- Open Access
Measuring the compressive modulus of elasticity of pith-filled plant stems
© The Author(s) 2017
- Received: 14 May 2017
- Accepted: 1 November 2017
- Published: 9 November 2017
The compressional modulus of elasticity is an important mechanical property for understanding stalk lodging, but this property is rarely available for thin-walled plant stems such as maize and sorghum because excised tissue samples from these plants are highly susceptible to buckling. The purpose of this study was to develop a testing protocol that provides accurate and reliable measurements of the compressive modulus of elasticity of the rind of pith-filled plant stems. The general approach was to relying upon standard methods and practices as much as possible, while developing new techniques as necessary.
Two methods were developed for measuring the compressional modulus of elasticity of pith-filled node–node specimens. Both methods had an average repeatability of ± 4%. The use of natural plant morphology and architecture was used to avoid buckling failure. Both methods relied up on spherical compression platens to accommodate inaccuracies in sample preparation. The effect of sample position within the test fixture was quantified to ensure that sample placement did not introduce systematic errors.
Reliable measurements of the compressive modulus of elasticity of pith-filled plant stems can be performed using the testing protocols presented in this study. Recommendations for future studies were also provided.
- Corn stalk tissue
- Compression stiffness
- Strain measurement
The measurement of mechanical properties of plant stems helps in investigating early and late season stalk lodging . But in spite of the economic significance of plants with thin-walled stems (e.g., maize, sorghum, wheat, etc.), few studies have investigated reliable methods for obtaining their mechanical properties under compressive loading. One of the most important mechanical properties is the modulus of elasticity, which provides a linear relation between stress and strain . This mechanical property is essential for calculating stress states as well as physical deformation of a structure or a plant [3, 4].
The modulus of elasticity can be measured in a number of ways, including bending, tension, compression, vibration, and acoustic excitation tests. Bending tests have been used in a number of studies, including those focused on the mechanical properties of wood [5–8], sunflower stalks , sorghum stalks , wheat stems , and maize stalks [12, 13]. Bending tests are popular because they involve low loads, easily measurable deformation, and require little sample preparation. Bending tests can only be performed on test samples that are long and slender , and produce one estimate of the modulus of elasticity for each sample. As a result, this method produces rather poor spatial resolution for the modulus of elasticity. The accuracy of the modulus obtained by bending tests is also adversely affected by the nonlinear form of the bending equations, which tends to amplify measurement uncertainty.
Tensile testing is another common technique for obtaining the modulus of elasticity. This approach has been used to measure the modulus of elasticity of wood , excised rind sections of maize stems [15, 16], excised longitudinal sections of switchgrass stems , rice stems, and Arabidopsis stems . However, sample preparation is more laborious as compared to bending and specimens must be gripped securely without inducing tissue damage. The gripping aspect of tensile test is often quite challenging.
Compression testing is very common in the wood literature [7, 19], but is not commonly used in the testing of thin-walled plant stems. This is because the plant rind tends to be highly susceptible to buckling deformation. Consequently, information on the compressive modulus of thin-walled plant stems is often not available.
Studies have reported that the tensile and compressive modulus of elasticity values can be different for lumber, wheat straw, and barley straw [6, 20]. This indicates that tensile testing alone may be insufficient for measuring the modulus of elasticity, and that bending tests (which induce both bending and compression) may yield modulus values which are unreliable. Techniques for measuring the compressive modulus of elasticity of plant stems are therefore needed.
The goal of this study was to develop a robust method for obtaining the compressive modulus of elasticity of the rind of pith-filled plant stems, and to study the factors that influence the accuracy and reliability of this method. For the sake of brevity, the abbreviated term “modulus of elasticity” will be used in place of the more precise term “longitudinal compressive modulus of elasticity” in the remainder of this paper.
Dry maize stalks were used as test specimens in this study. Maize can be highly susceptible to late-season stalk lodging, which occurs due to compression-induced buckling of the rind . Maize stalks were sampled from 2 replicates of four commercially available hybrids of dent corn (maize) seeded at 5 planting densities (119,000, 104,000, 89,000, 74,000, and 59,000 plants ha−1) . Stalks were cut just above the ground and just above the ear node immediately before harvest. To prevent fungal growth, stalks were placed in forced-air dryers to reduce stalk moisture to approximately 10–15% moisture by weight, which closely mimics the state of stalks in the field just prior to harvest. To avoid confounding factors, only stalks found to be free of disease and pest damage were included in the study. One hundred (100) samples were selected for compression testing.
Self-aligning compression platens are used in situations where the perpendicularity of sample end-faces is difficult to achieve. As a load is applied, these platens rotate until they are in alignment with the testing surface, thus accommodating any discrepancies in the angle of the end-face. Self-aligning platens (Cat No: S5722A, Instron Corp., Norwood, MA, USA) were therefore used at both ends of the specimens to accommodate any angular inaccuracies in the cutting process. Figure 2 provides a diagram and a photograph of a specimen situated for testing.
Compression testing equipment
Compression tests were performed using a universal testing machine (Instron 5965, Instron Corp., Norwood, MA, USA). Loads were measured with a 5 kN Instron load cell. Instrumentation control and data acquisition were managed with Instron software (Bluehill 3.0).
Two types of strain were measured for each sample in this study; overall strain (ε overall ) and local strain (ε local ). Overall strain was based on the total displacement of the universal testing machine, (i.e., the displacement between the two spherical platens) divided by the total initial length of the sample prior to loading. Local strain was measured using an Instron extensometer, which recorded the displacement of two points on the surface of the specimen (see Fig. 2). The extensometer had a reference length of 50 mm (Instron 2630 Series Dynamic Extensometer, Instron Corp., Norwood, MA, USA) (Fig. 2).
Compression testing procedure
When testing biological tissues, a preload and repeated application of load cycles is commonly used to bring the samples to a repeatable reference state . This procedure is used to reduce measurement variability and is referred to as pre-conditioning [28–31]. The loading process is described below.
An initial load of 200 N was applied to each specimen. Five loading cycles were then applied. In each loading cycle, the load increased from 200 to 700 N and then returned to the 200 N initial state. The first cycle was used as a conditioning cycle. Only measurements from the latter four cycles were employed in the modulus of elasticity calculations. A strain rate of 0.1 mm/s and a sampling frequency of 33 Hz were used in this study. This rate is similar to that used in a previous report (0.0833 mm/s), where corn stalk specimens with a length to diameter ratio of 1:1 were tested . Lower rates have been used in testing wheat/barley straw (0.04 mm/s) , lumber (0.005 mm/s)  and timber (0.042 mm/s) specimens . Further investigation is needed in the future to elucidate the effect of strain rate on the compressive elastic moduli values of pith-filled plant stems.
Modulus of elasticity calculations
Assessing the contribution of pith tissue
After all specimens were tested, the contribution of pith tissue to overall stiffness was assessed by carefully drilling a hole of 5 mm in diameter through the nodal tissue at the end-face of each specimen. A common wood drill bit was used for this purpose. A round wood file was then used to gently abrade the pith tissue until only rind tissue remained. These hollow samples were then re-tested using the techniques described above.
Sensitivity of the compressive modulus to sample placement
The cross-sectional shape of the maize stalk is somewhat irregular (see Fig. 4). Placement of each specimen on the two self-aligning platens is therefore somewhat subjective. The sensitivity of the compressive modulus measurements to specimen placement was therefore assessed to determine if sample placement affected compressive modulus results.
These tests were performed by first placing a specimen at the apparent center of each self-aligning platen. After measuring the compressive modulus in the typical fashion, the specimen was shifted away from the center and the test was repeated. This process was repeated for shift distances of 2 mm and 4 shift directions (0°, 90°, 180°, and 270°). The compressive modulus was therefore measured at each of the 12 resulting shift locations. These measurements were balanced by 12 tests performed with the specimen in the center position. Testing alternated between centered and shifted positions to avoid potential bias caused by temporal effects.
Repeatability of the compression test methodologies in this paper was performed according to standard procedures . A set of 10 specimens were tested repeatedly according to the protocols described above. Each specimen was tested 5 times, and both methods for obtaining compressive modulus were used for each test. The standard deviation was used to quantify the test repeatability for each specimen.
Representative stress–strain curves of pith-filled maize samples
Sensitivity of the compressive moduli to pith-filled sample placement
Repeatability analysis for pith-filled samples
Repeatability statistics obtained from repeated tests on a set of 10 specimens
Mean repeatability (95% confidence interval)
Repeatability variation (SD) (%)
Upper bound for variation between any two tests (95% confidence) (%)
3.9% (± 2.2%)
3.9% (± 1.7%)
Averaging local strains of pith-filled samples
Self-aligning platens induced slight circumferential variation in strain. This variation was captured by taking strain measurements at 4 circumferential locations for each specimen. To examine the effect of averaging circumferential strains, compressive modulus values were calculated by using 1, 2, 3, and 4 strain values. Equation 3 describes the calculation of compressive modulus for a single strain measurement while Eq. 4 describes the calculation process for four strain measurements. Similar expressions can be obtained for two and three strain measurements.
Neglecting the contribution of pith tissue
Statistical effects of pith removal
Mean effect of pith removal (95% confidence interval)
Variation in pith removal (i.e., SD) (%)
− 4.4% (± 1.7%)
− 3.8% (± 2.5%)
Local versus overall compressive moduli of pith-filled samples
We now examine differences between local and overall compressive moduli (E overall and E local ). These values were calculated for all specimens in this study. Recall that E overall is the stiffness of the entire specimen; whereas E local is the stiffness obtained near the center of each specimen (see Fig. 2).
This study involved the compressional testing of dry, non-diseased maize stalk segments consisting of two nodes and the intervening internode (see Fig. 1). Specimens were cut just below the node lines because tough nodal tissues and thicker rind in this region effectively distribute stresses, thus preventing premature tissue failures that can occur during compression testing when test specimens involve only internode tissues.
Certain challenges were encountered in this study. One of these was the difficulty of cutting two parallel end faces on maize stalk specimens, both of which should (according to compression testing standards) be perpendicular to the stalk axis. This challenge was addressed by using two self-aligning compression platens. However, this solution then generated a new challenge: the lack of structural symmetry induced circumferential variation in strain, thus necessitating the measurement of strain at multiple locations. These strains were averaged to obtain the compressive modulus of internodal tissues.
Accuracy, reliability, and test duration
Two different compressive modulus values were obtained for each specimen in this study: E overall and E local . The overall compressive modulus value is based on deformation that occurs throughout the entire specimen, including at the end faces, meristematic tissue, and internodal tissues. As such, the overall compressive modulus should be considered as an aggregate stiffness value, with tissue stiffness within the specimen varying above and below this value. The local modulus approach measures tissue strain in a region where tissue is regular and uniform and thus is likely more accurate. Deformation of the testing apparatus was negligible as compared to deformation in test specimens. The repeatability values of both tests were comparable.
The local compressive modulus values were higher than overall modulus values for every specimen in this study. Although spatial variation in stiffness was not the focus of this study, we believe that this is due to a lower tissue stiffness near each node and in the meristematic region . More detailed studies will be necessary to confirm this. The calculation of the compressive modulus values was based on an assumption that the pith tissues have a negligible effect on stalk stiffness. The removal of pith tissue was found to decrease modulus values by an average of 4%. Thus, the values obtained for rind stiffness in this study are (on average) 4% higher than their true values.
As shown in Fig. 7, the reliability of local compressive modulus values improved as the number of circumferential sample points increased. However, unless multiple circumferential samples can be acquired simultaneously, each circumferential sample point increases the testing duration. Excluding sample preparation (which was similar for both test types), local modulus testing required approximately 10 min per specimen.
As shown in Fig. 7, the mean value is relatively insensitive to the number of circumferential strain values. However, a decrease in circumferential measurements also decreases test-to-test repeatability, thus artificially increasing the observed variation in the compressive modulus. The use of fewer circumferential measurements may be suitable in certain situations where the mean value is the primary objective.
If relative differences between plants is of primary concern, absolute accuracy may not be a primary concern. In such a case, the overall modulus may be a better choice. The overall modulus provides a single, average rind stiffness value for the entire specimen with reasonable reliability. Test duration for prepared samples was approximately 2 min per specimen.
Recommendations for future studies
One of the most important considerations when performing compression tests is the perpendicularity of end faces. This is a particular challenge when dealing with plant stems, which typically do not have straight edges that can be used as a reference. Spherical platens can be used to address this issue, and are recommended for future studies. If for some reason, spherical platens cannot be used, special attention should be paid to the preparation of end faces as well as the resulting load/deformation curves. An alternative approach is to embed each end of the sample in polymethyl methacrylate (PMMA) or some other kind of resin, a technique used in the testing of bone specimens [43, 44].
In the current study, rind thicknesses were obtained from X-ray computed tomography 2D images, but this approach requires special equipment and software. A more accessible technique is to obtain areas of rind and pith areas based on cross-sectional images obtained with a flatbed scanner .
Two methods were developed for measuring the compressive elastic modulus values of the rind of pith-filled plant stems such as maize. The two elastic modulus values were calculated using two different strain measurements. These test methodologies did not require that end faces were strictly parallel, and both methods produced consistent results (mean repeatability of 4%). Both methods utilized the natural shape of the plant stem to avoid stress concentrations and buckling failure which are common challenges when performing compression tests, especially with thin-walled specimens.
Both elastic moduli measurements presented in this study neglected the contribution of the pith tissue. This assumption had a mean effect of overestimating the rind stiffness by 4%, which was deemed to be acceptable for these purposes.
Each of these methods possesses unique advantages and disadvantages. The overall compressive modulus technique provides a single, average value for all rind tissue in the specimen, but can be obtained relatively quickly. In contrast, the measurement of local modulus required multiple strain measurements, thus requiring additional tests, but provided results which are likely more accurate.
The modulus of elasticity values reported in this study are relevant from the stalk-level down to scales of a few centimeters. At scales smaller than this, the cellular architecture of the stalk tissue should be considered. Finally, although these measurements were developed and tested for dry maize specimens, the methods and principles introduced in this study are likely applicable for other types of plant stems, such as sorghum, reed, bamboo, etc.
LA, DR, and DC designed the research and wrote the manuscript. LA, DR, and DC developed the experimental procedure of the approach. LA, JE, and WS performed the experimental procedure. All authors read and approved the final manuscript.
We thank Monsanto Company, St. Louis, MO, USA for providing the maize stalk samples used in this study. This work was funded in part by the National Science Foundation (Award # 1400973), and the U.S. Department of Agriculture (Award # 2016-67012-24685).
The authors declare that they have no competing interests.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Consent for publication
No consent was required in this study.
Ethics approval and consent to participate
No human subjects or animals were used in this study.
This study was supported by the National Science Foundation, Arlington, VA, USA (Grant # 1400973) and the U.S. Department of Agriculture, Washington, DC, USA (Grant # 2016-67012-24685). The funding agencies did not have any role in designing the study or in collecting, analyzing, interpreting the data or in writing the manuscript.
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