**3.1. Linear viscoelasticity**

**3. Behavior of viscoelastic biocomposites**

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behavior CREEP [7, 10–12, 57].

The biocomposites inherit the behavior of the matrix with which they were manufactured, making their mechanical properties strongly dependent on the ratio of applied strain; therefore the mechanical behavior and viscoelastic structural products that are designed as sustainable products, which can be applied to the construction industry and automotive, mainly be affected by the dependence of applied stress and temperature conditions at the time. When biocomposites are processed and take the desired shape, e.g., extruded beams, molded housings, or any product which may be subjected to a constant load, will be generated on these products efforts, bending or tension or combinations thereof, constants, the effect of a constant effort on a product manufactured in biocomposites can be seen reflected in unwanted time warps, inclusive could produce the product failure. In this context, the durability of biocomposites can limit their applications, and implement risk of all the efforts of previous research, in order to develop sustainable materials for sustainable products. Studying the behavior of NFPCs under constant load conditions, where the deformation increases in time, that is, the material flows under the load (effect of creep), can understand that in a system biocomposite load between redistributes the matrix and natural fibers during deformation, when these materials are subjected to constant loads, can be affected by various effects of creep, the matrix, fiber, and the interface. There are several applications that have achieved biocomposites for extrusion with an addition 40–60%, mixed with thermoplastics, such as HDPE, PP, PVC, and materials [6, 49]. Compounds where manufacturers use natural fibers from different sources, as one of the fillers or reinforcements. These thermoplastic biocomposites can be used as tables for decks, fences, railway sleepers, etc. When used under these requirements, the CREEP or viscoelastic deformation becomes a problem, because the application of the effort takes the material to work under load long periods of time (months and years). This has been studied extensively in the case of advanced thermoset composites, and nowadays the investigations on biocomposites observed that the viscoelastoplastic behavior can lead to failure sustainable product, when subjected to large deformations and long periods of time, under conditions of dynamic or static load and temperature variations. These materials progressively accumulate deformation, causing internal damage occurs due to creep and/or fatigue, both cause cumulative damage [7, 50, 51]. There have also been efforts to correlate effects at smaller scales, relating effort plastic flow [52–54], according to the nonlinear response which it is due to permanent deformation. Investigations of some thermoplastic compounds have focused on deformation patterns, and have shown the strain-fluence compounds with particulate wood plastic, with alteration of the compositions and components of compound [49, 55, 56]. It has also been observed that with increased fiber content, the effect of creep decreases. Agro compounds used to develop products for structural construction, often requiring improved mechanical properties, particularly creep performance. It has been shown that the fluence of biocomposites varies with the type of filler and content, coupling treatment, and types of polymer matrices [6, 10]. Several molding techniques have also been applied to analyze the

At present, it is of interest to develop new thermoplastic biocomposites for sustainable products, and it is about the future course of implementation and sustainability over time of

Biocomposites have a typical response to mechanical loads, and can be studied as materials in some cases behave as elastic solids, and other, as viscous fluids. It is known that the mechanical and viscoelastic properties depend on the application time of loading, the type of load, temperature, micromechanics relationship between the natural fiber and the matrix, the type of anchor prevailing for the transfer effort to micro- and nanolevels, and cannot be treated mathematically only by the laws of solids or fluids, as viscoelastic behavior of biocomposites has high temperature dependence, especially if the work environment exceeds the glass transition temperature of the biocomposite, from the foregoing, the biocomposites in working conditions at constant load can be considered as super cold fluids. The above findings were mooted at the time of Boltzmann and others, but it is now clear that the vision of Boltzmann was the right approach. As the understanding of the physical nature of the biocomposites and matured techniques has increased they have been developed many biocomposites. Since these materials are motivating the development of sustainable products, it is essential to analyze and understand from an engineering perspective, the response of biocomposites when load is applied and other environmental variables such as temperature and humidity. The difference between an elastic solid biocomposite and a viscous liquid is not an absolute difference, the ability to detect the elastic or viscous responses biocomposite object of study often depends on the time scale of the experiment and the conditions required recreate. Thus, from a strict point of view, all biocomposites have a viscoelastic behavior, i.e., depends not only on the state of stress to which the material is subjected, but also the history of preloading the material and all condition biocomposite that may affect the macrolevel, micro and nanolevel. The biocomposites are complex viscoelastic systems for manufacturing and high dependence on renewable raw materials, such as natural fibers. Viscoelastic behavior can be investigated using various methods; the use of dynamic mechanical analysis (DMA) is the most common nowadays. For example, in an experiment fluence (CREEP) a constant *σ* 0 effort applied to a sample and the deformation *ε* is observed as a response function of time *t*. Normally effort increases with time and the flow curves (as a function of time) may exhibit three regions (**Figure 2**): primary creep in which the curve is concave downward; the secondary creep deformation in which it is proportional to time; and tertiary creep where the deformation is accelerated until the creep rupture occurs. Strain rate, which would be represented by the derivative of the deformation curve, also exhibits three regions.

**Figure 2.** Schematic yield curve (CREEP).

In the yield curve (CREEP) high, the material has a linear viscoelastic behavior, so it is possible to apply the principle of superposition time TTSP temperature. However, nonlinearity presents high deformation speeds. In other words, the stress curves as a function of strain rate could show the transition from linear to nonlinear behavior in flow experiments (**Figure 2**).

A composite thermoplastic polymer matrix subjected to constant loads for periods of time and prolonged temperatures above the glass transition of the matrix work, regardless of the direction of load application, the material works to tension, bending, compression, or some combination of these efforts; its response to deformation over time is a combination of deformation, micromechanics, elastic, and viscous, which can be expressed in terms of compliance creep *D*, as:

was the right approach. As the understanding of the physical nature of the biocomposites and matured techniques has increased they have been developed many biocomposites. Since these materials are motivating the development of sustainable products, it is essential to analyze and understand from an engineering perspective, the response of biocomposites when load is applied and other environmental variables such as temperature and humidity. The difference between an elastic solid biocomposite and a viscous liquid is not an absolute difference, the ability to detect the elastic or viscous responses biocomposite object of study often depends on the time scale of the experiment and the conditions required recreate. Thus, from a strict point of view, all biocomposites have a viscoelastic behavior, i.e., depends not only on the state of stress to which the material is subjected, but also the history of preloading the material and all condition biocomposite that may affect the macrolevel, micro and nanolevel. The biocomposites are complex viscoelastic systems for manufacturing and high dependence on renewable raw materials, such as natural fibers. Viscoelastic behavior can be investigated using various methods; the use of dynamic mechanical analysis (DMA) is the most common nowadays. For example, in an experiment fluence (CREEP) a constant *σ* 0 effort applied to a sample and the deformation *ε* is observed as a response function of time *t*. Normally effort increases with time and the flow curves (as a function of time) may exhibit three regions (**Figure 2**): primary creep in which the curve is concave downward; the secondary creep deformation in which it is proportional to time; and tertiary creep where the deformation is accelerated until the creep rupture occurs. Strain rate, which would be represented by the derivative of

In the yield curve (CREEP) high, the material has a linear viscoelastic behavior, so it is possible to apply the principle of superposition time TTSP temperature. However, nonlinearity presents high deformation speeds. In other words, the stress curves as a function of strain rate could

show the transition from linear to nonlinear behavior in flow experiments (**Figure 2**).

the deformation curve, also exhibits three regions.

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**Figure 2.** Schematic yield curve (CREEP).

$$
\varepsilon\_{(t)} = \sigma\_o D(t, T, \sigma\_{\mathcal{O}}) \tag{1}
$$

The creep compliance *D*(*t*) is the ratio of stress and strain generally as a function of time, as seen in Eq. (1). When considering the case of the response to creep as linear material, creep deformation is independent of the level of effort, which makes it look as a property of the material between different systems of composite materials, taken under similar environmental conditions. The total deformation at any instant of time *ε*(*t*) in a creep test of a biocomposite can be represented as the sum of the instantaneous elastic deformation *εE* (i.e., the initial deformation when the constant voltage is applied) and *εV* viscoelastic deformation. Similarly, compliance can be divided with elastic and viscous component. By submitting the biocomposites constant loads, regardless of your work address, the response of the material is creep or creeps. Where compliance depends on the deformation function in the time and effort that is subjected in Eq. (2) shows an expression for compliance:

$$D\_{(l)} = \frac{E\_{(l)}}{\sigma\_o} \tag{2}$$

For the design and manufacture of products based on biocomposites require to define the CREEP as the change in function of time in the dimensions of a product polymer or composite when subjected to constant stress in different working conditions, which may include, temperature, environmental, cyclic loading, and among others. The biocomposites usually have CREEP behavior at room temperature; which is due mainly to its micromechanical relationship fiber-filler with the matrix, and the combined efforts to which the material may be subjected to some cases also the flow behavior may be generally negligible. Therefore, design procedures are simpler because the module can be considered constant (except at high temperatures). However, the modulus of a polymer or composite material is not constant (as shown in Eq.(2)), because the deformation is a function of time, and compliance is directly related to the stiffness of the material. Whenever variation is known, the behavior CREEP of biocomposites can be compensated by the precise use and well-established design procedures, or by modifying the composition of the biocomposite, using reinforcements and/or fillers to correct their mechanical performance and viscoelastic. For biocomposites, the aim of the design methods to determine the stress values does not cause permanent deformation intolerable products or fractures. Excessive deformation becomes a limiting factor in the selection of work effort, leading to the conclusion that it is essential to qualify and specifically quantify the deformation behavior of the biocomposites, depending on time and temperature. A schematic diagram of flow behavior (creep) can be seen in **Figure 3**; given load shows a configuration of four point bending biocomposite. The weight or load, along with gravity, provides a constant effort in biocomposite. After 5 days in this condition no significant unfavorable deformation occurs. However, after 7 months deformation caused by the effort has increased, and deforms further after 2 years.

**Figure 3.** CREEP response of a biocomposite beam subjected to bending at four points, an illustrative estimate given by the author.

The biocomposites polymer matrix has significant sensitivity to use a function of time and temperature, resulting in a limited use of structural applications demanding applications or in dimensional stability value. When the biocomposite is subjected to high stresses, it can result in the material, and excessive deformations that may cause the product to lose its functionality, one could get the material to the tertiary region where creep occur until fracture. This is called the upper region and is also known as the acceleration phase of CREEP. The importance of the tertiary region for normal operation and design to CREEP is also important, since parts of polymer or compound should be designed to avoid this area; safety factors must ensure away from this region over the lifetime of the products developed with biocomposites.

#### **3.2. Mathematical models**

The experimental response of a dynamic test to tension, bending, or compression creep compliance of a biocomposite can be modeled with provisions of springs and dampers, where the springs represent the elastic solid behavior and cushion the behavior of a viscous liquid. It represents the Hooke spring deformation force that is proportional to the applied stress and the damper flow proportional to the strain rate Newtonian. To model mathematically one biocomposite, the stress, strain and time, you can relate to the constant characteristics of the mechanical elements [57]. The mechanical model mimics the actual behavior of biocomposites, although the elements themselves may not have direct analogies with real material. However, these models represent a mathematical understanding of the problems of viscoelastic performance of biocomposites, studied by accelerated tests in the laboratory, which can easily be articulate studies of continuum mechanics means to solve even more complex models with the

help of numerical methods and approach to more realistic models that include visco-elasticplastic. It is emphasized that mathematical models presented in this chapter are classical performances already studied by several authors, that when applied to biocomposites, approximate their behavior and allow you to compare and study relationship deformation at short times and long-term predictions that might suggest designers, which are the most desirable when applying for the development of sustainable products made from biocomposite materials.
