Theory of critical distances: A discussion on concepts and applications

Abstract

Theory of Critical Distances (TCD) collects several methods adopted in failure prediction of components provided with stress concentration features. The idea of evaluating stress effect in a zone rather than in a single point was proposed decades ago but, only thanks to relatively recent works, TCD concepts showed to be a successful extension of Linear Elastic Fracture Mechanics (LEFM), able to assess strength and fatigue life. The increasing computational power has made Finite Element Method (FEM) widespread, hence stress fields can be easily extracted and used as input data for fatigue post-processing and durability analyses. In this scenario, TCD reveals as a powerful tool which, thanks to the introduction of a single material parameter (critical distance, [Formula: see text]), integrates classical fracture models by considering the presence of microscale phenomena acting in fracture process. In this sense, TCD behaves as a link between continuum mechanics and LEFM. Modalities and reasons for this connection to occur are interesting points of further investigations. Literature on TCD and its theoretical-experimental background is quite extended, nevertheless few industrial applications are available in literature to the best of authors’ knowledge. In this paper, an overview of concepts and applications related to TCD are reported highlighting the relevance of theoretical arguments in actual applications.

Bright white light emission from lanthanide oxide LaGdO3 for LED lighting by Bi3+ to Eu3+ energy transfer

“…The optimal doping content was determined to be 0.005. The quenching of the concentration results from the energy transfer between the Bi 3+ ions, and the critical distance ( R c ) can be approximately determined by the formula below: 16–18 where V is the volume of the unit cell, X c is the critical content proportion of Bi 3+ , and N is the total number of Bi 3+ sites in the unit cell. Here, V = 470.038 Å 3 , X c = 0.005 and N = 6, and the value of R c can be calculated as 31.05 Å.…”

Using the Stress Concentration Factor in Determining the Fracture Toughness

“…The constant Keff is obtained by placing the found critical fracture stress in Eq. (10). It can be seen in Table 7 that Keff is 1222 MPa.mm 1/2 for the sample under consideration.…”

“…Establishing a relationship between the stress concentration at the crack tip and the stress intensity factor (SIF) would be meaningful approach in determining the critical fracture stress. Therefore, it is much more appropriate to consider tensile methods and fracture toughness together [9,10]. In order to define the crack nucleation mechanism in the stress concentration region in brittle materials, theories have been put forward to use the energy and stress criteria in combination instead of applying them separately.…”

Shafts with U-shaped circumferential grooves: design charts for stress concentration factors, radial displacement and Poisson’s ratio influence

“…4 Non-local approaches, which are beyond the scope of this paper, may be suitable when high-stress gradients are present. 31 Few contributions investigate the influence of the material elastic constants on the SCF. While in two-dimensional problems, the stress field may be independent of both Young's modulus E and the Poisson's ratio ν; according to Michell's theorem, 32,33 the solution for axisymmetric problems, under bending moment and normal force, generally depends on ν, [34][35][36][37][38] whereas their counterpart in torque does not.…”

“…4 Non-local approaches, which are beyond the scope of this paper, may be suitable when high-stress gradients are present. 31…”