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.

Small crack propagation and closure behaviours and mechanisms in a powder metallurgy superalloy at high temperature in air

To investigate small crack propagation and closure mechanisms in a powder metallurgy superalloy FGH4096 at room and high (600 °C) temperatures in air, meso-scale digital image correlation (DIC) was applied. CODs of small cracks did not increase monotonically as cracks propagated, which was related to the potential role of subsurface crack morphology. Roughness induced crack closure was found to be the leading mechanism at times. Oxidation induced crack closure was negligible at 600 °C, resulting from the oxidation-resistance of FGH4096. Crack opening stress intensity factors were generally higher at 600 °C, which ascribed to the higher level of plasticity induced crack closure.

In situ synchrotron radiation µCT indentation of cortical bone: Anisotropic crack propagation, local deformation, and fracture

The development of treatment strategies for skeletal diseases relies on the understanding of bone mechanical properties in relation to its structure at different length scales. At the microscale, indention techniques can be used to evaluate the elastic, plastic, and fracture behaviour of bone tissue. Here, we combined in situ high-resolution SRµCT indentation testing and digital volume correlation to elucidate the anisotropic crack propagation, deformation, and fracture of ovine cortical bone under Berkovich and spherical tips. Independently of the indenter type we observed significant dependence of the crack development due to the anisotropy ahead of the tip, with lower strains and smaller crack systems developing in samples indented in the transverse material direction, where the fibrillar bone ultrastructure is largely aligned perpendicular to the indentation direction. Such alignment allows to accommodate the strain energy, inhibiting crack propagation. Higher tensile hoop strains generally correlated with regions that display significant cracking radial to the indenter, indicating a predominant Mode I fracture. This was confirmed by the three-dimensional analysis of crack opening displacements and stress intensity factors along the crack front obtained for the first time from full displacement fields in bone tissue. The X-ray beam significantly influenced the relaxation behaviour independent of the tip. Raman analyses did not show significant changes in specimen composition after irradiation compared to non-irradiated tissue, suggesting an embrittlement process that may be linked to damage of the non-fibrillar organic matrix. This study highlights the importance of three-dimensional investigation of bone deformation and fracture behaviour to explore the mechanisms of bone failure in relation to structural changes due to ageing or disease. Statement of significanceCharacterising the three-dimensional deformation and fracture behaviour of bone remains essential to decipher the interplay between structure, function, and composition with the aim to improve fracture prevention strategies. The experimental methodology presented here, combining high-resolution imaging, indentation testing and digital volume correlation, allows us to quantify the local deformation, crack propagation, and fracture modes of cortical bone tissue. Our results highlight the anisotropic behaviour of osteonal bone and the complex crack propagation patterns and fracture modes initiating by the intricate stress states beneath the indenter tip. This is of wide interest not only for the understanding of bone fracture but also to understand other architectured (bio)structures providing an effective way to quantify their toughening mechanisms in relation to their main mechanical function.

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.

Estimation of Impact Toughness Transition Temperatures of As-Quenched Steels

High strength and sufficient toughness are key requirements for modern high-performance structural steels. In an attempt to develop a suitable estimation of impact toughness transition temperatures for as-quenched steels, we investigated the determiners of low-temperature toughness with a group of thermomechanically rolled direct-quenched steels with varying martensite contents. These were produced by altering chemical composition, finish rolling temperature and reduction below the non-recrystallization temperature, i.e. austenite pancaking, and characterised in terms of microstructural constituents, grain size distributions, texture and fractography. Provided the finish rolling temperature is high enough to avoid the formation of granular bainite on subsequent cooling, high levels of austenite pancaking yield the best combinations of low-temperature toughness and strength by effectively refining the size of the coarsest grains and randomizing the texture. While absolutely no direct correlation is found within as-quenched steels between the impact toughness transition temperatures and yield strength alone, T28J and T50 do closely follow a dynamic reference toughness, i.e. the opening stress intensity factor defined by yield strength and the size of the coarsest grains in the effective grain size distribution. This parameter reflects the transition temperatures – the lower the temperature, the lower the reference toughness needed to cause a local brittle fracture. Finally, we show that the impact toughness transition temperatures T28J and T50 of as-quenched steels can be accurately estimated, irrespective of the test specimen orientation, by utilizing just the dynamic reference toughness and the fraction of {100} cleavage planes within ± 15° of the specimen notch plane.

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.

Measurement of opening displacement and stress intensity factor of two branches of bifurcated notch by Moiré interferometry

Static experiments on dynamic crack branching are carried out, in which Y-shaped notches in plate specimens are regarded as rapidly bifurcating cracks. Moiré interfrometry is applied to measure crack opening displacement, COD, of two branch notches as well as the mother notch of the Y-shaped notch. Stress intensity factor of the branch notches are calculated through the formula for COD of linear elastic fracture mechanics. From the measurement results, it is clarified that how far the singular stress field is developed around the branch crack tip.

High-R low growth rate fatigue crack propagation at elevated temperatures

While fatigue cracking is widely considered as the primary cracking mode under cyclic loading conditions, this is not the case for high-R (Kmin/Kmax) low growth rate fatigue crack propagation at elevated temperatures. Creep cracks can sometimes be observed in such situations when the stress intensity factor range ΔK is around the fatigue crack growth threshold stress intensity factor ΔKth. A Time Dependent Failure Assessment Diagram (TDFAD) has been adopted in this study for predicting creep cracking in high-R cyclic loading conditions at elevated temperatures. In addition, attention is also paid to oxide-induced crack closure which is greatly influential at high temperatures. Three power plant steels with different chromium contents, namely 1%Cr, 9%Cr and 18%Cr steels, have been investigated at temperatures between 550°C and 650 °C. The experiments were performed by reducing ΔK continuously to ΔKth. Good accordance has been found between fracture surface observations and the TDFAD approach predictions of creep crack initiation. Apart from creep cracking, high-R ΔKth values have also been found to be influenced by oxide-induced crack closure at elevated temperatures. The enhancement is studied through the relationship between the crack tip opening displacement and stress intensity factor.

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.

Configurational fracture toughness from the perfectly plastic field ahead of the tip of a sharp V-notch under longitudinal shear

Abstract To be considered is an infinite elastic-perfectly plastic material with a sharp V-notch under longitudinal shear, and the closed-form solution of K I I I N -dominant field is presented for the general case of elastic–plastic boundary in small-scale yielding. The equivalent identity of the physical parameter S W , notch tip opening displacement (NTOD) and elastic energy release rate is established. The equivalent identity includes a characteristic length, which depends on the critical perfectly plastic field sizes, tip opening displacements and stress intensity factors of both sharp V-notch and crack.

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.

Numerical study of contact forces for crack closure analysis

Plasticity induced crack closure (PICC) has been widely studied using numerical models. Different numerical parameters can be considered to quantify the opening level, namely one based on the analysis of contact stresses at minimum load. A modified version of this parameter is proposed here, based on nodal contact forces instead of contact stresses. The predictions were found to be similar to those obtained from the contact status of 2nd node behind crack tip. The PICCcontact parameter was also found to be very consistent and adequate for parametric studies of the influence of different physical parameters. The contributions to the opening stress intensity factor of different points along crack flank were found to strongly decrease with distance to crack tip. The cumulative Kopen between the crack tip and a distance of 0.1mm was found to vary from 30% to 100%, increasing with stress ratio, R. Finally, a K solution was developed for punctual forces applied on crack flank and compared with a literature solution for infinite plates. A good agreement was found for plane strain state but significant differences of about 10% were found for plane stress state.

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.

313 平板試験片中の分岐切欠の開口変位と応力拡大係数の測定(OS3.計算力学に貢献する実験的アプローチ(4),OS・一般セッション講演)

313 平板試験片中の分岐切欠の開口変位と応力拡大係数の測定(OS3.計算力学に貢献する実験的アプローチ(4),OS・一般セッション講演)

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.

Experimental Investigation of Static Interfacial Fracture in Orthotropic Polymer Composite Bimaterials Using Photoelasticity

The effects of static Mode I (opening mode) loading on orthotropic-orthotropic bimaterial interface cracks have been investigated using the experimental technique of transmission photoelasticity. For successful implementation of this experimental technique transparent and birefringent glass fiber reinforced polyester composite materials were developed, enabling the direct observation and recording of photoelastic fringes in the vicinity of the interface crack in the orthotropic bimaterial. It is our belief that this is the first of such experimental investigation. Opening and shearing mode stress-intensity factors and the strain energy release rates have been calculated for various combinations of the bimaterial halves. Results have been verified by mathematically regenerating the observed isochromatic fringe patterns. This study has made it feasible to investigate interfacial fracture in orthotropic-orthotropic bimaterials and orthotropic-isotropic bimaterials using photoelasticity.