# The mechanical behaviour of SentryGlas\(^{\circledR }\) ionomer and TSSA silicon bulk materials at different temperatures and strain rates under uniaxial tensile stress state

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## Abstract

An innovative type of connections for glass components, called laminated connections, has been developed in the last years. Two materials have been used for laminated connections: the transparent ionomer SentryGlas\(^{\circledR }\) (SG) from Kuraray (former Dupont) and the Transparent Structural Silicon Adhesive (TSSA) from Dow Corning. In this paper, the mechanical behaviour of SG and TSSA bulk materials is studied under uniaxial tensile stress condition. The effects of strain rate and temperature variations are investigated. Particular attention is paid (i) to the study of these polymers in cured condition and (ii) to the computation of true stress and strain field during the tests. Firstly, it is observed that the mechanical behaviour of both SG and TSSA are temperature and strain rate dependent. These effects are quantitatively determined in the paper. Secondly, two additional phenomena are observed. For TSSA, it is observed that the material goes from fully transparent to white colour, exhibiting the so-called whitening phenomenon. For SG, instead, it is observed that the strain field distribution is dependent on the temperature. More specifically, the material exhibits a non-uniform strain field distribution due to the occurring of the necking phenomenon. Measurements along the specimens, using Digital Image Correlation techniques, showed that the localized strain propagates over the full specimen length, resulting in a cold-drawing phenomenon. Finally, it is also shown that engineering and true stress–strain definition exhibits large deviation indicating that the finite deformation theory should be used for the computation of the stress–strain curves to be implemented in numerical modelling.

## Keywords

SentryGlas\(^{\circledR }\) ionomer TSSA silicon Laminated connections Polymer Temperature Strain rate## Introduction

An innovative type of connections for glass components, called laminated connections, has been developed in the last years (Peters 2007; O’Callaghan and Coult 2007; O’Callaghan 2012; Lenk and Lancaster 2013). This bonding technique makes use of transparent adhesive materials produced in solid foils to bond metal to glass. The concept of laminated connections is to use the same production process of laminated glass components. Laminated glass components are made of several glass panels bonded together with transparent adhesive polymeric foils. Once together, glass panels and polymeric foils are placed in a vacuum bag and go through an autoclave lamination process. Similarly, in laminated connections, metal, adhesive and glass parts are placed together in a vacuum bag and then go through the same autoclave process as applied for laminated glass components. For the current publication, two materials used for laminated connection are of specific interest: the transparent ionomer SentryGlas\(^{\circledR }\) (SG) from Kuraray (former Dupont) and the Transparent Structural Silicon Adhesive (TSSA) from DowCorning.

SentryGlas\(^{\circledR }\) (SG) is a thermoplastic transparent ionomer used in laminated glass applications as interlayer. The glass transition temperature of SG is approximately 50–55 \(^{\circ }\hbox {C}\) (Decourcelle et al. 2009; Calgeer 2015). Compared to other interlayers for glass applications (e.g. PVB and EVA) SG is characterized by higher stiffness, enhanced durability and higher mechanical resistance. The SG is typically produced in foil thickness of 0.76, 0.89 and 1.52 mm. SG foils are rather rigid at room temperature. In literature, the bulk SentryGlas\(^{\circledR }\) material has been investigated under uniaxial stress state by several authors (Bennison 2005; Meissner and Sackmann 2006; Belis 2009; Biolzi et al. 2010; Puller et al. 2011; Schneider 2012; Kuntsche and Schneider 2014). Tests were performed at room temperature and different displacement rates. Nominal or so-called engineering stress–strain definitions are generally used. Limited results are available on uniaxial tensile tests at different temperatures (Puller 2012).

^{1}. The glass transition temperature of the polymer is around \(-\)120 \(^{\circ }\hbox {C}\)

^{2}. The curing process is activated by heat and it occurs rather rapidly. Rheometry tests showed that 90 % of the mechanical response is achieved after 15 min at 130 \(^{\circ }\hbox {C}\) (Sitte 2011). TSSA is produced in foils of 1mm thickness. In literature, the available studies on TSSA are mainly focused on connections tested at room temperature (Sitte 2011). Limited studies are performed on TSSA bulk material at different temperature and strain rate. In (Sitte 2011), TSSA bulk material is tested at room temperature and constant displacement rate. Nominal or so-called engineering stress–strain definitions are usually used.

In this paper, the mechanical behaviour of TSSA and SG bulk material is studied under uniaxial tensile stress condition. The effects of strain rate and temperature variations are investigated. The goals of this work are to (i) increase the mechanical understanding of SG and TSSA behaviour in different conditions, (ii) derive the stress–strain curves of SG and TSSA, (iii) investigate the effects of temperature and strain rate and (iv) evaluate the mechanical parameters useful for FEM material modelling (e.g. Young modulus, Poisson’s ratio, etc.) as a function of temperature and strain rate. In this work, particular attention is paid to investigate the polymers in cured condition (as such as they are in laminated connections) and to compute stress and strain field distribution using true definitions.

## Material and method

### Specimens production, measurements system and test setup

Uniaxial tensile tests are performed on dumbbell shaped specimens cut out of laminated SentryGlas\(^{\circledR }\) ionomer and TSSA silicon foils. The adhesive foils went through an autoclave process before testing to investigate their material properties in cured condition. Constant thickness and straightness of the specimens must be guaranteed during the lamination. The polymeric foils are therefore placed between two glass plates before lamination. Teflon foils (PTFE) are placed between glass and adhesives foils to avoid the polymers to stick to the glass. The full pack is then vacuumized and laminated in autoclave. The scheme of Fig. 1a describes the specimen preparation. The autoclave protocol is the same used to produce the laminated connections, as earlier discussed in this work. After lamination, dumbbell specimens are cut out of the laminated foils by Computer Numerically Controlled (CNC) cutting machine.

The dumbbell specimens are based on EN ISO 37-type 2 (International Organization for Standardization 2011) which is equal to EN ISO 527-B type 5a (CEN-European Committee for Standardisation 1996). Figure 1b shows the specimens’ geometry. In the current study, the transversal dimensions are increased with a factor of 2.5. This permits to have sufficient area for clear observation of necking phenomenon, to have accurate Poisson’s ratio measurements and to avoid any sliding in the grips. All the other dimensions are as per EN ISO 37-type 2. The thickness of the SG specimens is 1.5mm. The thickness of TSSA specimens is 1mm.

A Digital Image Correlation (DIC) system is used to compute the full strain field during the tests. Each component of the strain tensor is measured at every location, i.e. vertical elongation, horizontal elongation and shear distortion. These measurements permit to calculate the magnitudes and directions of principal strains, the Poisson’s ratio, the actual cross section of the specimens and the actual stress in the specimens during the test. The use of DIC usually requires the application of a random speckle pattern over a white background painted on the specimen surface. However, this is not here applicable due to the large elongation exhibited by the polymers at failure. Indeed, after a certain level of strain, the white paint would detach from the surface and the strain calculation would consequentially fail. To address this issue a different method is here adopted, which makes use of the material transparency. Firstly, only a speckle random pattern is applied on the specimens without background (see Fig. 2). Then a white panel is placed behind the specimens along both cameras axes (see Figs. 3, 4). This method allows to compute the strain field distribution at large deformation level. If not differently specified, strains are always measured in the narrow parallel-sided portion of the specimens as indicated by EN ISO 38 and EN ISO 527, depicted by Fig. 1 by \(l_{1}\) and here defined as initial *specimen length*.

### Test configurations

According to the guideline ETAG 002 (European Organisation for Technical Approvals 2001), \(-\)20^{3} and 80 \(^{\circ }\hbox {C}\) can be considered as temperature limits for practical purpose in civil engineering, while 23 \(^{\circ }\hbox {C}\) is considered as reference value. According to this indication, TSSA silicon is tested at \(-\)20, 23 and 80 \(^{\circ }\hbox {C}\). SG instead is tested at seven different temperatures within this range: \(-\)20, 0, 23, 30, 40, 60 and 80 \(^{\circ }\hbox {C}\). SG is tested at more temperatures due to its expected high temperature sensitivity. This is because its glass transition temperature, \(T_{g}\), falls within this temperature range (i.e. \(T_{g} \cong 50\)–55 \(^{\circ }\hbox {C}\)) (Decourcelle et al. 2009; Calgeer 2015).

Both materials are then tested at three different crosshead machine displacement rates, in this work indicated as \({\dot{d}}\): 1, 10 and 100 mm/min. Tests at 10mm/min are repeated three times at the same configuration to evaluate results variability. These displacements rates are defined based on practical limitation of the machine. Further tests at very high displacement rate (e.g. m/s) should be performed to evaluate the mechanical response of TSSA and SG in case of impact or blast scenario.

## Results

This section collects the test results of TSSA and SG behaviour under uniaxial tensile stress. The \(x-y\) reference system is defined with *y* along the vertical axis (parallel to the testing direction) and *x* along the horizontal axis (orthogonal to the testing direction) (see Fig. 1). Herein, longitudinal stress and longitudinal strain are here called as \(\sigma _{yy}\) and \(\varepsilon _{yy}\), while transversal strain is defined as \(\varepsilon _{xx}\). The convention of positive strain for material elongation and negative for contraction is here assumed. In the parallel narrow section of the specimen the directions of *y* and *x* axes coincide with the principal directions.

*F*, and initial cross section of the specimens, \(A_{0}\) (see Eq. (1)). Engineering strain is defined as the ratio between length variation, \(\varDelta l\), and initial specimen length under consideration, \(l_{1}\) (see Eq. (2)). The longitudinal stress–strain curves are presented for different temperatures and displacement rates. The correlation between displacement rate and strain rate is later calculated in the following section on results analysis. The ratios between transversal strains and longitudinal strains are also plotted with respect to the longitudinal strain.

### TSSA uniaxial tensile behaviour at different temperatures and displacement rates

This section presents the results of the uniaxial tensile tests on TSSA silicon. The stress–strain curves of TSSA and the effects of temperature and displacement rate variations are presented.

Figure 6a shows the response of TSSA at \(-\)20, 23 and 80 \(^{\circ }\hbox {C}\). The stress–strain curve firstly exhibits a short linear behaviour up to engineering stress approximately equal to 2 MPa. This is then followed by nonlinear behaviour that continues up to failure. The material seems to exhibit hyperelastic behaviour, confirming preliminary results of (Sitte 2011). Tests repeated in the same configuration (see Fig. 6b) give similar results with limited variation. Initial stiffness and the stress–strain curve are not significantly affected by temperature. This is in line with expectation since the glass transition temperature of silicon is below the investigated range of temperature. It is observed that the \(80\,^{\circ }\hbox {C}\) curve is comprised between 23 and \(-\)20 \(^{\circ }\hbox {C}\) curves. Further tests should be performed to assess if this is due to statistical variation or a temperature effect. The maximum stress and strain are observed to be temperature dependent. If compared to the one at 23 \(^{\circ }\hbox {C}\), the maximum stress at failure increases when the temperature goes down to \(-\)20 \(^{\circ }\hbox {C}\) and decreases when temperature goes up to 80 \(^{\circ }\hbox {C}\). The maximum strain also increases at low temperature and decreases at high temperatures.

Figure 6c shows the behaviour of transversal strain over time for TSSA material at different temperatures. The results are expressed in terms of ratio between transversal and longitudinal strain. This ratio corresponds to the definition of Poisson’s ratio. The curves firstly show a constant horizontal behaviour around a value of 0.44. At large deformation, the ratio decreases linearly with the logarithm of the longitudinal strain. The effects of temperature variation appear to be negligible.

### SG uniaxial tensile behaviour at different temperature and displacement rates

This section presents the results of the uniaxial tensile tests on SG ionomer. The stress–strain curves of SG and the effects of temperature and displacement rate variations are presented.

Figure 8a shows the response of SG at \(-\)20, 0, 23, 30, 40, 60 and 80 \(^{\circ }\hbox {C}\). All curves initially exhibit a linear behaviour at any temperature. The slope of the curve decreases as temperature increases (see Fig. 8b). Then, each curve shows large non-linear behaviour up to failure. However, the shape of the curve depends on the temperature. Two behaviour types can be distinguished: (i) SG response at temperature above or equal to 40 \(^{\circ }\hbox {C}\) and (ii) SG response at temperature below 40 \(^{\circ }\hbox {C}\). For a temperature above or equal to 40 \(^{\circ }\hbox {C}\) the curve gradually tends to a plateau value where large deformation occurs. This is then followed by a strain hardening behaviour up to failure. For temperature below 40 \(^{\circ }\hbox {C}\) instead, it is possible to observe a clear yielding stress, defined as the relative maximum occurring after the linear part. After this relative maximum, the stress–strain curve exhibits a softening branch. This is then followed by a hardening behaviour. The maximum stress at failure is usually comparable or larger than the yielding stress. This behaviour of SG at temperatures below 40 \(^{\circ }\hbox {C}\) is in line with results in literature (Puller et al. 2011) and it is common for polymeric material in the so-called “glassy state” i.e., adhesives at temperature below their glass transition temperature.

Figure 8c shows the behaviour of transversal strain over time for SG material at different temperatures. The results are expressed in terms of ratio between transversal and longitudinal strain. This ratio corresponds to the definition of Poisson’s ratio. The curves firstly show a constant horizontal behaviour. Here, the Poisson’s ratio value falls in the range of 0.4–0.5 and it is temperature dependent. It is about 0.4 for low temperature and tends to 0.5 when temperature increases. In case of large deformation, the ratio decreases linearly with the logarithm of the longitudinal strain.

The yielding stress and the maximum stress at failure are strongly temperature dependent. The yielding stress and the maximum stress at failure increase when temperature decreases. The maximum strain at failure instead decreases when temperature decreases, going from more than 300 % to 70 %. For temperatures above 40 \(^{\circ }\hbox {C}\) the maximum displacement capacity of the machine is reached before failure. Tests repeated in the same configuration (see Fig. 9b) give similar results with limited variation. However, comparison between SG and TSSA (Figs. 6b, 9b) denotes that the silicon variation is smaller than the ionomer one. For the sake of comparison, Fig. 9c shows TSSA and SG curves at high temperature.

## Analysis of results

### Necking effect on SG

A relevant difference between the SG ionomer behaviour at high and low temperatures is observed by analysing in detail the strain field distribution during the test. Figure 10 shows the strain field distribution computed by DIC during the tests. For temperatures equal to or above 40 \(^{\circ }\hbox {C}\) the strain field distribution is uniform along the specimens length for both small and large strain range (Fig. 10a) (where *specimens length* is the narrow parallel-sided portion of specimens indicated Fig. 1 by \(l_{1})\). On the contrary, for temperatures below 40 \(^{\circ }\hbox {C}\), the strain field behaviour is more complex. Indeed, for small strain values (i.e. elastic region) the strain field distribution is uniform (such as shown in Fig. 10a). When stress increases and approaches the yielding point, a local strain concentration starts to occur (Fig. 10b).

*necking effect*(Ehrenstein 2001), is clearly visible even with the naked eye, and occurs for all tests performed below 40 \(^{\circ }\hbox {C}\). The necking effect corresponds to the softening phase of the stress–strain curve.

*cold drawing*(Ehrenstein 2001; Roylance 1996). When the plastic propagation is fully extended, which corresponds to the beginning of the hardening phase, the strain field is uniform again and increases until failure.

The necking effect is observable also from Fig. 11. The latter shows the longitudinal strain versus time in case global measurement (average along the specimens length) or local measurement (locally measured in the necking region). Firstly, there is an initial linear behaviour, i.e. constant strain rate over time, where global and local measurements give same results. Once the yielding stress is reached the two strain curves deviate. The local strain increases more rapidly if compared to the global one. This phenomenon corresponds to the strain intensification that occurs in the necking region mentioned above. Once the necking has propagated along the full specimens length, the two curves tend again to have similar behaviour. This corresponds with the start of the hardening phase of the stress–strain curve. The propagation of the necking effect is also shown by Fig. 12. More specifically, Fig. 12a shows the measurements of the longitudinal strain at different location along the specimen versus time.

From the aforementioned consideration it follows that for material exhibiting necking behaviour local strain measurement in the necking region should be preferred, as it is done in the present work. This allows obtaining the real local material behaviour rather then global response of the specimens^{4}. When the necking is not occurring, global and local strain measurements give identical results. In this case, material properties can be directly implemented from the global measurement.

*Lüders band*(Pelleg 2008). One of the main causes behind the yielding phenomena in metallic materials is the movement of dislocations. In the case of SG, the yielding could be related to the movement of polymer chains dislocations (Roylance 1996; Pelleg 2008), with subsequent cold drawing and hardening response, rather then dislocation movement of metallic crystal.

In ionomer materials, like SG, additional ionic groups are attached to the polymer chains (Eisenberg and Rinaudo 1990; Macknight and Earnest 1981; Varley 2007). These ionic groups are then attracted to each other due to their chemical reactivity resulting in additional bonds between the polymeric chains (Fig. 14). These bonds increase the material stiffness and strength since additional resistance against stretching of the polymeric network is provided. It follows that, when the material is subjected to tensile stress, the presence of these ionic groups make the stretching of polymer network less favourable than the sliding of polymer chains over each other. This could explain the role of the deviatoric stress on SG yielding and the \(45^{\circ }\) inclination of necking phenomenon, at temperature below 40 \(^{\circ }\hbox {C}\). If external energy is provided to the material (e.g. heat source) the bonds can be overcome more easily with a subsequent decrease in stiffness and yielding stress. Consequently, the polymeric chains show less resistance against network stretching at high temperature, which could explain the uniform strain distribution at temperature \(>\)40 \(^{\circ }\hbox {C}\).

### Whitening effect of TSSA

^{5}(e.g. Fig. 15c).

### Finite deformation theory and true stress–strain

The definitions given by Eqs. (1) and (2) in the previous section belong to the infinitesimal strain theory of continuum mechanics. It assumes the hypothesis of modulus of displacements and its first gradient to be largely smaller than the unit in each point of the body. The deformed and non-deformed configurations of the body can be therefore considered coincident.

*true stress*) and the actual strain (called

*true strain*) are defined by (3) and (4) instead of (1) and (2). In (3) and (4),

*l*is the actual length and

*A*is the actual cross section area.

*A*, is computed by means of Eq. (5), i.e. accounting the transversal strain occurring due to the Poisson’s effect and the related material contraction. As stated before, it is assumed the convention of positive strain to indicate elongation while negative strain indicates contraction. In case of very small deformations, both finite and infinitesimal theory definitions give similar results and

*A*tends to \(A_{0}\).

In the previous sections it is shown that SG and TSSA under uniaxial tensile stress state develops large deformations before failure. It follows that the finite strain theory should be applied for SG and TSSA instead of the infinitesimal one. This means that *true stress* and *true train *should be used. For the sake of example, in Fig. 16 SG stress–strain curves are plotted using either engineering or true definitions. It can be seen that, for large deformation, both stress and strain values show large differences between engineering and true values. As expected, this difference reduces in case of small deformation and it tends to zero for very small deformation (see close view at elastic part of Fig. 16b).

Figure 17 shows then the ratio between transversal and longitudinal strain measured during the test of SG and TSSA. Two types of curves are computed: one according to the engineering strain definition of Eq. (2) and one according to the true strain definition of Eq. (4). At the beginning (i.e. low deformation), the two curves show similar constant horizontal behaviour. Once the strain increases, the two curves start to deviate. The curves with true definition do not decrease as the engineering one but gradually tend to a value of 0.5. This confirms that true strain definition should be used. Indeed, in case of plastic deformation, it is commonly assumed to have no volume changes in the material during the plastic strain flow. This means, in the case of uniaxial tensile test, ratio between transversal and longitudinal strain close to 0.5, which is in line with the experimental observation.

### Mechanical material properties

Mechanical material properties of TSSA at different temperatures and engineering strain rates

T | \({\dot{d}}\) | \({\dot{\varepsilon }}\) | | | \(\sigma _{yy.max}\) | \(\sigma _{yy.max.true}\) | \(\varepsilon _{yy.max}\) | \(\varepsilon _{yy.max.true}\) |
---|---|---|---|---|---|---|---|---|

\(({}^{\circ }\hbox {C})\) | (mm/min) | (\(-\)/s) | (MPa) | (–) | (MPa) | (MPa) | (–) | (–) |

80 | 1 | 4E\(-\)04 | 6.79 | 0.46 | 5.00 | 10.91 | 1.33 | 0.85 |

23 | 1 | 4E\(-\)04 | 6.23 | 0.44 | 6.13 | 15.89 | 1.99 | 1.09 |

\(-\)20 | 1 | 4E\(-\)04 | 6.39 | 0.46 | 7.52 | 23.39 | 2.21 | 1.17 |

80 | 10 | 4E\(-\)03 | 6.95 | 0.45 | 6.06 | 14.68 | 1.60 | 0.95 |

23 | 10 | 4E\(-\)03 | 6.45 | 0.44 | 7.87 | 21.31 | 2.58 | 1.28 |

\(-\)20 | 10 | 4E\(-\)03 | 6.57 | 0.44 | 9.57 | 31.70 | 2.82 | 1.34 |

23 | 100 | 4E\(-\)02 | 7.10 | 0.46 | 8.02 | 22.80 | 2.13 | 1.11 |

Table 1 summarizes the values of the mechanical material properties of TSSA. The maximum stress at failure, \(\sigma _{yy,max}\), the maximum longitudinal strain at failure, \(\varepsilon _{yy,max}\), the modulus of elasticity, *E*, and the Poison’s ratio, *v*, are calculated. Maximum stress and maximum strain at failure are computed using both engineering and true definitions. The full set of results is given in Appendix Table 4, 5, 6.

^{6}. Fig. 19a and b show the effect of temperature on the modulus of elasticity,

*E*, and Poisson’s ratio,

*v*, respectively. It is observed that temperature variations have limited effects on

*E*and

*v*at any strain rate. This is because the TSSA \(T_{g}\) is out of the investigated range of temperature. The modulus of elasticity is around 6.6MPa and the Poisson’s ratio around 0.44.

Mechanical material properties of SG at different temperatures and engineering strain rates

T | \({\dot{d}}\) | \({\dot{\varepsilon }}\) | | | \(\sigma _{yy.max}\) | \(\sigma _{yy.max.true}\) | \(\varepsilon _{yy.max}\) | \(\varepsilon _{yy.max.true}\) |
---|---|---|---|---|---|---|---|---|

\(({}^{\circ }\hbox {C})\) | (mm/min) | (\(-\)/s) | (MPa) | (–) | (MPa) | (MPa) | (–) | (–) |

40 | 1 | 4.E\(-\)04 | 37.65 | 0.47 | 14.21 | 42.82 | n/a | n/a |

23 | 1 | 4.E\(-\)04 | 505.52 | 0.43 | 29.88 | 120.16 | 2.86 | 1.35 |

\(-\)20 | 1 | 4.E\(-\)04 | 966.19 | 0.41 | 39.49 | 99.39 | 1.62 | 0.96 |

80 | 10 | 4.E\(-\)03 | 3.13 | 0.49 | 0.73 | 3.08 | n/a | n/a |

60 | 10 | 4.E\(-\)03 | 13.53 | 0.49 | 5.00 | 18.68 | n/a | n/a |

40 | 10 | 4.E\(-\)03 | 86.26 | 0.48 | 22.80 | 83.64 | 3.61 | 1.53 |

30 | 10 | 4.E\(-\)03 | 498.96 | 0.44 | 31.24 | 118.01 | 2.98 | 1.38 |

23 | 10 | 4.E\(-\)03 | 670.21 | 0.43 | 32.97 | 117.34 | 2.77 | 1.33 |

0 | 10 | 4.E\(-\)03 | 864.11 | 0.41 | 38.33 | 113.81 | 2.12 | 1.14 |

\(-\)20 | 10 | 4.E\(-\)03 | 1012.58 | 0.40 | 44.96 | 167.45 | 1.70 | 0.99 |

23 | 100 | 4.E\(-\)02 | 700.96 | 0.43 | 34.47 | 136.54 | 3.00 | 1.39 |

Mechanical material properties of SG: yielding stress at different temperatures and engineering strain rates

T | \({\dot{d}}\) | \({\dot{\varepsilon }}\) | \(\sigma _{y}\) | \(\sigma _{y02}\) |
---|---|---|---|---|

\(({}^{\circ }\hbox {C})\) | (mm/min) | (\(-\)/s) | (MPa) | (MPa) |

40 | 1 | 4.E\(-\)04 | n/a | 2.77 |

23 | 1 | 4.E\(-\)04 | 19.62 | 19.00 |

\(-\)20 | 1 | 4.E\(-\)04 | 42.77 | 35.82 |

80 | 10 | 4.E\(-\)03 | n/a | 0.64 |

60 | 10 | 4.E\(-\)03 | n/a | 2.18 |

40 | 10 | 4.E\(-\)03 | n/a | 5.28 |

30 | 10 | 4.E\(-\)03 | 22.28 | 20.79 |

23 | 10 | 4.E\(-\)03 | 28.66 | 27.45 |

0 | 10 | 4.E\(-\)03 | 39.33 | 35.71 |

\(-\)20 | 10 | 4.E\(-\)03 | 48.35 | 40.72 |

23 | 100 | 4.E\(-\)02 | 32.92 | 28.43 |

Table 2 summarises the values of the mechanical material properties for SG. The maximum stress at failure, \(\sigma _{yy,max}\), the maximum longitudinal strain at failure, \(\varepsilon _{yy,max}\), the modulus of elasticity, *E*, and the Poison’s ratio, *v*, are calculated. Maximum stress and maximum strain at failure are computed using both engineering and true definitions.

The modulus of elasticity of the SG is dependent on the temperature, as shown by Fig. 21a. It goes from a value of around 1000 MPa at \(-\)20 \(^{\circ }\hbox {C}\) to around 3 MPa at 80 \(^{\circ }\hbox {C}\). These results confirm and extend the values given by (Bennison 2005; Stelzer 2010). The modulus of elasticity versus temperature exhibits a behaviour similar to the maximum stress at failure: going from \(-\)20 to 80 \(^{\circ }\hbox {C}\) a first gradual decrease with temperature can be observed, followed by a significant drop when temperature overcomes 40 \(^{\circ }\hbox {C}\). This is in line with expectation because above 40 \(^{\circ }\hbox {C}\) the material is approaching the glass transition temperature that correspond to the material softening.

Figure 21b shows the effect of temperature on the Poisson’s ratio. The latter varies in the range of 0.4–0.5. In particular, the Poisson’s ratio goes from around 0.4 at \(-\)20 \(^{\circ }\hbox {C}\) and approaches 0.5 at high temperature. This is explained by the fact that above 40 \(^{\circ }\hbox {C}\) the material goes from glassy state to rubber state, typically characterized by incompressible behaviour.

Finally, the yielding stress is plotted against temperature in Fig. 22. It can be observed that also the yielding stress is temperature and strain rate dependent. It varies from 43 to 0.2 MPa going from \(-\)20 to \(+\)80 \(^{\circ }\hbox {C}\). As it happens for the maximum stress and the modulus of elasticity, also the yielding stress shows a significant drop for temperature above 40 \(^{\circ }\hbox {C}\). When compared to the test at 10mm/min, yielding stress at 23 \(^{\circ }\hbox {C}\) are 15 % larger and 31 % smaller at 100 and 1 mm/min respectively.

### Stress–strain curves at constant true strain rates for model input

*t*is the time variable).

^{7}. However, in case of large deformations, the finite deformation theory and the true strain definitions should be applied. In this case, constant engineering strain rate does not correspond to true constant strain rate over time. This is shown by Eqs. (8) and (9). The latter expresses true strain rate as a function of time and of the engineering strain rate, which in this case is constant over time.

The mechanical material values and the stress–strain curves obtained in this study are used in (Santarsiero 2015) as input for the numerical modelling of laminated connections. In order to implement these material constitutive laws, the stress–strain curves at constant true strain rate are obtained as it follows. The stress–strain curves at variable true strain rate are plotted over a 3D diagram. The three axes of this graph represent stress, strain and strain rate. A 3D surface is then obtained from the plotted data^{8} for each temperature. Curves at constant true strain rate are then obtained cutting the surface with stress–strain planes at constant strain rate. Figure 24 shows an example of the three-dimensional stress–strain surface.

## Conclusions

In this work the mechanical response of TSSA and SG bulk material under uniaxial tensile stress is studied, at different configurations of strain rate and temperature. From the experimental results and data analysis the following conclusions can be drawn.

Mechanical material properties of TSSA: values at different temperatures and engineering strain rates

T | \({\dot{d}}\) | \({\dot{\varepsilon }}\) | | | \(\sigma _{yy.max}\) | \(\sigma _{yy.max.true}\) | \(\varepsilon _{yy.max}\) | \(\varepsilon _{yy.max.true}\) |
---|---|---|---|---|---|---|---|---|

\(({}^{\circ }\hbox {C})\) | (mm/min) | (\(-\)/s) | (MPa) | (–) | (MPa) | (MPa) | (–) | (–) |

80 | 1 | 4E\(-\)04 | 6.79 | 0.46 | 5.00 | 10.91 | 1.33 | 0.85 |

23 | 1 | 4E\(-\)04 | 6.23 | 0.43 | 6.13 | 15.89 | 1.99 | 1.09 |

\(-\)20 | 1 | 4E\(-\)04 | 6.39 | 0.46 | 7.52 | 23.39 | 2.21 | 1.17 |

80 | 10 | 4E\(-\)03 | 6.85 | 0.45 | 6.12 | 14.96 | 1.62 | 0.96 |

80 | 10 | 4E\(-\)03 | 6.97 | 0.46 | 5.91 | 14.25 | 1.58 | 0.95 |

80 | 10 | 4E\(-\)03 | 7.04 | 0.44 | 6.15 | 14.83 | 1.59 | 0.95 |

23 | 10 | 4E\(-\)03 | 6.48 | 0.44 | 7.81 | 20.86 | 2.61 | 1.28 |

23 | 10 | 4E\(-\)03 | 6.42 | 0.44 | 7.76 | 21.26 | 2.52 | 1.26 |

23 | 10 | 4E\(-\)03 | 6.44 | 0.42 | 8.03 | 21.81 | 2.62 | 1.29 |

\(-\)20 | 10 | 4E\(-\)03 | 6.42 | 0.44 | 9.90 | 32.66 | 3.02 | 1.39 |

\(-\)20 | 10 | 4E\(-\)03 | 6.67 | 0.42 | 9.96 | 33.11 | 2.86 | 1.35 |

\(-\)20 | 10 | 4E\(-\)03 | 6.63 | 0.44 | 8.87 | 29.32 | 2.58 | 1.27 |

23 | 100 | 4E\(-\)02 | 7.1 | 0.46 | 8.03 | 22.82 | 2.14 | 1.13 |

Mechanical material properties of SG: values at different temperatures and engineering strain rates

T | \({\dot{d}}\) | \({\dot{\varepsilon }}\) | | | \(\sigma _{yy.max}\) | \(\sigma _{yy.max.true}\) | \(\varepsilon _{yy.max}\) | \(\varepsilon _{yy.max.true}\) |
---|---|---|---|---|---|---|---|---|

\(({}^{\circ }\hbox {C})\) | (mm/min) | (\(-\)/s) | (MPa) | (–) | (MPa) | (MPa) | (–) | (–) |

40 | 1 | 4.E\(-\)04 | 37.65 | 0.47 | 14.21 | 42.82 | n/a | n/a |

23 | 1 | 4.E\(-\)04 | 505.52 | 0.43 | 29.88 | 120.16 | 2.86 | 1.35 |

\(-\)20 | 1 | 4.E\(-\)04 | 966.19 | 0.41 | 39.49 | 99.39 | 1.62 | 0.96 |

80 | 10 | 4.E\(-\)03 | 2.96 | 0.48 | 0.66 | 2.65 | n/a | n/a |

80 | 10 | 4.E\(-\)03 | 3.09 | 0.49 | 0.70 | 3.08 | n/a | n/a |

80 | 10 | 4.E\(-\)03 | 3.35 | 0.49 | 0.83 | 3.50 | n/a | n/a |

60 | 10 | 4.E\(-\)03 | 12.58 | 0.48 | 5.16 | 19.31 | n/a | n/a |

60 | 10 | 4.E\(-\)03 | 13.14 | 0.49 | 4.61 | 17.77 | n/a | n/a |

60 | 10 | 4.E\(-\)03 | 14.86 | 0.49 | 5.22 | 18.96 | n/a | n/a |

40 | 10 | 4.E\(-\)03 | 86.22 | 0.48 | 22.90 | 84.77 | n/a | n/a |

40 | 10 | 4.E\(-\)03 | 86.29 | 0.48 | 22.70 | 82.50 | n/a | n/a |

40 | 10 | 4.E\(-\)03 | 84.90 | 0.48 | 25.18 | 105.54 | 3.61 | 1.53 |

30 | 10 | 4.E\(-\)03 | 479.46 | 0.44 | 31.40 | 114.70 | 2.97 | 1.38 |

30 | 10 | 4.E\(-\)03 | 520.65 | 0.45 | 31.68 | 120.38 | 2.93 | 1.37 |

30 | 10 | 4.E\(-\)03 | 496.78 | 0.44 | 30.65 | 118.95 | 3.03 | 1.39 |

23 | 10 | 4.E\(-\)03 | 700.67 | 0.42 | 34.35 | 120.74 | 2.80 | 1.33 |

23 | 10 | 4.E\(-\)03 | 659.92 | 0.44 | 32.22 | 115.78 | 2.75 | 1.32 |

23 | 10 | 4.E\(-\)03 | 650.05 | 0.43 | 32.34 | 115.50 | 2.77 | 1.33 |

0 | 10 | 4.E\(-\)03 | 868.20 | 0.41 | 38.25 | 109.17 | 2.09 | 1.13 |

0 | 10 | 4.E\(-\)03 | 846.96 | 0.40 | 37.80 | 111.70 | 2.15 | 1.15 |

0 | 10 | 4.E\(-\)03 | 877.16 | 0.40 | 38.94 | 120.57 | 2.13 | 1.14 |

\(-\)20 | 10 | 4.E\(-\)03 | 961.75 | 0.40 | 44.22 | 115.40 | 1.72 | 1.00 |

\(-\)20 | 10 | 4.E\(-\)03 | 1036.00 | 0.41 | 44.22 | 176.37 | 1.67 | 0.98 |

\(-\)20 | 10 | 4.E\(-\)03 | 1040.00 | 0.41 | 46.43 | 210.60 | 1.72 | 1.00 |

23 | 100 | 4.E\(-\)02 | 700.96 | 0.43 | 34.47 | 136.54 | 3.00 | 1.39 |

Mechanical material properties of SG: values of yielding stress at different temperatures and engineering strain rates

T | \({\dot{d}}\) | \({\dot{\varepsilon }}\) | \(\sigma _{y}\) | \(\sigma _{y02}\) |
---|---|---|---|---|

\(({}^{\circ }\hbox {C})\) | (mm/min) | (\(-\)/s) | (MPa) | (MPa) |

40 | 1 | 4.E\(-\)04 | n/a | 2.77 |

23 | 1 | 4.E\(-\)04 | 19.62 | 19.00 |

\(-\)20 | 1 | 4.E\(-\)04 | 42.77 | 35.82 |

80 | 10 | 4.E\(-\)03 | n/a | 0.69 |

80 | 10 | 4.E\(-\)03 | n/a | 0.61 |

80 | 10 | 4.E\(-\)03 | n/a | 0.61 |

60 | 10 | 4.E\(-\)03 | n/a | 2.06 |

60 | 10 | 4.E\(-\)03 | n/a | 2.27 |

60 | 10 | 4.E\(-\)03 | n/a | 2.22 |

40 | 10 | 4.E\(-\)03 | n/a | 5.27 |

40 | 10 | 4.E\(-\)03 | n/a | 5.30 |

40 | 10 | 4.E\(-\)03 | n/a | 5.17 |

30 | 10 | 4.E\(-\)03 | 21.65 | 19.85 |

30 | 10 | 4.E\(-\)03 | 23.19 | 21.87 |

30 | 10 | 4.E\(-\)03 | 22.01 | 20.64 |

23 | 10 | 4.E\(-\)03 | 29.75 | 28.50 |

23 | 10 | 4.E\(-\)03 | 28.52 | 27.11 |

23 | 10 | 4.E\(-\)03 | 27.72 | 26.73 |

0 | 10 | 4.E\(-\)03 | 40.22 | 35.69 |

0 | 10 | 4.E\(-\)03 | 37.61 | 34.69 |

0 | 10 | 4.E\(-\)03 | 40.17 | 36.76 |

\(-\)20 | 10 | 4.E\(-\)03 | 47.60 | 39.40 |

\(-\)20 | 10 | 4.E\(-\)03 | 48.79 | 39.96 |

\(-\)20 | 10 | 4.E\(-\)03 | 48.65 | 42.81 |

23 | 100 | 4.E\(-\)02 | 32.9 | 28.43 |

Secondly, two additional phenomena are observed during the uniaxial tests. For the TSSA material, the so-called whitening phenomenon is observed. The colour of TSSA goes from fully transparent to white when the stress goes above around 5 MPa. For the SG material, it is observed that the strain field distribution is dependent on the temperature. More specifically, at temperature below 40 \(^{\circ }\hbox {C}\), the material exhibits a non-uniform strain field distribution due to the occurring of a necking phenomenon. The latter consists in a strong strain concentration in the field distribution, occurring when the stress approaches the yielding stress. The necking is consistently inclined at approximately \(45^{\circ }\) with the uniaxial stress direction, forming the so-called Lüders band. Measurements along the specimens showed that the localized strain propagates over the full specimen length, resulting in the cold-drawing phenomenon. It is therefore concluded that local strain measurements are necessary to correctly perform material characterization when the necking phenomenon is occurring.

Finally, it is also shown that engineering and true stress–strain and Poisson’s ratio definition exhibits large deviations. This is because both TSSA and SG materials fail at deformation largely over 100 %. It follows that the finite deformation theory should be used for the computation of the stress–strain curves implemented in numerical models.

## Footnotes

- 1.
This is at the time of writing. The reason might be related to technological and production matters.

- 2.
P. V. Dow Corning Europe, Personal Communication, July 22th, 2015.

- 3.
According to ETAG 002 low temperature limit could be extended to \(-\)40 \(^{\circ }\hbox {C}\) for European Nordic countries if required. This is not here considered because of practical limitation.

- 4.
In case of local measurement are not possible, inverse material characterization is suggested. This should be done either with user-choice based method or using automatic iterative algorithms with statistical convergence criteria.

- 5.
- 6.
A second order polynomial seems to provide a better fit than linear one.

- 7.
This is assumed to be true under the following hypothesis: (i) the specimen does not slide in the grips during the test and therefore there is no change in the constant displacement rate applied the reference length, (ii) uniform strain field along the specimens, i.e. necking phenomena is not occurring and (iii) constant strain rate in the non-parallel region of the specimens.

- 8.
Matlab non-linear fitting algorithm is used.

## Notes

### Acknowledgments

The authors would like to thank the Swiss National Science Foundation for founding the present research (Grants 200020_150152 and 200021_134507). In addition, Glas Trösch AG Swisslamex, Kuraray (former Dupont) and Dow Corning are gratefully acknowledged for the material support and specimens preparation. Finally, the COST Action TU0905 “Structural Glass – Novel Design Methods and Next Generation Products” is also acknowledged for facilitating the research network.

### Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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