Semina: Ciências Agrárias ISSN: 1676-546X [email protected] Universidade Estadual de Londrina Brasil

Cabral de Oliveira, Daniel Emanuel; Resende, Osvaldo; Alessandro Devilla, Ivano Mechanical properties of baru ( alata Vogel) Semina: Ciências Agrárias, vol. 38, núm. 1, enero-febrero, 2017, pp. 185-196 Universidade Estadual de Londrina Londrina, Brasil

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How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the , Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative DOI: 10.5433/1679-0359.2017v38n1p185 Mechanical properties of baru fruit ( Vogel)

Propriedades mecânicas dos frutos de baru (Dipteryx alata Vogel)

Daniel Emanuel Cabral de Oliveira1*; Osvaldo Resende2; Ivano Alessandro Devilla3

Abstract

This paper aimed to verify the influence of moisture content and drying temperature on the values of maximum compression strength for fixed strains (1; 2; 3; 4; 5; 6; and 7 mm), rupture force, and proportional deformity modulus on the baru fruit (Dipteryx alata Vogel) under compression in a natural resting position. Baru with a moisture content ranging from 0.333 to 0.053 (decimal dry basis – db) were used. The fruits were uniaxially compressed between two parallel plates, in the natural resting position, and the nuts were dried at temperatures of 60, 80, and 100 °C. The reduction in the moisture content during drying was monitored using a gravimetric method (weight loss) to determine the initial moisture content of the product and the final moisture content. Based on our results, the compression force needed to deform the baru fruit decreased with increasing moisture content, regardless of the drying temperature. The proportional deformity modulus increased with the reduction of moisture content for all the studied temperatures. The reduced moisture content increased the force required to rupture the baru fruit, regardless of the drying temperature. The rupture forces of temperatures of 60 to 100 °C may be represented by one model. Key words: Rupture force. Proportional deformity modulus. Moisture content.

Resumo

Neste trabalho objetivou-se verificar a influência do teor de água e da temperatura de secagem nos valores da força máxima de compressão para deformações fixas (1, 2, 3, 4, 5, 6 e 7 mm), força de ruptura e no módulo proporcional de deformidade nos frutos de baru (Dipteryx alata Vogel), submetidos à compressão na posição natural de repouso. Foram utilizados frutos de baru com teores de água variando de 0,333 a 0,053 (decimal b.s.), secos nas temperaturas de 60, 80 e 100 °C. A redução do teor de água ao longo da secagem foi acompanhada pelo método gravimétrico (perda de massa), conhecendo-se o teor de água inicial do produto, até atingir o teor de água final. Concluiu-se que a força de compressão necessária para deformar os frutos de baru diminui com o aumento do teor de água, independentemente da temperatura de secagem. O módulo proporcional de deformidade aumenta com a redução do teor de água para todas as temperaturas estudadas. A redução do teor de água eleva a força necessária à ruptura dos frutos de baru, independentemente da temperatura de secagem. As forças de ruptura para as temperaturas de 60 e 100 °C podem ser representadas por um único modelo. Palavras-chave: Força de ruptura. Módulo proporcional de deformidade. Teor de água.

1 Prof., Instituto Federal de Educação, Ciência e Tecnologia Goiano, IFGoiano, Campus Iporá, GO, Brasil. E-mail: oliveira.d.e.c@ gmail.com 2 Prof., IFGoiano, Campus Rio Verde, Rio Verde, GO, Brasil. E-mail: [email protected] 3 Prof., Universidade Estadual de Goiás, UEG, Anápolis, GO, Brasil. E-mail: [email protected] * Author for correspondence Received: Apr. 06, 2016 – Approved: Aug. 09, 2016 185 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017 Oliveira, D. E. C. de; Resende, O.; Devilla, I. A.

Introduction products is essential for the development of new equipment to achieve a maximum efficiency without Dipteryx alata Vogel is a fruit of the compromising the final quality. During the steps and has had a good acceptance in the market due to of processing and storage, agricultural products its significant economic value and pleasant flavour suffer from impacts, which may cause damage and, mainly chestnut; (SANO et al., 2004). Dipteryx consequently, increase their susceptibility to decay alata Vogel, also popularly known as cumbaru, (BARGALE et al., 1995). cumaru, baru, barujo, feijão coco or emburena- brava, is a that occurs in the states of Goiás, Various factors, such as the drying conditions, , , moisture content, type of force applied and region and São Paulo (LORENZI, 2008). in which the force is applied, directly affect the mechanical properties (MOHSENIN, 1986). Ribeiro The fruits of baru are a drupe type and have a et al. (2007) indicate that by using the “force- light brown colour with a single edible that has deflection” curve obtained from the compression an elliptical shape and is dark brown; the seed is test, parameters can be obtained that characterize commonly called an . This seed has regional the response of a material when it is subjected to importance and has attracted scientific interest a load. Among the various mechanical properties, because of its nutritional composition. the modulus of deformability allows relative from baru have higher levels of monounsaturated strength comparisons between different materials fatty acids (51.1%) and lower levels of saturated (RESENDE et al., 2007). fatty acids (BENTO et al., 2014). Almond from baru contain approximately 40% and 30% Studying the mechanical properties of the baru and have a high content, especially fruit is important for assessing the strength required , calcium, , and to break the pericarp of the fruit and obtain the (SILVÉRIO et al., 2013). almond extract and for checking the resistance of the fruit to the impacts that may occur during their Knowledge on the mechanical properties processing. Generally, after the fruits are collected, of native fruits of the Cerrado as a function of the kernel is removed and processed. However, the moisture content and drying temperature is essential fruits are collected with the highest moisture content for developing machine designs to assist in the and must be dried such that its quality is maintained. processing of these fruits, particularly for adapting the equipment that is currently used to process other The lack of information on the mechanical products. properties of baru fruits and the need to develop equipment that can be used more efficiently for In this regard, numerous studies have been processing led to the present work. The influences developed to identify the mechanical properties of of moisture content and drying temperature on the various agricultural products with different moisture full-strength compression for fixed deformations contents, such as coffee fruit (COUTO et al., 2002; (1, 2, 3, 4, 5, 6 and 7 mm), tensile strength and BATISTA et al., 2003), hazelnut (GÜNER et al., proportional deformity modulus in baru fruits 2003), soybean (RIBEIRO et al., 2007), pistachios (Dipteryx alata Vogel), under compression in a (GALEDAR et al., 2009), rice (RESENDE et al., natural resting position, are examined. 2013) and wheat (FERNANDES et al., 2014). However, information about the mechanical properties of baru fruits is not found in the literature. Materials and Methods Resende et al. (2007) note that information The experiment was conducted at the Laboratory on the mechanical characteristics of agricultural of Postharvest Products of the Federal

186 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017

(Dipteryx alata Vogel) that had been collected manually in the municipality of Santa Helena de Goiás,

Goiás, 17 °48' S 50º35' W, at Mechanicalaltitude of properties 568 m, withof baru an fruit initial (Dipteryx moisture alata Vogel)content of 0.333 dry basis (dry basis, db). The geometrical dimensions of used baru fruits were 0.05280.0041; 0.03960.0033 and 0.02920.0026 Institute of Education, Science and Technology reduction of the moisture content during drying was m length, width and thickness, respectively. Goiano – Campus Rio Verde and drying Laboratory monitored by gravimetric analysis (weight loss) to and StorageTo conductProducts the Plant experiment, of the State the Universitymoisture content determine was obtained the initial by moisturedrying the content fruit in of an the oven product with a forcedof Goiás ventilation (UEG) inair Anapolis-GO. flow rate of 0.3313 Baru fruitm3 s - were1 and maintaininguntil it reached the fruit the atfinal temperatures moisture contentof 60, 80 of and0.053 100 °C,used which (Dipteryx promoted alata an Vogel) average that relative had been humidity collected of 25.1;(db), 12.2 using and a 5.3%, semi-analytical respectively. scale The with whole a resolution fruits were manually in the municipality of Santa Helena de of 0.01 g. dried in perforated trays that contained approximately 1 kg of product per temperature. The reduction of the Goiás, Goiás, 17 °48’ S 50º35’ W, at altitude of 568 The fruit moisture content was determined using moisturem, with an content initial moistureduring drying content was of monitored0.333 dry basis by gravimetric analysis (weight loss) to determine the initial the oven method at a temperature 105 ± 3 °C for (dry basis, db). The geometrical dimensions of used moisture content of the product until it reached the 24final hours moisture with three content replicates of 0.053 (BRASIL, (db), using 2009). a Forsemi - baru fruits were 0.0528±0.0041; 0.0396±0.0033 analytical scale with a resolution of 0.01 g. each obtained moisture content, the samples were and 0.0292±0.0026 m length, width and thickness, The fruit moisture content was determined usinghomogenized the oven methodand submitted at a temperature to compression 105 ± tests. 3 °C for respectively. 24 hours with three replicates (BRASIL, 2009). For eachThe obtained experimental moisture compression content, the testssamples were were To conduct the experiment, the moisture content conducted, in which 15 fruits per temperature were homogenizedwas obtained andby dryingsubmitted the tofruit compression in an oven tests. with a tested individually using a universal testing machine forced ventilationThe experimental air flow compressionrate of 0.3313 tests 3m s were-1 and conducted, in which 15 fruits per temperature were tested test EMIC GR049 model with a 1000 kN load cell. individuallymaintaining usingthe fruit a universal at temperatures testing machineof 60, 80 test and EMIC GR049 model with a 1000 kN load cell. 100 °C, which promoted an average relative humidity The fruits were subjected to uniaxial The fruits were subjected to uniaxial compression between two parallel plates. The compression of 25.1; 12.2 and 5.3%, respectively. The whole compression between two parallel plates. The wasfruits applied were driedwith thein perforatedfruits in their trays natural that containedresting position, compression as shown wasin Figure applied 1, with with fifteen the fruits repet itions. in their approximately 1 kg of product per temperature. The natural resting position, as shown in Figure 1, with fifteen repetitions. Figure 1. Guidance of baru fruit (Dipteryx alata Vogel) during the compression test in the natural resting position. Figure 1. Guidance of baru fruit (Dipteryx alata Vogel) during the compression test in the natural resting position.

After After obtaining obtaining the power the power curves curves for the for fruit the fruitassociated deformation, with athe decrease strength in theand compressive elongation atforce break deformation, the strength and elongation at break (ASAE, 1974), which indicates the point where were extract to provide the "bioyield point". This point is defined as the position on the curve where there is were extract to provide the “bioyield point”. the product’s structure begins to break and become anThis increase point in is product defined deformation as the position associated on with the a curve decreasedisorganized. in the compressive force (ASAE, 1974), which indiwherecates there the pointis an whereincrease the in product’s product structuredeformation begins to break and become disorganized. 187 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017

The proportional deformity modulus of fruit (Ep) was determined, according to Equation 1, for deformations of 1x10-3, 2x10-3, 3x10-3, 4x10-3, 5x10-3, 6x10-3 and 7x10-3 m, and was adapted from the deformations used by Batista et al. (2003).

3 1 2 E 0,531×F 1 1 3    (1) Ep 2 3 2 + 1-μ  2 rR D Oliveira, D. E. C. de; Resende, O.; Devilla, I. A.

The proportional deformity modulus of fruit D: Total deformation (elastic and plastic) body at where(Ep) was determined, according to Equation 1, for the contact points with the top and bottom plates, m; The proportional deformity modulus of fruit (Ep) was determined, according to Equation 1, for Ep:deformations proportional of deformity 1x10-3, 2x10 modulus,-3, 3x10 N-3 m, 4x10-2; -3, 5x10- -3 -3 -3 -3 F:- 3Strength,-3 N; -3 3 deformations-3 of -31x10 , 2x10 , 3x10 , 4x10 , 5x10 , 6x10 and 7x10 m, and was adapted from the E: modulus, 6x10 andof deformability, 7x10 m, and N wasm-2; adapted from the deformationsdeformations used used by by Batista Batista et et al. al. (2003). (2003). µ: Poisson’s ratio; and D: Total deformation (elastic and plastic) body at the contact points with the top and bottom plates, m; R and r: radius of curvature at the contact point, m. F: Strength, N; 3 1 2 : Poisson's ratio;E and 0,531×F  1 1 3 Ep   2 + (1) (1) 2 3  The values of the radii of curvature (r and R) R and r: radius1-μ of curvatureD 2 at the contactrR point, m.  of the fruit at the contact points were obtained by adjusting the curvature of the circumference of the The values of the radii of curvature (r and R) objectof the coordinatefruit at the planescontact according points were to theobtained relevant by wherewhere -2 compression position (COUTO et al., 2002), as adjustingEp: proportional the curvature deformity of the modulus,circumference N m-2 ; of the object coordinate planes according to the relevant Ep: proportional deformity modulus, N m ; illustrated in Figure 2. compressionE: modulus position of deformability, (COUTO et Nal., m 2002),-2; as illustrated in Figure 2. E: modulus of deformability, N m-2; D: Total deformation (elastic and plastic) body at the contact points with the top and bottom plates, m; F: Strength, N; Figure 2. Radius of curvature of the fruits in the Figure 2. Radius of curvaturecontact of the region fruits betweenin the contact the fruitregion and between the compression the fruit and the compression plate. : Poisson's ratio; andplate. R and r: radius of curvature at the contact point, m.

The values of the radii of curvature (r and R) of the fruit at the contact points were obtained by adjusting the curvature of the circumference of the object coordinate planes according to the relevant compression position (COUTO et al., 2002), as illustrated in Figure 2.

Figure 2. Radius of curvature of the fruits in the contact region between the fruit and the compression plate.

Source:Source: Couto Couto et al. et (2002). al. (2002).

The experiment was conducted according to a randomized design with fifteen repetitions. The factorial 3x5x7 (3 drying temperatures, 5 moisture data were analysed with an analysis of variance and content levels and 7 strains) in a completely regression.

188 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017

Source: Couto et al. (2002).

Mechanical properties of baru fruit (Dipteryx alata Vogel)

Results and Discussion there was no clear trend in relation to these variables. This result can be explained by the fact Table 1 shows the mean values and standard that the baru fruits do not present a homogeneous deviation of the radii of curvature of baru fruits shape. Fernandes et al. (2014) studied the influence for each temperature and moisture content used to of moisture content on mechanical properties of determine the proportional deformity modulus. The wheat grain and observed similar behaviour. radii of curvature varied as a function of moisture content; in contrast, for the drying temperature,

Table 1. Mean and standard deviation values for the radii of curvature of baru fruit (Dipteryx alata Vogel) (x10-3 m) for each position and moisture content.

Temperature Moisture content 100 °C 80 °C 60 °C (db) R r R r R r 0.333 41.23±2.07 24.54±2.91 43.23±1.31 23.86±1.86 43.47±1.80 25.42±2.54 0.250 42.42±2.27 25.68±2.32 46.04±2.81 26.70±2.07 42.53±2.46 24.96±2.14 0.177 42.68±1.35 24.81±2.42 41.63±1.88 25.54±2.74 43.26±1.80 24.63±2.82 0.111 45.62±3.32 25.458±3.03 41.60±1.97 24.56±2.45 43.36±1.99 26.05±2.47 0.053 42.15±2.05 26.63±2.70 43.15±2.30 24.15±2.71 43.24±1.85 24.40±2.52

Figure 3 shows the average values of the Vursavuş and Özgüven (2004) and Ribeiro maximum compressive force in the three drying et al. (2007) studied the mechanical properties temperatures, depending on the moisture content, of apricot fruit and soybean, respectively, and for various deformations. The compressive force observed similar behaviour. When Resende et al. required to deform the baru fruits decreased with (2013) studied the mechanical properties of the rice increasing moisture content for all temperatures. grains with and without bark, they found different Similar results were observed by Resende et al. behaviours, in which the compression force values (2007) and Ribeiro et al. (2007) for bean and ranged somewhat randomly, regardless of the type soybean, respectively. of processing. The average compressive force required for Using the compressive strength data, it was the different deformations due to the moisture possible to determine the proportional deformity content ranged from 8.09 to 1516.37 N, from 7.19 modulus, as shown in Figure 4, which showed the to 1672.25 N and from 5.06 to 605.33 C for 60, same behaviour as the compression force and was a 80 and 100 °C, respectively (Figures 3A, B and function of moisture content and deformation. C). Reducing the moisture content increased the Table 2 shows the regression equations fitted force required to deform the fruit. This behaviour to the experimental values of the proportional was observed for all of the studied temperatures. deformity modulus of baru fruit, which depended Increasing the compressive strength by reducing the on the moisture content and deformation for each moisture content may thus affect the integrity of the drying temperature. By analysing the results, it was matrix by reducing the moisture content (GUPTA; observed that the adjusted equations seem to be DAS, 2000) and other characteristics that can satisfactory, with high values of the coefficient of influence the increase of the compressive strength determination (R2). and shrinkage of the fruit. 189 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017

modulus, as shown in Figure 4, which showed the same behaviour as the compression force and was a function of moisture content and deformation.

Oliveira, D. E. C. de; Resende, O.; Devilla, I. A.

Figure 3. Mean maximum compression force values for drying temperatures of 60 (A), 80 (B) and 100 (C) °C versus Figure 3. Mean maximum compression force values for drying temperatures of 60 (A), 80 (B) and 100 (C) moisture content for deformations of 1x10-3, 2x10-3, 3x10-3, 4x10-3, 5x10-3, 6x10-3 and 7x10-3 m. °C versus moisture content for deformations of 1x10-3, 2x10-3, 3x10-3, 4x10-3, 5x10-3, 6x10-3 and 7x10-3 m.

(A) (B)

(C)

Table 2 shows the regression equations fitted to the experimental values of the proportional Table 2. Equations fitted to experimental values of the proportional deformity modulus of baru fruit Dipteryx( alata Vogel;deformity Ep) as amodulus function ofof thebaru moisture fruit, which content depended (X) and the on deformation the moisture (D) content for each and drying deformation temperature. for each drying temperature. By analysing the results, it was observed that the adjusted equations seem to be satisfactory, Temperature Model2 R2 (%) with(°C) high values of the coefficient of determination (R ). Ep = 20.9643 – 167.1678 X + 1255.9089 D + 384.8782 X2 + 338189.5976 D2 – 60 93.47* 12959.6428 X D Table 2. EquationsEp = 20.5188 fitted to– 200.2462 experimental X + 922.2225 values Dof + 490.4072the proportional X2 + 263175.0655 deformity D 2 modulus– of baru fruit 80 82.13* (Dipteryx alata 10540.6016Vogel; Ep) X as D a function of the moisture content (X) and the deformation (D) for each drying temperature. Ep = 3.1422 – 17.3821.X – 29.4599 D + 74.6832.X2 + 274936.9633 D2 – 6520.3826 100 84.902* TemperatureX (°C) D Model R (%) 60 Ep = 20.9643 – 167.1678 X + 1255.9089 D + 384.8782 X2 + 93.47* *Significant to 5% by F test. 338189.5976 D2 – 12959.6428 X D

190 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017

80 Ep = 20.5188 – 200.2462 X + 922.2225 D + 490.4072 X2 + 82.13* 263175.0655 D2 – 10540.6016 X D 100 Ep = 3.1422 – 17.3821.X – 29.4599 D + 74.6832.X2 + 84.90* 274936.9633 D2 – 6520.3826 X D *Significant to 5% by F test. Mechanical properties of baru fruit (Dipteryx alata Vogel) Figure 4 illustrates the response surfaces adjusted in accordance with the equations obtained; Table Figure 4 illustrates the response surfaces adjusted deformation for each drying temperature. Note that in 2accordance shows the with proportional the equations deformity obtained; modulus Table of2 baruregardless fruit, which of the dependeddrying temperature, on the moisture the values content of and showsdeformation the proportional for each deformitydrying temperature. modulus of Note baru that the regardless proportional of the deformity drying temperature, modulus increased the values with of the fruit,proportional which depended deformity on modulusthe moisture increased content with and the decreasethe decrease in moisture in moisture content. content.

FigureFigure 4. Mean 4. Mean proportional proportional deformity deformity modulus modulus (Ep) of baru(Ep) fruit of baru (Dipteryx fruit alata(Dipteryx Vogel) alata as a functionVogel) ofas moisturea function of contentmoisture and deformation content and for deformation drying temperatures for drying of 60temperatures (A), 80 (B) andof 60 100 (A), (C) 80°C. (B) and 100 (C) °C.

(A) (B)

(C)

Resende Resendeet al. (2007) et al. and (2007) Ribeiro and etRibeiro al. (2007) et al. (2007)value withevaluated a lower the proportional moisture content deformity indicates modulus of evaluatedbean and the soybean, proportional respectively, deformity and modulusfound that of the theproportional need to applydeformity a greater modulus force increases for a with certain red uced beanmoisture and soybean, content respectively,and deformation. and found Batista that et theal. (2003)deformation. noted that a higher deformity modulus value with a proportional deformity modulus increases with For the moisture contents studied, the values reduced moisture content and deformation. Batista of the proportional deformity modulus ranged et al. (2003) noted that a higher deformity modulus 191 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017 Oliveira, D. E. C. de; Resende, O.; Devilla, I. A.

from 0.96 x 106 to 31.14 x 106, from 0.84 x 106 to and dehulled rice, for the moisture content range 34.46 x 106 and from 0.5 x 106 to 12.15 x 106 N m-2 from 0.30 to 0.12 (db), ranged from 5.5x109 to for 60, 80 and 100 °C, respectively. Batista et al. 7.4x109 N m-2 for the shelled rice grains and from (2003) studied the proportional deformity modulus 9.5x109 to 12.3x109 N m-2 to the rice grains in the of coffee fruits (Coffea arabica L.) in three stages husk. of maturation and three temperatures (40, 50 and Figure 4 shows that the proportional deformity 60 °C) for the moisture content range from 1.50 to modulus decreases with the decreasing deformation 0.14 (bs) and found that the proportional deformity of the product. Different results were observed by modulus of the coffee fruits varied by deformity and Resende et al. (2007) and Fernandes et al. (2014) ranged from 2.0x107 to 18.0x107 N m-2 for the coffee for beans and wheat, respectively. cherry fruits, from 5.0x107 to 40.0x107 N m-2 for the green fruits and from 1.0x107 to 50x107 N m-2 for Table 3 shows the parameters from the linear verdoengos fruit. Resende et al. (2013) found that models that can be used to determine the rupture the proportional deformity modulus of rice grains force as a function of moisture content for baru fruit for all of the studied drying conditions.

Table 3. Linear model parameters adjusted to the tensile strength of baru fruit (Dipteryx alata Vogel) under different drying conditions

Temperature (°C) Parameters 60 80 100 A 9006.8778** 8028.1154** 9455.8561** B 10186.6531* 10911.6666** 10192.6240** R2 (%) 91.79 97.39 94.72 **Significant at 1% by t test. * Significant at 5% by t test.

The linear equation adequately represents the and b3) were compared to verify their equality. The experimental data and can be used to estimate the following hypotheses were formulated: rupture force for the baru fruits; it presents high H (1): a = a = a = a versus H (1): not all a are equal coefficients of determination2 (R ). Resende et al. o 1 2 3 a i (2) (2) (2013) studied the rupture force of the rice grains Ho : b1= b2 = b3 = b versus Ha : not all bi are equal both with and without shells during the drying (3) (3) Ho : a1= a2 = a3= a e b1= b versus Ha : there is at process and found that the linear equation can least one inequality be used to represent the rupture force. Bargale et The decision rule was based on the chi-square al. (1995) found that the rupture force decreases test (χ2) according to the following expression: linearly with the increased moisture content of both wheat grains and canola. Thus, it proceeded to model identity test aiming  2 SQR to enable the use of a single linear model to represent  calculated = -N ln  (2) (2) SQR wi the rupture force of the baru fruit, regardless of the drying temperature, according to the methodology where where described by Regazzi (2003). N: number of observations; N: number of observations; The parameters of the linear model for rupture SQR : sum of residual squares of the complete Ω SQR: sum of residual squares of the complete model; and force at 60 (a1 and b1), 80 (a2 and b2) and 100 °C (a3 model; and SQRWi: sum of residual squares restricted parameter space. 192

Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017 The tabulated value (2) is a function of the level of significance  (p = 5%) and the number of degrees of freedom:

 = pp-  wi (3) where : degrees of freedom of the model;

p: number of complete model parameters; and

pwi: number of model parameters with constraint.

Initially, the three air conditions at 60, 80 and 100 °C were tested. Then, the air conditions were compared in pairs. Table 4 presents the results of hypothesis analysed by a chi-square test.

Table 4. Test of hypothesis (Ho) using the chi-square test to determine the tensile strength of baru fruit (Dipteryx alata Vogel). 2 2 Hypotheses GL  tabulated  calculated 60 e 80 °C 2 5.991 18.010 60 e 100 °C 2 5.991 5.157 80 e 100 °C 2 5.991 26.933 60. 80 e 100 °C 4 9.488 31.545

2 The  calculated value for the tensile strength of the baru fruit at 60 and 100 °C was lower than the 2  tabulated value. Thus, the proposed hypothesis (Ho) was accepted, which suggested that the linear models used to determine the breaking strengths at 60 and 100 °C are not significantly different from each other. Thus, a single model may be used for both of these temperatures. 2 2 For the other combinations, the  calculated value was greater than the  tabulated values. Thus, we rejected the hypothesis formulated and noted that the tensile strength of the baru fruit differs for each temperature considered. The average breaking strengths of baru fruits based on the moisture content and drying temperature are shown in Figure 5. The reduction of moisture content for all temperatures resulted in a linear increase in the force required to achieve the "bioyield point"; this increase was from 5988.63 to 8609.82 N, from 4406.50 to 7594.96 N and 6274.28 to 9014.51 N at 60, 80 and 100 °C, respectively. The results confirm those obtained

 2 SQR  calculated = -N ln  (2) SQR wi where Mechanical properties of baru fruit (Dipteryx alata Vogel) N: number of observations;

2 SQRWi: sum of SQRresidual: sum squares of residual restricted squares parameter of the completeFor model; the other and combinations, the χ calculated value space. was greater than the χ2 values. Thus, we SQRWi: sum of residual squares restricted parameter space. tabulated 2 rejected the hypothesis formulated and noted that The tabulated value (χ ) is a function of the the tensile strength of the baru fruit differs for each level of significance α (p = 5%) and the number2 of The tabulated value ( ) is a temperaturefunction of theconsidered. level of significance  (p = 5%) and the number of degrees of freedom: degrees of freedom: The average rupture force of baru fruits based on the moisture content and drying temperature are  = pp - w (3) (3) i shown in Figure 5. where where The reduction of moisture content for all ν: degrees of freedom: degrees of theof freedommodel; of the model; temperatures resulted in a linear increase in the force required to achieve the “bioyield point”; this increase p : number of completep: number model of complete parameters; model and parameters; and Ω was from 5988.63 to 8609.82 N, from 4406.50 to pwi: number of model parameters with constraint. pwi: number of model parameters with constraint. 7594.96 N and 6274.28 to 9014.51 N at 60, 80 and 100 Initially, the three air conditions at 60, 80 and °C, respectively. The results confirm those obtained 100 °C were tested. Then,Initially, the air the conditions three air wereconditions by researchersat 60, 80 and who 100 worked °C were with differenttested. Then, agricultural the air conditions were products (GÜNER et al., 2003; VURSAVUŞ; compared in pairs.compared Table in 4 pairs. presents Table the 4 resultspresents of the results of hypothesis analysed by a chi-square test. hypothesis analysed by a chi-square test. ÖZGÜVEN, 2004, 2005; SAIEDIRAD et al., 2008;

2 SHARMA et al., 2009; RESENDE et al., 2013). This The χ calculated value for the tensile strength of Table 4. Test of hypothesis (Ho) usingbehaviour the chi may-square be related test to todetermine the cell density,the tensile which strength of baru the baru fruit at 60 and 100 °C was lower than fruit (Dipteryx alata Vogel). changes upon the exit of water during the drying of the χ2 value. Thus, the proposed hypothesis 2 2 tabulated Hypotheses baru fruit,GL that is, the cells oftabulated the fruit to approach; calculated (H ) was accepted, which suggested that the linear o 60 e 80 °C therefore,2 the resulting product5.991 will have a greater18.010 models used to determine the rupture force at 60 60 e 100 °C resistance2 to compression with5.991 a lower moisture 5.157 and 100 °C are not significantly different from each 80 e 100 °C content.2 Goneli (2008) indicated5.991 that reducing the26.933 other. Thus, a single model may be used for both of 60. 80 e 100 °C moisture4 content promotes a 9.488change in cell integrity,31.545 these temperatures. which tends to become more organized and, thus, 2 The  calculated value for the tensilemore strengthresistant ofto compression.the baru fruit at 60 and 100 °C was lower than the 2  tabulated value. Thus, the proposed hypothesis (Ho) was accepted, which suggested that the linear models

Table 4. Test of hypothesisused to determine (Ho) using the the breakingchi-square strengthstest to determine at 60 theand tensile 100 °Cstrength are not of baru significantly fruit (Dipteryx different alata from each other. Vogel). Thus, a single model may be used for both of these temperatures. 2 2 For the other combinations, the  calculated 2value was greater than 2the  tabulated values. Thus, we Hypotheses GL χ tabulated χ calculated 60rejected e 80 °C the hypothesis formulated2 and noted that 5.991the tensile strength of 18.010the baru fruit differs for each 60 e 100 °C 2 5.991 5.157 temperature considered. 80 e 100 °C 2 5.991 26.933 60. 80 e 100 °CThe average breaking4 strengths of baru fruits9.488 based on the moisture31.545 content and drying temperature are shown in Figure 5. The reduction of moisture content for all temperatures resulted in a linear increase in the force required to achieve the "bioyield point"; this increase was from 5988.63 to 8609.82 N, from 4406.50 to 7594.96 N and 6274.28 to 9014.51 N at 60, 80 and 100 °C, respectively. The results confirm those obtained

193 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017

by researchers who worked with different agricultural products (GÜNER et al., 2003; VURSAVUŞ; ÖZGÜVEN, 2004, 2005; SAIEDIRAD et al., 2008; SHARMA et al., 2009; RESENDE et al., 2013). This behaviour may be related to the cell density, which changes upon the exit of water during the drying of baru fruit, that is, the cells of the fruit to approach; therefore, the resulting product will have a greater resistance to compression with a lower moisture content. Goneli (2008) indicated that reducing the moisture content promotes a change in cell integrity, which tends to become more organized and, thus, more resistant to compression.

Oliveira, D. E. C. de; Resende, O.; Devilla, I. A. Figure 5. Mean values of tensile strength as a function of moisture content for baru fruit (Dipteryx alata Vogel) for all drying temperatures. Figure 5. Mean values of tensile strength as a function of moisture content for baru fruit (Dipteryx alata Vogel) for all drying temperatures.

In addition,In addition, Figure Figure 5 shows5 shows that that the the dryingdrying temperatureTable 5 influence presents the equationsbreaking strength;used to estimatehowever, theretemperature was no clear influence trend when the comparingrupture force; the drying however, temperatures:the values of the the lowest rupture moisture force (Rf) content of the values baru fruit were there was no clear trend when comparing the drying to temperatures of 60-100 and 80 °C, due to the observed at 80 °C, and the highest were obtained at 100 °C. Liu et al. (1990) studied the mechanical temperatures: the lowest moisture content values reduction of moisture content. All of the parameters propertieswere observed of soybeans at 80 and °C, found and the that highest the drying were airwere temperature significant and atmoisture the 1%content level influenced by a t-test the and mechanicalobtained atperformance 100 °C. Liu of etthe al. product (1990) and studied that with the a reductionshowed high of the coefficients drying air oftemperature, determination there (R2 ).was an mechanical properties of soybeans and found that increase in the force required to rupture the fruit; however,The increasing results obtained the moisture for proportional content of thedeformity product the drying air temperature and moisture content reduced this force. modulus and rupture strength show that baru influenced the mechanical performance of the fruit with lower moisture contents exhibit greater product Table and that5 presents with athe reduction equations of used the to drying estimate the values of the rupture force (Rf) of the baru fruit resistance to breakage during the stages of toair temperatures temperature, of there 60-100 was and an 80increase °C, due in tothe the force reduction of moisture content. All of the parameters were processing. significantrequired to at rupture the 1% thelevel fruit; by however,a t-test and increasing showed highthe coefficients of determination (R2). moisture content of the product reduced this force.

Table 5. Equations fitted to the experimental values of fruit baru breaking strength (Dipteryx Table 5. Equations fitted to the experimental values of fruit baru ruptureDipteryx force( alata Vogel) (Br) as a alata Vogel) (Br) as a function of moisture content (X) for each drying temperature function of moisture content (X) for each drying temperature Temperature (°C) Model R2 (%) Temperature (°C) Model R2 (%) 60 e 100 Rf = 9231.3621** – 10189.6179** X 89.15 80 Rf = 8028.1154** – 10911.6666** X 97.39 **Significant to 1% by F test.

Conclusions strength, decrease with increasing moisture content, regardless of the drying temperature; thus, there The obtained results show that the compressive was greater resistance to impacts. The rupture force force required to deform the fruit, i.e., the for drying temperatures of 60 to 100 °C may be proportional deformity modulus and tensile represented by one model. 194 Semina: Ciências Agrárias, Londrina, v. 38, n. 1, p. 185-196, jan./fev. 2017 Mechanical properties of baru fruit (Dipteryx alata Vogel)

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