Applied Stress Intensity Factor Research Articles

Fatigue crack growth behavior in an aluminum alloy Al–Mg–0.3Sc produced by wire based directed energy deposition process

AbstractAdditive manufacturing (AM) of Al–Mg–Sc alloys has received considerable interest from the aerospace industry owing to their high specific strength and suitability for AM processes. This study has investigated the fatigue crack growth behavior in an Al–Mg–0.3Sc alloy made by wire and arc additive manufacturing. Tests were conducted with two different crack orientations at cyclic load ratios of 0.1 and 0.5. At the lower load ratio, the horizontal crack showed a faster growth rate owing to the smaller grains and coarser second‐phase particles that the crack tip had encountered when it propagated along the material build direction. The anisotropy in crack growth rate was mainly caused by the grain size effect. When the applied stress intensity factor range exceeded the value of 10 MPa m1/2, an isotropic crack growth rate between the two crack orientations was measured. This is due to the microstructural influence being overcome by the governing parameter of fracture mechanics. At the higher load ratio of 0.5, crack growth rate is isotropic, and the threshold stress intensity factor range was much lower than that tested under load ratio 0.1. Finally, the modified Hartman–Schijve equation has been successfully employed to represent the crack growth rates in all three regions.

In situ measurement of plasticity accompanying hydrogen induced cracking in a polycrystalline AlZnMg alloy

Hydrogen induced single crack propagation is studied in an embrittled aluminum alloy. Hydrogen is introduced into the system by electrochemical reactions in an acidic aqueous medium. After hydrogen charging, tensile tests are performed in air, on notched samples, with a microtensile machine under an optical microscope. A high magnification of × 2000 is used to follow the single crack initiation and propagation. Digital Image Correlation gives the displacement field on the surface with a spatial resolution of approximately 1 μm. It enables the determination of the position of the crack tip and the local velocity at a sub-grain scale. The von Mises strain is calculated and provides a precise measure of the local plastic field that accompanies crack propagation. In addition to the primary plasticity which is emitted from the crack tip or its immediate neighborhood in the form of two intense slip bands, a secondary plastic zone that spreads over several microns ahead of the tip is sytematically found. The characteristics of the plastic zone are measured, together with the velocity and the applied stress intensity factor. In addition, different fracture mechanisms are found on the fracture surface. In particular there are transitions in the fracture mode from intergranular smooth to transgranular parallel to the grain boundary plane. The local fracture mechanisms, in the vicinity of the surface, are linked to the local velocities and plastic deformations. Surprisingly no strong velocity/plasticity correlations are found while the velocities are scattered over a wide range, which is interpreted as a strong polycrystalline effect.

External work rate and dissipation during crack growth in a viscoelastic material

We analyse crack growth in viscoelastic material by use of a correspondence principle that allows elasticity solutions for traction boundary value problems in plane strain to be converted to viscoelasticity solutions. We consider an edge cracked strip in tension and assess 2 limiting cases of the geometry. In one case, we allow the component to become a geometry that is an infinite body with a semi-infinite crack, or a large body with a long crack. In the other case, we consider a component of finite width with a remaining ligament that is very small compared to the width of the strip. In these geometries we compute the work done by the applied load per unit area of crack growth and a measure that we consider to represent the dissipation per unit area of crack growth. We do so for a standard viscoelastic material with a single retardation time and for a Maxwell material with a single viscous element. In the latter case, our computation of the dissipation per unit area of crack growth is definite. We consider various aspects of the behaviour of the work done per unit area of viscoelastic crack propagation and the dissipation per unit area of crack advance. These include the extent to which these parameters depend on the rate of crack propagation, the extent to which these parameters are independent or dependant on component geometry, and the extent to which these parameters exhibit transient behaviour during crack growth at a steady rate under a constant applied stress intensity factor. A motivation is the common insight that a parameter is probably more useful as a measure of material behaviour if it is relatively insensitive to component geometry and if, during steady state response in terms of crack growth rate and applied stress intensity factor, the parameter also exhibits a steady state. We find outcomes that vary quite considerably depending on the case that we consider. We provide our results for the reader to use when considering the various models that have been proposed in the literature for viscoelastic crack propagation. We observe, however, that crack propagation models based on a rupture process zone interacting with material viscoelasticity are much simpler to implement in bodies with finite geometry than those based on quantifying the dissipation per unit area of crack growth. In this regard, we conclude that viscoelastic crack growth models that are based on quantifying the dissipation per unit area of crack growth are, by themselves, not a promising concept as we see no obvious way to extend them to provide unique results in components having a finite geometry. We further conclude that a reliable viscoelastic crack growth model should include a crack tip rupture process zone at the crack tip.

Equivalent crack growth model for correlation and prediction of fatigue crack growth under different stress ratios

An equivalent crack growth model that accounts for the effect of stress ratio is proposed for the correlation and prediction of crack growth under different stress ratios. A previously proposed equivalent driving force ΔKeq that yields the same growth rate (da/dN)R as combined applied stress intensity factor range ΔKR and stress ratio, R is modified, and its corresponding equivalent growth rate (da/dN)eq is derived. This yields an equivalent crack growth model of (da/dN)eq versus ΔKeq capable of collapsing data of different R-ratios unto a common curve. The model was validated with excellent agreement between the model and published data.

Effect of direct metal laser sintering build parameters on defects and ultrasonic fatigue performance of additively manufactured AlSi10Mg

AbstractThe high cycle fatigue behaviour of additively manufactured AlSi10Mg is evaluated using ultrasonic fatigue as a means to accelerate fatigue testing. Build parameters during the additive manufacturing process are varied, and their effect on defect type, size, and distribution is determined. These defects are further found to influence fatigue behaviour, which is analysed using a Murakami model. Finally, the ultrasonic fatigue test results are interpreted in the context of applied stress intensity factor and an optimized fatigue limit fit. Two different kinds of physical behaviour, representing Murakami dependence and a long crack regime, are found to better correlate the fatigue life behaviour than the Murakami model alone. With this information, we can tailor defect size, type and distribution, within the context of an optimized processing route, to obtain necessary high cycle fatigue properties.

Crack velocity measurements through continuous stiffness monitoring of cyclically loaded notched micro-beams of thin graded Pt–Ni-Al bond coats

The notched clamped beam geometry has proven to be a useful geometry in evaluating local mechanical properties like fracture and fatigue of thin graded platinum nickel aluminide bond coats. Cyclic fatigue tests performed on different zones of these coatings have shown that the structural stiffness of the beam is a useful parameter in estimating localized damage in front of the notch root, which can arise either due to cyclic softening from micro-crack nucleation and propagation in the crack wake or due to work hardening in the plastic zone surrounding the crack tip. This paper describes the use of finite element method-based analysis to quantify different geometrical factors that affect cyclic stiffness data in the micro-beam bending methodology employed in the present study. Variations in the stiffness values measured at the beginning of each loading cycle can occur due to factors such as the effect of loading line offsets (both lateral and angular) and the notch length to width ratio (a/W). Using this analysis, it was found out that lateral offsets affect the starting stiffness of the beam more profoundly compared to angular offsets. It has also been shown that for beams having lengths of $$\sim $$ $$80-90\,\upmu \mathrm{m}$$ and an a/W ratio of $$\sim $$ 0.3–0.4, the starting stiffness variations can be kept under 10%. The stiffness can also be used to estimate crack velocities (da/dN) in an approximate sense using the finite element method. Detailed finite element analysis has been performed to estimate through thickness crack lengths from cyclic stiffness drops. The applied stress intensity factor for real crack geometries observed during testing have been computed using the extended finite element methodology and da/dN vs $$\Delta $$ K plots have been generated for two cases. This paper highlights the importance of using computational analysis in optimizing and augmenting micro-scale fatigue testing data and thus providing for a richer dataset through such analysis.

On the fatigue crack growth behavior of Ti–10V–2Fe–3Al in gaseous hydrogen

The fatigue crack growth behavior of Ti–10V–2Fe–3Al in gaseous hydrogen (H2) was assessed through comparative experiments conducted in laboratory air and 8.3 MPa H2. The measured fatigue crack growth rate (da/dN) versus applied stress intensity factor range (ΔK) relationships and observed fracture morphologies for laboratory air and H2 were comparable up to ΔK ≈ 6.9 MPa√m, when tested at a load ratio of 0.1 and frequency of 10 Hz. At higher ΔK values, significant crack deflection and subsequent catastrophic failure occurred in the specimen tested in H2. This degradation was not observed in a specimen pre-exposed to 8.3 MPa H2 for 96 h and then immediately tested in laboratory air. X-ray diffraction of the failed H2-tested specimen revealed that the material remnants were predominantly composed of TiH2, suggesting that hydride formation was the catalyst for catastrophic failure in H2. The mechanistic implications of these results and their impact on current material compatibility assessments for Ti alloys in hydrogen service are then discussed.

Quantitative Fracture Mechanics Approach to Fatigue Life Improvement by Shot Peening Application

Stress intensity factor has been a favorite tool in fracture mechanics due to its simplicity. Here, it is used to study the influence of the shot peening application in fatigue life improvement. Using a CT-specimen, the study of shot peening effect on fatigue life was performed. Here, the compressive residual stress is converted into residual stress intensity factor, Kres.. Together with the applied stress intensity factor, Kapl., the superposition principle can be used. The result of the investigation clarifies quantitatively what has been widely believed that one of the easiest ways to improve fatigue life is by perfecting the surface via shot peening. Compressive stresses are beneficial not only in postponing fatigue crack initiation but also in preventing the crack propagation, which lead to increasing fatigue strength.

Fatigue Crack Growth for Ferritic Steel Under Negative Stress Ratio

Abstract The phenomenon of crack closure is important in the prediction of fatigue crack growth behavior. Many experimental data indicate crack closures during fatigue crack growths both under tensile–tensile loads and tensile–compressive loads at constant amplitude loading cycles, depending on the magnitude of applied load amplitudes and stress ratios. Appendix A-4300 of the ASME Code Section XI provides two equations of fatigue crack growth rates for ferritic steels expressed by stress intensity factor ranges at negative stress ratios. The boundary of the two equations is classified with the magnitude of applied stress intensity factor ranges, in consideration of the crack closures. However, the boundary value provided by the ASME Code Section XI is not technically well known. The objective of this paper is to investigate the influence of the magnitudes of the applied stress intensity factor ranges on the crack closures. Fatigue crack growth tests using ferritic steel specimens were performed in air environment at room and high temperatures. From the crack closures obtained by the tests, it was found a new boundary which is smaller than the definition given by the Appendix A-4300.

Weld line strength factors in a reinforced injection molded part: Relationship with predicted fiber orientation

In this work, the residual strength of a fiber-reinforced injection molded part containing a hot weld line—or meld line—was evaluated. Injected plates were generated using a double-gated mold under four different process conditions. Quantification of the weld line detrimental effect was made in base on a fracture mechanics experiment. Specimens with and without the weld line—obtained from the same plates—were tested under a clamped single edge notched tension (SENT) configuration. For each set of process conditions, a relative weld line strength factor was defined in terms of the maximum applied stress intensity factor (KImax) as: KImax of specimens with weld line/KImax of specimens without weld line. In parallel, the fiber distribution pattern was obtained by process simulation software Moldex3D. An orientation factor was determined from simulation in order to quantify the effect of the local fiber orientation around the weld line. Optimal process condition and the most significant variable influencing the weld line strength were calculated via statistical analysis. Results showed a clear correlation between the weld line strenght factors and the orientaion factor. It was demonstrated that the fracture performance of the weld line region is controlled by the fiber orientation arrangement developed on that zone.

Fatigue crack growth in a material with coarse brittle phases

The paper explores the effect of brittle particles on fatigue crack growth. A model based on the theory of slightly curved crack fronts predicts that fatigue crack growth is enhanced if the applied stress intensity factor is greater than the fracture toughness of the particles. In the other case, the crack front advances in the matrix before it can traverse the particles (crack pinning). Below a certain stress intensity factor, the crack is completely arrested by the particles causing a fatigue threshold. The predictions are compared with experiments on Al alloys. Limitations of the linear perturbation theory are discussed.

Estimation of environment-induced crack growth rate as a function of stress intensity factors generated during slow strain rate testing of aluminum alloys

Abstract In this contribution, we introduce a simple approach to quickly estimate the environment-induced crack velocity (CV) as a function of the calculated applied stress intensity factor (K) developed during the slow strain rate testing of aluminum alloys exposed to aqueous or humid air-type environments. The CV-K behavior for a commercial aluminum-magnesium alloy, AA5083-H131, sensitized and pre-exposed to a 0.6 m NaCl solution has been estimated from slow strain rate test data. The predicted threshold K and crack velocities match recently published data for the same alloy in similarly sensitized conditions where the CV-K data were obtained using state-of-the-art fracture mechanics-based testing.

Understanding the effect of crack tip deformation on fatigue crack growth behavior in 300-series austenitic stainless steel

Fatigue crack growth rates (FCGRs) of Type 304/304L stainless steel at stress ratios above 0.7 in elevated temperature (250–320 °C), high purity water are observed to be accelerated by 10× to 100× (relative to comparable tests in air) during testing at low frequencies (0.167–0.000167 Hz). These effects are most prominent for fatigue tests with applied stress intensity factor amplitudes (ΔK) less than ∼10 MPa√m and has been attributed to a hydrogen-based mechanism. This work evaluates that hypothesis, at ambient temperature, through a combination of fatigue testing (using deuterium pre-charged and uncharged specimens) and materials characterization. Over a range of ΔK values (∼6 to 12 MPa√m), the FCGRs of pre-charged specimens are found to be marginally higher (at most 20–30%) relative to comparable tests of uncharged specimens. However, while the FCGRs between pre-charged and uncharged specimens are comparable, the morphology of the fracture surface of the pre-charged specimens is predominately faceted while the morphology of the fracture surface of the uncharged specimen is quasi-cleavage with some poorly defined faceted regions. Planar slip (and few cell structures) is predominate ahead of the crack tips in which the faceted fracture surface morphology is observed. In contrast, quasi-cleavage and poorly defined faceted fracture surfaces are associated with a cellular structure embedded within a planar slip region ahead of crack tips. These differences in deformation suggest the fracture surface morphology may form by either cracking along slip planes in the case of deuterium pre-charged specimens or by cracking along cell walls in the case of uncharged specimens. The fracture mechanism that operates is controlled by differences in the number of cycles required to evolve the deformation structures ahead of the fatigue crack tip, the grain orientation, and local hydrogen concentration.

A simple fracture mechanics estimation of the fatigue endurance of welded joints

The use of fracture mechanics based methodologies to assess the influence of defects on welded components has become increasingly important for industrial applications and design, in the last decades. However, there are still objections against these approaches due to their complexity and the consequent need of qualified personnel with certain level of knowledge of fracture mechanics. Therefore, development of simplified methods to evaluate severity of defects can be valuable for practical purposes. In the present work, a manageable expression is proposed to calculate the applied stress intensity factor for crack growth, which is proportional to the square root of crack length and the stress concentration factor at the location of the crack in the un-cracked body. The latter was obtained with numerical simulation of transversely loaded butt, T and cruciform joints. By means of the resistance curve method that accounts for short crack behaviour, these results can be compared with threshold for crack propagation to estimate the fatigue resistance of welded joints. Besides, a simple expression was derived to estimate the fatigue endurance, which can be used to understand and analyse in a simplified manner the influence of the main geometrical and mechanical parameters, like weld geometry, residual stresses and size of defects, among others. Estimations were compared with experimental results from literature for different weld configurations, and they proved to be conservative. Methodology is valid for toe cracks in as-welded joints.

Characterization of stress corrosion crack growth in austenitic stainless steel under variable loading in small- and large-scale yielding conditions

To investigate the factors that influence stress corrosion crack growth, crack growth testing was conducted using type 304 stainless steel in a tetrathionate solution under various applied stress intensity factors in small- and large-scale yielding conditions. The crack growth rate increased with increasing equivalent stress intensity factor, as defined by the J integral, and its gradient, and we found that the crack growth could be characterized by these values. Then, we developed an equation to evaluate the crack growth as a function of equivalent stress intensity factor and its gradient.

Strength and reliability of WC-Co cemented carbides: Understanding microstructural effects on the basis of R-curve behavior and fractography

Strength and reliability of WC-Co cemented carbides (hardmetals) are dependent on effective fracture toughness as well as on nature, size and distribution of processing flaws. Regarding toughness, they exhibit a crack growth resistance (R-curve) behavior, derived from the development of a multiligament bridging zone at the crack wake. Accordingly, successful implementation of fracture mechanics requires consideration of tangency criterion, between applied stress intensity factor and R-curve, in addition to fractographic inspection. It is the aim of this study to evaluate the strength behavior of a series of experimental WC-Co grades on the basis of R-curve failure criteria. Results indicate that microstructural effects on the strength of hardmetals may be satisfactorily rationalized following the referred criterion. The analysis includes consideration of nature and distribution of fracture origins, found to be more diverse and wider, respectively, for the harder fine-grained grades. This experimental evidence, together with the fact that these hardmetals exhibit steeper rising R-curves than tougher coarse-grained ones, leads to lower reliability for the former. This investigation documents and validates the great relevance of R-curve behavior for optimizing the mechanical performance of WC-Co cemented carbides on the basis of microstructural design.

Evaluation of different crack driving forces for describing the fatigue crack growth behaviour of PET-G

To predict the fatigue crack growth in full-scale components made of polymeric materials, a methodology to transfer laboratory crack-growth data to structures is needed. This requires the similitude hypothesis to be applicable using a valid crack driving force, which allows the description of the R-ratio effect on the crack growth behavior. Whereas in metals it is common to use the range in the applied stress intensity factor, ΔK, as the crack driving force, in polymeric materials and composites the use of the energy release rate G has been considered and ΔG has been proposed as the crack driving force to ensure the similitude principle. Therefore, the aim of this paper is to assess the validity of ΔG as a proper crack driving force and to explore the way of practical application in an amorphous thermoplastic copolyester Polyethylene terephthalate glycol (PET-G).

Creep crack growth by grain boundary cavitation under monotonic and cyclic loading

Plane strain finite deformation finite element calculations of mode I crack growth under small scale creep conditions are carried out. Attention is confined to isothermal conditions and two time histories of the applied stress intensity factor: (i) a monononic increase to a plateau value subsequently held fixed; and (ii) a cyclic time variation. The crack growth calculations are based on a micromechanics constitutive relation that couples creep deformation and damage due to grain boundary cavitation. Grain boundary cavitation, with cavity growth due to both creep and diffusion, is taken as the sole failure mechanism contributing to crack growth. The influence on the crack growth rate of loading history parameters, such as the magnitude of the applied stress intensity factor, the ratio of the applied minimum to maximum stress intensity factors, the loading rate, the hold time and the cyclic loading frequency, are explored. The crack growth rate under cyclic loading conditions is found to be greater than under monotonic creep loading with the plateau applied stress intensity factor equal to its maximum value under cyclic loading conditions. Several features of the crack growth behavior observed in creep-fatigue tests naturally emerge, for example, a Paris law type relation is obtained for cyclic loading.

Interacting sensitivities of alloy 600 PWSCC to stress intensity factor, yield stress, temperature, carbon concentration, and crack growth orientation Alloy 600

Analyses of Alloy 600 primary water stress corrosion cracking data show there are interacting sensitivities of crack growth rate to applied stress intensity factor, yield stress, temperature, carbon concentration and crack growth orientation. The effects of these variables are expressed quantitatively using a crack advance model that is rate-limited by crack-tip-strain rate. Crystallographic texture and dynamic strain aging are considered to account for contrasting behavior observed for ST and LT orientation crack growth. Crack growth is conjectured to be rate-limited by “junction” pinning of mobile dislocations strengthened by interstitial carbon (ST) and “lineal” pinning by substitutional Cr and Fe (LT).

Fatigue crack growth rate in miniature specimens using resonance

The method of crack growth rate measurement in miniature single edge notched (SEN) cantilever specimen at stress ratio R∼−1 is presented. The resonance circuit is formed by the cantilever specimen with inertial yoke at its free end excited by alternating electromagnetic field. The parameters of the harmonic excitation are controlled by the phase shift technique. The crack length is estimated from specimen compliance added by the crack opening. The stress intensity factor is computed from the applied bending moment. Linear elastic fracture mechanics with standard shape functions corresponding to the particular specimen geometry and applied loading are used. The analysis of signal from single piezoelectric accelerometer provides data for the estimation of crack length and applied stress intensity factor, making the method very simple and inexpensive, yet reasonably accurate.The crack length measurement was calibrated using fractographic marking technique. The presented method was validated by performing crack growth rate tests in miniature 4×3×32mm beam specimens with 150° chevron notch. 7075 aluminium alloy and 4043 high strength steel were tested at load frequency of 110 and 160Hz respectively. The crack growth curves were measured in both load increase and load reduction mode and the resulting crack compare well with the baseline data available for standard central crack (CCT) specimens.