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Bruise susceptibility and energy dissipation analysis in pears under impact loading conditions
Postharvest Biology and Technology 163 (2020) 111120
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Bruise susceptibility and energy dissipation analysis in pears under impact loading conditions
T
Zbigniew Stropek*, Krzysztof Gołacki Department of Mechanical Engineering and Automatic Control, University of Life Sciences in Lublin, Głęboka 28, 20-612 Lublin, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Internal damage energy Bruise susceptibility Pear Impact
The relationship between bruise susceptibility and internal damage energy with impact velocity has been investigated using two pear cultivars. Bruise susceptibility of both pear cultivars increased with the increasing impact velocity, stabilizing at the highest impact velocity of 3 cm3 J−1. Internal damage energy also increased with higher impact velocity. The internal damage energy was close to 0 for impact velocities at which pear bruising did not occur. The bruise depth and width measured 48 h after the impact, as well as the peak deformation and contact width directly during the impact were also determined. For the three largest velocities (11.5 m s−1) the bruise depth was 2.5 times larger than the peak deformation. For the same velocities the contact width was 1.4 times greater than the bruise width which can lead to erroneous estimation of critical stress from the bruise width. The impact results recorded by means of high speed camera were analyzed using Tema Motion software to obtain displacement and velocity in time. Additionally, the software allowed calculating the contact width of the pear with a flat rigid plate at any time of impact.
1. Introduction Bruising of fruit and vegetables as a result of impacts cause loss of quality and shelf life. Knee and Miller (2002) estimated that 6 % of apples in the New York markets were bruised, while Van Zeebroeck et al. (2003) found that between 8 and 15 % of apples were bruised during sorting. Pang et al. (1996) found that apple bruising can be as high as 50 %, although a losses are more typically 10–25 % (Van Zeebroeck et al., 2007b). Measurement techniques to determine the size and beginning of the bruise occurrence with precision are not available but would be useful. Experiments to measure impacts have employed various devices (Stropek and Gołacki, 2013, 2019b; Gancarz, 2018; Stopa et al., 2018) designed to obtain specific impact velocities and amounts of energy during impacts on individual fruit and vegetables. Two basic measuring methods are pendulum (Komarnicki et al., 2016; Stropek and Gołacki, 2018; Azadbakht et al., 2018; Rasli et al., 2019) and free fall devices (Ozbek et al., 2014; Gancarz, 2016; Hussein et al., 2019). Free fall devices do not control the site of impact on the fruit and the use of the guiding element leads to additional friction. Pendulum devices are more commonly used as they are free from these faults. The fruit impact into a rigid surface area is only about 5 ms and therefore the main problem is the displacement measurement. The common method used
⁎
for the displacement calculation is double integration of the acceleration-time course (Lichtensteiger et al., 1988; Jaren and Garcia-Pardo, 2002; Lu and Wang, 2007). However, this method has large errors leading to poor accuracy of the results (Fluck and Ahmed, 1973; Musiol and Harty, 1991; Van Zeebroeck et al., 2003; Abir et al., 2016). To avoid this, displacement has been measured more directly using the: photoelectric system (Finney and Massie, 1975), angular displacement transducer to measure position of the pendulum during the impact (Bajema et al., 1998), electro-optical displacement follower (Jarimopas et al., 1990) and incremental optical encoder (Van Zeebroeck et al., 2003). An additional problem in the direct deformation measurement is the need to eliminate the oscillations during the impact generated by a measuring device. However, it is not possible to completely eliminate vibrations during the impact (Bentini et al., 2005; Dintwa et al., 2008; Abedi and Ahmadi, 2013) in spite of their amplitude minimization by increasing the device elements stiffness. (Van Zeebroeck et al., 2003; Scheffler et al., 2018). The other solution is the use of the high speed camera which is not rigidly fixed to the research apparatus (Stropek and Gołacki, 2016b; Lewis et al., 2007; Horabik et al., 2017; Liang et al., 2018; Surdilovic et al., 2018) thereby eliminating the vibrations. Impact causes loading of dynamic character in the plant material. It can be developed by rapid deformation or applied force and is characterized by the propagation of a stress wave in the material (Stropek
Corresponding author. E-mail address: [email protected] (Z. Stropek).
https://doi.org/10.1016/j.postharvbio.2020.111120 Received 18 September 2019; Received in revised form 9 January 2020; Accepted 9 January 2020 0925-5214/ © 2020 Elsevier B.V. All rights reserved.
Postharvest Biology and Technology 163 (2020) 111120
Z. Stropek and K. Gołacki
replications in the site of the largest diameter were made at every 120°. The firmness measurements were read with the accuracy of 1 N.
and Gołacki, 2016a). The deformation velocity causing a stress wave is a material feature dependent on its density and stiffness (Bajema et al., 1998). The most dangerous phenomenon is damage of cell walls which results in the flow of cell saps and a physiological response of the material as the bruising development visible in tissue discoloration. Mechanical damage of cellular tissues is closely related to their microstructure. Most research assumes that fruit and vegetables behave as a continuum material regardless of cellular structure. However, the fruit flesh is composed of parenchyma cells, middle lamella and intercellular spaces. In addition, the cell walls are responsible for the mechanical strength of the whole cell structure. Therefore, the behaviour of fruit under loading depends on many microstructural features such as: cell size, thickness and stiffness of cell wall, cell orientation and turgor pressure. Alamar et al. (2008) compared the micromechanical behaviour of two apple cultivars stored under different conditions to study their mechanical properties at the micro and macro scales. Devaux et al. (2005) studied the proportion of intact cells and tissue fragments obtained after the mechanical breakdown of pericarp tissue to estimate cell adhesion and wall rigidity. Gancarz et al. (2014) determined the influence of direction and site of sampling on the size and shape of parenchyma tissue cells in potato tubers. Vanstreels et al. (2005) found that the cell area of onion tissue has an influence on the stiffness and strength of the samples. In this research the authors attempted to estimate the energy causing various material responses studying its reversible and irreversible nature at different impact velocities. This allowed to deduce the degree of internal damage of pear flesh depending on the impact velocity. The aim of the experiment was to determine the force-time and displacement-time courses and next to combine them so as to obtain the force-displacement courses. The use of two independent measuring systems to determine the force response and displacement courses is undoubtedly a novelty of this research. It allowed to determine impact and rebound energy based on the calculation of surface area below the force-displacement curve. Then the above mentioned quantities were compared with those obtained from the formulae for the energy conservation law. The determined energies were used to calculate the internal damage energy. The dependences of bruise volume, bruise susceptibility and time difference between the peak force and the peak displacement on impact velocity were also determined. The comparison between the bruise depth and bruise width measured after 48 h from the impact as well as the peak deformation, contact width recorded directly during the impact was also made.
2.3. Experimental device The measuring device had a pendulum structure including a pair of 1 m long fishing lines and a fastening element. The fastening element was composed of a plastic plate and two tangs which were stuck into a pear. During the experiment a fruit in the place of its maximum diameter impacted against a flat, vertical plate screwed into the force sensor. The force sensor was fastened to a sliding sleeve which through the clamp was permanently fixed to a concrete wall. The sliding sleeve with the force sensor was able to be moved towards the fixed clamp. This allowed the pear attached to the pendulum to be positioned in relation to the vertical surface of the plate in such a way that at the impact moment the fruit was in a vertical position. In this way the perpendicularity of the force direction to the impact surface was obtained. The pendulum device was also equipped with control screws which enabled positioning of the pendulum rotation axis so that the impact force direction passed both the fruit and sensor centres.Thus the central collision conditions were met. The drop height (impact velocity) was determined on the basis of the scale placed on a vertical board. The impact force was measured by means of the piezoelectric force sensor (Endevco, Sunnyvale, USA), model 2311-100 with a sensitivity of 23.2 mV N−1 and a measurement range of ± 220 N (Technical manual, 2013). The measuring stand is presented in Fig. 1.
2.4. Measuring apparatus Two measuring systems were applied in the research. The LMS SCADAS recorder (Siemens, Munich, Germany) together with the LMS Test.Xpress software was used to determine the force response during the impact. It was recorded with a frequency of 10.24 kHz. The measurement was triggered after exceeding 0.5 N. The pear displacement course was recorded by means of the Phanton Miro M320S high speed camera (Vision Research, Wayne, USA) with a constant focal length of 50 mm lens and the Phantom Camera Control (PCC-2) software at a resolution of 1024 × 768 pixels and velocity of 3413 frames per second. The value of the recording velocity resulted from the fact that the force response was fitted to the recording frequency in order to obtain a total multiple which made later determination of the forcedisplacement course easier. In this case, the frequency of force response recording was 3 times larger than that of displacement recording. The applied measurement method with the high-speed camera required due diligence in the preparation of the measuring path. Measurement errors during the image recording may be due to:
2. Materials and methods 2.1. Material 'Lukasówka' and 'Xenia' pear that were stored in a refrigerator at 4 °C for less than 2 weeks after the harvest were used. All tests were carried out on pears that had been kept at room temperature for 24 h. Fruit of 215−225 g and 70−75 mm diameter fruit were selected to minimize effect of weight and curvature radius on the bruise size. The fruit were impacted with the velocities 0.25, 0.5, 0.75, 1, 1.25, 1.5 m s−1. For each impact velocity 10 repetitions were made which resulted in 60 measurements for each cultivar. For the firmness measurements 15 pears were used from each cultivar. In total 150 pears were tested. 2.2. Firmness measurements Firmness was measured with a Magness-Taylor penetrometer (Model FT 327, Facchini srl company, Italy). The 8 mm diameter cylindrical plunger was manually inserted into pared flesh to the 8 mm depth at constant velocity. The measurements were made using 15 pears of each cultivar with the same weight and size as those in the impact tests. Due to the differences in the flesh firmness in one fruit, 3
Fig. 1. The measuring stand for impact tests. 2
Postharvest Biology and Technology 163 (2020) 111120
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calculate the impact energy and the rebound energy from the formulae for the kinetic energy:
- a deviation from perpendicularity of the camera optical axis towards the fruit motion plane, - inappropriate image focus of the observed object, - conversion of the pear image dimensions from pixels into the length expressed in millimeters (in this case the scale factor amounted to 0.138 mm/pixel). To minimize positioning errors, the camera was placed on a special head that allowed the rotation in three perpendicular planes with an accuracy of 1°. The large contrast of the pear image with the surrounding background was obtained by the object lighting with the LED panel. For further analysis an absolute error of pear mass center displacement of 0.138 mm was taken. To determine the pear displacement and velocity courses in time, the software Tema Motion Version 3.8 (Image Systems, Linköping, Sweden) was used, which allowed the fruit movement analysis to be made.
Eimp _ k =
mv12 2
(3)
Ereb _ k =
mv22 2
(4)
The most important for determining the fruit resistance to damage is determination of the internal damage energy. To calculate this energy, the elastic deformation energy Ereb_k and the viscous deformation energy during the impact and rebound (Ereb -Ereb_k) should be subtracted from the impact energy Eimp. Assuming that the viscous deformation energy during the impact and rebound is of a similar value, then the general formula for the internal damage energy Eid can be presented as follows: x max
Eid = 2.5. Making measurements and data processing
BS =
BV =
0
F2 (x ) dx −
mv22 ⎤ 2 ⎥ ⎦
(5)
BV Eimp _ k
(6)
πdD 2 6
(7)
where: d is the bruise depth (mm), D is the bruise width (mm). In formula (6) the impact energy was calculated from formula (3) for the kinetic energy. 2.8. Statistical analysis
(1)
Data were analyzed using Statistica 13 (Statsoft, Tulsa, Oklahoma). The statistical significance of differences between the average values of studied quantities was determined based on a one-way analysis (ANOVA). The LSD test at a significance level of 0.05 was applied.
(2)
3. Results and discussion
F1 (x ) dx
x max
∫
∫
where: BV is the bruise volume (mm3), Eimp_k is the impact energy (J). The bruise volume BV was calculated from the formula given by Chen and Sun (1981)
x max
Ereb =
x max
The bruise susceptibility was determined from the formula:
The determination of the force-displacement courses allowed to calculate the impact energy Eimp and the rebound energy Ereb from the following formulae:
0
mv22 ⎡ − 2⋅⎢ 2 ⎣
2.7. Bruise susceptibility
2.6. Energy calculation
∫
F1 (x ) dx −
0
Before each test each pear was weighed with an accuracy of 0.2 g and the maximum diameter was measured with an accuracy of 0.1 mm. The fruit was attached to the pendulum with two metal tangs. The control screws were used to place the pear in such a position that the impact axis passed the sensor axis. In this way the central collision conditions were met. After being dropped from a given height and its impact course recorded by the camera and the force sensor, the pear was left for 48 h at room temperature to discolour. After this time the pear was cut along the vertical plane going through the fruit centre where the bruise site. Next the bruise depth d and the bruise width D were measured by means of a calliper with an accuracy of 0.1 mm (Fig. 2).
Eimp =
∫
F2 (x ) dx
0
The impact energy is the area below the F1(x) curve for the displacement from 0 to xmax, the rebound energy is the area below the F2(x) curve for the displacement from 0 to xmax (Fig. 4). The velocity-time courses enabled determination of the impact velocity v1 and the rebound velocity v2, thereby it was possible to
3.1. Firmness The firmness of 'Xenia' pears (48.1 N) was higher than that of 'Lukasówka' (38.5 N) which provided different research material. The mean values of firmness between both cultivars differed in a statistically significant way. 3.2. Measurement results The tests allowed to determine the courses of force response, velocity and displacement in time, as shown in Fig. 3. Knowing the values of force response and displacement at the same time, it was possible to determine the relationship between the force response and the displacement. Fig. 4 presents the course of the force response depending on the displacement during the impact and the rebound of pear against a rigid, flat and vertical plate. 3.3. Energy dissipation analysis
Fig. 2. The firmness of ‘Lukasówka’ and ‘Xenia’ pear cultivars.
The experiment allowed to determine four types of energy: 3
Postharvest Biology and Technology 163 (2020) 111120
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Fig. 3. The typical force response-time, displacement-time and velocity-time curves during the impact of ‘Lukasówka’ pear at an impact velocity of 1 m s−1.
Fig. 5. The relationship between the impact energy and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
Fig. 4. The typical relationship between the force response and the displacement during the impact and rebound of ‘Lukasówka’ pear at an impact velocity of 1 m s−1.
with the increasing impact velocity. This situation occurred for both the energies calculated from the formulae for kinetic energy and those obtained from the force-displacement curves. The impact energy determined from the formulae for the kinetic energy was bigger than those obtained from the force-displacement curves for both pear cultivars and at each impact velocity (Fig. 5). In the range of velocities from 0.5 to 1.5 m s−1 the differences between the mean values of the impact velocity resulting from formulae (1) and (3) were statistically significant. A different result was found for the rebound energy (Fig. 6). In this case the mean values of the rebound energy from formulae (2) and (4) did not differ in a statistically significant way at each impact velocity for both tested cultivars This indicates that the energy dissipation occurs mainly in the first stage of the impact from its beginning until the peak displacement is obtained. However, similar values of the rebound energy obtained from formulae (2) and (4) show that mainly elastic deformations are observed during the rebound. The internal damage energy increased with the increasing impact velocity (Fig. 7). Previous research found that initiation of bruising was detected at impact velocities of 0.5 m s−1 and 0.75 m s−1 for 'Lukasówka' and 'Xenia' pears, respectively (Stropek and Gołacki, 2019a). These impact velocities corresponded to the internal damage energy values of 0.019 J and 0.023 J for 'Lukasówka' and 'Xenia' pears, respectively. When considering the impact process, it is important to take into account different phenomena causing energy dissipation not only in the bruising area but also throughout the fruit. Hence, many researchers suggested different ways of energy dissipation during an impact. Gao et al. (2018) studied the dynamic response of potatoes to impact loading and found that the kinetic energy converted into the internal
1 The impact energy Eimp is the energy absorbed by the fruit in the first stage of the impact from the beginning of the fruit contact with the plate until its stopping. This energy is dissipated in the fruit in the form of elastic deformations, cells damage energy (plastic deformations) and energy causing the gas and liquid flows in the intercellular spaces (viscous deformations) (form. 1). 2 The rebound energy Ereb causes the rebound of the fruit from the plate (elastic deformations) and the flow of gases and liquids in the intercellular spaces as the fruit is still subjected to stress during the rebound (form. 2). 3 The kinetic energy of the fruit Eimp_k includes all the components of the energy dissipated in the fruit in the form of elastic deformations, cells damage, liquid and gas flows in the intercellular spaces and multiple propagation of stress waves. Moreover, this energy contains energy components causing fruit and measuring stand vibrations which was the cause of errors in the measurement of different quantities during the impact in many papers presented in the literature (form. 3). 4 Kinetic energy Ereb_k is an energy of fully reversible elastic deformations (form. 4). Based on the defined types of energy there can be presented a formula which allows to estimate the energy dissipated in the fruit causing the internal damage (form. 5). The first component of formula 5 indicates the impact energy Eimp from which the elastic deformation energy Ereb_k (the second component) and the approximate value of the viscous deformations energy during the impact and rebound 2(Ereb -Ereb_k) (the third component) are subtracted. The research showed that the impact and rebound energy increased
Fig. 6. The relationship between the rebound energy and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err. 4
Postharvest Biology and Technology 163 (2020) 111120
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3.4. The difference in time between the force response and displacement peaks The peak force response was found to be before the peak displacement (Fig. 3). The dt values change was from 0.2 to 0.5 ms. The apples under the impact loading conditions showed force response and displacement peaks at different time values which amounted to (0.1-0.3) ms (Stropek and Gołacki, 2015). According to the other researchers of Persian lime (Fluck and Ahmed, 1973), apple and pear (Jaren and Garcia-Pardo, 2002), apple (Tijskens et al., 2003) and potato (Van Zeebroeck et al., 2003) the force response and displacement peaks were shifted relative to each other in time but they did not provide quantitative assessment which can result from stress propagation in the wave form. The wave speed of stress propagation in apple was 48 m s−1 (Bajema et al., 1998) being much higher than that causing specific deformations.
Fig. 7. The relationship between the internal damage energy and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
3.5. The impact parameters and bruise quantities energy during the impact. In turn, the internal energy was composed of strain, creep dissipation and viscous energies. The last two quantities accounted for a very small contribution to the internal energy. Therefore the strain energy could be treated as an indicator measuring the elastic deformations. According to Dintwa et al. (2008) the kinetic energy of colliding bodies was converted into three energy forms. The first was potential energy related to the material resistance to deformation. It showed itself as a static stress-strain state. The second was the vibration energy due to the stress wave propagation in the colliding bodies. The third was energy dissipation as a result of inelastic deformation related to the visco-elasto-plastic processes and fractures in the cellular tissue of plant material. A similar energy division was made by Bajema and Hyde (1998). The applied Constant Height Multiple Impact (CHMI) technique allowed distinguishing of elastic, viscous and plastic energies from the impact energy. Thus the viscous energy was related to vibrations and other irreversible viscous losses. In addition, the constant value of viscous losses was assumed for each drop from a given height. The plastic energy was determined based on the sum of the bruise energy for each impact until a specified rebound height was obtained. Van Zeebroeck et al. (2007a) made the bruise prediction models for tomatoes to relate the fruit properties to the bruise damage extent. As a result not whole absorbed energy was transformed into plastic deformation and it could be divided into viscous and plastic energies. They also made the hypothesis that higher absorbed energy corresponded to larger bruise damage at the same impact energy. They claimed that the hypothesis is true assuming that the proportion between the viscous and plastic energies is constant (Fig. 8).
Peak deformation and contact width during the pear impact into a flat, rigid surface were determined by means of the high speed camera and Tema Motion software which enabled comparison of the parameters characterizing the course of the impact (peak deformation, contact width) and its effects (bruise depth, bruise width). As follows from Figs. 9 and 10 the mean values of the above quantities increased with the increasing impact velocity. The 'Lukasówka' pear bruising started at the impact velocity 0.5 m s−1 and that of 'Xenia' at 0.75 m s−1 as evidenced by great values of the standard deviation of the bruise depth (Fig. 9) and the bruise width (Fig. 10). The impact velocities corresponding to the contact width values were 14 and 16 mm for 'Lukasówka' and 'Xenia', respectively. The average peak deformation was 42 % of the bruise depth for 'Lukasówka' and 39 % for 'Xenia' (Fig. 9). Thus the bruise depth was 2.5 times greater than the peak deformation at the highest velocities (1–1.5) m s−1. The average contact width was 146 % and 135 % of the bruise width for 'Lukasówka' and 'Xenia', respectively. Thus the contact width was 1.4 times greater than the bruise width at the three highest velocities (1–1.5) m s−1. This shows some errors in pear tissue stress determination resulting in overestimation and wrong conclusions. The mean values of the contact width were found to be greater than those of the bruise width which was also confirmed by other researchers. For example Yuwana and Duprat (1998) found the contact diameter over 6 % greater than its corresponding bruise diameter in all apples. Komarnicki et al. (2017) found a larger contact surface area than the real bruise surface at the drop heights from 20 to 150 mm applying the Tekscan measuring system. Stropek and Gołacki (2015) proved that the same impact velocities corresponded to larger values of contact diameter compared to the bruise diameter testing three apple cultivars. Studying the
Fig. 8. The dependence of difference in time dt between the force response and displacement peaks on the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
Fig. 9. The relationship between the peak deformation, the bruise depth and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err. 5
Postharvest Biology and Technology 163 (2020) 111120
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Fig. 12. The relationship between the bruise susceptibility and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
Fig. 10. The relationship between the bruise width, the contact width and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
susceptibility increase with the increasing drop height or impact velocity was also proved for pomegranate (Hussein et al., 2017, 2018), kiwifruit (Du et al., 2019), apple (Stropek and Gołacki, 2016b). However, the bruise susceptibility decrease with the increasing impact energy was found by Zhu et al. (2016). These differences may be accounted for by different research methodology and kind of measuring apparatus. In the latter case a fixed half of an apple was impacted by the pendulum device composed of an aluminum rod tipped wooden ball. In the former research the fruit impacted into a rigid surface. Then the effect of fruit mass and curvature on the bruise size leading to a different bruise susceptibility course was taken into account (Fig. 12).
'McIntosh' apples bruise Studman et al. (1997) found that the bruise area to be much smaller than the contact area during the apple-to-apple impact. The bruise area according to Lewis et al. (2008) should be much smaller than the contact area assuming that the apple flesh will be damaged enough to be discoloured.
3.6. The bruise susceptibility The relationship between the bruise volume and the impact velocity is shown in Fig. 11. The bruise susceptibility increases with the increasing impact velocity. It increased from 0 to the fixed value i.e. 2.8-3.3 cm3 J−1 for 'Lukasówka' and 2.9-3.4 cm3 J−1 for 'Xenia'. The bruise susceptibility was 0 at 0.25 m s−1 for both pear cultivars and 0.5 m s−1 for 'Xenia' due to the lack of bruising. At 0.5 m s−1 for 'Lukasówka' and 0.75 m s−1 for 'Xenia' the bruise susceptibility was calculated for the bruised and not bruised pears. It was close to 3 cm3 J−1 for both pear cultivars in the range 1-1.5 m s−1. However, then no significant differences were found for them at the same impact velocity. These results are confirmed by other mechanical studies. Thus during the impact test dropping from the heights of 10, 15 and 20 cm for the pears 'Williams' and 'Ankara' Yurtlu and Erdogan (2005) found that the bruise susceptibility increased with the increasing drop height. It was 3 cm3 J−1 at the largest drop height. Physical deformation and such properties as: modulus of elasticity, bioyield and tensile points were determined by Celik (2017) on the pears 'Ankara' by the compression tests under the quasi-static loading conditions. Thus the above parameters were used for simulation of pear drop onto different surfaces, at different fruit orientation from the height 0.25−1 m applying the finite element method (FEM) which showed stable bruise susceptibility values, 16 cm3 J−1. The bruise
4. Conclusions The research showed that the internal damage energy increased with the increase of the impact velocity. For the velocities, at which the pear bruise was not observed (0.5 m s−1 for 'Lukasówka' and 0.75 m s−1 for 'Xenia') the values of the internal damage energy were close to 0.02 J. The bruise susceptibility of both pear cultivars increased with the increasing impact velocity. At the highest impact velocities from 1 to 1.5 m s−1 the bruise susceptibility was close to 3 cm3 J−1 for both pear cultivars. Peak deformation and contact width were determined during the pears impact into a flat, rigid surface by means of the high speed camera and Tema Motion software and compared with the tissue bruising parameters (bruise depth and bruise width) 48 h after the impact. It turned out that the peak deformation was on the average 42 % of the bruise depth for 'Lukasówka' and 39 % for 'Xenia'. However, at the three highest velocities (1-1.5 m s−1) the bruise depth was 2.5 times greater than the peak deformation. The contact width was on the average 146 % of the bruise width for 'Lukasówka' and 135 % for 'Xenia'. At the three highest velocities (1-1.5 m s−1) the contact width was 1.4 times greater than the bruise width. These differences may lead to significant errors in the estimation of normal stress in fruit flesh and thus to wrong conclusions in bruise prediction.
CRediT authorship contribution statement Zbigniew Stropek: Conceptualization, Formal analysis, Investigation, Resources, Writing - original draft, Writing - review & editing, Methodology. Krzysztof Gołacki: Conceptualization, Methodology, Writing - review & editing.
Declaration of Competing Interest Fig. 11. The relationship between the bruise volume and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
There is no conflict of interest between the authors of the paper.
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Van Zeebroeck, M., Van linden, V., Ramon, H., De Baerdemaeker, J., Nicolai, B.M., Tijskens, E., 2007b. Impact damage of apples during transport and handling. Postharvest Biol. Technol. 45, 157–167. https://doi.org/10.1016/j.postharvbio. 2007.01.015. Yurtlu, Y.B., Erdogan, D., 2005. Effect of storage time on some mechanical properties and bruise susceptibility of pears and apples. Turk. J. Agric. For. 29 (6), 469–482. Yuwana, Y., Duprat, F., 1998. Prediction of apple bruising based on the instantaneous impact shear stress and energy absorbed. Int. Agrophys. 12, 133–140. Zhu, Q., Guan, J., Huang, M., Lu, R., Mendoza, F., 2016. Predicting bruise susceptibility of’ Golden Delicious’ apples using hyperspectral scattering technique. Postharvest Biol. Technol. 114, 86–94. https://doi.org/10.1016/j.postharvbio.2015.12.007.
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Instrumented pendulum for impact characterization of whole fruit and vegetable specimens. Trans. ASAE 41 (5), 1399–1405. https://doi. org/10.13031/2013.17274. Bajema, R.W., Hyde, G.M., Peterson, K., 1998. Instrumentation design for dynamic axial compression of cylindrical tissue samples. Trans. ASAE 41 (3), 747–754. https://doi. org/10.13031/2013.17203. Bentini, M., Caprara, C., Rondelli, V., 2005. Mechanical properties of sugar beet roots. Trans. ASAE 48, 1429–1439. https://doi.org/10.13031/2013.19168. Celik, H.K., 2017. Determination of bruise susceptibility of pears (Ankara variety) to impact load by means of FEM-based explicit dynamics simulation. Postharvest Biol. Technol. 128, 83–97. https://doi.org/10.1016/j.postharvbio.2017.01.015. Chen, P., Sun, Z., 1981. Impact parameters related to postharvest bruising of apples. ASAE Paper 81-3041. Devaux, M.F., Barakat, A., Robert, P., Bouchet, B., Guillon, F., Navez, B., Lahaye, M., 2005. Mechanical breakdown and cell wall strusture of mealy tomato pericarp tissue. Postharvest Biol. Technol. 37, 209–221. https://doi.org/10.1016/j.postharvbio. 2005.04.013. Dintwa, E., Van Zeebroeck, M., Ramon, H., Tijskens, E., 2008. Finite element method of the dynamic collision of apple fruit. Postharvest Biol. Technol. 49, 260–276. https:// doi.org/10.1016/j.postharvbio.2008.01.012. Du, D., Wang, B., Wang, J., Yao, F., Hong, X., 2019. Prediction of bruise susceptibility of harvested kiwifruit (Actinidia chinensis) using finite element method. Postharvest Biol. Technol. 152, 36–44. https://doi.org/10.1016/j.postharvbio.2019.02.013. Finney, E.E., Massie, D.R., 1975. Instrumentation for testing the response of fruits to mechanical impact. Trans. ASAE 18 (5), 1184–1187. https://doi.org/10.13031/ 2013.36766. 1192. Fluck, R.C., Ahmed, E.M., 1973. Impact testing of fruits and vegetables. Trans. ASAE 16 (4), 660–666. https://doi.org/10.13031/2013.37597. Gancarz, M., Konstankiewicz, K., Zgórska, K., 2014. Cell orientation in potato tuber parenchyma tissue. Int. Agrophys. 28, 15–22. https://doi.org/10.2478/intag-20130023. Gancarz, M., 2016. Correlation between cell size and blackspot of potato tuber parenchyma tissue after storage. Postharvest Biol. Technol. 117, 161–167. https://doi. org/10.1016/j.postharvbio.2016.03.004. Gancarz, M., 2018. At harvest prediction of the susceptibility of potato varieties to blackspot after impact over long-term storage. Postharvest Biol. Technol. 142, 93–98. https://doi.org/10.1016/j.postharvbio.2018.01.009. Gao, Y., Song, C., Rao, X., Ying, Y., 2018. Image processing-aided FEA for monitoring dynamic response of potato tubers to impact loading. Comput. Electron. Agric. 151, 21–30. https://doi.org/10.1016/j.compag.2018.05.027. Horabik, J., Beczek, M., Mazur, R., Parafiniuk, P., Ryżak, M., Molenda, M., 2017. Determination of the restitution coefficient of seeds and coefficient of visco-elastic Hertz contact models for DEM simulations. Biosyst. Eng. 161, 106–119. https://doi. org/10.1016/j.biosystemseng.2017.06.009. Hussein, Z., Fawole, O.A., Opara, U.L., 2017. Investing bruise susceptibility of pomegranate cultivars during postharvest handling. Afr. J. Rur. Devel. 2 (1), 33–39. Hussein, Z., Fawole, O.A., Opara, U.L., 2018. Bruise damage susceptibility of pomegranates (Punica granatum L.) and its impact on fruit physiological response. Acta Hortic. 1201, 55–64. https://doi.org/10.17660/ActaHortic.2018.1201.9. Hussein, Z., Fawole, O.A., Opara, U.L., 2019. Bruise damage susceptibility of pomegranates (Punica granatum L.) and impact on fruit physiological response during short term storage. Sci. Hortic. 246, 664–674. https://doi.org/10.1016/j.scienta. 2018.11.026. Jaren, C., Garcia-Pardo, E., 2002. Using non-destructive impact testing for sorting fruits. J. Food Eng. 53, 89–95. 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Bruise susceptibility and energy dissipation analysis in pears under impact loading conditions
T
Zbigniew Stropek*, Krzysztof Gołacki Department of Mechanical Engineering and Automatic Control, University of Life Sciences in Lublin, Głęboka 28, 20-612 Lublin, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Internal damage energy Bruise susceptibility Pear Impact
The relationship between bruise susceptibility and internal damage energy with impact velocity has been investigated using two pear cultivars. Bruise susceptibility of both pear cultivars increased with the increasing impact velocity, stabilizing at the highest impact velocity of 3 cm3 J−1. Internal damage energy also increased with higher impact velocity. The internal damage energy was close to 0 for impact velocities at which pear bruising did not occur. The bruise depth and width measured 48 h after the impact, as well as the peak deformation and contact width directly during the impact were also determined. For the three largest velocities (11.5 m s−1) the bruise depth was 2.5 times larger than the peak deformation. For the same velocities the contact width was 1.4 times greater than the bruise width which can lead to erroneous estimation of critical stress from the bruise width. The impact results recorded by means of high speed camera were analyzed using Tema Motion software to obtain displacement and velocity in time. Additionally, the software allowed calculating the contact width of the pear with a flat rigid plate at any time of impact.
1. Introduction Bruising of fruit and vegetables as a result of impacts cause loss of quality and shelf life. Knee and Miller (2002) estimated that 6 % of apples in the New York markets were bruised, while Van Zeebroeck et al. (2003) found that between 8 and 15 % of apples were bruised during sorting. Pang et al. (1996) found that apple bruising can be as high as 50 %, although a losses are more typically 10–25 % (Van Zeebroeck et al., 2007b). Measurement techniques to determine the size and beginning of the bruise occurrence with precision are not available but would be useful. Experiments to measure impacts have employed various devices (Stropek and Gołacki, 2013, 2019b; Gancarz, 2018; Stopa et al., 2018) designed to obtain specific impact velocities and amounts of energy during impacts on individual fruit and vegetables. Two basic measuring methods are pendulum (Komarnicki et al., 2016; Stropek and Gołacki, 2018; Azadbakht et al., 2018; Rasli et al., 2019) and free fall devices (Ozbek et al., 2014; Gancarz, 2016; Hussein et al., 2019). Free fall devices do not control the site of impact on the fruit and the use of the guiding element leads to additional friction. Pendulum devices are more commonly used as they are free from these faults. The fruit impact into a rigid surface area is only about 5 ms and therefore the main problem is the displacement measurement. The common method used
⁎
for the displacement calculation is double integration of the acceleration-time course (Lichtensteiger et al., 1988; Jaren and Garcia-Pardo, 2002; Lu and Wang, 2007). However, this method has large errors leading to poor accuracy of the results (Fluck and Ahmed, 1973; Musiol and Harty, 1991; Van Zeebroeck et al., 2003; Abir et al., 2016). To avoid this, displacement has been measured more directly using the: photoelectric system (Finney and Massie, 1975), angular displacement transducer to measure position of the pendulum during the impact (Bajema et al., 1998), electro-optical displacement follower (Jarimopas et al., 1990) and incremental optical encoder (Van Zeebroeck et al., 2003). An additional problem in the direct deformation measurement is the need to eliminate the oscillations during the impact generated by a measuring device. However, it is not possible to completely eliminate vibrations during the impact (Bentini et al., 2005; Dintwa et al., 2008; Abedi and Ahmadi, 2013) in spite of their amplitude minimization by increasing the device elements stiffness. (Van Zeebroeck et al., 2003; Scheffler et al., 2018). The other solution is the use of the high speed camera which is not rigidly fixed to the research apparatus (Stropek and Gołacki, 2016b; Lewis et al., 2007; Horabik et al., 2017; Liang et al., 2018; Surdilovic et al., 2018) thereby eliminating the vibrations. Impact causes loading of dynamic character in the plant material. It can be developed by rapid deformation or applied force and is characterized by the propagation of a stress wave in the material (Stropek
Corresponding author. E-mail address: [email protected] (Z. Stropek).
https://doi.org/10.1016/j.postharvbio.2020.111120 Received 18 September 2019; Received in revised form 9 January 2020; Accepted 9 January 2020 0925-5214/ © 2020 Elsevier B.V. All rights reserved.
Postharvest Biology and Technology 163 (2020) 111120
Z. Stropek and K. Gołacki
replications in the site of the largest diameter were made at every 120°. The firmness measurements were read with the accuracy of 1 N.
and Gołacki, 2016a). The deformation velocity causing a stress wave is a material feature dependent on its density and stiffness (Bajema et al., 1998). The most dangerous phenomenon is damage of cell walls which results in the flow of cell saps and a physiological response of the material as the bruising development visible in tissue discoloration. Mechanical damage of cellular tissues is closely related to their microstructure. Most research assumes that fruit and vegetables behave as a continuum material regardless of cellular structure. However, the fruit flesh is composed of parenchyma cells, middle lamella and intercellular spaces. In addition, the cell walls are responsible for the mechanical strength of the whole cell structure. Therefore, the behaviour of fruit under loading depends on many microstructural features such as: cell size, thickness and stiffness of cell wall, cell orientation and turgor pressure. Alamar et al. (2008) compared the micromechanical behaviour of two apple cultivars stored under different conditions to study their mechanical properties at the micro and macro scales. Devaux et al. (2005) studied the proportion of intact cells and tissue fragments obtained after the mechanical breakdown of pericarp tissue to estimate cell adhesion and wall rigidity. Gancarz et al. (2014) determined the influence of direction and site of sampling on the size and shape of parenchyma tissue cells in potato tubers. Vanstreels et al. (2005) found that the cell area of onion tissue has an influence on the stiffness and strength of the samples. In this research the authors attempted to estimate the energy causing various material responses studying its reversible and irreversible nature at different impact velocities. This allowed to deduce the degree of internal damage of pear flesh depending on the impact velocity. The aim of the experiment was to determine the force-time and displacement-time courses and next to combine them so as to obtain the force-displacement courses. The use of two independent measuring systems to determine the force response and displacement courses is undoubtedly a novelty of this research. It allowed to determine impact and rebound energy based on the calculation of surface area below the force-displacement curve. Then the above mentioned quantities were compared with those obtained from the formulae for the energy conservation law. The determined energies were used to calculate the internal damage energy. The dependences of bruise volume, bruise susceptibility and time difference between the peak force and the peak displacement on impact velocity were also determined. The comparison between the bruise depth and bruise width measured after 48 h from the impact as well as the peak deformation, contact width recorded directly during the impact was also made.
2.3. Experimental device The measuring device had a pendulum structure including a pair of 1 m long fishing lines and a fastening element. The fastening element was composed of a plastic plate and two tangs which were stuck into a pear. During the experiment a fruit in the place of its maximum diameter impacted against a flat, vertical plate screwed into the force sensor. The force sensor was fastened to a sliding sleeve which through the clamp was permanently fixed to a concrete wall. The sliding sleeve with the force sensor was able to be moved towards the fixed clamp. This allowed the pear attached to the pendulum to be positioned in relation to the vertical surface of the plate in such a way that at the impact moment the fruit was in a vertical position. In this way the perpendicularity of the force direction to the impact surface was obtained. The pendulum device was also equipped with control screws which enabled positioning of the pendulum rotation axis so that the impact force direction passed both the fruit and sensor centres.Thus the central collision conditions were met. The drop height (impact velocity) was determined on the basis of the scale placed on a vertical board. The impact force was measured by means of the piezoelectric force sensor (Endevco, Sunnyvale, USA), model 2311-100 with a sensitivity of 23.2 mV N−1 and a measurement range of ± 220 N (Technical manual, 2013). The measuring stand is presented in Fig. 1.
2.4. Measuring apparatus Two measuring systems were applied in the research. The LMS SCADAS recorder (Siemens, Munich, Germany) together with the LMS Test.Xpress software was used to determine the force response during the impact. It was recorded with a frequency of 10.24 kHz. The measurement was triggered after exceeding 0.5 N. The pear displacement course was recorded by means of the Phanton Miro M320S high speed camera (Vision Research, Wayne, USA) with a constant focal length of 50 mm lens and the Phantom Camera Control (PCC-2) software at a resolution of 1024 × 768 pixels and velocity of 3413 frames per second. The value of the recording velocity resulted from the fact that the force response was fitted to the recording frequency in order to obtain a total multiple which made later determination of the forcedisplacement course easier. In this case, the frequency of force response recording was 3 times larger than that of displacement recording. The applied measurement method with the high-speed camera required due diligence in the preparation of the measuring path. Measurement errors during the image recording may be due to:
2. Materials and methods 2.1. Material 'Lukasówka' and 'Xenia' pear that were stored in a refrigerator at 4 °C for less than 2 weeks after the harvest were used. All tests were carried out on pears that had been kept at room temperature for 24 h. Fruit of 215−225 g and 70−75 mm diameter fruit were selected to minimize effect of weight and curvature radius on the bruise size. The fruit were impacted with the velocities 0.25, 0.5, 0.75, 1, 1.25, 1.5 m s−1. For each impact velocity 10 repetitions were made which resulted in 60 measurements for each cultivar. For the firmness measurements 15 pears were used from each cultivar. In total 150 pears were tested. 2.2. Firmness measurements Firmness was measured with a Magness-Taylor penetrometer (Model FT 327, Facchini srl company, Italy). The 8 mm diameter cylindrical plunger was manually inserted into pared flesh to the 8 mm depth at constant velocity. The measurements were made using 15 pears of each cultivar with the same weight and size as those in the impact tests. Due to the differences in the flesh firmness in one fruit, 3
Fig. 1. The measuring stand for impact tests. 2
Postharvest Biology and Technology 163 (2020) 111120
Z. Stropek and K. Gołacki
calculate the impact energy and the rebound energy from the formulae for the kinetic energy:
- a deviation from perpendicularity of the camera optical axis towards the fruit motion plane, - inappropriate image focus of the observed object, - conversion of the pear image dimensions from pixels into the length expressed in millimeters (in this case the scale factor amounted to 0.138 mm/pixel). To minimize positioning errors, the camera was placed on a special head that allowed the rotation in three perpendicular planes with an accuracy of 1°. The large contrast of the pear image with the surrounding background was obtained by the object lighting with the LED panel. For further analysis an absolute error of pear mass center displacement of 0.138 mm was taken. To determine the pear displacement and velocity courses in time, the software Tema Motion Version 3.8 (Image Systems, Linköping, Sweden) was used, which allowed the fruit movement analysis to be made.
Eimp _ k =
mv12 2
(3)
Ereb _ k =
mv22 2
(4)
The most important for determining the fruit resistance to damage is determination of the internal damage energy. To calculate this energy, the elastic deformation energy Ereb_k and the viscous deformation energy during the impact and rebound (Ereb -Ereb_k) should be subtracted from the impact energy Eimp. Assuming that the viscous deformation energy during the impact and rebound is of a similar value, then the general formula for the internal damage energy Eid can be presented as follows: x max
Eid = 2.5. Making measurements and data processing
BS =
BV =
0
F2 (x ) dx −
mv22 ⎤ 2 ⎥ ⎦
(5)
BV Eimp _ k
(6)
πdD 2 6
(7)
where: d is the bruise depth (mm), D is the bruise width (mm). In formula (6) the impact energy was calculated from formula (3) for the kinetic energy. 2.8. Statistical analysis
(1)
Data were analyzed using Statistica 13 (Statsoft, Tulsa, Oklahoma). The statistical significance of differences between the average values of studied quantities was determined based on a one-way analysis (ANOVA). The LSD test at a significance level of 0.05 was applied.
(2)
3. Results and discussion
F1 (x ) dx
x max
∫
∫
where: BV is the bruise volume (mm3), Eimp_k is the impact energy (J). The bruise volume BV was calculated from the formula given by Chen and Sun (1981)
x max
Ereb =
x max
The bruise susceptibility was determined from the formula:
The determination of the force-displacement courses allowed to calculate the impact energy Eimp and the rebound energy Ereb from the following formulae:
0
mv22 ⎡ − 2⋅⎢ 2 ⎣
2.7. Bruise susceptibility
2.6. Energy calculation
∫
F1 (x ) dx −
0
Before each test each pear was weighed with an accuracy of 0.2 g and the maximum diameter was measured with an accuracy of 0.1 mm. The fruit was attached to the pendulum with two metal tangs. The control screws were used to place the pear in such a position that the impact axis passed the sensor axis. In this way the central collision conditions were met. After being dropped from a given height and its impact course recorded by the camera and the force sensor, the pear was left for 48 h at room temperature to discolour. After this time the pear was cut along the vertical plane going through the fruit centre where the bruise site. Next the bruise depth d and the bruise width D were measured by means of a calliper with an accuracy of 0.1 mm (Fig. 2).
Eimp =
∫
F2 (x ) dx
0
The impact energy is the area below the F1(x) curve for the displacement from 0 to xmax, the rebound energy is the area below the F2(x) curve for the displacement from 0 to xmax (Fig. 4). The velocity-time courses enabled determination of the impact velocity v1 and the rebound velocity v2, thereby it was possible to
3.1. Firmness The firmness of 'Xenia' pears (48.1 N) was higher than that of 'Lukasówka' (38.5 N) which provided different research material. The mean values of firmness between both cultivars differed in a statistically significant way. 3.2. Measurement results The tests allowed to determine the courses of force response, velocity and displacement in time, as shown in Fig. 3. Knowing the values of force response and displacement at the same time, it was possible to determine the relationship between the force response and the displacement. Fig. 4 presents the course of the force response depending on the displacement during the impact and the rebound of pear against a rigid, flat and vertical plate. 3.3. Energy dissipation analysis
Fig. 2. The firmness of ‘Lukasówka’ and ‘Xenia’ pear cultivars.
The experiment allowed to determine four types of energy: 3
Postharvest Biology and Technology 163 (2020) 111120
Z. Stropek and K. Gołacki
Fig. 3. The typical force response-time, displacement-time and velocity-time curves during the impact of ‘Lukasówka’ pear at an impact velocity of 1 m s−1.
Fig. 5. The relationship between the impact energy and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
Fig. 4. The typical relationship between the force response and the displacement during the impact and rebound of ‘Lukasówka’ pear at an impact velocity of 1 m s−1.
with the increasing impact velocity. This situation occurred for both the energies calculated from the formulae for kinetic energy and those obtained from the force-displacement curves. The impact energy determined from the formulae for the kinetic energy was bigger than those obtained from the force-displacement curves for both pear cultivars and at each impact velocity (Fig. 5). In the range of velocities from 0.5 to 1.5 m s−1 the differences between the mean values of the impact velocity resulting from formulae (1) and (3) were statistically significant. A different result was found for the rebound energy (Fig. 6). In this case the mean values of the rebound energy from formulae (2) and (4) did not differ in a statistically significant way at each impact velocity for both tested cultivars This indicates that the energy dissipation occurs mainly in the first stage of the impact from its beginning until the peak displacement is obtained. However, similar values of the rebound energy obtained from formulae (2) and (4) show that mainly elastic deformations are observed during the rebound. The internal damage energy increased with the increasing impact velocity (Fig. 7). Previous research found that initiation of bruising was detected at impact velocities of 0.5 m s−1 and 0.75 m s−1 for 'Lukasówka' and 'Xenia' pears, respectively (Stropek and Gołacki, 2019a). These impact velocities corresponded to the internal damage energy values of 0.019 J and 0.023 J for 'Lukasówka' and 'Xenia' pears, respectively. When considering the impact process, it is important to take into account different phenomena causing energy dissipation not only in the bruising area but also throughout the fruit. Hence, many researchers suggested different ways of energy dissipation during an impact. Gao et al. (2018) studied the dynamic response of potatoes to impact loading and found that the kinetic energy converted into the internal
1 The impact energy Eimp is the energy absorbed by the fruit in the first stage of the impact from the beginning of the fruit contact with the plate until its stopping. This energy is dissipated in the fruit in the form of elastic deformations, cells damage energy (plastic deformations) and energy causing the gas and liquid flows in the intercellular spaces (viscous deformations) (form. 1). 2 The rebound energy Ereb causes the rebound of the fruit from the plate (elastic deformations) and the flow of gases and liquids in the intercellular spaces as the fruit is still subjected to stress during the rebound (form. 2). 3 The kinetic energy of the fruit Eimp_k includes all the components of the energy dissipated in the fruit in the form of elastic deformations, cells damage, liquid and gas flows in the intercellular spaces and multiple propagation of stress waves. Moreover, this energy contains energy components causing fruit and measuring stand vibrations which was the cause of errors in the measurement of different quantities during the impact in many papers presented in the literature (form. 3). 4 Kinetic energy Ereb_k is an energy of fully reversible elastic deformations (form. 4). Based on the defined types of energy there can be presented a formula which allows to estimate the energy dissipated in the fruit causing the internal damage (form. 5). The first component of formula 5 indicates the impact energy Eimp from which the elastic deformation energy Ereb_k (the second component) and the approximate value of the viscous deformations energy during the impact and rebound 2(Ereb -Ereb_k) (the third component) are subtracted. The research showed that the impact and rebound energy increased
Fig. 6. The relationship between the rebound energy and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err. 4
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3.4. The difference in time between the force response and displacement peaks The peak force response was found to be before the peak displacement (Fig. 3). The dt values change was from 0.2 to 0.5 ms. The apples under the impact loading conditions showed force response and displacement peaks at different time values which amounted to (0.1-0.3) ms (Stropek and Gołacki, 2015). According to the other researchers of Persian lime (Fluck and Ahmed, 1973), apple and pear (Jaren and Garcia-Pardo, 2002), apple (Tijskens et al., 2003) and potato (Van Zeebroeck et al., 2003) the force response and displacement peaks were shifted relative to each other in time but they did not provide quantitative assessment which can result from stress propagation in the wave form. The wave speed of stress propagation in apple was 48 m s−1 (Bajema et al., 1998) being much higher than that causing specific deformations.
Fig. 7. The relationship between the internal damage energy and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
3.5. The impact parameters and bruise quantities energy during the impact. In turn, the internal energy was composed of strain, creep dissipation and viscous energies. The last two quantities accounted for a very small contribution to the internal energy. Therefore the strain energy could be treated as an indicator measuring the elastic deformations. According to Dintwa et al. (2008) the kinetic energy of colliding bodies was converted into three energy forms. The first was potential energy related to the material resistance to deformation. It showed itself as a static stress-strain state. The second was the vibration energy due to the stress wave propagation in the colliding bodies. The third was energy dissipation as a result of inelastic deformation related to the visco-elasto-plastic processes and fractures in the cellular tissue of plant material. A similar energy division was made by Bajema and Hyde (1998). The applied Constant Height Multiple Impact (CHMI) technique allowed distinguishing of elastic, viscous and plastic energies from the impact energy. Thus the viscous energy was related to vibrations and other irreversible viscous losses. In addition, the constant value of viscous losses was assumed for each drop from a given height. The plastic energy was determined based on the sum of the bruise energy for each impact until a specified rebound height was obtained. Van Zeebroeck et al. (2007a) made the bruise prediction models for tomatoes to relate the fruit properties to the bruise damage extent. As a result not whole absorbed energy was transformed into plastic deformation and it could be divided into viscous and plastic energies. They also made the hypothesis that higher absorbed energy corresponded to larger bruise damage at the same impact energy. They claimed that the hypothesis is true assuming that the proportion between the viscous and plastic energies is constant (Fig. 8).
Peak deformation and contact width during the pear impact into a flat, rigid surface were determined by means of the high speed camera and Tema Motion software which enabled comparison of the parameters characterizing the course of the impact (peak deformation, contact width) and its effects (bruise depth, bruise width). As follows from Figs. 9 and 10 the mean values of the above quantities increased with the increasing impact velocity. The 'Lukasówka' pear bruising started at the impact velocity 0.5 m s−1 and that of 'Xenia' at 0.75 m s−1 as evidenced by great values of the standard deviation of the bruise depth (Fig. 9) and the bruise width (Fig. 10). The impact velocities corresponding to the contact width values were 14 and 16 mm for 'Lukasówka' and 'Xenia', respectively. The average peak deformation was 42 % of the bruise depth for 'Lukasówka' and 39 % for 'Xenia' (Fig. 9). Thus the bruise depth was 2.5 times greater than the peak deformation at the highest velocities (1–1.5) m s−1. The average contact width was 146 % and 135 % of the bruise width for 'Lukasówka' and 'Xenia', respectively. Thus the contact width was 1.4 times greater than the bruise width at the three highest velocities (1–1.5) m s−1. This shows some errors in pear tissue stress determination resulting in overestimation and wrong conclusions. The mean values of the contact width were found to be greater than those of the bruise width which was also confirmed by other researchers. For example Yuwana and Duprat (1998) found the contact diameter over 6 % greater than its corresponding bruise diameter in all apples. Komarnicki et al. (2017) found a larger contact surface area than the real bruise surface at the drop heights from 20 to 150 mm applying the Tekscan measuring system. Stropek and Gołacki (2015) proved that the same impact velocities corresponded to larger values of contact diameter compared to the bruise diameter testing three apple cultivars. Studying the
Fig. 8. The dependence of difference in time dt between the force response and displacement peaks on the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
Fig. 9. The relationship between the peak deformation, the bruise depth and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err. 5
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Fig. 12. The relationship between the bruise susceptibility and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
Fig. 10. The relationship between the bruise width, the contact width and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
susceptibility increase with the increasing drop height or impact velocity was also proved for pomegranate (Hussein et al., 2017, 2018), kiwifruit (Du et al., 2019), apple (Stropek and Gołacki, 2016b). However, the bruise susceptibility decrease with the increasing impact energy was found by Zhu et al. (2016). These differences may be accounted for by different research methodology and kind of measuring apparatus. In the latter case a fixed half of an apple was impacted by the pendulum device composed of an aluminum rod tipped wooden ball. In the former research the fruit impacted into a rigid surface. Then the effect of fruit mass and curvature on the bruise size leading to a different bruise susceptibility course was taken into account (Fig. 12).
'McIntosh' apples bruise Studman et al. (1997) found that the bruise area to be much smaller than the contact area during the apple-to-apple impact. The bruise area according to Lewis et al. (2008) should be much smaller than the contact area assuming that the apple flesh will be damaged enough to be discoloured.
3.6. The bruise susceptibility The relationship between the bruise volume and the impact velocity is shown in Fig. 11. The bruise susceptibility increases with the increasing impact velocity. It increased from 0 to the fixed value i.e. 2.8-3.3 cm3 J−1 for 'Lukasówka' and 2.9-3.4 cm3 J−1 for 'Xenia'. The bruise susceptibility was 0 at 0.25 m s−1 for both pear cultivars and 0.5 m s−1 for 'Xenia' due to the lack of bruising. At 0.5 m s−1 for 'Lukasówka' and 0.75 m s−1 for 'Xenia' the bruise susceptibility was calculated for the bruised and not bruised pears. It was close to 3 cm3 J−1 for both pear cultivars in the range 1-1.5 m s−1. However, then no significant differences were found for them at the same impact velocity. These results are confirmed by other mechanical studies. Thus during the impact test dropping from the heights of 10, 15 and 20 cm for the pears 'Williams' and 'Ankara' Yurtlu and Erdogan (2005) found that the bruise susceptibility increased with the increasing drop height. It was 3 cm3 J−1 at the largest drop height. Physical deformation and such properties as: modulus of elasticity, bioyield and tensile points were determined by Celik (2017) on the pears 'Ankara' by the compression tests under the quasi-static loading conditions. Thus the above parameters were used for simulation of pear drop onto different surfaces, at different fruit orientation from the height 0.25−1 m applying the finite element method (FEM) which showed stable bruise susceptibility values, 16 cm3 J−1. The bruise
4. Conclusions The research showed that the internal damage energy increased with the increase of the impact velocity. For the velocities, at which the pear bruise was not observed (0.5 m s−1 for 'Lukasówka' and 0.75 m s−1 for 'Xenia') the values of the internal damage energy were close to 0.02 J. The bruise susceptibility of both pear cultivars increased with the increasing impact velocity. At the highest impact velocities from 1 to 1.5 m s−1 the bruise susceptibility was close to 3 cm3 J−1 for both pear cultivars. Peak deformation and contact width were determined during the pears impact into a flat, rigid surface by means of the high speed camera and Tema Motion software and compared with the tissue bruising parameters (bruise depth and bruise width) 48 h after the impact. It turned out that the peak deformation was on the average 42 % of the bruise depth for 'Lukasówka' and 39 % for 'Xenia'. However, at the three highest velocities (1-1.5 m s−1) the bruise depth was 2.5 times greater than the peak deformation. The contact width was on the average 146 % of the bruise width for 'Lukasówka' and 135 % for 'Xenia'. At the three highest velocities (1-1.5 m s−1) the contact width was 1.4 times greater than the bruise width. These differences may lead to significant errors in the estimation of normal stress in fruit flesh and thus to wrong conclusions in bruise prediction.
CRediT authorship contribution statement Zbigniew Stropek: Conceptualization, Formal analysis, Investigation, Resources, Writing - original draft, Writing - review & editing, Methodology. Krzysztof Gołacki: Conceptualization, Methodology, Writing - review & editing.
Declaration of Competing Interest Fig. 11. The relationship between the bruise volume and the impact velocity for ‘Lukasówka’ and ‘Xenia’ pear cultivars. I - ± Std. dev., □ - ± Std. err.
There is no conflict of interest between the authors of the paper.
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