Modeling of the elastic properties of compressed expanded graphite - A material used in spiral wound gaskets

doi:10.1016/j.ijpvp.2020.104158

International Journal of Pressure Vessels and Piping

Volume 187, November 2020, 104158

https://doi.org/10.1016/j.ijpvp.2020.104158 Get rights and content

Highlights

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This work presents the way of the numerical modeling of the spiral wound gasket.
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The non-linear elastic properties of expanded graphite were modeled with hyperelastic material model.
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The numerical results were compared with the experimental tests.

Abstract

The paper presents the method of modeling the elastic deformations of expanded graphite, a material used as flexible filling in spiral wound gaskets. Five methods (from A to E) were proposed, by means of which the mean values of the effective elasticmodulus were determined on the basis of the experimentally determined stress-strain characteristics of expanded graphite. The values determined in this way constituted the data set into the isotropic material model, reflecting the elastic properties of the expanded graphite tape in the numerical spiral wound gasket model. A different way of modeling the graphite's elastic properties using the numerical model was method F, in which a nonlinear hyperelastic material model proposed by Blatz-Ko was adapted. The basic purpose of the numerical calculations was to determine both the compression curve of the gasket and the stress distribution in the gasket's windings. The obtained numerical results of the gasket's compression were compared with the experimental test, which allowed the assumptions of the numerical models to be validated. The best way to reflect the elastic behavior of expanded graphite in the gasket's numerical model turned out to be the nonlinear material model presented in method F.

Introduction

Expanded Graphite (EG) is a material produced from Natural Graphite (NG) through a thermo-chemical process called exfoliation. As a result of this process, the volume of graphite increases by about several hundred percent. Due to very good plasticity, low thermal expansion and, above all, low fluid permeability, this material has found a vast application in sealing technology [1,2]. The most common form of its use are gaskets made of Compressed Expanded Graphite (CEG) of a thickness from 0.3 to 5 mm and a density from 0.8 g/cm³ to 1.2 g/cm³. In order to increase the strength of such gaskets, they are internally reinforced with a perforated metal mesh made of stainless steel. After cutting out the gasket from such a sheet, its edges are additionally covered with metal overlaps in order to shield the graphite from the influence of a sealed medium and external agents. In joints operating at medium and high pressure, CEG is used as a material that enhances the tightness of the top layers of metal gaskets or, which is a more adequate term, semi-metal gaskets. This group includes the Spiral Wound Gasket (SWG). A standard construction of such a gasket consists of two tapes (metal and flexible) spirally wound to form a ring. Such a ring, depending on the flange design, can be additionally embedded in two metal rings, internal and external, whose primary task is to increase the strength and axial rigidity of the gasket [3]. The use of an internal ring is mandatory and its task is to prevent the so-called buckling effect of the internal windings [[4], [5], [6], [7]]. The biggest advantage of the SWG over other types of semi-metal gaskets is its good flexibility and high tightness [8]. These properties mostly depend on the quality of graphite filler, as well as its packing density in a spiral structure [9,10]. The advantages of using a SWG with graphite filler were presented in paper [11]. The optimal design should have adequate elasticity (due to filling the unevenness of the flange surfaces), as well as a large elastic recovery due to the joint deformation caused by creep-relaxation and vibrations that reduce the tension of bolts. Proper (required) flexibility of semi-metal gaskets can be achieved, e.g. as demonstrated in Ref. [[12], [13], [14]] by the proper shaping of the metal part. The gasket has to be designed in a way that it does not exceed the allowable stress during both the assembly process and the in-service time, both in the gasket and in all the joint's components, i.e. bolts and flanges. The selection of appropriate gasket features (material and geometry), and the testing of their impact on the load state of the Flange Bolted Joint (FBJ) in a traditional trial and error method is time consuming and not very effective. The most common tool for this type of analysis, accelerating work and optimizing the structure, are commercial programs based on the Finite Element Method (FEM). By using this method to analyze the FBJ, stress and strain in particular components can be accurately assessed [[15], [16], [17], [18]]. The basic step when preparing the computational model of the analyzed joint, besides a previously prepared geometric model, is the correct mapping of material properties. For metal components, i.e. bolts, flanges, nuts and washers, this step is not complicated. Regardless of whether elastic or elastic-plastic simulation is planned, isotropic models of steel with associated data are available in the library of commercial software. In the case of the gasket model, a necessary step is to determine (experimentally) the characteristic that describes the relationship between the stress and strain of the gasket, and then assign it to the “GASKET” material model. Such a model is also available in material libraries of commercial software such as ANSYS, ABAQUS or Solid Works. Nevertheless, the “GASKET” material model has some limitations of its use, since the geometry of the gasket has to be flat with a rectangular cross-section. For gaskets with a more complex shape, such as the SWG, its modeling by means of FEM can by performed in two ways, simplified or exact. In the simplified method, a geometric model of the SWG is treated as a ring with a rectangular cross-section without division onto metal windings and elastic filler. The whole structure is uniform, with the properties of the metal tape and filler tape being treated as a one solid material. The above mentioned simplified method of the SGW's modeling by means of FEM was presented in Ref. [19,20]. In the exact method, the geometric model of the SWG reflects the real shape of the gasket's cross-section, including the metal tape, elastic tape (CEG filler) and distance rings. In this case, material properties should be assigned to the individual gasket's components. Moreover, the geometry of the filler (CEG) is not flat (usually “V” shape), so the “GASKET” material model is not applicable. After analyzing papers [4,21,25] (concerning numerical modeling of the SWG), in which the exact method was used, the properties of the elastic filler (CEG material) were defined as a linear elastic and isotropic material model with a constant value of Young's modulus. Taking an improper value of the Young's modulus in CEG simulation can lead to large discrepancies between numerical and experimental results. In this paper, based on the experimentally determined compression characteristics of CEG, five methods have been proposed to determine the average value of the effective Young's modulus. Each of them was used to define the elastic, isotropic properties of CEG material in a numerical model of a SWG structure. An alternative method of CEG modelling in a SWG structure involved the use of the nonlinear hyperelastic material model proposed by Blatz-Ko. As a result, six numerical SWG models with the same geometry were subjected to compression simulation. The numerically determined stiffness characteristic of each model was analyzed and compared with the stiffness characteristic obtained in an experimental way.

Section snippets

Object, purpose and scope of tests

The research subjects were two basic elements:

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the spiral wound gasket DN40 PN40 with a thickness of 6.0 mm, embedded in metal rings - internal and external. The metal rings and the spiral metal tape were made of 1.4301 steel. The material of the filler was CEG with a density of 1 g/cm³ and a nominal thickness of 0.7 mm. The gasket assigned DN40 PN40 (in accordance with standard EN 1514–2 2014) indicates that the nominal sealing pressure is equal to 40 bar and the nominal gasket's diameter is

Determination of CEG elasticity

Based on the conducted test and data taken from work [22], it was shown that the elastic modulus of CEG strongly depends on the compression level which causes the reduction of the material porosity. In accordance with [23], dependence of the elastic modulus as a function of porosity is described by equation: $E = E_{0} {(1 - a P)}^{b}$ where:

E₀ – elastic modulus at zero porosity.

P - porosity,

a, b - material constants.

Using equation (2) and the material constants taken from work [23], the elastic modulus at the

Method F

In this case, the hyperelastic Blatz-Ko material model was adapted in order to reflect the elastic properties of the CEG. It is a model to simulate deformations of highly compressible materials characterized by an open cell structure. It provides a very good result when modeling Polyurethane Foam (PUF) with low density [26]. The following general equation describes the energy accumulated in a unit of volume of the deformed material: $W (J_{1}, J_{2}, J_{3}) = \frac{μ f}{2} [(J_{1} - 3) - \frac{2}{q} (J_{3}^{q} - 1)] + \frac{μ ((1 - f)}{2} [(J_{2} - 3) - \frac{2}{q} (J_{3}^{- q} - 1)]$

Computational model

An axisymmetric model of the SWG located between two plates is presented in Fig. 10. The upper and lower plates represented the hydraulic press plates of the test rig. The material of the press plates, as well as the metal strip of spiral windings, were modeled with an isotropic, elastic-plastic bilinear model, in which the following parameters were set: elastic modulus E = 180 000 MPa, Poisson ratio v = 0,3 elastic limit R_e = 250 MPa, elastic modulus in a plastic zone E_u= 8000 MPa. The gasket

Conclusion

On the grounds of the conducted experimental and numerical tests, the following conclusions can be drawn:

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Compressed expanded graphite subjected to compression exhibits a nonlinear relationship between stress-strain.
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The basis for determining the elastic effective modulus presented in this work was the compression curve determined at the maximum allowable stress of CEG material. For CEG material with a density of 1 g/cm³, the maximum allowable stress was 150 MPa.
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During compression, the density of

Summary

As demonstrated in this work, an important issue in modeling the deformation of a spiral wound gasket is the proper definition of the material model of a CEG's tape, since its elastic properties have a strong influence on the shape of the gasket's compression curve. Out of the five methods determining the value of the CEG's effective elastic modulus in the isotropic material model, the most appropriate (in the whole range of deformation) was the one presented in method E. In this method, the

Declaration of competing interest

The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in

Acknowledgment

“Calculations were carried out using resources provided by the Wroclaw Centre for Networking and Supercomputing (http://wcss.pl), grant No. 444"

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View full text

Modeling of the elastic properties of compressed expanded graphite - A material used in spiral wound gaskets

Highlights

Abstract

Introduction

Section snippets

Object, purpose and scope of tests

Determination of CEG elasticity

Method F

Computational model

Conclusion

Summary

Declaration of competing interest

Acknowledgment

J. Phys. Chem. Solid.

Int. J. Pres. Ves. Pip.

Int. J. Pres. Ves. Pip.

Int. J. Pres. Ves. Pip.

Int. J. Pres. Ves. Pip.

Mater. Char.

Carbon

Prog. Mater. Sci.

Procedia Engineering

Flexible graphite for gasketing, adsorption, electromagnetic interference shielding, vibration damping, electrochemical applications, and stress sensing

J. Mater. Eng. Perform.

Analysis of the compression behavior of spiral wound gasket

Buckling and lateral pressure in spiral wound gaskets

Experimental and analytical evaluation of buckling forces of a spiral wound flexible gasket

Proceedings of the ASME Pressure Vessels and Piping Conference - Computer Technology, PVP-