2. Analysis of the properties of selected PU foam samples

Mechanical, chemical, and physical properties together with the experimentally identified structural properties of samples of different densities ρPU PU foams have been published in Refs. [1, 2, 5]. The structure of the polyurethane foam is formed by a chemical process polyaddition from alcohols with two or more hydroxyl groups and isocyanates. Isocyanate reacts with water to form carbon dioxide that creates cell structure of polyurethane foam. According to the applied type of ingredients and their ratio, PU foam can be divided into soft, moderately stiff, rigid, or hard. The flexibility of the cell structure is among others dependent on its density <sup>ρ</sup>PU <sup>¼</sup> weight=volume, which for comfort application is in the range from 10 to 100 kg m�<sup>3</sup> . Samples of polyurethane foams can be characterized with low-permeable envelop, which arises as a consequence of heat removal from polyurethane with a mold wall. The internal cell structure is characterized by a distribution curve of the cell diameters, and it is significantly more porous, which, for porous structure, can be expressed by a dimensionless quantity Ψ in accordance with Eq. (1). The relationship describes the ratio of the polyurethane structure volume and total volume of structure, which is important for obtaining of the parameter named as a packing density. A number of porous cells and the connecting edges (edge connecting air cells) are significantly influenced by the diameter of cells as indicated in Ref. [1]. He also states that the structure of PU foam created by combining of individual cells is the macroscopic homogeneous system and regardless of the variability of cell diameters, and therefore it can replace a continuum or rheological models. In terms of a deformation mechanism, the behavior of foams can be characterized by the following aspects: during foam compression, the air escapes from the cell, the cell walls are bent, and from a certain phase, cell walls are in a contact with specific friction. During unloading, the air is sucked again into the structure. Therefore, for the fast compression of the cellular structure of the foam, the mechanical properties depend especially on the amount of air and the breathability of porous cells and thus on strain rate ε\_ðtÞ. Already in 1970 in Ref. [10], it was published that the rate of air cells has an influence on the value of an energy dissipation ϑðtÞ, which PU foam can absorb. From the viewpoint of the mechanical properties, polyurethane foams are nearly isotropic viscoelastic materials. It has been published in 1987 by Ref. [11]. They state that during tri-axial test, wherein the sample is simultaneously loaded in three main directions of the basic coordinate system (X, Y, and Z), approximately same course of the loading curves is obtained. They differ only in constant. As a result, deformation/strain ε in the main axis of the load and a volumetric deformation γ can be expressed with Eqs. (2) and (3). The results of analysis of the structure of PU foam samples with dimensions of 100 � 100 � 40 mm, which were numbered 1–6, are shown in Table 1. Air volume in the analyzed samples reached 96.5 � 0.5%, wherein the parameter of the packing density Ψ was from 0.033 to 0.034. It is due to the density of pure polyurethane polymer (for the comfort stuff, it is from 1200 to 1500 kg m�<sup>3</sup> ). Depending on the increasing amount of polyurethane in the PU foam sample, the air volume decreases. This fact can be illustrated with a parametric graph (Figure 1).

$$
\Psi' = \frac{V\_{\text{polymer}}}{V\_{air}},
\tag{1}
$$

where Ψ [�] is the parameter of the packing density of PU foam, Vpolym is the volume of PU foam [m<sup>3</sup> ], and Vair [m<sup>3</sup> ] is volume of the air.


Table 1. Parameters of tested PU samples.

.

mechanical properties under compression than commonly used PU foams [2]. Another solution that can change mechanical properties is a vertical layering of polyurethane foams having different physical and mechanical properties. But it does not bring an expected improvement of characteristics corresponding with a composite behavior [6, 7], which may be due to the fact that only the layering of polyurethane foams does not bring the desired synergistic effect as stated by Ref. [8]. Also, a significant improvement in energy savings and vibroisolation characteristics or other parameters such as a permeability of PU foam is not achieved. The improvements are reflected only in reduced values of contact pressures from the load body [9]. The mechanical behavior of polyurethane foams can be considered substantially non-linear, with a

Mechanical, chemical, and physical properties together with the experimentally identified structural properties of samples of different densities ρPU PU foams have been published in Refs. [1, 2, 5]. The structure of the polyurethane foam is formed by a chemical process polyaddition from alcohols with two or more hydroxyl groups and isocyanates. Isocyanate reacts with water to form carbon dioxide that creates cell structure of polyurethane foam. According to the applied type of ingredients and their ratio, PU foam can be divided into soft, moderately stiff, rigid, or hard. The flexibility of the cell structure is among others dependent on its density <sup>ρ</sup>PU <sup>¼</sup> weight=volume, which for comfort application is in the range from 10 to 100 kg m�<sup>3</sup>

Samples of polyurethane foams can be characterized with low-permeable envelop, which arises as a consequence of heat removal from polyurethane with a mold wall. The internal cell structure is characterized by a distribution curve of the cell diameters, and it is significantly more porous, which, for porous structure, can be expressed by a dimensionless quantity Ψ in accordance with Eq. (1). The relationship describes the ratio of the polyurethane structure volume and total volume of structure, which is important for obtaining of the parameter named as a packing density. A number of porous cells and the connecting edges (edge connecting air cells) are significantly influenced by the diameter of cells as indicated in Ref. [1]. He also states that the structure of PU foam created by combining of individual cells is the macroscopic homogeneous system and regardless of the variability of cell diameters, and therefore it can replace a continuum or rheological models. In terms of a deformation mechanism, the behavior of foams can be characterized by the following aspects: during foam compression, the air escapes from the cell, the cell walls are bent, and from a certain phase, cell walls are in a contact with specific friction. During unloading, the air is sucked again into the structure. Therefore, for the fast compression of the cellular structure of the foam, the mechanical properties depend especially on the amount of air and the breathability of porous cells and thus on strain rate ε\_ðtÞ. Already in 1970 in Ref. [10], it was published that the rate of air cells has an influence on the value of an energy dissipation ϑðtÞ, which PU foam can absorb. From the viewpoint of the mechanical properties, polyurethane foams are nearly isotropic viscoelastic materials. It has been published in 1987 by Ref. [11]. They state that during tri-axial test, wherein the sample is simultaneously loaded in three main directions of the basic coordinate system (X, Y, and Z), approximately same course of

large viscoelastic deformation, relaxation, and recovery of the structure.

74 Aspects of Polyurethanes

2. Analysis of the properties of selected PU foam samples

Figure 1. Characteristic structure of PU foam.

Figure 2. (a) Inner structure (low-porous envelop). (b) Inner structure of PU foam with characteristic shape of cell (left) and detail of inner structure (right).

Figure 3. The volume of air and material in the structure of polyurethane foams depending on the specific weight of pure polymer.

Measurement and Numerical Modeling of Mechanical Properties of Polyurethane Foams http://dx.doi.org/10.5772/intechopen.69700 77

$$\Gamma = \frac{\Delta V}{V\_0} = \frac{V\_0 - V\_{comp}}{V\_0} = \frac{\left(V\_{air} + V\_{polym}\right) - V\_{comp}}{\left(V\_{air} + V\_{polym}\right)} = 1 - \Phi\_\prime \tag{2}$$

$$\varepsilon = \frac{L\_0 - \delta}{L\_0} = 1 - \left[1 - \frac{V\_0 - V\_{comp}}{V\_0}\right]^{1/3} = 1 - \left[1 - \gamma\right]^{1/3}\text{\AA} \tag{3}$$

where <sup>Γ</sup>[�] is total volume strain of PU foam, Vcomp [m3 ] is compressed volume, V<sup>0</sup> [m<sup>3</sup> ] is undeformed volume, Vpolym [m3 ] is volume of the polymer in PU foam, Vair [m3 ] is volume of air in cells, Φ [�] is ratio of compressed and uncompressed volume, ε [�] is strain, δ [mm] is value (length) of compression, and L<sup>0</sup> [mm] is origin undeformed length (Figures 2 and 3).
