Experimental Study on Static and Dynamic Fracture Toughness of Cured Epoxy Resins

The paper investigates experimental results of static and dynamic fracture toughness. The three-point bending test and the Charpy pendulum test were performed for two kinds of polymers: Epidian 5 epoxy resin cured with Z1 curing agent and Epidian 53 epoxy resin cured with Z1 curing agent. The comparison between the values of a maximum static and a maximum dynamic force are discussed as well as the values of static and dynamic fracture toughness, with special emphasis on microscopic views of crack propagation.


INTRODUCTION
The definition of epoxy resins states that they constitute low-molecular-weight pre-polymers containing more than one epoxide group.Epoxy resins are widely used in many applications such as paints, coatings, adhesives, industrial tooling, aerospace industry, electronic materials and biomedical systems.The materials of that kind possess excellent mechanical properties and are chcaracterized by high adhesiveness to many substrates [4].The main advantages of polymer matrix composites based on epoxy resins are their high elastic modulus and high tensile strength [16].
Furthermore, due to their wide curing temperature range, low coefficient of thermal expansion, high insulation resistance, and good resistance to chemical corrosion, epoxy resins have been also used e.g. in cryogenic engineering [17].However, variable thermal conditions of the environment which are found in such industries as aircraft, automotive or medicine, can affect the strength of adhesive joints.As discussed in [5], a thermal shock provoked a 50% decrease in the shear stress values for the steel specimens bonded with Epidian 5 epoxy adhesive with Z1 curing agent.Thermal fatigue could also cause a decrease of the Young's modulus for epoxy adhesives [6].
Moreover, epoxy resins are rigid and brittle materials which possess low resistance to crack initiation and growth.Hence, their use is limited in some applications, such as structural materials [4].For brittle materials -where cracks are most involved in the mechanical failure and hardness measurement -it is crucial to predict the fracture toughness which represents the ability of the material to resist crack propagation.It is one of the most essential parameters in fracture mechanics of solid materials [8,14,15].Fracture toughness is determined as a delamination resistance with reference to such materials as carbon fiber reinforced polymeric (CFRP) laminates, the main disadvantage of which is a tendency to delaminate.The finite elements (FE) simulations of the fracture toughness test configurations prior to the physical experiments are helpful and could be an invaluable source of knowledge.The example of such a modeling method is the virtual crack closure technique (VCCT) [11,12].
The dynamic fracture toughness plays an important role in the engineering applications where brittle materials are used in structural elements and a dynamic event may occur during e.g.crash, explosion, blast, projectile penetration [9].However, in the case of the dynamic toughness, e.g.determined by the Charpy pendulum test, it is quite difficult to analyze the complicated fracture behavior because the propagation and linkage of microcracks are caused almost simultaneously during the dynamic load [2].
In this paper, the behavior of two cured epoxy resins under static and dynamic loading was analyzed.For brittle materials such as polymers or ceramics, it is recommended to use the same formula to compute both static and dynamic fracture toughness [1,7].The criterion of the loading dynamic force oscillations fading in time must be fulfilled as the necessary condition for the abovementioned approach [13].Thus, the criterion was fulfilled during dynamic examination.
In the study, static and dynamic fracture toughness (K IC and K ID , respectively) were calculated according to [13]: where: F st MAX is the maximal static force, F dyn MAX is the maximal value of the dynamic force read from its time course; R st is a span of supporting rollers in a three-point bending device, R dyn is a span of Charpy pendulum's buttresses; b and h are dimensions of a specimen's cross-section; ψ(ũ) is the function of notch dimensions which has the following form [1,3,7,10]: (3) where: ũ = u / h is a normalized notch depth.All specimen's dimensions are presented in Figure 1.

EXPERIMENTAL PROCEDURE
Two kinds of strength test were performed on polymer notched beams: quasi-static, i.e. a three-point bending, as well as dynamic -an instrumented impact test.During the experiment, samples of two groups of materials were used: Epidian 5 epoxy resin cured with Z1 curing agent (E5+Z1(10%)) and Epidian 53 epoxy resin cured with Z1 curing agent (E53+Z1(10%)).The amount of the curing agent in both cases was 10% of a total weight of epoxy resin.Each specimen had a shape of beam with a rectangular crosssection and a notch in the midspan, as shown in Figure 1.Such specimens were used for static and dynamic tests.Four sets of E5+Z1(10%) samples and four sets of E53+Z1(10%) samples were examined.The dimensions of specimens were as follows: b×h×L = 4×10×100 mm.
The samples were fabricated in the laboratory of the Department of Production Engineering at room temperature 17-18ºC and humidity 21-23%.First of all, the epoxy resin and the curing agent were mixed together for 5 min using a mechanical paddle mixer with rpm=1130.Then, a chamber with a vacuum pump was used to deair the mixture.Two cycles of deairing were performed (2×5 min).Subsequently, the assigned mold was filled with the mixture.Both E5+Z1(10%) and E53+Z1(10%) samples were fabricated using the same method.A few days later, the beam samples were taken out of the mold and milled to obtain b = 4 mm.The milling process was conducted using the vertical machining center FV580a.A shell mill made of high shear steel HSS with diameter d = 35 mm and a number of cutting edges z = 6 was used.Milling rotation speed was 1150 rpm while feed rate V f = 52 mm/min.Afterwards, V-notches were cut with an angle needle file and deepened with a cutter knife.By this technique, notches with the depth u = 2.7-2.9 mm and the bottom width n = 3.1-3.3mm were fabricated.
All examinations took place at an ambient temperature.The three-point bending test was conducted with the universal testing machine (model Autograph AGS-X 5 kN, Shimadzu Corporation, Japan) equipped with an adequate loading device.First of all, a preliminary examination on two specimens was performed.The span (R) of the supporting rollers was 80 mm.It was observed that the crack propagation for E53+Z1(10%) sample was growing much slower than the one for E5+Z1(10%) sample.Thereby, a shorter span was adjusted for E53+Z1(10%) specimens.Finally, for the main examination the span was 80 mm for E5+Z1(10%) and 60 mm for E53+Z1(10%).The samples were loaded vertically very slowly (quasi-statically).Loading crosshead's velocity was 1 mm/min.Time, force and displacement were registered on a computer hard drive.The view of a loaded specimen during the three-point bending test is shown in Figure 2.
Dynamic tests were conducted with the instrumented Charpy pendulum (KB Prueftechnik GmbH, Hochdorf-Assenheim, Germany) equipped with a 7.5 J tup.A maximum velocity was 3.815 m/s and a fall angle was 157.32º.The time course of the impact force at a frequency of 1 MHz was registered by a built-in resistive sensor while the tup touched the specimen.The data such as force, energy, time and displacement were recorded on a hard drive by an appropriate A/D PC card (model NuDAQ PCI-9812, AdLink Technology Inc., Taipei, Taiwan).

RESULTS AND DISCUSSION
As a result of the three-point bending test E5+Z1(10%) the specimens were broken in a brittle way whereas E53+Z1(10%) specimens were not completely broken into two parts but a growing crack was observed.The microscopic views of a V-notch before and after the three-point bending test are presented in Figures 3  and 4 for both kinds of specimens.In the case of E53+Z1(10%) sample the dimensions of a crack growth are given.The values of the static force F st versus displacement s are plotted in Figures 5 and 6 for four E5+Z1(10%) and E53+Z1(10%) specimens.As can be noticed, the static force for E53+Z1(10%) samples was about four times higher than for E5+Z1(10%).The value of the maximum static force F st MAX for each specimen is given in Table 1.The average value of F st MAX for E5+Z1(10%) specimens equals 19.7 N whereas for E53+Z1(10%) it equals 78.4 N. The maximum difference between F st MAX values for E5+Z1(10%) and E53+Z1(10%) samples is equal to 2.1 N and 12.1 N, respectively.
As a result of the dynamic-Charpy test, the values of the dynamic force F dyn versus time t were obtained and plotted in the next two graphs.Figure 11 shows the average values of static and dynamic fracture toughness.As can be seen in the graph, for E5+Z1(10%) specimens, the dynamic feature was over two times higher than the static one.Moreover, for E53+Z1(10%) static fracture toughness was approximately equal to dynamic fracture toughness.

CONCLUSIONS
The examination of static and dynamic fracture toughness were performed for E5+Z1(10%) and E53+Z1(10%) specimens.The maximum values of static and dynamic forces were obtained for two kinds of materials.The average maximum dynamic force was about six times higher than the average maximum static force for E5+Z1(10%) and was about two times higher for E53+Z1(10%).It was noticed that E53+Z1(10%)      was more flexible than E5+Z1(10%) which was quite brittle.K ID was much higher than K IC for E5+Z1(10%) samples whereas for E53+Z1(10%) specimens it was a bit lower.As can be inferred, the more flexible the resin is, the less visible the differences between K IC and K ID are.In the case of E53+Z1(10%) the fracture resistance was at a similar level for both static and dynamic test.For E5+Z1(10%) a stress wave was probably growing gradually during the static loading but it had no time to propagate during the dynamic loading.
As described above, a value of dynamic fracture toughness could be different from its static counterpart.Thus, it would be interesting to examine the values for other materials.Furthermore, it also appears to be worth analyzing the influence of changing conditions on the fracture toughness of materials, e.g. the influence of thermal shock on the value of static and dynamic fracture toughness of polymers.Moreover, it would be interesting to deeply analyze the microscopic views of V-notches after the tests and discuss the directions of crack propagation.It was observed that microcracks had appeared in the fracture surface of the tested specimens.

Fig. 1 .
Fig. 1.Shape and dimensions of a specimen Figures 7 and 8 show the values for four E5+Z1(10%) and E53+Z1(10%) specimens.As inferred, the dynamic force in both cases is at a similar level.The value of the maximum dynamic force F dyn MAX for each sample is given in Table 2.The average value of F dyn MAX for E5+Z1(10%) specimens equals 120.6 N whereas for E53+Z1(10%) it equals 134.4 N. The maximum difference between F dyn MAX values for E5+Z1(10%) and E53+Z1(10%) samples is equal to 26.7 N and 20.5 N, respectively.The microscopic views of a fracture surface after the Charpy test are shown in Figures 9 and 10.Crack propagation and microcracks are clearly visible.

Fig. 2 .
Fig. 2. The view of a loaded specimen during the three-point bending test

Fig. 11 .
Fig. 11.Average value of K IC and K ID for two kinds of specimens

Table 1 .
Value of the maximum static force for each specimen

Table 2 .
Value of the maximum dynamic force for each specimen