Effect of cross-linking on dynamic mechanical and fracture behavior of epoxy variants

Accepted Manuscript Effect of cross-linking on dynamic mechanical and fracture behavior of epoxy variants R. Rahul, Sr. Project Associate, R. Kitey, Assistant Professor PII:

S1359-8368(15)00552-1

DOI:

10.1016/j.compositesb.2015.09.017

Reference:

JCOMB 3784

To appear in:

Composites Part B

Received Date: 12 March 2015 Revised Date:

6 May 2015

Accepted Date: 16 September 2015

Please cite this article as: Rahul R, Kitey R, Effect of cross-linking on dynamic mechanical and fracture behavior of epoxy variants, Composites Part B (2015), doi: 10.1016/j.compositesb.2015.09.017. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

ACCEPTED MANUSCRIPT

EFFECT OF CROSS-LINKING ON DYNAMIC MECHANICAL AND FRACTURE BEHAVIOR OF EPOXY VARIANTS Rahul R.1, R. Kitey2

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Department of Aerospace Engineering, Indian Institute of Technology Kanpur Abstract

Anhydride cured epoxy systems are examined to elucidate the effect of cross-linking on

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viscoelastic and fracture behaviour of polymers. Dynamic mechanical and quasi-static fracture tests are conducted on epoxy variants, prepared by mixing diglycidyl ether of

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bisphenol-A (DGEBA) and methyl tetra hydrophthalic anhydride (MTHPA) in several proportions. The molecular weight (Mc) of the epoxy system increases monotonically as its composition deviates from the stoichiometry, indicating decreasing cross-link density. Significant influence of constituents’ proportion is observed on glassy, glass transition and

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rubbery states, however, the damping characteristics remain largely unaffected in adequately cross-linked epoxies. An inverse correlation is demonstrated between the glass transition temperature (Tg) and the molecular weight of epoxy variants. A relative change in

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constituents’ proportion from stoichiometry monotonically increases the fracture toughness (KIc) value of the material. Fracture surface micrographs reveal distinct composition

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dependent toughening mechanisms. While highly cross-linked stoichiometric system provides least resistance to material fracture, crazing and plastic deformation lead to increased fracture toughness values in hardener-rich and resin-rich epoxy systems, respectively. The KIc when plotted with Mc shows increasing trend until it reaches a plateau value at higher molecular weights even if the variation distinctly differs in resin-rich and

1

Sr. Project Associate Assistant Professor and corresponding author, [email protected] (Ph: +91-512-259-7060, Department of Aerospace Engineering, IIT Kanpur India 208016) 2

ACCEPTED MANUSCRIPT anhydride-rich cases. A model correlating Mc and KIc is proposed while addressing the effect of unreacted constituents on the fracture behaviour of epoxy system.

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Keywords: A. Thermosetting resin, B. Cure behaviour, B. Fracture toughness, D. Fractography, Toughening mechanisms

1. Introduction

Highly cross-linked thermosetting polymers have evolved into versatile engineering

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materials due to their ability to attain application oriented material characteristics. Chemical and thermo-mechanical properties of polymers can be tailored by varying the combination

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and composition of constituent resin and curing agents; by controlling the cure kinetics, or by reinforcing secondary phase fillers. Epoxy is perhaps the most widely used resin, since the material assumed commercial importance. It has found a wide range of applications in areas including MEMS devices, aerospace and structural components and bio-mechanical systems

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because of its excellent thermo-mechanical, adhesive and dielectric properties. In addition, epoxy also provides favourable matrix material properties such as easy processibility and

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resistance to corrosion and moisture ingression. While curing the chemical reaction between resin and the curing agent develops three

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dimensional cross-linked polymeric chains. It is well recognized that the degree of crosslinking, also known as cross-link density, and the flexibility of chains between cross-links control the physical and thermo-mechanical properties of epoxy systems [1]. The gelling time and (elevated) temperature at which the curing takes place are key process parameters that affect cross-linking. It is difficult to maintain a uniform temperature throughout the material while fabricating large components. Also, because of the difference in thermal properties of constituent phases in composite materials, compositional uncertainty is prevalent, especially in the vicinity of interfaces. Non-uniform cross-linking may have little effect on macroscopic

ACCEPTED MANUSCRIPT properties, such as elastic modulus, but the fracture properties could be significantly influenced due to the presence of localized weaker zones, acting as the sources of failure initiation.

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For understanding the dependence of material properties on the polymer crosslinking, researchers have induced variations in molecular structure of various epoxy systems by changing the functionality [2-4] or the chemical contents [5-7] of curing agent; by controlling the curing temperature [8-10]; or by altering the proportion of resin/hardener

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(R/H) mixture [11,12]. Although similar effects of molecular level material parameters on

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thermal properties (such as glass transition temperature) are documented [2,4,12,13], the contradictory conclusions in regards to the fracture properties can not be ignored. While some researchers have reported an increase in fracture toughness as the molecular weight decreases [2,5,8,11], others suggested either a decreasing trend [3,9] or an optimal molecular weight corresponding to the maximum fracture toughness [6,12]. Similar differences can be noticed

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in case of other mechanical properties. In the current investigation we have developed epoxy variants by mixing phenolic resin with anhydride based curing agent in several proportions

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and performed a systematic dynamic mechanical and fracture analysis. A new model, correlating molecular weight with the fracture toughness, is proposed while addressing the

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effect of unreacted constituents on the fracture mechanisms of epoxy systems. 2. Materials

The curing agent, methyl tetra hydrophthalic anhydride (MTHPA), is first liquefied by heating at 120 0C for ~ 20 minutes. The liquid MTHPA is then mixed with diglycidyl ether of bisphenol-A (DGEBA) epoxy resin and a small amount of accelerator, 2,4,5tris[(dimethylamino)methyl]-Phenol. The mixture is stirred at 240 rpm for ~ 45 minutes before being poured into a silicone smeared aluminium mould. The curing profile consisted

ACCEPTED MANUSCRIPT of two steps, a pre-curing at 85 0C for 3 hours, followed by a post curing at 140 0C for 12 hours. In addition to the stoichiometric composition, 100:80 R/H ratio by weight [14], a set of resin-rich and anhydride-rich epoxy systems are prepared. The two considered resin-rich systems have 100:40 and 100:60 R/H ratios, whereas 100:100, 100:120, and 100:140 R/H

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compositions constitute the systems with excess of anhydride. The amount of catalyst added remains 0.5% of the mixture by weight irrespective of the epoxy composition. The samples for conducting dynamic mechanical, thermomechanical and quasi-static fracture tests are

3.1 Dynamic mechanical analysis

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3. Experimental methods and measurement

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prepared by machining cast sheets into the required dimensions.

Viscoelastic properties of epoxy variants are measured by using Dynamic Mechanical Analyzer (DMA), Diamond DMA, Perkin Elmer®. Specimens of dimension 50 mm x 10

0

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mm x 2.5 mm are loaded in tensile mode and the temperature is gradually increased from -25 C to 170 0C at a heating rate of 3 0C/min. Experiments are performed at 10 Hz frequency

with a 5 µm dynamic displacement. Representative data obtained from a test conducted on

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the epoxy system with stoichiometric composition are plotted in Fig. 1(a). The variation of storage modulus (E’) with temperature (T), illustrated by a solid curve in the figure, shows

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glassy (T < 130 0C), glass transition (130 0C < T < 146 0C) and rubbery states (T > 146 0C), typically observed in polymers. In the glassy state polymer chain segments are frozen, therefore material’s response is predominantly elastic whereas in the rubbery state the material provides very little resistance to the movement of polymeric chains. A rapidly decreasing E’ value in the glass transition zone nearly stabilizes to a very small magnitude in the rubbery state.

ACCEPTED MANUSCRIPT The loss modulus (E”), represented by a dashed curve in Fig. 1(a), shows bell shaped variation with temperature in the glass transition zone. The temperature corresponding to the peak of E” is considered as the glass transition temperature (Tg). It is observed that the measured Tg (138 0C) is marginally higher compared to the respective value when determined

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using the tangent method3 (135 0C). The difference between the two temperatures remains less than 4 0C in all epoxy samples. The loss factor (Tan δ) curve also shows a bell shaped

comparative plots in Fig. 1(d)).

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3.1.1 Molecular weight and cross-link density

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variation with temperature, however, with a peak shifted to 149 0C temperature (See, the

With an assumption that the material will behave as an ideal elastomer in rubbery regime, average molecular weight of the material between cross-links (Mc) is calculated

 ' E '  φ ρ RT , G =  = 3  Mc 

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based on the rubber elasticity theory, using [15-17],

(1)

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where G’ and E’ are rubbery shear modulus and rubbery elastic modulus, respectively. The ρ represents the material’s density at temperature T; R is the universal gas constant, and the

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front factor ɸ is a correction factor for free, unreacted chain ends which is defined as the ratio between mean square end-to-end distance of a networked chain and the length of a randomly coiled chain [18].

While determining molecular weight using Eq. (1) the value of E’ corresponds to the temperature Tg+40 0C in the rubbery state [17,18]. The ρ is calculated by weighing test samples at room temperature, T = 25 0C. The ɸ is assumed to be unity as suggested in Ref. 3

In tangent method, glassy, glass transition and rubbery state data are approximated by three straight line fits. The Tg is considered as the temperature corresponding to the midpoint of the intersection of glassy and glass transition state lines, and the intersection of glass transition and rubbery state lines (See, Fig. 1(a)).

ACCEPTED MANUSCRIPT [9,18]. Pearson and Yee [19] defined T as the temperature at which G’ is obtained, however, they compensated for the density measurement at room temperature by adopting a front factor of 0.75. In the current investigation no significant change is observed as far as the Mc

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calculation is concerned when different methods are used. Following Mc calculations, cross-link density (µ) of epoxy system is determined by

µ=

ρN Mc

,

3.2 Thermo-mechanical analysis

(2)

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where N represents Avogadro’s number.

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using kinetic theory of rubber elasticity which relates Mc with µ by [5,20],

The Tg values of epoxy variants are independently measured by using ThermoMechanical Analyzer (TMA) – Q400, TA Instruments®. Tests are conducted by heating 6

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mm cuboid shaped specimens from 20 0C to 200 0C at a constant rate of 3 0C/min. The Tg is determined by applying the tangent method (the plots are not shown for brevity).

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3.3 Fracture Analysis

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ASTM Standard D5045-99 is followed to prepare single edge notch beam (SENB) specimens. First, an edge notch of 2 mm depth is machined at the midspan of 62 mm x 14 mm x 6 mm beam sample. A sharp razor blade is then placed into the notch and gently tapped with a hammer to initiate a natural crack. Care is taken to ensure that the a/W ratio is maintained between 0.45 and 0.55 where a and W represent initial crack length and the specimen width, respectively. SENB specimens are symmetrically loaded in a three-point-bend fixture of universal testing machine INSTRON-3345. The tests are conducted in displacement control mode at a

ACCEPTED MANUSCRIPT constant crosshead speed of 0.1 mm/min and at an ambient temperature of 25 0C. A

linear

load vs. crosshead displacement curve is observed with an instantaneous drop in the load upon fracture initiation (not illustrated for brevity). This indicates that the material provides negligible resistance to crack growth. From linear elastic fracture mechanics, the stress

where the geometric factor f(ξ), ξ =

f (ξ ) =

a W

{

, is given by,

}

3 ξ 1.99 − ξ (1 − ξ ) ( 2.15 − 3.93 ξ + 2.7 ξ 2 ) 2 (1 + 2 ξ )(1 − ξ )

3

(3)

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PS f (ξ ) , 3 BW 2

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KI =

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intensity factor (SIF) is calculated by [21],

.

(4)

2

In Eq. (3) P is the concentrated load applied on SENB specimen. The S and B, are the beam

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span and the thickness, respectively. The load corresponding to the fracture initiation is substituted for P in Eq. (3) and for calculating critical mode-I SIF, KIc (fracture toughness).

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4. Results and Discussions

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4.1 Dynamic mechanical properties The effect of R/H ratio on viscoelastic properties of epoxy system is illustrated in Fig.

(1). Except for the case of extreme resin-rich (100:40 R/H) and anhydride-rich (100:140 R/H) materials, E’ vs. T plots of epoxy variants are nearly parallel in glassy, glass-transition and rubbery states, respectively (See, Fig. 1(b)). This indicates that the storage modulus gradient with respect to temperature is largely unaffected by R/H ratio. The temperature span of glass transition zone is observed to be greater in anhydride-rich systems (23 0C to 30 0C) when compared to the stoichiometric (19 0C) and the resin-rich (< 23 0C) cases.

ACCEPTED MANUSCRIPT The loss modulus and loss factor variations with temperature are plotted in Figs. 1(c) and (d), respectively. The peak values of E” are observed to vary between 0.40 and 0.45 GPa for all epoxy variants. Although, only two resin-rich epoxy systems are tested, the plots clearly show that the magnitude of Tan δ peaks increases monotonically with increasing resin

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proportion (~ 1.65 for 100:40 R/H epoxy). This suggests that the damping characteristics of an epoxy system can be enhanced by increasing resin proportion in the epoxy composition. On the contrary the peak values of Tan δ remain unaffected in case of hardener-rich epoxy

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systems (~ 1.2). The temperatures corresponding to the peak values of E” and Tan δ decrease

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monotonically as the epoxy composition deviates from the stoichiometry. The two peaks are attained the latest for the 100:80 R/H epoxy system, whereas the earliest is observed in 100:40 resin-rich and 100:140 hardener-rich epoxy cases. 4.1.1 Glass transition temperature

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The glass transition temperature of epoxy systems are tabulated in Table 1. The Tg values measured by DMA are consistently higher (by 14 to 18 0C) when compared to the ones determined by TMA. The stoichiometric composition exhibits the highest glass

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transition temperature. The deviation from stoichiometry monotonically decreases the Tg value. Interestingly, the decrease in glass transition temperature is in tandem with an increase

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in storage modulus in the glassy state (see, Fig. 1(b)). This phenomenon is known as internal anti-plasticization which was earlier reported by Bellenger et al. [22] for a different epoxy system.

4.1.2 Molecular weight The molecular weight of epoxy variants, calculated by substituting rubbery state storage modulus (See, Table 1) into Eq. (1), is plotted with hardener content in Fig. (2). The crosslink density, computed by using Eq. (2), is also plotted in the figure. The data corresponding

ACCEPTED MANUSCRIPT to the resin-rich and the hardener-rich epoxy systems are represented by unfilled and filled symbols, respectively, whereas a filled symbol with a border corresponds to the stoichiometric composition. Similar data representation is followed in other figures. The lowest molecular weight at stoichiometric composition (or the highest cross-link density)

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indicates that most of the resin chain ends are cross-linked by anhydride reactants. When the epoxy system deviates from the stoichiometry, the unreacted resin or hardener chains decrease the cross-link density, and hence increase the molecular weight. Figure (2) shows a

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steep rise in molecular weight with increasing resin content when the epoxy system is resinrich. On the other hand the molecular weight increases gradually with increasing hardener

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proportion in the anhydride-rich case. Except for the extreme resin-rich 100:40 R/H material which has the molecular weight of 1150 g/mol, the value of Mc remains below 400 g/mol in all epoxy variants. Unusually long gelling time, noticed while preparing the material, was also an indication of very low cross-link density in case of 100:40 R/H epoxy system.

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4.1.3 Correlation between Tg and Mc

The Tg is plotted with the inverse of Mc in Fig. 3 to illustrate the effect of molecular

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weight on glass transition temperature. A linear correlation is clearly evident between Tg and 1/ Mc. The plots indicate similar behaviour for both DMA and TMA measured Tg values. The

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observations are in agreement with the trends reported earlier in the literature [3,17,18]. Accordingly, the empirical relation between Tg and Mc is presented in the following form.

Tg = Tgo +

ζ

MC

,

(5)

where ζ represents the slope of Tg vs. 1/Mc curve with Tgo being the intercept on the Tg axis. In the current investigation ζ is measured to be ~2.0 x 104 g/mol-0C.

ACCEPTED MANUSCRIPT 4.2 Fracture properties The fracture toughness values of epoxy variants (See, Table 1) are plotted with molecular weight in Fig. 4(a). The minimum value of KIc is obtained for the epoxy system

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which has the lowest molecular weight. It is evident from the plot that the KIc increases monotonically with increasing value of Mc, although the rate of increase of KIc with Mc is different for resin-rich and hardener-rich epoxy systems (the higher for the later case).

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The fracture surfaces are analysed next in order to understand the influence of excess resin and hardener on fracture mechanisms. The micrographs illustrated in Figs. 5(a)-(c)

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correspond to the resin-rich 100:40, stoichiometric 100:80, and hardener-rich 100:140 R/H compositions, respectively. The notch surface in each photograph is marked by ‘1’. The fracture surface developed during the natural crack initiation process is indicated by ‘2’ whereas ‘3’ represents the crack growth region due to quasi-static loading. The bold arrow

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points the initial crack front besides indicating the crack propagation direction. Nearly clean fracture surface in both rapid (‘2’) and quasi-static (‘3’) crack growth regions suggests cleavage fracture in case of stoichiometric composition (See, Fig. 5(b)). This implies very

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small energy dissipation during fracture process which can also be inferred from the material’s (lowest) fracture toughness value (See, Table 1 or Fig. 4(a)). The fracture surface

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of resin-rich epoxy system, illustrated in Fig. 5(a), shows extremely high surface roughness at the notch root in region ‘2’. This indicates very high energy dissipation during the crack development process. In the magnified image the crack surface appeared to have densely spread fractured cavities. The region ‘3’, on the other hand, shows negligible surface roughness even if the fracture toughness values are higher in resin-rich epoxies compared to the stoichiometric case (See, Fig. 4(a)). This could be due to the plastic deformation followed by crack-tip blunting in quasi-static crack growth region. In case of hardener-rich epoxy composition the craze formation in front of natural crack-tip as well as at the notch-root is

ACCEPTED MANUSCRIPT visibly evident (See, Fig. 5(c)). In the rapid crack growth region ‘2’ which is developed due to instantaneous loading, smaller but large number of evenly spaced distinct parallel lines has evolved. A closure look at the fracture surface shows that the thin crazing lines, developed at the notch root, merge together to form larger craze marks. The craze development mechanism

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is better evident from the fracture surface morphology at ‘3’ where thick vein-like structure is visible in the material. The whole region, ahead of initial crack front, appears to have turned into a crazing zone. This is attributed to the quasi-static loading due to which there was

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enough time for the crazes to develop and merge together.

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Fracture surface micrographs reveal composition dependent distinct toughening mechanisms. While highly cross-linked (stoichiometric) epoxy system provides least resistance to material fracture, crazing and (possibly) plastic deformation contribute towards higher fracture toughness values in hardener-rich and resin-rich epoxy systems, respectively. Due to different toughening mechanisms the scale at which the material provides resistance

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to fracture will be different in resin-rich and the hardener-rich epoxy systems, therefore, KIc increases at different rates with Mc in non-stoichiometric cases (see, Fig. 4(a)).

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4.2.1 Mc - KIc relationship

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Beginning with the lowest value at stoichiometric composition, monotonically increasing KIc tends to saturate and attains a plateau value as the molecular weight is increased (see, Fig. 4(a)). In order to incorporate the effect of constituent proportion on the fracture behaviour of epoxy system, we express the fracture toughness KIc of epoxy variant as,

KIc = ( KIc )min + α ∆K ,

(6)

ACCEPTED MANUSCRIPT where the minimum and maximum fracture toughness values that can be obtained by varying the composition of epoxy system are referred by, (KIc)min and (KIc)max, respectively, with

∆K = ( KIc )max − ( KIc )min .

In the current study

( KIc )min

corresponds to the fracture

toughness value of stoichiometric composition, represented by K Ic (= 0.625 MPa√m; See,

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Table 1).The factor α signifies a measure of compositional deviation of epoxy system from the stoichiometry. The ( KIc )max (plateau value) can be determined by extrapolating either of

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the resin-rich or hardener-rich KIc vs. Mc curves. Alternatively, as illustrated in Fig. 4(b) the value of (extrapolated) KIc at µ = 0 can also be considered as (KIc)max. Hypothetically, zero

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cross-link density corresponds to the polymer with unconstrained molecular network, the case in which the material would exhibit extremely high resistance to fracture. In current investigation

( KIc )max

is calculated to be ~1.0 MPa√m (See, Fig. 4(b)). Justifiably, the

maximum fracture toughness value determined from both resin-rich and anhydride-rich cases

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is the same since the proportion of resin or hardener content is irrelevant at zero cross-link density.

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By considering M as a function of molecular weight of the epoxy system and β governing the rate at which KIc varies with Mc, the α is assumed to be of the form Mβ.

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Therefore,

K Ic = K Ic + M β ∆ K .

Clearly, M should be chosen such that its value varies between 0 and 1.

(7) From the

experimental observations the limiting values of M correspond to the stoichiometric composition (M = 0) and the extreme resin-rich or hardener-rich case (M = 1), respectively. We have the considered following form of M which is consistent with its limiting constraints.

ACCEPTED MANUSCRIPT M = 1−

Mc , Mc

(8)

where M c is the molecular weight of epoxy system with stoichiometric composition. 2

and β = 1 , for resin-rich and 2

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Equation (7) is plotted in Fig. 4(a) by choosing β = 3

anhydride-rich epoxy systems, respectively. Notably, the curves represented by Mc - KIc model closely follow the experimentally observed KIc variation with Mc. The ∆K in the model

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can be considered as a measure of Mc - KIc dependence, whereas the non-linearity parameter β represents a material characteristic that depends upon the process influencing the molecular

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weight of the epoxy system. In the current investigation, the molecular weight dependent fracture behaviour of resin-rich epoxy system is distinguished from the hardener-rich epoxy

5. Conclusions

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case by choosing distinct values of β.

DGEBA epoxy resin is mixed with anhydride MTHPA curing agent in several

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proportions for studying the effect of cross-link density and molecular weight on viscoelastic and fracture properties of epoxy system. The molecular weight of epoxy variant increases as

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the composition deviates from the stoichiometry, indicating decreasing cross-link density. It is observed that the glassy state sustains for longer duration (delayed glass transition) if the polymer exhibits lower storage modulus in the (glassy) state. A moderate variation in loss modulus and loss factor peaks is observed in adequately cross-linked epoxy systems. The glass transition temperature measured by dynamic mechanical analysis is consistently higher when compared to the ones measured by thermomechanical analysis. The glass transition temperature is observed to be monotonically decreasing from its maximum value at stoichiometric composition when either of the resin or hardener proportion is increased in the

ACCEPTED MANUSCRIPT epoxy system. The glass transition temperature shows a linear correlation with the inverse of molecular weight. Fracture toughness of epoxy variants KIc increases monotonically with increasing molecular weight Mc. The KIc is observed to vary more rapidly around stoichiometric

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composition in resin-rich system when compared to the anhydride-rich case. Distinctly different toughening mechanisms are evident from the fracture surface micrographs. While cleavage fracture is noticed in stoichiometrically prepared epoxy system, crazing and plastic

β

 M  = K Ic +  1 − c  ∆ K , is proposed for correlating Mc  

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systems, respectively. A model, K Ic

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deformation are dominating fracture mechanisms in hardener-rich and resin-rich epoxy

fracture toughness and molecular weight of epoxy systems (parameters with bar correspond to the stoichiometric composition). In the proposed Mc - KIc relationship ∆K represents the range of fracture toughness that can be attained by varying the epoxy composition. The value

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of parameter β which governs the nonlinear variation of KIc with Mc, is influenced by the presence of unreacted group (epoxide or anhydride) in the epoxy system.

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Acknowledgement

Authors would like to thank Aeronautics Research & Development Board (ARDB) for

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supporting this research through the grant DARO/08/1051629/M/I. Authors would also like to thank Professor Kamal Kar for extending DMA facility to the investigators for viscoelastic measurements.

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ACCEPTED MANUSCRIPT Figure Captions Figure 1. The storage modulus (E’) and loss modulus (E”) variation with temperature (T) in a representative 100:80 R/H ratio epoxy system (a). Effect of curing agent proportion on storage modulus (b), loss modulus (c), and loss factor (d), of epoxy variants.

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Figure 2. Effect of curing agent proportion on molecular weight (Mc) and cross-link density (µ) of epoxy variants. Figure 3. Effect of molecular weight on the glass transition temperature of epoxy systems. Figure 4. Effect of molecular weight (a), and cross-link density (b) on the fracture toughness of epoxy variants.

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Figure 5. Fracture surface micrographs of epoxy systems prepared with (a) 100:40, (b) 100:80 and, (c) 100:140 R/H ratios.

ACCEPTED MANUSCRIPT

S. No.

Resin

Density

Glass transition

Storage

Molecular

Fracture

hardener

ρ

temperature

modulus at

weight

toughness

ratio by

(g/cm3)

Tg (oC)

Tg+40

Mc

E’ (MPa)

(g/mol)

weight

DMA

TMA

100:40

1.208

68.0 ± 3.0

59.0 ± 2.0

7.92 ± 0.13

1147 ± 15

0.885 ± 0.032

2

100:60

1.199

114.5 ± 0.5

99.5 ± 1.0

24.17 ± 2.33

325 ± 11

0.703 ± 0.021

3

100:80

1.202

138.0 ± 1.0

121.0 ± 0.5

40.05 ± 1.45

222 ± 8

0.625 ± 0.030

4

100:100

1.201

132.0 ± 1.0

116.0 ± 0.5

38.00 ± 0.40

232 ± 5

0.707 ± 0.040

5

100:120

1.216

116.0 ± 0.5

98.5 ± 0.5

30.95 ± 0.65

292 ± 6

0.799 ± 0.036

6

100:140

1.216

98.5 ± 0.5

85.0 ± 1.0

24.35 ± 0.45

371 ± 7

0.865 ± 0.025

M AN U

SC

RI PT

1

AC C

EP

TE D

Table 1. Viscoelastic and fracture properties of resin/hardener ratio based epoxy variants. Error range is determined based on the data obtained from at least three experiments.

ACCEPTED MANUSCRIPT

Anhydride-rich Stoichiometric Resin-rich

100:80

E’

100:80 100:100

100:40

E”

Tg

100:140

100:140

(c)

SC

(b)

(a)

100:120

Anhydride-rich Stoichiometric Resin-rich

100:100

100:40

M AN U

100:60

RI PT

100:60

100:120

100:80

100:140 100:120 100:100 100:80

100:40

Anhydride-rich Stoichiometric Resin-rich

100:60

TE D

(d)

AC C

EP

Figure 1. The storage modulus (E’) and loss modulus (E”) variation with temperature (T) in a representative 100:80 R/H ratio epoxy system (a). Effect of curing agent proportion on storage modulus (b), loss modulus (c), and loss factor (d), of epoxy variants.

ACCEPTED MANUSCRIPT Anhydride-rich Stoichiometric Resin-rich

M AN U

SC

Mc

RI PT

µ

EP

TE D

Figure 2. Effect of curing agent proportion on the molecular weight (Mc) and cross-link density (µ) of epoxy variants.

AC C

ζ

DMA

TMA

Anhydride-rich Stoichiometric Resin-rich

Figure 3. Effect of molecular weight on the glass transition temperature of epoxy systems.

ACCEPTED MANUSCRIPT (a)

β = 1/2

RI PT

β = 3/2

Anhydride-rich

SC

Stoichiometric

(b)

M AN U

Resin-rich

Anhydride-rich

(KIc)max

Stoichiometric

AC C

EP

TE D

Resin-rich

(KIc)min

Figure 4. Effect of molecular weight (a), and cross-link density (b) on the fracture toughness of epoxy variants.

ACCEPTED MANUSCRIPT

(a)

2

1

3

2 mm

2

1

3

2 mm

(b)

500 µm

(c)

3

2 mm 500 µm

M AN U

SC

250 µm

2

RI PT

1

AC C

EP

TE D

Figure 5. Fracture surface micrographs of epoxy systems prepared with (a) 100:40, (b) 100:80 and, (c) 100:140 R/H ratios.