Opening Stress Intensity Factor Research Articles

Four coplanar Griffith cracks moving in an infinitely long elastic strip under antiplane shear stress

This paper concerns with the problem of determining the anti-plane dynamic stress distributions around four coplanar finite length Griffith cracks moving steadily with constant velocity in an infinitely long finite width strip. The two-dimensional Fourier transforms have been used to reduce the mixed boundary value problem to the solution of five integral equations. These integral equations have been solved using the finite Hilbert transform technique to obtain the analytic form of crack opening displacement and stress intensity factors. Numerical results have also been depicted graphically.

Prediction of Notch Fatigue Threshold Based on R-Curve Method.

Single-edge-notched specimens of a structural carbon steel and a low-alloy steel were fatigued under axial loading. The initiation and propagation behavior of short fatigue cracks emanating from a sharp notch was investigated. The resistance-curve (R-curve) method was used to predict the fatigue thresholds of notched members. The R curve was constructed in terms of the experimentally determined threshold value of the maximum stress intensity factor which was the sum of the threshold effective stress intensity range ΔKeffth and the opening stress intensity factor Kopth. The value of ΔKeffth was constant and the R curve was independent of crack length and notch geometry. The predicted values of the fatigue limit for crack initiation, the fatigue limit for fracture, and the nonpropagating crack length agreed well with the experimental results. The effect of the material property or Vickers hardness on the fatigue notch sensitivity was discussed on the basis of the R-curve method. A simplified method to determine the R curve using Vickers hardness or the tensile strength was proposed for design applications.

Diffraction of elastic waves by three coplanar Griffith cracks in an orthotropic medium

The dynamic response of three co-planar Griffith cracks situated in an infinite orthotropic medium due to elastic waves incident normally on the cracks has been treated. The Fourier transform technique has been used to reduce the elastodynamic problem to the solution of a set of four integral equations. These integral equations have been solved by using the finite Hilbert transform technique and Cook's result. The analytical forms of crack opening displacement and stress intensity factors have been derived for low frequency vibration. Numerical results of crack opening displacement and stress intensity factors for several orthotropic materials have been calculated and plotted graphically to display the influence of the material orthotropy.

Fracture and fatigue behavior of scrim cloth adhesively bonded joints with and without rivet holes

—Tensile and fatigue disbond propagation studies on scrim cloth structural adhesive lap joints without and with rivet holes were performed. The geometry of the rivet holes is similar to that in a fuselage part of an aircraft. The joints were cycled in tension-tension fatigue at a frequency of 3 Hz and a maximum load, below the linear limit of the joint, which was obtained from the tensile tests of similar joints. The disbond length at each corner of the joint was viewed using a travelling optical microscope attached to a video camera. It was found that the static-tensile behavior of both types of joints (without and with rivet holes) consists of three stages: a linear stage followed by a region of increased non-linearity and then a 'yield' region. It is within this yield region that the rivet holes affect the strength of the joint. Stress analysis of the disbond problem under static loading revealed a strong mixed mode between the opening and shear mode stress intensity factors for both types of joints. T...

FINITE ELEMENT ANALYSIS OF CLOSURE BEHAVIOUR OF FATIGUE CRACKS IN RESIDUAL STRESS FIELDS

AbstractAn elastic‐plastic finite element analysis with high order elements is performed to examine closure behaviour of fatigue. cracks in residua1 stress fieids and the numerical results are then compared with experimental results. The finite element analysis, performed under plane stress using 8‐node isoparametric elements, can predict fatigue crack closure behaviour through residual stress fields very well. The crack opening and closing behaviour through a compressive residual stress field is found to be complicated and influenced by the applied load magnitude and the location of the crack tip. Three different types of crack opening behaviour, namely, normal, unsymmetric partial and symmetric partial crack opening behaviour are observed through a compressive residual stress field. The partial crack opening stress intensity factor including the partial crack opening effect is recommended for the prediction of fatigue crack growth through a compressive residual stress field.

Axially symmetric thermal stress of a penny-shaped crack subjected to general surface temperature

Axially symmetric stress distribution in the neighbourhood of a penny-shaped crack stituated in an infinite isotropic elastic solid under general surface loadings and general surface temperature is considered. Surface loadings and surface temperature applied on the crack surfaces are axisymmetric but they are unsymmetrical about the crack planez=0. The equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel integral operator of the second kind. The stresses, displacements, temperature and flux functions at a general point in the solid are derived in terms of stress, displacement, temperature and heat flux discontinuities at the plane of the crack. Using the boundary conditions and the continuity conditions problem is reduced to that of solving Abel integral equations of the first and the second kind. Explicit expressions are obtained for stress components, crack opening displacement and stress intensity factors in terms of the prescribed surface temperature functions. For some special cases of thermal loading these quantities are compared with those available in the literature. Stress at a general point of the medium is obtained in the special case, when the one face of the crack is subjected to constant temperature while the other face is kept at the reference temperature.

Fatigue crack closure and growth behavior under random loading

Fatigue crack closure and growth behavior under random loading is investigated by performing various random loading tests. The effects of random load spectrum and history length on the behavior of crack closure and growth are discussed. Moreover, single overloading, periodic single overloading, and Hi-Lo (high-low) block loading tests are performed to compare the crack closure behavior under random loading and under simple variable amplitude loadings. The crack opening load is nearly constant during a random loading block of history length ranging from 500 cycles to 2000 cycles and is mainly governed by the largest load cycle in a random load history, irrespective of random load spectrum and history length. The crack opening load under random loading is different from that under constant amplitude loading, indicating that the crack closure behavior under random loading cannot be estimated from constant amplitude tests. The crack opening stress intensity factor under random loading is linearly proportional to the maximum stress intensity factor of the largest load cycle in a random load history. Fatigue crack growth under random loading can be successfully described by the crack closure concept. It is found that the crack closure behavior under random loading can be estimated from single overloading or periodic single overloading tests. Based on the results obtained, a relatively simple method is proposed to predict crack growth under random loading.

Crack opening displacements and stress intensity factors caused by a concentrated load outside a circular crack

This paper gives an evaluation of crack opening displacements and stress intensity factors in terms of elementary functions for the problem of a concentrated load outside a circular crack. The results are obtained for both transversely isotropic and purely isotropic cases. A particular case of a concentrated load at a point on the normal axis is discussed and compared with the previous analysis. Some results for stress intensity factors are presented in a graphical form.

An elastic strip with three co-planar moving Griffith cracks

The dynamic anti-plane problem of determining stress and displacement due to three co-planar Griffith cracks moving steadily at a subsonic speed in an infinite elastic strip has been considered. Employing Fourier integral transform, the problem when the rigidly clamped edges of the strip are pulled apart in opposite directions has been reduced to solving a set of four integral equations. These integral equations have been solved using the finite Hilbert transform technique and Cook's result [ Glas. Math. J. 11, 9 (1970)] to obtain the exact form of crack opening displacement and stress intensity factors. Numerical results for stress intensity factors are presented in the form of graphs.

Interface crack loaded by a time-harmonic plane wave

In this paper, the two-dimensional problem of a finite crack along the interface between two dissimilar solids loaded by a plane wave is considered. Through use of the Fourier transform method, the boundary value problem of wave scattering is reduced to a vectorial Cauchy singular integral equation for the dislocation density on the crack face. A Jacobi polynomial technique is then used to solve the integral equation numerically. Crack opening displacements and stress intensity factors are obtained for various incident frequencies and incident angles. It is found that the crack faces interpenetrate each other near the crack-tips, and the crack-tip singular fields are oscillatory. The oscillatory index is the same as that for an interface crack under static loading, which can be expressed by the second Dundurs bimaterial constant. For practical purposes, an engineering approximation is proposed to remedy these pathological behaviors near the crack tips.

高周波表面焼入れ材における表面疲労き裂進展とき裂開閉口挙動

Surface fatigue crack growth tests under constant amplitude loading were carried out on three different materials of a medium carbon steel, JIS S38C, namely quenched and tempered material, quenched material and induction surface hardened material. It was found that the crack opening stress at the surface of hardened material was higher than those of the other materials, and the fatigue crack growth resistance in terms of the stress intensity range of surface hardned material was superior to the other materials. These differences resulted from the surface residual stress and there found little difference among three materials in the relationship between fatigue crack resistance and the effective stress intensity range. The higher crack opening stress intensity factor of the surface hardned material, Kop, could be well estimated by considering the actual stress ratio at the fatigue crack tip, R', which is defined as R'=(Kmin+Kr)/(Kmax+Kr), where Kmax and Kmin are the maximum and minimum applied stress intensity factors and Kr is the stress intensity factor induced by residual stress.

Three co-planar moving Griffith cracks in an infinite elastic medium

The dynamic in-plane problem of determining the stress and displacement due to three co-planar Griffith cracks moving steadily at a subsonic speed in a fixed direction in an infinite, isotropic, homogeneous medium under normal stress has been treated. The static problem of determining the stress and displacement around three co-planar Griffith cracks in an infinite isotropic elastic medium has also been considered. In both the cases, employing Fourier integral transform, the problems have been reduced to solving a set of four integral equations. These integral equations have been solved using finite Hilbert transform technique and Cook's result [16] to obtain the exact form of crack opening displacement and stress intensity factors which are presented in the form of graphs.

Solids with periodically distributed cracks

A systematic method is presented for estimating the overall properties of solids with periodically distributed cracks. In view of the periodicity, the displacement, strain and stress fields of the cracked solid can be expressed in Fourier series. Elastic solids with periodically distributed flat voids are considered first. The results for cracks are then obtained by letting the thickness aspect ratio of the void approach zero. This limiting process is performed with care. The only approximation involved is the distribution of the homogenization eigenstrains, which is assumed to be piecewise constant. The estimate of overall elastic moduli, crack opening displacements and stress intensity factors eventually reduces to the calculation of several infinite series. The formulation is valid for elliptic as well as two-dimensional line (slit-like) cracks and cracks with arbitrary shapes. It fully includes the interaction effects.

Fatigue Crack Growth Behavior of Large Crack in Silicon Nitride

Fatigue crack propagation under cyclic loading was observed in CT specimens of silicon nitride by employing an electrical resistance technique with crack gage made of platinum film. The crack growth rate was not uniform even if the fatigue condition was constant. The crack growth behavior in maximum stress intensity factor KImax-increasing condition was different from that in KImax-decreasing condition. The effect of stress ratio R(=σmin/σmax) was not significant when the minimum stress intensity factor (KImin) was greater than crack opening stress intensity factor (Kopen). Fracture toughness measured by CT specimens after fatigue testing was smaller than that by SEPB method. The experimental results, indicated that the unloading may cause fretting and/or crashing of the asperities between the crack faces in silicon nitride, where toughening is achieved by grain bridging. Therefore, the cyclic loading may accelerate the static fatigue crack propagation caused by stress corrosion cracking.

Four co-planar Griffith cracks in an infinite elastic medium

The dynamic in-plane problem of determining the stress and displacement due to four co-planar Griffith cracks moving steadily at a subsonic speed in a fixed direction in an infinite, isotropic, homogeneous medium under normal stress has been treated. The static problem of determining the stress and displacement in an infinite isotropic elastic medium has also been considered. In both cases, employing the Fourier integral transform, the problems have been reduced to solving a set of five integral equations. These integral equations have been solved using the finite Hilbert transform technique to obtain the exact form of crack opening displacement and stress intensity factors which are presented in the form of graphs.

Finite element modelling of crack closure during simulated fatigue threshold testing: McClung, R.C. Int. J. Fract.52 2 (15 Nov 1991) 145–157

Several fatigue cracks growth laws have been suggested over the past 50 years. Recently, a fatigue crack propagation law was proposed by Castillo-Canteli-Siegele (CCS model) based on the assumption that fatigue crack growth takes the form of a Gumbel cumulative distribution function. Besides many physical aspects, the fatigue crack propagation laws need to account for fatigue crack opening and closure effects. Thus, in this paper a modification of the CCS fatigue crack growth law is proposed to account for the crack opening and closure effects, as well as the stress R-ratio effect, Rσ. The fatigue crack opening and closure effects are taken into account using a plasticity-induced crack-closure model. Other fatigue crack closure models can also be used in the proposed modification of the CCS crack growth model through the quantitative parameter U = ΔKeff/ΔK. This modified CCS crack propagation model using the effective stress intensity factor range, ΔKeff, is a new version of an explicit fatigue crack propagation model, supported by mathematical and physical assumptions. In this paper, the proposed model is applied using the fatigue crack growth data and mechanical properties that were collected for the 2219-T851 aluminium alloy. Based on the plasticity-induced crack-closure model, which was first formulated by Newman, and in this paper modified with a boundary correction factor, Fw, the crack opening stress intensity factor, Kop, and quantitative parameter U are determined. The results showed a good agreement between the proposed modification of the CCS fatigue crack propagation model taking into account the plasticity-induced crack-closure model with the boundary correction factor and experimental results of the fatigue crack propagation data for the 2219-T851 aluminium alloy.

Effect of measurement location and fatigue-loading parameters on crack closure behaviour

The plasticity-induced fatigue crack closure behaviour has been studied in aluminium alloys 2024-T3 and 7075-T6 using a compliance gauge. Centre-cracked sheet specimens have been tested with stress ratios in the range 0.1–0.4 under a similar stress amplitude condition. The opening stress intensity factor K op as well as the K op/ K max ratio have been investigated as functions of measurement location, yield strength, maximum stress intensity factor K max and stress ratio R. K op and K op/ K max decrease with increasing distance behind the crack tip and decreasing crack length. The K op/ K max ratio is, however, independent of crack length in the close vicinity of crack tip. Whereas R is found to have only a marginal effect on K op, the latter is found to increase with K max and then subsequently to decrease. The findings have been discussed. Empirical formulae have been suggested to predict ΔK eff, R and K max using the multiple-regression method. ΔK eff is found to increase with increasing K max and ΔK.

Failure resistance in static loading of steels with ?0.2 > 600 MPa and their welded joints

Investigations were carried out into the failure resistance in the temperature range +20 to −60°C in static bending of 13KhGMRB, 14KhG2SAFD, and 14KhGN2MDAFB steels with σ0.2=600–700 MPa and also the weld metal and the heat affected zone (HAZ) of their welded joints. Evaluation of the cracking resistance of these steels and welded joints was carried out using fracture mechanics criteria: critical crack opening displacement δc and stress intensity factor Kc. The values of the effective factor of stress concentration, generated by the crack {ie746-01}, and critical stress σcr are also determined. The results show that of the three steels tested, the lowest failure resistance was exhibited by 14KhGN2MDAFB steel. The heat affected zones of the welded joints in the 13KhGMRB and 14KhGM2MDAFB steels have higher cracking resistance than the HAZ of the welded joints in 14KhG2SADF steel. The weld metal of welded joints produced in CO2 with PP-AN54 wire and in a Ar+CO2 mixture with Sv-08KhN2GNYu wire is characterized by higher failure resistance than the weld metal of welded joints produced in CO2 with Sv-10KhG2SMA wire. The welded joints in 13KhGMRB steel produced in CO2 with PP-AN54 wire, and in 14KhGN2MDAFB steel produced in the Ar+CO2 mixture, have high failure resistance at temperatures to −60 and −50°C, respectively. The welded joints in 14KhG2SAFD steel, produced in CO2 with Sv-10KhGSMA wire, can be used in service at temperatures not lower than −40°C.

き裂開口変位分布に基づく疲労き裂伝ぱ挙動の考察 （切欠き付近の残留応力分布に注目して）

A method was proposed which evaluates crack opening stress distribution and stress intensity factor from the crack opening displacement distribution near a circular-hole. The fatigue crack and the low-temperature annealed crack emanating from the hole were prepared and the crack opening displacements were measured along their faces. The difference in the crcak opening stress distribution between the fatigue and the annealed cracks was used to estimate the residual stress distribution along the fatigue crack. They showed the compressive residual stresses near the hole and the crack tip, but the tensile ones between them, which were caused by cyclic deformation near the hole and subsequently redistributed due to fatigue crack propagation. The stress intensity factors estimated from the fatigue crack opening displacements were smaller than those calculated from the applied stress and were closely related to the change in fatigue crack propagation rate.

A Method of Evaluating Crack Opening Stress Distributions and Stress Intensity Factors Based on Opening Displacements Along a Crack

In linear fracture mechanics, stress intensity factors controlling fracture behavior of materials are calculated from stress distributions acting on the crack surface by the aid of superposition even for remote applied stresses: These stress distributions, however, cannot be measured directly in the crack opening state because of the stress relief, which is seen in tensile residual stress fields for instance. In this report, such stress distributions are assessed by measuring the opening displacements along a crack under tensile loading, using the equation that was derived based on the complex-valued formulas on the stress and displacement of a two - dimensional crack. The known analytical opening displacements for cracks whose surfaces are subjected to a given stress distribution are used for numerically checking the validity of the equation. Using a rectangular specimen, it was found that this method was useful for the estimation of the stress intensity factors of central cracks opened by axial tensile loading.