Large deformations · relaxation · post- Finite Element Simulation … · 2018-07-27 ·...

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KONSTRUKTION UND SIMULATION CONSTRUCTION AND SIMULATION 46 KGK · 7-8 2018 www.kgk-rubberpoint.de Large deformations · relaxation · post- vulcanization · seal · leakage Service conditions in rubber compo- nents may provoke damage in them, leading to their incapability to develop their original functions. Ageing pro- vokes non-recoverable changes in their structure due to relaxation and post- vulcanization processes. This paper presents a computational methodology to reproduce the thermomechanical ageing in elastomers in the long term and at high temperatures within the large deformation hyperelasticity. A better understanding of this phenom- enon is described qualitatively by simu- lating the mechanics of an O-ring seal. It is proved that leakage is prone to appear under certain severe conditions. Finite Elemente Simulation der gummimechanischen Eigenschaften unter Thermo- Mechanischer Alterung Große Deformationen · Relaxation · Postvulkanisationsprozesse · Dichtung · Leckage Die Anwendungsbedingungen von Gummi-Komponenten können zu Schäden in ihnen führen und zum Funktionsverlust. Alterung provoziert irreversible Veränderungen in ihrer Struktur durch Relaxation und Postvul- kanisationsprozesse. In diesem Artikel legen wir eine rechnerische Methode dar, um die thermomechanische Alte- rung in Elastomeren für lange Zeiträu- me und bei hohen Temperaturen unter großer Verformungshyperelastizität zu reproduzieren. Am Beispiel einer Simu- lation der Mechanik einer O-Ring Dich- tung wird ein besseres Verständnis die- ses Phänomens qualitativ erreicht. Es wird bewiesen, dass unter bestimmten harschen Anwendungsbedingungen, die Leckageanfälligkeit sehr wahr- scheinlich ist. Figures and Tables: By a kind approval of the authors. 1. Introduction The long-term mechanical behaviour of elastomers has a substantial interest in industry since their specifications have to be maintained along their service life [1, 2, 3, 4]. Moreover, in certain areas of engineering, real-life service conditions have to be considered in order to deter- mine mechanical properties along time and the lifetime prediction of industrial components. Ageing consists of an alteration of the chemical and/or physical structure of a material due to the environmental ef- fects. This phenomenon generally leads to a detrimental effect on the mechani- cal behaviour which provokes a gradual loss of its original functionality so dura- bility is limited [5]. Furthermore, damage in elastomeric components is brought forward due to high temperatures [3, 6, 7]. Specifically, physical processes are re- versible whereas chemical processes are non-recoverable (see Figure 1) [3, 8, 9]. Generally, it has been proved that the stress decreases during a relaxation test but post-vulcanization may not allow having a pure relaxation state. Post-vul- canization appears when the second newly formed network provokes shrink- age of the specimen due to an increase of the stiffness. Some authors have ob- served the strong influence of the second phenomenon in some elastomers [8, 10]. The newly formed network is stress free in the assembly configuration but it in- creases the stiffness when the specimen is deformed again or unloaded and pro- vokes residual strains (see Figure 1). From an experimental standpoint, dif- ferent procedures have been described in the literature. Tests commonly used are the continuous relaxation test, the per- manent set and the intermittent relax- ation test [8, 11, 12, 13, 14, 15]. On the other hand, numerical modelling of in- dustrial applications is used to analyze the long-term mechanical response to real-life service conditions including high temperature states [2]. Some authors have proposed numerical models to re- produce the ageing behaviour of elasto- mers within the continuum mechanics and some of their works have been vali- dated using experimental data. The works developed by Septanika et al. [16, 17] proposed a kinematic formulation within the large deformation hyperelas- ticity for rubber materials. Moreover, Septanika et al. [17] validated their nu- merical results with experimental data from intermittent and stress-relaxation tests. Some years later, Shaw et al. [18] presented a numerical and experimental study to reproduce the mechanics of elastomers at temperatures within the chemo-rheological range (90-150 ºC, natural rubber). Other constitutive mod- el was proposed by Budzien et al. [9]. They assumed the independent network hypothesis [19, 20] and validated it by means of two experimental data sets. Recently, Lion et al. [3] presented a three- dimensional numerical model under fi- nite deformations to define the chemical ageing phenomenon accounting for the incompressibility, the temperature de- pendence within a hyperelastic model and the creation of a new network. Other authors deal with the thermo-oxidative ageing of elastomers as the contribution of Johlitz et al. [21] shows. Some other Finite Element Simulation of the Rubber Mechanical Behaviour due to thermomechanical Ageing Authors Belén Hernández-Gascón, José M. Bielsa, Leticia A. Gracia, Ángel Escolán, Zaragoza, Spain Sergio Sádaba, Madrid,Spain, Thomas Pütz, Koblenz, Germany Corresponding Author: Dr. Belén Hernández-Gascón ITAINNOVA – Aragon Institute of Technology Materials and Components Division– C/ María de Luna, 7 50018, Zaragoza, Spain E-Mail: [email protected]

Transcript of Large deformations · relaxation · post- Finite Element Simulation … · 2018-07-27 ·...

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Large deformations · relaxation · post-vulcanization · seal · leakage

Service conditions in rubber compo-nents may provoke damage in them, leading to their incapability to develop their original functions. Ageing pro-vokes non-recoverable changes in their structure due to relaxation and post-vulcanization processes. This paper presents a computational methodology to reproduce the thermomechanical ageing in elastomers in the long term and at high temperatures within the large deformation hyperelasticity. A better understanding of this phenom-enon is described qualitatively by simu-lating the mechanics of an O-ring seal. It is proved that leakage is prone to appear under certain severe conditions.

Finite Elemente Simulation der gummimechanischen Eigenschaften unter Thermo-Mechanischer Alterung Große Deformationen · Relaxation · Postvulkanisationsprozesse · Dichtung · Leckage

Die Anwendungsbedingungen von Gummi-Komponenten können zu Schäden in ihnen führen und zum Funktionsverlust. Alterung provoziert irreversible Veränderungen in ihrer Struktur durch Relaxation und Postvul-kanisationsprozesse. In diesem Artikel legen wir eine rechnerische Methode dar, um die thermomechanische Alte-rung in Elastomeren für lange Zeiträu-me und bei hohen Temperaturen unter großer Verformungshyperelastizität zu reproduzieren. Am Beispiel einer Simu-lation der Mechanik einer O-Ring Dich-tung wird ein besseres Verständnis die-ses Phänomens qualitativ erreicht. Es wird bewiesen, dass unter bestimmten harschen Anwendungsbedingungen, die Leckageanfälligkeit sehr wahr-scheinlich ist.

Figures and Tables: By a kind approval of the authors.

1. IntroductionThe long-term mechanical behaviour of elastomers has a substantial interest in industry since their specifications have to be maintained along their service life [1, 2, 3, 4]. Moreover, in certain areas of engineering, real-life service conditions have to be considered in order to deter-mine mechanical properties along time and the lifetime prediction of industrial components.

Ageing consists of an alteration of the chemical and/or physical structure of a material due to the environmental ef-fects. This phenomenon generally leads to a detrimental effect on the mechani-cal behaviour which provokes a gradual loss of its original functionality so dura-bility is limited [5]. Furthermore, damage in elastomeric components is brought forward due to high temperatures [3, 6, 7]. Specifically, physical processes are re-versible whereas chemical processes are non-recoverable (see Figure 1) [3, 8, 9]. Generally, it has been proved that the stress decreases during a relaxation test but post-vulcanization may not allow having a pure relaxation state. Post-vul-canization appears when the second newly formed network provokes shrink-age of the specimen due to an increase of the stiffness. Some authors have ob-served the strong influence of the second phenomenon in some elastomers [8, 10]. The newly formed network is stress free in the assembly configuration but it in-creases the stiffness when the specimen is deformed again or unloaded and pro-vokes residual strains (see Figure 1).

From an experimental standpoint, dif-ferent procedures have been described in the literature. Tests commonly used are the continuous relaxation test, the per-manent set and the intermittent relax-ation test [8, 11, 12, 13, 14, 15]. On the other hand, numerical modelling of in-dustrial applications is used to analyze the long-term mechanical response to real-life service conditions including high temperature states [2]. Some authors have proposed numerical models to re-produce the ageing behaviour of elasto-mers within the continuum mechanics

and some of their works have been vali-dated using experimental data. The works developed by Septanika et al. [16, 17] proposed a kinematic formulation within the large deformation hyperelas-ticity for rubber materials. Moreover, Septanika et al. [17] validated their nu-merical results with experimental data from intermittent and stress-relaxation tests. Some years later, Shaw et al. [18] presented a numerical and experimental study to reproduce the mechanics of elastomers at temperatures within the chemo-rheological range (90-150 ºC, natural rubber). Other constitutive mod-el was proposed by Budzien et al. [9]. They assumed the independent network hypothesis [19, 20] and validated it by means of two experimental data sets. Recently, Lion et al. [3] presented a three-dimensional numerical model under fi-nite deformations to define the chemical ageing phenomenon accounting for the incompressibility, the temperature de-pendence within a hyperelastic model and the creation of a new network. Other authors deal with the thermo-oxidative ageing of elastomers as the contribution of Johlitz et al. [21] shows. Some other

Finite Element Simulation of the Rubber Mechanical Behaviour due to thermomechanical Ageing

AuthorsBelén Hernández-Gascón, José M. Bielsa, Leticia A. Gracia, Ángel Escolán, Zaragoza, Spain Sergio Sádaba, Madrid,Spain, Thomas Pütz, Koblenz, Germany

Corresponding Author:Dr. Belén Hernández-GascónITAINNOVA – Aragon Institute of TechnologyMaterials and Components Division– C/María de Luna, 750018, Zaragoza, SpainE-Mail: [email protected]

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works focus on industrial applications [1, 22, 23]. A predicting lifetime tool for sealing elements was presented by Achenbach et al. [2]. They used a chemi-cal approach to model the degradation due to chain scission.

Within the objective of giving support to the mechanical design of rubber com-ponents, this report presents a computa-tional methodology to reproduce quali-tatively and macroscopically the me-chanical effects of chemical ageing in elastomers in the long term and at high temperatures within the large deforma-tion hyperelasticity, being capable to re-produce both, the relaxation and the post-vulcanization processes at the same time. Specifically, this contribution fo-cuses only on thermal ageing when a component is subjected to mechanical loads, i.e. thermomechanical ageing. The major concern is the deterioration of the mechanical response of components used as sealing elements which may pro-voke a loss of interference leading to leakage. Thus, the scheme proposed fo-cuses on obtaining an efficient numeri-cal tool which allows observing the me-chanical response due to thermal ageing from a phenomenological point of view. Then, the numerical methodology is used to reproduce the mechanical re-sponse of an O-ring seal.

2. Finite element model applicationThe mechanics of an elastomeric element subjected to a target temperature in the long term is studied. For that, a typical sealing application has been selected. Specifically, an axisymmetric model of a high diameter O-ring seal is defined. The O-ring is assembled between the housing and a rod, being both defined through analytical surfaces (see Figure 2).

2.1. General overview of the mathematical modelThe constitutive modelling is defined within the large deformation hyperelas-ticity for quasi-incompressible materi-als. In general, a common way to formu-late the mathematical model is to pos-tulate a strain energy function (SEF), ψ (F), which depends on the actual de-formed state. The general mathematical representation of the SEF is expressed as follows:

(1)

Where and are given scalar-valued functions of the Jaco-bian (J) and the isochoric part of the right Cauchy Green tensor , respec-tively, that describe the volumetric and isochoric responses of the material [26]. The tensor is the standard defor-mation gradient and its isochoric part is expressed as . Likewise, the Cau-chy stress tensor (σ) can then be ob-tained by means of the push-forward operation of the second Piola-Kirchhoff stress, . The second Piola-Kirch-hoff S [27] is defined as:

Fig. 1: Definition of the different confi-gurations during thermal ageing.

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Fig. 2: Finite element model representing the O-ring seal in the undeformed configura-tion. An extruded view of the axisymmetric model is shown.

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(2)

Particularly, the SEF can be also ex-pressed as the contribution of different terms:

(3)

where the different terms define inde-pendent contributions. Specifically, ψ0 corresponds to the SEF for the initial vul-canized elastomer, ψR is the energy rep-resenting the relaxation phenomena and ψPV represents the SEF associated with the post-vulcanized network. The model is projected to reproduce the post-vulca-nization process from a phenomenologi-cal standpoint.

2.2. Mesh superposition techniqueDue to the additive form of the SEF (see Equation 3), the numerical resolution of the problem may be developed as the su-perposition of the different contributions as a simplified approach. Thus, the current problem is solved with the mesh superpo-sition technique (see Figure 3) [9, 20].

The first and second terms in Equati-on 3 represent the hyperelastic and vis-

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coelastic behaviour. These responses are purely associated with the relaxation process. Let us assume the geometry of interest does not change significantly during the thermal ageing process. Therefore, the variation in the stiffness coefficient corresponds to the chain-scis-sion rate. The material associated with this mechanical response is denoted by “Material a” from now on and it is repre-

sented by one network. Then, the last term in Equation 3 is associated with the post-vulcanization process and, conse-quently, with the creation of new cross-links. This contribution to the global be-haviour is accounted for with the last term in Equation 3 and it is modelled by the second network (Material b). Note that since the mesh superposition tech-nique is being used, only the mechanical

response of one material is defined inclu-ding a hybrid formulation to account for the incompressibility.

2.3. Material modelingTwo different materials (“a” and “b”) are considered in the model in order to sepa-rate the different contributions. Both material models are defined on the basis of the ageing kinetics and lately related to neo-hookean models. Considering the statistical mechanical treatments of rub-ber elasticity given by [28], let the neo-hookean constant be expressed as:

(4)

where is the effective number of crosslinks, k is the Boltzmann constant and θ is the absolute temperature. Note that i refers to relaxation when i=R or to post-vulcanization when i=PV so NR (t) is the number of chains remaining from the initial network and NPV (t) is the number of new chains due to post-vulcanization.

The first network (Material a) repre-sents the relaxation process and the

Fig. 3: Scheme of the mesh superposition technique.

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Fig. 4: Maximal nominal strain after the whole process plotted in the unde-formed shape, before the assembly (“Step 1”), and in the defor-med shape, after the disassembly (“Step 5”) after 1h (a), 10h (b) and 100h (c). Values are norma-lized.

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Fig. 5: Von Mises stresses in the model after 1h, 10h and 100h at the end of the ageing step (“Step 3”) (a) and at the end of the disas-sembly step (“Step 5”) (b). Note that re-sults are displayed separately for the different networks. “Relaxation ele-ments” and “Post- vulcanization” refer to “Material a” and “Material b”, respec-tively. Values are nor-malized.

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chain-scission is modeled as a statistical process being approximated as a first order kinetic reaction as follows:

(5)

whose solution is:

(6)

where τR is the time constant related to the chain-scission.

With regard to the finite element mo-del, this contribution is modelled using the library material model included in the commercial software used (Abaqus). For the sake of simplicity, the incompres-sibility is considered with a hybrid for-mulation for “Material a”.

On the other hand, the mechanical response due to post-vulcanization con-siders a non hybrid formulation and the corresponding constitutive model is defi-ned in a user subroutine. It is assumed

that the post-vulcanization network does not add additional stiffness while the seal is placed in its housing, i.e. in the assembly configuration (see Figure 1) without external loads. However, the post-vulcanization occurs while the com-ponent is fixed in a given position. The additional stiffness appears when the assembly configuration changes due to thermal or mechanical loads. The materi-al model representing the post-vulcani-zation process is also defined according to ageing kinetics and with a neo-hooke-an model. It is postulated that its stiff-ness constant is variable while the samp-le is placed in the assembly configurati-on. Specifically, the creation of new crosslinks during the post-vulcanization process is defined statistically according to the following differential equation:

(7)

whose solution is:

(8)

In these expressions, NS represents the saturation value of vulcanized network and τPV is the time constant related to the new crosslink generation.

Temperature dependence is conside-red in both networks and is included in another user subroutine. It is described according to the Arrhenius equation [2] which depends on a constant represen-ting the activation energy (Ei ):

(9)

In Equation 9, R is the gas constant, θ is the temperature of interest and θ0 is the reference temperature. Note that i=PV for the post-vulcanization process and i=R for the relaxation.

Regarding thermo-rheologically simple materials, it is assumed that experimen-tal curve is the same for each tempera-ture but temporal scale is modified by a

Fig. 6: Total reaction force during the thermal ageing (“Step 3”) and the cooling down step (“Step 4”) obtained in a reference node on the housing. The ageing process lasts 1h (a-d), 10h (b-e) and 100h (c-f). Values are normalized.

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shift factor from a “master curve” accor-ding to:

(10)

Experimental data were obtained from the literature [24]. Ziegler et al. [24] char-acterized an NBR70 in air. “Material a” is defined with C10(0)=1.17 MPa, the time constant for relaxation (τR=133000s) and the activation energy in the relax-ation process ( 12381K). On the other hand, data which describe “Material b” are the time constant for post-vulcaniza-tion (τPV=13840000s), the activation en-ergy in the post-vulcanization process ( 1346K) and the saturation value of vulcanized network (NS=17.02NR(0)). In both cases, the reference temperature is θ0 =100ºC.

2.4. LoadsThe computational model reproduces the different steps of the whole process which

starts when the O-ring seal is assembled and it finishes when the sealing element is disassembled from the housing. The dif-ferent numerical steps are described next. Firstly, the assembly consists of the pro-cess when the seal is assembled in its po-sition at room temperature (θ0) and its duration is assumed to be several orders of magnitude lower than thermal ageing (“Step 1”). Then, the seal is heated from room temperature (θroom=25ºC) until the target temperature (θ), i.e the ageing temperature (“Step 2”). Specifically, two different temperatures are studied, 100ºC and 200ºC. After that, thermal ageing starts and the seal is maintained at the target temperature along a certain time (“Step 3”). For this research, ageing is ana-lyzed at 1h, 10h and 100h. The fourth stage consists of cooling down the seal until room temperature, θroom=25ºC, (“Step 4”) and, finally, the last step is the disassembly process when the seal is re-moved from the seal housing (“Step 5”).

Numerically, the analytical surface of the housing remains fixed in the last step whereas the analytical surface corre-sponding to the rod is removed from the system. Note that in this problem, the geometry reached after the second step corresponds to the assembly configura-tion where post-vulcanization occurs, i.e. during “Step 3”.

3. Results

3.1. Comparison at different ageing timesThe mechanical response of the O-ring seal is compared after different ageing times: 1h, 10h and 100h. The post-vulca-nization temperature reached is 100 ºC, i.e. the reference temperature.

Figure 4 shows the undeformed and deformed shape of the O-ring seal, before the assembly of the O-ring (“Step 1”) and after its disassembly (“Step 5”), respec-tively. The initial shape is not completely recovered in any case, meaning that resi-dual strains appear after the whole pro-cess. The initial shape is almost recovered after 1h whereas permanent deformation becomes significant after 100h.

Von Mises stresses are shown in Figu-re 5 and they represent residual stresses after the different stages of the process. A better understanding of the solution is achieved due to the fact that the mesh superposition technique is used. Thus, both meshes can be shown separately (note that “Material a” refers to relaxati-on and “Material b” refers to post-vulca-nization). Specifically, Figure 5 shows stresses after the ageing step and after the disassembly step. Focusing on the end of the thermal ageing step (“Step 3”), relaxation in “Material a” occurs along time and residual stresses beco-

Fig. 7: Total contact area between the housing and the O-ring seal during the cooling down step (‘Step 4”). The plots correspond to different studied cases: 1h and 100ºC (a), 10h and 100ºC (b), 100h and 100ºC (c) and 100h and 200ºC (d). Values are normalized.

Fig. 8: Maximal nominal strain after the whole process plotted in the undeformed shape, before the assembly (“Step 1”), and in the deformed shape, after the disassembly (“Step 5”), after 100h when the process reaches ageing temperatures of 100ºC (a) and 200ºC (b). Values are normalized.

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mes null after 100h (see Figure 5.a). On the other hand, “Material b” does not add significant stiffness after 100h as expected since the newly formed net-work is stress-free in the assembly confi-guration (see Figure 1).

Results after the disassembly step (Step 5) are shown in Figure 5.b. “Material a” shows residual stresses after 10h and 100h since the stiffness provoked due to post-vulcanization does not allow the ma-terial to recover. Note that residual stres-ses after 10h are higher than after 100h. That is due to the fact that the partial re-covery of the seal provokes some strains in the seal which cause an increase in the stiffness. On the other hand, results in “Material b” also give interesting informa-tion about the recovery of the seal. After 100h, the material is stiff enough so that it does not allow any recovery. When ageing time is 10h, “Material b” can reco-ver slightly, which physically is related to the creation of a lower amount of new crosslinks. As found in “Material a”, the partial recovery of the seal leads to some strains which provoke a stiffening of the material. Finally, 1h of post-vulcanization does not generate significant residual stresses since that this time is low.

Since the housing and the rod are de-fined as analytical surfaces, the reaction force can be computed at a reference node of each surface, and this force value represents the total reaction force on the corresponding surface. From a physical point of view, a reduction in the reaction force suggests that leakage can occur due to the loss of interference between the O-ring seal and the housing or rod, respectively. In order to clarify the re-sults, graphs distinguish the results du-ring the thermal ageing (“Step 3”) and

the cooling (“Step 4”), see Figure 6. Ac-cording to Figure 6, the reaction force decreases over time in all cases. Note that the reaction force becomes null af-ter 100h (Figure 6.f). On the other hand, the loss of sealing capability can be also analyzed by means of the calculation of the total area in contact between the O-ring seal and the housing. According to Figure 7, an increase in ageing time leads to a sooner loss in the total contact area. The total area in contact after 100h reaches the zero value in the same way as the reaction force does (Figure 7.c and Figure 6.f, respectively).

3.2. Comparison at different ageing temperaturesThis subsection is focused on analyzing the differences in the mechanical behav-iour of the O-ring seal under analysis when the ageing temperature reaches 100ºC and 200ºC (at the end of “Step 2”). In both cases, the ageing time is equal to 100h. Figure 8 displays in each of the plots the undeformed and deformed shape of the O-ring seal, before the as-sembly (“Step 1”) and after the disas-sembly (“Step 5”), respectively, and the final maximal nominal strain after the whole process is represented. Note that permanent deformations appear so the initial shape is not recovered. Although the ageing time is the same in both cas-es, nominal strains are 14.8% higher when the temperature increases up to 200ºC than when it goes up to 100ºC. In terms of residual stresses, results sug-gest that, at 200ºC, stresses are 68.4% higher in comparison with the other case. This means that the higher tem-perature provokes the creation of a big-ger amount of new crosslinks. It was

previously observed that the reaction force between the seal and the housing and the total area in contact become null after 100h when the seal is subjected to 100ºC (Figure 6.f and Figure 7.c). In this subsection results show that an increase in temperature up to 200ºC leads to a sooner loss in both, the reaction force and the total area in contact, according to Figure 7.d and Figure 9.

4. Discussion and conclusionsThe thermomechanical ageing process in elastomers under high temperatures could lead to substantial changes in their mechanical properties along time. Like-wise, these changes could provoke their incapability to develop their original me-chanical functions. Within this back-ground, this research presents a numeri-cal framework to analyze thermal ageing in elastomers subjected to mechanical loads in the long term and at high tem-peratures. Moreover, the study is defined within the large deformation hyperelas-ticity and the numerical methodology aims at reproducing the effect of two phenomena that act simultaneously, namely relaxation and post-vulcaniza-tion, from a phenomenological stand-point.

One of the main features observed in this study is the presence of residual strains in the aged seal after the disas-sembly step. This mechanical feature is caused by the additional stiffness gene-rated in the material due to post-vulcani-zation. In other words, the creation of new crosslinks does not allow the mate-rial to recover the original shape (see Fi-gure 10). Specifically, the final shape of the O-ring seal differs significantly after 100h of ageing. Therefore, we conclude

Fig. 9: Total reaction force during the thermal ageing step (“Step 3”) and the cooling down step (“Step 4”). The ageing process lasts 100h whereas the target temperature is 100ºC (a-c) or 200ºC (b-d). Values are normalized.

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that residual strains are higher as the ageing time increases since the newly formed network becomes denser. Our findings are in agreement with some works in the literature. Boyce et al. [29] studied experimentally the stress-strain relationship of elastomeric materials and found residual strains in uniaxial and plain strain compression tests. Likewise, Achenbach et al. [2] also found irreversi-ble stress relaxation when studying the mechanics of sealing elastomers.

Some authors in the literature have proven the validity of the mesh superpo-sition technique [9, 20] which was ap-plied in this work. The main advantage of this numerical approach is that the con-tribution given by each mesh can be analyzed separately in terms of the stress-strain relationship. Stresses pre-sented in Figure 5 allow us to conclude that residual stresses decreases in “rela-xation elements” as the ageing time in-creases whereas “post-vulcanization ele-ments” show an increase in the stiffness after the process.

It is known that the most important mechanical feature of an O-ring seal is its capability to avoid leakage. The analyses of the reaction force in the housing and the total contact area between compo-nents suggests if leakage is prone to ap-pear. Our simulations show that there is a reduction in the reaction force in all cases (see Figure 6 and Figure 9). Moreo-ver, this decrease is more significant at longer ageing times. On the other hand, the total contact area diminishes abrupt-ly in the cooling down step under certain conditions (see Figure 7). Specifically, our results suggest that leakage would ap-pear when ageing lasts 100 h and the material is cooled down from 100ºC, since the total reaction force was found to be null and there was no contact area between the O-ring seal and the housing.

This phenomenon is more evident when the ageing temperature reaches 200ºC (see Figure 7.d). Our findings agree with those in Achenbach et al. [2]. These au-thors found that a gap could appear between the O-ring seal and the surface in contact. Therefore, under certain con-ditions, the contact area between both elements can be null, thus leading to the loss of interference. Regarding the influ-ence of the temperature, our study sug-gests that processes at high temperatu-res provoke an accelerated deterioration in the mechanical response of compo-nents. Therefore, leakage would appear sooner when a process takes place at higher temperatures.

Few limitations are associated with the present study. Firstly, the experimen-tal data was obtained from the literature [24]. Thus, although important conclusi-ons were found from our study and they agree with the mechanics from the rela-xation and post-vulcanization processes, the main implication of this limitation is that our results should be understood from a qualitative and phenomenologi-cal point of view. Likewise, further works will consider an improved constitutive model in order to achieve a best fit bet-ween numerical and experimental data [17].

To sum up, our study presents a nume-rical model capable of describing the time and temperature dependence of the me-chanical behaviour due to thermomecha-nical ageing in elastomers within the large deformation hyperelasticity. We conclu-ded that higher ageing times and higher temperatures accelerate the damage of the seal. Therefore, the functionality of the seal may not be appropriate under certain working conditions. Specifically, useful life should be determined for each specific rubber component in order to avoid un-desirable consequences such as leakage.

Furthermore, the model is capable of re-producing both tendencies, relaxation and post-vulcanization processes, and the mesh superposition technique allows us to analyze how both phenomena behave separately in order to understand the irre-versible strains and residual stresses of elastomers after thermal ageing. Further works will apply this numerical methodo-logy in order to predict the performance and mechanical behaviour of some speci-fic rubber components, as a tool for the support in the design of new parts and improvement of the existing ones.

6. AcknowledgementsThe authors gratefully acknowledge the collaboration of the company TRW Auto-motive to carry out this research.

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Fig. 10: Definition of different configura-tions during thermal ageing process applied to the O-ring.

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Hybride Leichtbautechnologie für Nutzfahrzeugkabinen

HyLIGHT CAB Struktureller, be-zahlbarer Leichtbau durch Mul-ti-Material-Bauweise – das ist das Ziel des Forschungsvorha-bens Hylight Cab. Dabei hat das Projektkonsortium die Kabinen-struktur eines Nutzfahrzeuges im Visier. Ein großer Anteil der weltweiten CO2-Emissionen stammt aus dem Gütertrans-port. Diese können über einen verringerten Kraftstoffver-brauch der eingesetzten Nutz-fahrzeuge reduziert werden. Der dominierende Faktor für den Verbrauch ist dabei die Fahrzeugmasse. Neben der rei-nen Verbrauchsminderung er-gibt sich bei Nutzfahrzeugen ein weiterer Vorteil durch die Leichtbauweise: Sie führt zu ei-ner Reduktion des Leergewichts und damit zu einer Steigerung

der maximal möglichen Zula-dung. Um den hybriden Leicht-bau weiter voran zu bringen, werden diesbezüglich gezielt verfahrenstechnisch hochbean-spruchte Komponenten des LKW-Fahrerhauses erforscht: die Kabinenstruktur. Für die hochbelasteten Bereiche in der Kabine sollen materialhybride Fertigungsverfahren zu einer si-gnifikanten und gleichzeitig be-zahlbaren Gewichtsreduktion führen. Mittelfristig wird die Großserienfähigkeit des Multi-Material-Designs angestrebt. Dazu werden verschiedene Bau-teile in Multi-Material-Bauwei-se entwickelt und in die Kabi-nenstruktur integriert. Dieser anwendungsorientierte Ansatz stellt die Systemintegration in einem Fahrzeug, einschließlich

der dafür erforderlichen Füge-technologien, in das Zentrum der Forschung und soll eine schnelle Umsetzung ermögli-chen. Zudem werden zukünfti-ge Anforderungen an die Kabi-ne, wie geänderte Crash-Anfor-derungen als auch alternative Antriebssysteme, betrachtet. Struktur- sowie Prozesssimula-tionen dienen dem Entwick-lungsprozess im Hinblick auf die Absicherung sowie Maxi-mierung des Leichtbaupotenzi-als. Durch Umsetzung der Kabi-nenstruktur in Multi-Material-Bauweise wird eine Gewichtsre-duktion von 30 Prozent bei Kostenneutralität im Vergleich zur bisherigen Stahlbauweise angestrebt. Weiterhin sollen die entwickelten Lösungen prob-lemlos in die laufende Produkti-

on implementiert werden kön-nen, um schnellstmögliche Seri-entauglichkeit zu erreichen. Ge-fördert wird das Projekt vom Bundesministerium für Wirt-schaft und Energie. Projektpart-ner sind Green Ing, Leutenbach; Fraunhofer ICT, Pfinztal; KIT–Fast, Karlsruhe; Fritzmeier Com-posite, Bruckmühl; Sieben-wurst, Dietfurt a.d. Altmühl. n

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