Publications
Authors: WV Mars, JD Suter
Published: 08/10/2019
Journal: Paper C08, Presented at the Fall 196th Technical Meeting of the Rubber Division of the American Chemical Society, Inc.
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Breaking the computational barrier to simulating full road load signals in fatigue
Abstract
In this work, we present the Endurica EIETM 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...
In this work, we present the Endurica EIETM 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-, 2- and 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. The results show that EIE can quickly compute strain histories interpolated from a precomputed set of results with an error that can be controlled to a desired accuracy via map discretization. EIE’s benefit of efficiently interpolating results becomes more pronounced as signal length increases, in this study reaching nearly as high as a 4 orders of magnitude speed-up. However, EIE becomes less efficient as the number of problem dimensions increases (from one dimension to three dimensions). The lower benefit is due to the high cost of producing a higher dimensional map of FEA results for EIE to interpolate from. Even in this case, however, as seen for the 3D transmission mount analysis, the cost of creating the EIE map is still worthwhile when signal length is sufficiently long.
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Authors: William V. Mars, Yintao Wei, Wang Hao, Mark A. Bauman
Published: 01/03/2019
Journal: Tire Science and Technology
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Computing Tire Component Durability via Critical Plane Analysis
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 behavio...
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.
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Authors: A. Ramachandran, R. P. Wietharn, S.I. Mathew, W. V. Mars, and M. A. Bauman
Published: 12/10/2018
Journal: Presented at the 2018 Great Lakes Simulia Regional User Meeting
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Experimental Validation of Crystallizing & Non-Crystallizing Models of Rubber Fatigue Behavior
Abstract
The orientation of cracks initiating under cyclic loading in rubber may depend not only on maximizing the energy release rate, but also – in the case of a strain crystallizing rubber – on minimizing the life-lengthening effect of strain-crystallization associated with nonrelaxing loads. Crack orientations in a series of fully relaxing and nonrelaxing fatigue tests were computed with Endurica’s critical plane analysis, and compared with cracks developed in experiments on strain-crystallizin...
The orientation of cracks initiating under cyclic loading in rubber may depend not only on maximizing the energy release rate, but also – in the case of a strain crystallizing rubber – on minimizing the life-lengthening effect of strain-crystallization associated with nonrelaxing loads. Crack orientations in a series of fully relaxing and nonrelaxing fatigue tests were computed with Endurica’s critical plane analysis, and compared with cracks developed in experiments on strain-crystallizing Natural Rubber, and amorphous Styrene Butadiene Rubber. The specimen used for experimentation was a rectangular flat dumbbell prepared according to the ASTM D4482 Standard. Five strain histories were tested, two fully relaxing (0-80% and 0-100%), and three nonrelaxing (20-120%, 50%-150%, and 50%-170%). Critical plane analysis was performed with Endurica CL. As predicted, all fully relaxing tests, for both NR and SBR, developed cracks on the plane perpendicular to the maximum principal stress (90 degrees). Also as predicted, all nonrelaxing tests for the amorphous SBR develop in the same 90 degree plane. Finally, nonrelaxing tests for the crystallizing NR develop on specific planes that were accurately predicted by minimizing the fatigue life with respect to crack orientation.
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Authors: W. V. Mars, C. G. Robertson, R. Stocek, C. Kipscholl
Published: 09/10/2018
Journal: Paper B03, presented at the Fall 194th Technical Meeting of the Rubber Division of the American Chemical Society, Inc., Louisville, Kentucky
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Why Cutting Strength is an Indicator of Fatigue Threshold
Abstract
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 at nominally similar conditions. ...
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 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.
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Authors: Joshua R. Goossens, William V. Mars
Published: 01/10/2018
Journal: Rubber Chemistry and Technology
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Finitely Scoped, High Reliability Fatigue Crack Growth Measurements
Abstract
Classical procedures for characterizing fatigue crack growth behavior often suffer from uncertainties that make it difficult to plan for productive use of test instrument time, and that can result ultimately in too noisy measurements. An enhanced procedure has been implemented that is based on a fixed test time budget, and that establishes operating conditions that produce crack growth rates down to minimum measurable rates. The procedure features (1) a haversine pulse deformation test cycle fol...
Classical procedures for characterizing fatigue crack growth behavior often suffer from uncertainties that make it difficult to plan for productive use of test instrument time, and that can result ultimately in too noisy measurements. An enhanced procedure has been implemented that is based on a fixed test time budget, and that establishes operating conditions that produce crack growth rates down to minimum measurable rates. The procedure features (1) a haversine pulse deformation test cycle followed by a rest period, (2) a strain peak that ramps linearly over time, (3) minimum and maximum limits on the strain peak chosen to avoid unproductive test time, and (4) a stress–strain probe cycle for purposes of observing strain energy density. A set of replicates of a carbon black filled, natural rubber bushing compound has been characterized via both procedures, and a statistical analysis is made to compare both. The new procedure significantly improves the quality of crack growth rate curve measurements.
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Authors: R. Harbour, A. Fatemi, and W. V. Mars
Published: 01/03/2018
Journal: Journal of Material Science, 43, 1783-1794, 2008
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Fatigue Crack Orientation in NR and SBR Under Variable Amplitude and Multiaxial Loading Conditions
Abstract
The orientations of cracks as they develop in a material indicate the planes that have experienced the maximum damage. For the purpose of fatigue life analysis and prediction, these planes are referred to as the failure or critical planes. In order to study the planes on which cracks develop for different types of loading, the development of cracks was observed during constant and variable amplitude experiments using the multiaxial ring specimen. Two filled rubber materials were compared in this...
The orientations of cracks as they develop in a material indicate the planes that have experienced the maximum damage. For the purpose of fatigue life analysis and prediction, these planes are referred to as the failure or critical planes. In order to study the planes on which cracks develop for different types of loading, the development of cracks was observed during constant and variable amplitude experiments using the multiaxial ring specimen. Two filled rubber materials were compared in this study: NR, which strain crystallizes, and SBR, which does not. Multiaxial test signals composed of alternating blocks of axial and torsion cycles (each of which acts on different critical planes) produced crack orientations that fell between those occurring for signals composed only of axial or of torsion cycles. Plane-specific fatigue damage parameters of cracking energy density and normal strain were evaluated for their ability to predict the experimentally observed planes of crack development.
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Authors: A. Ramachandran, R. P. Wietharn, S.I. Mathew, W. V. Mars, and M. A. Bauman
Published: 10/10/2017
Journal: Presented at the Fall 192nd Technical Meeting of the Rubber Division, ACS, Cleveland, Ohio
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Critical Plane Selection Under Nonrelaxing Simple Tension with Strain Crystallization
Abstract
The orientation of cracks initiating under cyclic loading is normally set by the maximum principal direction of the applied stress. In simple tension, this causes cracks to appear perpendicular to the tension direction. In contrast, for a strain-crystallizing natural rubber compound, we have observed an exception that occurred during nonrelaxing simple tension fatigue tests. In this case, cracks initiated in a markedly different orientation. The specimen used for experimentation was a rectangula...
The orientation of cracks initiating under cyclic loading is normally set by the maximum principal direction of the applied stress. In simple tension, this causes cracks to appear perpendicular to the tension direction. In contrast, for a strain-crystallizing natural rubber compound, we have observed an exception that occurred during nonrelaxing simple tension fatigue tests. In this case, cracks initiated in a markedly different orientation. The specimen used for experimentation was a rectangular flat dumbbell prepared according to the ASTM D4482 Standard. Critical plane analysis of this case, with and without strain crystallization, was
performed with Endurica CL to predict the plane on which crack nucleation is favored. The analysis shows that the nonrelaxation ratio R, and therefore the degree of strain crystallization and associated crack growth rate, depend on plane orientation in a way that predicts the effect. This information is useful as additional validation when comparing fatigue life predictions to experiments, or as a first step towards understanding the loading experienced at the failure location. Nonrelaxing cycles in a rubber that strain crystallizes improve fatigue life, and also cause crack initiation in a direction not perpendicular to the maximum tension direction.
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Authors: R. Stocek, W. V. Mars, R. Kipscholl, and C. G. Robertson
Published: 10/10/2017
Journal: Presented at the Fall 192nd Technical Meeting of the Rubber Division, ACS, Cleveland, Ohio
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Characterizing Rubber’s Resistance Against Chip and Cut Behavior
Abstract
Tires in service - especially in rough terrain - show a behavior which is well known as the cut and chip (CC) effect. This work describes unique analytical methods to characterize the fracture in rubber occurring during lab-simulated operation of the tire tread in rough terrain. The new test device controls and records multiple applied loads and displacements during cyclic impact to the surface of a solid rubber wheel to mimic and quantify the cut and chip damage experienced by tire tread compo...
Tires in service - especially in rough terrain - show a behavior which is well known as the cut and chip (CC) effect. This work describes unique analytical methods to characterize the fracture in rubber occurring during lab-simulated operation of the tire tread in rough terrain. The new test device controls and records multiple applied loads and displacements during cyclic impact to the surface of a solid rubber wheel to mimic and quantify the cut and chip damage experienced by tire tread compounds on off-road and poor road conditions. To demonstrate the testing capabilities, characterization results are examined for carbon black filled rubber
compounds suitable for tire tread applications. The instrument provides a reliable method for evaluating the resistance of rubber against CC damage, and it can also be used in full contact mode for measurement of friction and wear.
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Authors: C. G. Robertson, R. Stocek, C. Kipscholl, and W. V. Mars
Published: 12/09/2017
Journal: Presented at the Annual Business Meeting and Conference on Tire Science and Technology, Akron, Ohio
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Characterizing the Intrinsic Strength of Natural Rubber / Butadiene Rubber Blends
Abstract
Tires require rubber compounds capable of enduring more than 108 deformation cycles without crack growth. One strategy for evaluating candidate compounds is to measure the intrinsic strength. The intrinsic strength is the residual strength remaining in the material after the strength-enhancing effects of energy dissipation in crack tip fields are removed. If loads stay always below the intrinsic strength (taking proper account of the possibility that the intrinsic strength may degrade with aging...
Tires require rubber compounds capable of enduring more than 108 deformation cycles without crack growth. One strategy for evaluating candidate compounds is to measure the intrinsic strength. The intrinsic strength is the residual strength remaining in the material after the strength-enhancing effects of energy dissipation in crack tip fields are removed. If loads stay always below the intrinsic strength (taking proper account of the possibility that the intrinsic strength may degrade with aging), then cracks cannot grow. Using the cutting protocol proposed originally by Lake and Yeoh, as implemented on a commercial Intrinsic Strength Analyzer, the intrinsic strength is determined for a series of carbon black (CB) reinforced blends of natural rubber (NR) and butadiene rubber (BR) typical of tire applications. The intrinsic strength benefits of the blends over the neat NR and BR compounds are only observed after aging at temperatures in the range from 50 °C to 70 °C, thus providing fresh insights into the widespread durability success of CB-filled NR/BR blends in tire sidewall compounds and commercial truck tire treads.
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Authors: W.V. Mars and M.D. Ellul (2017)
Published: 01/06/2017
Journal: Rubber Chemistry and Technology
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Fatigue Characterization of a Thermoplastic Elastomer
Abstract
The capacity to resist crack development in an olefinic thermoplastic elastomer (TPE) has been measured via a set of experiments that quantify (1) the fracture mechanical strength of the material under quasi-static loads, (2) the rate of growth of a crack under dynamic solicitations as a function of the energy release rate, and (3) the size of crack precursors in new material. Because the subject TPE exhibited strong inelasticity in the stress–strain response, it also was necessary to characte...
The capacity to resist crack development in an olefinic thermoplastic elastomer (TPE) has been measured via a set of experiments that quantify (1) the fracture mechanical strength of the material under quasi-static loads, (2) the rate of growth of a crack under dynamic solicitations as a function of the energy release rate, and (3) the size of crack precursors in new material. Because the subject TPE exhibited strong inelasticity in the stress–strain response, it also was necessary to characterize the development of an inelastic set under cyclic loading as a function of the applied strain. Combined with the multiplicative kinematic split, this additional measurement yields the elastic part of the strain. It also enables engineering calculations to be made of fatigue life.
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