Strain amplitude controlled fatigue of Flax-epoxy laminates

Journal Pre-proof Strain amplitude controlled fatigue of Flax-epoxy laminates Zia Mahboob, Habiba Bougherara

PII: DOI: Reference:

S1359-8368(19)31342-3 https://doi.org/10.1016/j.compositesb.2020.107769 JCOMB 107769

To appear in:

Composites Part B

Received date : 28 March 2019 Revised date : 23 August 2019 Accepted date : 15 January 2020 Please cite this article as: Z. Mahboob and H. Bougherara, Strain amplitude controlled fatigue of Flax-epoxy laminates. Composites Part B (2020), doi: https://doi.org/10.1016/j.compositesb.2020.107769. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

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Strain amplitude controlled fatigue of Flax-epoxy laminates Zia Mahbooba , Habiba Bougherara∗,a Department of Mechanical & Industrial Engineering, Ryerson University, Toronto, ON, CANADA

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Abstract

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Fatigue longevity and evolving material properties of Flax-epoxy laminates is

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examined under constant strain amplitude cycling. Several recent fatigue studies

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on Flax-composites, all of which were conducted under stress-control, found that

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certain laminates demonstrate a modulus increase over fatigue life, even while

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accumulating internal damage and permanent deformation. This study investigates

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whether such fatigue-stiffening phenomena are also observed under strain-control.

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Specimens of four layups ([0]16 , [0/90]4S , [±45]4S , and [0/45/90/−45]2S ) are tested

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min =0.1. Strain-life (–N ) plots are generated, under 5 Hz and strain ratio R = max

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which are found to follow a consistent trend that can be modelled by a linearised

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relationship with identifiable parameters. No evidence of stiffening is observed. All

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specimens demonstrate stiffness degradation, thereby contradicting previous

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studies. The extent of degradation is proportional to loading applied. A directly

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proportional relationship is observed between strain-rate and measured modulus.

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It is proposed that the reported modulus increase in existing literature does not

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reflect any physical improvement of material stiffness, but is a consequence of

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stress-amplitude controlled loading conditions. As such, strain-controlled cycling

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may be more appropriate for fatigue studies on natural fibre composites.

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Key words: A. Fabrics/textiles; B. Fatigue; B. Plastic deformation; C. Statistical properties; Flax fibre.

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Corresponding author Email address: [email protected] (Habiba Bougherara)

Preprint submitted to Composites Part B: Engineering

August 23, 2019

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1. Introduction Naturally occurring fibres, particularly those extracted from the bast layer of certain plants (like flax, hemp, jute, etc.), have been shown to be sustainable

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alternatives to traditional engineering fibres as composite reinforcement [1–6].

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Plant-based natural fibres are relatively low-cost and lightweight, offer comparable

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density-normalised mechanical properties [4, 7, 8], greater energy absorption at

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high strain rates [9], good thermal and acoustic insulation [7]. They require less

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energy to manufacture [3], are CO2 -neutral [10], are easier to tool, are less toxic

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during processing [3, 10], and result in simpler, non-toxic recycling towards their

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end-of-life [1, 10, 11]. Of all plant fibres, those of Flax (Linum usitatissimum L.)

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have proven to be the best candidate to replace Glass as reinforcing fibres

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[2, 5, 7, 12]. Flax fibres are comparable to, or exceed, Glass in specific strength

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(1300 vs 1350 MPa/g-cm-3 ) [2], specific modulus (20-70 vs 30 GPa/g-cm-3 ) [2, 7],

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cost per weight (0.5-1.5 vs 1.6-3.25 USD/kg) [2], cost per length required to resist

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100 kN (0.05-0.65 vs 0.1-0.4 USD/m) [2], and production energy consumption

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(11.4 vs 50 MJ/kg) [5]. Despite a steadily expanding body of work demonstrating

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the potential of Flax fibres, industry adoption of natural fibre composites (NFC) in

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engineering applications remains hesitant due to a general lack of confidence in

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their mechanical performance – a consequence of the relative immaturity of

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research on the topic, compared to that for synthetic fibres.

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As fatigue-related mechanisms are a common failure mode in dynamically loaded structures, examining fatigue endurance and fatiguing mechanical

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properties is essential for durable, predictable design of load-bearing components.

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To date, research on NFC fatigue behaviour remains limited, albeit with a rapidly

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proliferating scholarly output towards that end [13]. This article describes original

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strain-amplitude controlled fatigue tests of Flax-epoxy laminates, and examines the

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progressive evolution of their damaged-condition modulus and permanent

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deformation. As will be elaborated later, the motivation for this strain-controlled

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investigation is to clarify the unusual stiffening behaviour of certain Flax-epoxy

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laminate configurations as reported by several recent stress-amplitude controlled

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fatigue studies [14–17].

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1.1. Stiffness evolution To-date, tension-tension fatigue studies on Flax-epoxy have revealed an

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unusual behaviour in laminates with 0° plies. When at least half the fibrous

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reinforcement is oriented in the loading direction, the composite modulus is found

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to progressively increase during fatigue cycling [4, 14–17] – instead of

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demonstrating a decreasing trend that is typical of a fibre-composite accumulating

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internal damage, shown in Figure 1(a). This stiffening phenomenon has been

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observed for up to 80% of specimen fatigue life, as shown in Figures 1(b)-(e), after

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which the measured modulus appears to return to the initial magnitude as failure

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becomes imminent. This is not to infer that these specimens were immune to

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material degradation, since the same studies also observed physical micro-cracking

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and reported a parallel increase in permanent deformation (residual strain), which

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are results of internal damaging mechanisms.

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To further complicate matters, similar NFC laminates reinforced by Hemp fibres (which are structurally comparable to Flax in strength, hierarchical

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microstructure, cellulosic content and crystallinity [18]) do not exhibit any

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fatigue-stiffening, as reported by [19] and reproduced in Figure 1(f). Complicating

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matters further still, a very recent Flax-epoxy study [20], published while this

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paper was being submitted, confirms the fatigue-stiffening phenomenon in

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specimens cycled at 5 Hz, but observes no stiffening in some of the same specimens

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when cycled at a higher frequency of 30 Hz! This odd behaviour is clearly evident

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from Figure 2.

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Based on the above existing literature, concerning ambiguities can be identified amongst the available results of plant-based NFC fatigue studies [13, 20]: • While fatigue-stiffening phenomena were independently observed by several 3

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studies [4, 14–17], they were all conducted at the same 5 Hz and R = 0.1

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stress ratio (we shall call these the ‘standard’ parameters). This observed

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stiffening, and the typical ‘micro-structural’ root-cause explanations proposed

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by these studies (e.g. amorphous cellulose reorganising or straightening into

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crystalline chains, etc.) is contradicted by two aforementioned reports where

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NFC specimens were tested under different cycling parameters:

– Hemp-epoxy study by de Vasconcellos et al. [19], which showed no

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evidence of fibre-direction stiffening despite Hemp being materially

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similar to Flax, was conducted under slower cycling at 1 Hz and lower

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ratio R = 0.01.

– Flax-epoxy study by Jeannin et al. [20], where UD specimens were

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cycled at the ‘standard’ stress ratio R = 0.1 but a much higher 30 Hz

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frequncy, only observed fatigue-stiffening at the lowest tested loading

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level (55% of ultimate strength) – but not at higher peak stress levels

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(see Figure 2(b)).

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• For layups that exhibit fatigue-stiffening (e.g. [0] and [0/90]), conflicting

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trends are reported for relationship between applied loading and resulting

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stiffness evolution:

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– Under the same load ratio R, a specimen cycled at a higher applied load may or may not exhibit a higher stiffness rise, than one cycled at a

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lower applied load. Tests on UD Flax-epoxy by El Sawi et al. [15]

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indicate that higher loading levels lead to higher stiffness rise (see Figure 1(c)), while similar studies by Liang et al. [14] and Ueki et al. [21] suggest the opposite (Figures 1(b) and (d)).

– Both reducing and increasing the testing frequency beyond the ‘standard’ 5 Hz seems to eliminate the stiffening phenomenon to some

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extent. As noted earlier, tests at 1 Hz by de Vasconcellos et al. [19], and

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at 30 Hz by Jeannin et al. [20] observed no fatigue-stiffening.

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It can thus be safely concluded that modulus measurement of NFCs is sensitive to testing parameters such as frequency and loading amplitude. As will

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be elaborated and evidenced later, we posit that the apparent fatigue-stiffening

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does not represent any actual improvement in material stiffness, but is a

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demonstrable consequence of fatigue testing method and parameters chosen.

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The ambiguities in fibre-dependent characteristics noted above must be urgently clarified, as (i) fibre behaviour is the defining feature of NFCs when

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proposing comparisons with other synthetic-fibre composites (e.g. Glass), (ii) the

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observed progressive behaviour will influence the development of future predictive

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models for NFCs, and (iii) the implications of a fibre-composite that increases in

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stiffness is significant to the goal of promoting NFCs as realistic alternatives to

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existing engineering composites [13].

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1.2. Hypothesis of strain-rate dependence

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We propose that the apparent fatigue-stiffening observed in previous studies, all of which were stress-controlled (i.e. specimen cycled between defined stress

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levels), may be attributed to an increasing strain rate experienced by the

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specimens. It is reasoned that, while the commanded stress amplitude remains

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constant in such tests, as the specimens accumulate residual strain due to internal

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damage, the total strain amplitude response may steadily increase. The frequency

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being constant, this would result in higher strain rates during loading and

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unloading, as cycling progresses. There is evidence from quasi-static tests on NFC

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configurations that the measured modulus is proportional to applied deformation

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rate, as shown in studies by Jeannin et al. [20] on unidirectional Flax-epoxy,

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Fotouh et al. [22] on random-oriented Hemp-polyester, and by Kim et al. [9] on

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UD short-fibre Hemp-vinylester and cellulose-vinylester specimens. At the least, a

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changing strain rate introduces an additional (and, perhaps, unnecessary) variable

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in stress-controlled fatigue tests, which may have influenced the observed

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mechanical properties (e.g. modulus) and, subsequently, the conclusions derived

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from those observations. Considering the above, this study initiates with the hypothesis that

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fibre-direction stiffening in spite of damage, as reported in recent Flax-epoxy

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fatigue studies, is not an inherent material property of the natural fibre composite,

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but a consequence of the fatigue test method adopted. In order to eliminate or

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limit the effect of a continuously varying strain rate, mechanical tests in this study

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are conducted under constant strain amplitude cycling, thereby enforcing a

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near-consistent strain rate during the loading and unloading phases, throughout

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the duration of each fatigue test. In doing so, this study aims to investigate if a

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fatigue-stiffening phenomenon persists even under strain-controlled conditions, and

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also attempts to clarify the ambiguities in existing knowledge of NFC fatigue as

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described in the previous section.

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2. Materials and methods

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2.1. Manufacturing

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Composite manufacturing methods are identical to those in earlier studies by some of the authors [23, 24]. Commercially available dry UD FlaxPlyr (Lineo NV,

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Belgium [25]) with areal density 150 g/m2 was used as reinforcement in a

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thermoset-polymer matrix of hot-curing epoxy resin Aralditer LY 1564 and

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hardener Aradurr 22962 (Huntsman Corporation, The Woodlands, TX, USA).

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The FlaxPly fabric is shown in Figure 3. Sixteen plies were used to manufacture

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the four symmetric laminate types tested in this study: unidirectional [0]16 ,

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crossply [0/90]4S , angled-crossply [±45]4S , and quasi-isotropic [0/45/90/−45]2S .

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Composite plates were manufactured by hand-layup in a custom flat mould,

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followed by a heated platen press consolidation procedure (Figure 4). The fabric

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was not subjected to any treatment before composite manufacture. Per resin

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supplier specifications, the cure cycle began at 120℃ for 15 minutes, followed by

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150℃ for 2 hours. The densities and constituent fractions of the manufactured

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laminates are given in Table 1.

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2.2. Specimen preparation

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All plates were ∼4 mm thick. Rectangular 250×25 mm specimens were cut

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from the manufactured plates by fine-cutting 0.35 mm diamond-edge saw, followed

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by edge grinding for a flat finish. Laboratory trials indicated that specimens fitted

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with tapered Aluminium tabs often fractured near the grips during fatigue testing,

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while those with rectangular Flax-epoxy tabs (quasi-isotropic layup) fractured in

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the middle gauge section – so tests specimens for this study were tabbed with

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Flax-epoxy tabs. Specimen and tab dimensions are within the guidelines of fatigue

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testing standard ASTM D3479 [26].

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2.3. Testing

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All tests were carried out at room temperature and pressure in a

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servo-hydraulic MTS 322 (Eden Prairie, MN, USA) test frame. The baseline

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monotonic properties of each laminate are given in Table 2, taken from a previous

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study on the same composites [23]. The monotonic tensile response plots are given

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in Figure 5.

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For fatigue tests, loading to enforce a constant strain amplitude was controlled via feedback from a 1.0-in (25.4 mm) gauge uniaxial extensometer. The typical

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fatigue test sequence carried out in this study is a combination of alternating

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fatigue and quasi-static stages, as demonstrated by the command waveform

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diagram Figure 6. In order to follow the evolution of residual ‘static-condition’

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stiffness of the specimen, a typical test initiates with quasi-static cycle, followed by

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a fatigue regime that is periodically interrupted for interim quasi-static cycles. The

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quasi-static cycles were displacement-controlled at 2 mm/min, while the fatigue

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cycles were run at a commanded frequency of 5 Hz and strain ratio

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R =

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in published stress-controlled fatigue studies on Flax-epoxy material [13]. Since

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testing frequency has been shown to influence (i.e. have a reducing effect) on

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fatigue life [20], maintaining the same frequency as in existing publications should

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offer results that are readily comparable with these studies, with minimal

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difference in testing conditions.

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= 0.1. This cycling frequency of 5 Hz was chosen following the practice

Before initiating the fatigue stage, the specimen is loaded up to the mean (max +min ) . 2

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min max

During the interim quasi-static stages, the specimen is

strain level, ¯ =

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typically brought down to a zero-force load (at which point, strain may be

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non-zero due to accumulated plasticity), then loaded to the maximum strain max .

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All specimens are tested until failure, or up to a maximum of 2 million fatigue

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cycles if failure is not observed.

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From Figure 5, the 2/3 to failure strain point for most of the considered laminates is in the range of ∼1.0-1.2%. So, values around this range were chosen

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as the upper limit of fatigue loading for all laminate types. Considering the

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bilinear nature of the laminates’ monotonic response, the particular strain loading

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levels (max ) for fatigue testing were chosen from either side of the inflection point

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– shown graphically in Figure 8. At least 5 replicate tests are conducted for each

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peak strain max .

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2.4. Strain rate

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The strain rate ˙ attained in our tests is a function of max-min strain levels and frequency. Strain rate is formulated as change in strain over half a cycle:

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˙ =

max − min = 2f · (max − min ) 0.5T

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where max and min are applied peak and valley strains, respectively; and period 1 (duration of one cycle) is T = , where f is cycling frequency. In terms of strain f 8

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loading ratio R =

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the above relation (1) can be rewritten as:

˙ = 2f · (1 − R ) · max

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Since, in this study, f and R are constants 5 Hz and 0.1, respectively, (2) can be

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reduced to:

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˙ = 9 · max per second

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(3)

For the reader’s convenience, Table 3 lists the estimated loading-unloading strain rate for each laminate type and loading level. Note that the cycling strain

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rate should remain near-constant throughout an individual test run, so any rate

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variation, or influence thereof on fatigue behaviour during a test is expected to be

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minimal, if not eliminated – which is an important feature of our approach.

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2.5. Data processing

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To calculate material properties evolution over the fatigue life, the following are measured from the response plots (also demonstrated in Figure 7): • Initial modulus E0 measured from the initial ramp-up response as shown in

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Figure 7(a), considered to be the stiffness of the undamaged material. This

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initial linear region differs in size from laminate to laminate. In our our data,

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the typical strain range of E0 measurement is 0.01–0.12% for UD [0]

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(comparable to 0.01–0.15% used in [27]), 0.015–0.12% for crossply [0/90],

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0.015–0.14% for quasi-isotropic, and 0.06–0.2% for angled crossply [±45].

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• Fatigue secant modulus E f , i.e. slope of line passing through both extrema of

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the fatigue cycle hysteresis loop (max and min points), as shown in Figure 7.

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• Static secant modulus E st , i.e. slope of line passing through both extrema of the interim quasi-static cycle hysteresis loop. 9

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• Inelastic strain component p , measured at the intersection of secant modulus line and zero-stress axis. Note that under constant amplitude strain cycling, in order to maintain the commanded strain range, the stress amplitude tends to relax (demonstrated in

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Figure 7(b)) due to accumulating permanent deformation p .

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3. Results and discussion

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3.1. Fatigue life

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The observed fatigue lives are plotted in Figure 9. Samples that survived 2×106 cycles (run-outs) are plotted with ‘filled-in’ markers. The typically wide

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scatter in specimen fatigue lives necessitate the application of statistical methods

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for data analysis and failure prediction. In this constant strain amplitude study,

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log-normal distribution is assumed for fatigue life, following recommended

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procedures in ASTM D3479 [26] and ASTM E739 [28]. It is found that the

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observed fatigue lives can be modelled by a linearised strain-life (-N ) relationship:

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log (Nf ) = A + B (max )

(4)

where Nf is fatigue life, i.e. number of cycles until failure (dependent variable),

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max is the commanded peak strain (independent variable), A and B are

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material-specific parameters to be determined by fitting -N test data. This

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log-linear fatigue life trend is also consistent with the results of stress-controlled

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studies [13, 20]. Note that Equation (4) assumes a normal distribution for log(Nf ),

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and that the variance of log(Nf ) is assumed constant over the entire range of

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tested max levels. Following ASTM E739 [28] and ASTM STP313 [29], the linear

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median trend and 95% confidence bounds are estimated for all laminates, shown

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plotted in Figure 9. The modelled hypothesis of linearity in Equation (4) was

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found acceptable for all laminates. The parameters of this linearised model are

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given in Table 4.

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A natural high-cycle fatigue limit cannot be identified for any of the

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specimens, as all log-lives consistently follow a linearly increasing trend with

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decreasing strain levels, eventually exceeding the maximum limit of 2×106 cycles

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at a low enough strain amplitude. To compare, previous stress-controlled studies

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have also not observed a natural fatigue limit [13], even when cycling extended to

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108 cycles [20]. As such, the fatigue limit for each laminate is considered to be the

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lowest tested strain level at which a specimen survives 2×106 cycles. The

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strain-life medians are all plotted collectively in Figure 10. It can be seen that

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composites wherein response is fibre-dominant ([0], [0/90], and quasi-isotropic)

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produce plots that are closely placed and have similar slopes, suggesting their

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comparable fatigue endurance; while the FE [±45] plot is located further apart,

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demonstrating its considerably longer survival. It can be inferred that, on account

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of their linear max -log(N ) relationship, Flax-composites lend themselves to reliable

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fatigue failure prediction, and are therefore suitable for engineering components.

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3.2. Residual strain

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Permanent deformation in NFCs are a result of several mechanisms: irreversible damage like transverse cracking in fibre walls and fibre-matrix

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interfacial debonding, reorganisation of Flax fibre microconstituents such as

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separation of elementary fibres and irreversible extension of hellically-would

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microfibrils due to ‘stick-slip’ mechanisms, and inherent material inelastic

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phenomena like matrix polymer plasticity [14, 15, 30, 31]. In this study, permanent

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deformation, as quantified by the inelastic component of strain response, is found

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to progressively accumulate over fatigue life for all tested specimens, as shown in

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Figure 11. Recall that, before fatigue cycling, the specimens were subjected to an

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initial quasi-static tensile ramp-up to the peak strain level, followed by complete

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unloading, as shown earlier in Figure 6 (this was done to measure initial

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static-condition properties). So, fatigue testing began with some pre-existing

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permanent deformation in the specimen, which is reflected in the non-zero inelastic

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strain at N =0 in the evolution trends. For all laminate configurations, under all tested load levels, it appears that the bulk of permanent deformation occurs within the first 10% of fatigue life (before

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0.1Nf ). Inelastic strains are higher at higher load amplitudes, as expected. This is

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similar to that in the case of stress-controlled fatigue [14–17]. An interesting

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observations is that, for fibre-dominant FE laminates ([0], [0/90], and

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quasi-isotropic), there appears to be a threshold loading level below which the

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inelastic strain response does not vary significantly. For instance, for FE [0], the

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trends for loading below max =0.54% appear to overlap (Figure 11(a)). Likewise

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for FE quasi-isotropic at max ≤0.64% (Figure 11(b)), and for FE [0/90] at

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max ≤0.47% (Figure 11(c)). This suggests that inelasticity-causing mechanisms

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are less active during cycling at these lower amplitudes. This reasoning is

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supported by the observation that these ‘threshold’ strain levels happen to be

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located at the transition region of the laminate’s monotonic response curve (shown

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in Figure 5), indicating a period preceding the development of significant internal

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damaging mechanisms. Furthermore, investigation of inelasticity evolution during

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quasi-static loading of FE [0], [90], and [±45], as conducted by [23], show that

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inelastic mechanisms are minimal below these threshold levels (quasi-static

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inelasticity charts are reproduced here in Figure 12). The angled-crossply [±45]

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specimens show considerable ply rotation as they fatigue, and delamination is a

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prominent failure mode in such specimens – so both characteristics contribute

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towards the high inelastic accumulation. Of all the FE specimens, FE [0]

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accumulates the least permanent strain, suggesting that fibre-direction damage

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mechanisms (microfibril reorientation, fibre cracking, fibre-matrix debonding) do

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not contribute as much to permanent deformation as delamination-related

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mechanisms in crossply and quasi-isotropic layups.

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3.3. Modulus

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3.3.1. As measured from fatigue cycles

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Figure 13 shows the evolution of stiffness in all tested laminates. Recall that secant modulus E f of a fatigue cycle is normalised by initial undamaged modulus

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E0 , both measured from mechanical response data as previously indicated in

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Figure 7. All specimens, including those of fibre-dominant FE, show a net loss of

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stiffness. With the exception of the angled-crossply [±45] laminates, the stiffness

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degradation matches the expected typical 3-stage evolution of fibre-composites

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(Figure 1(a)). The matrix-dominant [±45] also show a loss of stiffness, but the

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trend appears to have 2 stages, and is missing the third stage of rapid-degradation

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just before failure. The loss of stiffness appears to be proportional to the applied

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strain amplitude for all tested laminates. For fibre-dominant specimens under

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lower strain loading levels (max < 0.8%), after an initial reduction, the modulus

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appears to remain constant past 0.1-0.2Nf . In the matrix-dominant specimens,

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modulus degradation is continuous throughout fatigue cycling, though more rapid

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during the first half of fatigue life.

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The degrading stiffness of FE [0] and [0/90] seen here under strain-amplitude controlled fatigue is completely contradictory to the increasing trend observed for

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the same laminates under stress-controlled fatigue, reported in the work of Liang

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et al. [4, 14], El Sawi et al. [15], Bensadoun et al. [16], and Ueki et al [17]. This

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stiffening phenomenon under stress-controlled fatigue was analysed by Mahboob et

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al. in [13]. It was reported that FE [0] specimens experienced up to 2–11%

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modulus increase (see Figure 1), depending on the applied stress-amplitude, and

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that FE [0/90] showed 1–4% modulus increase. In contrast, under constant strain

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amplitude test of the present study, a modulus loss of up to 30% under the highest

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strain-amplitude levels is evidenced for the same composites (Figures 13(a) and

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(c)).

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As noted earlier, the stiffening of fibre-dominant FE specimens in reported 13

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studies was attributed to structural reorganisation of, and within, Flax fibres that

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enhanced stiffness, i.e. straightening of initial ‘waviness’ of flax fibres, movement of

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microfibrils toward loading axis (reorientation), and rearrangement of

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irregularly-folded cellulose polymer chains into regular straight chains parallel to

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loading axis (crystallisation) [4, 14–16]. However, these mechanisms should still

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exist when the same specimens are tested under strain-controlled fatigue, and

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therefore should exert the same stiffening influence on specimen modulus – but

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this is not evidenced in the present study. Considering that measureable NFC

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material properties have been shown to be sensitive to strain-rate [9, 22], it is thus

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concluded that composite stiffening reported by stress-controlled fatigue studies is

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not solely due to structural changes in the natural fibre, and therefore not an

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inherent physical property of NFC material, but is more likely a result of

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increasing strain-amplitude, and consequently strain-rate, over fatigue life.

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Furthermore, this conclusion also suggests that such rate-dependent stiffening

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tendency is significant enough to counter, and even overcompensate for, the

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degrading effects of internal damage that surely occurs under cyclic loading,

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thereby giving a fictitious impression of structural improvement.

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3.3.2. As measured from quasi-static cycles

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Per test plan, fatigue cycling was interrupted at intervals to conduct a quasi-static load-unload cycle at a constant 2 mm/min displacement rate. This

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loading rate is, of course, slower than that experienced during 5 Hz fatigue cycling.

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These interim static cycles were conducted in order to compare the fatigue and

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static-condition secant moduli, and investigate the influence of testing strain-rate

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on modulus measurement. A direct comparison of static- and fatigue-cycle moduli

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during early, mid, and late fatigue life can be made from Figure 14, where the

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moduli are plotted against applied peak strain. It can be seen that static modulus

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values are consistently lower than those from fatigue. In other words, stiffness

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measured from static cycles (slower strain rate) are lower than that from fatigue

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cycles (quicker strain rate), confirming that increased strain rate results in a

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higher-estimated modulus for these laminates.

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4. Further discussion and future work Following the results of this study, it appears that strain-controlled, or rather

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strain-amplitude-controlled cycling may be better suited to investigate the fatigue

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behaviour of NFCs, since no counter-intuitive stiffening phenomenon is observed

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under such loading. To extrapolate from the findings of this study, further research

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may be advisable along the following lines of inquiry:

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1. In our strain-controlled study, we did not conduct parallel stress-controlled

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fatigue tests since there is already a considerable body of work by several

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independent research groups on the topic (as discussed in the introductory

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sections). However, since most published results do not provide strain

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amplitude or max-min strain data, their achieved strain rates are difficult to

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estimate, if not impossible. It would be beneficial to repeat similar constant

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stress-amplitude tests to quantify the strain rate variation during fatigue

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cycling, and correlate it to observed stiffness evolution. Such an investigation

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may also offer answers to why Flax-epoxy specimens tested at a much higher

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frequency of 30 Hz by Jeannin et al. [20] did not demonstrate fatigue-stiffening

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like their 5 Hz counterparts – perhaps there is an upper limit on increasing

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strain rate beyond which the apparent tensile response of NFCs is no longer

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rate-dependent.

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2. Since the ultimate goal of current NFC research is to offer viable alternatives to

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traditional engineering composites, the fatigue behaviour of Flax-epoxy (or

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other NFC) specimens must be compared with that of synthetic fibre

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composites, such as Glass, under stain-controlled conditions similar to those

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applied in this study.

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3. Modulus and residual strain are the most common measures of internal damage

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in fatigue studies. However, it would be useful to study the evolution of other

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indirect damage indicators under strain controlled fatigue loading conditions,

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which may prove to better capture the extent of material damage. 4. Examining specimen micro-structure via microscopy would offer direct

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observation of physical cracking and the characteristics of internal damage

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(initiation, progression, development of failure), which should be correlated to

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the evolving or degrading mechanical properties of a fatiguing specimen.

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5. This study did not investigate the fatigue response of [90] laminates (which

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would have provided insight on ‘transverse’ fatigue strength), since engineering

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components made of laminates are rarely designed to be loaded perpendicular

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to the fibre axis. However, in the interest of generating a complete dataset of

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Flax-composites (or other NFC) performance in all orthotropic directions,

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testing of [90] and other off-axis orientations may be desirable.

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6. Real engineering operations commonly involve variable amplitude cyclic

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loading. Future research on Flax-composite performance may be tested under a

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spectrum loading regime that is representative of a specific application, e.g.

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biomechanical prosthetics, or non-primary structure in aircraft.

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7. Future ‘durability’ studies may involve fatigue testing of Flax-laminates after structural distress, e.g. water ageing, high-temperature exposure, impact

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loading, etc. Post-fatigue microstructure observations in such studies may

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reveal different damage mechanisms, or evolution at different intensities, than

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that observed in this study.

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5. Conclusion

This study conducted constant strain amplitude fatigue tests on select Flax-epoxy laminates ([0]16 , [0/90]4S , [±45]4S , and [0/45/90/−45]2S ), and presents 16

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original data on their response under strain-controlled tension-tension cycling (5

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Hz cycling frequency, loading strain ratio R =

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control was chosen in order to maintain a constant strain rate (and strain-ratio)

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during fatigue cycling, since it was argued in a previous study [13] that frequency

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or loading-ratio may influence the measured stiffness and strength. Strain-life plots

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are generated to quantify fatigue endurance of the tested laminates, and are found

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to be well-modelled by a linearised relationship, for which parameters are also

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identified. All specimens demonstrate a degrading modulus over fatigue life,

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thereby contradicting previous studies that report an increasing modulus for

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laminates with 0° plies [14–17]. The extent of modulus loss is found to be

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proportional to loading level applied, a finding that is in agreement with [15], but

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differs from [14, 17]. Furthermore, it is observed that modulus measured from

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quasi-static cycles is consistently lower than that measured from the

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quicker-loading fatigue cycles – indicating that a directly proportional relationship

426

does exist between strain-rate and measured modulus. It is concluded that there is

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not, in fact, any real stiffening or modulus improvement in Flax-composites, as

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implied in studies to date. Based on the results and findings of this study, which

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has none of the ambiguities of previously published studies (as discussed earlier in

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the introductory sections), it is proposed that the apparent fatigue-stiffening in

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previous studies was a consequence of stress-amplitude controlled loading

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conditions, wherein the measured modulus may have been influenced by a

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progressively increasing strain-rate. This implies that such rate-dependent

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stiffening tendency of NFCs is significant enough to compensate for, and totally

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mask, the internal damage and material degradation that surely occurs during

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cyclic loading, thereby giving a false impression of structural improvement.

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Considering the above, strain-amplitude controlled cycling is better suited for

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fatigue studies on NFCs.

= 0.1). Strain-amplitude

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Acknowledgements The authors gratefully acknowledge Huntsman Corporation (The Woodlands, TX, USA) for their generous supply of resin and accelerant material. The authors

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remain indebted to Dr. Zouheir Fawaz and the FRAMES laboratory (Facility for

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Research on Aerospace Materials and Engineered Structures) at Ryerson

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University (Toronto, ON, Canada) for mechanical testing privileges.

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Funding. This research is supported in part by Natural Sciences and Engineering

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Research Council of Canada – Discovery Grants program (NSERC-DG).

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Conflict of interest. None declared.

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Data availability

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time as the data also forms part of an ongoing study. References

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The raw data required to reproduce these findings cannot be shared at this

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Figure 1: Modulus evolution over fatigue life: (a) as expected of typical fibre-composite [32]; (b)(d) Flax-epoxy UD (5 Hz, R = 0.1), from [14], [15], and [17], respectively; (e) Flax-epoxy crossply (5 Hz, R = 0.1), from [14]; and (f) Hemp-epoxy crossply (1 Hz, R = 0.01), from [19].

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Figure 2: Modulus evolution over fatigue life for Flax-epoxy UD specimens cycled at: (a) 5 Hz, and (b) 30 Hz; from [20]. All 5 Hz specimens exhibit Stage I stiffening, but most 30 Hz specimens do not.

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Figure 3: FlaxPlyr fabric is predominantly unidirectional, held together by a periodic cross-weave. Ratio of 0° strands to 90° cross-weave strands is 40:3.

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10 5 0 0 6%1.5%

(c) Crop dimensions (pts)

pdfXchange: LRTB 50, 516, 46, 372 516, 46, 372 strain evolution during quasi-static tensilepdfXchange: loadingLRTB for50,Flax-epoxy laminates (a) [0], (b) [90], and (c) [±45], from [23].

29

Inelastic laminate strain εLP

0 1.5%

FE [90] static response inelasticity FE [±45] 4S static 40 300

Laminate stress σL (MPa)

0.0% 0.0%

50

Inelastic strain ε22P

0.54%

100

Inelasstic strain ε11P

0.4% 0.3%

Stress σ11 (MPa)

250

150

0.2% 0.1%

0.4% 0.5%

200

Jo

Inelasstic strain ε11P

Inelastic strain Stress

0.3%

300

Stress σ11 (MPa) Inelastic laminate strain εLP

staticresponse inelasticity FE FE [90][0] static

FE [0] static response 0.4%

3%

Str

2%

1%

0.64%

0% 0%

2% Laminate st

Journal Pre-proof

(a)

FE [0]16

1

0.8 0.7 0.6

0.27%

0.40%

0.54%

0.81%

0.94%

1.08%

0.67%

0.5

0.9 0.8 0.7

of

0.9

Fatigue secant modulus Ef/E0

Fatigue secant modulus Ef/E0

1

0.6 0.5

0.2

0.4

0.6

0.8

1

N/Nf

(c)

FE [0/90]4S

0.64%

0.96%

1.12%

0.2

0.4

0.6

0.80%

0.8

1

N/Nf

(d)

FE [±45]4S

1

0.9

re-

0.9

Fatigue secant modulus Ef/E0

1

0

0.48%

pro

0

0.8 0.7 0.6

urn al P

Fatigue secant modulus Ef/E0

(b)

FE Quasi-isotropic

0.31%

0.47%

0.62%

0.78%

0.94%

1.09%

0.5 0

0.2

0.4

0.6

0.8

0.8 0.7 0.6

0.8%

0.9%

1.0%

1.1%

1.2%

1.3%

0.5

1

0

0.2

0.4

N/Nf

0.6

0.8

1

N/Nf

Figure 13: Evolution of normalised secant modulus E f measured from fatigue cycles for tested H 8.8cm, v 0.1cm max levels. The mean trendlines are shown with standard deviation bars. Crop borders AdobePro (pts): 0.1 Nf at 0.5 Nf at 0.9 Nf pdfXchange (pts)atLRTB: 50, 82, 58, 322

0.8 0.7 0.6

FE [0] fatigue FE QIso fatigue FE [0/90] fatigue FE [±45] fatigue FE [0] static FE QIso static FE [0/90] static FE [±45] static

0.5 0.0%

0.5%

1.0%

Applied peak strain ϵmax

1.5%

1

(b)

0.9 0.8 0.7 0.6

0.5 0.0%

0.5%

1.0%

Applied peak strain ϵmax

1.5%

Normalised modulus E/E0

0.9

1

Normalised modulus E/E0

(a)

Jo

Normalised modulus E/E0

1

(c) 0.9 0.8 0.7 0.6 0.5 0.0%

0.5%

Label location H 2.28”, V 0.48” Crop borders14: Comparison of modulus measured from fatigue and quasi-static cycles (a) at Figure Letter landscape ning of fatigue life (0.1 Nf ), (b) at mid-life (0.5 Nf ), and (c) towards the end (0.9 Nf ). pdfXchange (pts): LRTB 50, 118, 44, 372

30

1.0%

Applied peak strain ϵmax

the begin-

1.5%

Journal Pre-proof

Table 1: Measured densities and constituent fractions of Flax-epoxy test specimens

1.47 ±0.24

1.15 ±0.04

Fibre volume fraction vf (%)

–

–

Porosity vp (%)

–

–

Density ρ (g/cm3 )

a b

1.26 ±0.02c

51.0 ±3.9

50.0 ±2.3

3.4 ±2.6

3.3 ±3.0

[0/90]4S , [±45]4S Quasi-isotropic laminate [0/+45/90/−45]2S Averaged density for all FE laminate types (densities of all layups are similar)

urn al P

re-

c

FE crossplya and quasi-isob

FE UD

of

Epoxy neat

pro

Flax fibre

Table 2: Tested mechanical properties of neat epoxy and laminates of Flax-epoxy (FE), from [23] Epoxy cured

FE [0]16

FE Quasi-isoa

FE [0/90]4S

FE [±45]4S

Initial modulus E0 (GPa)

3.0 ±0.5

31.4 ±1.5

13.1 ±1.4

16.7 ±0.7

6.4 ±0.4

Strength σ tu (MPa)

67.2 ±2.5

286.7 ±13

124.6 ±3.3

155.8 ±9.6

74.3 ±3.6

3.61 ±0.23

1.53 ±0.07

1.70 ±0.02

1.57 ±0.08

11.0 ±0.4

0.403 ±.007

0.353 ±0.011

0.357 ±0.05

0.111 ±0.027

0.62 ±0.07

Failure strain ε

tu

(%)

a

Jo

Poisson’s ratio νLT

Quasi-isotropic laminate [0/+45/90/−45]2S

31

Journal Pre-proof

Table 3: Strain rate during fatigue loading and unloading for tested laminate types at each commanded peak strain level, estimated per relation (3)

max

˙ (s

−1

max

˙

max

−1

)

(s

)

FE [±45]4S

˙ (s

−1

max

)

˙

1.30%

)

9.7%

1.25%

11.3%

1.28%

11.7%

0.94%

8.5%

1.09%

9.8%

1.12%

10.1%

1.20%

10.8%

0.81%

7.3%

0.94%

8.5%

0.96%

8.6%

1.10%

9.9%

0.67%

6.0%

0.78%

7.0%

0.80%

7.2%

1.00%

9.0%

0.54%

4.9%

0.62%

5.6%

0.64%

5.8%

0.90%

8.1%

0.40%

3.6%

0.47%

4.2%

0.48%

4.3%

0.80%

7.2%

0.27%

2.4%

0.31%

2.8%

0.32%

2.9%

0.75%

6.8%

re-

pro

11.5%

(s

−1

1.08%

Quasi-isotropic laminate [0/+45/90/−45]2S

urn al P

a

FE QIsoa

FE [0/90]4S

of

FE [0]16

Table 4: Identified parameters of linearised strain-life relation (4)

b c d

na

Varb

A

FE [0]16

30

0.03218

7.472

FE QIsod

30

0.06826

FE [0/90]4S

32

FE [±45]4S

30

Jo

a

Laminate

CI0.95 c

B

CI0.95 c

±

0.226

-402.42

±

29.18

7.480

±

0.329

-376.76

±

36.67

0.05514

8.198

±

0.289

-433.55

±

31.71

0.05505

9.822

±

0.572

-484.65

±

53.27

total number of specimens tested to failure; not including run-outs variance s2 of the normal distribution of log(Nf ), where s is standard deviation 95% confidence interval quasi-isotropic laminate [0/+45/90/−45]2S

32