Short crack approach for multiaxial fatigue assessment

A significant part of the fatigue life is spent during short crack growth. Therefore, modelling of short fatigue crack growth offers an opportunity to improve the accuracy of numerical life assessment. Besides stating some general remarks on the short crack approach itself and on multiaxial fatigue criteria, a short crack growth based fatigue life prediction approach for multiaxial non‐proportional loading is presented. This approach accounts for the geometrical size effect by considering the geometry correction functions for semi‐elliptical surface cracks in inhomogeneous gradient stress fields. The geometrical size effect is becoming significant for notch radii smaller than four times the defined technical crack size. Additionally, life influencing factors due to the statistical size effect have been taken into account. The comparison of calculated and experimentally observed fatigue lives of shouldered shafts made of S460N with notch radii of 0.2 to 4.0 mm under non‐proportional tension and torsion loading yields a satisfying accuracy.     

Vorhersagemodell für die Wachstumsraten kurzer Risse auf der Basis von Kmax‐konstant‐Versuchen an M(T)‐Proben

Prediction model for the growth rates of short cracks based on K_max‐constant tests with M(T) specimens The fatigue crack growth behaviour of short corner cracks in the Aluminium alloys Al 6013‐T6 and Al 2524‐T351 was investigated. The aim was to determine the crack growth rates of small corner cracks at stress ratios of R = 0.1, R = 0.7 and R = 0.8 and to develop a method 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 pre‐cracks 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 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 developed on the basis of K_max‐constant tests with long cracks that gives a good and conservative prediction of the short crack growth rates.     

Langsames Ermüdungsrisswachstum in Aluminium‐ und Magnesiumgusslegierungen in Raumluft und in Vakuum

Slow fatigue crack growth in aluminium and magnesium cast alloys in ambient air and in a vacuum The influence of ambient air on near threshold fatigue crack growth in the magnesium cast alloys AZ91 hp, AM60 hp and AS21 hp and in the aluminium cast alloy AlSi9Cu3 has been investigated. Fatigue crack growth properties at a cycling frequency of 20 kHz in ambient air and in a vacuum are significantly different. In a vacuum, the threshold stress intensity amplitude of the aluminium alloy is 30% higher than in ambient air, and the threshold values of the magnesium alloys in a vacuum are up to 85% higher than in ambient air. Moisture of ambient air is responsible for accelerated crack growth at growth rates below 1–3 × 10⁻⁹ m/cycle (AlSi9Cu3) and 2–5 × 10⁻⁸ m/cycle (magnesium alloys), respectively. In ambient air a minimum crack growth rate of 5 × 10⁻¹¹ − 2 × 10⁻¹⁰ m/cycle was observed, whereas far lower minimum growth rates were found in a vacuum.     

Einfluss der Schweißparameter auf das Ermüdungsverhalten hochfester Baustähle

High strength low alloy steels are used in many different engineering areas. A commonly used joining technique for those steels is fusion welding. Generally, these components have to withstand fatigue due to dynamic loading. Using thermal joining techniques affect the mechanical properties of the steel. This study focuses on the influence of the heat input on the microstructure of high strength low alloy steels (S690). Furthermore, the fatigue behaviour with special regard to crack initiation and crack propagation is characterized.     

Modellierung des Ermüdungsrisswachstums in Schweißverbindungen unter Berücksichtigung von Schweißeigenspannungen

The present paper contains research results determined within the framework of a project called IBESS (?Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“) by the Materials Mechanics Group of the Technische Universität Darmstadt [1]. Aim is to calculate the fatigue life of welded joints by taking into account the effect of residual stresses and the influence of the weld toe geometry. Here, the fatigue life is regarded as period of short fatigue crack growth. Two and three dimensional finite element models, with cracks as initial defects, are constructed for this purpose. Fatigue crack growth analyses are performed by using the node release technique together with the finite element program ABAQUS. The welding residual stresses as well as the plasticity induced crack closure effects are considered. Structural calculations are performed in order to introduce residual stress fields in finite element models. The calculated compressive residual stress field matches the measured one especially in the weld notch area. The effective cyclic J‐integral (ΔJ_eff) is used as crack tip parameter in a relation similar to the Paris equation for the calculation of the fatigue life. For this purpose, a Python code was written for the determination of ΔJ_eff at every crack length phase. The calculated fatigue lives were compared with experimental data and a good accordance between both results was achieved. The impact of welding residual stresses on ΔJ_eff as well as on the fatigue life during short crack growth was investigated. As expected, results revealed that at lower stress amplitude, a compressive residual stress field is favorable to the fatigue life, whilst a tensile residual stress field is unfavorable. The influence of residual stresses can be neglected only for large load amplitudes.     

Verfahren zur vollständigen Ermittlung der R‐Abhängigkeit des Rissausbreitungsverhaltens mit nur einer Probe

Procedure for the determination of the complete R‐dependency of the crack growth behaviour with only one specimen A new concept for fatigue crack propagation tests has been developed. Using a single specimen, it is possible to determine fatigue crack growth curves (da/dN ‐ ΔK) for every stress ratio between R = 0.9 and R = ‐1. Additionally, the new concept also provides threshold values for fatigue crack growth for different values of R and K_max. In combination with a continuous crack length measurement tool (such as the DC potential drop method) this testing procedure can be performed with minimal effort of personnel and time. The test procedure consists of a sequence of K_max‐constant tests with decreasing crack growth rates. As the applied K_max is increasing stepwise there should be no load history effects. According to the procedures described in the ASTM Standard E 647, the results using this new testing procedure fit very well to the da/dN ‐ ΔK curves generated with different specimens. The tests also fulfil all the requirements of ASTM Standard E 647.     

Rissfortschritts‐ und Ermüdungsverhalten der Aluminiumlegierung EN AW‐6060 nach ECAP und nachgelagerter Wärmebehandlung

Crack growth and high cycle fatigue behaviour of an AA6060 aluminium alloy after ECAP combined with a subsequent heat treatment Crack growth properties of the Al‐Mg‐Si alloy AA6060 as well as the high cycle fatigue behaviour have been investigated after equal‐channel angular pressing (ECAP). In our study, experiments have been conducted on different stages of microstructural breakdown and strain hardening of the material as they were present after different numbers of ECAP passes. A bimodal condition, obtained after two pressings, and a homogeneously ultrafine‐grained condition after eight repetitive pressings have been investigated. Furthermore, optimized conditions with an enhanced ductility, produced by ECAP processing combined with a following short‐time aging treatment were included into the study. Crack growth experiments have been conducted in the near‐threshold regime and the region of stable crack growth, covering a range of load ratios from R = 0.1 up to 0.7. It was found that the lowered fatigue threshold ΔK_th of the as‐extruded material can be enhanced by the combination of ECAP and short‐time aging, owing to the increased ductility and strain hardening capability of this material. By means of SEM investigations and tensile tests, the crack growth properties of the different conditions were related to microstructural and mechanical features. In fatigue tests, load reversals up to failure and the fatigue limit for an as‐extruded condition and an optimized condition after two ECAP‐passes have been compared to the coarse grained initial condition and a remarkable increase in fatigue strength was noted.     

Artgleiche und artverschiedene reibrührgeschweißte Verbindungen aus AA2124+25 % SiC und AA2024

Similar and dissimilar friction stir welded joints made from AA2124+25 % SiC and AA2024 An aluminium matrix composite (AMC) consisting of an AA2124 matrix reinforced by 25 vol.% SiC particles was used to produce similar AMC+AMC and dissimilar AMC+2024‐T3 joints by friction stir welding. When the particle reinforced composite was located on the retreating side, material mixing was less intense for dissimilar joints. Nevertheless, a higher strength has been determined for this arrangement due to a hook‐like interlocking of both materials. Tensile test and S‐N fatigue behaviour is shown to be compromised by alignment of the reinforcement particles perpendicular to loading direction already in the particle reinforced base material. Welding residual stresses were determined through the cut‐compliance method in terms of stress intensities acting at the crack tip. The underlying residual stress distribution in the un‐cracked structure was calculated by the weight function method. Longitudinal tensile residual stresses were found to be higher in the monolithic material as compared to the particle reinforced composite. This held true both for similar and within dissimilar joints. Growth behaviour of cracks crossing the joint line was described and correlated with residual stresses for similar joints.     

Crack growth predictions using a strip‐yield model for variable‐amplitude and spectrum loading

Fatigue‐crack‐growth tests were conducted on compact, C(T), specimens made of D16Cz aluminum alloy. Constant‐amplitude tests were conducted over a range of stress ratios (R = P_min/P_max = 0.1 to 0.75). Comparisons were made between test data from middle‐crack tension, M(T), specimens from the literature and C(T) specimens. A crack‐closure analysis was used to collapse the rate data from both specimen types into a fairly narrow band over many orders of magnitude in rates using proper constraint factors. Constraint factors were established from single‐spike overload and constant‐amplitude tests. The life‐prediction code, FASTRAN, which is based on the strip‐yield‐model concept, was used to calculate the crack‐length‐against‐cycles under constant‐amplitude (CA) loading and the single‐spike overload (OL) tests; and to predict crack growth under variable‐amplitude (VA) loading on M(T) specimens and simulated aircraft loading spectrum tests on both specimen types. The calculated crack‐growth lives under CA and the OL tests were generally within ±20 % of the test results, the predicted crack‐growth lives for the VA and Mini‐Falstaff tests on the M(T) specimens were short by 30 to 45 %, while the Mini‐Falstaff+ results on the C(T) specimens were within 10 %. Issues on the crack‐starter notch effects under spectrum loading are discussed, and recommendations are suggested on avoiding these notch effects.     

Bending rotation HCF testing of pseudoelastic Ni‐Ti shape memory alloys

In the present work, a computer‐controlled test rig for simultaneous fatigue testing of several pseudoelastic NiTi wires through bending rotation is described. Bending rotation fatigue (BRF) testing represents a displacement‐controlled experiment where a straight wire is bent into a semi‐circle und forced to rotate around its axis. Thus, each point on the wire surface is subjected to alternating tension and compression. A test rig, which allows to control loading amplitudes, rotation frequencies and temperatures is described. We report preliminary results of an experimental program, which aims for a better understanding of fatigue lives, crack initiation, and crack growth in pseudoelastic NiTi wires. It was found that a good surface quality is of utmost importance to avoid early crack initiation. Wöhler curves of pseudoelastic NiTi wires typically show two different regimes depending on the maximum imposed surface strain during bending rotation fatigue testing. Larger strain amplitudes, which are associated with macroscopic formation of stress‐induced martensite, result in relatively low fatigue lives (LCF regime). In contrast, cycle numbers exceeding 10⁷ were obtained for strain amplitudes where no large scale stress‐induced formation of martensite occurred (HCF regime).     

Thermisch‐mechanisches Ermüdungsverhalten der partikelverstärkten Aluminiumknetlegierung EN AW‐6061‐T6 und die Entwicklung von Eigenspannungen im Matrixwerkstoff unter thermisch‐mechanischer Beanspruchung

Thermal mechanical fatigue behaviour of particle reinforced EN AW‐6061‐T6 and development of residual stresses in the matrix material by thermal mechanical loading The behaviour of non reinforced and 15 Vol.‐% α‐alumina particle reinforced wrought aluminium alloy EN AW‐6061‐T6 in thermal mechanical fatigue loading was investigated at different maximum temperatures. The tests were performed in strain controlled mode by means of an electro‐mechanical testing machine. Alternating load deformation and life cycle behaviour either materials were compared. It came out, that the reinforcement leads to an decreasing thermal mechanical fatigue life cycle while keeping constant the maximum temperature and mechanical loading. The two materials showed softening behaviour due to high maximum temperatures of 573 K to 673 K. However, there is an intense scatter of the number of cycles to failure of the non reinforced alloy aggravating the interpretation of the results. On the other hand the thermal mechanical life cycle increases in combination with increasing maximum temperatures. Simultaneously the part of plastic deformation in mechanical loading increases for both materials, while for a constant total strain range the effective maximum and minimum stresses are decreasing. Furthermore, the development of residual stresses in the matrix of the reinforced alloy by thermal mechanical fatigue loading was analysed. It was observed that only small absolute values of residual stresses will be obtained for these loads. Nevertheless, tendencies of mounting tensile residual stresses can be identified in the direction of thermal mechanical fatigue loading and subsequently reduction of the residual stresses.     

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.     

Determination of local characteristics for the application of the Weakest‐Link Model

The Weakest‐Link model is based on defects that are statistically distributed within the material with local stress. The failure at least at one defect causes the failure of the total structure. Based on this model, the so‐called statistic size effect can be evaluated in the case of cyclic loading and in the case of static loading the failure behaviour of ferritic steel within the brittle fracture range is highlighted. The application of the Weakest‐Link model requires the allocation of the local characteristics ‐ surface and / or volume ‐ to the discrete points of the stress. By using the method “SPIEL” which is independent from the FE code used, the allocation of couples of values ‐surface and stress and / or volume and stress ‐ by a suitable choice of unit load cases is possible. In consequence of the method “SPIEL” particularities are to be taken into consideration. In the present paper these particularities will be described exemplarily for the FE programs ABAQUS¹ and ANSYS².