A theory for multifield analysis of the consequences of sliding asperities on a rubber surface has been developed. The analysis considers (1) the multiaxial mechanical fields set up via the asperity contact, (2) the thermal field set up due to friction and heat generation, (3) the material property fields that evolve due to thermochemistry, and (4) the growth of crack precursors near the sliding interface. The theory considers two distinct Eulerian directions: the first direction considers strain history along streamlines oriented in the direction of sliding, and the second direction considers the progression of material toward the wear surface as material is removed. Considering the mechanical and thermal fields set up around an asperity, the theory simplifies what would otherwise be a large and complex analysis. The theory produces an estimate of the variation with depth of fatigue damage (residual life; as calculated via critical plane analysis), from which may be derived the wear rate for a particular surface sliding under a given set of conditions. Results of the calculation for two cases (two-dimensional sine wave and square wave asperity surfaces) with varying normal contact pressure are compared with Gent and Pulford’s blade abrader experiments.

The intrinsic strength of rubber, T0 is one of the key parameters when describing fracture behaviour of elastomer because it is at this specific value of energy that crack growth initiates within loaded rubber material. The Coesfeld Intrinsic Strength Analyzer (ISA) has been established as the most efficient equipment to directly analyse T0 for various rubber materials. However, to obtain the most reliable and reproducible results it is crucial to understand the influence of boundary conditions of the ISA measuring methodology. Therefore, in this study sets of boundary conditions were chosen to be analysed through mechanical response of reference EPDM material with known T0 value. For the purposes of this study the effects of individual boundary conditions were compared through directly measured value of intrinsic cutting energy, S0 which is proportional to T0. Blade sharpness and geometry showed the greatest impact followed by repetition of blade and specimen milling direction whereas the relaxation time and number of measuring strains showed no significant influence. The results of this study show that the knowledge of blade micro-geometry is at its most importance during the T0 analyses. Moreover, the data clearly indicates possible future modification of boundary conditions to achieve a very efficient testing procedure with significantly reduced time required for the analyses.

The qualification requirements of automakers derive from track testing in which road load and moment inputs to a part in x, y and z directions are recorded over a set of driving conditions selected to represent typical operation. Because recorded histories are lengthy, often comprising many millions of time steps, past industry practice has been to specify simplified block cycle schedules for purposes of durability testing or analysis. Simplification, however, depends on imprecise human judgement, and risks fidelity of the inferred life and failure mode relative to actual. Fortunately, virtual methods for fatigue life prediction are available that are capable of processing full, real-time, multiaxial road load histories. Two examples of filled natural rubber ride bushings are considered here to demonstrate. Each bushing is subject to a schedule of 11 distinct recorded track events. Endurica EIETM map building procedures are first used together with a finite element solution to map the 6 channel loading space and to obtain stress/strain solutions at each gridpoint in the load space. EIE is then used with the recorded histories to interpolate from the recorded road load inputs on the bushing to stress-strain history at each element centroid in the finite element model. The interpolated stress-strain histories are then used to compute damage accrual and fatigue life across all 11 events. The computational requirements of this workflow are benchmarked with the outcome that the entire schedule in full detail can be analyzed on a timescale well suited for use at the earliest stages of business development and engineering.

ABSTRACT Tensile stress–strain testing is used to investigate the fracture behavior of carbon black–reinforced styrene–butadiene rubber, using 50 replicate specimens. Four vulcanized rubber compounds are studied: a CB-filled SBR with standard mixing conditions (control), the same formulation with intentional poor mixing of the CB, and materials identical to the control material but formed by adding minor amounts of 0.5-mm-diameter glass microspheres (beads)—serving as large model defects/inclusions—using a two-roll mill at two levels, corresponding to average values of 0.78 and 6.24 beads per gauge section region of the tensile test specimen. Microscopy analysis of the resulting fracture surfaces was conducted to complement our recent publication on Weibull failure statistics for distributions of tensile strength and crack precursor size. All 200 fractured specimens from tensile testing at 23°C were imaged with light microscopy and exhibited fracture surfaces characterized by relatively smooth planes perpendicular to the uniaxial loading direction. Most tensile failures originated from the edges of the dumbbell specimens, in line with expectations from fracture mechanics. Light microscopy revealed concentric fracture ring features of high specular reflectance emanating from crack precursors, which are a universal feature of the failure process for these compounds and independent of precursor type, size, or location. Noncontact interferometric microscopy confirmed that the rings resulted from variations in surface micro-roughness, proceeding outward from the precursor as rough–smooth–rough to the edge of the fracture surface. Fracture rings were also observed for tensile tests performed at 80°C. The variation in surface roughness of the fracture surface has parallels to the stick–slip tearing behavior seen for rubbers torn at medium to high rates. To the best of the authors’ knowledge, this is the first time that such striking features have been reported.

Applying the critical plane method to the computation of fatigue performance requires the identification and tracking of a set of material planes. Although the procedure is well established for hyperelastic materials, its application to materials exhibiting large inelasticity remains to be developed. This work investigates the question of whether material planes are best identified with their original stress-free configuration, or with the unstressed evolved configuration. The question is explored using digital image correlation to study cracks of varying initial orientation in a thermoplastic elastomer exhibiting large inelasticity. The cracks’ initial and final orientations are observed and related via multiplicative decomposition to the history of far-field straining.

The degradation of polymeric adhesives in dissimilar joints is a menace to electric and structural components of the automotive industry. In polymeric adhesives, failure often occurs due to damage accumulated from discrete environmental sources—thermal degradation, oxidation, hydrolysis, radiation, and moisture—that are combined with progressive damage mechanisms, such as aging and fatigue. Because most damage mechanisms that lead to degradation act in parallel, the estimation of the lifetime of a polymeric material becomes a significant reliability issue, no study currently exists that can simultaneously consider even two of these phenomena. Most current efforts are directed toward a single-phenomenon, single-model approach in which a model is developed to cover one specific damage mechanism. While this approach is advantageous in exploring single mechanisms, it is strongly inconclusive for degradation that occurs by multiple damage mechanisms. Our team plans to take a fresh perspective by designing a hybrid constitutive/data-driven approach that allows models of different damage mechanisms to be integrated into one model and then used to explore the degradation-induced failure of polymeric adhesives. The theoretical-computational part of this work is divided into four research components as described in the Approach section below.

The hysteresis of rubber materials due to deformation and viscoelasticity is the main reason for the heat build-up (HBU) and rolling resistance (RR) of the rolling tire. It is important to realize the high precision prediction of HBU and RR of tire for the optimal design of high-performance fuel-saving tire. In this work, a thermo-mechanical coupling method based on Endurica and Abaqus co-simulation was used to predict the steady-state temperature distribution and RR of three finite element models (Lagrangian–Eulerian model, Lagrangian model, and Plane Strain model) of the solid tires under different loads and rotating speeds. The simulation results were compared with the experimental results. The Kraus self-heating model was utilized in the thermo-mechanical coupling method, which realized the quantitative relationship between the dynamic loss modulus of rubber and the loading conditions (temperature, strain, and strain rate). Special attention was paid to the determination of the material parameters in the Kraus self-heating model. The comparison between simulation results and experimental results shows that the Lagrangian model had the highest prediction accuracy, and the average prediction errors of the steady-state surface temperature and RR under three loading conditions were 3.4% and 7.9%, respectively. The Lagrangian–Eulerian model came in the second with average errors of 9.7% and 11.1%, respectively. The Plane Strain model had the worst prediction accuracy, with the average errors of 21.4% and 44.6%, respectively. In terms of the simulation time, the Plane Strain model had the lowest cost, and the average calculation time was 1143 s. The Lagrangian–Eulerian model took the second place, with an average calculation time of 2621 s. The Lagrangian model had the highest computation cost, with an average time of 5597 s. The comparison between the simulation results and the experimental results verified the effectiveness of the thermo-mechanical coupling analysis method. The methods of three finite element models of the solid tires in this work can provide some reference for the optimization design of elastomeric components (Lagrangian model), pneumatic tires (Lagrangian–Eulerian model), and non-pneumatic tires (Plane Strain model).

ABSTRACT Tire speed ratings derive from regulatory testing in which tire structural integrity is validated over a series of steps with successively increasing speed. For the FMVSS 139 high-speed standard, there are four half-hour duration speed steps at 80, 140, 150, and 160 kph. Speed ratings from Q through Y may be attained through the UN ECE R30 regulation high-speed testing. For either protocol, a tire must demonstrate the ability to operate without crack development at high speed for a specified period. After the test, “there shall be no evidence of tread, sidewall, ply, cord, inner liner, belt or bead separation, chunking, broken cords, cracking, or open splices.” A workflow for simulating regulatory high-speed durability performance has been developed based upon (1) recent improvements to the Abaqus steady-state transport formulation that now permit converged solutions to be obtained at high speed (including after the development of standing waves in the tire) and (2) Endurica DT self-heating and incremental fatigue simulations that account for thermal effects and for damage accumulation occurring due to a schedule of load cases. The self-heating calculation features the Kraus model and accurately captures viscoelastic loss modulus dependence on strain amplitude and temperature. For each step of the high-speed procedure, steady-state structural and thermal solutions are first computed. The deformation history in the presence of standing waves is shown to require rainflow counting due to the occurrence of multiple load cycles per tire revolution. Crack growth is finally integrated for each potential critical plane through each step of the test until failure is indicated. Standing waves at high speed induce significant self-heating and damage, rapidly limiting high-speed performance. The temperature dependence of self-heating and strength properties also plays a major role in limiting high-speed durability. The simulations were executed on both a flat surface and on the regulation specified 1.7 m diameter road wheel. As expected, durability testing on the road wheel is more severe, and the beneficial effect of a nylon overwrap is predicted.

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.

Below a limiting value of tearing energy called the intrinsic strength or fatigue threshold (T-0), 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 T-0 in terms of fracture of polymer network chains in crosslinked elastomers. The various testing approaches for quantifying T-0 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 T-0 that is essentially identical to the T-0 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.

Undispersed filler agglomerates or other substantial inclusions/contaminants in rubber can act as large crack precursors that reduce the strength and fatigue lifetime of the material. To demonstrate this, we use tensile strength (stress at break, σb) data from 50 specimens to characterize the failure distribution behavior of carbon black (CB) reinforced styrene-butadiene rubber (SBR) compounds. Poor mixing was simulated by adding a portion of the CB late in the mixing process, and glass beads (microspheres) with 517 μm average diameter were introduced during milling to reproduce the effects of large inclusions. The σb distribution was well described with a simple unimodal Weibull distribution for the control compound, but the tensile strengths of the poor CB dispersion material and the compounds with the glass beads required bimodal Weibull distributions. For the material with the lowest level of glass beads—corresponding to less than one microsphere per test specimen—the bimodal failure distribution spanned a very large range of σb from 13.7 to 22.7 MPa in contrast to the relatively narrow σb distribution for the control from 18.4 to 23.8 MPa. Crack precursor size (c0) distributions were also inferred from the data, and the glass beads introduced c0 values in the 400 μm range compared to about 180 μm for the control. In contrast to σb, critical tearing energy (tear strength) was unaffected by the presence of the CB agglomerates and glass beads, because the strain energy focuses on the pre-cut macroscopic crack in the sample during tear testing rather than on the microscopic crack precursors within the rubber. The glass beads were not detected by conventional filler dispersion measurements using interferometric microscopy, indicating that tensile strength distribution characterization is an important complementary approach for identifying the presence of minor amounts of large inclusions in rubber.

ABSTRACT Rubber surfaces exposed to concentrated, sliding impacts carry large normal and shearing stresses that can cause damage and the eventual removal of material from the surface. Understanding this cut-and-chip (CC) effect in rubber is key to developing improved tread compounds for tires used in off-road or poor road conditions. To better understand the mechanics involved in the CC process, an analysis was performed of an experiment conducted on a recently introduced device, the Instrumented Chip and Cut Analyzer (ICCA), which repetitively impacts a rigid indenter against a rotating solid rubber wheel. The impact process is carefully controlled and measured on this lab instrument, so that the contact time, normal force, and shear force are all known. The numerical evaluation includes Abaqus finite element analysis (FEA) to determine the stress and strain fields during impact. The FEA results are combined with rubber fracture mechanics characteristics of the material as inputs to the Endurica CL elastomer fatigue solver, which employs critical plane analysis to determine the fatigue response of the specimen surface. The modeling inputs are experimentally determined hyperelastic stress-strain parameters, crack growth rate laws, and crack precursor sizes for carbon black–filled compounds wherein the type of elastomer is varied in order to compare natural rubber (NR), butadiene rubber (BR), and styrene-butadiene rubber (SBR). At the lower impact force, the simulation results were consistent with the relative CC resistances of NR, BR, and SBR measured using the ICCA, which followed the order BR > NR > SBR. Impact-induced temperature increases need to be considered in the fatigue analysis of the higher impact force to provide lifetime predictions that match the experimental CC resistance ranking of NR > SBR > BR.

Extended Abstract In this work, we present the Endurica EIE nonlinear load mapping procedure, which provides a means by which the strain/stress histories resulting from full road load signals can now be rapidly generated. The procedure utilizes a series of pre-computed finite element solutions to populate a nonlinear map relating global load/displacement inputs to local strains/stresses within each finite element. For each time step of the full road load signal, the nonlinear map is used to obtain stress/strain results via interpolation. Examples are provided for 1-, 2and 3-channel signal inputs, and applied to the following automotive components: a sway bar link, a control arm bushing, and a transmission mount. Input signals of several durations were studied as follows: 1000, 10000 and 100000 time steps.

ABSTRACT Tire developers are responsible for designing against the possibility of crack development in each of the various components of a tire. The task requires knowledge of the fatigue behavior of each compound in the tire, as well as adequate accounting for the multiaxial stresses carried by tire materials. The analysis is illustrated here using the Endurica CL fatigue solver for the case of a 1200R20 TBR tire operating at 837 kPa under loads ranging from 66 to 170% of rated load. The fatigue behavior of the tire's materials is described from a fracture mechanical viewpoint, with care taken to specify each of the several phenomena (crack growth rate, crack precursor size, strain crystallization, fatigue threshold) that govern. The analysis of crack development is made by considering how many cycles are required to grow cracks of various potential orientations at each element of the model. The most critical plane is then identified as the plane with the shortest fatigue life. We consider each component of the tire and show that where cracks develop from precursors intrinsic to the rubber compound (sidewall, tread grooves, innerliner) the critical plane analysis provides a comprehensive view of the failure mechanics. For cases where a crack develops near a stress singularity (i.e., belt-edge separation), the critical plane analysis remains advantageous for design guidance, particularly relative to analysis approaches based upon scalar invariant theories (i.e., strain energy density) that neglect to account for crack closure effects.

Crack tip fields during cutting and tensile loading have been computed via finite element analysis, and measured using Digital Image Correlation during experiments executed on the Coesfeld Intrinsic Strength Analyser. The results show that cutting with a sharp blade while the specimen is under a small amount of tension produces a much-reduced dissipative process zone in front of the crack tip, in comparison with the process zone produced by tensile loading alone (no blade) at nominally similar conditions. Because the energy released by a growing crack supplies both the process of breaking polymer chains to form crack faces, and the dissipative process at the crack tip, minimizing crack tip dissipation causes the observed remaining energy release rate during a cutting experiment to approach the limit reflecting the breakage of polymer chains. Conveniently, this implies that a relatively brief cutting experiment may be used as an indicator of long-term fatigue behavior. The continuum-based analysis provided here offers an interpretation of cutting experiments that does not depend upon arguments about polymer chain details, and that is complementary to classical molecular theories about the origins of the threshold effect.

Understanding the cut and chip (CC) effect in rubber is important for successful product development for tires used in off-road or poor road conditions and for other demanding applications of rubber. This research describes a laboratory testing method for characterising the CC fracture behaviour of rubber using a device that controls and records multiple applied loads and displacements during cyclic impact to the surface of a solid rubber specimen to mimic and quantify the CC damage experienced by tire tread compounds. To study the capabilities of the instrument, three model compounds were studied that are based on carbon black reinforced compounds of common elastomers used in tire treads: natural rubber (NR), styrene-butadiene rubber (SBR), and butadiene rubber (BR). These polymers have well-established CC tendencies in field performance of tire treads, with NR exhibiting the best CC resistance followed by SBR and finally BR. The same trend was found with the rubber impact testing approach that allowed the CC behaviour to be quantified using a new physical parameter which is the CC propensity (P). The relative ranking for CC resistance for the three compounds followed the fatigue crack growth resistances of the materials but was exactly opposite to the ranking of DIN abrasion resistance. This provides evidence that CC damage from impact by mm-scale asperities and abrasion of rubber against mu m-scale asperities exhibit distinct characteristics in rubber.