W a local W b local . Then, by means of Eqs (19) and (25), it is possible to write: Eq. (31) makes it evident that when the behaviour of the two components is fully plastic, the scale effect law becomes:…”

Asymptotic thermal and residual stress distributions due to transient thermal loads

“…To overcome this, the fatigue strength assessments in the presence of failures from the weld root and the weld toes with different opening angle have been later carried out in a unified manner after introduction of the concept of local strain energy density over a control volume. [11][12][13] By proceeding on parallel tracks, many researchers analysed cracks and V-notches under different elastic-plastic conditions taking different loading modes: [14][15][16][17][18][19] in this case the guidelines are those provided by the well-known HRR (Hutchinson, Rice and Rosengren) solution. 20,21 Thanks to the local yielding, the degree of singularity of stress distributions decreases with respect to the linearelastic case, mainly as a function of the strain-hardening exponent.…”

The Use of Matlab in Advanced Design of Bonded and Welded Joints

“…According to the direct approach, first suggested by Ponte Castanêda (1985) and then used also in (Yuan et al, (1994); Lazzarin et al (2001)), a variable separable two term expansion is used for the stresses:…”