Dale Wilson Dale Wilson. The Johns Hopkins University. Leif A. Carlsson Leif A. Florida Atlantic University. Page range:. Publication history Created:. Cite Icon Cite. Abstract This article begins with a review of the purposes of mechanical characterization tests and the general considerations related to the mechanical properties of anisotropic systems, specimen fabrication, equipment and fixturing, environmental conditioning, and analysis of test results. You do not currently have access to this chapter.
Sign in. You could not be signed in. Reset Password. Despite the challenges associated with using reference material property values to assess whether test results are correct , they are of value in determining whether the results are reasonable. Material properties from these data sheets and databases may provide a feel for the approximate magnitudes and the amount of variability in the mechanical properties of interest for composites with fiber variations, matrix material variations or both. In addition to using published data, two mechanical properties of unidirectional composites may be predicted relatively accurately based on properties of the fiber and matrix, as well as the fiber volume fraction of the composite.
The modulus E 1 may be calculated using the equation. Using these equations, the fiber-direction stiffness and strength of a unidirectional composite can be approximated with reasonable accuracy simply by knowing the fiber stiffness and strength as well as the volume fraction of the constituents. G, Daniel O. Adams, professor of mechanical engineering and director of the Composite Mechanics Laboratory at the University of Utah, and the vice president of Wyoming Test Fixtures Inc. Donald F.
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First subject? The challenges of tensile testing unidirectional composites. Adams Wyoming Test Fixtures Salt Lake City, Utah takes look at flexural testing and promises recommendations, next time, for a unified standard. A digital approach to automation. Composite catamaran hits high watermarks.
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Tabbing composite test specimens: When and why Dr. Once part of the stem yields or fractures, it may form a mechanism causing the stem to collapse, known as a failure mechanism.
Stems have evolved strategies to avoid particular failure mechanisms, as described in the text. Strength is the maximum total stress a material can withstand before failure. Because bending tests are such a common way of estimating structural properties, there is a specific term for the strength measured in this test.
The modulus of rupture is, therefore, the estimated peak stress for a stem at failure, as measured using a bending test such as three-point bending. When a compressive force is applied to a slender structure such as a plant stem, it does not fail by pure crushing of the material. Before the force necessary for pure crushing is reached, any lack of straightness however small will cause an initially straight stem to bend. The bending deformation increases the bending forces on the stem, and eventually the stem will become unstable, and fail in bending. The force at which this happens is called the buckling load.
This process can occur in entire stems, as illustrated in Fig. In hollow stems, the Brazier effect Brazier, may occur, in which, as it bends, the stem cross-section becomes more oval, reducing its ability to resist bending and further reducing the buckling load. Research into buckling of plant stems is described in the text. Fibre-reinforced composite. Slender fibres can have extremely high strength and stiffness.
In compression, however, these fibres alone do not exhibit their full strength because they are susceptible to buckling. If the fibres are instead used as reinforcement in a matrix of material capable of restraining against buckling and suitable to distribute the load around the fibres, then the strength and stiffness of the fibres can be effectively used. Stems may be described as fibre-reinforced composites at two scales. Often, the matrix has isotropic material properties, while the fibres and the resulting aligned-fibre composite exhibit anisotropy.
Many of the factors governing stem mechanics are based on the stem architecture, which manifest at both the microstructure and the macrostucture scales. These factors need to be accounted for when designing testing methodologies, and understood to explain the observed mechanical behaviour. In addition, knowledge of the stem structural hierarchy may be useful in inferring material properties at the tissue and cell wall level from measured properties of the stem structure. Stems and roots are the two main structural axes of all vascular plants: a group which includes gymnosperms, angiosperms, and ferns.
Ferns typically lack vertical, overground stems. All gymnosperm stems are woody, and they tend to form near cylindrical, solid stems. Angiosperms can be further categorized as i herbaceous monocots including grasses such as bamboo; ii herbaceous dicots such as flax and the model plant Arabidopsis thaliana ; and iii woody dicots including trees Table 2.
Angiosperms display a wide variety of strategies for structural resistance, both in the arrangement of stiffer and more flexible cells, and in their global geometry, as depicted by the schematics in Table 2. While upward, primary growth, mediated by the shoot apical meristem , is common for vascular plants, dicots also have the ability for secondary growth, which means that their stems can get thicker. Here, we focus on herbaceous stems, while also drawing relevant knowledge from existing work on mechanical characterization of woody stems.
The structure of three principal categories of angiosperm plant stems at a macroscale , and the functions of principal tissue and principal cell types that exist in stems.
Schematics of plant stems are adapted from Kirkby Schematics of cells are adapted from Taiz and Zeiger Each tissue type is composed of various cell types, with the structure of the cells having evolved for specific functions Table 2. Parenchyma cells in the ground tissue have a soft, thin, flexible primary cell wall. The primary cell wall layers are typically lignin deficient and contain a low content of stiff cellulose fibrils.
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Through cell pressure probes and mechanical tensile or bending tests on parenchymatic tissue, such as plugs of potato tubers Niklas, and Caladium petioles Caliaro et al. The presence of large vacuoles in these thin-walled cells implies that turgor pressure has a substantial effect on its measured mechanical response Niklas, ; Leroux, Collenchyma cells in the ground tissue have unevenly thickened primary cell walls with higher cellulose content, and therefore can offer some rigidity to young stems Leroux, Typically, the principal structure-supporting cells are specialized sclerenchyma fibre cells found to some extent in the ground tissue, but primarily in the vascular tissue.
In addition to primary cell walls, these elongated cells have thick, lignified, cellulose-rich secondary cell wall layers. Vascular cells with secondary cell walls, such as in the xylem as fibres and vessels e. These cells have elastic moduli, measured typically through tensile tests, in the range of 10—35 GPa the higher modulus being that of wood cell walls Karam and Gibson, , but even up to 70 GPa in the dry state such as in flax phloem fibres Shah, For comparison, the elastic moduli of native cellulose, hemicellulose, and lignin, which are the principal polymer constituents in plant cell walls, are estimated using computational models to be in the range of 74—, 7—8, and 2—4 GPa, respectively Shah, While measuring the exact properties of the different tissue and cell types is difficult Karam and Gibson, , an appreciation of their relative contributions to the mechanical properties of a stem has been reflected in experimental investigations.
For example, testing grasses with a dense outer shell comprising sclerenchyma, vascular bundles, and collenchyma and a pithy core comprising mainly parenchyma, but also some collenchyma and vascular bundles , Karam and Gibson measured the stiffness ratio of the shell to the core to a range between 10 and Similarly, Kohler and Spatz separated the outer tissues and inner core of the herbaceous dicot Aristolochia macrophylla , and measured the tensile stress—strain curve of each of these for comparison with that of the complete stem, as shown in Fig.
Their results show the outer strengthening tissues made up of collenchyma, parenchyma, and sclerenchyma to have an elastic modulus and strength approximately four times higher than the core tissues phloem, xylem, interfascicular parenchyma, and pith. All these studies validate the idea that collenchymatous and sclerenchymatous tissues are the principle structure supporting cells against tension and bending loads [note that parenchymatous core cells, much like foam cores in sandwich-structured composites, provide resistance to buckling of the stem Gibson, , ].
In woody dicots, Onoda et al. Stress—strain curves for parts of a stem of Aristolochia macrophylla from Planta, Micromechanics of plant tissues beyond the linear—elastic range. Figure 4 illustrates the hierarchical and multiphase nature of stems. From the view of micromechanics, stems can be analysed as laminated fibre-reinforced composites Speck and Burgert, , Gibson, , Hofstetter and Gamstedt, , Faisal et al.
Plant stems have a hierarchical structure Phyllostachys pubescens bamboo, a herbaceous monocot, as an example. The stem comprises multiple cell types and therefore can be analysed as a cellular solid. Stems may also be considered as multiscale composite structures, with sclerenchyma fibres in a matrix of parenchyma cells, and the fibres themselves as multilayered cellulose fibril-based composites.
As fibre-reinforced composites, one can simplistically consider vascular tissue bundles e. Each lamina is then regarded as a fibre-reinforced composite composed of helically wound cellulose microfibrils, oriented at specific angles to the cell axis, embedded in a pectin—hemicellulose in primary cell walls or lignin—hemicellulose in secondary cell walls matrix Bledzki and Gassan, ; Gassan et al.
Cellulose fibrils are substantially up to 40 times stiffer than pectin, hemicellulose, and lignin Shah, In sclerenchymatous cells, since the S2 cell wall layer, which is the second sublayer of the secondary cell wall, is typically substantially thicker than all other layers combined, one could simplify this model Gassan et al. The principal governing factors in such a model Equation 2 are the cellulose content and microfibril orientation in the S2 layer Bledzki and Gassan, ; Shah, On the other hand, given the cellular and in some cases porous nature of plant stems, describing their behaviour through cellular solid micromechanics is attractive Fig.
Sclerenchymatous cells are tube like long, slender, and often tapered , forming a honeycomb-like structure, while parenchymatous cells are box like short and flat , forming a polyhedral, closed-cell foam-like structure. Their mechanical properties can be described by the properties of the solid material and the relative density of the cell Equation 3 Gibson, , ; Karam and Gibson, At the macrostructural level, the key parameters that affect stem mechanical properties and behaviour fall broadly into three categories: i composition; ii geometry; and iii structural features.
Basic dry density dry mass per unit of fresh volume is a useful indicator of composition in biological systems. The density of a plant stem increases with the solid fraction i. Apparent through Equation 3, there is a strong, positive correlation between density and mechanical properties, both stiffness and strength Fournier et al.
Indeed, density is considered as an easy-to-measure property for structural timber, and therefore it is used as one parameter to segregate timber into structural grades, based on extensive empirical data Forest Products Laboratory, ; Ridley-Ellis, Moreover, density affects both longitudinal and transverse mechanical properties, and therefore anisotropy: in comparison with dense stems, light stems tend to have a lower transverse strength relative to longitudinal strength i.
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Consequently, when bent, stems of lower density fail by local buckling in the compression zone, while stems of higher density break by tensile fracture, exhibiting longitudinal cracks Ennos and van Casteren, This explains why plant stems grown in shaded environments, having lower density, fail by buckling in the compression zone, while stems of the same species grown in artificially adjusted light, having higher density, break via catastrophic longitudinal crack propagation Ludwig et al.
Notably, this serves as an example of how a difference in growing conditions and habitats may have a non-trivial impact on the mechanical behaviour of plant stems. Indeed, the relationship between growth and density is more complex. Softwoods with very wide growth rings have a lower density than softwoods with small growth rings.
Manual on Experimental Methods for Mechanical Testing of Composites
In ring-porous hardwoods, it is vice versa. These effects, of course, tend to be larger in longer running and time-dependent tests, such as creep and cyclic loading. The fibre saturation point also defines the point above which any change in moisture content has little effect on mechanical properties, but below which strength and stiffness increase substantially with decreasing moisture content Forest Products Laboratory, The existence of a fibre saturation point in other plant stems is expected, although yet to be investigated in detail, and humidity and temperature and consequently moisture content would therefore be expected to influence mechanical properties.
While a fresh or living stem would be above the fibre saturation point, once cut for testing, moisture content may drop rapidly, reaching equilibrium moisture content typically below the fibre saturation point. Systematic stem tests would require control of these moisture-influencing factors, including dwell times between stem preparation and testing, and conditions during preparation, storage, and testing. An important consequence of the living nature of plant stems, and the dependence of growth, morphology, composition, and properties on environmental conditions, is that any analysis of stem mechanical properties, and resulting statistical analysis of the data, should be based on several repeats at least 10 over a number of biological replicas at least three.
Geometric factors, such as the stem cross-section shape and dimensions, can affect stress development within a stem, and consequently its behaviour and properties. There is a large diversity in stem sectional shape: stems can have circular and elliptical as in Euphorbia peplus , polygonal including triangular as in Carex pensylvanica , square as in Mentha piperita , hexagonal as in Dipsacus sylvestris , octagonal as in Sericocarpus asteroides , and even non-polygonal cross-sections Smith, For solid, isovolumetric stems, the orientation of load and the neutral axis as a result; see Fig.
For example, while square cross-section stems with the neutral axis through opposite vertices i. Consequently, stems with square cross-sections often have most of the strengthening material i. Schematic of a square cross-section stem with the neutral axis a passing through diagonal vertices and b bisecting the sides of opposite cells at the corners, to support bending stresses that arise when the neutral axis passes through opposite vertices as in a Smith, It has been experimentally shown that non-circular stems are characterized by higher twist-to-bend ratios Niklas, , which is a strategy against typical stresses, such as buckling and bending Vogel, , , ; Etnier and Vogel, ; Etnier, Specifically, higher ratios, as in triangular cross-section stems of sedges, enable the stems to shed wind loads by twisting readily into low-drag configurations i.
Other than the cross-section shape, which is usually irregular and can change with factors such as moisture content e. The effect of inaccurate dimension measurements on the second moment of area would be even more substantial due to a fourth power effect , leading to grossly incorrect bending stiffness and strength. Upon experiencing mechanical loading, such as during wind flexing, plants actively modify growth and development processes; this phenomenon is well known as thigmomorphogenesis. Thigmomorphogenesis significantly influences stem mechanical behaviour Badel et al.
Stems may also have a taper in their cross-section with increasing height. In general, in the absence of critical defects and constant material properties, mechanics would dictate failure to occur where stress is maximum, namely at the smallest cross-section. The extent of taper would dictate ideal gauge lengths to use during testing. A critical aspect of stem sectional properties is their hollowness ratio. This is a logical solution when biomass production is a constraint. While not all plant stems have a central cavity e. The hollowness ratio represents the ratio of rind thickness to stem diameter.
This ratio determines whether the stem is thin walled or thick walled, thereby governing its failure mechanism Wegst and Ashby, The core is a foam-like, parenchymatous, compliant material, whereas the dense, sclerenchymatous outer shell rind is stiff. Despite being compliant, the core provides buckling resistance under axial compression and resistance to kinking failure under bending load. The improvement in buckling and bending capacity of the stem is related to the hollowness ratio and the ratio of the elastic modulus of the core material to the rind material Gibson, Stems can improve both local and global properties by incorporating and modifying structural features, such as nodes and preferential distribution of stiffening fibres to the outermost parts of the stems.
If stems are analysed purely on the basis of their overall bending stiffness, then locating stiff fibres towards the outer edge of the stem is advantageous, as tensile and compressive stresses under bending load increase away from the central axis Fig. Schulgasser and Witztum showed, however, that this encourages failure by local compressive buckling or kinking, both of which involve the buckling of groups of fibres within the stem, rather than the stem as a whole.
This can be shown by the theory of composite materials to occur because the shear strength of the outer material does not increase as rapidly as its compressive strength Schuerch, Local compressive buckling may be particularly prevalent in hollow stems such as reed and bamboo Niklas, Such stems have often developed to be septate, where diaphragms at nodes act to restrain the wall against this form of failure Robertson et al.
Nodes are a common feature in many hollow stems, particularly grasses, that prevent local buckling and provide transverse reinforcement. Nodes can also act as spring-like joints to store and release energy when subjected to axial or transverse forces Niklas, b , However, stress and strain gradients at the interface of nodes and antinodes results in these being likely sites for failure when subjected to axial or bending loads.
The stress and strain gradients are a result of changes in microstructure e. Bending moment is represented by the solid curved arrows at the beam ends. Adapted from Ennos and van Casteren Junctions and nodes e. This is well known in wood science, where knots stem—branch junctions in trees are counted to assess the quality of the wood.
Knots have a local increase in microfibril angle and density to improve local fracture toughness and density by promoting mixed modalities in failure Speck and Burgert, This refers to a system where turgor pressure from internal fluids withstands compressive loads, while the sclerenchymatous rind supports tensile loads. A drop in turgor pressure, visually observed as the wilting of a stem when a plant is not watered, leads to buckling. Turgor pressure can also pre-stress and stretch the internal cell walls of the stem Karam and Gibson, When measuring the mechanical properties of stems that do rely on turgor pressure for support, it is important to control the turgor pressure of the system, or account for it when analysing the data.
For example, Paul-Victor and Rowe conducted turgor tests on Arabidopsis stems prior to mechanical testing. Excised stems were tested for bending properties at regular intervals to examine the effect of loss of turgor pressure on mechanical properties. Sealing segment ends, and either rapid testing or significantly delayed testing segment extraction Robertson et al.
Some researchers have also submerged plant stem tissues into osmotic solutions to adjust the turgor pressure before testing Falk et al. There are also methods to predict and back-calculate the properties of the solid cell wall material for any turgor pressure Nilsson et al. In general, the models suggest that the relative stiffness ratio between the cell walls and the stem is proportional to the ratio between the internal turgor pressure and the stem stiffness. For reference, turgor pressure varies between 0. Table 1 lists typical tests that stems are subjected to for mechanical property measurement.
In nature, plant stems most commonly fail due to a bending moment by either yield or local buckling on the compression edge Fig. Both of these failure types originate from the axial stress dashed straight arrows in Fig. Consequently, flexural testing has become an important tool to assess stem mechanical properties. A pure bending test does not fully replicate conditions in nature, however, where failure may be due to a combination of axial overload, from the weight of the plant and anything supported by it e. An understanding of the response to combined loads may be gained through modelling or calculation based on the fundamental properties of the stem material.
In flexural tests, specimens are subjected to mixed-mode conditions, with tensile and compressive stresses arising linearly on opposite sides of the neutral axis, and shear stresses increasing to a maximum towards the neutral axis Fig. It can be difficult, therefore, to identify the fundamental mechanical properties of the stem material from such a test.
Axial load testing has therefore been used to measure the elastic modulus or stiffness and tensile strength or failure load of stem tissue material or stem structures , which may be different in tension and compression. Furthermore, plant materials exhibit time-dependent, viscoelastic behaviour, as they are based on polymeric building blocks i. The full mechanical characterization of stems, therefore, requires tests which include a time component of load.
This can be in the form of creep sustained constant loading , stress relaxation sustained constant deformation , or cyclic loading as in oscillation due to wind loading. Here, these various possible testing methods are discussed and evaluated. Recommendations are also given in designing suitable test procedures. To estimate stresses in the material due to a force applied to the structure, some geometric properties of the stem cross-section are required.
As discussed earlier, the accuracy of these cross-section properties can have a significant impact on the accuracy of stress estimations. In flexural tests, the second moment of area of the cross-section is required, so not only the transverse area, but also the shape of the cross-section must be measured or assumed. In shear, the cross-section shape also affects the distribution of stress. In the literature, it is most common to assume a cylindrical stem, and measure its diameter or width and possibly rind thickness if hollow , at one or more points along its length Skubisz, ; Lemloh et al.
Microscopy may be used to justify the assumed section shape after testing Lemloh et al. A more direct assessment of second moment of area, and of the contribution of the different tissues to bending stiffness through image analysis, is possible Moulia and Fournier, We recommend this to become more common practice. Under axial loading, only the cross-sectional area is required, which may be determined either indirectly or directly. There are two principal indirect methods. One approach is to determine the total volume of a stem segment of known length by a volume displacement technique Skubisz, ; this, alongside a known mass of the segment, would yield an estimate of the average cross-section area.
Another indirect measurement technique, borrowed from textile engineers Shah et al. This, combined with either a measured density of solid cell wall material using gas pycnometry, for instance or an assumed density, would give an estimate of the average cross-section area of solid cell wall material resisting the applied load neglecting the hollow lumen Cosgrove, ; Shah et al.
Direct measurement techniques, in the case of small stems less than a few millimetres in diameter , include the use of X-ray micro-computed tomography CT scanning prior to testing Zeng et al. The latter can be done by mounting stems vertically onto card frames and even casting these into resin blocks which are then polished for imaging Thomason et al. For larger stems e. Direct measurement of stem cross-section area can be done by confocal microscopy a of a fresh Arabidopsis stem , optical microscopy b [from Shah et al.
Flexure can be induced in a stem by any applied load which includes a pair of loads forming a couple. This is most simply done using a cantilever fixed at one end and loaded at the other. Cantilever, or two-point, bending can be carried out on in vivo stems in a pot Caliaro et al. This is particularly useful where turgor pressure is expected to play a significant part in the mechanical resistance of the stem, as was the case for the Abutilon theophrasti tested by Henry and Thomas and Caladium bicolor by Caliaro et al. The American standard test method for flexural testing of tree stems is a cantilever test ASTM, The drawback of this technique is that the largest shear stress occurs in the same area as the largest bending stresses, making it difficult to isolate the two effects to estimate the fundamental properties of the material under test.
For large deflections, more complex equations and computational methods may be required to determine the mechanical properties Morgan and Cannell, ; Vogel, This is because the equilibrium equations based on the undeformed shape are no longer valid after substantial deformation. Alternatively, paired measurements of change in curvature and bending moment can be made Moulia et al. The latter arises from self-weight and tip-load of some stems.
In three-point bending, the largest bending deflection is at mid-span, and the highest shear near the supports. This is the most common form of mechanical test carried out on stems Skubisz, , ; Lim et al. The deformation is characterized by a single displacement measurement at mid-span , and no clamping is required: the stem rests on two simple supports, and is subject to a point load. This test set-up has been applied for spans from a few millimetres Lemloh et al.
The stem segment to be tested must be sufficiently slender that the contribution of shear to the measured deflection is small. Shear leads to an underestimation of strength and elastic modulus van Casteren et al. Standards for tests on small timber specimens use a span-to-depth ratio of 14 BSI, The span-to-depth ratio i.
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For example, for solid stems, researchers have suggested a minimum span-to-depth ratio of 20 van Casteren et al. In a mechanical study of 42 grass species which included hollow and solid stems , Evans et al. Other studies have suggested that, for example when testing the stems of the herbaceous dicot A.