Microscopic mechanism of multiaxial fatigue of vulcanised natural rubber

Materials and specimens

The materials studied are two kinds of vulcanised natural rubber with different formulas, which include natural rubber, charcoal, zinc oxide, stearic acid, antioxidant and accelerant, etc. The formulations are shown in Table 1. The cure condition is 30 min at 142°C. Their basic mechanical properties are listed in Table 2. The specimen geometry is shown in Fig. 1. The specimen is designed with the purpose of carrying out multiaxial fatigue tests so that the gauge length is short to avoid torsional buckling. Because of non-uniformity deformation of the specimen, the gauge length of the specimen cannot be taken directly as the grip-to-grip distance. Instead, an effective material element gauge length is estimated via comparison of the experiment and predicted axial load–displacement relationships by finite element analysis (FEA), which is known as inverse method.8 Therefore, a three-dimensional (3D) finite element analysis model is built with the software of ANSYS. The element used in FEA is solid182 U-P element. An incompressible, Ogden34 hyperelastic constitutive model is used in the analysis. It is expressed as follows (1) where W is the strain energy density, λ_i (i = 1,2,3) is the principal stretch ratio, and μ_i, α_i are material constants. A tensile test is conducted on a rectangle film specimen. Thus the material constants can be fitted for N = 3 as follows:

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Figure 1

Dimensions of specimen (units: mm)

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Table 1

Experimental compound formulation used in this study

Components		Natural rubber	Carbon black	Zinc oxide	Stearic acid	Sulphur	Accelerating agent	Others
Phr	Rubber A	100	50	5	2·5	1·6	1·5	13·3
	Rubber B	100	55	5	2·0	2·0	0·8	18·1

*

Part per hundred rubber by weight.

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Table 2

Mechanical properties of vulcanised natural rubber

Material type	Density/g cm−3	A shore hardness	ϵfail/%	UTS/MPa	300% elongation modulus/MPa
Rubber A	1·12	60	625	22	2·1
Rubber B	1·13	70	530	26·5	3·7

Material A

Material B The experimental and optimised numerical stress–strain curve is shown in Fig. 2. It can be found that the FEA result is in good agreement with the experimental strain, which is obtained by the ratio of measured displacement and an effective gauge length determined to be 5·7 mm. The stress and strain are engineering stress and strain in the paper.

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Figure 2

Comparison of test results and FEA results for two kinds of materials

Fatigue loading conditions

All the tests were conducted on a self-built mini type tension–torsion material testing apparatus which provides strain or stress control mode and controllable testing environmental temperature. The capacity of the testing apparatus was axial force of 100 N and torque of 1 Nm. Resolution of displacement was 1 μm and resolution of rotation was 0·004 degree, which met the demand of tests. The load was measured by a load cell. The displacement and rotation angle were measured by an optics encoder. The data were collected by an automatic data acquisition system. All the tests employed triangle wave and were conducted at room temperature.

Figure 3 shows the loading paths adopted in rubber fatigue tests, which are uniaxial tension and rhombus loading path. A rapid loading drop knee point is defined as fatigue failure, normally about 30% loading drop for material A and 20% loading drop for material B, which usually causes a visible crack about 1 mm in size on the specimen. Fatigue test conditions and results for rubber material are listed in Table 3. The strain is engineering strain. Specimen 1-A means path 1 for material A, and the rest may be deduced by analogy.

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Figure 3

Proportional and non-proportional loading paths

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Table 3

Fatigue test results

Rubber	Specimen	Path	Time/cycle/s	ϵmin/%	ϵmax/%	γmin/%	γmax/%	fatigue life/cycles
A	1-A	1	1·5	0	150	0	0	25 250
	2-A	2	1·5	0	150	−35	35	13 160
B	1-B	1	1·5	0	150	0	0	6400
	2-B	2	1·5	0	150	−35	35	3700

Observation of scanning electron microscopy

The failure section of vulcanised natural rubber was cut down from specimens. An XL30E SEM was used to take photographs for the failure sections. Energy spectrum analysis was also conducted.

Fatigue property analysis

According to Table 3, under the same engineering strain amplitude, the fatigue life under non-proportional loading is much lower than uniaxial loading. On the one hand, this is because under non-proportional loading, the maximum shear stress plane rotates continuously leading to faster fatigue damage accumulation. This makes the van der Waals bond between the charcoal particles break much greatly. Thus, stress descends more rapidly due to the damage of rubber molecule chains. On the other hand, under the same condition, multiaxial case is more complicated loading path, leading to the increase in potential energy in multidirections.

At the same strain amplitude, the cyclic stable axial and shear stress–strain curves are shown in Fig. 4 for material A and material B under uniaxial and multiaxial loading. It can be seen from Fig. 4a that hysteresis loops of axial stress–strain are almost the same under uniaxial and multiaxial loading for the same material. However, the existence of the shear stress–strain hysteresis energy in Fig. 4b for multiaxial loading will induce more fatigue damage than that of uniaxial fatigue. Thus, the fatigue life under non-proportional loading is relatively short in Table 3. It also shows that the axial and shear stress response of material B is much higher than material A, so fatigue life of material B decreases due to easier chemical bonds breaking under higher stress.

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Figure 4

Stress–strain diagram for two rubbers under same strain amplitude

The stress amplitude drop curves with cycles under uniaxial and multiaxial loading for the two materials are shown in Figure 5 Figs. 5 and 6 respectively. Here, the stress is engineering stress. It can be seen from the figures that under either uniaxial or multiaxial loading, the dynamic fatigue process of rubber can be divided into three stages. The first stage is the initial part of test with a stress softening phenomenon. This significant initial decrease in material stiffness is believed to be related to the irreversible breakage of various types of bonds in the elastomer network.9 Then in the second stage, in half-logarithm coordinates, the load drop rate of material keeps a constant value, and stress changes slowly. Microcracks generate inside the material or on the surface, which results in macrocracks with a stable extending stage of cracks. In the third stage, cracks grow rapidly until failure occurs with an instable extending stage of cracks. A knee point is observed between the second and third stage. The stress drop rule in the torsional direction is similar with the uniaxial case, which can be divided into three stages.

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Figure 5

Stress amplitude evolutions with cycles for two kinds of materials under uniaxial loading

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Figure 6

Stress amplitude evolutions with cycles for two kinds of materials under rhombic loading path

It can be seen from Figure 5 Figs. 5 and 6 that under either uniaxial or multiaxial loading, with the same strain value, the stress response of material A is much lower than that of material B, while the life of material A is much longer than that of material B. According to the viewpoint of molecule, dynamic fatigue failure is due to the break of chemical bond. During the cyclic strain load, stress concentrates on the weaker bonds continuously. When the stresses arrive the strength of bond, the bond breaks and microcracks occur. Hence, in the stress concentration point, the molecule chain in the tip of the cracks will elongate with viscoelasticity until breakage. Therefore, the fatigue life of material A is much longer than that of material B.

Micrography study of failure surface

Based on the research of carbon black filled natural rubber, Le Cam et al.31 pointed out that the cavitation induced by the decohesion between zinc oxides and rubber matrix was the major fatigue damage. In the research of natural rubber, Saintier et al.18 reported that two main mechanisms of crack initiation were found to be independent of the type of loading (i.e. uniaxial or multiaxial) but depending on the nature of the inclusion: decohesion and cavitation. Hainsworth30 pointed out that the cracks were found to initiate at the defects associated with sample geometry and thickness. In this study, energy dispersive spectroscopy analysis revealed that a large variety of inclusions are present in natural rubber. The most often encountered are ZnO, SiO₂ and CaCO₃, which must be added into the material during the production of materials. High resolution SEM analysis showed that the agglomerates (generated from ZnO/carbon black) resulted from inhomogeneous mixing during material processing, as shown in Fig. 7. In Fig. 7a, plenty of small particles and cavitations are found. It can be seen that agglomerates do not show a clear interface with the rubber matrix. Flat and smooth fracture surface shows brittle failure, which is in accordance with those observed, that is, when the crack on the surface occurs with 1 mm length, the specimen breaks suddenly during cyclic loading. Figure 7b shows a scale-like fracture surface, which may be due to the incremental crack propagation during fatigue. The blunt ends and dimples on the surface are caused by the ductile failure of matrix. It can be observed from Fig. 7b that a number of small ligaments occur in the interface.

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Figure 7

Fatigue fractured surface under uniaxial loading ×500

It can be observed in Fig. 7 that the interfacial adhesion between filler and rubber matrix in rubber A is better than that in rubber B, which is helpful to reduce the amount of heat produced during deformation and the chain breaking and consequently further increases the fatigue life. In addition, better interfacial adhesion also results in better dispersion and improves wettability of filler particles in the rubber matrix, which reduces the formation of stress concentration and then enhances the fatigue life.35 As more and more filler is added into the rubber matrix, it can be anticipated that filler particles and agglomerates will not be dispersed and wetted efficiently by the rubber matrix.35 These inherent defects can act as stress concentration points and shorten the fatigue life of the vulcanisates.36 Again, it can be seen in Table 1 that material B contains more filler than material A. Therefore, material B is easier to be failure and exhibits lower fatigue life than material A (see Table 3).

For the sake of comparison on the effect of multiaxial loading on fatigue life, the fatigue failure surfaces were examined for material A and material B under uniaxial and multiaxial loading at the same strain amplitude. Figure 8 Figures 8 and 9 show the fatigue failure surfaces of material B and material A under uniaxial and multiaxial non-proportional loading. For the same material, fatigue life under multiaxial loading is much lower than that under uniaxial loading (see Table 3). As observed previously, fatigue crack growth is driven by ligaments breakage.30^–32 It can be observed from fracture surface in Fig. 8 that the pattern of ligaments is different between specimen 1-B and specimen 2-B. Fracture surface for specimen 1-B shows scale-like fracture surface, and the shape and size of ligaments are relatively sharp and small compared with that of specimen 2-B. However, fracture surface for specimen 2-B shows a rougher surface that corresponds with broken ligaments shrunk. Therefore, under path 2 loading for filler NR, ligaments breakage is easier due to the existence of multiaxial loading. Brittle failure occurs on the failure surface of both specimens 1-A and 2-A. However, comparing with the failure surface of specimen 1-A, there are more cavities formed by escaped more agglomerates for specimen 2-A as shown in Fig. 9. Therefore, the decreased fatigue life of natural rubber under path 2 loading can be explained as it is poor interfacial adhesion between the filler and the matrix with multiaxial loading. Therefore, under non-proportional loading, the chemical bond of the material breaks faster and then the fatigue damage develops faster.

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Figure 8

Fatigue fracture surface of material B×500

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Figure 9

Fatigue fracture surface of material A ×500