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Measuring ring tensile stress and strain of surimi gels using a novel ring tensile test with image analysis
Accepted Manuscript Measuring ring tensile stress and strain of surimi gels using a novel ring tensile test with image analysis Hyeon Woo Park, Won Byong Yoon PII: DOI: Reference:
S0260-8774(15)00188-0 http://dx.doi.org/10.1016/j.jfoodeng.2015.04.021 JFOE 8146
To appear in:
Journal of Food Engineering
Received Date: Revised Date: Accepted Date:
6 February 2015 27 March 2015 16 April 2015
Please cite this article as: Park, H.W., Yoon, W.B., Measuring ring tensile stress and strain of surimi gels using a novel ring tensile test with image analysis, Journal of Food Engineering (2015), doi: http://dx.doi.org/10.1016/ j.jfoodeng.2015.04.021
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Measuring ring tensile stress and strain of surimi gels using a novel ring tensile test with image analysis Hyeon Woo Park, Won Byong Yoon*
Department of Food Science and Biotechnology, College of Agricultural and Life Science, Kangwon National University, Chuncheon, Gangwon, 200-701, Republic of Korea
*Corresponding authors: Won Byong Yoon Department of Food Science and Biotechnology, College of Agricultural and Life Science, Kangwon National University, Chuncheon, Gangwon, 200-701, Republic of Korea E-mail: [email protected] Tel.: 82-33-250-6459 Fax: 82-33-241-0508
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Abstract A ring tensile test with image analysis to measure failure properties, such as failure ring tensile stress ( ) and strain ( ), of surimi (Itoyori A grade) gels with varying moisture content (76 to 80 %) was developed using Laplace’s law. The novel approach was validated for different inside diameters and thicknesses. Digital image correlation (DIC) was used to identify the validity of Laplace's law. For normalization, Laplace's law was applied to eliminate the dependence of the width and inside diameter. The values of
by thickness,
including the zero point, was accurately described using linear regression analysis (r2 > 0.99). This shows that
can estimate the reference
regardless of thickness. The values of
of the ring specimen were best fit with a linear function to moisture content (r2 > 0.94). The results of
for differing moisture content and thickness showed no significant differences
(p < 0.05).
Key word: surimi, ring tensile test, Laplace’s law, true stress-strain, image analysis
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1. Introduction Surimi is a refined and stabilized fish myofibrillar protein (Park and Lin, 2005) and is a major ingredient for surimi seafood, including steamed or fried fish cakes, fish sausage, and crab sticks (Park, 2013). The elastic and/or viscoelastic properties of fish myofibrillar protein gels are considered as the most important parameter in determining the textural properties of surimi seafood (Park, 2000). Several mechanical tests are used to characterize the textural properties of surimi seafood. Although the failure tensile properties of surimi gels are highly related to sensory results (r2 = 0.82) and consumer preference (Hamann and McDonald 1992), compressive and/or the punch test have been widely used in the surimi and surimi seafood related industries and research institutes due to the simplicity of the measuring process (Hamann et al., 2006; Lee and Chung, 1989; Shi et al., 2014; Tabilo-Munizaga and BarbosaCánovas, 2004). For elastomers, the compression method fundamentally generates the same information as the tensile test does. However, because the magnitude of the displacement or the strain in the compressive test is limited by the height of specimen, the compression test does not fully support the force or stress data at the high value of displacement or strain, especially as the strain becomes close to unity. Indeed, the maximum strain during compressive testing cannot be higher than 1. For many food gels, the strain values exceeds unity. Torsion test using a Hamann Torsion Gelometer (Gel Consultant, Raleigh, NC, USA) has been recognized as an excellent method for providing failure tensile properties of surimi gels by twisting their unique dumbbell shapes (Park, 2013). However, the preparation of the dumbbell (or hourglass) shape of the samples is time consuming, and the variation of the diameter at the center of the specimen highly influences the resulting measurements (Park, 2013). 3
The ring tensile test is widely used in the metal and tissue industries to measure tensile properties (Bae et al., 2006; Berglund et al., 2004; Konig et al., 2009; Laterreur et al., 2014; Nieponice et al., 2008; Wang et al., 2012; Yoshitake et al., 2004). The ring tensile test method is conducted by inserting a ring specimen into the outside of two pins. However, the stress concentration and slip at the holding parts are observed in many food materials. The ring shape of the specimen may minimize such stress concentrations and slip during the tensile measurement. Applications of the ring tensile test in measuring the failure tensile properties with Laplace's law have been discussed in many studies (Berglund et al., 2004; Konig et al., 2009; Laterreur et al., 2014; Nieponice et al., 2008). However, there has been no report on the use of the ring tensile test to measure the failure tensile properties of food. Application of the ring tensile test may be useful for measuring the failure tensile properties of surimi gels, because it is easy to prepare the ring shape of a specimen by perforation of a board shape of surimi gel. Because the surimi gel is highly flexible, changes in the shape of the specimen during measurement could cause an error during stretching the specimen. Therefore, changes in shape during measurement must be accurately monitored, and the data related to changes in shape have to be used to calculate mechanical properties such as true strain. Image analysis can continuously measure the changes in the shape of specimen without contacting the specimen (Du and Sun, 2005; Huang et al., 2014; Lee and Yoon, 2015; Shei and Lin, 2012; Yu et al., 2014). Additionally, the adaptability of this technique can be demonstrated by digital image correlation (DIC) to quantify the local displacement and strains. The objectives of this study were to 1) develop novel equipment to measure the tensile properties of surimi gels, 2) normalize the ring tensile test for dimensions, such as width,
4
diameter, and thickness of ring specimens, and 3) develop mathematical models to estimate the tensile properties of surimi gels using Laplace's law and regression models.
2. Materials and methods 2.1. Surimi gel preparation According to Yoon et al. (1997), the surimi paste and gel were prepared. Frozen Itoyori (threadfin bream) surimi (A grade) was kindly provided by Pulmuone Co. (Seoul, S. Korea) and partially thawed at room temperature for 1 h before being cut into approximately 3 cm cubes. Surimi cubes were chopped for 10 sec using a mixer (HMF-260S, Hanil electric, Seoul, Korea). Chopping continued for 10 sec with addition of sodium chloride (2 g/100 surimi paste) to extract myofibrillar proteins. Moisture content was adjusted to 76, 78 and 80 % (w/w) using ice water (0 °C) before chopping for another 30 sec. During chopping, cold temperature (< 5 °C) was maintained continuously using ice packs. The paste was stuffed into stainless steel cylinders (diameter, 50 mm; length, 45 mm). The cylinders were heated in a water bath at 90 °C for 30 min. Cooked gels were chilled quickly in ice water (0 °C). The gels were kept refrigerated (5 °C) overnight.
2.2. Preparation of rings and conduction of ring tensile tests The cylinder gels were cut to be disk shaped (diameter, 50 mm; length, 10 mm). The ring shaped specimens were prepared by perforation of gels using a ring cutter (Fig. 1). The ring specimen dimensions had a width = 10 mm, inside diameter = 31 mm and varying thickness = 3, 6 and 9 mm. Cold gels (5 °C) were placed at room temperature for 1 h before the 5
perforation. The ring tensile measurement system was developed as shown in Fig. 2. Top pin of equipment moved upward at constant speed (2 mm/sec) to increase the distance from bottom pin of equipment until the sample failed. The pin displacement and the load required for rupture were measured by a CT3 texture analyzer (Brookfield Inc., Middleboro, USA) with a 50 kg load cell. The diameter of the pins was 19 mm. As shown in Fig. 3, the origin of the displacement of the pins (Δs = 0) was defined as the position where the pins come into contact. By combining the diameter and the displacement of the pins (Δs), it is possible to evaluate the instantaneous inside circumference and instantaneous inside diameter using eq. (1) and (2),
where
is the instantaneous inside circumference of the ring specimen during ring tensile
testing,
is the instantaneous inside diameter of the ring sample during ring tensile testing,
is the diameter of the pins and Δs is the distance between the pins (Fig. 3). All experiments were conducted 5 times.
2.3. Image analysis 2.3.1. Measurement of instantaneous widths of ring specimens To estimate instantaneous widths of ring specimens, an image processing technique was used. The image processing steps for this study were (1) image acquisition, (2) image segmentation, and (3) image analysis. A digital single-lens reflex camera (DSLR-500D, 6
Canon Inc., Tokyo, Japan) with a lens (EF-S 18–55 mmf/3.5–5.6, Canon Inc., Tokyo, Japan) was located horizontally over the sample at a distance of 13.5 cm. The camera recorded the front view of the ring specimen at frame rates of up to 20 fps and with a resolution of 2.07 million pixels during the tensile test. All images were saved in JPEG format from selected frames of the video. The image processing tool in MATLAB (Mathworks® Inc., Natick, MA, USA) was used for analysis of the instantaneous deformation of the ring specimen. Threshold-based segmentation was a particularly effective technique for scenes containing solid objects placed on a contrasting background. After image segmentation, the Canny edge operator in MATLAB was used for edge detection, the shape of the object was extracted with white color in a black background and then lines of the pictures less than reference value (200 pixel) were cropped (Fig. 4). The average width of ring specimens during ring tensile testing was calculated using Eq. (3)
where,
is the instantaneous width of the ring specimen,
the ring specimen obtained by the number of pixels in the image and
is the front view area of is the front view
height of ring specimen (Fig. 4e).
2.3.2. Digital image correlation (DIC) Digital image correlation (DIC) is a versatile, non-contact optical technique that came into popularity during the 1980s (Peters and Ranson, 1982; Sutton et al., 1983), and is used as a reliable tool in experimental mechanics to obtain whole field displacement and strain fields. 7
It is based on image comparisons of the specimens coated with a random speckle pattern. Speckle patterns are nothing but random black dots sprayed over the specimen. The speckle pattern of the undeformed specimen (reference image) is compared with the images of the deformed specimen. Using pattern matching principles, displacements are then computed. The presented results were obtained by manual spraying of black ink (Pelikan 4001, Pelikan Inc., Schindellegi, Switzerland). Since it was not practical to compare each pixel in the image, a small area containing multiple pixels (subsets) were relatively traced. The pattern matching was based on obtaining a maximum correlation between subsets of the image in the undeformed and deformed states. The recorded successive frames were also used for analysis by two dimensional DIC using MATLAB. The DIC code in this work was obtained from an open source code by Jones (2013). A detailed description of the methods applied to assess the local strain can be found in Jones et al. (2014).
2.4. Calculation of mechanical properties The inside diameter dramatically changed while surimi gels undergo large strains during the ring tensile test. The inside diameter at failure is significantly different from the initial unloaded inside diameter. To calculate mechanical properties such as
, changes in the
dimensions of the surimi ring throughout the tensile test must be considered. According to Laterreur et al. (2014), the failure stress of tissue-engineered vascular substitutes estimated based on the unloaded diameter was significantly different from those measured from the experiment, while the failure stress estimated based on the failure diameter showed no significant difference from the experimental values. This clearly demonstrated that a better estimation of the failure ring tensile stress is obtained when the failure diameter is used with 8
Laplace׳s law. It should be emphasized here that the theory of true stress-strain accounted for instantaneous changes in inside diameter during tensile testing and can be applied to estimate the correct
using the ring tensile test.
Ring tensile stress was calculated using Laplace's law and true stress, which is given by Eq. (4). It states that the internal stress across a curved membrane in a state of tension is equal to the tension in the specimen divided by its radius of curvature (Woods, 1892). It relates the wall circumferential stress to the internal pressure and the geometry of the ring specimen. Moreover, in the case of the ring tensile test method, the circumferential stress may be calculated as stated by Eq. (5), and links the load recorded to the instantaneous perpendicular area on which the load is applied. The estimated pressure may then be defined with Eq. (6), which is a combination of Eqs. (4) and (5).
where T is the wall tension by unit width, thickness of the ring specimen,
is the wall circumferential stress,
is the internal stress,
is the instantaneous inside
diameter, F is the load measured during ring tensile testing and
is the instantaneous
width of the ring specimen. Ring tensile stress testing of the surimi gels used Eq. (6).
9
is the
During ring tensile testing, the ring specimen was deformed in the circumferential direction. Based on the true strain defined according to Dieter (1986), ring tensile strain was evaluated using Eq. (7).
where ε is the strain,
is the instantaneous inside circumference, and
is the initial
inside circumference.
3. Results and Discussion 3.1. Evaluation of ring tensile stress and strain The local strain of surimi specimens during tensile testing was estimated by DIC analysis (Fig. 5). DIC analysis of surimi specimens was conducted until failure at 78 % moisture content and with a thickness of 6 mm. Surimi specimens showed similar values for local strain for the entire region. For failure regions, no strain concentration was observed until near failure, and no necking phenomena was observed before failure. Generally, during the tensile test, stress-strain curves for ductile materials such as steel and aluminum were nonlinear with the onset of necking, which can be used to estimate true stress using the crosssectional area of the neck (Considère, 1885; Hart 1967; Nikhare et al., 2011). But, for highly elastic materials, during the tensile test, the stress-strain curve shows a linear form without the onset of necking, which means that there is no difference in local strain. Typical ring tensile stress-strain curves applied Laplace’s law for the surimi gels at different moisture content and had a linear form, as shown in Fig. 6. It should be noted here that our observation 10
demonstrates that surimi gels showed a prototypical tendency of elastic rather than ductile materials. Thus, it would be possible to estimate the tensile stress from the results of a ring tensile test by applying Laplace’s law (Berglund et al., 2004; Konig et al., 2009; Laterreur et al., 2014; Mauri et al., 2013; Nieponice et al., 2008). The validity of Laplace's law to estimate
of surimi gels from the results of a ring
tensile test was examined. The inside diameter dependence of the ring tensile test was evaluated by measuring failure stress,
, which was measured for a constant thickness (3
mm) and moisture content (80 %) at varied initial inside diameters (Fig. 7). Failure stress was calculated by the following equation:
where
is failure stress,
and
are the initial width and thickness of ring specimen,
respectively. Although a significant difference in failure stress was observed, there was no significant difference in failure ring tensile stress at different initial inside diameters (p < 0.05). It should be noted here that, based on such an independency of failure stress, Laplace’s law was suitable for estimating the failure ring tensile stress of surimi gels. This implies that the failure ring tensile stress and strain can be estimated for different initial inside diameters of the ring specimen for surimi gels. 3.2. Failure ring tensile stress and strain estimation Failure properties, such as
and
, by thickness of ring specimen for varying
moisture content are shown in Fig. 8. Linear equations to estimate
, including zero point,
by thickness of the ring specimen for differing moisture content were developed using a 11
linear regression analysis with high r2 values (Fig. 8a). As moisture content increased, the slop of the regression equation decreased, because the protein concentration which mainly contribute to develop crosslinks for surimi gels is relatively decreased as increase of moisture content. Generally less protein contents showed a strong correlation with hardness of surimi gels (Park, 2005; Treloar, 1975; Yoon et al., 1997; Yoon et al., 2004a; Yoon et al., 2004b). Our study clearly demonstrated that
of surimi corresponded to theoretical result of the
internal pressure in a pressurized cylinder, which is that the internal pressure in a pressurized cylinder is proportional to thickness of the cylinder (Gere, 2006), in contrast to the results of compressive force testing of surimi by sample size, which was that the compressive force is not proportional to sample size including zero point (Lee and Chung, 1989). It should be noted here that our estimations of
were possible regardless of specimen thickness when
using the following equations:
where
is the dimensionless thickness ratio,
thickness of the ring specimen, and
is the reference thickness,
is the reference
. As shown in Fig. 8b,
is the by
thickness of ring specimen did not show any significant differences (p < 0.05). Generally, the initial cross-sectional area of the tensile specimen does not influence failure tensile strain during tensile testing (Callister, 2007). Our results showed a general pattern in varying thickness of the ring specimen.
12
for
Failure properties, such as
and
, were analyzed by moisture content for varying
thicknesses of ring specimens (Fig. 9). The results of
were best fit with a linear function
to moisture content (Fig. 9a). It has been reported that the failure shear stress or textural properties related to the hardness of surimi gels show a linear function with moisture content (Park, 2005; Yoon et al., 1997). As moisture content increased, the concentration of protein in the gel decreased, also decreasing the probability of forming 3 dimensional networks from the myofibrillar protein. This moisture content dependence of surimi gels can be explained by the classic rubber elastic theory (Treloar, 1975; Yoon et al., 2004a; Yoon et al., 2004b). In addition, the slope and intercept of regression equations are in agreement with a general pattern of size dependence of force–distance relation. The slope and intercept increased with increasing thickness of samples (Gere, 2006; Lee and Chung, 1989). The results of
based
on the moisture content for varying thickness of ring specimens are shown in Fig. 9b. No significant differences were observed between groups (p < 0.05). Breaking deformation or textural properties related to the deformation, such as failure shear strain or failure strain, of surimi gels commonly refers to as an indicator of protein quality (Park, 2005). In general, such deformation ability was not affected within a certain range of moisture content (Park, 2005; Yoon et al., 1997).
4. Conclusion The tensile properties of Itoyori surimi gels by moisture content (76, 78 and 80 %) were measured for varying inside diameters (31, 37 and 43 mm) and thicknesses (3, 6, 9 mm) of ring specimens. A possible experimental error associated with changes in the width of specimen during measurement was identified by applying image analysis. The validity of 13
Laplace's law to estimate the failure ring tensile properties of surimi gels was identified using DIC analysis. Laplace' law was successfully applied to normalize ring tensile testing by removing the dependence of width and inside diameter for tensile properties of ring shaped surimi gels. In addition,
by thickness of the ring shaped surimi gel, including at zero
point, was accurately described using linear regression analysis (r2 > 0.99). This suggests that could be estimated regardless of thickness using the dimensionless thickness ratio. Our novel approach including the ring tensile test, image analysis and mathematical models, was successfully applied to estimate the tensile properties of ring shaped surimi gels regardless of width, inside diameter and thickness. This novel approach may greatly support previously established measurements such as compressive, punch and torsion test to understand the textural properties of surimi gels.
Acknowledgement This research was financially supported of "Cooperative Research Program for Agriculture Science & Technology Development (Project No. PJ009227, C1009365-0103) "Rural Development Administration, Republic of Korea.
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with
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Fig. 1. Preparation of rings: (a) Ring cutter. (b) Disk shaped surimi gel. (c) Ring specimen for ring tensile test. Fig. 2. The ring tensile measurement system: (a) side view of schematic of the imaging acquisition system for ring tensile test, (b) front view of the ring tensile test. Fig. 3. Illustration of the geometry of the pins, distance between the pins and initial length of the ring specimen. Fig. 4. The overall procedure for image analysis: (a) original image, (b) segmented image, (c) edge detected image (d) extracted shape of the object, (e) cropped image, (f) successive image for image analysis during tensile test. Fig. 5. Contour plots of strain components for surimi specimen untill failure at 78% moisture content and 6mm thickness. Fig. 6. The ring tensile stress-strain curve applied Laplace’s law for the surimi gels at different moisture content and 9mm thickness. Fig. 7. Mechanical properties of surimi ring specimen at different inside diameter: (a) (failure stress) vs. inside diameter, (b)
(failure ring tensile stress) vs. inside diameter.
Fig. 8. Failure properties by thickness of ring specimen: (a)
(failure ring tensile stress), (b)
(failure ring tensile strain). Fig. 9. Failure properties at different at different moisture content: (a) stress), (b)
(failure ring tensile strain). 20
(failure ring tensile
Fig. 1. Preparation of rings: (a) Ring cutter. (b) Disk shaped surimi gel. (c) Ring specimen for ring tensile test.
21
Fig. 2. The ring tensile measurement system: (a) side view of schematic of the imaging acquisition system for ring tensile test, (b) front view of the ring tensile test.
22
Fig. 3. Illustration of the geometry of the pins, distance between the pins and initial length of the ring specimen.
23
Fig. 4. The overall procedure for image analysis: (a) original image, (b) segmented image, (c) edge detected image (d) extracted shape of the object, (e) cropped image, (f) successive image for image analysis during tensile test.
24
Fig. 5. Contour plots of strain components for surimi specimen untill failure at 78% moisture content and 6mm thickness.
25
Fig. 6. The ring tensile stress-strain curve applied Laplace’s law for the surimi gels at different moisture content and 9mm thickness.
26
Fig. 7. Mechanical properties of surimi ring specimen at different inside diameter: (a) (failure stress) vs. inside diameter, (b)
(failure ring tensile stress) vs. inside diameter. 27
Fig. 8. Failure properties by thickness of ring specimen: (a) (failure ring tensile strain).
28
(failure ring tensile stress), (b)
Fig. 9. Failure properties at different at different moisture content: (a) stress), (b)
(failure ring tensile strain).
29
(failure ring tensile
Nomenclature front view area of the ring specimen obtained by the number of pixels in the image (pixel)
initial width of ring specimen (mm)
instantaneous inside circumference of the ring instantaneous width of the ring specimen (mm) specimen during ring tensile testing (mm) initial inside circumference (mm) instantaneous inside diameter of the ring Greek symbols sample (mm) diameter of the pins (mm) failure ring tensile strain front view height of ring specimen (pixel) internal stress (Pa) dimensionless thickness ratio failure ring tensile stress (Pa) wall circumferential stress (Pa) reference failure ring tensile stress (Pa) The distance between the pins failure stress (Pa) wall tension by unit width (Pa mm) thickness of the ring specimen (mm) Subscripts reference thickness (mm) DIC digital image correlation initial thickness of ring specimen (mm)
Highlights ▶ The concept of true stress-strain was applied to estimate tensile properties. ▶ Laplace’s law was applied to remove the dependence of the width and inside diameter. ▶ Digital image correlation (DIC) was used to identify the validity of Laplace's law. ▶ The dimensionless thickness ratio was developed to estimate ring tensile stress.
30
S0260-8774(15)00188-0 http://dx.doi.org/10.1016/j.jfoodeng.2015.04.021 JFOE 8146
To appear in:
Journal of Food Engineering
Received Date: Revised Date: Accepted Date:
6 February 2015 27 March 2015 16 April 2015
Please cite this article as: Park, H.W., Yoon, W.B., Measuring ring tensile stress and strain of surimi gels using a novel ring tensile test with image analysis, Journal of Food Engineering (2015), doi: http://dx.doi.org/10.1016/ j.jfoodeng.2015.04.021
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Measuring ring tensile stress and strain of surimi gels using a novel ring tensile test with image analysis Hyeon Woo Park, Won Byong Yoon*
Department of Food Science and Biotechnology, College of Agricultural and Life Science, Kangwon National University, Chuncheon, Gangwon, 200-701, Republic of Korea
*Corresponding authors: Won Byong Yoon Department of Food Science and Biotechnology, College of Agricultural and Life Science, Kangwon National University, Chuncheon, Gangwon, 200-701, Republic of Korea E-mail: [email protected] Tel.: 82-33-250-6459 Fax: 82-33-241-0508
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Abstract A ring tensile test with image analysis to measure failure properties, such as failure ring tensile stress ( ) and strain ( ), of surimi (Itoyori A grade) gels with varying moisture content (76 to 80 %) was developed using Laplace’s law. The novel approach was validated for different inside diameters and thicknesses. Digital image correlation (DIC) was used to identify the validity of Laplace's law. For normalization, Laplace's law was applied to eliminate the dependence of the width and inside diameter. The values of
by thickness,
including the zero point, was accurately described using linear regression analysis (r2 > 0.99). This shows that
can estimate the reference
regardless of thickness. The values of
of the ring specimen were best fit with a linear function to moisture content (r2 > 0.94). The results of
for differing moisture content and thickness showed no significant differences
(p < 0.05).
Key word: surimi, ring tensile test, Laplace’s law, true stress-strain, image analysis
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1. Introduction Surimi is a refined and stabilized fish myofibrillar protein (Park and Lin, 2005) and is a major ingredient for surimi seafood, including steamed or fried fish cakes, fish sausage, and crab sticks (Park, 2013). The elastic and/or viscoelastic properties of fish myofibrillar protein gels are considered as the most important parameter in determining the textural properties of surimi seafood (Park, 2000). Several mechanical tests are used to characterize the textural properties of surimi seafood. Although the failure tensile properties of surimi gels are highly related to sensory results (r2 = 0.82) and consumer preference (Hamann and McDonald 1992), compressive and/or the punch test have been widely used in the surimi and surimi seafood related industries and research institutes due to the simplicity of the measuring process (Hamann et al., 2006; Lee and Chung, 1989; Shi et al., 2014; Tabilo-Munizaga and BarbosaCánovas, 2004). For elastomers, the compression method fundamentally generates the same information as the tensile test does. However, because the magnitude of the displacement or the strain in the compressive test is limited by the height of specimen, the compression test does not fully support the force or stress data at the high value of displacement or strain, especially as the strain becomes close to unity. Indeed, the maximum strain during compressive testing cannot be higher than 1. For many food gels, the strain values exceeds unity. Torsion test using a Hamann Torsion Gelometer (Gel Consultant, Raleigh, NC, USA) has been recognized as an excellent method for providing failure tensile properties of surimi gels by twisting their unique dumbbell shapes (Park, 2013). However, the preparation of the dumbbell (or hourglass) shape of the samples is time consuming, and the variation of the diameter at the center of the specimen highly influences the resulting measurements (Park, 2013). 3
The ring tensile test is widely used in the metal and tissue industries to measure tensile properties (Bae et al., 2006; Berglund et al., 2004; Konig et al., 2009; Laterreur et al., 2014; Nieponice et al., 2008; Wang et al., 2012; Yoshitake et al., 2004). The ring tensile test method is conducted by inserting a ring specimen into the outside of two pins. However, the stress concentration and slip at the holding parts are observed in many food materials. The ring shape of the specimen may minimize such stress concentrations and slip during the tensile measurement. Applications of the ring tensile test in measuring the failure tensile properties with Laplace's law have been discussed in many studies (Berglund et al., 2004; Konig et al., 2009; Laterreur et al., 2014; Nieponice et al., 2008). However, there has been no report on the use of the ring tensile test to measure the failure tensile properties of food. Application of the ring tensile test may be useful for measuring the failure tensile properties of surimi gels, because it is easy to prepare the ring shape of a specimen by perforation of a board shape of surimi gel. Because the surimi gel is highly flexible, changes in the shape of the specimen during measurement could cause an error during stretching the specimen. Therefore, changes in shape during measurement must be accurately monitored, and the data related to changes in shape have to be used to calculate mechanical properties such as true strain. Image analysis can continuously measure the changes in the shape of specimen without contacting the specimen (Du and Sun, 2005; Huang et al., 2014; Lee and Yoon, 2015; Shei and Lin, 2012; Yu et al., 2014). Additionally, the adaptability of this technique can be demonstrated by digital image correlation (DIC) to quantify the local displacement and strains. The objectives of this study were to 1) develop novel equipment to measure the tensile properties of surimi gels, 2) normalize the ring tensile test for dimensions, such as width,
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diameter, and thickness of ring specimens, and 3) develop mathematical models to estimate the tensile properties of surimi gels using Laplace's law and regression models.
2. Materials and methods 2.1. Surimi gel preparation According to Yoon et al. (1997), the surimi paste and gel were prepared. Frozen Itoyori (threadfin bream) surimi (A grade) was kindly provided by Pulmuone Co. (Seoul, S. Korea) and partially thawed at room temperature for 1 h before being cut into approximately 3 cm cubes. Surimi cubes were chopped for 10 sec using a mixer (HMF-260S, Hanil electric, Seoul, Korea). Chopping continued for 10 sec with addition of sodium chloride (2 g/100 surimi paste) to extract myofibrillar proteins. Moisture content was adjusted to 76, 78 and 80 % (w/w) using ice water (0 °C) before chopping for another 30 sec. During chopping, cold temperature (< 5 °C) was maintained continuously using ice packs. The paste was stuffed into stainless steel cylinders (diameter, 50 mm; length, 45 mm). The cylinders were heated in a water bath at 90 °C for 30 min. Cooked gels were chilled quickly in ice water (0 °C). The gels were kept refrigerated (5 °C) overnight.
2.2. Preparation of rings and conduction of ring tensile tests The cylinder gels were cut to be disk shaped (diameter, 50 mm; length, 10 mm). The ring shaped specimens were prepared by perforation of gels using a ring cutter (Fig. 1). The ring specimen dimensions had a width = 10 mm, inside diameter = 31 mm and varying thickness = 3, 6 and 9 mm. Cold gels (5 °C) were placed at room temperature for 1 h before the 5
perforation. The ring tensile measurement system was developed as shown in Fig. 2. Top pin of equipment moved upward at constant speed (2 mm/sec) to increase the distance from bottom pin of equipment until the sample failed. The pin displacement and the load required for rupture were measured by a CT3 texture analyzer (Brookfield Inc., Middleboro, USA) with a 50 kg load cell. The diameter of the pins was 19 mm. As shown in Fig. 3, the origin of the displacement of the pins (Δs = 0) was defined as the position where the pins come into contact. By combining the diameter and the displacement of the pins (Δs), it is possible to evaluate the instantaneous inside circumference and instantaneous inside diameter using eq. (1) and (2),
where
is the instantaneous inside circumference of the ring specimen during ring tensile
testing,
is the instantaneous inside diameter of the ring sample during ring tensile testing,
is the diameter of the pins and Δs is the distance between the pins (Fig. 3). All experiments were conducted 5 times.
2.3. Image analysis 2.3.1. Measurement of instantaneous widths of ring specimens To estimate instantaneous widths of ring specimens, an image processing technique was used. The image processing steps for this study were (1) image acquisition, (2) image segmentation, and (3) image analysis. A digital single-lens reflex camera (DSLR-500D, 6
Canon Inc., Tokyo, Japan) with a lens (EF-S 18–55 mmf/3.5–5.6, Canon Inc., Tokyo, Japan) was located horizontally over the sample at a distance of 13.5 cm. The camera recorded the front view of the ring specimen at frame rates of up to 20 fps and with a resolution of 2.07 million pixels during the tensile test. All images were saved in JPEG format from selected frames of the video. The image processing tool in MATLAB (Mathworks® Inc., Natick, MA, USA) was used for analysis of the instantaneous deformation of the ring specimen. Threshold-based segmentation was a particularly effective technique for scenes containing solid objects placed on a contrasting background. After image segmentation, the Canny edge operator in MATLAB was used for edge detection, the shape of the object was extracted with white color in a black background and then lines of the pictures less than reference value (200 pixel) were cropped (Fig. 4). The average width of ring specimens during ring tensile testing was calculated using Eq. (3)
where,
is the instantaneous width of the ring specimen,
the ring specimen obtained by the number of pixels in the image and
is the front view area of is the front view
height of ring specimen (Fig. 4e).
2.3.2. Digital image correlation (DIC) Digital image correlation (DIC) is a versatile, non-contact optical technique that came into popularity during the 1980s (Peters and Ranson, 1982; Sutton et al., 1983), and is used as a reliable tool in experimental mechanics to obtain whole field displacement and strain fields. 7
It is based on image comparisons of the specimens coated with a random speckle pattern. Speckle patterns are nothing but random black dots sprayed over the specimen. The speckle pattern of the undeformed specimen (reference image) is compared with the images of the deformed specimen. Using pattern matching principles, displacements are then computed. The presented results were obtained by manual spraying of black ink (Pelikan 4001, Pelikan Inc., Schindellegi, Switzerland). Since it was not practical to compare each pixel in the image, a small area containing multiple pixels (subsets) were relatively traced. The pattern matching was based on obtaining a maximum correlation between subsets of the image in the undeformed and deformed states. The recorded successive frames were also used for analysis by two dimensional DIC using MATLAB. The DIC code in this work was obtained from an open source code by Jones (2013). A detailed description of the methods applied to assess the local strain can be found in Jones et al. (2014).
2.4. Calculation of mechanical properties The inside diameter dramatically changed while surimi gels undergo large strains during the ring tensile test. The inside diameter at failure is significantly different from the initial unloaded inside diameter. To calculate mechanical properties such as
, changes in the
dimensions of the surimi ring throughout the tensile test must be considered. According to Laterreur et al. (2014), the failure stress of tissue-engineered vascular substitutes estimated based on the unloaded diameter was significantly different from those measured from the experiment, while the failure stress estimated based on the failure diameter showed no significant difference from the experimental values. This clearly demonstrated that a better estimation of the failure ring tensile stress is obtained when the failure diameter is used with 8
Laplace׳s law. It should be emphasized here that the theory of true stress-strain accounted for instantaneous changes in inside diameter during tensile testing and can be applied to estimate the correct
using the ring tensile test.
Ring tensile stress was calculated using Laplace's law and true stress, which is given by Eq. (4). It states that the internal stress across a curved membrane in a state of tension is equal to the tension in the specimen divided by its radius of curvature (Woods, 1892). It relates the wall circumferential stress to the internal pressure and the geometry of the ring specimen. Moreover, in the case of the ring tensile test method, the circumferential stress may be calculated as stated by Eq. (5), and links the load recorded to the instantaneous perpendicular area on which the load is applied. The estimated pressure may then be defined with Eq. (6), which is a combination of Eqs. (4) and (5).
where T is the wall tension by unit width, thickness of the ring specimen,
is the wall circumferential stress,
is the internal stress,
is the instantaneous inside
diameter, F is the load measured during ring tensile testing and
is the instantaneous
width of the ring specimen. Ring tensile stress testing of the surimi gels used Eq. (6).
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is the
During ring tensile testing, the ring specimen was deformed in the circumferential direction. Based on the true strain defined according to Dieter (1986), ring tensile strain was evaluated using Eq. (7).
where ε is the strain,
is the instantaneous inside circumference, and
is the initial
inside circumference.
3. Results and Discussion 3.1. Evaluation of ring tensile stress and strain The local strain of surimi specimens during tensile testing was estimated by DIC analysis (Fig. 5). DIC analysis of surimi specimens was conducted until failure at 78 % moisture content and with a thickness of 6 mm. Surimi specimens showed similar values for local strain for the entire region. For failure regions, no strain concentration was observed until near failure, and no necking phenomena was observed before failure. Generally, during the tensile test, stress-strain curves for ductile materials such as steel and aluminum were nonlinear with the onset of necking, which can be used to estimate true stress using the crosssectional area of the neck (Considère, 1885; Hart 1967; Nikhare et al., 2011). But, for highly elastic materials, during the tensile test, the stress-strain curve shows a linear form without the onset of necking, which means that there is no difference in local strain. Typical ring tensile stress-strain curves applied Laplace’s law for the surimi gels at different moisture content and had a linear form, as shown in Fig. 6. It should be noted here that our observation 10
demonstrates that surimi gels showed a prototypical tendency of elastic rather than ductile materials. Thus, it would be possible to estimate the tensile stress from the results of a ring tensile test by applying Laplace’s law (Berglund et al., 2004; Konig et al., 2009; Laterreur et al., 2014; Mauri et al., 2013; Nieponice et al., 2008). The validity of Laplace's law to estimate
of surimi gels from the results of a ring
tensile test was examined. The inside diameter dependence of the ring tensile test was evaluated by measuring failure stress,
, which was measured for a constant thickness (3
mm) and moisture content (80 %) at varied initial inside diameters (Fig. 7). Failure stress was calculated by the following equation:
where
is failure stress,
and
are the initial width and thickness of ring specimen,
respectively. Although a significant difference in failure stress was observed, there was no significant difference in failure ring tensile stress at different initial inside diameters (p < 0.05). It should be noted here that, based on such an independency of failure stress, Laplace’s law was suitable for estimating the failure ring tensile stress of surimi gels. This implies that the failure ring tensile stress and strain can be estimated for different initial inside diameters of the ring specimen for surimi gels. 3.2. Failure ring tensile stress and strain estimation Failure properties, such as
and
, by thickness of ring specimen for varying
moisture content are shown in Fig. 8. Linear equations to estimate
, including zero point,
by thickness of the ring specimen for differing moisture content were developed using a 11
linear regression analysis with high r2 values (Fig. 8a). As moisture content increased, the slop of the regression equation decreased, because the protein concentration which mainly contribute to develop crosslinks for surimi gels is relatively decreased as increase of moisture content. Generally less protein contents showed a strong correlation with hardness of surimi gels (Park, 2005; Treloar, 1975; Yoon et al., 1997; Yoon et al., 2004a; Yoon et al., 2004b). Our study clearly demonstrated that
of surimi corresponded to theoretical result of the
internal pressure in a pressurized cylinder, which is that the internal pressure in a pressurized cylinder is proportional to thickness of the cylinder (Gere, 2006), in contrast to the results of compressive force testing of surimi by sample size, which was that the compressive force is not proportional to sample size including zero point (Lee and Chung, 1989). It should be noted here that our estimations of
were possible regardless of specimen thickness when
using the following equations:
where
is the dimensionless thickness ratio,
thickness of the ring specimen, and
is the reference thickness,
is the reference
. As shown in Fig. 8b,
is the by
thickness of ring specimen did not show any significant differences (p < 0.05). Generally, the initial cross-sectional area of the tensile specimen does not influence failure tensile strain during tensile testing (Callister, 2007). Our results showed a general pattern in varying thickness of the ring specimen.
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for
Failure properties, such as
and
, were analyzed by moisture content for varying
thicknesses of ring specimens (Fig. 9). The results of
were best fit with a linear function
to moisture content (Fig. 9a). It has been reported that the failure shear stress or textural properties related to the hardness of surimi gels show a linear function with moisture content (Park, 2005; Yoon et al., 1997). As moisture content increased, the concentration of protein in the gel decreased, also decreasing the probability of forming 3 dimensional networks from the myofibrillar protein. This moisture content dependence of surimi gels can be explained by the classic rubber elastic theory (Treloar, 1975; Yoon et al., 2004a; Yoon et al., 2004b). In addition, the slope and intercept of regression equations are in agreement with a general pattern of size dependence of force–distance relation. The slope and intercept increased with increasing thickness of samples (Gere, 2006; Lee and Chung, 1989). The results of
based
on the moisture content for varying thickness of ring specimens are shown in Fig. 9b. No significant differences were observed between groups (p < 0.05). Breaking deformation or textural properties related to the deformation, such as failure shear strain or failure strain, of surimi gels commonly refers to as an indicator of protein quality (Park, 2005). In general, such deformation ability was not affected within a certain range of moisture content (Park, 2005; Yoon et al., 1997).
4. Conclusion The tensile properties of Itoyori surimi gels by moisture content (76, 78 and 80 %) were measured for varying inside diameters (31, 37 and 43 mm) and thicknesses (3, 6, 9 mm) of ring specimens. A possible experimental error associated with changes in the width of specimen during measurement was identified by applying image analysis. The validity of 13
Laplace's law to estimate the failure ring tensile properties of surimi gels was identified using DIC analysis. Laplace' law was successfully applied to normalize ring tensile testing by removing the dependence of width and inside diameter for tensile properties of ring shaped surimi gels. In addition,
by thickness of the ring shaped surimi gel, including at zero
point, was accurately described using linear regression analysis (r2 > 0.99). This suggests that could be estimated regardless of thickness using the dimensionless thickness ratio. Our novel approach including the ring tensile test, image analysis and mathematical models, was successfully applied to estimate the tensile properties of ring shaped surimi gels regardless of width, inside diameter and thickness. This novel approach may greatly support previously established measurements such as compressive, punch and torsion test to understand the textural properties of surimi gels.
Acknowledgement This research was financially supported of "Cooperative Research Program for Agriculture Science & Technology Development (Project No. PJ009227, C1009365-0103) "Rural Development Administration, Republic of Korea.
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with
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Fig. 1. Preparation of rings: (a) Ring cutter. (b) Disk shaped surimi gel. (c) Ring specimen for ring tensile test. Fig. 2. The ring tensile measurement system: (a) side view of schematic of the imaging acquisition system for ring tensile test, (b) front view of the ring tensile test. Fig. 3. Illustration of the geometry of the pins, distance between the pins and initial length of the ring specimen. Fig. 4. The overall procedure for image analysis: (a) original image, (b) segmented image, (c) edge detected image (d) extracted shape of the object, (e) cropped image, (f) successive image for image analysis during tensile test. Fig. 5. Contour plots of strain components for surimi specimen untill failure at 78% moisture content and 6mm thickness. Fig. 6. The ring tensile stress-strain curve applied Laplace’s law for the surimi gels at different moisture content and 9mm thickness. Fig. 7. Mechanical properties of surimi ring specimen at different inside diameter: (a) (failure stress) vs. inside diameter, (b)
(failure ring tensile stress) vs. inside diameter.
Fig. 8. Failure properties by thickness of ring specimen: (a)
(failure ring tensile stress), (b)
(failure ring tensile strain). Fig. 9. Failure properties at different at different moisture content: (a) stress), (b)
(failure ring tensile strain). 20
(failure ring tensile
Fig. 1. Preparation of rings: (a) Ring cutter. (b) Disk shaped surimi gel. (c) Ring specimen for ring tensile test.
21
Fig. 2. The ring tensile measurement system: (a) side view of schematic of the imaging acquisition system for ring tensile test, (b) front view of the ring tensile test.
22
Fig. 3. Illustration of the geometry of the pins, distance between the pins and initial length of the ring specimen.
23
Fig. 4. The overall procedure for image analysis: (a) original image, (b) segmented image, (c) edge detected image (d) extracted shape of the object, (e) cropped image, (f) successive image for image analysis during tensile test.
24
Fig. 5. Contour plots of strain components for surimi specimen untill failure at 78% moisture content and 6mm thickness.
25
Fig. 6. The ring tensile stress-strain curve applied Laplace’s law for the surimi gels at different moisture content and 9mm thickness.
26
Fig. 7. Mechanical properties of surimi ring specimen at different inside diameter: (a) (failure stress) vs. inside diameter, (b)
(failure ring tensile stress) vs. inside diameter. 27
Fig. 8. Failure properties by thickness of ring specimen: (a) (failure ring tensile strain).
28
(failure ring tensile stress), (b)
Fig. 9. Failure properties at different at different moisture content: (a) stress), (b)
(failure ring tensile strain).
29
(failure ring tensile
Nomenclature front view area of the ring specimen obtained by the number of pixels in the image (pixel)
initial width of ring specimen (mm)
instantaneous inside circumference of the ring instantaneous width of the ring specimen (mm) specimen during ring tensile testing (mm) initial inside circumference (mm) instantaneous inside diameter of the ring Greek symbols sample (mm) diameter of the pins (mm) failure ring tensile strain front view height of ring specimen (pixel) internal stress (Pa) dimensionless thickness ratio failure ring tensile stress (Pa) wall circumferential stress (Pa) reference failure ring tensile stress (Pa) The distance between the pins failure stress (Pa) wall tension by unit width (Pa mm) thickness of the ring specimen (mm) Subscripts reference thickness (mm) DIC digital image correlation initial thickness of ring specimen (mm)
Highlights ▶ The concept of true stress-strain was applied to estimate tensile properties. ▶ Laplace’s law was applied to remove the dependence of the width and inside diameter. ▶ Digital image correlation (DIC) was used to identify the validity of Laplace's law. ▶ The dimensionless thickness ratio was developed to estimate ring tensile stress.
30