Cyclic loadings and crystallization of natural rubber: An explanation of fatigue crack propagation reinforcement under a positive loading ratio

Natural rubber is known to have excellent fatigue properties. Fatigue crack propagation studies show that, under uniaxial tension loading, fatigue crack growth resistance increases with the loading ratio, even if the peak stress increases. Studies dealing with crack initiation confirm this trend. If strain induced crystallization is believed to play a major role in this reinforcement process, it is not clear yet by which mechanism this reinforcement takes place. Using SEM investigation, it is shown here that the reinforcement process is associated with strong crack branching in the crack tip region. From experimental results it is shown that under particular reinforcing loading condition a cyclic strain hardening process can be observed on the natural rubber which is able to overcome classically observed softening effects. A cumulative strain induced crystallization process is proposed to explain the stress ratio effect on fatigue crack initiation and propagation properties of natural rubber.     

Fatigue resistance of natural rubber in seawater with comparison to air

Fatigue properties of filled natural rubber in seawater environment are investigated by uniaxial fatigue and crack propagation experiments, and the damage is analyzed by scanning electron microscopy. The behavior under relaxing and non-relaxing loading conditions is studied and the results are compared to those obtained in air environment. For relaxing loading conditions, fatigue behavior is the same in both environments. Under non-relaxing conditions at large strain levels, for which the influence of strain-induced crystallization is important, fatigue life is longer in seawater. Such behavior could be explained by increased internal temperatures of specimens tested in air due to lower heat conductivity of air as compared to seawater. Such conclusion is also supported by the damage mechanisms observed under non-relaxing loading conditions.     

Experiment and modeling of uniaxial tension fatigue performances for filled natural rubbers

A tension fatigue model of filled natural rubbers is investigated to study the contributions of two key factors, namely, the damage parameter and the specimen geometry used in the fatigue experiment. The uniaxial tension fatigue experiments were carried out for three filled natural rubber specimens with different geometry: a dumbbell simple tension specimen (STS), a dumbbell cylindrical specimen (DCS), and a hollow cylindrical specimen (HCS). The commonly used damage parameters for fatigue life prediction are discussed. The fatigue life prediction models are formulated using the measured tension fatigue life of the STS together with different damage parameters. The effectiveness of the models is established in terms of a correlation coefficient characterizing the error between the measured and predicted fatigue lives. It is concluded that all the damage parameters considered in the study can effectively estimate the tension fatigue life with correlation coefficients exceeding 0.9. The fatigue life model formulated for the STS was also found to be appropriate for predicting the fatigue life of specimens with different geometry (DCS and HCS) suggesting that the relationship between the tension fatigue life and the damage parameters is independent of the specimen geometry. One may thus conduct tension fatigue tests with STS alone in order to model the tension fatigue life of rubbers with alternate geometry.     

More insights into fatigue crack growth from experiments on steels and aluminium alloys—Thresholds

The paper deals with the influence of the R-ratio on the fatigue crack propagation threshold of different metallic materials. Based up on threshold data of steels, aluminium-alloys and two particulate-reinforced aluminium-alloys the threshold behaviour has been analyzed and a new model to describe the threshold behaviour has been deduced. With this model, which contains two quantities that can be deduced from special fatigue crack propagation tests, the threshold behaviour of different kind of materials can be explained. Finally, the existence of the threshold can be attributed to specific elastic parameters of the materials (shear modulus) and their microstructure.     

Derivation of crack closure and crack growth rate data from effective-strain fatigue life data for fracture mechanics fatigue life predictions

This study deals with the behavior of short cracks growing out of notches. Three types of load histories are used: (a) a fully-reversed constant amplitude history; (b) a periodic compressive overload history consisting of repeated load blocks containing one fully-reversed constant amplitude yield–stress magnitude cycle (the overload) followed by a group of smaller constant amplitude cycles having the same maximum stress as the overload cycle; (c) and a service strain history. Procedures are presented for deriving crack closure data and crack growth rate vs effective stress intensity factor range data from data obtained by subjecting a small number of smooth laboratory specimens to simple periodic compressive overload tests to obtain closure-free strain-life data. These procedures are illustrated in an example in which fatigue life predictions are made for a service strain history applied to notched plate specimens. The fatigue life predictions based on the measured and the derived crack closure and crack growth rate data are in good agreement with the experimentally determined fatigue lives.     

Improvements of multiaxial fatigue criteria computation for a strong reduction of calculation duration

Fatigue life criteria are tools used for engineering and designing against fatigue. Even if computers capacities increase more and more, the complex geometry of mechanical components treated nowadays require to improve the swiftness of the calculations realized in any point of the structure. This paper contains two proposals concerning the computation of the most commonly used fatigue criteria, whatever their formulation is based upon the critical plane concept or upon a global approach. The application of many fatigue criteria requires to examine all the material planes passing through the considered point either to find out the critical plane or to make some average of stress quantities over all of them. In both cases, all the possible oriented planes have to be explored. The first proposal deals with the way to obtain an homogeneous distribution of the orientation of the practically considered planes. The second proposal of this paper concerns the determination of the smallest circle surrounding to the loading path that describes the tip of the shear stress vector acting on a material plane during one stress cycle. The mean shear stress is determined by the centre of this circle; the shear stress amplitude and the alternate component of the shear stress are established from this circle also. The principles of these two proposals are explained in detail and the algorithms for the fastest calculations are given. The efficiency of the new proposals relatively to what is commonly realized is assessed in terms of time saving.     

Self-assembled natural rubber/silica nanocomposites: Its preparation and characterization

A novel natural rubber/silica (NR/SiO₂) nanocomposite is developed by combining self-assembly and latex-compounding techniques. The results show that the SiO₂ nanoparticles are homogenously distributed throughout NR matrix as nano-clusters with an average size ranged from 60 to 150 nm when the SiO₂ loading is less than 6.5 wt%. At low SiO₂ contents (4.0 wt%), the NR latex (NRL) and SiO₂ particles are assembled as a core-shell structure by employing poly (diallyldimethylammonium chloride) (PDDA) as an inter-medium, and only primary aggregations of SiO₂ are observed. When more SiO₂ is loaded, secondary aggregations of SiO₂ nanoparticles are gradually generated, and the size of SiO₂ cluster dramatically increases. The thermal/thermooxidative resistance and mechanical properties of NR/SiO₂ nanocomposites are compared to the NR host. The nanocomposites, particularly when the SiO₂ nanoparticles are uniformly dispersed, possess significantly enhanced thermal resistance and mechanical properties, which are strongly depended on the morphology of nanocomposites. The NR/SiO₂ has great potential to manufacture medical protective products with high performances.     

Computations of fatigue crack growth with strain gradient plasticity and an irreversible cohesive zone model

Computations of fatigue crack growth with a first-order strain gradient plasticity (SGP) model and an irreversible cohesive zone model are reported. SGP plays a significant role in the model predictions and leads to increased fatigue crack growth rates relative to predictions with classical plasticity. Increased magnitudes of tractions and material separation at the crack tip together with reduced crack closure appear as the cause for accelerated crack growth in SGP. Under plane strain conditions SGP appears as an essential feature of the development of the crack closure zone. Size effects are explored relative to changes in internal material length scale as well as to structural length scales.     

Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.     

Improvement of impact property of natural fiber–polypropylene composite by using natural rubber and EPDM rubber

In this research, vetiver grass was used as a filler in polypropylene (PP) composite. Chemical treatment was done to modify fiber surface. Natural rubber (NR) and Ethylene Propylene Diene Monomer (EPDM) rubber at various contents were used as an impact modifier for the composites. The composites were prepared by using an injection molding. Rheological, morphological and mechanical properties of PP and PP composites with and without NR or EPDM were studied. Adding NR or EPDM to PP composites, a significant increase in the impact strength and elongation at break is observed in the PP composite with rubber content more than 20% by weight. However, the tensile strength and Young’s modulus of the PP composites decrease with increasing rubber contents. Nevertheless, the tensile strength and Young’s modulus of the composites with rubber contents up to 10% are still higher than those of PP. Moreover, comparisons between NR and EPDM rubber on the mechanical properties of the PP composites were elucidated. The PP composites with EPDM rubber show slightly higher tensile strength and impact strength than the PP composites with NR.     

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.     

A method for modelling of fatigue life for rubbers and rubber isolators

A method for modelling fatigue life of rubbers and rubber isolators is presented in this paper. Firstly, a fatigue experiment is carried out for a rubber dumbbell cylindrical specimen and a rubber isolator. Based on the finite element analysis, the damage parameters including the strain energy density, the maximum principal Green–Lagrange strain and the effective stress are calculated and discussed. Secondly, three fatigue life prediction models are established by using the three damage parameters and using the relation between the measured fatigue life of a dumbbell cylindrical specimen and the computed value of the damage parameters. Thirdly, three proposed prediction models are used to investigate which one can be best used to predicting fatigue life of rubber isolators, taking a typical powertrain rubber isolator as studying example. The fatigue lives of the rubber isolator predicted by the three models are compared with the experimental life. The results demonstrate that the predicted fatigue lives of the rubber isolator using the three fatigue models agree well with the experimental fatigue life within a factor of four, and the model using the effective stress as the damage parameter can predict the fatigue life within a factor of two, which has the best accuracy among the three models.     

A fatigue model developed by modification of Gough’s theory, for random non-proportional loading conditions and three-dimensional stress fields

As a first stage, fatigue damage models proposed by some well-known references and the corresponding assumptions are discussed and some enhancements are proposed. Generally, these models are suitable for bending–torsion fatigue problems with zero mean stress and are restricted to cases where the numbers of cycles of the stress components are identical. In the present paper, a general fatigue model for the HCF regime is proposed. This model overcomes most of the shortcomings of the previous theories and is suitable for life assessment in three-dimensional stress fields. Furthermore, a different critical plane concept is introduced and a different life assessment algorithm is presented. Since results of the previous fatigue theories are generally validated by experiments done on simple components with simple loading time histories, the discrepancies exist among the various theories have not been invoked appropriately. In the current paper, validity of these theories as well as the modified versions proposed in the current paper and the new criterion is examined for more general cases with non-proportional random loadings and complicated geometries. Finally, results of the various theories are compared with the experimental results. Experimental results are prepared for both proportional and non-proportional cases. Significant enhancements are observed due to employing the proposed modifications, especially for three-dimensional stress fields and random loadings.     

Efficiency of algorithms for shear stress amplitude calculation in critical plane class fatigue criteria

Fatigue criteria that belong to the critical plane class necessitate unambiguous definitions of the amplitude and mean value of the shear stress acting on a material plane. This is achieved through the construction of the minimum circle circumscribing the path described by the tip of the shear stress vector on each plane. By definition, the centre and the radius of this circle provide the mean shear stress and the shear stress amplitude, respectively. The search of the minimum enclosing circle is an optimisation problem for which efficient numerical solution schemes are required. Several algorithms exist for similar situations; however these are not necessarily related to the fatigue strength of metals. In this paper some algorithms are studied to assess their computational efficiency within the engineering framework of the application of fatigue criteria of the critical plane type.     

A material and environment-dependent criterion for the prediction of fatigue crack paths in metallic structures

Crack growth under mode II cyclic loading was investigated in maraging steel, ferritic–pearlitic steel and TA6V. When ΔK_II exceeds a threshold value, cracks do not bifurcate but grow in mode II over a distance which increases with ΔK_II. Shear mode crack growth was much more extensive in maraging steel than in TA6V and ferritic–pearlitic steel. This result is discussed in relation with the cyclic behaviour of the materials and the importance of friction along the crack faces. The maximum growth rate criterion is shown to be suitable for the prediction of crack paths when shear mode crack growth is likely to occur.     

Correlation between the acoustic and dynamic mechanical properties of natural rubber foam: Effect of foaming temperature

Acoustic absorbing foam materials are produced from dry natural rubber (NR) with the addition of sodium bicarbonate as a blowing agent. The acoustical efficiencies of NR foams were studied, and the results show a significant influence of the viscoelastic and damping properties of the base matrix. Both of these properties are governed by the average cell size, relative density, crosslink density and number of cells per unit volume. The lowest foaming temperature, 140 °C, yielded the NR foam (NR 140) with the highest relative density, crosslink density, smallest average cell size and greatest number of cells per unit volume. Consequently, these foam cell characteristics resulted in a superior sound absorption coefficient and a high storage modulus, which indicates that the NR 140 foam exhibits a better elastic behavior. On the other hand, the NR foam that expanded at 160 °C (NR 160) exhibited great potential for insulating sound and possessed good damping properties, which was characterized by its high transmission loss and tan δ values.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Numerical simulation of plasticity induced fatigue crack opening and closure for autofrettaged intersecting holes

The autofrettage of intersecting holes leads to extremely high compressive residual stress fields. These stresses in combination with the plastic deformations decelerate fatigue cracks initiated at the hole intersection notch. Simulations of plasticity induced crack closure of such cracks are presented based on the strip yield and a finite element model. The strip yield model has been extended to allow for an input of residual stresses coming from elsewhere, e.g. from a finite element calculation or measurements. The calculations are applied for constant as well as variable amplitude loading. The numerical expense of the finite element based modelling for variable amplitude loading is still too high if millions of cycles have to be considered. Therefore, a new approximation method is proposed introducing compensatory load sequences. Simulation results are compared to experimentally determined results showing good agreement. However, the accuracy of crack initiation life estimates has turned out to provide a high potential for further improvement.