Monitoring the degradation in shear and bulk moduli of rubber for inclusion in viscoelastic FE models - pt. 2.

(The first part of this article appeared in the December 2000 issue of Rubber World)

Viscoelastic characterization of rubber

First, a washer was simulated in a Jamak jig. Modeling used MARC non-linear code suited for rubber analysis, and assumed axial symmetry. Figure 8 shows a mesh along with contact bodies - deforming washer and rigid plunger and base.

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Figure 9 shows contours of the axial stress (component 11) upon compressing the section of seal to 50% of its original height. Note bulging of the washer at both inner and outer bores. Note also a lack of uniformity of stresses within the compressed section of the washer.

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Researchers today emphasize data acquisition (usage of continuous methods, locating cells at the ambient, round robin testing, etc.), whereas analysis at WIDL clearly shows the non-uniform state os stress within the washer used in the industry. Shouldn't we give importance to the shape of the sample first? Similarly, the ratio of free surface to cross section compressed is still open to debate.

Relaxation samples

As indicated earlier, FEA requires decay in shear and bulk moduli, not the compressive. Tests were developed at WIDL to strain rubber samples in deviatoric and hydrostatic modes of deformation. Figure 10 shows the samples and hardware WIDL advances to the left of the washer in the Jamak jig that was modeled.

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Modeling SSR samples

Shear stress relaxation (SSR) samples were modeled using MARC. Figure 11 shows a section of the SSR apparatus in the background and a close-up to the mesh and boundary conditions in the front. The outer face of the tubular rubber sample was fixed in the radial and axial directions. Nodes at the inner bore of the sample were moved axially.

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Figure 12 shows contours of the shear stress in the foreground, at a nominal strain of 50%. The axial symmetric model and boundary conditions are still shown in the background. Note the uniformity of the stress field and the absence of shear. Note also the zero shear stress in the plan r-[Theta] on figure 12. Shear stresses in z-[Theta] were also null.

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Modeling VSR samples

Figure 13 is a three-dimensional representation of the volumetric stress relaxation (VSR) test at WIDL. This is a modification to the quasi-static hydrostatic test. The base is notched to hold the cylinder hosting the rubber button. A piston compresses the button as forces are transmitted to a load cell at the ambient. The lid of the main coffin (bottom of three) is sealed using o-rings. Rods and liquid nitrogen lines heat and cool off the main coffin. Insulation maintains the temperature constant; and, an outer coffin holds the system together. Load cells can be compressed to specific levels in the system by WIDL. These are hooked to a data acquisition system.

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WIDL made use of the MARC code in designing samples and holders for SSR and VSR testing. Figure 15 shows a VSS button model as per axial symmetry. Figure 16 is a close-up to the mesh and highlights restraints and rigid contacts. Nodes facing the plunger were moved in the compressive axial direction (negative x). Figure 17 shows contours of x-displacements in the section of VSR button modeled. Figure 18 presents contours of the normal stress. Figures 17 and 18 show deformed mesh along with the undetormed contour of the button. Note the bands in axial displacements.

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Figure 18 expresses values at the edges of the modeled button. Figure 19 presents contours of shear stresses on a WIDL VSR button. Note the absence of shear stresses. As total stresses are made of shear and volumetric components, stresses in buttons by WIDL are hydrostatic. These are therefore appropriate for the characterization of rubber in time. Further, SSR and VSS tests at WIDL provide data that can directly be used in finite element modeling (no need to assume Poisson's ratio equal to 0.5).

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Viscoelastic analysis of a seal

A 60A durometer silicone rubber used in making a perimeter pressed-in-place (PIP) gasket for a valve cover for Ford was characterized under SSR and VSR at WIDL. Figure 20 shows the gasket in the groove and through a rear retainer.

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Rubber was also characterized under quasi-static conditions. Independent modes of deformations (uniaxial tension and compression, planar tension and volumetric compression) were completed at WIDL. Data collected under deviatoric modes of deformation was fitted strain energy functions. Also, relaxation data defined Prony series for the viscoelastic response of rubber.

Figure 21 presents contours of the compressive stress on the section of seal at 3.88 and 10% nominal strains. Sealing lines are defined in light of leak testing rings made of the silicone rubber. Figures 22 and 23 highlight degradation in sealing across the gasket, initially compressed to 10% of its original height.

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The images on figures 22 and 23 are snapshots taken at 12.9, 103, 410 and 1,000 hours from first installation of the seal between valve cover and head cylinder. It appears that viscoelastic modeling could shed light as to the life of seals and their onset of leakage in time.

Conclusion

Trends in the rubber industry to develop seals that remain fit over extended periods of time create a need for virtual testing. This consists of (1) material characterization to (2) computer simulation.

This article reviewed the theory of viscoelasticity as coded in finite element software. It reviewed methods developed to characterize rubber for quasi-static and viscoelastic modeling. The article presented a new technique to monitor shear and bulk moduli of rubber for FEA. Modeling samples used in the testing were presented in the article along with that of a PIP gasket for a valve cover.

By and large, research found that:

* Current relaxation methods in the rubber industry are compressive, whereas finite element codes require decay in shear and bulk moduli;

* size and shape of CSR samples are still to define; washers commonly used in the Jamak jig do not yield in uniform compressive stresses: also, exposure to fluids, amount of straining and thermal cycling are still not understood.

While much work is needed in both testing and nonlinear FEA, both should combine in developing and optimizing rubber products.

Dr. Ben Chouchaoui is a graduate of Polytechnic School of Montreal and the University of Waterloo in Canada. He specializes in materials and FEA and currently runs the Windsor Industrial Development Laboratory concentrating on material and process testing and simulation to aid in product design and manufacturing.