Applied Stress Intensity Factor Research Articles

Application of Mechanoluminescence for the Dynamic Visualization of an Alumina Fracture

The propagation of cracks was quantitatively analyzed in Al2O3 ceramic using the mechanoluminescence (ML) of SrAl2O4:Eu,Dy. The bridging zones behind the crack tip were clearly detected in the crack path of Al2O3 within a realistic time frame. The magnitudes and shapes of the bridging stress distributions changed with the advancing cracks. They continued to change with the change in the applied load even after the cessation of crack propagation. Effective toughening then commenced, and the applied stress intensity factors dramatically increased up to ∼50 MPa√m . The expected KTip values based on the instantaneous bridging stress distributions obtained from the ML observations deviated greatly from those obtained from the measurement using the conventional crack tip lengths; rather, they support the results obtained when bridging tips were used in the quasidynamic crack propagations.

Fatigue crack growth resistance of ECAPed ultrafine-grained copper

This work presents the experimental results of fatigue crack growth resistance of ultrafine-grained (UFG) copper. The UFG copper has a commercial purity level (99.90%) and an average grain size of 300 nm obtained by a 8-passes route Bc ECAP process. The fatigue propagation tests are conducted in air, at load ratios R = Kmin/Kmax varying from 0.1 to 0.7, on small Disk Shaped CT specimens. Both stage I and stage II regime of growth rate are explored. Results are partially in contrast with the few experimental data available in the technical literature, that are by the way about high purity UFG copper. In fact, the present material shows a relatively high fatigue crack resistance with respect to the unprocessed coarse-grained alloy, especially at high values of applied stress intensity factor ΔK. At higher R-ratio a smaller threshold intensity factor is found, together with a lower stage II fatigue crack growth rate. The explanation of such crack growth retardation is based on a diffuse branching mechanism observed especially at higher average ΔK.

Simulation and comparison of several crack closure assessment methodologies using three-dimensional finite element analysis

Plasticity induced fatigue crack closure simulations were performed using a three-dimensional finite element analysis of a single edge-cracked tension specimen under constant amplitude loading and load ratio R = 0. Four different methodologies were considered to assess fatigue crack closure: (a) a node displacement method monitoring the first and second nodes behind the crack tip, (b) a contact stress method, (c) the traditional compliance offset method, and (d) the adjusted compliance ratio (ACR) technique. The evolution of crack driving force was compared in terms of U = Δ K eff / Δ K , where Δ K eff and Δ K are the effective and applied stress intensity factor ranges, respectively. The node displacement method using the first node behind the crack tip and the contact stress method produced the lowest levels of U. Larger U levels were obtained from the node displacement method using the second node behind the crack tip followed by those from the compliance offset technique. The ACR methodology provided the highest U values for the range of applied loading considered in this study.

Fatigue crack growth behaviour and life prediction for 2324-T39 and 7050-T7451 aluminium alloys under truncated load spectra

This paper presents a study of crack growth behaviour in aluminium alloys 2324-T39 and 7050-T7451 subjected to flight-by-flight load spectra at different low-stress truncation levels. Crack branching was observed in the higher truncation levels for the 2324 and in all truncation levels for the 7050. Mode I crack growth life can be predicted for the 2324 alloy by the NASGRO equation and the Generalised Willenborg retardation model. However, quantitative prediction of the fatigue life of a significantly branched crack is still a problem. Material properties, test sample’s orientation and applied stress intensity factor range all play dominant roles in the fracture process.

An Efficient Way to Characterize the Fatigue Crack Growth Based on Numerical Analysis

The behavior of plasticity induced fatigue crack closure (PICC) in middle tension specimen was analyzed by the elastic-plastic finite element method. For the constant-K (CK) loading cases, the opening stress intensity factor are independent of crack length. The level of increases with the maximal applied stress intensity factor for given load ratio and increases with for fixed . The in plane strain state is much smaller than that in plane stress state. The results under CK loadings can be deduced to constant amplitude cyclic loading case during which the load ratio, maximal load level, crack length and specimen thickness are all the factors affecting the crack closure effect. The phenomena revealed in the analysis are beneficial in understanding the driving force mechanism of the fatigue crack growth.

Characterisation of the fatigue properties of cast irons used in the water industry and the effect on pipe strength and performance

As part of an on going programme to characterise the residual properties and understand the failure mechanisms of in-service grey cast iron water pipes, the fatigue crack propagation behaviour of grey cast iron samples has been studied. Specimens were sourced from three ex-service pipes. For each pipe the microstructure and composition were characterised and the fracture toughness was determined. The fatigue behaviour was investigated in terms of the crack growth rate (da/dN) as a function of the applied stress intensity factor range. Clear differences in the fatigue behaviour of the samples from different pipes were observed. The result from these investigations, which indicate that microstructural differences play a role in mechanical behaviour, will support the development of asset management tools for use in the water industry.

Quasi-dynamic visualization of crack propagation and bridging evolution in Si3N4 and SiC ceramics by mechano-luminescence

The propagations of macro-scale cracks were visualized in Si3N4 and SiC ceramics using a mechano-luminescence (ML) of SrAl2O4:Eu,Dy. The bridging zones behind the crack tip were also clearly detected in the crack path within realistic time frames. The ML made it possible to detect cracks propagating within a speed range of 200 m/s to 250 m/s, thereby realizing so-called quasi-dynamic R-curves. The magnitudes and shapes of the bridging stress distributions were found to change with the advancing cracks, continuing to change as the applied load changes, even after the cessation of crack propagation. The effective toughening then commenced and the applied stress intensity factors increased dramatically up to ∼120 MPa√m in Si3N4 and 150 MPa√m in SiC. The KTip values expected on the basis of the instantaneous bridging stress distributions obtained from ML observations deviated greatly from those measured using the conventional crack tip lengths; rather, the values support the results obtained by using bridging tips in quasi-dynamic crack propagations.

Investigation of Hydrogen Assisted Cracking in High and Low Strength Steels

Hydrogen assisted cracking (HAC) has been investigated in a high strength 4140 steel and a low strength AISI-SAE grade 1022 steel (supplied by Amoco, Naperville, IL—now BP), charged at −50 mA/cm2 in 1N H2SO4+25 mg/lAs2O3 and tested under three-point-bend decreasing load. The HAC growth rate for the 1022 steel (1.4×10−7 cm/s) was found to be approximately two orders of magnitude slower than that of the 4140 steel (3.3×10−5 cm/s), while the threshold stress intensity factor for the 1022 steel (37.0±1.0 MPa m1/2) was significantly higher than that of the 4140 steel (7.0±0.5 MPa m1/2). This research develops an analytical model, based on the hypothesis that hydrogen both reduces crack resistance (R) and increases crack driving force (G), to explain HAC in 4140 and 1022 steels. The model predicts the hydrogen concentration required to initiate HAC as a function of the applied stress intensity factor and yield strength of the steel. Hydrogen-induced reduction in R was found to dominate HAC in the 4140 steel, while hydrogen-induced reduction in R was combined with an increase in G for HAC cracking of the 1022 steel.

Interaction of Hydrogen Transport and Material Elastoplasticity in Pipeline Steels

The technology of large scale hydrogen transmission from central production facilities to refueling stations and stationary power sites is at present undeveloped. Among the problems that confront the implementation of this technology is the deleterious effect of hydrogen on structural material properties, in particular, at gas pressures of the order of 15MPa, which are the suggested magnitudes by economic studies for efficient transport. In order to understand the hydrogen embrittlement conditions of the pipeline materials, we simulate hydrogen diffusion through the surfaces of an axial crack on the internal wall of a vessel coupled with material deformation under plane strain small scale yielding conditions. The calculation of the hydrogen accumulation ahead of the crack tip accounts for stress-driven transient diffusion of hydrogen and trapping at microstructural defects whose density evolves dynamically with deformation. The results are analyzed to correlate for a given material system the time after which hydrogen transport takes place under steady state conditions with the level of load in terms of the applied stress intensity factor at the crack tip and the size of the domain used for the simulation of the diffusion.

Effect of crack depth on fatigue crack growth rates for a C–Mn pipeline steel in a sour environment

Setting conditions for the avoidance of in-service crack growth in aggressive corroding environments has long been a major challenge owing to the number of variables that have a significant effect on material behaviour. The fatigue behaviour of API 5L X65 pipeline steel parent material tested in a sour environment has been investigated. Fatigue crack growth rate (FCGR) tests have been performed to evaluate the influence of crack depth on crack growth rate (d a/d N), over the range 2–10 mm. The results obtained showed crack growth rates for deep flaws to be a factor of 5–30 higher in the sour environment than in air, dependent on the applied stress intensity factor range (Δ K). Shallow flaws have been shown to grow up to an order of magnitude faster than deep flaws in a sour environment at the same value of Δ K. The results highlight a potential non-conservatism associated with using deep-crack data to predict the behaviour of shallow flaws. The observed behaviour is attributed to the uptake of hydrogen at specimen surfaces exposed to the sour environment.

The Behavior of Shallow Cracks in a Pipeline Steel Operating in a Sour Environment

Setting conditions for the avoidance of in-service crack growth in aggressive corroding environments has long been a major challenge due to the number of variables that have a significant effect on material behavior. One area where both experimental data and a validated assessment methodology are lacking is the behavior of shallow cracks. This paper describes the early results of an ongoing research program aimed at addressing the shortfall in experimental data to characterize material behavior in the shallow-crack regime, with the long-term aim of improving the understanding and assessment of the early stages of environment assisted cracking. There is an industry need for a better understanding of material behavior under these conditions and for the development of a more robust assessment methodology. API 5L X65 pipeline steel parent material was tested in a sour environment with initial flaw sizes in the range 1–2 mm. Fatigue crack growth rate tests have been performed to investigate the influence of crack depth on crack growth rate (da/dN). Initial results suggest that crack growth rates for deep flaws can increase by a factor of 5–100 compared with air depending on the applied stress intensity factor range (ΔK). Shallow cracks have been shown to grow up to 130 times faster in a sour environment than in air and up to an order of magnitude faster than deep cracks in a sour environment at the same value of ΔK. Constant load tests have also been performed to investigate the influence of crack depth on the threshold stress intensity factor for stress corrosion cracking (KISCC). Preliminary results suggest that in this case there is no crack depth dependence in the range of flaw sizes tested. While further experimental work is required, the results obtained to date highlight the potential nonconservatism associated with extrapolating deep-crack data. Guidance is therefore provided on how to generate appropriate experimental data to ensure that subsequent fitness for service assessments are conservative.

Near tip stress intensity factor for an edge-crack in a Pb(Zr xTi 1−x)O 3 thin film with 90° domain switching under a continuous laser irradiation

The near tip stress intensity factor K I tip for an edge-crack in a Pb(Zr x Ti 1− x )O 3 thin film was investigated by superposition of the applied stress intensity factor K I app under a continuous laser irradiation and the shielding stress intensity factor Δ K I for 90° domain switching. Both K I app and Δ K I were solved by the weight function method, and switching toughening was analyzed based on the small scale domain switching theory. Results show that K I tip of the edge-crack in the thin film is significantly affected by the initial poling angle, and the edge-crack tip is toughened by the domain switching area with the increase of the initial poling angle. The methodology can predict the fracture toughening of Pb(Zr x Ti 1− x )O 3 thin films quantitatively.

Fatigue crack growth prediction in concrete slabs

A new method to predict crack growth and fatigue life of concrete slabs is presented based on similar models for 2-D specimens. Four large-scale concrete slabs on ground subjected to three different stress ranges have been tested to fatigue failure. Geometric correction factors to calculate the effective crack length and stress intensity factor from the experimental fatigue compliance are derived based on 3-D finite element modeling. Crack length versus the number of cycles curves are constructed and fitted to a modified logistic function, which enables for the calculation of the crack propagation rates and critical crack lengths from the first and second derivative of the logistic function. Fatigue crack growth is separated into a decelerating and accelerating crack growth functions based on the initial crack length and the applied stress intensity factor, respectively. The proposed method is able to predict the fatigue life of the tested slabs and the fatigue resistance of several independent slabs cast with the same geometry and material. The analysis of the tested slabs shows that load pulses with higher minimum loads generated more fatigue damage as indicated by greater crack growth rates. The principles of this slab fatigue crack growth procedure can now be extended to estimate the remaining life in uncracked or partially-cracked concrete slabs on ground.

Application of Paris’s law to thermal cycling-induced failure in semiconductor device patterns

The present work provides a semi-empirical model to show that the growth rate of thermal displacement-induced cracks in semiconductor devices depends on pattern thickness. Paris’s law is adopted to characterize the growth rate of cracks during thermal-cycling. The crack propagation rate is estimated from the semi-empirical relation (dc/dN)v=C(ΔK)n, where ΔK indicates the range of an applied stress intensity factor, and C is a scaling constant. The applied stress intensity factor is related to the initial crack length as ΔK=YΔσ(πc)1/2, where σ represents the thermal displacement-induced normal stress, c describes the pre-existing crack length, and Y is a geometrical factor. The resulting crack growth rate can be expressed as a function of device pattern thickness: dc/dN∞(1/t)m, where t describes the pattern thickness, and m is another constant. The present semi-empirical results showing the relationship between the crack growth rate and pattern thickness indicate that if a semiconductor device pattern becomes thinner by 68%, its susceptibility to thermal cycling-induced damage will be enhanced by 76%.

Hydrogen-Assisted Fatigue Lifetime Characteristic of AF1410 Steel

Results of hydrogen-assisted fatigue lifetime testing indicated a substantial but gradual increment in crack growth rate as a function of increasing hydrogen content. Hydrogen was introduced into both sides of the specimen simultaneously via galvanostatic charging. Extensive scanning electron microscope fractographic analyses revealed a clear shift in the modes of failure and changes in fracture surface morphology as a function of increasing hydrogen content. A methodology is outlined that can be used to predict fracture surface features as a function of applied stress intensity factor. A convenient deterministic model is proposed that seems to reasonably accurately capture the crack growth rate behavior under strain controlled testing conditions. In addition, successful application of acoustic emission technique to classify various cracking stages in full spectrum testing was performed on hydrogen charged samples.

Seamless interpretation of the strength and fatigue lifetime of polycrystalline silicon thin films

Thin film polycrystalline silicon was subjected to strength and fatigue tests. A model is proposed which correlates the strength of this material under monotonic loading and its fatigue lifetime under cyclic loading in a seamless manner on a three-dimensional surface. This surface describes the cumulative failure probability as a function of both applied stress and fatigue cycles. In the first step, the statistical distribution of equivalent initial crack lengths corresponding to the defects introduced into the specimens in the etching process is deduced from the strength distribution of the specimens fabricated on a silicon wafer. From this distribution, the fatigue lifetime under different stress levels is estimated by applying the well-known Paris law of fatigue crack extension. The Paris law exponent determining the crack extension behavior as a function of the applied stress intensity factor was obtained by solving an inverse problem by fitting the estimated lifetime to the experimental results.

Analysis of temperature distribution near the crack tip under constant amplitude loading

ABSTRACTAn analytical/numerical method has been developed to find the temperature rise near the crack tip under fatigue loading. The cyclic plastic zone ahead of the crack tip is assumed to be the shape of the source of heat generation and some fraction of plastic work done in cyclic plastic zone as heat generation. Plastic work during fatigue load was found by obtaining stress and strain distribution within the plastic zone by Hutchinson, Rice and Rosengren (HRR) crack tip singularity fields applied to small scale yielding on the cyclic stress strain curve. A two‐dimensional conduction heat transfer equation, in moving co‐ordinates, was used to obtain temperature distribution around the crack tip. Temperature rise was found to be a function of frequency of loading, applied stress intensity factor and thermal properties of the material. A power–law relation was found between the rise in temperature at a fixed point near the crack tip and range of stress intensity factor.

Quasi-Dynamic Visualization of Crack Propagation and Wake Evolution in Y-TZP Ceramic by Mechano-Luminescence

The propagation of a macro-scale crack was visualized in yittria-tettragonal zirconia polycrystal (Y-TZP) ceramics using a mechano-luminescence (ML) of SrAl2O4:Eu, Dy. The transformation zone around the crack was also clearly detected in both the crack front and side areas of the Y-TZP in a realistic time frame. The ML made it possible to precisely detect a relatively fast crack propagating in the speed range from 20 m/s to 140 m/s, thereby realizing so-called quasi-dynamic R-curve. Effective toughening then commenced and the applied stress intensity factor increased to 20 MPa \(\sqrt m \). The ho values obtained from the ML observation deviated slightly from those predicted by the Evans-McMeeking model, and support Marshall's simple power law model of quasi-static crack propagation.

Two-Dimensional Mapping of Crack-Face Bridging Stresses in Alumina Using Synchrotron Micro X-Ray Beam

In order to understand an effect of crack-face bridging stress field of alumina ceramics on its fracture toughness, local residual stress distribution due to crack face grain bridging behind the crack tip was measured using synchrotron x-ray beam at SPring-8 in Japan. The SEPB (Single Edge Precracked Beam) specimens of two types of polycrystalline Al2O3 were used for stress measurement; one was pressureless sintered Al2O3 (AL1) and the other was hot-press sintered Al2O3 (TAL). Pop-in precracks were introduced by bridge-indentation method. Before residual stress mapping, the SEPB specimens were unloaded from a constant applied load to zero using four points bending device. Two-dimensional residual stress field was mapped by scanning a micro X-ray beam of 50×50 μm2 with the scanning interval of 12.5 or 25 μm. As a result, in the case of AL1 having conventional fracture toughness and strength, the compressive residual stresses due to crack-face bridging were only observed in the close vicinity of crack tip. On the other hand, in the case of TAL having higher fracture toughness and strength, the compressive residual stresses were widely distributed behind the crack tip. Larger compressive stress was locally generated along the crack path at interlocked grains. The compressive bridging stresses distributed behind the crack tip were found to enlarge with a decrease in the crack opening displacement against a constant applied stress intensity factor, Kapp. It was concluded that the difference in residual stress fields behind crack tip was attributed to the differences in its microstructure and microcrack propagation behavior, such as deflections and interlocked grains.

Advances in the characterisation of domain switching in ferroelectric ceramics

In ferroelectric materials, extrinsic contributions such as domain wall vibrations, domain switching, and interphase boundary motion contribute to fatigue and aging, nonlinearity, and hysteresis in the piezoelectric response. It also affects the deformation behaviour, and influences the fracture mechanics. The most prevalent extrinsic contribution is ferroelectric/ferroelastic domain switching. Recent advances in diffraction techniques offer many opportunities for novel characterisation of domain switching and its influence on macroscopic properties. This paper presents the results of two such techniques which have been used to characterise extrinsic mechanisms in situ in a soft lead zirconate titanate (PZT) ceramic. In the first example, stroboscopic, time-resolved neutron diffraction is used to represent the ferroelectric/ferroelastic domain switching during a single cycle of a 1 kHz unipolar electric field with a magnitude of half of the coercive field. In the second example, highenergy X-ray microdiffraction is used to measure the spatial distribution of ferroelastic domain switching around a crack tip in transmission geometry under an applied stress intensity factor of KI=0.71 MPa•m. Introduction Ferroelectric ceramics are used in a wide variety of electromechanical devices including sonar, ultrasound, sensors and actuators, non-volatile memories, and micro-electromechanical systems (MEMS). In ferroelectric ceramics, changes in the ferroelectric/ferroelastic domain structures can affect the measurable bulk properties in an advantageous or disadvantageous manner. For example, domain wall motion during dynamic actuation increases the electric-field-induced strain but also contributes to nonlinearity, hysteresis, and fatigue [1]. Domain switching also contributes to fracture toughness enhancement in ferroelectric/ferroelastic ceramics, which is expressed both as an increase in the initiation toughness as well as a rising R-curve behaviour. It is therefore important to characterise such mechanisms in order to reveal their exact role in these and other cases. 442 European Powder Diffraction Conference, EPDIC 10 A schematic diagram of the process of domain switching is shown in figure 1. As shown, the application of an electric field or stress along particular directions of a bulk ceramic sample leads to a change in the volume fraction of domain types present within individual grains. Domain structures have been characterised using diffraction for decades [2]. The essence of such measurements is the relationship between the diffracted intensity of particular Bragg peaks and the volume fraction of ferroelectric/ferroelastic domains present within the sample. The simplest representation (i.e., for a sample with tetragonal symmetry) of the changes in the diffraction pattern is shown in figure 1(c).