Description of fatigue damage in carbon black filled natural rubber

The present paper describes macroscopic fatigue damage in carbon black‐filled natural rubber (CB‐NR) under uniaxial loading conditions. Uniaxial tension‐compression, fully relaxing uniaxial tension and non‐relaxing uniaxial tension loading conditions were applied until sample failure. Results, summarized in a Haigh‐like diagram, show that only one type of fatigue damage is observed for uniaxial tension‐compression and fully relaxing uniaxial tension loading conditions, and that several different types of fatigue damage take place in non‐relaxing uniaxial tension loading conditions. The different damage types observed under non‐relaxing uniaxial tension, loading conditions are closely related to the improvement of rubber fatigue life. Therefore, as fatigue life improvement is classically supposed to be due to strain‐induced crystallization (SIC), a similar conclusion can be drawn for the occurrence of different types of fatigue damage.     

Deformation behaviour of elastomeric matrix composites under static loading conditions

Damage mechanisms of elastomeric matrix composites (EMCs), propose a complex interplay between material properties and service conditions. The occurrence of defects such as the cavitations in EMCs specimens in using conditions is an important problem. This situation requires the well understanding of the damage mechanisms of EMCs used in automotive and aeronautical fields.Elastomeric matrix composites subjected to static and fluctuating loads basically fail due to the initiation and growth of defects (cracks, cavities, etc.). In fact, high hydrostatic pressures influence mechanical behaviours of EMCs. This paper reviews the damage mechanism of EMCs under static loading. In order to evaluate mechanical properties and fracture behaviour of EMCs, in situ observations were made by using X-rays computed tomography (CT). Two types of specimens are investigated in this work; Natural rubber, NR vulcanised and reinforced by carbon black, and synthetic rubber (styrene-butadiene-rubber), SBR. A detailed study was carried out by scanning electron microscopy (SEM) for a better understanding the damage mechanisms and confirming the CT results.     

Deformation and life assessment of high temperature materials under creep fatigue loading

The knowledge of mechanical long term behaviour under static and cyclic loading for high temperature components requires methodologies for life assessment in order to employ the full potential of materials. A phenomenological life time prediction concept which was developed for multi‐stage creep fatigue loading demonstrates the applicability of rules for synthesis of stress strain path and relaxation including an internal stress concept, as well as mean stress effects. Further, a creep fatigue interaction concept which was also developed covers a wide range of creep dominant loading as well as fatigue dominant loading. Service‐type experiments conducted at different strain rates and hold times for verification purposes demonstrate the acceptability of life prediction method for variation of conventional 1 %Cr‐steels as well as modern high chromium 9‐10 %Cr‐steels. Generally, the service life of components is influenced by multi‐axial behaviour. Multi‐axial experiments with e.g. notched specimens and with cruciform specimens accompanied by advanced methods for calculation of stress strain path and life time prediction stress conditions are of future interest.     

Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions

Service conditions experienced by rubber components often involve cyclic loads which are more complex than a constant amplitude loading history. Consequently, a model is needed for relating the results of constant amplitude characterization of fatigue behaviour to the effects of variable amplitude loading signals. The issue is explored here via fatigue crack growth experiments on pure shear specimens conducted in order to evaluate the applicability of a linear crack growth model equivalent to Miner's linear damage rule. This model equates the crack growth rate for a variable amplitude signal to the sum of the constant amplitude crack growth rates associated with each individual cycle. The variable amplitude signals were selected to show the effects of R-ratio (ratio of minimum to maximum energy release rate), load level, load sequence, and dwell periods on crack growth rates. In order to distinguish the effects of strain crystallization on crack growth behaviour, two filled rubber compounds were included: one that strain crystallizes, natural rubber, and one that does not, styrene-butadiene rubber. The linear crack growth model was found to be applicable in most cases, but a dwell effect was observed that is not accounted for by the model.     

Interactive creep–fatigue crack growth of 2024‐T3 Al sheets: selective transitional functions

Interactive creep–fatigue on aeronautical materials has been of a great concern to engineers and researchers. There are still more fundamental issues to be addressed. In this regard, 2024‐T3 Al sheets are considered to study the transitional behaviours that incorporatematerial, loading and geometry effects in the interactive creep–fatigue process. A dual‐scale fatigue crack growth da/dN‐ΔS model that includes microscale, macroscale and large scales is proposed based on the volume energy density criterion. The model generates the transitionalised crack length (TCL) compared with the fictitious crack length (FCL) yielded from the da/dN‐ΔK model that is only restricted to monoscaling. Crossover points are observed across TCL and FCL curves. With stress amplitude being fixed, three levels of mean stress are employed to discuss the variational effects of transitional functions (TFs). Applied loading conditions have an appreciable effect on the fatigue life cycles of 2024‐T3 Al sheets. Variation of R ratios leads to the interactive creep–fatigue behaviour and further enforces the selective TFs in the inherent multiscaling process. TCLs and FCLs are compared with test data of the 2024‐T3 Al sheet. Rationality and superiority of the dual‐scale crack growth model are validated.     

多壁碳纳米管填充丁苯橡胶复合材料的研究

采用浓硝酸(HNO3)氧化处理后的多壁碳纳米管(MWNTs)与丁苯橡胶(SBR)及其他配合剂在开炼机上进行混炼加工制备MWNTs／橡胶复合材料，并与炭黑补强橡胶体系进行对比，进而研究了MWNTs／橡胶复合材料的物理性能，并初步探讨了该材料微观结构与性能之间的关系。结果表明：随着MWNTs质量百分含量的增加，橡胶复合材料的力学性能也随之增高；MWNTs／橡胶复合材料的抗撕裂强度(25．9kN／m)、硬度(58)、磨耗(0．22mL/1．61km)性能较炭黑／橡胶体系要好。由MWNTs补强的橡胶对开发具有低滚动滞后性和抗疲劳损失的轮胎胎面胶将有很大的实用潜力。     

Effects of particle size and structure of carbon blacks on the abrasion of filled elastomer compounds

The effects of the particle size and structure of various carbon blacks on friction and abrasion behavior of filled natural rubber (NR), styrene–butadiene rubber (SBR) and polybutadiene (BR) compounds were investigated using a modified blade abrader. The effect of particle size and structure on abrasion resistance should be considered for the optimum design of desired wear properties. Characteristic parameters were introduced from the particle size and the structure of carbon blacks, with a linear relationship between the Young’s modulus and these characteristic parameters. The frictional coefficient depended not only on the particle size, but also on the structure of carbon black. The rates of abrasion were decreased with increasing surface area and developing structure of carbon blacks. Abrasion rates of the compounds were found to be proportional to a power n of the applied frictional work input. It was also observed that BR compounds caused much slower wear than NR and SBR compounds. The worn surfaces of the rubber compounds filled with carbon black having smaller particle size and a more developed structure showed narrower spaced ridges and better abrasion resistance. It means that smaller particle size and better structure development of carbon black resulted in improved abrasion resistance.     

Monotonic and Cyclic Deformations of Case‐Hardened Steels Including Residual Stress Effects

Abstract: Monotonic and cyclic deformations of case‐hardened steel specimens under axial loading were investigated experimentally and analytically. A finite element (FE) model for the case‐hardened specimens was constructed to study multiaxial stresses due to different plastic flow behaviour between the case and the core, as well as to evaluate residual stress relaxation and redistribution subsequent to cyclic loading. The multiaxial stress is shown to increase the effective stress on the surface, and, therefore, unfavourable to yielding or fatigue crack nucleation. The residual stresses are shown to relax or redistribute, even in the elastic‐behaving region, when any part of a case‐hardened specimen or component undergoes plastic deformation. Multi‐layer models were used to analyse and predict monotonic and cyclic deformation behaviours of the case‐hardened specimen based on the core and case material properties, and the results are compared with the experimental as well as FE model results. The predicted monotonic stress–strain curves were close to the experimental curves, but the predicted cyclic stress–strain curves were higher than the experimental curves.     

Prediction of creep crack growth in the presence of residual stress

Abstract

The mechanisms of creep crack growth are presented and the relationship between creep crack growth rate and uniaxial creep properties identified. Cracking under primary, secondary and combined primary and secondary loading is considered. The concepts described are applied to cracking in compact tension specimens of Type 316H austenitic stainless steel and Type 347 weld metal, each of which had previously been subjected to pre-compression to generate a tensile residual stress adjacent to the crack tip. Examples of the residual stress distributions produced before and after creep relaxation are presented and used to predict the crack growth anticipated. Comparisons are made between the behaviour of the two steels. Sensitivity studies are included to determine the extent to which the predictions are affected by the choice of material properties and analysis employed. For secondary loading only, it is shown that the amount of cracking predicted is relatively insensitive to the initial residual stress present.     

Modelling tail effects in creep-crack initiation and growth for 316L stainless steel

For complex loading history (creep and fatigue) applied to engineering components, assessment procedures generally estimate the crack initiation and growth by using the summation of continuous fatigue and pure creep crack growth rates. This text deals with the pure creep correlation established in laboratory tests and applied to components subjected to creep-fatigue loading. The trend of the creep opening displacement history superimposed onto the crack progress is sufficient to predict what kind of tail effect will occur when plotting ? vs. C*. The exponent of this correlation is demonstrated to be very close to unity, whatever creep stage is concerned. The contribution of either the material behaviour or the crack extension to the ? -C* correlation is discussed.     

Damage mechanisms in natural (NR) and synthetic rubber (SBR): nucleation,growth and instability of the cavitation*

Elastomeric matrix composites (EMCs) subjected to static and fluctuating loads basically fail due to the nucleation and growth of defects. Also, high hydrostatic pressure can influence the mechanical behaviour of EMCs. The change in behaviour of EMCs due to the nucleation of cavitations under hydrostatic pressure is studied here to understand the mechanics underlying the damage mechanism. Two types of materials for pancake specimens are used in this study; natural rubber (NR) vulcanized and reinforced by carbon black and synthetic rubber (styrene‐butadiene‐rubber, SBR). In situ observations of uniaxial tension and torsion tests are also presented by using X‐ray computed tomography (CT) (medical scanner) and the results are compared with those from scanning electron microscopy (SEM).     

Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions

This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.     

Influence of surface residual stresses on gigacycle fatigue response of high chromium cold work tool steel

The effect of surface compressive residual stresses (RS) induced by surface grinding and polishing on the gigacycle fatigue behavior of medium‐carbon high‐chromium alloy cold work tool steel was evaluated. Two test series were performed: Specimens of series I revealed high compressive RS of about ‐800 MPa at the surface, resulting from grinding with fine emery paper, which treatment had definitely a beneficial influence on the fatigue endurance strength. The existence of surface RS was also revealed to be responsible for the location of the fatigue crack initiation. High compressive RS favored internal crack origins. In this case crack nucleation sites were primary carbide clusters in the interior of the specimen, forming so‐called fish‐eyes at the fracture surface. In contrast, specimens of test series II had only very low RS, which enabled crack initiation near/at the surface at primary carbides/clusters. Furthermore, it has been shown that the high initial RS are prone to partial relaxation through cyclic loading for which the mechanisms are currently unknown. In this case near‐surface induced failure was obtained. It was possible to confirm the experimentally obtained data by the use of the concept of local fatigue strength as function of effective RS. The relaxation of high initial RS was experimentally confirmed through RS measurements at runout specimens (10¹⁰ cycles without failure).     

Study of the fatigue lifetimes and crack propagation behaviour of a high speed steel as a function of the R value

High speed steels, such as the alloy H‐13, when used as forging dies are subjected to both wear and cyclic loading, and both of these factors can affect the useful life of such dies. It follows that it is of some importance to determine the fatigue characteristics of such steels. However, fatigue studies of such alloys are limited, especially with respect to fatigue crack propagation (FCP) behaviour as a function of mean stress, and therefore more detailed studies are necessary. In the present study, the fatigue lifetimes and the crack propagation behaviour of a high speed steel were experimentally investigated in laboratory air under different stress ratios, R. A modified linear‐elastic fracture mechanics (LEFM) approach was applied to analyze the experimentally‐obtained FCP behaviour. The predicted S–N curves and crack growth behaviour for a wide range of R ratios agree well with the experimental data, and the modified LEFM approach is therefore considered to be useful for evaluation of the fatigue behaviour of this class of high strength steels.     

Characterization of the nonlinear fracture resistance parameters for an aviation GTE turbine disc

The effects of crack growth rate model formulation, based on the elastic‐plastic and undamaged/damaged creep crack tip fields on the behaviour of low‐cycle fatigue and creep fracture resistance parameter behaviour, are represented by numerical calculations. The crack growth rate models include the fracture process zone size and damage parameters. An aviation gas turbine engine (GTE) rotating turbine disc is the focus of this innovative application of basic analytical and numerical solutions. For the GTE turbine disc, the constraint parameters, local fracture process zone sizes, and nonlinear plastic (K_p) and creep (K_cr) stress intensity factors are calculated by finite element analysis to characterize the fracture resistance along the semielliptical crack front as a function of the flaw aspect ratio, operation temperature, and disc rotation speed. Predictions of the creep‐fatigue crack growth rate and residual lifetime are given for different combinations of operation loading conditions and damage of the GTE turbine disc.     

TIME-DEPENDENT FATIGUE CRACK GROWTH IN TITANIUM METAL MATRIX COMPOSITES

Abstract The interaction of fatigue and creep in a titanium metal matrix composite was studied by employing loading frequencies of 10 Hz (in both air and vacuum environment) and 0.1 Hz with and without hold times (in air) at 500°C. It was shown that, for the same loading frequency, the crack growth rate is lower in vacuum than in air. In an air environment, however, where the influence of load-related creep and environmental effects exist, it was shown that a decrease in the loading frequency leads to a decrease in the crack growth rate. This behavior is interpreted in terms of the redistribution of fiber and matrix stresses occurring in response to the creep-related relaxation of matrix stresses. The result of this stress redistribution is the generation of a compressive axial residual stress in the matrix phase in the region of the composite ahead of the crack tip. As the crack bridges the fibers in this region, the release of the matrix residual compressive stress leads to the closure of the matrix fractured surfaces at the crack tip, thus leading to a decrease in the crack tip driving force. To support this concept, experimental measurements of the crack opening displacement at different loading frequencies are presented. In addition, a simple model is proposed to describe the nature of the residual stresses developed in the matrix phase during cyclic loading. Results of this model have been examined using finite element analysis. The influence of time-dependent effects during a fatigue cycle was, furthermore, investigated by carrying out high frequency fatigue tests on specimens which have been previously subjected to creep deformation. Results of these tests in terms of the crack growth rate and associated crack closure, support the conclusion that a predeformed matrix produces a decrease in the crack growth rate of the corresponding composite.     

Crack growth behaviour of P92 steel under creep and creep–fatigue conditions

Abstract

High temperature creep and creep–fatigue crack growth tests were carried out on standard compact specimens machined from ASME P92 steel pipe. The effects of various loading conditions on crack growth behaviours were investigated. Crack initiation time was found to decrease with the increasing initial stress intensity factor under creep condition and further to decrease by the introduction of fatigue condition. For creep test, the crack growth rate can be well characterised by the facture mechanics parameter C*. For creep–fatigue test, the crack growth behaviour is dominated by the cycle dependent fatigue process when the hold time is shorter, but it becomes dominated by the time dependent creep process when the hold time becomes longer.     

Festigkeit und Spannungsabbau bei der dynamischen Belastung von Stahl- und Aluminiumproben mit bekannten Eigenspannungen

Strength and Relaxation of Stress During Dynamic Loading of Steel and Aluminium Specimens with known Residual Stress Distributions Residual stresses of the first kind can be introduced in multiply – connected bodies without accompanying changes in the material. The circular ring represents the simplest example in this group. For the circular ring the residual and applied stresses in a fatigue test can be calculated accurately with relations from the theory of elasticity. Circular rings with and without residual stresses were subjected to fatigue testing. It was established that tensile residual stresses reduce the fatigue life and compressive residual stresses have the opposite effect, with the stresses referred to the point of crack initiation. The fatigue behaviour is altered appreciably even by small magnitudes of residual stress. The effect on fatigue life is the same, whether at the point of crack initiation a residual stress or a mean stress of the same magnitude and direction acts. The stress relaxation depends primarily on the difference between the maximum superposed stress and the yield strength or the 0.2% proof stress. The degree of relaxation is particularly high when the yield strength is reached. The first few cycles in a fatigue test are important for the fading of stress. The state of residual stress changes only slightly thereafter. The stress relaxation increases again somewhat only after a very large number of cycles. The changes observed when the sum of residual and loading stresses is below the yield strength may be attributed to the small plastic deformations in favourably oriented crystallites.     

Fracture Parameters for Natural Rubber Under Dynamic Loading

Abstract: An experimental study was conducted to evaluate the tear energy of unfilled and 25 phr carbon black‐filled natural rubber with varying loading rates. The variation of the tear energy with far‐field sample strain rate between 0.01 to 10 s^?1 was found to be different from tensile strip and pure shear specimens. Above a sample strain rate of 10 s^?1, the tear energy calculated from either specimen was comparable. The differences in the tear energy derived from the tensile strip and pure shear specimens were attributed to differences in the local crack tip stress state and strengthening of the material due to strain‐induced crystallisation. Both of these factors resulted in crack speeds 3–4 times higher in the pure shear specimen as compared to the tensile strip specimen. Finite element analysis (FEA) indicated that fracture would initiate at the crack tip either when the strain energy density approached the material toughness or when the maximum principal stress and strain approached the material tensile strength and fracture strain, respectively. It was concluded that these parameters would be better than the tear energy in predicting fracture of natural rubber under dynamic loading.