Mechanical and Processing Properties of Rice Grains

: Strength properties of grains have a signiﬁcant impact on the energy demand of grinding mills. This paper presents the results of tests of strength and energy needed the for destruction of rice grains. The research aim was to experimentally determine mechanical and processing properties of the rice grains. The research problem was formulated in the form of questions: (1) what force and energy are needed to induce a rupture of rice grain of the Oryza sativa L. of long-grain variety? (2) what is the relationship between grain size and strength parameters and the energy of grinding rice grain of the species Oryza sativa L. long-grain variety? In order to ﬁnd the answer to the problems posed, a static compression test of rice grains was done. The results indicate that the average forces needed to crush rice grain are 174.99 kg m · s − 2 , and the average energy is 28.03 mJ. There was no statistically signiﬁcant relationship between the grain volume calculated based on the volumetric mass density V ρ and the crushing energy, nor between the volume V ρ and other strength properties of rice grains. In the case of Vs, a low negative correlation between strength σ min and a low positive correlation between the power inducing the ﬁrst crack were found for the grain size related volume. A low negative correlation between the grain thickness a 3 , stresses σ min and work W Fmax was found as well as a low positive correlation between thickness a 3 and the force inducing the ﬁrst crack F min .


Introduction
The strength properties of grains have a significant impact on the energy demand of grinders [1][2][3][4]. During grinding of grains in a five-disc mill, a complex state of stress occurs in the material, with shear and compressive stresses prevailing [5,6]. Identification of the forces causing grain cracking (rupture) can be considered as the first step to determine the energy demand in the grain grinding process [7,8]. Two cases can be distinguished: static squeezing of grains and shearing of grains [9]. In the case of static compression, in order to determine the forces and stress and consequently, the work (energy) needed to crush one grain and then more than a dozen grains, a static compression test can be carried out. The ranges of probable forces destroying the grain may be determined in an experimental manner, and subsequently, the energy ranges of destroying its structure [10].
The subject of research on the physical-mechanical properties of rice grains has already been addressed by researchers, because the specificity of rice grain processing and the energy demand of processing lines, e.g., grinding, drying, pelleting, etc., depends largely on these properties [11][12][13][14][15][16][17]. In their research, Zeng, et al. [18] focused on modeling cracking of rice grains depending on the grain indicators for the grinding process and modeling grinding and crushing processes using the discrete element method DEM.
The research problem was formulated in the form of questions: (1) what strength and energy is needed to induce a rupture of rice grain of the species Oryza sativa L. long-grain variety? (2) what is the relationship between grain size and strength parameters and the energy of grinding rice grain of the species Oryza sativa L. long-grain variety?

Rice Grains Preparation
To determine the force needed to break the grain, a static compression test was carried out for 100 grains of rice of the species Oryza sativa L., a long-grained variety with a stabilized humidity equal to 13% ± 0.1%. Oryza sativa L., a long-grained variety of rice was accepted to be the research object due to its popularity, among others, in food industry [32]. Knowing the processing properties of this species, in particular, crushing energy, can significantly affect power demand of the processing devices, e.g., grinders. Samples of 100 individual rice grains were prepared and described by numbers ( Figure 1). Then, three dimensions were measured with the vernier caliper: length, width and height of the grain.

Test Stand
A static compression test was carried out on an Instron 5966 testing machine ( Figure 2). The samples were placed in the machine in a horizontal orientation, in such a way that the dimensions a1 and a2 were the large axis and small axis of cross-sectional areas of the grain subjected to the load ( Figure 3). The load speed was 2 mm·min −1 .

Test Stand
A static compression test was carried out on an Instron 5966 testing machine ( Figure 2). The samples were placed in the machine in a horizontal orientation, in such a way that the dimensions a 1 and a 2 were the large axis and small axis of cross-sectional areas of the grain subjected to the load ( Figure 3). The load speed was 2 mm·min −1 .

Research Methods
The analysis of the grain strength properties during a static compression test of a single grain was performed according to the plan shown in Figure 4. Three dimensions were measured with the vernier caliper: length, width and height of the grain.

Research Methods
The analysis of the grain strength properties during a static compression test of a single grain was performed according to the plan shown in Figure 4. Three dimensions were measured with the vernier caliper: length, width and height of the grain.

Research Methods
The analysis of the grain strength properties during a static compression test of a single grain was performed according to the plan shown in Figure 4. Three dimensions were measured with the vernier caliper: length, width and height of the grain.  The volume of the studied seeds was determined in two ways: on the basis of the three measured dimensions a1, a2 and a3 (Vs) and on the basis of the relationship of the grain mass and density (Vρ).
The first method of determining the volume takes into consideration three basic grain sizes, i.e., the height and width length, and allows a simplified grain volume estimation with a certain error by aligning the grain shape to the cuboid with dimensions a1, a2, a3 (Figure 5.).
For this interpretation, the formula for the estimated volume of grain will be: and equal to the volume of a cuboid circumscribed on the grain.  The volume of the studied seeds was determined in two ways: on the basis of the three measured dimensions a 1 , a 2 and a 3 (V s ) and on the basis of the relationship of the grain mass and density (V ρ ).
The first method of determining the volume takes into consideration three basic grain sizes, i.e., the height and width length, and allows a simplified grain volume estimation with a certain error by aligning the grain shape to the cuboid with dimensions a 1 , a 2 , a 3 ( Figure 5). The volume of the studied seeds was determined in two ways: on the basis of the three measured dimensions a1, a2 and a3 (Vs) and on the basis of the relationship of the grain mass and density (Vρ).
The first method of determining the volume takes into consideration three basic grain sizes, i.e., the height and width length, and allows a simplified grain volume estimation with a certain error by aligning the grain shape to the cuboid with dimensions a1, a2, a3 (Figure 5.).
For this interpretation, the formula for the estimated volume of grain will be: and equal to the volume of a cuboid circumscribed on the grain.  For this interpretation, the formula for the estimated volume of grain will be: and equal to the volume of a cuboid circumscribed on the grain. The second method of determining the volume is based on the knowledge of density ρ of the grain and its mass m. The grain density is determined from the dependence [43]: Hence, the volume determined on the basis of density V ρ, will be [43]: The relationship between computational volume (V s ) and determined based on the grain density (V ρ ) can be determined by calculating the correction factor for the grain volume k v taking into consideration the grain spherical and uneven shape. It can be determined experimentally and expressed by the dependence: hence: The static compression test is mainly used for brittle materials, i.e., not showing significant plastic deformation. Rice can be considered as a fragile material with some (small) plastic deformability due to the internal structure that differentiates it from the cross-linked metal structure. A feature that characterizes fragile materials is compressive strength (R c ) [24]: where F c -the largest value of the compressive load at which the sample is crushed, A 0 -the initial cross-section of the sample. If the compression diagram l = f (F) has a part where shortening (∆l) is directly proportional to compressive force (F), then, on this basis, we determine Young's modulus (E) for this material. If this relationship is not directly proportional, then based on the first few results (where it is possible to assume that the material behaves linearly and elastically), we determine the mean value of Young's modulus (E). The value of the Young's modulus is determined by Hooke's law [24]: where: F-compressive force, kg·m·s −2 , ∆l-sample shortening corresponding to force (F), m, l-the initial length of the sample, m, A 0 -area of the initial sample cross-section, m 2 . During the compression, some force F affects the grain and causes it to break (displacement s), so the elementary work done over the grain by force F causing the crack can be determined [24,44]: During compression, we deal with a variable force F and displacement s → 0, then, this characterized work can be determined by integrating both sides of the equation [24]: Sustainability 2020, 12, 552 7 of 17 Then, the work during compression of one grain is the area under graph F = f (s) ( Figure 6).

Analytical Methods
The statistical analysis tools available in MS Excel and Statistica were used in processing the results. Basic descriptive statistics of the examined physical and mechanical properties and rupture energy of rice grains were determined. The relationship between the grain volume and physicalmechanical properties and rupture energy was examined using Spearman's correlation analysis. A significance level p < 0.05 was adopted.

Results of Research on the Physical Properties of Rice Grains and Their Discussion
Firstly, the physical properties of rice grains were determined, such as grain length a1, grain width a2, grain height a3, and grain volume determined based on the knowledge of grain mass and density Vρ, volume determined on the basis of dimensions Vs, correction factor for volume kv. The results of the tests after a basic statistical analysis are presented in Figures 7 and 8 in the form of a box plot.
Based on the analysis, it was found that the average grain length of rice was 6.38 mm, the average width was 1.91 mm, the average height was 1.51 mm. The average grain volume determined on the basis of the grain weight and density was equal to 14.82 mm 3 , while the volume determined on the basis of grain size 18.44 mm 3 . The correction factor for given volumes Vρ and vs. assumed an average value of 0.82. The obtained results allowed to formulate the dependence of the real volume of the grain determined on the basis of density as a function of the volume determined on the basis of dimensions: The results obtained for rice dimensions a1, a2, and a3, are similar, although slightly smaller than those reported in the literature by other researchers, e.g., Sadeghi et al., Zareiforoush et al., and Zeng et al. [18,19,30]. Differences in dimensions may be caused primarily by the difference in the varieties and types of rice grains studied, the country of origin (the study of rice originated from Burma), grain humidity and growing conditions of grains (e.g., extensive, intensive cultivation, weather conditions that affect the grain size). The presented grain size results are an indispensable element of building models in computer simulations based on the DEM discrete element method [18], e.g., in the RockyDEM environment.

Analytical Methods
The statistical analysis tools available in MS Excel and Statistica were used in processing the results. Basic descriptive statistics of the examined physical and mechanical properties and rupture energy of rice grains were determined. The relationship between the grain volume and physical-mechanical properties and rupture energy was examined using Spearman's correlation analysis. A significance level p < 0.05 was adopted.

Results of Research on the Physical Properties of Rice Grains and Their Discussion
Firstly, the physical properties of rice grains were determined, such as grain length a 1 , grain width a 2 , grain height a 3 , and grain volume determined based on the knowledge of grain mass and density V ρ , volume determined on the basis of dimensions V s , correction factor for volume k v . The results of the tests after a basic statistical analysis are presented in Figures 7 and 8 in the form of a box plot.
Based on the analysis, it was found that the average grain length of rice was 6.38 mm, the average width was 1.91 mm, the average height was 1.51 mm. The average grain volume determined on the basis of the grain weight and density was equal to 14.82 mm 3 , while the volume determined on the basis of grain size 18.44 mm 3 . The correction factor for given volumes V ρ and vs. assumed an average value of 0.82. The obtained results allowed to formulate the dependence of the real volume of the grain determined on the basis of density as a function of the volume determined on the basis of dimensions: The results obtained for rice dimensions a 1 , a 2 , and a 3 , are similar, although slightly smaller than those reported in the literature by other researchers, e.g., Sadeghi et al., Zareiforoush et al., and Zeng et al. [18,19,30]. Differences in dimensions may be caused primarily by the difference in the varieties and types of rice grains studied, the country of origin (the study of rice originated from Burma), grain humidity and growing conditions of grains (e.g., extensive, intensive cultivation, weather conditions that affect the grain size). The presented grain size results are an indispensable element of building models in computer simulations based on the DEM discrete element method [18], e.g., in the RockyDEM environment.   Figure 9 presents examples of graphs showing the characteristic of rice grain cracks during a compression test. Based on the presented curves, it can be stated that for each grain, the crack proceeded differently. This is caused by differences in internal structure between each grain, which is characteristic for biomaterials. However, noticeable are the characteristic points in the forcedisplacement graph marked as Fmin and Fmax. The point marked as Fmin symbolizes the first crack of the grain, while the Fmax point corresponds to the forces causing the breakdown of the grain into smaller fragments ( Figure 10). Similar conclusions are presented in the work of Sadeghi et al. [19].

The Results of Testing the Strength Properties of Rice Grains and Their Discussion
For rice grains, the forces inducing fracture Fmin of the grain structure were within the range    Figure 9 presents examples of graphs showing the characteristic of rice grain cracks during a compression test. Based on the presented curves, it can be stated that for each grain, the crack proceeded differently. This is caused by differences in internal structure between each grain, which is characteristic for biomaterials. However, noticeable are the characteristic points in the forcedisplacement graph marked as Fmin and Fmax. The point marked as Fmin symbolizes the first crack of the grain, while the Fmax point corresponds to the forces causing the breakdown of the grain into smaller fragments ( Figure 10). Similar conclusions are presented in the work of Sadeghi et al. [19].

The Results of Testing the Strength Properties of Rice Grains and Their Discussion
For rice grains, the forces inducing fracture Fmin of the grain structure were within the range   Figure 9 presents examples of graphs showing the characteristic of rice grain cracks during a compression test. Based on the presented curves, it can be stated that for each grain, the crack proceeded differently. This is caused by differences in internal structure between each grain, which is characteristic for biomaterials. However, noticeable are the characteristic points in the force-displacement graph marked as F min and F max . The point marked as F min symbolizes the first crack of the grain, while the F max point corresponds to the forces causing the breakdown of the grain into smaller fragments ( Figure 10). Similar conclusions are presented in the work of Sadeghi et al. [19].

The Results of Testing the Strength Properties of Rice Grains and Their Discussion
For rice grains, the forces inducing fracture F min of the grain structure were within the range         [30,31], where the rupture energy assumed values of about 30 mJ. Figures 12-18 summarize the results of mechanical properties of rice grains depending on its volume. The graphs show that mechanical properties of rice grains do not depend on its volume.                   The analysis of the Spearman correlation shows that there are no statistically significant relationships between the volume of the grain Vρ and the tested strength properties, so there are no interdependencies between the variables (Tab 2). In the case of the grain dimension related volume vs. a low negative correlation between strength σmin and low positive correlation between the force inducing the first crack were found (Table 2). An analysis of the correlation between the grain size related variables, that is, length a1, width a2, height a3, mass m and volumes Vρ and vs. showed that the volume of grains Vρ is moderately positively correlated with length a1 and height a3 (Table S1). The surface of compression cross-section A0 was in turn significantly correlated with the grain length a1 and width a2 (Table S1). However, no relevant correlations between the grain dimensions, volume and mass and its strength properties and energy needed to crush the grains, were found. Only low correlations occurred, including negative ones between the grain width a2 and stresses σmin and σmax (Table S1). Contrarily to wheat, a dependence of grinding energy proportionality and its mass was not confirmed [35]. It was not possible to confirm distinct dependencies between the grain thickness (a3) and the force value, either (for Fmin positive correlation R = 0.271, statistically significant p < 0.05, for Fmax statistically insignificant correlation (Table S1)) and work (WFmin and WFmax low correlations), which could be observed for wheat [37]. The volume is related to the grain dimensions, including compression cross-section A0, whereas the cross section is related to compressive strength (according to dependence (6)). However, it was not possible to show significant dependencies between the grain cross section A0 and values of compressive strength (low negative correlations between A0 and σmin, σmax (Table S1)). The obtained results, including the results of dimension and volume scatter, confirm the significant variability and diversity of biological materials within one species. The diversity of the values confirms that each grain is characterized by a different internal structure. Such a diversification can indicate low quality of the grain and poor conditions of cultivation.

Average of W Fmax
Average of V ρ Figure 18. The scatter diagram of stress W Fmax for individual rice grains in relation to volume.
The analysis of the Spearman correlation shows that there are no statistically significant relationships between the volume of the grain V ρ and the tested strength properties, so there are no interdependencies between the variables (Tab 2). In the case of the grain dimension related volume vs. a low negative correlation between strength σ min and low positive correlation between the force inducing the first crack were found ( Table 2). An analysis of the correlation between the grain size related variables, that is, length a 1 , width a 2 , height a 3 , mass m and volumes V ρ and vs. showed that the volume of grains V ρ is moderately positively correlated with length a 1 and height a 3 (Table S1). The surface of compression cross-section A 0 was in turn significantly correlated with the grain length a 1 and width a 2 (Table S1). However, no relevant correlations between the grain dimensions, volume and mass and its strength properties and energy needed to crush the grains, were found. Only low correlations occurred, including negative ones between the grain width a 2 and stresses σ min and σ max (Table S1). Contrarily to wheat, a dependence of grinding energy proportionality and its mass was not confirmed [35]. It was not possible to confirm distinct dependencies between the grain thickness (a 3 ) and the force value, either (for F min positive correlation R = 0.271, statistically significant p < 0.05, for F max statistically insignificant correlation (Table S1)) and work (W Fmin and W Fmax low correlations), which could be observed for wheat [37]. The volume is related to the grain dimensions, including compression cross-section A 0 , whereas the cross section is related to compressive strength (according to dependence (6)). However, it was not possible to show significant dependencies between the grain cross section A 0 and values of compressive strength (low negative correlations between A 0 and σ min , σ max (Table S1)). The obtained results, including the results of dimension and volume scatter, confirm the significant variability and diversity of biological materials within one species. The diversity of the values confirms that each grain is characterized by a different internal structure. Such a diversification can indicate low quality of the grain and poor conditions of cultivation. It is noteworthy that the grains were tested for only one orientation of grains in the strength testing machines. It is expected that the longitudinal and transverse orientation of grains would provide different values of destructive compression, forces and strength [28][29][30].

Conclusions
The main objectives of the study were achieved through the determination of energy (work) and compressive forces in the test of static compression and analysis of the dependence between the grain size and the grain strength parameters and grinding energy.
Based on the analyzes, it was found that the average grain length of rice was 6.38 mm, the average width was 1.91 mm, the average height was 1.51 mm. The average grain volume determined on the basis of the grain weight and density was equal to 14.82 mm 3 , while the volume determined on the basis of grain size 18.44 mm 3 . The correction factor for given volumes V ρ and vs. assumed an average value of 0.82. The values of the grain dimension distribution can be a determinant in selection of structural features of the materials used, that is, performance parameters of roller mills: diameters of rollers and the size of the inter-roller gap; selection of the screen eye sieve The average values of strength properties of rice grains were determined, such as F min = 117.9 kg·m s −2 , F max = 174.99 kg·m·s −2 , σ min = 9.80 MPa, σ max = 14.71 MPa, C k = 1150.26 N·mm −1 , W Fmin = 7.26 mJ, W Fmax = 28.03 mJ, which coincided with the results of research carried out by other researchers. The determined ranges of forces, strength and compressive energy (work) are of applicable character and can be used in the design of machines dedicated to process rice. Knowing these values will allow, among others, the estimation of the power of devices, e.g., grinding machines, and roller mills, and in consequence, will minimize energy losses and energy demand for dedicated machines.
The analysis of the Spearman correlation showed that there are no statistically significant relationships between the volume V ρ of the grain and the tested strength properties, so there are no interdependencies between the variables. In the case of the grain size volume vs. a low negative correlation between strength σ min and low positive correlation between the force inducing the first crack (Table 2) were found. Dependence of grinding energy proportionality and the grain mass as well as clear, distinct dependencies between the grain thickness and the value of force and work (low negative correlation between thickness co a 3 and stresses σ min and work W Fmax , low positive correlation between thickness a 3 and force inducing the first crack F min ), that was proven for other biological grainy materials (wheat grains) could not be confirmed either. Based on these results, it was not possible to find significant dependencies between the grain cross-section A 0 and the values of compressive strength (only low negative correlations were found).
Based on the conducted tests, the crack was found to be different for each grain (Figure 9). The results, including the scatter of dimensions and volume, confirm the high variability and diversity of biological materials within one species. Diversification of the obtained values confirms that each grain is characterized by a different internal structure. Such a differentiation can indicate a poor quality of grain and weak cultivation conditions. An analysis of the test results of rice grain strength properties provides the basis for determining the impact of biomass properties on the grinding process and, in subsequent stages, for the development of procedures for monitoring the grinding process using energy-environmental grinding efficiency models, the original CO 2 emission index for the intelligent monitoring system of usable characteristics of the grinding process.
The results can be used by other researchers to create models of materials (rice grains) for computer simulations of cracking, crushing, mixing using the discrete element method DEM.
Supplementary Materials: The following are available online at http://www.mdpi.com/2071-1050/12/2/552/s1, Table S1: Results of correlation analysis between the size of grain and its strength properties

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.