MECHANICAL PROPERTIES OF COWPEA BEANS AT DIFFERENT MOISTURE CONTENTS

Cowpea production has gained considerable ground in Brazil. Cowpea grain undergo different types of pressure and may crack and break during processing and storage, thus, there is a need to classify the mechanical properties of the beans. Therefore, this study aimed to evaluate the influence of the moisture content of cowpea beans on the maximum compressive force for fixed deformation and determine the proportional modulus of deformity under compression. The cowpea cultivars Novaera and Tumucumaque were evaluated at different moisture contents (0.12; 0.15; 0.18; 0.20; and 0.23 decimal d.b.). The experiment was arranged in completely randomized design for each moisture content and 10 deformation rates were applied (0.02; 0.04; 0.06; 0.08; 0.10; 0.12; 0.14; 0.16; 0.18; and 0.20 mm). The compression force was assessed using a universal testing machine and the proportional deformation modulus was determined. Following, hardness and elasticity of cowpea beans as a function of the moisture content were established. The compressive force required to deform cowpea beans decreases with increasing moisture content: between 2 and 105 N (Tumucumaque) and between 2 to 97 N (Novaera). The proportional deformation modulus of cowpea increased as the moisture content and deformation reduced, ranging from 4.9 x 107 to 31.9 x 107 Pa (Tumucumaque) and from 5.9 x 107 to 42 x 107 Pa (Novaera).


INTRODUCTION
Brazilian grain production in the 2017/2018 harvest was estimated at 3166.2 thousand tons (CONAB, 2018), with 786.80 thousand tons of cowpea, accounting for 25.5% of the total bean production.
The classification of cowpea beans regarding color, shape, grain size, and hilum ring is important not only to describe cultivars, but also for commercial purposes (FREIRE FILHO et al., 2011). The study of the mechanical properties can assist in the design or adaptation of equipment used to process other grain types (OLIVEIRA et al., 2017), without compromising the cowpea final quality.
During the harvesting, handling, transportation, and storage, grain undergo a set amount of static pressures of different magnitudes and dynamics such as high-speed impacts that cause abrasion, crushing, and cracking of beans and increase susceptibility to deterioration during storage (BARGALE-PRAVEEN et al., 1995). Therefore, it is essential to understand the production process as a whole to ensure the quality of the grain. Products may present cracks and breaks if they undergo physical stresses that exceed resistance (FERNANDES et al., 2014). Ribeiro et al. (2007) indicated that the forcedeflection curve from compression tests can produce parameters that characterize material responses to a force load. Among the different mechanical properties, the deformation modulus allows comparisons of relative resistance between different materials .
This study aimed to determine the influence of the moisture content on the maximum compression force for fixed deformations and determine the proportional modulus of deformity for cowpea cultivars under compression.

MATERIAL AND METHODS
The experiment was carried out at the Postharvest Laboratory of Vegetable Crops of the Federal Institute of Education, Science and Technology of Goiás -Campus Rio Verde (IF Goiano -Campus Rio Verde). The cultivars Novaera and Tumucumaque of cowpea (Vigna unguiculata (L.) Walp.) were used in the study.
Initially, the moisture content of the beans (0.12 decimal dry basis) was determined in a forced air circulation oven, at 105 ± 3ºC for 24 hours, with three repetitions (BRASIL, 2009). Starting from the initial moisture content (0.12 decimal dry basis, d.b.), the grains were moistened in a B.O.D., at 20 o C and 70% relative humidity. With the high water vapor in the environment, the beans absorbed water to the hygroscopic balance. Several researchers used grain moisture to determine the physical properties of plant products (GARNAYAK et al., 2008;NIKOOBIN et al., 2009;DI LANARO et al., 2011). Mass gain was recorded by weighing the beans on a scale (0.01 g resolution) until the desired moisture content was reached (0.15; 0.18; 0.20 and 0.23 decimal d.b.). Temperature and relative humidity were monitored using a digital psychrometer in the BOD chamber. Uniaxial compression tests were carried out with 15g samples for each moisture content to determine compression resistance. The compression tests were individually analyzed using a TA Hdi Texture Analyzer universal test machine, with a 250N load cell. Beans were compressed at their natural rest position, i.e., in the thickness direction (smallest axis) ( The software Sigma Plot 11.0 was used to plot the compressive force curves as a function of grain deformation for each moisture content. The following deformation values were used: 0.02; 0.04; 0.06; 0.08; 0.10; 0.12; 0.14; 0.16; 0.18, and 0.20 mm. The proportional deformity modulus was determined using Equation 1, according to Batista et al. (2003). The test was carried out in a completely randomized design with the 10 deformation values. The data were analyzed with analysis of variance and regression. The model was selected based on the significance of the regression coefficients, using the "t" test at 5% significance level, on the magnitude of the determination coefficient, mean relative error and considering the biological significance.
Hardness and elasticity of cowpea beans were determined as a function of the moisture content, using the Equation 2 suggested by Henry et al. (1996). This equation shows that the force required to deform biological materials can be described as a function of the deformation, according to the Taylor series, where: x = deformation, mm; d; e; f = model elastic coefficients, units of N mm -1 , N mm -2 and N mm -3 , respectively.  x + e . x 2 +f . x 3 ; for e> 0; f <0; IP = inflection point (HENRY et al., 1996) The slope of the force x deformation curve for any point is the tangent (T), obtained from the first derivation of Equation 3: The maximum tangent was obtained at the inflection point of the curve, where x = -e/3f , which is considered an indicator of product hardness. The secant (S), which intersects the curve at origin and any point on the curve, is expressed as Equation 4: The maximum secant corresponded to the point where the deformation x = -e/2f , describing elasticity at different levels of deformation.
The software R Core Team (2017) was used for the statistical analysis and for model adjustments. Graphics were produced using the software SigmaPlot®11 (Systat Software Inc.).

Figures 4a and 4b
show that the compression force needed to deform cowpea beans decreased as the moisture content increased. The average force required for deformation as a function of the moisture content varied between 2 and 105 N for cultivar Tumucumaque and between 2 and 97 N for cultivar Novaera. Beans with higher moisture contents were less resistant to compression, but resistance increased in proportion to reduction in the moisture content.
In common bean, Resende et al. (2007) reported average compression force between 22.3 and 551.7 N for moisture contents between 0.13 and 0.42 bs. In soybean, Ribeiro et al. (2007) reported an average compression force from 21.72 to 110.86 N for moisture contents between 0.09 and 0.58 bs. In rice, Resende et al. (2013) found average compression force ranging from 131 to 171 N for moisture contents between 0.12 and 0.29 bs. Fernandes et al. (2014) found average compression force between 21.4 and 139.8 N for moisture content in the range of 0.14 to 0.26 bs for wheat grain, and Sousa et al. (2018) reported average compression force between 0.17 and 25.68 N for moisture contents ranging from 0.05 to 0.31 bs. This tendency is probably due to a gradual change in the integrity of the cellular matrix with the reduction of the moisture content (GUPTA; DAS, 2000). Table 1 shows the regression equations adjusted to the experimental values of the proportional modulus of deformity as a function of moisture content and deformation for each cultivar. The adjusted equations had high values of coefficient of determination (R 2 ), indicating a good fit for the model. Equations with high R² values were obtained by Fernandes et al. (2014), Oliveira et al. (2017) and Sousa et al. (2018). Figures 5a and 5b show the response surfaces adjusted according to the equations in Table 1 for the proportional deformation modulus of cowpea beans as a function of moisture content and deformation for each cultivar. For both cultivars the values the of proportional deformation modulus increased with moisture content decrease.  The values of the proportional deformation modulus for the moisture contents varied from 4.9 x 10 7 to 31.9 x 10 7 Pa for the cultivar Tumucumaque and from 5.9 x 10 7 to 42 x 10 7 Pa for the cultivar Novaera. For common beans, Resende et al. (2007) found proportional deformation modulus ranging from 4.1 x 10 7 to 71.3 x 10 7 Pa for moisture contents varying between 0.13 and 0.42 bs. For soybean, Ribeiro et al. (2007) reported deformation modulus ranging from 1.02 x 10 7 to 5.43 x 10 7 Pa for moisture content varying between 0.09 and 0.58 d.b.. Resende et al. (2013) found for husked rice, with moisture contents between 0.12 and 0.29 d.b. reported deformation modulus from 5.5 x 10 9 to 7.4 x 10 9 Pa. For wheat, Fernandes et al. (2014) found proportional deformation modulus ranging from 8.9 x 107 to 51.2 x 107 Pa for moisture contents between 0.14 and 0.26 d.b., and for radish seeds, Sousa et al. (2018) reported proportional deformation modulus ranging from 0.11 x 10 10 to 1.72 x 10 10 Pa for moisture content from 0.05 to 0.31 d.b. Figure 5a and Figure 5b also show that proportional deformation modulus increases with the reduction of the moisture content and with product deformation. These results are in accordance with the findings by Fernandes et al. (2014). Table 2 shows the values of the elastic coefficients d, e, f obtained with Equation 2, and the values of the maximum tangent and maximum secant obtained with Equations 3 and 4, respectively, for the cultivars Tumucumaque and Novaera.  The maximum tangent and secant for the deformations were x = -2e/3f and x = -e/6f, respectively. There was an increase in the maximum tangent and secant values with reduce in moisture content. Values of the maximum tangent were higher than the maximum secant for the same moisture content. These values are in agreement with the results of Ribeiro et al., (2007).

CONCLUSIONS
• The compressive force required to deform cowpea beans decreases with increase in moisture content of bean. Results between 2 and 105 N were found for the cultivar Tumucumaque and between 2 and 97 N for the cultivar Novaera.
• The proportional deformation modulus increases with the reduction of the moisture content and product deformation. The moisture contents assessed varied between 4.9 x 10 7 and 31.9 x 10 7 Pa for the cultivar Tumucumaque and between 5.9 x 10 7 and 42 x 10 7 Pa for the cultivar Novaera.

DECLARATION OF INTERESTS
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.