Multiaxial fatigue assessment of welded joints – Recommendations for design codes

In the assessment of welded joints submitted to multiaxial loading the calculations method applied, independently of the concept (nominal, structural, hot-spot or local), must consider primarily the materials ductility. While proportional loading can be assessed by von Mises, the principal stress hypothesis, the Findley method or the Gough–Pollard relationship, using any of the mentioned concepts, difficulties occur when the loading is non-proportional, i.e. the principal stress (strain) direction changes. This causes a significant fatigue life reduction for ductile steel welds, but an indifferent behaviour for semi-ductile aluminium welds. This different response to non-proportional loading can be assessed when ductility related mechanisms of fatigue failures, i.e. the mean value of plane oriented shear stresses for ductile materials and a combination of shear and normal stresses for semi-ductile materials, are properly considered.However, as these methods require a good expertise in multiaxial fatigue, for design codes used by non-fatigue experts, simpler but sound calculation methodologies are required. The evaluation of known fatigue data obtained with multiaxial constant and variable amplitude (spectrum) loading in the range N > 10⁴ cycles suggests the application of the modified interaction algorithm of Gough–Pollard. In the case of variable amplitude loading, constant normal and shear stresses are replaced by modified reference normal and shear stresses of the particular spectrum. The modification of the reference stresses is based on the consideration of the real Palmgren–Miner damage sum of D_PM = 0.5 (for spectra with constant mean loads) and the modification of the Gough–Pollard algorithm by consideration of the multiaxial damage parameter D_MA = 1.0 or 0.5, which is dependent on the material’s ductility and on whether the multiaxial loading is proportional or non-proportional. This method is already part of the IIW-recommendations for the fatigue design of welded joints and can also be applied by using hot-spot or local stresses.     

Consideration of mean-stress effects on fatigue life of welded magnesium joints by the application of the Smith–Watson–Topper and reference radius concepts

Three types of welded joints have been assessed with regard to their fatigue strength based on the mean-stress damage parameter model according to Smith, Watson, and Topper (P_SWT) and on the reference notch radius concept. These analyses were performed with three different stress ratios, R = −1, R = 0 and R = 0.5, under axial loading. For each stress level, the corresponding Neuber-Hyperbolas, Masing-loops and their maximum stress and maximum strain values were determined in order to calculate damage parameter (P_SWT) values. For a given weld geometry, this damage parameter is able to unify the fatigue results for different R-values within at a tight scatter band and therefore to consider the mean-stress effect. The unification of the results for different weld geometries is performed by applying the reference radii r_ref = 0.05 and r_ref = 1.00 mm as suggested by the IIW-Recommendations.     

Compression fatigue performance of a fire resistant syntactic foam

Compression–compression fatigue test study of a fire resistant Eco-Core was conducted at two values of stress ratios (R = 10 and 5). Tests were conducted at S_min/S_o values of 0.9–0.6 for R = 10 and 0.95–0.8 for R = 5. Here S_min is the maximum compression stress and S_o is the compression strength. The study showed that Eco-Core has well defined failure modes and associated fatigue lives. The failure modes are: damage on-set; damage progression, and final failure. The damage on-set, propagation and final failure were characterized by 2%, 5% and 7% changes in compliance. The three failure modes were found to be same for both static and fatigue loadings. The endurance limit was found to be 0.72S_o, 0.75S_o and 0.76S_o, respectively for three failure modes for R = 10 and 0.81S_o, 0.82S_o and 0.82S_o, respectively for R = 5. The fatigue life is defined by a power law equation, S_min/S_o = A_oN^α. Constants of the equation were established for all three modes of failures and the two stress ratios. Finally, fatigue life was found to be less sensitive to R ratio when expressed in terms of stress range versus number of load cycles, which is similar to that of metallic materials.     

Cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameters

This work reports fatigue stress test results for AISI 304 steel (R = −1) that has been subjected to a high cycle number. It shows that the energetic effect (employing different temperature increments for equal loading of uniaxial stress) can be used to evaluate the cumulative damage caused by any prior loading. Various load histories were applied to AISI 304 specimens, and the resulting damage was evaluated in reference to the energy factor, Φ, which is dependent on the maximum temperature at the sample surface when irreversible plastic deformation begins. The time curves (Wöhler curves) and the damage ratio based on the consumed energy were compared to those obtained according to Palmgren–Miner rules; this comparison served to show how under-evaluations can occur with high damage ratios.     

Improvement of dry float–sink separation of smaller sized spheres by reducing the fluidized bed height

In this study, the influence of the fluidized bed height on the float–sink of different sized spheres in a gas–solid fluidized bed was investigated. Fluidized beds with heights h = 200, 150, 100 and 50 mm were prepared using a cylindrical column of inner diameter = 290 mm and a mixture of zircon sand and iron powder as the fluidized medium. Float–sink experiments were carried out using density adjusted spheres of diameter D_sp = 40, 30, 20 and 10 mm. It was found that the float–sink performance at D_sp ?20 mm is not affected by the height of the bed, and the sharpness of separation (the density range where spheres neither float nor sink completely) is less than or equal to 200 kg/m³. In the case of D_sp = 10 mm, the sharpness of separation is a larger value (1100 kg/m³ at h = 200 mm), whereas it decreases with decreasing h and is 400 kg/m³ at h = 50 mm. The fluctuation of the surface height of the fluidized bed was visually recorded. The fluctuation is reduced by reducing h. The fluctuation vs. h correlates with the sharpness of separation at D_sp = 10 mm vs. h. These results indicate that the dry float–sink separation of smaller sized spheres is improved as the fluctuation of fluidized bed surface is decreased by reducing the fluidized bed height.     

Crystal structure,thermal analysis and IR spectrometric investigation of l-tyrosine hydrazide diphosphate monohydrate

The monoclinic crystal structure of (C₉H₁₅N₃O₂)₂P₂O₇·H₂O denoted DLTHDP [a = 14.626(1), b = 6.1990(2), c = 14.562(1) Å, β = 97.289(3)°, Z = 2, monoclinic P2₁, D_cal = 1.508, D_mes = 1.49 g cm⁻³] has been solved using direct methods and refined to a reliability factor R = 4.37% for 2079 independent reflections. The DLTHDP structure can be described by infinite polyanions [P₂O₇·H₂O]_n⁴ⁿ⁻ organized in chains parallel to the b-direction and located at z = 1/2, alternating with organic cations associated in ribbons spreading along the a-direction. Multiple hydrogen bonds originating from amine, hydroxyl groups and water molecules donors [NH…O(N) and O(W)H…O] connect the different components of the lattice. The IR data of DLTHDP is reported and discussed according to the theoretical group analysis and by comparison with IR results of similar compounds. The coupled thermogravimetric analysis (TGA)–differential thermal analysis (DTA) thermal study shows the departure of one water molecule, confirming the hydrated character of this compound.     

Fatigue properties and fracture analysis of a SiC fiber-reinforced titanium matrix composite

Tension–tension fatigue properties of SiC fiber reinforced Ti–6Al–4V matrix composite (SiC_f/Ti–6Al–4V) at room temperature were investigated. Fatigue tests were conducted under a load-controlled mode with a stress ratio 0.1 and a frequency 10 Hz under a maximum applied stress ranging from 600 to 1200 MPa. The relationship between the applied stress and fatigue life was determined and fracture surfaces were examined to study the fatigue damage and fracture failure mechanisms using SEM. The results show that, the fatigue life of the SiC_f/Ti–6Al–4V composite decreases substantially in proportion to the increase in maximum applied stress. Moreover, in the medium and high life range, the relationship between the maximum applied stress and cycles to failure in the semi-logarithmic system could be fitted as a linear equation: S_max/μ = 1.381 − 0.152 × lgN_f. Fractographic analysis revealed that fatigue fracture surfaces consist of a fatigued region and a fast fracture region. The fraction of the fatigued region with respect to the total fracture surface decreases with the increase of the applied maximum stresses.     

Fluorescence properties and relaxation processes of Tb3+ ions in ZnCl2-based glasses

60ZnCl₂–20KCl–20BaCl₂–xTbCl₃ glasses (x = 0.10, 0.25, 0.50, 0.75, 1.00, and 1.25) were prepared by melt-quenching method, and Tb³⁺ fluorescence properties were investigated under 355 nm excitation. Regardless of x values, the electrons that were relaxed from the ⁵D₃ to ⁵D₄ level of Tb³⁺ ions by the multiphonon relaxation, were repressed to 28% of all the excited electrons because the ZnCl₂-based glass had much lower phonon energy than oxide glasses. For 0 < x ≤ 0.34, the cross relaxation, (⁵D₃ → ⁵D₄) → (⁷F₀ ← ⁷F₆), was repressed, and consequently 72% and 28% of all the excited electrons were radiatively relaxed by the ⁵D₃ → ⁷F_J (J = 6, 5, 4, 3, and 2) and ⁵D₄ → ⁷F_J (J = 6, 5, 4, and 3) transitions, respectively. The lifetimes of the ⁵D₃ and ⁵D₄ initial levels were obtained to be 1.1 and 2.1 ms, respectively.     

Fatigue of 2024-T351 aluminium alloy at different load ratios up to 1010 cycles

Fatigue properties of 2024-T351 aluminium alloy are investigated in the high cycle fatigue (HCF) and very high cycle fatigue (VHCF) regime. Endurance tests are performed with ultrasonic equipment at 20 kHz cycling frequency at load ratios of R = −1, R = 0.1 and R = 0.5 up to 10¹⁰ cycles. Additional servo-hydraulic tests between 8 and 10 Hz at R = 0.1 show no frequency influence on fatigue lifetimes. Linear lines in double logarithmic S–N plots are used to approximate data. Slope exponents of approximation lines increase with increasing numbers of cycles for all load ratios. Failures above 5 × 10⁹ cycles (R = −1 and R = 0.1) or 10¹⁰ cycles (R = 0.5) occur, and no fatigue limit is found. Fatigue cracks leading to failures above 10⁹ cycles are initiated at the surface or slightly below at broken constituent particles or at agglomerations of fractured particles, which are probably Al₇Cu₂(Fe, Mn). Specimens stressed with more than 10¹⁰ cycles at R = −1 without failure show several cracks starting at constituent particles. Maximum crack lengths are 30 μm, which is considerably below grain size.     

Influence of defects on fatigue strength and failure mechanisms in the VHCF-region for quenched and tempered steel and nodular cast iron

Investigations are presented in this paper on quenched and tempered steel 42CrMoS4 from two batches, with two different tensile strengths (R_m = 1100 MPa, 1350 MPa) but with similar microstructure, and a nodular cast iron EN-GJS-900-2 (R_m = 930 MPa). Fatigue tests with smooth (K_t = 1) and notched (K_t = 1.75) specimens were performed at R = −1 and R = 0 up to the number of cycles N = 2·10⁹ in order to determine the fatigue strength behaviour and failure mechanisms, especially in the VHCF-region. Failure in smooth specimens often initiated at material defects such as oxides in the quenched and tempered steel and shrinkage holes in the nodular cast iron. Firstly, a fatigue strength analysis was performed that did not consider these defects. A possibility of analysis of experimental data including VHCF-results has been discussed. Next, a linear elastic fracture mechanics analysis was performed in order to describe the defect behaviour, assuming that the defects act like cracks. The results showed that there are lower limit or threshold values of the stress intensity factor range ΔK for crack propagation in both materials. Analysis of defects and defect distribution in run-out specimens confirmed this conclusion. From the comparison of the results with an S–N curve from the design code FKM-Guideline Analytical strength assessment of components, recommendations for design and assessment of components have been derived.     

EPR and optical absorption studies of Cr3+ doped lithium potassium sulphate single crystals

X-band electron paramagnetic resonance (EPR) studies of Cr³⁺ doped lithium potassium sulphate single crystals have been done at room temperature. The Cr³⁺ crystal field and spin Hamiltonian parameters have been evaluated by employing resonance line positions observed in the EPR spectra for different orientations of external magnetic field. The evaluated g, D and E values are: g_x = 2.0763 ± 0.0002, g_y = 1.9878 ± 0.0002, g_z = 1.8685 ± 0.0002 and D = 549 ± 2 × 10^?4 cm^?1, E = 183 ± 2 × 10^?4 cm^?1. Using EPR data the site symmetry of Cr³⁺ ion in the crystal is discussed. Cr³⁺ ion enters the lattice substitutionally replacing K⁺ site. The optical absorption study of the single crystal is also done in 195–925 nm wavelength range at room temperature. By correlating optical and EPR data the nature of bonding in the crystal is discussed. The calculated values of Racah parameters (B and C), crystal field parameter (D_q) and nephelauxetic parameters (h and k) are obtained as: B = 697, C = 3247, D_q = 2050 cm^?1, h = 1.146 and k = 0.21.     

Crack growth behavior of 7075-T6 under biaxial tension–tension fatigue

Crack growth behavior of aluminum alloy 7075-T6 was investigated under in-plane biaxial tension–tension fatigue with stress ratio of 0.5. Two biaxiality ratios, λ (=1 and 1.5) were used. Cruciform specimens with a center hole, having a notch at 45° to the specimen’s arms, were tested in a biaxial fatigue test machine. Crack initiated and propagated coplanar with the notch for λ = 1 in L–T orientation, while it was non-coplanar for λ = 1.5 between L–T and T–L orientations. Uniaxial fatigue crack growth tests in L–T and T–L orientations were also conducted. Crack growth rate in region II was practically the same for biaxial fatigue with λ = 1 in L–T orientation and for the uniaxial fatigue in L–T or T–L orientations, while it was faster for biaxial fatigue with λ = 1.5 at a given crack driving force. However, fatigue damage mechanisms were quite different in each case. In region I, crack driving force at a given crack growth rate was smallest for biaxial fatigue with λ = 1.5 and for uniaxial fatigue in T–L orientation, followed by biaxial fatigue with λ = 1 and uniaxial fatigue in L–T orientation in ascending order at a given crack growth rate.     

Threshold crack growth behavior of shear and tensile cracks

Crack-face interference-free mode I and mode II crack-growth data was combined with smooth axial (λ = ε_xy/ε_xx = 0) and torsional (λ = ∞) endurance limit data to develop unified crack growth models that incorporate both shear and tensile cracking. The crack growth models incorporated growth from a slip band (including short crack behavior) size crack until the final failure of a long crack, and the ability to switch between crack growth on shear planes to growth on tensile planes. The models successfully predicted smooth specimen crack-face interference-free fatigue lives and gave reasonable estimates of the smooth specimen endurance limits of crack-face interference free tubular tests run at intermediate strain ratios (λ = 3/4, 3/2, and 3). The series of Kitigawa–Takahashi (threshold fatigue) diagrams developed from the models help illustrate the competition between shear and tensile cracking at the fatigue limit under crack-face interference-free crack growth.     

Heat treatment,surface roughness and corrosion effects on the damage mechanism of mechanical components in the very high cycle fatigue regime

Many engineering components are subjected to combined torsion and axial loading in their working conditions, and the cyclic combined loading can result in fatigue fracture after a very long life fatigue regime. The present investigation extends over a wider range of test conditions involving surface treatment and manufacturing effects such as machining, so as to understand the fatigue properties and damage mechanisms of the material beyond 10⁹ cycles.This work reviews the effect of surface conditions on the fatigue behaviour of mechanical components in the gigacycle regime. Evidently, surface conditions can be variable and are due to very different reasons such as manufacturing effects like machining or final surface processes on the parts, heat treatment before and after manufacturing or environmental conditions like corrosion. In fact, this is a detailed comparative study based on the results of experiments carried out by our research team working in this domain. For this reason, it reveals a continuous decrease of the fatigue strength in the VHCF domain for the investigated materials under different surface conditions as important information for design engineers.Experimental investigation on the test specimens was performed at a frequency of 20 kHz with different stress ratios varying between R = ?1 and R = 0.7 at room temperature. All of the fatigue tests were carried out up to 10¹⁰ cycles. The damage mechanism was evaluated by Scanning Electron Microscopy (SEM).     

Measurement of particle size distribution of silica nanoparticles by interactive force apparatus under an electric field

This paper describes the measurement of particle size distribution of silica nanoparticles by interactive force apparatus (IFA) under an electric field in order to suggest the application of the apparatus to the measurement of particle size distribution. The results were compared with results obtained from size measurement by dynamic light scattering. D₅₀ measured by IFA was closer to the average particle size determined by TEM (5 nm). Also, when compared the results under three different supply voltage, (1) the results at 0.01 and 0.02 V were almost identical while (2) these results were different from the one at 0.04 V. The results indicate that breakage of coagulated particles possibly occur due to electric breakdown. The distribution measured by IFA (D₅₀ = 5–7 nm) was larger than the one measured by DLS (D₅₀ = 1 nm). The electric breakdown was explained by curve fitting of three different particle size distribution functions with particle size distribution obtained from IFA measurement.     

Effect of stitch density on fatigue characteristics and damage mechanisms of stitched carbon/epoxy composites

The effect of stitch density (SD) on fatigue life, stiffness degradation and fatigue damage mechanisms in carbon/epoxy (T800SC/XNRH6813) stitched using Vectran thread is presented in this paper. Moderately stitched composite (SD = 0.028/mm²; ‘stitched 6 × 6’) and densely stitched composite (SD = 0.111/mm²; ‘stitched 3 × 3’) are tested and compared with composite without stitch thread (SD = 0.0; ‘unstitched’). The experiments show that the fatigue life of stitched 3 × 3 is moderately better than that of unstitched and stitched 6 × 6. Stitched 3 × 3 pattern is also able to postpone the stiffness degradation onset. The improvement of fatigue properties and postponement of stiffness degradation onset in stitched 3 × 3 is primarily due to an effective impediment of edge-delamination. Quantification of damage at various cycles and stress levels shows that stitch density primarily affects the growth rate of delamination.     

Short cracks initiated in Al 6013-T6 with the focused ion beam (FIB)-technology

The fatigue crack growth behaviour of short corner cracks in the Aluminium alloy Al 6013-T6 was investigated. The aim was to determine the crack growth rates of small corner cracks at a stress ratio of R = 0.1, R = 0.7 and R = 0.8 and to find a possible way to predict these crack growth rates from fatigue crack growth curves determined for long cracks. Corner cracks were introduced into short crack specimens, similar to M(T) – specimens, at one side of a hole (Ø = 4.8 mm) by cyclic compression (R = 20). The precracks were smaller than 100 μm (notch + precrack). A completely new method was used to cut very small notches (10–50 μm) into the specimens with a focussed ion beam. The results of the fatigue crack growth tests with short corner cracks were compared with the long fatigue crack growth test data. The short cracks grew at ΔK-values below the threshold for long cracks at the same stress ratio. They also grew faster than long cracks at the same ΔK-values and the same stress ratios. A model was created on the basis of constant K_max-tests with long cracks that gives a good and conservative estimation of the short crack growth rates.     

22 Cr 5 Ni duplex and 25 Cr 7 Ni superduplex stainless steel: Hydrogen influence on fatigue crack propagation resistance

Duplex stainless steels (DSS) fatigue crack propagation resistance is strongly affected by both microstructure and environment. In this work, environment influence on the fatigue crack propagation in a 22 Cr 5 Ni duplex and in a 25 Cr 7 Ni superduplex stainless steels is investigated considering three different stress ratios (R = K_min/K_max = 0.1, 0.5, 0.75). Tests are performed according to ASTM E 647 standard, both in air and under hydrogen charging conditions (0.1 M H₂SO₄ + 0.01 M KSCN aqueous solution, ?0.9 V/SCE). Crack fracture surfaces are extensively analysed by means of a scanning electron microscope. Furthermore, crack paths are investigated by means of a crack profile analysis performed through a light optical microscope. Nickel coated fracture surface sections obtained for constant ΔK values are considered in order to analyse the loading (R values) and environment influence on fatigue crack paths.     

Raman spectroscopy and dielectric properties of nanoceramic NdFeO3

The nanoceramic NdFeO₃ is synthesized by the sol–gel citrate method. The Rietveld refinement of X-ray diffraction pattern at room temperature (30 °C) shows the orthorhombic Pnma phase with lattice parameters a = 5.576 Å, b = 7.756 Å, c = 5.447 Å. Nano-sized crystallites of NdFeO₃ ranging from 45 to 75 nm have been verified by the transmission electron microscope image. The room temperature Raman spectrum is fitted with the sum of 18 Lorentzian peaks. Eigen frequencies of vibrational modes are calculated using density functional theory under generalized gradient approximation and compared with experimental results. Dielectric spectroscopy study of NdFeO₃ has been performed in the frequency range from 50 Hz to 1 MHz and in the temperature range from 50 °C to 240 °C. The frequency dependence of real and imaginary parts of dielectric permittivity is analyzed using Cole–Cole equation. The frequency dependent conductivity spectra follow the power law.     

A neutron-diffraction study of the low-cycle fatigue behavior of HASTELLOY® C-22HSTM alloy

The HASTELLOY^® C-22HS^TM alloy is a face-centered cubic (fcc), nickel-based, corrosion-resistant superalloy. In the present study, the low-cycle-fatigue behaviors of the alloy were examined by in situ neutron diffraction at room temperature. The fatigue parameters included a total strain range of Δε = 2% and a strain ratio of R = −1 (R = ε_min/ε_max, where ε_min and ε_max are the applied minimum and maximum strains, respectively). The effect of cyclic deformation on the lattice strains was studied as a function of cyclic straining. The cyclic hardening and softening behaviors during fatigue is discussed in light of the relationship between the peak widths and lattice strains.