Publications
Authors: M Aït-Bachir, WV Mars, E Verron
Published: 01/05/2012
Journal: International Journal of Non-Linear Mechanics 47 (2012)(4), 22-29
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Energy release rate of small cracks in hyperelastic materials
Abstract
The energy release rate of a small crack in an infinite hyperelastic medium, and subjected to large strain multiaxial loading conditions, is derived by considering the balance of configurational stresses acting on two planes: one cutting the center of the crack face, and the other at an infinite distance in front of the crack tip. The analysis establishes that the energy release rate of a small crack is always proportional to the size of the crack, irrespective of the loading conditions and the ...
The energy release rate of a small crack in an infinite hyperelastic medium, and subjected to large strain multiaxial loading conditions, is derived by considering the balance of configurational stresses acting on two planes: one cutting the center of the crack face, and the other at an infinite distance in front of the crack tip. The analysis establishes that the energy release rate of a small crack is always proportional to the size of the crack, irrespective of the loading conditions and the crack orientation. The balance of configurational stresses is illustrated for several benchmark cases including simple extension, pure shear and equibiaxial extension, and for perpendicular and inclined cracks.
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Authors: WV Mars
Published: 01/06/2011
Journal: Rubber Chemistry and Technology 84 (2011)(2), 178-186
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Analysis of Stiffness Variations in Context of Strain-, Stress-, and Energy-Controlled Processes
Abstract
In compounded material systems, such as rubber, a wide range of properties can be achieved by design. This flexibility poses a challenge–how to balance stiffness against other considerations, such as energy dissipation under dynamic loading, fatigue, etc. Negotiating this balance requires that adequate account be taken of how a given mechanical input (i.e., strain, stress, energy) is controlled, and how other mechanical outputs vary as the stiffness changes. We outline here a simple analysis b...
In compounded material systems, such as rubber, a wide range of properties can be achieved by design. This flexibility poses a challenge–how to balance stiffness against other considerations, such as energy dissipation under dynamic loading, fatigue, etc. Negotiating this balance requires that adequate account be taken of how a given mechanical input (i.e., strain, stress, energy) is controlled, and how other mechanical outputs vary as the stiffness changes. We outline here a simple analysis by which these considerations can be managed. The analysis is based on a novel split of the elasticity law into work-conjugate parts: one representing generally that which is to be held constant, and the other representing that which occurs in reaction to imposed control. The split gives rise to a scalar parameter suitable for quantifying the degree to which a given 1D mechanical process is strain-, energy-, or stress-controlled. The physical sense of the parameter is illustrated through the example of a two-spring system, where one spring represents the subject material, and the other represents the mechanical environment in which the material operates. The example shows that the parameter concisely summarizes the effects of the environment on the operating conditions of the material. We also provide a simple example illustrating how the parameter can be used to rank the fatigue performance of a set of compounds, taking into account the stiffness and the test control mode.
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Authors: B Näser, M Kaliske, WV Mars
Published: 01/09/2010
Journal: Tire Science and Technology 38 (2010)(3), 194-212
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Fatigue investigation of elastomeric structures
Abstract
Fatigue crack growth can occur in elastomeric structures whenever cyclic loading is applied. In order to design robust products, sensitivity to fatigue crack growth must be investigated and minimized. The task has two basic components: (1) to define the material behavior through measurements showing how the crack growth rate depends on conditions that drive the crack, and (2) to compute the conditions experienced by the crack. Important features relevant to the analysis of structures include tim...
Fatigue crack growth can occur in elastomeric structures whenever cyclic loading is applied. In order to design robust products, sensitivity to fatigue crack growth must be investigated and minimized. The task has two basic components: (1) to define the material behavior through measurements showing how the crack growth rate depends on conditions that drive the crack, and (2) to compute the conditions experienced by the crack. Important features relevant to the analysis of structures include time-dependent aspects of rubber’s stress-strain behavior (as recently demonstrated via the dwell period effect observed by Harbour et al.), and strain induced crystallization. For the numerical representation, classical fracture mechanical concepts are reviewed and the novel material force approach is introduced. With the material force approach at hand, even dissipative effects of elastomeric materials can be investigated. These complex properties of fatigue crack behavior are illustrated in the context of tire durability simulations as an important field of application.
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Authors: WV Mars
Published: 01/03/2009
Journal: Rubber Chemistry and Technology 82 (2009)(1), 51-61
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Computed dependence of rubber’s fatigue behavior on strain crystallization
Abstract
This work explores the consequences of strain crystallization on rubber's fatigue crack nucleation behavior over an extensive space of operating conditions, including tension and compression loading states, and relaxing and non-relaxing cycles. The study considers, via computation, how the nonlinear elastic stress-strain behavior, the fatigue crack growth characteristics, and the damage accumulation law combine to produce the Haigh diagram and the Cadwell diagram. Four hypothetical materials are...
This work explores the consequences of strain crystallization on rubber's fatigue crack nucleation behavior over an extensive space of operating conditions, including tension and compression loading states, and relaxing and non-relaxing cycles. The study considers, via computation, how the nonlinear elastic stress-strain behavior, the fatigue crack growth characteristics, and the damage accumulation law combine to produce the Haigh diagram and the Cadwell diagram. Four hypothetical materials are studied, which differ in their crystallization and associated fatigue crack growth behavior. The calculations demonstrate that a relatively simple idealization can credibly predict the unique shape and sensitivities of observed fatigue behavior over a wide range of conditions. They also clarify how features of the Haigh and Cadwell diagrams are linked to the occurrence of crystallization and to parameters such as the power-law slope and the fatigue threshold.
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Authors: R. Harbour, A. Fatemi, W. V. Mars
Published: 01/07/2008
Journal: International Journal of Fatigue Vol. 30, Issue 7, July 2008, pp. 1231-1247.
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Fatigue Life Analysis and Predictions in NR And SBR Under Variable Amplitude and Multiaxial Loading Conditions
Abstract
This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to ...
This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.
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Authors: R. Harbour, A. Fatemi, W. V. Mars
Published: 01/01/2008
Journal: ASME Journal of Engineering Materials and Technology, Vol. 130, 011005 (2008) (11 pages) DOI:10.1115/1.2806276
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Constitutive Behavior and Temperature Effects in NR and SBR Under Variable Amplitude and Multiaxial Loading Conditions
Abstract
Knowledge of the stress response of a material to the applied deformations is necessary for many engineering analysis and applications. This paper addresses the observed effects of load sequencing, Mullins effect, and multiaxial loading on the constitutive behavior of rubber under variable amplitude conditions for a series of experiments using multiaxial ring test specimens. Two filled rubber materials were used and compared in this study; natural rubber, which strain crystallizes, and styrene b...
Knowledge of the stress response of a material to the applied deformations is necessary for many engineering analysis and applications. This paper addresses the observed effects of load sequencing, Mullins effect, and multiaxial loading on the constitutive behavior of rubber under variable amplitude conditions for a series of experiments using multiaxial ring test specimens. Two filled rubber materials were used and compared in this study; natural rubber, which strain crystallizes, and styrene butadiene rubber (SBR), which does not. A pseudoelastic approach is used to model the cyclic stress-strain response for both materials. The implications of inelasticity when using hyperelastic material models are also discussed. Based on temperature results for the multiaxial ring specimen obtained via a thermal imaging system for SBR, a model capable of accurately predicting surface temperature for the multiaxial ring specimen as a function of hysteresis area and test frequency has been developed.
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Authors: M. A. Castellucci, A. T. Hughes, W. V. Mars
Published: 13/07/2007
Journal: Experimental Mechanics, 48, 1-8, 2008.
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Comparison of Test Specimens for Characterization of Dynamic Properties of Rubber
Abstract
Dynamic material properties inferred via experiment can be strongly influenced by the choice of test specimen geometry unless care is taken to ensure that mechanical fields (stress, strain, etc.) within the specimen adequately reflect the ideal homogeneous deformation state. In this work, finite element models of simple shear, cylindrical compression, simple tension, and bi-conical shear test specimens were analyzed in order to quantify the relative conformity of each specimen to its correspondi...
Dynamic material properties inferred via experiment can be strongly influenced by the choice of test specimen geometry unless care is taken to ensure that mechanical fields (stress, strain, etc.) within the specimen adequately reflect the ideal homogeneous deformation state. In this work, finite element models of simple shear, cylindrical compression, simple tension, and bi-conical shear test specimens were analyzed in order to quantify the relative conformity of each specimen to its corresponding ideal. Three metrics of conformity were evaluated, based respectively on the distributions of stress, strain, and strain energy density. The results show that a simple shear specimen provides superior conformity. Other factors involved in the selection of test specimen geometry are also discussed. Such factors include relative linearity and symmetry of measured stress–strain data, grip slip, and heat build up.
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Authors: W. V. Mars, A. Fatemi
Published: 01/07/2004
Journal: Rubber Chemistry and Technology
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Factors that Affect the Fatigue Life of Rubber: A Literature Survey
Abstract
Many factors are known to influence the mechanical fatigue life of rubber components. Four major categories of factors are reviewed here: the effects of mechanical loading history, environmental effects, effects of rubber formulation, and effects due to dissipative aspects of the constitutive response of rubber. For each category, primary factors are described, and existing literature is presented and reviewed. Rubber's fatigue behavior is extremely sensitive to both the maximum and minimum cycl...
Many factors are known to influence the mechanical fatigue life of rubber components. Four major categories of factors are reviewed here: the effects of mechanical loading history, environmental effects, effects of rubber formulation, and effects due to dissipative aspects of the constitutive response of rubber. For each category, primary factors are described, and existing literature is presented and reviewed. Rubber's fatigue behavior is extremely sensitive to both the maximum and minimum cyclic load limits. Other aspects of the mechanical load history are also discussed, including the effects of static loaded periods (“annealing”), load sequence, multiaxiality, frequency, and loading waveform. Environmental factors can affect both the short and long term fatigue behavior of rubber. The effects of temperature, oxygen, ozone, and static electrical charges are reviewed. A great range of behavior is available by proper manipulation of formulation and processing variables. Effects of elastomer type, filler type and volume fraction, antidegradants, curatives, and vulcanization are discussed. The role of dissipative constitutive behavior in the improvement of fatigue properties of rubber is also reviewed. Four distinct dissipative mechanisms are identified, and their effects on fatigue behavior are described.
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Authors: William Mars, Kevin Barbash, Matthew Wieczorek, Scott Braddock, Joshua Goossens, Ethan Steiner
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Durability of Elastomeric Bushings Computed from Track-Recorded Multi-Channel Road Load Input
Abstract
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 judgemen...
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.
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