Fatigue Crack Growth in Rubber Materials

Fatigue crack growth (FCG) characteristic of rubber materials is a very important factor in determining the durability of the rubber products. Slight variations in compounding ingredients, mixing and the curing process or even in the loading conditions and several physical factors have an impact on the final FCG behaviour of rubber vulcanisates. Thus, possible inaccuracies in the experimentally determined FCG characteristics can have direct consequences on the development of durable rubber compounds. Therefore, the aim of this work is focused on the experimental validation of the FCG characteristics of rubber in comparison with the recently customary theoretical background and functions describing the relationship between the FCG rate and the tearing energy. From the literature survey, the weak points directly influencing the accuracy of the FCG characteristics in the experimental approach were identified. The first weak point is the transient point or discontinuity of the FCG characteristics within the region of the stable FCG. To follow on, a visible deviation of the experimentally determined data within the region of the stable FCG from the theoretical function is necessary to be validated. FCG analyses of plane strain tension samples based on ethylene propylene diene monomer (EPDM) rubber filled with a varied content of carbon black were performed using a Tear and Fatigue Analyzer (TFA©, Coesfeld GmbH & Co. KG, Germany). The FCG characteristics were plotted for a broad range of tearing energies. The intrinsic strength and the ultimate strength were determined. The region of the stable FCG was studied in detail. The continuous function of the stable FCG within the region was found, and thus, the presence of a transient point was refuted. Moreover, a specific equation was validated to fit the data into the region of the stable FCG compared to a previously preferred power-law with a higher accuracy.

The plane strain (PS) tensile sample, which is very often named as pure shear sample, featured prominently in classic studies of fracture mechanics of rubbers while investigating fatigue crack growth (FCG) behaviour. A PS sample is shaped as a thin, rectangular strip. For the FCG investigation it is held by rigid clamps along its long edges. While straining in-plane, deformation of the sample originates mainly along the loading direction except in the regions near the free edges. Thus, when using the PS sample for FCG characterization while applying simple fracture mechanics, the crack growth is required to be investigated within the region, where the deformation of the sample originates mainly along the loading direction. Parametrical functions defining the region of PS sample, where the orientation of strain in the plane is in the loading direction or orthogonal to the crack growth, have experimentally been determined using a digital image correlation (DIC) system. In detail, the parametrical functions firstly describe the narrowing towards the edges and secondly the width of the region in which the FCG analysis should take place. This was observed over a broad range of the aspect ratio ‘width/length’ of the sample (<1/2, 10>) and the strain was varied in the interval ∈ <0, 0.5>. The strain over the complete horizontal axis across all applied aspect ratios has experimentally proven that no pure shear deformation (deformation strictly originating along the loading direction) is present in the PS sample in reality. Thus, thanks to the exponential character of the contraction over the complete horizontal axis of the PS sample, a novel criterion considering a deviation from the maximum achieved contraction in proportion ∈ <0.01, 0.05> has been established and it was included to the parametrical function defining the width of the region of deformation originating near the loading direction. Besides, it has been demonstrated that the deformation over the complete horizontal axis of sample is nearly independent of the applied rubber type. To conclude, based on the determined parametrical functions, the equation for calculating the minimal notch length required for FCG analyses within the region of deformation originating near the loading direction has been defined.

Polyglycols are mainly used as plasticizers to enhance the incorporation of polar fillers in non-polar elastomers. Polyglycols can help to prevent the self-agglomeration of the filler particles and thereby improve their dispersion in the rubber matrix. It can also prevent undesired chemical reactions of the polar components in the curing system with the surface of the filler particles. Therefore, it is expected that polyglycols can play a crucial role as plasticizer and coupling agent in a silica-filled rubber compound. In this work, polyethylene glycol (PEG) and polypropylene glycol (PPG) in two different concentrations were applied in a silica-filled natural rubber (NR). Their effects are compared with the influence of the coupling agent bis[3-(triethoxysilyl)propyl]tetrasulfide (TESPT), which is widely used in rubber industry as silica coupling agent. Firstly, the cure characteristics and fundamental mechanical properties have been studied, whereas the ability of polyglycols to improve cure efficiency as well as filler-elastomer interactions has been confirmed. Moreover, polyglycols are improving the fundamental mechanical properties in general, whereas the polyglycols-treated silica-filled NR composites show lower tensile strength and modulus with a higher elongation at break compared to the TESPT-treated silica-filled NR. Finally, the effect of polyglycols on fatigue crack growth (FCG) resistance was investigated using a Tear and Fatigue Analyzer (TFA^©, Coesfeld GmbH & Co. KG, Germany). It has been found that 2 phr of PEG leads to a higher improvement of FCG resistance in comparison with the corresponding content of TESPT. However, 4 phr of polyglycols significantly decreases this property again. Moreover, the application of PPG generally leads to decreasing FCG resistance. As conclusion, it was stated that the polyglycols act as agent leading to significant improvement of fundamental mechanical behaviour in general as well as to improvement of FCG behaviour using specific polyglycol.

Below a limiting value of tearing energy called the intrinsic strength or fatigue threshold (T₀), cracks will not grow in rubber due to fatigue; hence, this material characteristic is important to understand from both fundamental and practical perspectives. We summarize key aspects of the fatigue threshold, including the Lake-Thomas molecular interpretation of T₀ in terms of fracture of polymer network chains in crosslinked elastomers. The various testing approaches for quantifying T₀ are also discussed, with a focus on the classic Lake-Yeoh cutting method which was recently revived by the introduction of a commercial testing instrument that applies this procedure, the Intrinsic Strength Analyser (ISA). A validation of the cutting method is also given by demonstrating that a 2-h test on the ISA yields a value of T₀ that is essentially identical to the T₀ from near-threshold fatigue crack growth (FCG) measurements that require 7.5 months of continuous testing. Compound formulation effects – polymer type, crosslink density, type and amount of reinforcing fillers, and addition of oils/plasticizers – are examined based on the limited published research in this area and our new results. At the end, some insights are offered into using the fatigue threshold to develop highly durable rubber products.

Durability is an essential feature of most elastomer products, directly linked to safety and to perceptions of brand quality. Product designers must therefore consider the impact on product durability of typical and abusive end-user loading scenarios. This can be accomplished using critical plane analysis (CPA). CPA starts by acknowledging that a small crack precursor might exist at any point in a part, and in any orientation, and that the potential development of all crack precursors must be evaluated. The analysis produces a full accounting of which location and orientation maximizes crack growth (or, equivalently, minimizes fatigue life) at each point, the energy release rate history experienced, and of course the worst-case fatigue life across all possible orientations. This review provides an account of the development of the method over the last two decades and the validation case that has accumulated. This review also suggests directions for further development of the method.

A multiscale approach was proposed to investigate cavitation micro-mechanisms developing in silica-filled styrene-butadiene rubber exposed to fatigue and cyclic tensile testing. At the macro-/mesoscopic scale, a decrease in load amplitude observed in fatigue was corroborated with cavitation micro-mechanisms initiated by silica agglomerate-rubber debonding and silica agglomerate breakdown. In the case of cyclic tensile testing, a gradual decrease of Poisson’s ratio was correlated at the microscopic scale by similar cavitation micro-mechanisms than in fatigue. Both fatigue and cyclic tensile behaviors were considerably affected by an applied thermal treatment of the compound enhancing cavitation (especially agglomerate breakdown).

In this chapter we review some recent approaches to modeling failure and fracture of soft materials. By failure we mean the onset of damage via material instability. By fracture we mean further localization of damage into cracks with their subsequent propagation.

Mathematical description of failure is simple and it only requires some bounding of the strain energy density. The bounded strain energy automatically implies the bounded achievable stress, which is an indicator of material failure. By bounding the strain energy via energy limiters we show, for instance, how to explain cavitation, analyze strength of soft composites, and predict direction of possible cracks.

Mathematical description of fracture is more involved because it requires regularized formulations suppressing the so-called pathological mesh sensitivity. Most existing approaches utilize purely formal regularization schemes that lack physical grounds. We discuss a more physically based approach rooted in the idea that bulk cracks are not a peaceful unzipping of adjacent atomic layers but rather a catastrophic explosion of bonds localized within a finite characteristic area.

A concept for the estimation of lifetime cycles is discussed assuming non-dispersed filler particles as origins of initial cracks which propagate under dynamic load according to fatigue crack growth (FCG) characteristics until failure occurs. Reference EPDM compounds with glass spheres of well defined size show strong correlation of the fatigue to failure analysis (FFA) behavior of dumbbells with largest incorporated particles, but dependence on polymer filler interaction, too. For NR and EPDM compounds, the occurrence of incorporated large particles is investigated by computed tomography and evaluated to a flaw size statistic. Based on the assumption of initial crack sizes matching the flaw diameters and together with the characteristic material parameters from FCG analysis, a statistical concept for the prediction of FFA lifetime analysis is presented. Predictions for near-homogeneously deforming dumbbell samples with carbon black (CB) reinforced NR display a particle size distribution which in combination with FCG results allows to calculate quantitative lifetime accordant to experimental findings, i.e. compounding dependency by shorter lifetime for worse dispersion and geometry dependency by longer lifetime for smaller specimens. An extension of the prediction concept for non-homogeneous deformation states is shown through a Monte Carlo simulation varying the positions of flaws inside the sample together with a Finite Element Analysis based calculation of the accordant local J-integral value. The simulations of lifetime statistics for rotational-parabolic buffer samples made of CB filled NR or EPDM show significant effects in average value and distribution width similarly found in experiment. This lifetime prediction concept has the unique capability to take into account not only recipe controlled matrix properties as cyclic crack propagation resistivity but volume dependency and processing related dispersion state, too in a quantitative manner.

The material behaviour of polymeric materials under cyclic fatigue loads is complex and forms a vast field of research activities. Elastomer-like polyurethane materials form an excellent fit for cyclically loaded system components in many cases. The present work aims to quantify fatigue crack growth (FCG) in a high-performance, commercially available hydrolysis-resistant thermoplastic polyurethane (TPU). This TPU material is often used in water or oil hydraulics and applications in mining, tunneling, etc. due to its high resistance to abrasion and tear strength. For those heavy-duty applications, the critical lifetime is reached as soon as cracks reach a critical threshold in the TPU material. The first part of the current work illustrates the FCG analysis of the TPU material, i.e. crack propagation measurements on a Tear and Fatigue Analyzer (TFA, Coesfeld GmbH & Co. KG, Germany). Based on the TFA measurements, it is shown how the tearing energy and the FCG rate have a certain regularity at different strain levels and quite a different behaviour compared to standard rubber material. Secondly, a lifetime prediction of the TPU material is derived by means of advanced finite element analysis (FEA). By using Abaqus simulation software (Dassault Systèmes) with advanced material modeling concepts, simulations are performed under the identical conditions as the TFA experiments. The results are plotted in terms of total elastic strain energy density per element (ESEDEN) over FCG rate in the vicinity of the crack tip. In a third step, the lifetime prediction concept ESEDEN is cross-validated by comparing experimental results from a test bench that applies cyclic high strain rate loading to the TPU material with corresponding FEA. As demonstrated the ESEDEN data proves being a promising criterion for lifetime prediction of critical TPU components under cyclic loading conditions.

The deformation and failure behavior of rubbers is significantly influenced by the chemical composition and loading conditions. Investigations on how specific loading parameters affect the mechanical behavior of rubbers are elementary for designing elastomeric products. Suitable fracture mechanical concepts describing the failure behavior of rubbers are widely accepted in industrial and academic research. However, the most common failure analyses base on macroscopic approaches which do not consider microscopic damage, although a contribution of (micro)structural changes at the network scale on the overall mechanical properties is very likely. A special phenomenon in terms of microstructural failure is cavitation due to strain constraints. Under geometrical constraints, the lateral contraction is suppressed. As a result, stress triaxiality causes inhomogeneous deformation, and internal defects, so-called cavities, appear. The formation and growth of cavities release stress and reduce the degree of constraints. Cavitation in rubbers has been studied for several decades, but the knowledge about the fundamental mechanisms triggering this process is still very limited. The present study aimed to characterize and describe cavitation in rubbers comprehensively. Hence, advanced experimental techniques, such as dilatometry and microtomography, have been used for in situ investigations on pancake specimens. Such thin disk-shaped rubber samples are characterized by a high aspect ratio. As a result, the degree of stress triaxiality is high, and the dominating hydrostatic tensile stress component causes the initiation of cavitation. Of special interest was the often suspected cavitation in unfilled rubbers. In contrast to the literature, cavitation in rubbers is not exclusively attributed to interfacial failure between the soft rubber matrix and rigid filler particles, but occurs also in unfilled rubbers. The onset of cavitation was determined precisely by highly sensitive data acquisition. Both a stress-related and an energy-based cavitation criteria were found indicating that traditional approaches predicting cavitation overestimate the material resistance against cavitation. The presented experimental methods to characterize cavitation are suitable for future studies investigating further aspects of cavitation in rubbers and other rubberlike materials, e.g., the failure behavior under dynamic loading.

Tyre tread directly comes in contact with various road surfaces ranging from very smooth roads up to riding on rough road surfaces (e.g. gravel roads, roots, stalks) and is prone to damage due to cut from sharp asperities during service. As tyre experiences millions of fatigue cycles in its service life, these cuts propagate continuously and lead to varied fracture processes from simple abrasion, crack growth up to catastrophic failure. In this paper firstly the complete fatigue crack growth (FCG) characteristics of rubbers from the endurance limit up to the ultimate strength and, finally, compared the data with a fast laboratory testing method determining the Chip and Cut (CC) behaviour. The study is focussed on investigation of pure natural rubber (NR) and natural rubber/styrene butadiene rubber (NR/SBR) blends, based on industrial compound formulations used for tyre tread applications. These rubbers have well-established FCG characteristics in field performance of tyre treads, with NR exhibiting the higher FCG resistance at high region of tearing energies, whereas the advantage of SBR over NR can be realized in terms of the higher fatigue threshold for SBR occurring in the low range of tearing energies. The same trend was found from the FCG analyses consisting of the complete Paris-Erdogan curve from endurance limit up to ultimate strength as well as CC behaviour determined with a laboratory Instrumented Chip and Cut Analyser (ICCA) which operates under realistic practice-like conditions and quantifies the CC behaviour using a physical parameter.

The paper reviews recent investigations of fatigue crack propagation in filler-reinforced elastomer blends based on recipes referring to truck tire tread compounds. One focus lies on viscoelastic energy dissipation effects that explain the well-known power law behavior of the crack growth rate vs. tearing energy. It is demonstrated that the crack growth rate fulfills the time-temperature superposition principle by constructing master curves with shifting factors from viscoelastic data. In addition, energy dissipation mechanisms due to stress softening in vicinity of the crack tip are evaluated under quasi-static conditions by calculating the J-integral, which decreases significantly while approaching the crack tip. Therefore, we use combined experimental and theoretical techniques consisting of digital image correlation measurements of the strain field around the crack and calculations of the corresponding energy densities and stress fields based on a physically motivated stress-softening model of filled rubbers. A second focus lies on the role of phase morphology of carbon black (CB) filled NR/BR and NR/SBR blends in fatigue crack propagation. Therefore, the filler distribution is evaluated by an established technique referring to the variation of viscoelastic loss peaks in the glass transition regime. It is found that in NR/BR blends, almost all CB is located in the NR phase, while in NR/SBR blends, the majority of CB is located in the SBR phase. The effect of batching on the phase morphology is also considered, by mixing the NR first with CB and then blending with the second rubber phase. This leads to a more homogeneous distribution of CB in NR/SBR blends. Finally, the obtained fatigue crack growth rates of these blend systems, measured under pulsed harmonic excitations in analogy to rolling tires, are discussed on the basis of the evaluated phase morphology and filler distribution. Here, also the influence of the polymer-filler interphase on the filler distribution is considered.

The fracture and fatigue behavior of thermoplastic elastomers (TPE) is of prime practical importance for demanding engineering applications. The fatigue behavior of several TPE grades used for superior industrial application was characterized under displacement-controlled cyclic loading conditions by local strain based Wöhler curves (LSWC) and by fatigue crack growth (FCG) curves. The LSWC method is based on the determination of the local strain in diabolo-shaped cylindrical or flat specimens and the identification of cycle number-to-failure, N_f, values in the F_max/F_min-N_f diagrams. While these LSWC curves were successfully created for injection molded TPEs investigated using cylindrical specimens, the extrusion grade TPU did not reveal fatigue failure using flat specimens with 0.2 mm thickness. The LSWC curves were used for both supporting material development efforts and dimensioning cyclically loaded components. Notched Plane Strain (PS) tensile specimens were tested under displacement-controlled loading conditions and the crack length was measured optically. Tearing energy values have been calculated for the PS specimens and subsequently FCG curves were generated in terms of crack growth rate, da/dN, and tearing energy, T. The majority of the TPE grades investigated revealed extensive crack tip blunting. While the slope of the stable FCG revealed rather minor differences, the apparent fatigue threshold values were observed in the range of appr. 1.5 decades. The endurance strain limit has been estimated (1) by direct measurements in LSWC tests (2) by the determination of threshold values in the FCG curves and calculation of critical strain values and (3) by using Essential Work of Fracture (EWF) approach.

The aim of this chapter is to revisit the historical works, mechanisms, and modeling approaches available in the field of fatigue crack growth resistance and rupture properties. After introducing the methodology developed to evaluate these properties, the impact of testing parameters such as temperature, loading speed, and pre-deformation will be highlighted. We will then review the influence of some material characteristics on rupture and crack propagation and the local mechanisms involved. Finally, a theoretical framework primarily dedicated to the description of crack propagation under static load will be discussed that aims to underline the connection between resistance to crack growth and the ability of a material to dissipate energy.

This contribution is focused on the quasi-static and impact fracture behaviour of technical, filler-reinforced elastomer compounds containing plasticizers basing on renewable sources in various amounts. Beside the conventional plasticizer TDAE as benchmark, various plasticizer products like epoxidized rapeseed oil, rapeseed oil methyl or propyl ester, epoxidized canola oil or epoxidized ester of glycerol formal from canola oil were used. Main aims are to find products as replacement of traditional mineral oil-based plasticizers and to understand the interaction of polymer and plasticizer and the resulting properties, especially the deformation and fracture behaviour. It was shown that by using renewable plasticizers a comparable or better property level of technical rubber vulcanizates is possible.

We review a theory of crack propagation in viscoelastic solids. We consider both cracks in infinite systems and in finite-sized systems. As applications of the theory we consider two adhesion problems, namely pressure sensitive adhesives and the ball-flat adhesion problem. We also study crack propagation in the pig skin dermis, which is of medical relevance, and rubber wear in the context of tires.

Nowadays, different concepts to investigate the crack propagation in rubber materials are used. Most of them are based on the investigation of uniaxial loaded specimens and without taking into account the dissipative aspects of deformation.

Rubber parts are used for different kinds of applications like tires, vibration damper, sealing parts, gaskets, diaphragms, etc. These parts are often subjected to multiaxial cyclic loading during operation. To utilize the whole mechanical potential of the rubber, it is necessary to investigate and characterize the material and crack behaviour under application relevant conditions.

This study will work out that regardless of the deformation state (equibiaxial, asymmetrical biaxial, “pure shear”, uniaxial) the same amount of energy is dissipated if the amount of the equivalent strain (von Mises) is equal.

The present paper investigates, how different states of deformation possibly differently triggers the competitive dissipative processes of the material with the aim, to work out the different amount of dissipative effects as a function of the deformation state. It will be further shown how these effects influence the situation at the crack tip during cyclic loading. The correlations between von Mises equivalent strain, dissipative heating and crack propagation were analysed and used for the characterization of the material behaviour at the crack tip.

It is shown how the dissipated energy can be estimated and how the data describe the heating of the and the heat transfer to the surrounding in detail. The dissipated conditions in the whole sample and in the vicinity of the crack tip correlate with the crack behaviour. The dependence of the crack growth rate and thermal state at the crack tip from the von Mises strain is discussed in detail.

A physically motivated model approximates the strain at the crack tip and, finally, estimates the relationship between strain, energy dissipation and temperature state of the rubber material in the vicinity of the crack tip.

The used rubber is a solution-SBR loaded with 50 phr carbon black. The experiments were performed on a biaxial test machine from Coesfeld GmbH & Co. KG. The measurements were done using an optical digital image correlation (DIC) system ARAMIS from GOM, Germany, to measure and analyse the strain. The thermal behaviour was determined by infrared thermography from InfraTec, Germany.

In this paper, the relationship between the tearing energy and the far-field cracking energy density (CED) is evaluated for an embedded penny-shaped flaw in a 3D elastomer body under a range of loading modes. A 3D finite element model of the system is used to develop a computational-based fracture mechanics approach which is used to evaluate the tearing energy at the crack in different multiaxial loading states. By analysing the tearing energy’s relationship to the far-field CED, the proportionality parameter in the CED formulation is found to be a function of stretch and biaxiality. Using a definition of biaxiality that gives a unique value for each loading mode, the proportionality parameter becomes a linear function of stretch and biaxiality. Tearing energies predicted through the resulting equation show excellent agreement to those calculated computationally.

We investigated crack propagation in cyclic fatigue in filled (50 phR of N347 carbon black), highly crosslinked, natural rubber pure shear samples and, in parallel, mapped in detail the microstructure present at the crack tip with a microfocused X-ray synchrotron beam. We acquired data by wide-angle X-ray scattering (WAXS) to characterize strain-induced crystallization (SIC) and by small-angle X-ray scattering (SAXS) to detect nano-cavitation. Crack propagation experiments were carried out for a range of maximum energy release rates during the cycles varying from 1 to 4 kJ/m². Each material was tested at two temperatures: room temperature and 100°C and in new and aged conditions (10 days at 100°C in an inert atmosphere). We found that although significantly less SIC at the crack tip was present at the crack tip at 100°C, the resistance to crack propagation under cyclic loading was barely affected. In aged samples SIC at the crack tip was significantly lower than in new samples at room temperature, and was not detectable at all in aged samples at 100°C. The crack propagation rate, however, only increased with aging for the more crosslinked sample at 100°C and never increased catastrophically. Finally, a few percent of nano-cavities were detected at the crack tip and the comparison of X-ray transmission and digital image correlation suggested the presence of a significant fraction of large cavities at the very crack tip. In conclusion while strain-induced crystallization in NR may be affecting fatigue resistance we could not establish a quantitative correlation between the volume crystallized at the crack tip and the crack propagation rate in cyclic fatigue.