Abstract
A new micro-mechanical method for textiles dating was applied to flax fabrics. Notwithstanding that environmental factors like temperature and humidity can influence the mechanical parameters of ancient textiles, the method shows a relatively stable trend if some previous analysis is done to eliminate degraded samples. This method is based on a multi-parametric analysis of single fibers tested on a proper machine designed and calibrated for the purpose. Single fibers mounted on special supports are submitted to mechanical test consisting of multiple stress–strain cycles. The parameters sensitive to aging are tensile strength, Young modulus, and loss factor, the last two evaluated during particular phases of loading cycles. Five different calibration curves relating age to these mechanical parameters are determined by using a series of eleven textiles of known age from 3250 BC to 2000 AD that passed a proper pre-selection. The resulting age of the textiles derives from a combination of five independent dating. The relatively small number of textiles used for the analysis, due to the fact that it is not easy to find ancient textiles, gave results that can be improved by future analyses addressed to test a larger number of samples. For the moment, the relative standard uncertainty of the method is about 200 years but future test could reduce this uncertainty. This relatively simple method can also be useful to museums which wish to date themselves ancient textiles at low cost.
Introduction
Tension testing on single fibers is a widely used method in evaluating fundamental properties of textiles. Many research projects have been carried out to investigate the mechanical properties of natural fibers and also to improve the interfacial adhesion of fibers by chemical modification. 1
Mechanical testing of cellulose-based natural fibers is performed by applying tension loading with the use of either a standard tensile machine or a self-made device equipped with a stepper motor connected to displacement and force measurement gages.2,3
Tension tests provide information on the strength of natural fibers and produces stress–strain curves, 4 from which many parameters relative to the mechanical behavior of the fibers are obtained. Among them are the tensile strength, yield strength, elastic modulus, and percent elongation. Breaking strength and strain, together with the Young modulus, are frequently studied mechanical parameters of single fibers.
ASTM standards specify test conditions with reference to samples directly extracted from a plant and various experimental setups and measuring methods have been proposed to test mechanical properties of natural fibers.5,6 For example, the tensile behavior of elementary flax fibers glued onto a cardboard frame was studied under static and cyclic loading conditions with a standard strength machine. 7
Also, the mechanical behavior of fibers under loading–unloading cycles has been studied for tensile fatigue test. 8 Loading cycles have been only used to evaluate traditional parameters with no reference to the loss factor. Know-how based on space structure can be used in the present case to consider this important mechanical parameter too. Some studies have focused attention on the mechanical parameters relative to a multi-strand cable;9–11 the structural task was assigned to a strand made of Kevlar fibers. Both the mechanical behavior of the Kevlar strand and that of the whole cable have been characterized by the study of loss factor. Moreover, Yu et al. confirmed the absence of bibliographic references regarding the viscous behavior of fibers because only the stiffness has been studied as a function of the number of cycles. 12 Single wood-pulp fibers, 1 ramie yarns, 13 and flax show an increase of stiffness with number of cycles: 7 this behavior is assumed to be connected with changes in microfibril angle7,14 that produce a packing effect on the fiber. 10
The lack of tests found in the literature regarding ancient fibers can give a problem related to the fact that the breaking strength of modern fibers is much higher than that of very ancient fibers. This problem, coupled with others relative to some design criteria described in the methods section, meant that the authors faced a practical impossibility in the use of standard strength machines to test these fibers and the consequent necessity to design and build a new machine capable of measuring loading cycles characterized by lower tensions (corresponding to forces of a few µN) by using an analytic balance instead of a standard load cell.15,16
Mechanical analysis could supply investigation methods based on breaking strength, Young modulus, and loss factor useful in the field of dating because of their supposed correlation between a mechanical property and the structure of a given sample.
In the literature, the evaluation of the probable age of a cellulose-based handwork is normally carried out by using radiocarbon dating, 17 a relatively expensive and destructive method, not always easily applicable. On the other hand, museums have not always the necessity to know the date of samples with accuracy higher than a century to allocate them to a particular historical period. It is in this context that alternative dating methods, primarily those that are non-destructive and also cheaper, can be useful; a recent example is the dating of single fibers coming from ancient flax textiles using vibrational spectroscopy and in particular Raman and FT-IR methods. 18 The method proposed in this paper will therefore be useful, especially if used in comparison with these new methods as an alternative to radiocarbon dating. These dating methods could be primarily addressed to ancient textiles preserved in museums and recovered from excavations because it is important to assign a specimen to a certain historical period.
Natural vegetable textiles undergo a spontaneous and irreversible degradation as a function of time; in particular the polymerization degree of cellulose diminishes with time, thus reducing the crystalline part and increasing the amorphous cellulose. This variation influences the mechanical properties of the vegetable fibers, which can in some way be related to a historical period.
This degradation can be additionally accelerated either by environmental factors, 19 such as temperature, light, moisture, and soil acidity, or by attacks from lichens, molds and mites, and rotting. A first problem is the following: do these environmental factors affect the mechanical results relative to ancient fabric in such a way to mask the possible relation between a particular mechanical property and corresponding age? From the results that will be discussed in the comment section, it appears that these environmental effects show a relatively small bias if a proper preliminary selection of fabric is performed. If, therefore, the relative uncertainty of the dating method is sufficiently increased at the order of very few centuries, the possibility of relating a mechanical property to the historical data of a flax fabric is increased.
The present research is the first systematic approach to the study of the mechanical properties of ancient flax textiles. A series of samples of various historical periods has been acquired, coming from different geographic areas and environments. They have been analyzed by recording mechanical parameters relative to their loading cycles. The samples under examination date from about 3500 BC to present with the aim of determining correlations between date and one of their mechanical properties.
After a preliminary selection that dismissed some samples, only 11 samples have been used to build calibration curves, as it is not so easy to find ancient flax textiles for tests; future research will be addressed to the improvement of the accuracy of the resulting calibration curves.
Materials
Samples of new and ancient flax textiles from different archaeological sites have been analyzed. As the effects of environmental factors, such as temperature and humidity, can change the mechanical properties, in agreement with Hu et al., 20 an initial screening was performed in order to choose sufficiently undamaged flax fabrics. A preliminary analysis based on visual inspection by means of a stereomicroscope was performed, so as to select only samples suitable for the tests.
List of flax samples used for the tests, in order of date
To avoid testing fibers with defects, the following rules for sample selection were adopted, before subjecting the samples to the test. A sample must overcome:
a visual test consisting of a microscope analysis in the range 10 × –100 × in which the fabric color is also considered; a visual test consisting of a microscope analysis in the range 100 × –600 × using cross-polarized light to evidence structural defects of the fibers like micro-cracks; a preliminary mechanical test consisting of the analysis under microscope of the behavior of single flax fibers subjected to bending to check macroscopic anomalies. In addition to the specimen selection based on opto-mechanical type, two sample exclusion criteria have been applied after the test in order to consider the micro-damage and contamination not visible under stereomicroscopic analysis: fibers with an evident anomalous stress–strain curve have been excluded; a comparison between breaking strength σr has been done within each sample series. The average breaking strength σav has been evaluated and specimens having breaking strength σr falling outside the interval σav/K ≤ σr ≤ Kσav have been excluded. K has been assumed 2.5 ± 10% in the present case.
The sampling procedure is delicate because the tweezers must not crush or press too much the fiber under test. In addition, all the fibers of the present analysis have been selected from the external part of the flax thread. The mechanical results, in fact, have been revealed that they are quite sensitive to the position of the fiber in the thread.
Two samples of new flax fabrics, namely A and B, have been selected for comparison; sample A has been sized and bleached (using sodium hydroxide), while sample B is natural. Two samples, DII and D, of flax coming from Jericho (Israel) and Fayyum (Egypt), respectively, have been selected to represent a medieval age. Sample FII, coming from Masada (Israel), has been chosen to represent the Roman period of the first century AD, while samples NI from Lima (Peru), NII from Engedi (Israel), and E from (Egypt) have been selected for the first Roman age. Three samples, HII, K, and LII, coming from Egypt, have been selected to represent the period ranging from about 1000 BC to 3500 BC.
Number of samples tested for the dating procedure. This table only reports flax fibers that overcome the preliminary selection (rules a, b and c). Unsuccessful test was also caused by fiber ruptures during the positioning of the tabbed fibers in the machine
Methods
A new micro-cycling machine has been designed for the measurement of single fibers extracted from flax fabrics. A fiber has irregular cross-section of polygonal shape variable along its length, therefore many methods for its measurement have been proposed. A circular cross-section has been supposed and it has been measured at nine or at four positions along the fiber length using an optical microscope.21,22 In other cases, the diameter of the flax fiber is calculated by observing it in two perpendicular directions along the fiber length and assuming the smallest one. The more expensive cross-section measurement at breaking point has been applied not only to flax fibers, but also to sisal 22 and bamboo fibers. 12
The following hypotheses have been chosen: the flax fiber is a cylinder without voids, is homogeneous and isotropic, having circular cross-section A of constant diameter d (ranging from 5 to 25 µm), Young modulus E (in the range from 0.1 to 100 GPa), and simply subjected to a normal tensile force F, according to the equation:
It is supposed that these model hypotheses produce a standard uncertainty lower than 5%, if an additional hypothesis is considered: the diameter of the real fiber is that of its smallest cross-section because it is supposed that there it breaks. Taking advantage of information reported by Eichhorn et al. and Symington et al.,1,2 a micro-cycling machine has been built (Figures 1 and 2),15,16 trying to satisfy the following design criteria within a design uncertainty of the measured results better than 10% (the design uncertainty is intended here as the target uncertainty that an engineer defines before starting his design and it is useful as a comparison among the various uncertainties encountered during experiment planning):
– to measure cycles in correspondence of stresses ranging from zero to 2/3 of σr (breaking strength) with resolution better than about 100 measurement points per cycle; – to measure elongation λ of single fibers having serviceable lengths from 1 mm to 30 mm; – to measure elongation λ of 1% with a resolution of 0.1 µm; – to measure forces F from 0 to 0.5 N, with a resolution of 2 µN. (a) Schematic drawing representing the mechanical components of the micro-cycling machine for tensile tests of individual textile fibers. 1 – carrier beam; 2, 3 – columns; 4, 5 – bases regulated by screws; 6 – support blocks; 7, 8 – clamping blocks of the cantilever beam 9; 10 – micrometric screw gage coupling plate 11. (b) Schematic representation of the micro-cycling machine: cantilever beam 9 transfers, reduced, the displacement of screw gage 10 to the flax fiber; the corresponding force is measured by the analytical balance. (a) Photo of the micro-cycling machine. Depending on the reduction factor, the analytical balance is shifted so that the vertical axis of its plate coincides with the axis of the hook to be used. (b) Measurement detail with enlargement, on the left, of the special polyester mask in which the flax fiber is clamped (shown by the two arrows).
Calibration parameters, force and displacement, of the micro-cycling machine related to the reduction nominal factor of 1/20 (measured of 1/18.94) that has been used to perform the tensile tests.
The cantilever beam (9) of Figure 1a is in fact used as a vertical displacement reducer and the reduction factor of the imposed displacements depends on the distance from the clamps. The nominal reduction factor of 1/20, always used in the present analysis, derived from a theoretical evaluation and it corresponds to a measured reduction of 1/18.94 due to the fact that the designed clamp is obviously not perfect.
Starting from a zero-force condition applied on the fiber, the increasing displacements imposed by the micrometric screw gage (element 10 of Figure 1a) are registered with the corresponding forces read on the display of the analytical balance. In this way, the operator reaches about two-thirds of the breaking strength of the fiber under analysis and then begins to reduce the imposed displacements up to about a zero-force condition. This procedure is repeated for n-cycles.
Results
The Young’s modulus of natural fibers like hemp and jute decreases with increasing fiber diameter;23,24 but for flax fiber, contrarily to its breaking strength, the Young’s modulus seems to not depend on the fiber diameter if the diameter is measured near the rupture plane of the tested fiber with a scanning electron microscope. 25 For this reason, the diameter of the fiber has been measured in correspondence of the smallest cross-section of each specimen, using a vision system connected to a microscope.
In agreement with previous studies,23,24,26 the dependence of mechanical parameters on diameter, length, and environmental humidity of the laboratory has been considered. Thus, the measured stress σ of flax fibers, having various sizes, has been modified with respect to a reference flax fiber characterized by the following properties:
15
– length L between the two clamps: 1.0 mm; – diameter d: 15 µm; – relative humidity H: 50%,
considering the influence factors for linen fibers taken from Torluf.
26
The strain has not been changed while, using an affine transformation, the measured stress has been transformed into the stress σs according to:
The equation for the length coefficient KL is obtained interpolating with a line the data reported in a plot in Torluf. 26 A linear behavior in the length range 0.5–15 mm with the same slope of the line that fits the first two points of the technical flax fibers’ series and with constant term fixed at 1.5 GPa has been assumed. The equation of the diameter coefficient Kd (range 4–40 µm) corresponds to the ‘fitted line’ interpolating the flax data reported in the plot by Torluf. 26
Environmental factors can influence the mechanical properties of most of the cellulose based natural fibers and humidity is very important. Torluf reports that flax fibers are characterized by an increment of strain and tensile strength with increasing relative humidity, 26 even if not all agree. 2 A tensile strength versus humidity behavior according to Torluf has been assumed here. 26
The equation of the humidity coefficient KH is obtained (in the range from 30% to 65%) from the Torluf plot, 26 assuming the slope corresponding to the line of 3.5-mm-length. The gage lengths of the studied samples are actually less than 3.5 mm (they are between 0.75 and 1.65 mm), but no diagrams for such short length are available in the literature.
Following the proposed transformation, the dispersion of the data reported in the resulting plots has therefore been reduced. Figures 3a and 3b report an example of the resulting loading cycles relative to single flax fibers, whose stress–strain curves are in agreement with those obtained by Andersons et al.
27
It is obvious that the last cycles are the best ones for the calculation of the elastic parameters because sliding and plastic effects are generally typical of the very first cycles.
(a) Typical σ–ɛ cycles of a single flax fiber (Sample DII – 4, L = 1.4 mm, d = 20.6 µm). (b) An example of an inverse loading cycle.
Plastic effects are evident in the first cycle of Figure 3a where a non-reversible change of shape in response to applied force is shown. Sliding effects instead are due to instantaneous changes of the internal structure of the fiber, probably due to changes of the position of the bundle of microfibrils composing the flax fiber. This is clearly visible in a stress–strain plot as a sudden strain variation without a corresponding stress variation.
From Figure 3a, it can be seen that the first cycle (on the left) shows the presence of evident plastic effects probably also connected with the external thinner layer of the flax fiber that is stiffer than the inner very thicker cellulosic layer; the external layer therefore breaks easily producing the mentioned plastic effect. These breakings of the polysaccharide external layer, frequently positioned in correspondence of fiber kink bands, 28 are visible under cross-polarized light.
After the first cycles, Figure 3a presents cycles having a higher slope, thus showing both an increase of the Young modulus and a wider range of linear elasticity.
From a study of these plots, the following parameters, useful for the present analysis, can be evaluated.
– Breaking strength σr; – Young modulus Ef relative to the last part of the increasing loading cycles. Because the curve is not linear, the final part seems representative because it is more linear. – Young modulus Ei relative to the first part of the decreasing loading cycles (also named ‘inverse’ because relative to the inverse direction of the cycles). As the curve is not linear, this initial part seems representative because it is more linear. – Loss factor ηd relative to the last complete loading cycle representing the dissipated energy. The loss factor η is defined as:
Loss factor ηi relative to an inverse loading cycle. This is evaluated in reference to the last unloading phase of the cycle coupled with the last loading cycle that produced the fiber breaking (Figure 3b). This parameter is more significant than the previous one if the loading cycles are not too much numerous as in the case of premature breaking of the fiber under examination. Breaking strength σr relative to the flax fabrics reported in Table 1 as a function of textiles ages. Young modulus Ef relative to the flax fabrics reported in Table 1 as a function of textiles ages. Young modulus Ei relative to the flax fabrics reported in Table 1 as a function of textiles ages. Loss factor ηd relative to the flax fabrics reported in Table 1 as a function of textiles ages. Loss factor ηi relative to the flax fabrics reported in Table 1 as a function of textiles ages.
The mechanical parameters have been evaluated for the flax fabrics reported in Table 1: Figures 4–8, respectively, show the resulting breaking strength σr, Young moduli Ef and Ei, and loss factors ηd and ηi as a function of textiles ages.
Results relative to samples A and B
The limited availability of ancient textiles dated with relative uncertainty has been partially compensated by the fact that many fibers have been tested from the same sample, thus reducing the repeatability uncertainty. For example, 14 fibers taken from sample A have been tested and 15 fibers from sample B (Table 2).
As straining fibers coming out from different twisting conditions can produce different results, the fibers of each sample have been all picked up using the same procedure, taking them from the outside of the thread. A comparison among the mechanical results obtained in this way and those relative to different picking up procedures showed an evident bias. This suggests building different calibration curves as a function of the procedure adopted to select the fibers and this problem will be faced in the future.
In agreement with the BIPM guide, 29 the standard uncertainties are reported (because these data have to be further combined during the multi-parametric evaluation).
The interpolation curves with Pearson’s correlation coefficient R are the following:
Different behavior is manifested instead in the cases of loss factor that, not being directly related to the strength of the cellulosic chains but to the energy dissipated during strain application, seems better correlated to a linear model.
Starting from equations (8)–(12), has been named by authors Mechanical Multi-Parametric Dating Method a technique capable of combining the five mechanical dates in one unique value relative to the historic data of the sample in question. The resulting dates with reference to each of the five parameters can be obtained by inverting equations (8)–(12) and solving for x.
The resulting data in years yxx (positive if referred to AD or negative if referred to BC, where xx refers to one of the five mechanical parameters in question) has been therefore calculated. The value ym1 corresponding to the MMPDM obtained by averaging the five results is:
The uncertainty of the historical dates derived from the mechanical parameters calculated from equations (13) and (14) is therefore reduced to a standard uncertainty of about 200 years. The second result of 372 AD seems more reliable for the reasons mentioned above, and it is compatible with the previous one of 220 AD.
It must be observed that another parameter related to the reliability of the mechanical dating is the compatibility of the resulting dates obtained from equations (8)–(12) because they are relative to properties of the cellulose that are subjected to opposite bias if the flax fibers are subjected to environmental factors capable of changing the mechanical behavior.
From some experimental tests, for example, it is found that ancient fibers previously subjected to mechanical damage (repeated flexing and scraping) show non-mutually compatible dates, furnishing results too old relative to tensile strength and Young moduli data, and results too young relative to loss factor.
Comments
Due to the fact that it is not easy to find ancient textiles to be tested, this work has been preliminarily done on a reduced number of samples. Notwithstanding this, the calibration curves determined are in agreement with the theoretical models. Both breaking strength and Young moduli exhibit an exponential behavior between age of the sample and mechanical feature linked to the kinetic model of natural cellulose degradation as a first-order reaction. The loss factor instead shows a linear increase with age that can be related to the breaking of cellulosic chains with time; this produces an increase of sliding among the chains, thus increasing the dissipated energy.
The study of a possible correlation between a mechanical property and the age of the corresponding textile has not seemed viable up to now, because it is well known that environmental factors can drastically alter the chemical structure and therefore also the mechanical properties of the flax fibers under test.
This analysis shows that, if proper shrewdness is taken into account, the bias due to environmental effects can be reduced and therefore a more or less rough mechanical dating is possible. The data dispersion reported in Figures 4–8 appears to be due to environmental factors that obviously increase the variability of the mechanical behavior of the flax fibers, but this dispersion is not so high as to prevent a rough dating. Future detailed analysis of the influence of the environmental factors could then reduce the detected dispersion, making this method more competitive.
As has previously been discussed, some preliminary analyses are necessary to select textiles properly for the tests and therefore to discard other ones that are too much degraded. Also, the position of the fiber in the twisted thread is important because it means that fibers more external to the thread show a slightly different behavior than fibers taken from the middle of the thread, which are obviously more protected. This work is based on fibers coming from the external part of the thread, but future analyses should also produce calibration curves relative to fibers coming from the middle of the thread.
Temperature and humidity can in some case greatly affect aging, thus drastically changing the mechanical properties of the fibers. The interesting fact detected by the authors is that major effects can be evidenced by a preliminary procedure addressed to discard the samples highly influenced by environmental factors. The fibers remaining after this selection are also affected by these factors, but their effects on calibration curves can be restricted within a standard uncertainty of about 200 years.
Humidity becomes, therefore, an environmental factor that is not very influential in the analysis if a proper textile selection is performed. This is so because humidity both damages the chemical structure and darkens fiber color, thus altering the mechanical behavior of these fibers, and therefore are quite simple to discard during a preliminary selection.
Exposure of flax textiles to relatively high temperature (200℃ for some hundreds of seconds) can alter the mechanical properties of the fibers, thus producing bias of some hundreds years coupled with a more brownish coloration. Therefore, a darker color of the textile can be the sign of an exposure to heat sources. If, instead, the color of the textile is not appreciably different form the original one, it can be supposed that the bias produced by a heat source can be less than one century.
As has been discussed in the results section, the MMPDM performs a mutual comparison among the dates resulting from five different mechanical methods; this comparison also gives information about the goodness of the results: in fact samples altered by environmental factors give non-compatible dates.
From the stress–strain plots relative to multiple loading cycles it is found that the fiber stiffness of flax increases after the first 3–5 cycles, probably because of the packing effect of the microfibrils. This fact cannot be neglected in the use of natural fibers employed for reinforcement in polymer matrix. To the advantages with respect to currently used glass and carbon fibers, 32 such as low cost and density, reduced energy consumption, recyclability, and relatively high tensile properties, it could therefore be added that an increased stiffness that will make flax fibers more preferable than glass or carbon especially if properly pre-tensioned.
Conclusion
This work proposes a new relationship between age and the combination of five mechanical properties of ancient flax textiles using 11 samples, resulting from a preliminary selection, dated from about 3250 BC to 2000 AD. In fact, it is necessary to eliminate degraded samples from the analysis because environmental factors can influence the results. An example is a long conservation time in humid environments (e.g. Akeldama shroud of Jerusalem) that alters mechanical behavior of the fibers. This selection is based on visual inspection, also using an optical microscope and on proper bending tests of single fibers.
As it is not easy to find ancient textiles, this work has been preliminarily done on a reduced number of samples but the calibration curves are in agreement with the theoretical models. The MMPDM proposed here appears promising. The correlation curves allow definition of relations (see equations (8)–(12
Experiments now under analysis on flax textiles exposed to heat sources seem to show the presence of systematic aging effects coupled with color variation, but the resulting bias is less than a century if the sample is exposed to heat sources lower than about 150℃ for some hundreds of seconds.
The combination of the calibration curves at present gives the possibility to make a rough dating of ancient flax textiles, but future calibration based on a greater number of samples will significantly improve the MMPDM’s accuracy. Therefore, this method could be an alternative to others, such as the more accurate radiocarbon dating that works within some tens of years but requires destruction of larger amounts of textiles and has higher costs. Therefore, this mechanical method of dating at low cost could be of interest for archaeological museums which are interested in rougher measurements of their samples.
Footnotes
Funding
This work was supported by the Padua University, Scientific Research Fund (ex 60%) (grant number 60A10-8854/11).
Acknowledgements
Particular thanks go to Orit Shamir of the Israel Antiquities Authority in Jerusalem, who very kindly furnished many ancient samples of flax fabric, to the Egyptian Museum of Turin, Italy, to M. Moroni and A. Guerreschi, and to M. Alonso, who also supplied ancient samples. The authors thank the five reviewers, who all gave positive opinions, for their useful comments that allowed the paper to be improved.