Crack Opening Stress Intensity Factor Research Articles

On the Link between Plastic Wake Induced Crack Closure and the Fatigue Threshold

This purpose of this paper is to examine the relationship between crack growth equations based on Elber’s original plastic wake induced crack closure concept and the fatigue threshold as defined by the American Society for Testing and Materials (ASTM) fatigue test standard ASTM E647-15el. It is shown that, for a number of conventionally manufactured metals, the function U(R), where R is the ratio of the minimum to maximum applied remote stress, that is used to relate the stress intensity factor ΔK to the effective stress intensity factor ΔKeff is inversely proportional to the fatigue threshold ΔKth(R). This finding also results in a simple closed form equation that relates the crack opening stress intensity factor Ko(R) to ΔK, Kmax, and the fatigue threshold terms ΔKth(R) and ΔKeff,th. It is also shown that plotting da/dN as function of ΔK/ΔKth(R) would appear to have the potential to help to identify the key fracture mechanics parameters that characterise the effect of test temperature on crack growth. As such, for conventionally manufactured metals, plotting da/dN as function of ΔK/ΔKth(R) would appear to be a useful addition to the tools available to assess the fracture mechanics parameters affecting crack growth.

Study on fracture behavior of nickel-based single crystal superalloy subjected to high temperature fatigue using digital image correlation

Anisotropic mechanical behavior of nickel-based single crystal superalloy (NBSCS) is studied based on the displacement field near the crack tip during the fatigue crack growth at 980°C. A new distortion calibration technique for bi-prism-based single-lens 3D digital image correlation (BSL3DDIC) is proposed to in-situ and on-line characterize 3D full-field deformation with high precision. Virtual displacement extensometers (VDEs) are arranged from the displacement field for the crack opening displacement (COD) determination. To the best of our knowledge, the effect of VDEs locations on the precision of COD measurement is first theoretically analyzed, and the arrangement of VDEs has been optimized. Noticeably, similar quantitative analyses are conducted to determine crack opening ratio (COR) for crack closure evaluation. Moreover, via fitting full-field displacement data to a theoretical model for anisotropic material, not only mode-Ⅰ effective stress intensity factor (SIF) expressed as KeffI and mode-Ⅱ effective SIF (KeffΠ), but also theoretical SIF (KtheoI), crack opening SIF (KopenI) and crack opening load ratio (COLR) are obtained. Based on these important fatigue parameters, modified Paris’ law is used to describe the high-temperature anisotropic crack growth behavior.

Research on two-dimensional Linear Elastic Fracture Mechanics Analysis using Isogeometric Analysis

We propose a fracture mechanics analysis method using isogeometric analysis(IGA). IGA is a numerical analysis method that uses non-uniform rational B-spline, which is included in many computer aided design systems as a geometrical representation, as the shape function of conventional finite element method. In this research, two dimensional fracture mechanics problem with a center crack was analyzed. Here, when a singular patch using the coordinates of the shape function and the control point was introduced so as to express the stress singularity of the crack tip, a significantly improvement in accuracy of crack opening displacement, stress distribution and stress intensity factor was observed. Also, as application method, we considered s-version IGA method(S-IGA) applying s-version finite element method to IGA. S-IGA is a method that a local patch representing the local feature such as a hole or a crack is superposed on a global patch representing the shape of the whole analysis model. It is possible that the discontinuity can be expressed by superimposing the singular patch on the simple patch with no crack.

Effects of rolling reduction and direction on fatigue crack propagation in commercially pure titanium with harmonic structure

Cold rolling followed by heat treatment was performed on commercially pure titanium with a bimodal harmonic structure, which is defined as a coarse-grained region (Core) surrounded by a network structure of fine grains (Shell), and fatigue crack propagation tests were conducted to clarify the effects of the rolling reduction, rolling direction, and force ratio. From the relationship between the crack propagation rate da/dN and the stress intensity factor range ΔK, da/dN for the L-T orientation was always higher than that for the T-L orientation, and da/dN was higher for a higher force ratio and a higher rolling reduction for either rolling reduction. Crack closure resulting from the roughness of the fracture surface can be partially explained by the above effects; however, the relationship between da/dN and the effective stress intensity factor range ΔKeff also depended on the same factors, while the effects were smaller than those for the da/dN–ΔK relationship. The crack opening stress intensity factor Kop,th and effective stress intensity factor range ΔKeff,th under the threshold condition linearly increased with the square root of the average grain size in the Shell region, which decreased with rolling reduction. Thus, the threshold condition of the harmonic structured material is considered to be determined by the average grain size in the Shell region.

The effect of grain size on the fatigue overload behaviour of nickel

The fatigue overload behaviours of coarse grain (~30 μm), ultrafine grain (360 nm) and nanocrystalline (~30 nm) Ni are compared under constant amplitude loading at R = 0.1 after a 100% overload. Synchrotron X-ray diffraction is applied to map the elastic crack-tip strain fields at the mid-thickness of a compact tension specimen of nanocrystalline Ni at various stages through the loading cycles, from which the variation in stress before, during and after overload is estimated. Digital image correlation is used to measure the crack length and the displacement fields at the specimen surfaces for both grain sizes, from which the fatigue crack growth (FCG) rate, crack opening displacement and stress intensity factor range are determined. The FCG for coarse grain Ni is most significantly retarded whereas the nanocrystalline Ni is least affected by the overload due to an increased yield stress and a more planar crack surface morphology. As a result, FCG retardation by plasticity, surface roughness and residual stress-induced crack closure are reduced.

Comparative study of time and frequency domain approaches in contact problem for the I-mode crack under harmonic loading

In this paper two approaches, time-domain (TD) and frequency domain (FD) have been applied for the solution of the dynamic unilateral contact problem. We investigate crack in two-dimensional (2-D) plane, homogeneous, isotropic and linear elastic solids under action of the longitudinal P-wave with considering unilateral contact of the crack edges. For the problem solution a special iterative algorithm of the Udzava's type and boundary element methods (BEM) in the time-domain (TD) and frequency domain (FD) are used. For evaluation of the hypersingular integrals involved in BIEs a special regularization process that converts these integrals to regular ones is applied. Simple regular formulas for their calculation are presented. Numerical results for the crack opening, contact forces and dynamic stress intensity factor (SIF) for the case of a finite I-mode crack in an infinite 2-D domain which is subjected to a harmonic loading with considering crack edges unilateral contact interaction are presented and discussed.

Modified CCS fatigue crack growth model for the AA2019-T851 based on plasticity-induced crack-closure

Several fatigue cracks growth laws have been suggested over the past 50years. 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.

Crack Closure Effects on Fatigue Crack Propagation Rates: Application of a Proposed Theoretical Model

Structural design taking into account fatigue damage requires a thorough knowledge of the behaviour of materials. In addition to the monotonic behaviour of the materials, it is also important to assess their cyclic response and fatigue crack propagation behaviour under constant and variable amplitude loading. Materials whenever subjected to fatigue cracking may exhibit mean stress effects as well as crack closure effects. In this paper, a theoretical model based on the same initial assumptions of the analytical models proposed by Hudak and Davidson and Ellyin is proposed to estimate the influence of the crack closure effects. This proposal based further on Walker’s propagation law was applied to the P355NL1 steel using an inverse analysis (back-extrapolation) of experimental fatigue crack propagation results. Based on this proposed model it is possible to estimate the crack opening stress intensity factor,Kop, the relationship betweenU=ΔKeff/ΔKquantity and the stress intensity factor, the crack length, and the stress ratio. This allows the evaluation of the influence of the crack closure effects for different stress ratio levels, in the fatigue crack propagation rates. Finally, a good agreement is found between the proposed theoretical model and the analytical models presented in the literature.

Fatigue crack closure in submicron-thick freestanding copper films

The fatigue crack closure in approximately 500-nm-thick freestanding copper films were investigated by in situ field emission scanning electron microscope (FESEM) observations of the fatigue crack opening/closing behavior at three stress ratios of R=0.1, 0.5, and 0.8 in the low–Kmax (maximum stress intensity factor) region of Kmax<4.5MPam1/2. The direct observation of fatigue cracks clarified that crack closure occurred at R=0.1 and 0.5, while the fatigue crack was always open at R=0.8. Changes in the gage distance across the fatigue crack during a fatigue cycle were measured from the FESEM images, and the crack opening stress intensity factor Kop was evaluated on the basis of the stress intensity factor K vs. the gage distance relationship. The effective stress intensity factor range ΔKeff=Kmax−Kop was then evaluated. The R-dependence of the da/dN vs. ΔKeff relationship was smaller than that of the da/dN vs. ΔK relationship. This suggests that ΔKeff is a dominating parameter rather than ΔK in the fatigue crack propagation in the films. This paper is the first report on the presence of the fatigue crack closure in submicron-thick freestanding metallic films.

Time–Harmonic Behaviour of a Cracked Piezoelectric Solid by BIEM

Time–harmonic behaviour of a cracked piezoelectric finite solid is studied by nonhypersingular traction Boundary Integral Equation Method (BIEM). A numerical solution for Crack Opening Displacement (COD) and Stress Intensity Factor (SIF) is obtained by using Mathematica. Several examples are presented to demonstrate the dependence of the solution on the crack position.

Fatigue crack growth in fibre metal laminates with multiple open holes

ABSTRACTThe fatigue crack growth behaviour of hybrid S2‐glass reinforced aluminium laminates (Glare) with multiple open holes was investigated experimentally and analytically. It was observed that the presence of multiple‐site fatigue damage would increase crack growth rates in the metal layers as two propagating cracks converged. An analytical crack growth model was established for predicting crack growth rates based on empirical Paris equation. The effective stress intensity factor at crack tips is a function of mode I far‐field stress intensity factor, crack opening stress intensity factor and effective non‐dimensional stress intensity factor that incorporated the crack‐bridging effect in fibre metal laminates. The predicted results under different applied stress can capture the trend of averaged crack growth rates in experiments, although deviation exists in the predictions.

A mechanics based study of crack closure measurement techniques under constant amplitude loading

An elastic–plastic finite element model was used to simulate a growing fatigue crack in a middle-crack tension specimen made of an aluminum alloy. The finite element analysis provided the load–displacement curve at various locations as is commonly done in experimental work, and the crack opening stress intensity factor (Kop) was determined with ASTM standard methods, Elber’s method, and the Adjusted Compliance Ratio (ACR) method. The performance of ACR was compared against the established standard methods. Measurement location effects on Kop and ACR were investigated. ASTM (2% offset) and ACR methods gave values that were dependent upon measurement location. Whereas, Elber’s method (0% offset) gave values that were independent of measurement location.

Effect of Cold Expansion on Crack Opening Displacement and Stress Intensity Factor

Two-dimensional (2D) finite element analyses have been carried out to study the crack opening displacement and stress intensity factor of a cracked centre-hole plate. With the different interference levels (2%, 4%, 6% and 8%) and acted by residual stress caused by cold expansion, the crack opening displacement, the stress intensity factor and J-integral around the crack tip is presented. With the different interference levels and acted by different applied loads , the crack opening displacement, the stress intensity and J-integral around the crack tip is also presented. The results of the 2D FEM analysis show, 1) with the different interference levels and acted by residual stress caused by cold expansion, the crack mouth is throughout closed and the middle part is open, but the opening displacement is constant; 2) under some applied loads, with the interference levels up, the stress intensity factor on the crack tip and J-integral, become weak gradually, then they keep constant values; 3) with the interference increases, the stress intensity factor and J-integral decreases. When the interference increases a certain value, the stress intensity factor and J-integral do not decrease and keep constant values.

Slice Synthesis Methodology を用いた埋没き裂の応力拡大係数及び弾性き裂開口変位算定手法について

Applicability of slice synthesis methodology with weight function to calculate stress intensity factor and crack opening displacement in elastic condition for three dimensional cracks is investigated. Although slice synthesis methodology has already proposed, quantitative investigations of the applicability seem to be insufficient.The authors make it clear the applicable limits to the embedded elliptical cracks by comparing conventional formula based on finite element analyses. It is confirmed that the ratio of crack depth to plate thickness or back surface affects the accuracy of elastic crack opening displacement and stress intensity factor by applying slice synthesis methodology.Besides, the authors suggest modified SSM which enables to evaluate the effect of back surface. And it is concluded that modified SSM enables to give stress intensity factor and crack opening displacement of embedded cracks in elastic condition with high accuracy.

Fatigue crack growth in hybrid boron/glass/aluminium fibre metal laminates

ABSTRACTThe crack growth behaviour of hybrid boron/glass/aluminium fibre metal laminates (FMLs) under constant‐amplitude fatigue loading was investigated. The hybrid FMLs consist of Al 2024‐T3 alloy as the metal layers and a mixture of boron fibres and glass fibres as the fibre layers. Two types of boron/glass/aluminium laminates were fabricated and tested. In the first type, the glass fibre/prepreg and the boron fibre/prepreg were used separately in the fibre layers, and in the second type, the boron fibres and the glass fibres were uniformly mingled together to form a hybrid boron fibre/glass fibre prepreg.An analytical model was also proposed to predict the fatigue crack growth behaviour of hybrid boron/glass/aluminium FMLs. The effective stress intensity factor at a crack tip was formulated as a function of the remote stress intensity factor, crack opening stress intensity factor, and the bridging stress intensity factor. The bridging stress acting on the delamination boundary along the crack length was also calculated based on the crack opening relations. Then, the empirical Paris‐type fatigue crack growth law was used for predicting the crack growth rates. A good correlation between the predicted and experimental crack growth rates has been obtained.

A Model for Determining Crack Opening Stress Intensity Factor Ratio under Tri-Axial Stress State

When studying 3D fatigue crack growth behaviors of materials, to determine the crack opening stress intensity factor ratio is the key issue. Elastic-plastic Fracture Mechanics theory and physical mechanism of cracks’ closure phenomena caused by plastic deformation are employed here. A model for determining the crack opening stress intensity factor ratio under tri-axial stress state is presented. The comparison of the present model with available data and models shows quite good agreement.

Effect of oxide and nitride films on strength of silicon: A study using controlled small-scale flaws

Strength properties of silicon substrates containing dense oxide and nitride surface films are investigated using nanoindentations to introduce small flaws of predetermined scale. The indentation flaws provide favored sites for failure in subsequent flexure loading, even in the subthreshold region for indentations without visible corner cracking, confirming that microflaws generated within the indentation zone act as effective crack sources in the substrate. Deposition of the oxide films increases the strength while the nitride films diminish it at any given indentation load. The strength shifts are attributed primarily to the presence of residual compressive stress in the oxide, tensile stress in the nitride. A fracture mechanics formulation based on a previous analysis for monolithic substrates is here adapted to allow for a superposed crack closing or opening stress-intensity factor term associated with the residual stresses. Allowance is also made in the mechanics for the influence of the film on effective hardness and modulus of the substrate. The formulation accounts for the basic strength shifts and enables evaluation of the magnitude of the residual stresses. The results quantify the susceptibility of basic device materials to damage from small-scale contacts and impacts.

Ultrasonic NDE of Closed Cracks-Sizing and Evaluation of Crack Opening Stress Intensity Factor under a No Load Condition

Ultrasonic NDE of Closed Cracks-Sizing and Evaluation of Crack Opening Stress Intensity Factor under a No Load Condition

Ultrasonic Measurement of the Crack Depth and the Crack Opening Stress Intensity Factor Under a No Load Condition

This paper describes a new methodology for evaluating the crack depth and the crack opening stress intensity factor of small closed cracks using an ultrasonic technique. Surface connected back-wall cracks of depth ranging from 0.4 to 4.0 mm in steel specimens are considered. The crack corner echo amplitude of an ultrasonic shear wave, SW, beam of 50° incidence in material is used. First, the ultrasonic echo response of an open crack is determined as a function of crack depth. Next, based on changing the crack closure stress, an empirical relation between the crack closure stress and the crack-echo response is formulated. The crack depth and the crack closure stress of an unknown closed crack based on these relations are determined by inverse analysis of the ultrasonic response of the crack. From the evaluated crack depth and crack closure stress, the crack opening stress intensity factor is determined. The accuracy and reliability of this new nondestructive evaluation (NDE) method is verified by comparing the evaluated crack depth with the actual one. The latter is measured on the fractured surface obtained after carrying out ultrasonic testing. The ultrasonic method developed is proved to be a powerful tool for quantitative and nondestructive evaluation of the crack depth as well as the crack closure stress.

A comparative evaluation of Kop determination and ΔKeff estimation methods

Methods for determination of the crack opening stress intensity factor (Kop) and for estimation of the effective stress intensity factor range (ΔKeff) are evaluated for crack growth test data of aluminum alloys. Three methods of determining Kop, visual measurement, ASTM offset compliance method, and the neural network method proposed by Kang and Song, and three methods of estimating ΔKeff, conventional, the 2/P10 and 2/PI methods proposed by Donald and Paris, are compared in a quantitative manner by using evaluation criteria. For all Kop determination methods discussed, the 2/PI method of estimating ΔKeff provides good results. The neural network method of determining Kop provides good correlation of crack growth data. It is recommended to use 2/PI estimation with the neural Kop determination method. The ASTM offset method used in conjunction with 2/PI estimation shows a possibility of successful application. It is desired to improve the ASTM method.