Statistical planning and evaluation of fatigue tests. A survey of recent results

The great scatter of fatigue test results demands special planning and evaluation. A development of the Wöhler diagram is presented which splits up the fatigue ranges into ones of finite endurance, transition and infinite endurance. The two types of the Wöhler diagram with this conception are shown. Reasons are given why ranges rather than distinct divisions should be defined. The favorable values of probability of fracture P_F are discussed. Experiences with the mathematical functions are reported. For the transition range the classical evaluation is explained; the boundary technique is recommended, and the staircase method and the Prot and the Locati methods are not recommended. Some recommendations are given for planning tests expected to lie within the range of finite fatigue life.     

Analysis of relationships governing wear fatigue damage. Report 1

Wear-fatigue damage is classified and described. The main terms of tribometry are given. Complex damage is analyzed from the dialectic position and Wöhler curves in fatigue (mechanical), fretting fatigue, frictionmechanical, and contact-mechanical fatigue is schematized. The general form of the exponential equation for describing these curves is presented.     

Der Gradient der Wöhlerkurve

The Gradient of the S, N-curve. The classical two-parameter basic equations of Wöhler and Basquin and also the four-parameter equation of Palmgren/Weibull approximate the Wöhler curve in certain ranges only. They fail in particular when one attempts to use them to convert a service life increase into the appropriate gain in strength. For a more exacting analysis these approximations must be replaced by models of the Wöhler curve which are nearer to actual reality.     

Lebensdauer- und Dauerfestigkeitsabschätzung von zugdruckwechsel- und zugschwellbeanspruchtem Stahl mittels Temperaturmessung

Estimation of the Endurance and the Fatigue Limit of Steel by Measuring Specimens′ Temperatures. Microplastic deformation processes are pre-requisites for fatigue crack formation within metallic materials. If the testing frequency of a specimen, cyclically stressed by a progressively-increasing load test, is not too low it is no great metrological problem to ascertain that special stress amplitude, σ_f,th (f ? fatigue limit, th ? thermometrical), at which specimen's temperature begins to rise due to the start of ‘remarkable’ microplastic deformations. Investigations of this kind, recently carried out by rotating bending showed a very good correspondence between σ_f,th and a statistically ascertained estimate of the fatigue limit, \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \sigma _{({\rm P} \simeq {\rm 0}\%{\rm)}} $\end{document} (P ? Probability of fracture), derived from comparatively performed Wöhler-tests. The purpose of this paper is to investigate the relationship between σ_f,th and \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \sigma _{({\rm P} \simeq {\rm 0}\%{\rm)}} $\end{document} for some carbon steels when cyclically stressed by push-pull and pulsating tensile loading, respectively. Both, unnotched and notched specimes were tested. Moreover, thermometrically monitored Wöhler-tests revealed that temperature measurements can provide a short-cut prediction of specimens′ lives. Above all it has to be mentioned that a reliable clue is gettable at a very early experimental stadium whether the cyclic stressed specimen will later become a ‘break’ or – normally much later – a ‘run-out’.     

Relative importance of transformation temperatures and sulphur content on hot ductility of steels

Abstract

Low (0·3%) and high manganese (1·4%) plain C – Mn steels with varying sulphur levels have had their hot ductility determined over the temperature range 700 – 1000°C, both after 'solution treatment' at 1330°C and directly after casting. It has been established that the width, depth and position of the hot ductility curves after solution treatment is more related to the transformation behaviour than either the sulphur in solution or the sulphide volume fraction or distribution. The growth of deformation induced ferrite at the austenite boundaries seems to be mainly diffusion controlled, and the higher is the transformation temperature for the γ – α phase change, the faster is the growth. Large amounts of ferrite can then form, giving good ductility. Thus, high transformation temperatures Ae ₃ or Ar ₃ are required to produce narrow ductility troughs. It is believed that any detrimental influence of the sulphides on these 'solution treated' steels is swamped by the rapid increase in ferrite volume fraction. For the as cast state, as more sulphides are able to precipitate at the interdendritic boundaries and austenite grain boundaries than in the solution treated condition, increasing the sulphur level causes a small deterioration in ductility at the high temperature end of the trough. In the present work, only narrow troughs have been found. This is in contrast to previous work on as cast C – Mn – Nb – Al steels, which exhibited wide troughs in the ductility curves, where it was shown that higher total sulphur levels lead to considerably worse ductility and that sulphur can be as detrimental to the ductility as niobium. It is recommended that, to avoid transverse cracking during continuous casting, in addition to keeping the sulphur level low, the carbon and manganese should also be as low as possible.     

Empfehlungen für die statistische Abschätzung des Zeit-und Dauerfestigkeitsverhaltens von Stahl

Recommendations for the Statistical Estimation of Fatigue Resistance Characteristics of Steel The introduction of recommendations for the proper application of elementary statistical methods to the planning of fatigue testing procedures and the subsequent analysis of the experimental data into international standards is probably imminent. Consequently, the inclusion in national specifications and standards seems to be only a question of time. This paper gives some basic guidelines of such recommendations dealing in detail with one of the most elementary methods which is aiming at the realization of so-called ?statistically ascertained”? Wöhlerdiagrams. Therein, graphical explanations are preferred to computational ones. Additionally, the arc sine √P-transformation which until now has proved to be an outstanding evaluation method with special regard to engineering purposes, is reviewed. Both, the computational and the graphical way of evaluation are discussed and affiliated probability papers are given.     

Anwendung des FWK-Konzepts für die Berechnung der Lebensdauer bei mehrstufiger Kriechbelastung

The application of the Consecutive-Wöhler-Curve-Concept in Computation of the life values for multi-stage creep It is known that at multi-stage creep load there cannot be calculated any reliable life values by means of linear damage accumulation hypotheses. A practicable non-linear statement was proposed by Pantelakis. Besides the one-stage creep life curve, results from two-stage tests are required for determining the damage exponent, With this exponent, which is a function of temperature and stress in the load stage applied first, the life values can be calculated only for two-stage sequences whose stress stages have to be identical to those of the two-stage tests. For the application of the consecutive Wöhler curve concept described in the following there is required the knowledge of the one-stage creep life curve and of the creep function for increasing and decreasing stress sequences derived from two-stage tests. Then, the life values can be calculated for the most different multi-stage loads. The stages should lie within the stress range used in the two-stage tests.     

A Damage Estimation Method for Packaging Systems Based on Power Spectrum Densities Using Spectral Moments

Packaging systems always endure some type of damage during transportation, and Wöhler curves are typically used to determine the mechanical wear evolution of a packaging system. Damage estimations can be performed using a Rainflow method, but continuous stress recording is required. However, this recording is not always possible, so global transportation vibrations are represented by the power spectral density (PSD). In this paper, the damage of a system according to the Wöhler curve was studied. The Basquin model was used to determine the mechanical wear evolution of the system, and the mechanical behaviour was established by extracting the Basquin coefficient b and the constant system C from the Wöhler curves. A Wöhler curve was further realized for a packaging system, and its Basquin coefficient b and system constant C were also extracted. Damage is estimated by the accumulation of the stress cycles using the Palmgren–Miner rules. In this paper, the maximum peaks of the cycle were detected in a signal. The density probability of the maximum stress apparition was also constructed from a multivariate Gaussian model. PSDs have the same statistical properties as the corresponding temporal events, so these statistical properties were extracted by the spectral moment method. Furthermore, a damage equation was proposed using the PSD, and the damage induced by different PSDs was determined from the damage equation and compared with the actual duration on a vibration table.     

Determination of the surface tension of liquid stainless steel

The surface tensions (σ) and temperature dependencies (dσ/dT) of several commercial 4-series ferritic stainless steels have been measured using the sessile drop technique on an Al₂O₃ plate over the temperature range 1789 to 1883 K in an atmosphere of high purity (P _{O 2} < 10^?19 MPa) argon gas. Precise densities of liquid stainless steels have also been obtained using the modified sessile drop method in order to calculate accurate values of the surface tension. The surface tensions of liquid stainless steels decreased markedly with increasing sulphur concentration in the steels. The variation of surface tensions of liquid stainless steels can be described by the following equation σ = 1790 ? 182 ln (1 + 260a _S) (mN/m) when only S is considered or σ = 1820 ? 304 ln (1 + 383a _O) ? 182ln (1 + 260a _S) (mN/m) when both S and O are considered. The equations apply to the following compositional ranges: mass%O = 0.0022–0.0064, mass%S = 0.0008–0.05. The temperature coefficient of the surface tension (dσ/dT) of liquid stainless steel was found to change from negative to positive at a sulphur concentration of about 30 mass ppm in the steel. Nitrogen was found to have little effect on the surface tension of liquid stainless steel.     

Einfluss von Temperatur und Vorverformung auf das plastische Werkstoffverhalten von modernen Karosseriestählen

Influence of temperature and prestraining on the plastic material behaviour of modern sheet steels for autobody applications Within the scope of a common research project of the automotive and steel industry, characteristic values describing the plastical behaviour of 20 sheet steels have been determined. In detail, quasistatic tensile tests at the testing temperatures ‐40 °C, 23 °C and 100 °C were carried out to obtain flow curves for the as delivered materials as well as for steels after a defined prestraining or heat treatment. Additionally, sheet metal testing led to forming limit diagrams and limiting drawing ratios including the working ranges for deep drawing. The results of the tensile tests showed significant differences between steel groups with regard to their strain hardening behaviour, which can be described by the ratio of yield and tensile strength R_p0,2/R_m or the Θ_IV‐value, and their temperature sensitivity. Within one steel group, consisting of steels with similar strain hardening behaviour, it might be possible to determine flow curves of one steel in a defined condition in order to calculate the flow curves of other steels with different strength. An advantage would be a lesser number of experimental tests which have to be performed in order to supply reliable input data for numerical material and component modelling.     

Effect of stress dependent creep ductility on creep crack growth behaviour of steels for wide range of C*

Abstract

In this work, the effect of stress dependent creep ductility on the creep crack growth (CCG) behaviour of steels has been investigated by finite element simulations based on ductility exhaustion damage model. The relationship between the transition region of creep ductility and the transition behaviour of CCG rate on da/dt-C* curves has been examined and the CCG life assessments of components and CCG resistance of materials for a wide range of C* were discussed. The results show that with increasing the transition region size of creep ductility, the transition C* region size on da/dt-C* curves increases. With moving transition region position of creep ductility to high stress region (increasing transition stress levels), the transition C* region on the da/dt-C* curves also moves to high C* region. Decreasing transition stress levels and transition region sizes of creep ductility and increasing the lower shelf and upper shelf creep ductility values can improve the CCG resistance of materials. If the extrapolation CCG rate data from the high C* region or from the transition C* region are used in life assessments of the components at low C* region, the non-conservative or excessive conservative results may be produced. Therefore, the CCG rate data should be obtained for a wide range of C* by long term laboratory tests or numerical predictions using the stress dependent creep ductility and model.     

Scaling and fractality in fatigue resistance: Specimen‐size effects on Wöhler's curve and fatigue limit

The present contribution investigates size effects on Wöhler's curve in accordance with dimensional analysis and intermediate asymptotics theory. These approaches provide a generalised equation able to interpret the specimen‐size effects on Wöhler's curve. Subsequently, using a different approach based on lacunar fractality concepts, analogous scaling laws are found for the coordinates of the limit‐points of Wöhler's curve, so that a theoretical explanation is provided to the decrement in fatigue resistance by increasing the specimen size. Eventually, the proposed models are compared with experimental data available in the Literature, which seem to confirm the advantage of applying fractal geometry to the problem.     

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.     

Fatigue crack propagation in Ti–6Al–4V subjected to high strain amplitudes

Fatigue crack propagation in circular Ti–6Al–4V specimens subjected to high strain amplitudes has been investigated. Crack closure was measured with an electrical potential‐drop technique. Closure was shown not to depend on strain ratio but to be a function of the applied strain range. At higher strain ranges, the crack was found to be closed for a smaller part of the load cycle than at lower strain ranges due to blunting of the crack tip. Furthermore, the use of a strain‐intensity approach to predict crack‐propagation rate was investigated, and it was found that for the upper parts of the da/dN curves the effective strain intensity yields good predictions. Also, the effective stress‐intensity factor was found to collapse the da/dN curves for different load ratios.     

Schnellbewertung von Dispersionsgefüge und mechanischen Eigenschaften karbidbildender Stähle

Fast Evaluation of dispersed Microstructure and mechanical Properties of Carbide forming Steels A possibility of a fast evaluation concerning the dispersed microstructure and the properties of C-, Cr- and Mn-alloy steels is presented. The dispersed microstructure was adjusted by precipitation and coarsening from the martensitic initial condition. The quick recording coercive field strength H_C and microstructural parameters obtained from scanning electronmicroscopic investigations were used in the relationship H_C-particle diameter d_p relative to a microstructure fast evaluation. Due to the repeated nucleation the M₃C carbides grow and coarse parallel and in particle generations. Thus always a particle size spectrum is obtained. A fast evaluation of properties is realized by the connection H_C – yield strength R_p0.2 / tensile strength R_m / hardness HV. Since H_C reacts on the size of precipitated particles, and the course H_C – time t / d_p / particle volume (d_p/2)³ encloses two maxima, which both separate the precipitation (A) and coarsening stage (V), at any H_C-value one of the attaching possibilities (A or V) must be excluded. This can be reached by considering the obtained temperature and time limiting values. The magnetic measuring method with the structure-sensitive quantity H_C yields to an assertion relative to the microstructual condition within one minute. The error amounts to ≤0.5%. The application of the H_C-measurement is time- and cost-economic. A special sample preparing is not necessary. The condition of the surface does not enter into the measuring result. The yielded connections H_C – R_p0.2 / R_m / HV can be used like a standard referred to the tested grades of steel.     

Theory of hydrogen-assisted crack growth

A model for hydrogen-induced cracking is proposed and developed on the assumption that hydrogen enters the embrittling process zone (EPZ) ahead of the crack-tip and promotes localized plastic flow which is proportional to its concentration. The formulae of the criterion for crack propagation,K _IH, and the crack growth rate dl/dt, are derived and applied to the experimental data of AISI4340 superhigh-strength steels.     

Load dependence of the apparent Knoop hardness of SiC ceramics in a wide range of loads

Silicon carbide (SiC) ceramics is a material with increasing use, due to its excellent mechanical properties, especially high hardness. In order to integrate this material into design process, we need to know its hardness as precise as possible. The Knoop hardness number (HK) is calculated using the expression: HK = α·F/d², where F is the applied load, d is the long diagonal of the resulting 1₀indentation and a is the Knoop indenter geometrical constant. In this paper, the Knoop hardness of SiC ceramics was measured in the applied load range from 4.9 to 98.07 N. For some materials measured “apparent” hardness value decreases with increasing applied test load (normal indentation size effect – ISE), while for some materials measured “apparent” hardness increases with increasing applied test load (reverse indentation size effect – RISE). Obtained results show the measured hardness exhibits the ISE. In the literature several models are given for the phenomenon explanation. We used the following models: Meyer's law (F = K·dⁿ), proportional specimen resistance – PSR (F = a₁·d + a₂·d²) and modified proportional specimen resistance – MPSR model (F = a₀ + a₁·d + a₂·d²). Results of regression analysis for all applied models show they can all be used for ISE analysis. “True” hardness was determined based on the PSR and MPSR model (HK_T = α·a₂). The obtained results were similar. If the specimen surface is carefully prepared and the range of loads is wide, the a₀ coefficient from MPSR model reaches small values and can be excluded. Therefore, for the calculation of SiC ceramics Knoop hardness, the simpler model (PSR) can be used.     

Describing the Flexural Behaviour of Cross-ply Laminates Under Cyclic Fatigue

The objective of this work is to derive modelling of the fatigue behaviour of cross-ply laminates from the experimental results obtained in the case of three-point bending tests. Modelling the fatigue behaviour is based on the stiffness reduction of test specimens. Firstly, experimental results are described using interpolation functions. Then, the characteristic coefficients of these functions are studied as function of the laminate properties and loading conditions. This approach allows to predict the fatigue life of composite laminates while avoiding a large number of fatigue tests. Wöhler curves are used to compare the experimental and analytical results, and a good agreement is found between the results. Next, a simple approach is considered to define a damage parameter. It is based on the analogy between the mechanical behaviour and the fatigue damage evolution of composite laminates during fatigue tests. The developed models are applied to analyse the influence of constituents on the fatigue behaviour and damage development of composite materials under fatigue loading.     

Struktur der Randschicht nichtrostender Stähle nach Tieftemperatur‐Nitrierung – eine Mößbauerstudie

Case structure of stainless steel after low temperature nitriding – a Mössbauer study Due to the nitriding of stainless steel at temperatures between 300 °C and 400 °C cases of high hardness and nitrogen contents ranges between 8wt.% and 12 wt.% could be prepared. In the present work the nitriding was performed by gas and plasmanitriding. The phase generation was investigated by use of the Conversion‐Mössbauer‐specrtoscopy (CEMS and XCMS) and the X‐ray diffraction. The chemical composition was determined by GDOS and the hardness test using the Martens‐hardness under load. In spite of different principles of action no significant differences between the structure and properties of the gas and plasmanitrited samples could be observed within the bounds of the used test methods. Clear differences were found in the nitriding behaviour of different steels.     

Anisotropy of Young's Modulus of DD6 from 25 to 1200 °C Based on Nondestructive Dynamic Method

The Young's modulus is an essential factor for improving turbine blade design. The present study aims to obtain the flexural frequencies (f₁) and corresponding dynamic Young's modulus (E_d) of Ni-based single-crystal DD6 across a temperature range of 25–1200 °C using a nondestructive dynamic testing method. The relationship between the elastic constants and various crystal orientations is derived by employing the transformation of the elastic matrix. In addition, finite element (FE) simulation is conducted to calculate the flexural frequency (f₁) of the [001] crystal orientation. The findings indicate that the dynamic Young's modulus (E_d) decreases as the temperature increases within the range of 25–1200 °C. Furthermore, the E_d values for different crystal orientations follow the trend: E_d[1] < E_d[11] < E_d[111]. This suggests significant anisotropy in the material. The normalized model, matrix transformation calculation method, and finite element method demonstrate high accuracy in predicting the elastic modulus of DD6, as evidenced by the good correspondence between the fitting curves obtained using the normalization method and the test results. These results have practical applications in engineering, particularly in turbine blade design and other applications, and serve as valuable references for mechanical property testing and finite element simulations.