Determination of the stress intensity factor by methods of photoelastic simulation

Various methods of determination of stress intensity factors from the patterns of the isochromes, the isopachs, and the absolute differences in shape at the tip of a notch are analyzed. The range of extrapolation of the values of K_I within which the theoretically obtained stress distributions coincide with the stresses measured experimentally on a model with a finite radius of the stress raiser tip is established. Determination of the parameter K_I from the patterns of absolute differences of the shape is significantly more complex than from the patterns of the isochromes and isopachs but is justified on models of a high-modulus material when increased accuracy, reliability of the results, and an analysis of the stressed and strained state of a specimen with separation of the main stresses are necessary.Translated from Problemy Prochnosti, No. 1, pp. 33–37, January, 1990.     

A generalised notch stress intensity factor for U-notched components loaded under mixed mode

A novel notch stress intensity factor (NSIF) for U-notched specimens loaded under mixed mode is examined in this article. The concept is based on the averaged strain energy density criterion, or alternatively on the cohesive zone model, as well as the equivalent local mode approach. To a certain extent, it is a generalisation of Glinka’s NSIF for mode I, where σ_tip is replaced by σ_max.The applicability of a fracture criterion based on this new NSIF is checked against 171 fracture tests with PMMA (at −60 °C) performed on U-notched specimens, with different notch root radii and loaded under mixed mode. The asymptotic behaviour of the new NSIF as the notch becomes a crack (when the notch root radius tends to zero) or when the notch disappears (when the notch root radius tends to infinity) is also discussed.     

A simple method for the photoelastic determination of mode I stress intensity factors

A new simple method for the photoelastic determination of Mode I stress intensity factors from isochromatics is proposed. This method takes into account the fact that a considerable part of the error committed in the photoelastic determination of Mode I stress intensity factors K_I at crack tips, based on experimentally obtained isochromatic fringe patterns, is due to ignoring the non-singular part of the stress field near the crack tips for the evaluation of these factors. This error can, in most cases, be minimized by an appropriate selection of the polar direction from the crack tip on which the experimental measurements for the subsequent evaluation of the stress intensity factors K_I are made. The suitable polar direction for determining K_I depends in general on the distance of the point where measurements on the isochromatics are made from the crack tip. The method was applied to the problem of a simple crack inside an infinite medium under uniaxial and biaxial loading. A comparison of the present method whith the employed analogous methods shows the superiority of the proposed method.     

An assessment of far field effects on the photoelastic determination of mixed mode stress intensity factors

A limiting approach inquiry into far field effects on local field equations for mixed mode surface flaws is investigated by computer analysis. Curves showing the diminishing effect of the far field stress towards the cracks tip are plotted using fringe radii ratios vs fringe number. The zone used in the experimental determination of K₁ and K₂ is superimposed on these curves to investigate the extent to which K₁ and K₂ determined by the two parameter method are influenced by the far field stress.     

On the photoelastic determination of complex stress intensity factors

An improvement of the one-parameter extrapolation method of photoelastic determination of complex (mixed-mode) stress intensity factors at straight or curvilinear crack tips in a plane isotropic elastic medium due to Smith et al. [12, 13] can be achieved by measuring the absolute value of such a factor on the isochromatic fringes along properly selected polar directions and not at the maxima of the isochromatic fringes. In this way, the unknown value of the constant term of the stress field near the crack tip is taken into account. It is seen that it is always possible to find at least one appropriate polar direction to measure the absolute value of the stress intensity factor. In the case of Mode I stress intensity factors, these polar angles are = ± 120° and not = ± 90° as generally considered previously. Some numerical results are also presented in this special case and show the efficiency of the present method.     

Determination of stress intensity factors by means of the correction factor method

A method is proposed for determining stress intensity factors based on using the correction factor method. The correction factors obtained from solving similar simpler problems take into account the effect on the stress intensity factor of various factors: crack shape, size and shape of the body, character of loading, presence of several cracks, etc. The possibility of using this method for finding solutions of static and dynamic problems of crack theory is shown by examples.Translated from Problemy Prochnosti, No. 3, pp. 12–17, March, 1992.     

Sub-Region Mixed FEM for calculating stress intensity factor of antiplane notch in bi-material

The expression of displacement and stresses at the tip of an antiplane notch in bi-material is derived by the eigenfunction method; the stress intensity factor of the notch is calculated by Sub-Region Mixed FEM.     

Determination of the threshold stress intensity factor by the method of acoustic emission

The article presents the results of investigations into the correlation between fatigue crack growth and parameters of acoustic emission. It suggests an analytical model of the correlation between fatigue crack growth and the total count of acoustic emission per cycle. On the basis of the formulated model and of the obtained experimental results a method was worked out for determining the threshold values of the peak-to-peak values of the stress intensity factor.Translated from Problemy Prochnosti, No. 4, pp. 58–60, April, 1991.     

Calculation of mode III stress intensity factor by BEM for cracked axisymmetric bodies

This paper is concerned with the numerical calculation of Mode III stress intensity factor by BEM for cracked axisymmetric bodies, under torsion. Mode III stress intensity factors K _III are obtained using the asymptotic displacement field in the vicinity of the crack border. The asymptotic field is derived by integration along the boundary of the meridian of the cylinder. For traction free cracks no discretization of the crack surface was found necessary. Numerical results proving the efficiency of the proposed method are presented and compared with results given in the literature and with those obtained by FEM.     

Influence of notch geometry on the estimation of the stress intensity factor threshold by considering the Theory of Critical Distances

Recently the Theory of Critical Distances was applied to estimate the threshold stress intensity factor, ΔK_th, as an alternative to standard fracture mechanics tests. This strategy requires only a linear-elastic Finite Element Analysis (FEA) around the notch vicinity and fatigue limit data from notched and smooth specimens, usually available in the literature, or at least easier and cheaper to produce and test than fracture mechanics cracked specimens necessary in ΔK_th experiments. The aim of this work is to revisit this numerical–experimental strategy and to assess the effect of notch geometry in the predictive methodology in order to evaluate its domain of validity mainly, but not only, in terms of notch root radius bluntness. A wide range of experimental data for different metallic alloys and types of notches were selected to validate the analysis. The results showed that only fatigue data from notch root radii, normalized with respect to the net cross section of the specimen, smaller or equal to 0.01 can provide estimates of ΔK_th within an error interval about 20%.     

A technique for experimental evaluation of mixed mode stress intensity factors

High sensitivity moiré interferometry was used to obtain whole-field orthogonal components of displacement in the vicinity of cracks in centre-cracked plates of aluminium 6082. The plates had been prepared in such a way as to enable the application of load at angles of 75° and 60° to the planes of the fatigue pre-cracks. The form of the moiré fringe data enables convenient separation of the components of stress intensity factor K _I and K _II. The results are compared with analytical predictions. The method is, in principle, suitable for use with specimens of arbitrary geometry and loading.     

Notch effects on photoelastic determination of mixed-mode stress intensity factors

An investigation into the notch effect on the photoelastic determination of the mixed mode stress intensity factors is presented. This accomplished by comparing the isochromatic loops generated for a crack and an ellipse in an infinite plate. The generated mathematical loops are based on the exact solutions. A method of analysis is proposed and used to correct the distorted maximum angle $\text{θ}{}_{\mathrm{m}}$ and maximum shear stress $\text{τ}{}_{\max }$ due to the notch effect. The results obtained from the photoelastic measurements based on the proposed method compare favourably with those by an earlier investigation.     

Estimations of stress intensity factor for a short crack in an elastic–plastic notch

This note presents a simple method for estimating the stress intensity factor (SIF) for a short crack emanating from an elastic–plastic notch.