Mixed-mode I/III fracture toughness of polymer matrix composites toughened with waste particles

1 Introduction

Industrial applications of polymers have increased and are being continuously developed in various fields such as construction, automotive, marine, and aerospace industries using additive reinforcement. The inclusion of fillers into the polymers may contribute to enhance different mechanical properties like strength and fracture toughness in addition to providing a significant cost reduction of the polymer composite [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. In addition, the mechanical properties of the polymer-based particulate composites have been affected by particle content and adhesion strength of particle/matrix interface [2], [3], [4], [5]. There are many fillers that can improve the mechanical properties and fracture toughness of composites such as industrial wastes: sewage sludge ash (SSA), fly ash (FA), and rice husk ash or conventional ceramic powders: silicon carbide (SiC), glass, alumina, silica, etc. [6], [7], [8], [9], [10], [11], [12], [13]. The industrial wastes SSA and FA affect the environment hazardously; therefore, recycling of these wastes plays an important role in the reduction of their harmful effects [6], [7], [8], [9]. Generally, the usage of the polymer composite including FA particles has shown positive effects on tensile, flexural, and fracture properties at a certain weight fraction and particle sizes in the range of 26–152 μm [6], [7], [8].

Filler of SSA is produced from wastewater purification operation. A few studies examined the usage of SSA with particle sizes in the range of 1–250 μm and their applications in the construction industry have contributed to improve the mechanical properties [9], [10]. Bhagyashekar and Rao [11] indicated that the inclusion of microscale SiC particles up to a content of 30 wt% within the epoxy resin showed an increase in the tensile and flexural modulus of the composites.

In recent years, several researchers have conducted many experimental studies on the fracture behavior of particle-filled polymer composites of single edge notch bend (SENB) specimens under mode I fracture [12], [13], [14], [15], [16], [17]. Roulin et al. [17] showed that the mode I stress intensity factor of the SiC particles filled polymer composite for SENB specimens increased with the addition of SiC particles. In general, mixed-mode fracture is the most common fracture case related to crack bodies. Hence, various studies have been achieved with the aim of testing mixed-mode fracture toughness I/II [18], [19], [20] and I/III [21], [22], [23], [24], [25], [26]. Avci et al. [26] investigated the effect of varying crack angles for the SENB specimens on the mixed-mode I/III fracture toughness behavior of the polyester resin filled with sand particles and chopped glass fiber. Qinghua and Jianqiao [27] stated that the mechanical interaction between microsize particle and crack tip could give rise to composite toughness. They clarified that this behavior appeared especially in the form of crack tilting (opening and sliding) for mixed-mode I/II or crack twisting (opening and tearing) for mixed-mode I/III.

Based on the literature survey, many of these studies dealt with mode I or mixed-mode fracture toughness I and II and I and III with different particle types. But, to our knowledge, never has been studied the effect of microscale SSA, FA, and SiC particles in the polymer composite on the mixed-mode fracture toughness (I+III). The objective of this article is to study the effects of three particulate fillers on the mixed-mode fracture behavior of particle-filled polymer composites. The effects of industrial wastes FA and conventional particle SiC on the mechanical properties of the polymer composites are well known and have been studied by many researchers. Because of this, the fillers of FA and SiC were used to compare with new industrial waste SSA. The particle weight fractions were 5%, 10%, 15%, and 20% content of the total weight of the polymer composites. The SENB beams were tested with crack inclination angles 30°, 45°, 75°, and 90° using three-point bending (TPB) test. The critical crack tip stress intensity factors (K_Ic, crack angle 90° and K_IIIc), and the critical strain energy release rates (G_Ic and G_IIIc) were determined and results were compared.

2 Specimens preparation and tests

2.2 Specimens preparation

The particulate polyester-matrix composite specimens were produced by pouring the particulate mixture in the mold. The measured quantity of the particle was put in the polyester resin and evenly mixed using a mechanical stirrer with a speed of 750 rpm for 20 min in order to attain a homogeneous mixture. Then, 2 wt% of hardener was added to the mixture for quick setting of composite specimen. The polymer composites were molded and cured at room temperature for 1 day. Then, specimens were post-cured in the room temperature for 2 weeks preparing for mechanical testing.

The specimens were prepared according to the following procedures:

1. Tensile tests were performed according to the ASTM D 638 standard with dimensions of 165 mm× 13 mm×4 mm for a gauge length of 50 mm.

2. Fracture tests were performed according to ASTM D 5045 standard with dimensions of 88 mm× 20 mm×10 mm and a/W=0.45, where a and W are crack depth and thickness of the specimen, respectively.

3. To create notches having 9 mm deep with the angle θ inclined to the beam axis as shown in Figure 1, the SENB specimens were cut by using a 0.6 mm thick cutter. Surgery blade was used to sharpen the notch tips of the specimen with the crack inclination angles of θ=30°, 45°, 75°, and 90° to the beam axis.

Figure 1:

Schematics of the geometrical configuration SENB specimen.

2.3 Tensile tests

The tensile tests were performed to measure tensile modulus and Poisson ratio, which are needed to calculate fracture toughness properties. Tensile properties of the dog-bone-shaped particulate polymer composites were determined according to the ASTM D638-10 standard test method using the Shimadzu testing machine AG-X series (Shimadzu Corporation, Kyoto, Japan) and data acquisition card Ni-9237 (National Instruments Corporation, Austin, TX, USA) (Figure 2). During the testing, the crosshead speed was set to 2 mm/min. At least three specimens were tested for each particle content, and average value of the results was calculated.

Figure 2:

Tensile test devices.

3 Experimental results and discussion

3.1 Morphology

The morphology of the particle-filled polyester-matrix composites was investigated using a scanning electron microscope (SEM) (JEOL JSM-6390 lv, Gaziantep University, Gaziantep, Turkey), and their micrographs are given in Table 2. It can be noticed in the SEM micrographs (Table 2) that the well distribution of FA, SSA, and SiC particles occurred within the polymer resin. However, when the content of FA, SSA, and SiC particles within polyester composites was above 10 wt%, the particle agglomeration was increased resulting in a larger size of the particle, thus causing weakness in adhesion strength between the particle and matrix. [4], [16]. Therefore, for the FA, SSA, and SiC particle content of 20 wt%, the diameter of large particles reached about 41, 71, and 101 μm, respectively.

Table 2:

SEM micrographs of composite samples at various content of filler (images are at a magnification of 230×).

3.2 Tensile properties of the particulate polymer composite

Table 3 presents the tensile properties of the composites for various particle contents. In spite of the tensile tests presenting a nonlinear response of the elastic plastic curves of the studied particulate composite (Figure 3), all the fracture surfaces of the samples were flat without any nicking or shear edges. Accordingly, the samples failed in a brittle manner when they were tested. Moreover, there was no effective permanent decrease in samples’ cross-sectional area. Therefore, the samples of particulate composite exhibit a quasi-brittle behavior.

Table 3:

Tensile properties of the particulate polymer composites.

Material type	Filler content (wt%)	Tensile strength (MPa)	Tensile modulus (MPa)	Poisson ratio
Neat resin	0	48.1 (±1.31)	2075 (±56)	0.365
SSA	5	50.2 (±1.06)	2197 (±59)	0.354
	10	47.2 (±0.65)	2320 (±65)	0.337
	15	42.3 (±2.37)	2601 (±79)	0.326
	20	40.6 (±1.92)	2876 (±99)	0.311
FA	5	51.9 (±1.71)	2441 (±81)	0.340
	10	47.5 (±2.58)	2623 (±74)	0.315
	15	43.9 (±1.49)	2914 (±68)	0.310
	20	41.8 (±2.18)	3340 (±82)	0.302
SiC	5	52.0 (±2.05)	2516 (±83)	0.363
	10	49.0 (±1.58)	2646 (±58)	0.348
	15	47.4 (±1.21)	3050 (±71)	0.330
	20	42.2 (±2.52)	3532 (±95)	0.324

Figure 3:

Tensile stress-strain responses at particle contents of 5 and 20 wt%.

It is observed that for all the specimens of the particulate composites, the tensile strength increased up to 5 wt% content of FA, SSA, and SiC, then decreased because of particle agglomeration phenomenon. In addition, tensile strength as the largest stress value reached final value at specimen failure. As shown in the elastic part of stress-strain curves and corresponding data in Table 3, the tensile modulus of composites increases with increasing particle weight content due to higher stiffness of inorganic particles. It is clear that the Poisson ratio values decrease with increasing particle content.

3.3 Three-point bending test of un-notched specimens

The fracture load values of TPB test for un-notched specimens are presented in Table 4, and load-displacement curves are shown in Figure 4. The highest improvement of fracture load was at SSA, FA, and SiC content of 5 wt%, and then followed the trend of decreasing. Hence, the maximum fracture loads for SSA, FA, and SiC composites were 3272, 3163, and 3046 N with a maximum increment of 7.7%, 4.1%, and 0.2%, respectively, compared with that of unfilled composite.

Table 4:

Fracture loads of TPB test for un-notched specimens.

Composite type/content	Fracture load (N)
	Unfilled	5 wt%	10 wt%	15 wt%	20 wt%
SSA	3039 (±62)	3163 (±43)	2968 (±52)	2827 (±55)	2673 (±85)
FA	3039 (±62)	3273 (±58)	3059 (±115)	2868 (±106)	2747 (±61)
SiC	3039 (±62)	3046 (±57)	2857 (±42)	2640 (±43)	2420 (±54)

Figure 4:

Load-displacement curves for un-notched specimens at particle content of 5 and 20 wt%.

3.4 Three-point bending test of SENB specimens

The fracture load of SENB specimens reached its maximum value at SSA, FA, and SiC content of 5 wt%, for θ=90° (Table 5), the same behavior was observed when the crack inclination angle was decreased. This behavior was attributed to the effect of particle agglomeration. Furthermore, for high particle content the large particles caused low interfacial adhesion such that the particles could not pin the crack front and offered little resistance [4], [16], [28].

Table 5:

Fracture loads of TPB test for SENB specimens.

Composite type	Notch angle, θ (degree)	Fracture load (N)
		Unfilled	5 wt%	10 wt%	15 wt%	20 wt%
SSA	90o	237.7 (±7.3)	256.3 (±10.7)	243.8 (±4.5)	232.0 (±10.2)	213.6 (±6.3)
	75o	251.9 (±11.1)	270.3 (±7.5)	260.5 (±9.0)	243.4 (±9.4)	221.8 (±4.2)
	45o	272.5 (±5.8)	295.4 (±9.2)	282.9 (±10.3)	268.6 (±12.7)	238.6 (±8.1)
	30o	315.3 (±6.9)	348.7 (±5.7)	341.8 (±6.5)	317.8 (±7.9)	274.9 (±9.4)
FA	90o	237.7 (±6.5)	268.6 (±10.8)	251.2 (±6.7)	248.8 (±2.5)	236.3 (±5.9)
	75o	251.9 (±5.4)	284.1 (±12.1)	268.5 (±8.3)	250.1 (±4.1)	233.0 (±3.4)
	45o	272.5 (±10.1)	319.3 (±8.7)	297.8 (±5.5)	283.5 (±5.5)	269.7 (±8.5)
	30o	315.3 (±8.9)	332.9 (±4.5)	323.94 (±7.5)	306.5 (±9.8)	287.4 (±11.2)
SiC	90o	237.7 (±7.4)	247.0 (±5.8)	231.9 (±11.1)	208.7 (±5.9)	176.3 (±10.3)
	75o	251.9 (±5.8)	260.2 (±9.5)	236.8 (±12.8)	217.1 (±7.2)	190.7 (±7.5)
	45o	272.5 (±8.9)	281.0 (±6.4)	263.8 (±7.6)	229.6 (±10.3)	209.4 (±8.2)
	30o	315.3 (±8.5)	325.4 (±7.2)	304.7 (±9.5)	287.2 (±13.1)	255.8 (±12.4)

It is obviously seen that in Table 5 and Figure 5, the magnitude of the load for θ=30° is higher than the other inclination angles for all filler types. This failure was seen in all weight fractions of particulate composite specimens with the crack inclination of θ=30°. It is also clear in Figure 5 that the load-displacement curves of unfilled and particulate filled polyester seem to follow linear behavior up to fracture load.

Figure 5:

Load-displacement curves for SENB specimens having different crack inclination angles at content of 5 wt% (A) SSA, (B) FA, and (C) SiC.

3.5 Crack paths

The fracture surfaces of the SSA composite specimens for the content of 5 wt% with different crack angles are shown in Figure 6. In general, the crack forms continuously along the preliminary crack when θ=90^o. Hence, for θ< 90^o, not only crack propagated within an angle according to the preliminary crack, but also the crack twisted along the direction of propagation. The same behavior was observed by several researchers [21], [24] who showed that crack would propagate by the twisted path for θ<90^o. The bright crack surface (Figure 7A) showed the brittle behavior of the mode I fracture. When crack inclination angle was less than 90^o, crack propagation was turned from a nearly straight path of the crack (Figure 7A) to curved-path crack propagation (Figure 7B–D). Similar behavior was observed for various particle contents of the three particulate polyester composite systems.

Figure 6:

Crack kink angles of SENB specimens at SSA content of 5 wt% for: (A) mode I θ=90°, (B) mixed-mode θ=75°, (C) mixed-mode θ=45°, (D) mixed-mode θ=30°.

Figure 7:

Fracture surfaces of SENB specimens at SSA content of 15 wt% for: (A) mode I θ=90°, (B) mixed-mode θ=75°, (C) mixed-mode θ=45°, (D) mixed-mode θ=30°.

4 Determination of critical stress intensity factors

The stress intensity factors for SENB samples of linear elastic fracture mechanics (LEFM) were examined by some researchers [23], [24], [25], [26], [29], [30]. The critical stress intensity factor for mode I can be calculated by using initial notch depth method from the following equations:

where P is the fracture load for crack propagation, B is the specimen width, and s is the length of the span. f(aW) is the correction parameter depending on the (a/W) ratio as shown in Figure 1.

There is no standard method available to determine the critical stress intensity factor for mixed-mode I and III. However, for an inclined crack Pook [23], Manoharan and Lewandowski [25], and Avci et al. [26] indicated that the apparent stress intensity factor K_Acan be calculated by equation (1) for the mixed-mode I and III. The resulting values of K_Icand K_IIIcwere obtained by substitution K_Ainto equations (3) and (4) as follows:

and

The critical stress intensity factors K_Icand K_IIIcwere calculated from equations (1), (3) and (4), as:

and

The variation of the stress intensity factors (K_Ic and K_IIIc) with the crack inclination angle and particle content is shown in Figure 8. When the crack inclination angle changed from 0º to 90º, the K_Ic increased to reach the highest values at θ=90º as 1.67, 1.73, and 1.56 MPa√m at particle content 5 wt% of SSA, FA, and SiC composites, respectively. In contrary, K_IIIcreached maximum values at θ=30º, while these values decreased with inclusion of mode I loading condition to the system. As expected, at θ=90º K_IIIcvalues reached zero. K_Icand K_IIIc values were equal at the crack inclination of 45º due to equal loading condition.

Figure 8:

Mode I and mode III critical stress intensity factors of (A) SSA, (B) FA, and (C) SiC filled polyester composites.

The increment in K_IIIc values was attributed to the increase in the crack surface area due to the change in crack inclination angle as the crack propagates (fracture plane at an angle to the pre-crack), leading to an increase in the fracture toughness.

It was noticed that the studied particulate polymer composites exhibited brittle nature of composites; as even under a mixed-mode fracture, the fracture of these composites had a tendency to pure mode I. The results indicated clearly the effect of this phenomenon, as even at lower crack angles; the values of K_Icbecame significant and showed slight difference with K_IIIc.

The K_Ic and K_IIIcvalues of the particulate polymer composites were also affected by the particle content and filler type. Hence, the K_Ic and K_IIIc of the particulate composites start to decrease with SSA, FA, and SiC content above 5 wt%. This behavior was attributed to particles agglomeration that could have occurred and caused stress concentration areas and eventually weakened the interfacial adhesion between the matrix and particle. Therefore, the good interfacial adhesion lead to particles can pin the crack front and offer more crack growth resistance causing enhancement in the fracture toughness of the particulate polymer composite [16], [28].

5 Determination of critical strain energy release rate

In the initial notch depth method, as the particulate polymer composite is assumed to exhibit quasi-brittle behavior during SENB tests, LEFM can be implemented to calculate the K_Icand K_IIIcvalues, which can be used to calculate G_Icand G_IIIcaccording to equations (7) and (8), respectively:

and

where ν and E are Poisson ratio and tensile modulus of the composite, respectively. The strain energy release rate matches J-integral for linear elastic materials.

In general, the G_Icand G_IIIccurves behavior (Figure 9) followed the same behavior as the K_Icand K_IIIc curves. The G_Ic values increased as the crack inclination angle increased from θ=30° to θ=90°, while the G_IIIc values decreased. However, Figure 9A shows that for the SSA filler, the G_IIIc value momentarily increases from θ=30° to θ=45° and then continue to decrease up to θ=90°. The highest G_Ic and G_IIIc values were observed at FA content of 5 wt% with an increment of 13.0% and 27.3% (at θ=75^o) compared to bulk polyester, respectively. While the lowest G_Ic and G_IIIc values were recorded at SiC content of 20 wt% with a decrement of 66.3% and 68.9% (at θ=75^o) lower than bulk polyester, respectively. For SSA-filled composites, the maximum G_Ic and G_IIIc values were obtained at content of 5 wt% with an increment of 2.1% (at θ=45^o) and 4.5% (at θ=75^o) higher than bulk polyester, respectively.

Figure 9:

Mode I and mode III critical energy release rate of (A) SSA, (B) FA, and (C) SiC filled polyester composites.

6 Conclusion

The effects of industrial wastes, SSA and FA, and conventional ceramic powder, SiC with variations of particle contents on tensile strength and fracture toughness of particulate polyester composites were examined. The results showed that the composite strength and mixed-mode I and III fracture toughness were affected by the addition of particles, and that was attributed to the relation between the transferred stress between matrix and particle and the particle/matrix interfacial adhesion strength. The SEM micrographs results indicated good dispersion of SSA, FA, and SiC particles within the polymer matrix.

The mode I fracture toughness, K_Ic, values increased when the crack angle changed from 30^o to 90^o as the mode III fracture toughness, K_IIIc, values decreased. For SENB specimens, the highest values of K_Icand K_IIIcwere obtained at FA content of 5 wt%, with an increment of 17.1% (at θ=45^o) compared to bulk polyester. While the minimum K_Icand K_IIIc values were obtained at SiC content of 20 wt%, with a decrement of 25.2% and 24.1% (at θ=75^o) less than bulk polyester, respectively. For SSA-filled composites, the highest improvement in K_Icand K_IIIcvalues for SENB specimens were obtained at 5 wt% content, with a maximum increment of 8.4% (at θ=45^o) higher than bulk polyester.

The variations of G_Icand G_IIIcgraphs follow the same behavior of the K_Icand K_IIIc curves. The values of fracture toughness were consistent. The decreasing of critical strain energy release rate resulted from the high brittleness of composites at high particle content.

As a result, SSA and FA waste particles can be used as fillers for polymer due to good bonding between polymer matrix and these particles that significantly affected the tensile strength and fracture toughness values of the studied composites. This mechanism indicated the chemical compatibility of the SSA- and FA-filled polymer composites system.