Langzeit- und Dauerschwingfestigkeit des Vergütungsstahls 25CrMo4 bei mehrachsiger Beanspruchung durch drei schwingende Lastspannungen

High-Cycle and Long-Life Fatigue of 25CrMo4 under Multiaxial Load Conditions by three Alternating Stresses Statistically verified experimental results from high-cycle and long-life fatigue tests (HCF and LLF) with altogether 537 unnotched solid cylindrical and thin-walled hollow specimen are demonstrating the fatigue behaviour (S-N-characteristics, scatterband) of 25CrMo4 under uniaxial loading with superimposed static stresses (consideration of the mean stress effect) and under biaxial loadings in variation of phase differences between the three combined normal and torsional stresses σ_x, σ_y, τ_xy The fatigue strength is commonly decreasing with life time in the high-cycle regime until reaching the fatigue endurance limit in the transition range to infinite life. The “ductility level” τ_w/σ_w and the “mean stress sensibility” p = p (σ_w, σ_zSch, R_m) are relatively independent of the intensity by stress amplitudes and fatigue life to failure. In comparision with the specific case of biaxial combined loading with synchroneous amplitudes, the fatigue resistance characteristics are detrimentally influenced by out-of-phase normal stresses σ_x, σ_y; a phase difference of 180° between the normal stress amplitudes is the most critical state of combination, especially in the lower cycle regime caused by a greater slope coefficient (probability of survival P_s = 50%). On the contrary is there in the high-cycle regime as well as in the long-life range no significant influence to the fatigue strength by biaxial load conditions of simultaneously normal stresses with out-of-phase torsional stress τ_xy     

Mean stress and plasticity effect prediction on notch fatigue and crack growth threshold,combining the theory of critical distances and multiaxial fatigue criteria

In the present work, we propose a robust calibration of some bi‐parametric multiaxial fatigue criteria applied in conjunction with the theory of critical distances (TCD). This is based on least‐square fitting fatigue data generated using plain and sharp‐notched specimens tested at two different load ratios and allows for the estimation of the critical distance according to the point and line method formulation of TCD. It is shown that this combination permits to incorporate the mean stress effect into the fatigue strength calculation, which is not accounted for in the classical formulation of TCD based on the range of the maximum principal stress. It is also shown that for those materials exhibiting a low fatigue‐strength‐to‐yield‐stress ratio σ_fl,R = ?1/σ_YS, such as 7075‐T6 (σ_fl,R = ?1/σ_YS = 0.30), satisfactorily accurate predictions are obtained assuming a linear‐elastic stress distribution, even at the tip of sharp notches and cracks. Conversely, for any materials characterized by higher values of this ratio, as quenched and tempered 42CrMo4 (σ_fl,R = ?1/σ_YS = 0.54), it is recommended to consider the stabilized elastic‐plastic stress/strain distribution, also for plain and blunt‐notched samples and even in the high cycle fatigue regime still with the application of the TCD.     

A fatigue-to-creep correlation in air for application to environmental stress cracking of polyethylene

The present study was undertaken to determine whether the correlation between fatigue and creep established for polyethylene in air could be extended to environmental liquids. Fatigue and creep tests under various conditions of stress, R-ratio (defined as the ratio of minimum to maximum load in the fatigue loading cycle), and frequency were performed in air and in Igepal solutions. The load–displacement curves indicated that stepwise fatigue crack growth in air was preserved in Igepal solutions at 50 °C, the temperature specified for the ASTM standard. In air, systematically decreasing the dynamic component of fatigue loading by increasing the R-ratio to R = 1 (creep) steadily increased the lifetime. In contrast, the lifetime in Igepal was affected to a much smaller extent. The fatigue to creep correlation in air was previously established primarily for tests at 21 °C. Before testing the correlation in Igepal, it was necessary to establish the correlation in air at 50 °C. Microscopic methods were used to verify stepwise crack growth by the sequential formation and breakdown of a craze zone, and to confirm the fatigue to creep correlation. The crack growth rate under various loading conditions was related to the maximum stress and R-ratio by a power law relationship. Alternatively, a strain rate approach, which considered a creep contribution and a fatigue acceleration factor that depended only on strain rate, reliably correlated fatigue and creep in air at 50 °C under most loading conditions of stress, R-ratio and frequency. The exceptions were fatigue loading under conditions of R = 0.1 and frequency less than 1 Hz. It was speculated that compression and bending of highly extended craze fibrils were responsible for unexpectedly high crack speeds.     

Predicting long-term creep failure of bimodal polyethylene pipe from short-term fatigue tests

Short-term fatigue testing was used to predict long-term creep failure of a bimodal polyethylene (BMPE) pipe with superior creep resistance. The stepwise crack propagation was studied by increasing the R-ratio (defined as the ratio of the minimum to the maximum stress intensity factor in the fatigue loading cycle) at 50 °C from 0.1 approaching creep (R = 1). Crack growth rate (da/dt) was related to the maximum stress intensity factor K _I,max and R-ratio by a power law relationship \frac\textda\textdt = B^￠ K_\textI,max⁴ (1 + R) ^{- 8.5} {\frac{{{\text{d}}a}}{{{\text{d}}t}}} = B^{\prime } K_{{{\text{I}},\max }}^{4} (1 + R)^{ - 8.5} . The correlation in crack growth kinetics allowed for extrapolation to creep fracture from short-term fatigue testing. The temperature dependence of crack growth rate was contained in the prefactor B′. A change in slope of the Arrhenius plot of B′ at 67 °C indicated that at least two mechanisms contributed to crack propagation, each dominating in a different temperature region. This implied that a simple extrapolation to ambient temperature creep fracture from elevated temperature tests might not be reliable.     

Compressive Fatigue Behavior of Bovine Cancellous Bone and Bone Analogous Materials under Multi‐Step Loading Conditions

In this study the compressive cyclic behavior of bovine cancellous bone and three open‐cell metallic foams including AlSi7Mg foams (30 and 45 ppi) and CuSn12Ni2 foam (30 ppi) has been investigated. Multi‐step fatigue tests are carried out to study the deformation behavior under increasing compressive cyclic stresses. Short multi‐step tests, with steps of 300–500 cycles, are used to identify the cyclic yield stress (σ_cy) and the stress at failure (σ_fail). The residual strain accumulation, or cyclic creep, is observed during these tests. Long multi‐step tests, with 5000 cycles at selected stress ranges (0.4σ_cy, 0.6σ_cy, 0.8σ_cy, and σ_cy), are also carried out to study further the compressive fatigue behavior of the materials. Scanning electron microscopy (SEM) has been used to characterize the microstructure of the foams and the bone prior to and post mechanical testing. Particular attention is paid to the role of cyclic creep and buckling in the failure processes. The results show that residual strain accumulation seems to be the predominant driving force leading to failure of foams and bones. Although foams and bone fail by the same mechanism of cyclic creep, the deformation behavior at the transient region of each step is different for both materials. The maximum strain ε_max of foams decrease suddenly during the change of each step. This behavior may be explained by the rapidly developing microdamage in the cell struts that occur at the transient region of each step. Bones show more gradual decrease of ε_max, where microdamage may be accumulated progressively during the fatigue test.     

A Parametric Lifetime Model for the Prediction of High-Cycle Fatigue Based on Stress Level and Amplitude

The goal of this paper is to present a general parametric lifetime model for predicting fatigue behaviour at any stress level and amplitude (for example, at any combination of σ_max and σ_min pair) in the high‐cycle fatigue regime. The problem of the design of the experimental laboratory test required for such a prediction is dealt with. The surprising and relevant result is that running two groups of tests for two different constant stress levels of σ_max or σ_min is sufficient to predict the whole collection of Wöhler fields for any possible stress level. However, some combinations of tests, such as one for a fixed value of σ_max and one for a fixed value of σ_min, are shown to be insufficient. Closed formulas for obtaining any Wöhler field from the results of the experiments corresponding to the two different fixed values of σ_max or σ_min are given. Together the proposed model and lab tests allow any fatigue analysis to be performed in the current investigation. One example of application illustrates the proposed method.     

Investigation on the Fatigue Behaviors of Maraging Steel at Different Stress Ratios

Herein, the high-cycle fatigue behaviors of 18Ni maraging steel with different tensile strength in the stress ratio range from 0.1 to 0.5 are investigated, and compared with those at the stress ratio of −1. It is found that the relationship between the fatigue strength at the stress ratios of −1 and 0.1 and tensile strength is nonmonotonic, while the fatigue strength at the stress ratio of 0.5 improves as the tensile strength heightens. The tensile strength corresponding to the optimal fatigue strength state would change with the variation of the stress ratio, which is related to the alteration of key factors affecting the fatigue damage. Moreover, it is found that the Walker equation: σ_aR = σ₋₁ ⋅ [(1 − R)/2]^β gives reasonable results for the influence of stress ratio on the fatigue strength of 18Ni maraging steel.     

Cyclic creep behaviour under tension–tension loading cycles with hold time of modified 9Cr–1Mo steel

Abstract

Cyclic creep behaviour of modified 9Cr–1Mo steel was investigated by a series of cyclic creep (CC) tests at 600°C, which were performed under controlled tension–tension loading cycles with the magnitude of stress ranges in a constant stress ratio (R?=?0·1). Hold time was applied for a 10 min hold at the maximum stress (σ_max) and minimum stress (σ_min). The CC properties were compared with the static creep (SC) using Norton’s power law, Larson–Miller plot, and Monkman–Grant relation, and the microstructure was examined. For the test conditions employed in the present investigation, retardation in the CC behaviour in terms of a lower creep rate and longer rupture time compared to those in the SC was obtained. The retardation was ascribed to the effects associated with anelastic recovery during the 10 min hold time at the minimum load of the cyclic loading. The creep rupture ductility decreased with a general decrease in stress, and there was no difference in the creep ductility between the CC and SC. The steel displayed a transgranular fracture characterised by the presence of dimples resulting from micro-void coalescence. Carbide precipitation was more coarsened with increasing in exposure time in the CC tests.     

Low cycle deformation behaviour of Zircaloy-4 at elevated temperatures

The LC deformation behaviour of Zry-4 at 400°C and 600°C was examined by means of tension/compression experiments conducted in load and in strain control respectively. The main results were compared to those obtained at comparable conditions on the stainless steel type AISI 304. For both the materials the influence of the stress ratio R = σ_min/σ_max (where within one test σ_max > 0 was kept constant) upon the lifetime T_f at low and high homologeous temperature T_h was examined. Whereas at the lower T_h for R < 0 the lifetime decreased with decreasing R, the opposite was true at the higher T_h. The explanation of the influence of R upon t_f suggests that at high temperatures the fatigue damage rate Å_f drops below the rate for creep damage Å_c Two cases are considered. If the above damage mechanisms are sequentially independent the resulting damage rate Å ≈? Å_c and hence Å_c is the failure (rate) determining mechanism. In the case that the mechanisms are sequentially dependent then Å ≈? Å_f. TEM investigations conducted on Zry-4 cycled at 600° C have shown that the typical dislocation pattern revealed is a band structure consisting of dense dislocation walls separating denuded zones. The habit and the crystallographic characteristics of the band structure resemble the structure associated with PSBs observed in fee metals. The comparison of the values of the saturation stress τ_s and the wall spacing d for different fee and hep metals shows that there is a proportionality between τ_s and 1/d which is independent of stress and temperature.     

Variances of locally Minimum Variance Quadratic Unbiased Estimators (“MIVQUE's”) of Variance Components

Minimum variance quadratic unbiased estimators (MIVQUE's) of variance components from unbalanced data are functions of the components they are to estimate. To use the MIVQUE expressions for estimation under the one-way classification random model, for example, the unknown between- and within-treatments components, σ² _a and σ² _e , must be replaced by a priori estimates σ² _ao and σ² _eo the resulting estimators are called “MIVQUE's.” For the one-way classification, expressions for the variances and covariance of the “MIVQUE's” are obtained under normality. Numerical comparisons indicate that when σ² _a /σ² _e > 1 (approximately) and unless σ² _ao /σ² _eo Q σ² _a /σ² _e , (a) the “MIVQUE's” have variances near their lower bounds, and (b) the “MIVQUE” of σ² _a is more efftcient than the ANOVA estimator. When σ² _a /σ² _e < 1, the “MIVQUE's” are more dependent on accurate specification of σ² _ao /σ² _eo . The “MIVQUE” and ANOVA estimator of σ² _e have nearly equal variances unless σ² _eo /σ² _eo σ² _a /σ² _e , when the ANOVA estimator has smaller variance.     

Fretting fatigue behaviour of shot-peened Ti-6Al-4V at room and elevated temperatures

Fretting fatigue behaviour of shot‐peened titanium alloy, Ti‐6Al‐4V was investigated at room and elevated temperatures. Constant amplitude fretting fatigue tests were conducted over a wide range of maximum stresses, σ_max= 333 to 666 MPa with a stress ratio of R= 0.1 . Two infrared heaters, placed at the front and back of specimen, were used to heat and maintain temperature of the gage section of specimen at 260 °C. Residual stress measurements by X‐ray diffraction method before and after fretting test showed that residual compressive stress was relaxed during fretting fatigue. Elevated temperature induced more residual stress relaxation, which, in turn, decreased fretting fatigue life significantly at 260 °C. Finite element analysis (FEA) showed that the longitudinal tensile stress, σ_xx varied with the depth inside the specimen from contact surface during fretting fatigue and the largest σ_xx could exist away from the contact surface in a certain situation. A critical plane based fatigue crack initiation model, modified shear stress range parameter (MSSR), was computed from FEA results to characterize fretting fatigue crack initiation behaviour. It showed that stress relaxation during test affected fretting fatigue life and location of crack initiation significantly. MSSR parameter also predicted crack initiation location, which matched with experimental observations and the number of cycles for crack initiation, which showed the appropriate trend with the experimental observations at both temperatures.     

TRANSIENT RETARDATIONS IN FATIGUE CRACK GROWTH FOLLOWING A SINGLE PEAK OVERLOAD

Retardation in the fatigue crack growth rate following the application of a single peak overload in a fatigue loading sequence has been studied for a low carbon structural steel. Tests have been performed at load ratios of R= 0.2 and R= 0.6 at a baseline stress intensity range, ΔK_b, corresponding to fatigue crack growth rates in the Paris regime. Single peak overloads were applied at a crack-length to specimen-width ratio of a/W= 0.5. At the load ratio of R= 0.6 monotonic or “static” fracture modes were observed upon application of the overload, and these produced an immediate increase in growth rate. A subsequent retardation is attributed to the presence of a residual compressive stress field ahead of the crack tip. A similar retardation was observed at a load ratio of 0.2. The importance of residual stress was established by performing stress relieving experiments. In addition, removal of the surface deformation after an overload by machining “T” sidegrooves resulted in an extended transient, which could not be explained by residual machining stresses.     

Correlation of fatigue and creep crack growth in poly(vinyl chloride)

Slow crack growth in PVC pipe was studied in order to develop a methodology for predicting long-term creep fracture from short-term tension-tension fatigue tests. In all cases, the crack propagated continuously through a crack-tip craze. In fatigue, the density of drawn craze fibrils gradually increased with decreased frequency and increased temperature. At the lowest frequency, 0.01 Hz, the fibril density in fatigue approached that in creep. The kinetics of fatigue and creep crack growth followed the conventional Paris law formulations with the same exponent 2.7, da/dt = A _f K _I ^2.7, da/dt = BK _I ^2.7, respectively. The effects of frequency, temperature and R-ratio (the ratio of minimum to maximum stress intensity factor in the fatigue loading cycle) on the Paris law prefactors were characterized. Comparison of frequency and R-ratio tests revealed that the fatigue contribution depended on strain rate. Therefore, at each temperature, crack growth rate was modeled as the product of a creep contribution that depended only on the maximum stress intensity factor and a fatigue contribution that depended on strain rate: (da/dt) = BK _I,max ^2.7 (1 + C), where B is the prefactor in the Paris law for creep and C is a coefficient defining the strain rate sensitivity. A linear correlation allowed extrapolation of the creep prefactor (B) from fatigue data. The extrapolated values were systematically higher than the values measured directly from creep and only converged at T _g . The difference was attributed to damage of the craze fibrils during crack closure upon unloading in the fatigue cycle.     

Effect of stress ratios on tension–tension fatigue behavior and micro-damage evolution of basalt fiber-reinforced epoxy polymer composites

The tension–tension fatigue behavior and damage mechanism of basalt fiber-reinforced epoxy polymer (BFRP) composites at different stress ratios are studied in this paper. The fatigue experiments were performed under stress ratios, R?=?σ_min/σ_max of 0.1 and 0.5, while the lifetime and the stiffness degradation were monitored and analyzed to investigate the effect of stress ratios. The damage propagation during fatigue loading was periodically monitored by using an in situ scanning electron microscope (SEM). The results show that the fatigue life decreases and the fatigue life degradation rate increases with the decrease of stress ratio for examined BFRP composites. The stiffness degradation is also sensitive to different stress ratios, showing a greater stiffness loss before failure at lower stress ratio. From the SEM images, it is indicated that the micro-damage mode shifts from interface debonding and matrix cracking into fiber breaking with decreasing stress ratios.     

Fatigue life estimation after crack repair in 6005 A-T6 aluminium alloy using the cold expansion hole technique

In this paper, the hole drilling (HD) and the cold expansion (CE) processes, which were used as a technique for crack repair, were investigated in order to estimate the beneficial effects on fatigue crack initiation (FCI). The FCI life is defined as the number of cycles to initiate a new crack of 0.2 mm on the surface of the specimen. Three hole radii and three degrees of cold expansion (DCE%) values were tested after a crack propagation period. Crack retardation after the CE process was observed. This phenomenon is due to two mechanisms: retardation owing to both geometric and mechanical effects, which is produced by the stress concentration at the drilled hole, and the large strain‐induced compressive residual stresses around the hole. In this report, the influence of the loading conditions was studied. For high values of the stress intensity factor range ΔK_ρ around the hole (based on the pseudo crack length a + ρ), the number of cycles corresponding to crack initiation N_i is low. At the edge of the hole, the maximum stress range can be approximated by the following formula: Δσ_max = 2ΔK_ρ /√πρ , where ρ is the hole radius and ΔK_ρ is the related stress intensity factor range.The FCI life extension, defined by the number of cycles corresponding to crack re‐initiation N_i , is related to the relative maximum stress range ratio R_σ = [(Δσ_max )/(Δσ_max )_th ] where (Δσ_max )_th is the value of the threshold maximum stress range obtained when N_i = 2 × 10⁶ cycles. The relationship between N_i and R_σ may be written as a power function.     

Effects of various environments on fatigue crack growth in Laser formed and IM Ti–6Al–4V alloys

The fatigue crack growth behaviors of Laser formed and ingot metallurgy (IM) Ti–6Al–4V alloys were studied in three environments: vacuum, air and 3.5% NaCl solution. Taking the Unified Fatigue Damage Approach, the fatigue crack growth data were analyzed with two intrinsic parameters, stress intensity amplitude ΔK and maximum stress intensity K_max, and their limiting values ΔK^* and . Fatigue crack growth rates da/dN were found increase with stress ratio R, highest in 3.5% NaCl solution, somewhat less in air and lowest in vacuum, and higher in IM alloy than in Laser formed one. In 3.5% NaCl solution, stress corrosion cracking (SCC) was superimposed on fatigue at R=0.9 for where K_max>K_ISCC, the threshold stress intensity for SCC. This and environment-assisted fatigue crack growth were evidenced by the deviation in fatigue crack growth trajectory (ΔK^* vs. curve) from the pure fatigue line where . Furthermore, the fractographic features, identified along the trajectory path, reflected the fatigue crack growth behaviors of both alloys in a given environment.     

Weibull stress distribution for static mechanical stress and its stress/strength analysis

The method's steps to estimate the Weibull shape (β) and scale (η) parameters, based only on the ratio of the maximal and minimal principal stresses (σ₁/σ₂) and on the designed reliability (R(t)) are given in Section 4.1 . The method's efficiency is based on the following facts: (1) The square root of σ₁/σ₂ represents the base life on which the Weibull lifetimes are estimated (see Equation  61 ). (2) The mean of the logarithms of the expected lifetimes (g(x)) is completely determined by the determinant of the analyzed stress matrix (see Equation  13 ). (3) The Weibull distribution is a circle centered on the arithmetic mean (μ), and it covers the whole principal stresses' span (see Figure  5 ). (4) σ₁/σ₂ and g(x) completely determine the σ_1i and σ_2i values, which correspond to any lifetime in the Weibull analysis (see Equation  54 ). And (5) σ₁/σ₂ and η completely determine the minimal and maximal lifetime, which corresponds to any σ_1i and σ_2i values (see Equation  57 ). Additionally, by using the addressed stress β and η parameters, when the stress is either constant or variable, the formulation to estimate the designed R(t) index is given. The steps to determine both the material's strength average (μ_M) for a desired R(t) index and the R(t) index, which corresponds to a used μ_M value, are given.     

Foreword – Materialwissenschaft und Werkstofftechnik 10/2011

Load controlled fatigue tests were performed up to 10⁷ cycles on flat notched specimens (K_t = 2.5) under constant amplitude and variable amplitude loadings with and without periodical overloads. Two materials are studied: a ferritic‐bainitic steel and a cast aluminium alloy. These materials have a very different cyclic behaviour: the steel exhibits cyclic strain softening whereas the Al alloy shows cyclic strain hardening. The fatigue tests show that, for the steel, periodical overload applications reduce significantly the fatigue life for fully reversed load ratio (R_σ = –1), while they have no influence under pulsating loading (R_σ = 0). For the Al alloy overloads have an effect (fatigue life decreasing) only for variable amplitude loadings. The detrimental effect of overloads on the steel is due to ratcheting at the notch root which evolution is overload's dependent.     

Small fatigue crack growth behavior of titanium alloy TC4 at different stress ratios

In this paper, the small fatigue crack behavior of titanium alloy TC4 at different stress ratios was investigated. Single‐edge‐notch tension specimens were fatigued axially under a nominal maximum stress of 370 MPa at room temperature. Results indicate that fatigue cracks in TC4 initiate from the interface between α and β phases or within α phase. More than 90% of the total fatigue life is consumed in the small crack initiation and growth stages. The crack growth process of TC4 can be divided into three typical stages, ie, microstructurally small crack stage, physically small crack stage, and long crack stage. Although the stress ratio has a significant effect on the total fatigue life and crack initiation life at constant σ_max, its effect on crack growth rate is indistinguishable at R = ?0.1, 0.1, and 0.3 when crack growth rate is plotted as a function of ?K.     

Berechnung der Dauerschwingfestigkeit unter Berücksichtigung der spannungsmechanischen und statistischen Stützziffer

Fatigue Limit and Geometrical and Statistical Size Effect The ratio of the fatigue limit of an unnotched specimen to that of a notched one, the fatigue notch factor K_f, is usually smaller than the theoretical stress concentration factor K_t. With the assumption of a plastic cyclic deformation ?_apW at the level of the fatigue limit the fatigue limit for a notched specimen can be calculated. According to formula (4) this fatigue limit σ_naD is a function of K_t, ?_apW, the notch stress amplitude σ_a, the cyclic strengthening exponent n′ and the fatigue limit of a smooth specimen σ_W. Moreover, taking into account the statistical size effect with the known “weakest link concept”, see flow chart Fig. 9, the calculation is in a good agreement with 77 test results for steel.