Fatigue behavior for design optimization of parking brake bracket connections

ABSTRACT Numerical simulation based on finite element analysis is now widely used during the design optimization of tires, thereby drastically reducing the time investment in the design process and improving tire performance because it is obtained from the optimized solution. Rubber material models that are used in numerical calculations of stress–strain distributions are nonlinear and may include several parameters. The relations of these parameters with rubber formulations are usually unknown, so the designer has no information on whether the optimal set of parameters is reachable by the rubber technological possibilities. The aim of this work was to develop such relations. The most common approach to derive the equation of the state of rubber is based on the expansion of the strain energy in a series of invariants of the strain tensor. Here, we show that this approach has several drawbacks, one of which is problems that arise when trying to build on its basis the quantitative relations between the rubber composition and its properties. An alternative is to use a series expansion in orthogonal functions, thereby ensuring the linear independence of the coefficients of elasticity in evaluation of the experimental data and the possibility of constructing continuous maps of “the composition to the property.” In the case of orthogonal Legendre polynomials, the technique for constructing such maps is considered, and a set of empirical functions is proposed to adequately describe the dependence of the parameters of nonlinear elastic properties of general-purpose rubbers on the content of the main ingredients. The calculated sets of parameters were used in numerical tire simulations including static loading, footprint analysis, braking/acceleration, and cornering and also in design optimization procedures.

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Calculating Energy Release Rate as a Function of Crack Length Using a Multiple-Step Crack Closure Technique in Tire Finite Element Models

Tire Science and Technology ◽

10.2346/tire.18.460302 ◽

2018 ◽

Vol 46 (3) ◽

pp. 130-152

Author(s):

Dennis S. Kelliher

Keyword(s):

Finite Element ◽

Energy Release Rate ◽

Crack Length ◽

Energy Release ◽

Crack Closure ◽

Release Rate ◽

Fatigue Behavior ◽

Three Dimensions ◽

Quantitative Prediction ◽

Closure Technique

ABSTRACT When performing predictive durability analyses on tires using finite element methods, it is generally recognized that energy release rate (ERR) is the best measure by which to characterize the fatigue behavior of rubber. By addressing actual cracks in a simulation geometry, ERR provides a more appropriate durability criterion than the strain energy density (SED) of geometries without cracks. If determined as a function of crack length and loading history, and augmented with material crack growth properties, ERR allows for a quantitative prediction of fatigue life. Complications arise, however, from extra steps required to implement the calculation of ERR within the analysis process. This article presents an overview and some details of a method to perform such analyses. The method involves a preprocessing step that automates the creation of a ribbon crack within an axisymmetric-geometry finite element model at a predetermined location. After inflating and expanding to three dimensions to fully load the tire against a surface, full ribbon sections of the crack are then incrementally closed through multiple solution steps, finally achieving complete closure. A postprocessing step is developed to determine ERR as a function of crack length from this enforced crack closure technique. This includes an innovative approach to calculating ERR as the crack length approaches zero.

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