Effect of molding processes on multiaxial fatigue strength in short fibre reinforced polymer

This study concerns the multiaxial static and fatigue strength properties. Short-glass-fibre-reinforced phenolic-resin composites (SGP) molded by injection and compression processes were subjected to tensiontorsion combined static and fatigue tests at room temperature under various test conditions. Tension – torsion combined static strength well agreed with Tsai-Hill failure criteria without depending on processes. Relationships between the maximum principal stress, σp1, max, and the number of fracture cycles, Nf, were approximately linear in the whole range of up to 106 cycles. For a unified evaluation of multiaxial fatigue life for SGP, non-dimensional effective stress, σ*, defined by modifying Tsai-Hill failure criteria was applied. The slopes of σ*Nf curves according to Baskin’s law were almost identical to the injection (n = 26.3) and compression (n = 26.2). We finally confirmed that the multiaxial fatigue life of SFRP could be predicted by using σ* with a unique Wöhler curve without relying on molding processes.


INTRODUCTION
hort fibre reinforced thermo-set plastic (SFRP) has been mainly applied to automobiles and electrical industries owing to its superior mechanical properties and lower weight.However, a machine designer often faces difficulties using SFRP or predicting its mechanical properties.SFRP generally shows complex fracture behaviours combined with a matrix crack, fibre break, fibre pull-out, and others, and these make product design difficult.Therefore, a machine designed using SFRP often requires a production test and a strength test to be repeated until its reliability is confirmed.Because reducing the number of test repetitions decreases the cost of development, high-reliability strength evaluation methods will be required to meet the increase in products that will use SFRP in the future.Further, multiaxial stress generally occurs in a structure subjected to an external force.In the literature, Moosbrugger et al. [1,2] experimentally investigated and calculated the multiaxial fatigue behaviour of SFRP.They conducted some tensiontorsion combined fatigue tests and estimated the fatigue life on the basis of the failure criterion of laminate.Gaier et al. [3] established a simulation process for the multiaxial fatigue life prediction of orthotropic SFRP.They combined the resin flow simulation, finite element analysis, and fatigue analysis.The fatigue damage of a belt pulley was predicted by S comparing experimental and simulation results.Although some additional papers [4][5][6][7] have focused on investigating the multiaxial strength for SFRP, little attention has been paid to the effect of manufacturing process on that property.This study is concerned with the multiaxial fatigue evaluation in short-glass-fibre reinforced phenolic resin (SGP) among various volume fractions.Round-bar specimens molded by injection and compression processes were subjected to static and fatigue tests in room temperqature to clarify the effect of molding processes on the multiaxial strength.Tensiontorsion combined tests were conducted with various stress ratio parameters described as the ratio of torsion and tension stress as α = τ / σ.

EXPERIMENTAL DETAILS
ab. 1 details the configuration of SGP.Thermosetting phenolic resin was used as the matrix.The reinforcement was a short E-glass fibre 10 mm long and 10 μm in diameter.0.0V f , 0.2V f , and 0.5V f described at the first row means that the fiber volume fraction Vf is 0%, 20%, and 50%.Test specimens with three-types V f were molded by compression (C-SGP) and injection (I-SGP) respectively.In the compression molding, 300-mm-square and 30-mm-thick bulk plates were manufactured, and then test pieces were cut from the bulk plate to the dimensions as shown in Fig. 1.Edges of the sample surface were not polished.A machining surface roughness was confirmed by using a roughness tester to be approximately the same in each specimen.Compression molding temperature was 160 °C, press pressure was 20 MPa, and curing time was 250 seconds.In contrast, in injection molding, test specimens were directly manufactured to specimen shapes described as Fig.

Multiaxial test procedure
In this study, we conducted multiaxial static and fatigue tests at room temperature to compare strength properties in different manufacturing processes.All the tests were performed by combining tension-torsion electro-hydraulic servo systems under axial-loads up to ± 25 kN with standard displacements of ± 50 mm and torsion-torques up to 220 N･m with total rotations of 270°.Tension-torsion combined tests were performed by using the specimen as shown in Fig. 1.Tension stress σ1 is given by Eq. 1, where F is tension load and D is diameter at the gauge section.Torsion stress τ 12 is given by Eq. 2, where T is torque.
Axial-tension stress σ 1 was loaded in proportion to torsion stress τ 12 in accordance with a combined stress ratio α, which is defined in Tab. 2, on the gauge section surface.Static tests were controlled by Eq. 3 so as to achieve the stress loading speed ( ,  ) of 10 MPa/sec.Fatigue tests were conducted at the stress ratio R defined as the ratio of minimum stress to maximum stress of 0.1 and applied sinusoidal waves combined between axial-tension stress and torsion stress with cyclic frequency f of 2 Hz.Axial-tension stress was loaded to the specimen so as to be in the same phase with torsion stress in accordance with defined the combined stress ratio α in Tab. 2.
Table 2: Definitions of combined stress ratio α.

TEST RESULTS AND DISCUSSION
Multiaxial static strength evaluation xternal load acting on a structure is commonly considered to be not only a uni-axial stress but also a multiaxial stress state.Therefore, we discuss a multiaxial strength criterion in terms of the axial tension strength and the torsional shear strength in this chapter.From the micro observation and frequency analysis for fibre orientation in C-SGP and I-SGP, we deduced that they will have an orthotropic property.Then, we assumed the SGP multiaxial failure was followed by Tsai-Hill failure criterion given by Eq. 4 [8].
where σ L and τ S are tension and torsional strength in material reference axes, and σ 1 , and τ 12 are applied axial stress and torsional stress on the specimen surfaces.Suffixes 1 and 12, which are written in subscript to the right of strength parameters σ and τ, indicate the axial-stress direction and the torsional-stress direction, respectively.σ L and τ S are the material strengths determined by the static test on the basis of the experimental results in α = 0 / 1 and α = 1 / 0 in Tab. 2. Fig. 2 shows the static strength criterion for SGP in the multiaxial stress state, which is plotted on σL -τS plane.The white and gray plots on each chart indicate the strength data of C-SGP and I-SGP, respectively.The solid lines on the στ plane represent the failure criterion given by Eq. 4 for each V f .Broken lines represent α given in Tab. 2.
As C-SGP is molded by pressuring and heating after raw materials described at Tab. 1 are filled into the die, a microscopic void tends to be easily retained as a manufacturing defect in C-SGP.Furthermore, the authors [9] previously suggested that the strength properties of SGP depend on both short-fibres orientation and manufacturing defects in matrices.From these perspectives, we deduced that these manufacturing defects affected experiment variations in SGP.Considering such manufacturing defects, the static fracture strength of C-SGP approximately accords with the Tsai-Hill failure theory criteria in Eq. 4.

Fatigue strength properties
Fatigue strength in uni-axial loading is generally evaluated by using the S-N diagram.S-N diagrams are associated with the relationships among the number of cycles to failure and stress range, stress amplitude, or maximum stress in uni-axial loading.However, we have to deal with stress states of combined axial stress and torsion stress in this paper.Therefore, S-N diagrams are organized by using principal stress applied on specimen surfaces σ p1 , and the number of cycles to fracture Nf. σp1 was calculated as follows: where σ 1 and τ 12 are the axial stress and shear stress applied.Figs 3 and 4 show the relationships between σ p1,max as cyclic maximum principal stress and N f as fracture cyclic numbers on a double logarithmic chart obtained as S-N diagrams.Arrows in the diagrams show that the fatigue tests were terminated after reaching 1×10 6 cycles.do not seem to agree despite these properties being made of the same materials.V f , α, and molding processes strongly affect the multiaxial fatigue properties, hence those effects have to be removed from S-N diagrams to evaluate fatigue with high accuracy.

Definition of unified equivalent stress
We confirmed multiaxial fracture strengths well agreed with the Tsai-Hill failure criteria with dependence on processes and fibre volume fractions V f as shown in Fig. 2. Meanwhile, multiaxial fatigue properties are not able to be organized by the relationships between σp1,max and Nf because of being affected the dependence on the molding process, α, and Vf.Then, due to the static strength behaviours described above, the fatigue strength will be represented by expanding the Tsai-Hill failure rule [10].Hence, non-dimensional equivalent stress σ * was defined by modifying the Tsai-Hill failure rule as shown in Eq. 6 to evaluate the multiaxial fatigue behaviour without dependence on molding process effects.

Figure 2 :
Figure 2: Multiaxial static strength evaluation with Tsai-Hill failure rule.

Figure 3 :
Figure 3: Relationships between σp1, max and Nf with various α in C-SGP.Since the value of the fatigue life in C-SGP are scattered widely, fatigue life in C-SGP can no longer be expected to sort in V f and α by using the S-N diagram.Meanwhile, S-N diagram in I-SGP indicates the characteristic to decrease σ p1, max with increasing Nf without dependence on fatigue test conditions.Comparing the fatigue properties in molding processes, they

Figure 4 :
Figure 4: Relationships between σp1, max and Nf with various α in I-SGP.

Figure 5 :
Figure 5: Relationships between σ * and N f with various α in C-SGP.

Figure 6 :
Figure 6: Relationships between σ * and N f with various α in I-SGP.

Figure 7 :
Figure 7: A typical tensile fracture surface situations with scanning electron microscopes in C-SGP.(05Vf) cycles N f[cycles]

Table 1 :
Configuration of SGP material.