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BY 4.0 license Open Access Published by De Gruyter Open Access December 31, 2021

Failure analysis of motorcycle shock breakers

  • Afrizal Yose Mahendra , Aditya Rio Prabowo and Triyono Triyono EMAIL logo
From the journal Open Engineering


The shock breaker is one of the most important parts of a motorcycle, which functions as a vibration damper. This study aims to analyze the causes of motorcycle shock breaker failure. The research method used is comprised of visual observation, chemical composition testing, Vickers hardness testing, scanning electron microscopy-energy dispersive X-ray spectroscopy analysis, and tensile testing of a damaged shock breaker. From visual observation, it is found that the damage can be classified as a fatigue fracture, forming a damage pattern at 45°. The chemical composition testing results of the shock breaker fractures show that the material includes low-carbon alloy steel (of ST42 series) with a carbon content of 0.162%. The average hardness value of the damaged part of the shock breaker was increased to 204.87 HV, compared with 171.02 HV in areas far from the damage. The difference in hardness in the shock breaker was caused by the high stress acting on the shock breaker and the consequent strain hardening. The results of this study indicate that the failure mechanism of the motorcycle shock breaker was a functional failure due to errors in the shock breaker manufacturing process and fatigue.

1 Introduction

Previous research has tested shock breakers in a balanced state against a reference point, which are designed to dampen vibrations and to reduce the impact of road surfaces. It is expected that the shock breaker ensures comfort and safety when driving in a bumpy manner, and that the vibrations due to the work of the engine can be damped by the shock breaker, which causes vertical movements in the motorcycle suspension. For these reasons, shock breakers can have a direct effect on the comfort and safety of the rider. Constraint media are used in the study of oil, rubber as well as nitrogen gas in order to reduce the vibrations generated due to uneven roads. This is achieved by using oil and nitrogen gas, such that the piston can move more easily [1,2,3].

The purpose of a previous shock breaker study was to examine a 2004 Jupiter Z motorcycle having a suspension system that moves vertically, using the Matlab 6.4 software simulation [4]; in particular, considering motorcycle damper oil in comparison with viscous palm oil. The mechanical vibration of a telescopic motor Yamaha Jupiter was simulated and assessed. At the end of the research, it was concluded that, with the operation of the suspension system, the use of the shock breaker can enhance the comfort and safety of the motorcycle driver. Comfort and safety are very influential factors when driving, and are related to the suspension system in terms of interference with the system.

A motorcycle has a body, which serves for the placement of the engine, suspension system, and brakes, as well as the steering equipment. The frame of the motorcycle allows for the placement of components related to the functions of efficiency, comfort, and safety while driving [5]. On the motorcycle frame, a very important component – in terms of the safety and comfort of the rider – is the suspension system. The suspension system serves to increase the safety of the rider of the motorcycle, as well as maintains their stability or balance in the event of braking [6]. In modern motorcycles, the type of suspension that is most often used for the front suspension is telescope type. The suspension system functions as a vibration damper, where the vibration caused by braking at the front is a function of the front suspension [7,8]. The creation of vibrations from the rear wheels causes a vertical movement in the swing arm, which aims to dampen the vibrations by using the rear suspension. The front suspension system and the rear suspension are two suspension systems that must be possessed by a motorcycle. The composition of both the front and rear vibration damping systems consists of a suspension tube filled with air pressure, oil, and springs. When designing the suspension system of a motorcycle, components such as an upper arm, coil spring, and a lower arm must be included [9].

Therefore, the shock breaker experiences stress as a side effect of the strain, such that the loading on the motorcycle shock breaker can be divided into several types, including axial loading, bending moment, and torsion loading. These loading models have a large impact on the design of the shock breaker [10]. The load and the type of stress that occur in a shock breaker are subjected to external loading, which works parallel to the axis of the rod, such that the rod will cause a force. The load contained in the shock breaker includes static loading and dynamic loading. Static loading comprises the loadings that are fixed, while a dynamic loading is one that results when the loading value changes within one time interval [11]. Loading tests are intended to determine the maximum load, up to the maximum deflection, which can be analyzed as a failure condition.

Failure analysis involves assessing all possible solutions for the purpose of testing all damaged components and conditions that can lead to failure. In the current context, failure analysis can serve to investigate the root causes of shock breaker discomfort on motorcycles, as has been carried out by previous researchers. Much research has been done to improve the performance and life of motorcycle shock breakers [12]. Most researchers have conducted studies focused on the damage that often occurs in rolling damper, which can crack, as well as the cracks in the tube of the shock breaker. Previous research has investigated the failure of shock breakers, but investigations of failure in the connecting rods of motorcycle shock breakers remain limited. Failures that occur in the shock breaker result in discomfort when driving, as well as result in causing shocks to the motorcycle. This discomfort is affected by several things, such as the speed of the motorcycle, bumpiness of roads, and damaged parts. Furthermore, there is a uniqueness in the main cause and failure mechanism in each failure case. The existing information regarding the expected component failures of shock breakers is not complete; as such, it is necessary to conduct further research in this line. In this study, we aim to analyze the failure of a shock breaker by using multiple tests, including hardness test, tensile test, scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDS) analysis, and a test of the chemical composition of the components of the shock breaker. The motorcycle which was considered in this work as a research specimen was a Supra X [13]. The analysis of the damage is expected to be used as an alternative in handling the damage that occurred, with the hope of identifying the cause of the damage in the shock breaker, such that the occurrence of damage and failure in shock breakers can be prevented in the future [14].

2 Fundamentals of shock breakers

Motorcycles have two kinds of suspension systems: monoshock suspension systems and double shock breaker suspension systems [15,16]. Monoshock suspension systems are used in sport-type motorcycles. The characteristic of motorcycles that use monoshock suspension is that the shock breaker is installed in the middle frame, and the advantage of using a monoshock suspension system, compared with conventional types, is that it is softer, stable, and safe when turning [17,18]. Monoshock suspension systems have limitations, in terms of their carrying capacity, and are therefore not suitable for carrying heavy loads, as they are mostly installed on sport-style motorcycles with large engine capacities [19,20]. One motorcycle that uses a monoshock suspension system is an automatic motorcycle (100 cc) was designed to place the monoshock suspension on the left [21,22]. The suspension system is a very important component, placed between the body of the vehicle and the wheels, with the aim to protect the body from shocks that the vehicle may experience. The components of a shock breaker include a shock tube breaker, which acts as a container of fluid, as well as being the container in which the piston works [23,24], where the piston may be of large or small size. Shock breaker tubes have a complete (protective) seal, with the aim that the movements which occur does not cause fluid leakage, as the seal of the shock breaker has a connection with the fluid; as such, there will often be many seals in this system in order to prevent the fluid from coming out [25,26]. A shock breaker is not able to work optimally when damage to the tube causes the amount of oil in the tube to be reduced [27]. Therefore, a damaged shock breaker tube on a motorcycle can cause a feeling of insecurity or discomfort when riding.

It is not difficult to determine whether a shock breaker is in good or bad condition. A shock breaker that has experienced a leak must be repaired immediately, such as by replacing the shock breaker or adding oil to the shock breaker. The fluid in the shock breaker passes through one of the valves in one direction, through what is called the valve orifice. The valve orifice is a small channel on the piston, which is located in the inner shock breaker tube. The size of the orifice determines whether the suspension is hard or smooth. In a soft suspension, the valve orifice is large, contrary to the hard-type shock breakers (as well as racing-type), in which a small-sized channel orifice is used instead. The components that make up this kind of shock breaker include the cylinder, piston, piston valve, and piston rod. The piston rod on the shock breaker serves as a link between the piston and the motor wheel. An event that is often experienced by the driver at the time of driving is the occurrence of over-vibrations. Over-vibration, if it cannot be anticipated, can reduce the level of safety and comfort in passengers and the driver. Therefore, there may be a need for modification or development of the suspension system in the vehicle, and if no development is made to the suspension system, then the user of the vehicle (especially for two-wheelers) can experience discomfort while driving.

3 Highlights of previous works

Previous research conducted on shock breakers has tested them in a state balanced against a reference point, in order to optimize their design to dampen vibrations and reduce the impact of rough road surfaces. In addition, the shock breaker is expected to ensure comfort and safety when driving, enabling to drive in a bumpy place such that the vibrations due to the engine working can be dampened by the shock breaker, thus creating a sense of safety. Disturbances to the shock breaker can have a direct effect on the comfort and safety of the rider(s). The damping media considered in this study were oil, rubber, and nitrogen gas.

One shock breaker study considered a Jupiter Z motorbike 2004 with a vertical suspension system, using the Matlab 6.4 simulation software [28]. This study assessed the damping performance of motor oil, compared with palm oil. Another study has calculated mechanical vibration estimates for telescopic-type suspension in a Yamaha Jupiter Motorbike [29]. This study concluded that, when the suspension system is working, the shock breaker can ensure comfort and safety when motorbikes are used. The design of the motorbike was focused on the two most important aspects: comfort and safety.

Frequent shock breaker breakage can result in a lack of comfort and safety when driving. Shock breaker damage is typically associated with the cracking of a rolling damper and its impact on the shock breaker tube [30]. A study has been carried out to assess the damage to the rolling damper in a shock breaker. Damage to the rolling damper will affect the oil seeping out of the shock breaker tube and can cause malfunction of the shock breaker, given a style that matches the rider’s load, after the load has been lifted. The process that occurs at the rolling damper of a cracked shock breaker is caused by the tension generated by an imposition greater than the minimum weight of the material. A microstructural analysis of the material in the area that suffered a fracture, in the form of a fault, proved that the fracture movements came around the diameter in the pipe, moving to the left and right sides, thus leading to fatigue of the rolling damper. Further study needs to be carried out to determine the failure of the shock breaker, when used in a constant state of burden.

Components that suffer a structural breakdown may be revealed by conducting a test or simple condition check, which can lead to the diagnosis of failure; such testing is called failure analysis. Failure analysis has the primary objective of providing a solution which can be made to address the problem of failure, as well as to identify the underlying cause of the failure [31]. Such observations may reveal all the components that are defective. The key to all failure analyses is microscopic and macroscopic observation. Some of the most frequent contributing factors of failure are the result of material selection, poor design, and extreme working conditions. Failure is largely due to forces that affect the operation of components, leading to a need for mechanical testing. Mechanical testing includes analyses such as hardness testing, tensile testing, SEM-EDS analysis, and chemical composition testing.

4 Materials and method

Research was conducted on a damaged shock breaker from a motorcycle. The shock breaker is one of the most important components of a motorcycle, which functions to dampen or minimize the movements that cannot be controlled by a motorcycle driving along bumpy roads. The part that was damaged in the shock breaker was in the regulator. This shock breaker had been functioning for 1 year (2017–2018). Research on the damage that occurred to the shock breaker was carried out by several test methods, including visual observation, chemical composition testing, hardness testing, SEM-EDS testing, and tensile testing.

Through visual observation of the fracture surface on the shock breaker, we aimed to identify specific damage or special markings caused by a particular load before the component was damaged. With visual observations, the type of failure experienced by the component can be preliminarily judged, such that initial predictions are obtained before continuing with the next test.

A chemical composition test, using a Hilger machine type E-9 OA701 (Optical Emission Spectroscope, OES), was carried out to determine the content of chemical elements in the test object. Chemical composition tests are generally carried out when we want to start a study as, before carrying out a study, we first wish to classify the specimen that we want to examine. The elements contained in the test object can be determined using the difference in the characteristic wavelengths of each element, as assessed through observation of the emissions from the surface of the object being tested after excitation. The chemical composition test was conducted at Politeknik Manufaktur Ceper, Klaten, Central Java.

A hardness test was carried out with the aim to determine the (distribution of the) level of hardness in the damaged shock breaker. The Vickers hardness test is based on compression by a particular pressing force onto a metal surface, using an indentor in the form of an inverted pyramid diamond (which has a peak angle of 136°). The condition for carrying out this hardness test is that the metal surface must be clean and flat. The pressing force is applied to the surface, and a rectangular pyramidal form is indented onto it. The rectangular diagonal of the indent is then measured carefully, which is used to calculate the hardness of the metal tested. In this study, the Vickers hardness test was carried out using a HWMMT-X7 machine with a load of 100 g. The time of indentor pressing was 20 s, in accordance with ASTM E 92 standards. The value of hardness obtained is called Vickers hardness, commonly referred to as HV or HVN. Vickers hardness testing was conducted at the Vokasi of Gajah Mada University, Yogyakarta.

SEM was carried out to observe the condition of the surface topography of the sample, such that the type of damage that had occurred could be determined, while EDS testing was carried out with the aim to determine the chemical composition of the matrix and the particles of the (intermetallic) precipitate contained in the test sample. SEM–EDS was conducted using a Zeiss Evo 10 with a magnification of 5,000×. For this test, we used a square-shaped sample with a size of 1.8 cm × 1.7 cm × 0.2 cm, and the surface of the sample was required to be clean. SEM–EDS analysis was performed at the Institut Teknologi Sepuluh Nopember, Surabaya.

Tensile testing (Figure 1) has the function of obtaining an overview of the properties and condition of a metal. Tensile testing is carried out through the addition of a load slowly, after which the metal gains additional length proportional to the working force. In this research, we refer to the standard tensile test (ASTM A356) and the dimensions of the specimen used were of standard size. The test was carried out using a Hung Ta machine, and the standard sample tested in this study was in the form of a dogbone having the following parameters: L = 160 mm, D = 60 mm, D = 36 mm, G = 36 mm, R = 50, E = 8 mm, B = 45 mm, C = 48 mm, and F = 36.5 mm. Testing of the shock breaker sample was conducted at the University of Gajah Mada, Yogyakarta.

Figure 1 
               (a) Tensile testing apparatus and (b) standard specimen in ASTM A356.
Figure 1

(a) Tensile testing apparatus and (b) standard specimen in ASTM A356.

5 Result and discussion

5.1 Visual observations

Figure 2 shows the results of visual observation of the shock breaker part where failure occurred. The damage that occurred was apparent, with fault patterns to the right and left of the component, forming an angle of about 45o, and there was a smooth and rough surface pattern. Based on the results of observations of the fracture pattern, it can be concluded that fracture was brittle and caused by overload, where the load exceeded the limit of the yield of the material [32].

Figure 2 
                  Visual observation of the specimen.
Figure 2

Visual observation of the specimen.

5.2 Chemical composition test

Chemical composition testing on the shock breaker component was carried out using an OES tool. The purpose of this chemical composition test was to determine the chemical composition of the material that had failed. The results of chemical composition testing on the damaged material, showing the standard composition of the shock breaker, are provided in Table 1. Testing the chemical composition of the part suggests that the material was low-carbon steel, as the data obtained indicated that the regulator material in the shock breaker contained 0.216% carbon. The test found a difference in the chemical composition of the material that was damaged, compared with the JIS G4105 specification.

Table 1

Chemical composition data

Chemical element Specimen
Spectrometry result (%) Standard according to JIS G4105 (%)
C 0.216 0.13–0.18
Si 0.0084 0.15–0.35
Mg 0.304 0.60–0.85
P 0.0096 Max 0.03
S 0.0030 Max 0.04
Cr 0.032 0.90–1.20
Mo 0.011 0.15–0.30
Ni 0.028 Max 0.30
Cu 0.0020 Max 0.30
Al 0.016 0.020
Co 0.0030 0.001
Nb 0.0070 0.020
Ti 0.0020 0.03
V 0.0030 0.001
W 0.020 0.1
Fe 98.40 99.158

Table 1 indicates that the shock breaker suffered a decrease in the composition of the elements contained in the material, including deductions in iron (Fe) content by 0.758%, silicon (Si) content by 0.3916%, magnesium (Mg) content by 0.496%, nickel (Ni) content by 0.272%, and copper (Cu) content by about 0.298%. These chemical composition results indicate that the percentages of these elements were approximately 0.4% lower than that specified in the standard, resulting in a failure of oxygen or other dissolved gases found in the material to function, thus causing damage. Other alloy content, such as chromium (Cr), had a sub-prime percentage of 0.3%, which could cause the material to suffer declines in its tensile and corrosive properties; while, for this alloy, magnesium (Mg) had a value below that in the standard (80%), which could cause the force-bearing capacity of the material to decline at high temperatures. The nickel (Ni) content had a fractional percentage, 0.3% below the standard, which may have resulted in the materials and the regulator in the shock breaker being subjected to constant impact, thus causing damage. Another cause of damage may be due to the copper (Cu) element being 0.0020% below its required level in the standard, potentially influencing the corrosion behavior of the material [33].

These results suggest that the compositional decline in the shock breaker material had an effect on the interplay of elements comprising the material. These interactions may have caused a tension difference in the process of creating the shock breaker, resulting in residual tension [34]. The remaining stresses generated by the interactions of these compounds can cause small cracks or microcracks in the regulator material area of the shock breaker [35]. Fractures in the regulator areas over a long period of time can result in corrosion and overload buildup of the crust, resulting in long cracks and causing deterioration of the performance of the shock breaker and malfunctioning components [36].

Failure of the components of the shock breaker was likely caused by the differences in the main elements, one of which (carbon) had elemental content differing from that specified in the standard. Carbon content which is not in accordance with the standard can lead to changes in the mechanical properties of the material, including an increase in the hardness of the material accompanied by decreased ductility. This indicates that the processes occurring in the material of the shock breaker affected the interactions between the various elements in the material [37].

5.3 Hardness test

A Vickers hardness test was carried out with the aim to determine the (distribution of the) hardness of the damaged shock breaker material. The test, in accordance with the ASTM E92 standard, was carried out with a press, going from the outer diameter to the center of the inner diameter. Eight test points were used on both the damaged specimens and specimens that were far from the damage. The Vickers hardness test used a load of 100 g for 20 s. The loading locations and the results of the hardness test are shown in Figures 3 and 4, respectively.

Figure 3 
                  Designated indentation areas for the Vickers hardness test.
Figure 3

Designated indentation areas for the Vickers hardness test.

Figure 4 
                  Results of the Vickers hardness test (unit: HV).
Figure 4

Results of the Vickers hardness test (unit: HV).

Figure 4 shows the results of the hardness test on the damaged component. Based on the results obtained, it can be seen that the damaged area had varied hardness values at different locations [38]. The hardness values were: at point A, 210.2 HV; point B, 210.2 HV; point C, 191.6 HV; point D, 205.3 HV; point E, 196 HV; point F, 205.3 HV; point G, 210.2 HV; and point H, 210.2 HV. Meanwhile, the hardness values of the material far from the deformation area had almost the same value (homogeneous). The hardness values were: at point A, 172.07 HV; point B, 171.47 HV; point C, 171.09 HV; point D, 170.40 HV; point E, 170.09 HV; point F, 171.3 HV; point G, 170.39 HV; and point H, 172.2 HV.

In terms of the hardness values of the undamaged material, the hardness values were not much lower or higher than that of the standard (171.13 HV), and were also similar to that of the ST 41 standard (172 HV). In contrast, the hardness values in the area of the deformation of the shock breaker were increased, with an average of 204.87 HV. The increase in hardness at the damaged area, compared with areas far from the deformation, was likely caused by the high stress in the area and, consequently, strain hardening.

5.4 SEM-EDS analysis

SEM and EDS tests were carried out to observe the pattern of fractures that occurred in the materials at high magnification and to determine the composition of the chemical constituents, respectively, such that the elements that caused these materials to crack and fracture could be determined. SEM and EDS testing were carried out at the SEM laboratory of the Institut Teknologi Sepuluh Nopember, using a Zeiss Evo 10 with an optimal magnification of 5,000×. The shock breaker material was observed at the crack initiation area, the crack propagation area, and the final fracture. The results of the SEM test are shown in Figure 5, where Figure 5(a) shows the crack initiation area, as clarified by the results of observations made on the surface of the fracture, which found that there was wide propagation. Figure 5(c) shows the morphological pattern of the dimple fault in the propagation area, where the dimples on the fracture surface were due to overload and fatigue of the material.

Figure 5 
                  SEM imagery at surface magnification of: (a) 70×; (b) 200×; and (c) 500×.
Figure 5

SEM imagery at surface magnification of: (a) 70×; (b) 200×; and (c) 500×.

SEM observations of the fracture surface indicate that the cracks are streaked. These cracks elongated, causing the component to break. This further strengthens the analysis result of the fracture surface namely, the designation of fatigue failure. The results of the EDS test, shown in Figure 6, demonstrated that the fracture was an intergranular fracture (i.e., at grain boundary).

Figure 6 
                  Results of the EDS analysis: (a) specimen photo and (b) element chart.
Figure 6

Results of the EDS analysis: (a) specimen photo and (b) element chart.

Elemental oxygen can lead to corrosion process, as oxygen can form oxides in the metal. The process of corrosion, caused by air and water trapped in the gaps between the particles of metal, creates a damaging layer of oxides. If this process is continuous, corrosion cracking in the oxide layer can cause wider and deeper surface corrosion. At high concentration, oxygen can react with iron (Fe), forming small pores and leading to the occurrence of corrosion between grains (i.e., intergranular corrosion).

5.5 Tensile test

Tensile testing is conducted to determine the strength value of a material against a tensile force, as well as to determine the shapes of faults [38]. Figure 7 shows that the tensile strength of the shock breaker material in specimen 1 was 446.1 MPa, that in specimen 2 was 444.0 MPa, that in specimen 3 was 445.8 MPa, and that in specimen 4 was 450.6 MPa. Overall, the average obtained tensile strength was 446.3 MPa, compared with the standard tensile strength value of shock absorbing materials of 452 MPa. As for the value of yield stress in specimen 1 was 352.7 MPa, in specimen 2, 353.4 MPa, in specimen 3, 350.9 MPa, and in specimen 4, 345.2 MPa. Overall, the average obtained yield strength was 353.3 MPa, compared with the standard yield strength of shock breaker materials of 357.2 MPa. Although the shock breaker material was the same, it turned out that its ductility differed [39]. The elongation values obtained in the first, second, third and fourth specimens were 21.56, 21.65, 21.87, and 22.2%, respectively.

Figure 7 
                  Tensile test results for all specimens.
Figure 7

Tensile test results for all specimens.

The average elongation value obtained from the samples was 21.89%, which was lower, when compared with the typical elongation value of shock breaker material (22.10%) [39]. This decrease in the elongation value may have been caused by the increased hardness value and decreased tensile strength of the material, leading to decreased ductility; consequently, the shock breaker material experienced ductile failure.

6 Concluding remarks

Damage to the shock breaker is a failure phenomenon that must be analyzed and further investigated. If the motorcycle components that are damaged cannot be determined, there may be dangerous (or even fatal) consequences for the motorcycle and passengers. Factors that can cause damage to shock breakers must be found immediately and identified, such that appropriate solutions can be determined to prevent the damage. Prevention of damage is expected to reduce the level of accidents and improve the safety of transportation, such that shock breakers can be used throughout the full service life of vehicle.

Several tests were carried out with the aim to identify the damage to a shock breaker, including chemical composition testing, hardness testing, SEM-EDS analysis, and tensile testing. Damages occurring in the shock breaker may have occurred for several reasons, for example:

  1. Overload caused the material of shock breaker to experience cracks or defects on the surface. This is evidenced by the result of visual observations which found that the shock breaker experienced crack propagation resulting in deformation/fracture.

  2. The age factor of the shock breaker components caused by motorcycle users not taking good care of their motorcycles, causing the shock breaker to be damaged.

    • Errors in the assembly process that can cause the shock breaker to unable to withstand the load resulting in the shock breaker component being cracked, causing it to break.

      Based on the tests carried out, the results demonstrated that there were several causes of failure in the shock breaker, including overload such that the material crack, maintenance, and errors in the assembly process. As for future recommendations, we recommend the following:

    • Addition of Ni to the alloy, from 0.028% to 0.3%.

    • Increasing Cu content to 0.3%.

    • Increasing Cr content from 0.032% to 1.2%.

    • Carry out regular maintenance and periodic checking of motorcycle components.

    • Maintain proper lubrication inside of the shock breaker.

    • Use of a special protective coating on the shock breaker, in order to prevent corrosive environmental damage


This work was supported by the RKAT PTNBH Universitas Sebelas Maret, Surakarta under scheme of Hibah Penelitian Unggulan Terapan (PUT-UNS), with Grant/Contract No. 260/UN27.22/HK.07.00/2021. The support is gratefully acknowledged by the authors.

  1. Funding information: This work was financially supported by the RKAT PTNBH Universitas Sebelas Maret, Surakarta under scheme of Hibah Penelitian Unggulan Terapan (PUT-UNS), with Grant/Contract No. 260/UN27.22/HK.07.00/2021. The support is gratefully acknowledged by the authors.

  2. Conflict of interest: Authors state no conflict of interest.


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Received: 2021-07-22
Revised: 2021-09-16
Accepted: 2021-10-19
Published Online: 2021-12-31

© 2021 Afrizal Yose Mahendra et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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