EFFECT OF TENSION/TORSION LOAD SEQUENCES ON MULTIAXIAL FATIGUE LIFE PREDICTION

V. AnesDepartamento de Engenharia Mecânica, Instituto Superior Técnico,

Av. Rovisco Pais, 1049-001 Lisboa, Portugal

ABSTRACT

The objective of this paper is to evaluate the effect of sequences of tension and torsion loads (proportional, non-proportional and sequential) on the fatigue lives of specimens made of 42CrMo4 steel. A series of biaxial load controlled fatigue tests are carried out using a biaxial servo-hydraulic testing machine. Different sequential biaxial loading paths are applied, fatigue performances are observed and both fatigue lives and fracture surfaces are analysed. The results show that the axial/torsion load sequences have significant effects on both fatigue life and fractography. Multiaxial fatigue life prediction models are applied for sequential biaxial loadings, such as the von Mises approach and the MCE methodology applied to the Sines approach.

KEYWORDS

Multiaxial fatigue, Sequential loading effect, Proportional and non proportional loadings, Fractographic analysis, Damage.

1 INTRODUCTION

In real service, the loading histories are generally variable amplitude and the fatigue damage accumulation is a key issue for fatigue life predictions. The durability and reliability of components and structures depends on the robust design methods which are able to treat with various loading conditions [1].The sequential loading effects as well as the non-proportional loading effects are attracting growing attentions in the research field. In the literature, much research efforts have been paid in studying the proportional and non-proportional loading effects on the fatigue damage of 42CrMo4 steel, for example in [2] and so on.The objective of this paper is to study the sequential loading effect on fatigue damage of 42CrMo4 steel; focus is on the life prediction method appropriate for treating the sequential loading effects.For fatigue damage under sequential loading, Chen et al [3] proposed a modified damage model for the fatigue life prediction of the 304 stainless steel. Robillard and Cailletaud [4], Zhang and Miller [5], Harada and Endo [6] generated test data on ferritic stainless steel, Inconel 718, and medium carbon steels under tension-compression and torsion.Their results show that the damage value (n1/N1+n2/N2) tends to become greater than 1 for tension-compression followed by torsion and less than 1 for torsion followed by tension-compression.In this paper, systematic fatigue experiments are presented for a structural steel, 42CrMo4, quenched and tempered steel, under sequential axial-torsional biaxial loading paths. Tests were carried out under load control. It is proposed to evaluate the shear stress amplitude in the stress space appropriate to the material type. For the 42CrMo4 steel

studied, the shear stress space with the equivalence (=0.65*) is used for the shear stress amplitude evaluations under multiaxial loading conditions. Multiaxial fatigue life prediction models are applied for sequential biaxial loadings, such as the von Mises approach and the MCE approach applied to the Sines model are used for evaluating the shear stress amplitude and experimental results are correlated. In addition to analyse the effects of the sequential loading on fatigue lives, fractographic analyses are also carried out to study the effects of the sequential loading on the crack orientations.

2 EXPERIMENTAL

The selected material to carry through the tests is assigned by 42CrMo4, is characterized for being a laminated steel of high resistance. This type of steel is supplied in the treat state i.e. tempered and annealing at 525ºC admits high resistance, tenacity and aptitude to the nitriding, is a steel of construction, being particularly indicated for the cases of parts of average section stimulated by axial requests and alternating twist. The specimens used in the tests series had been produced through rods of 25mm of diameter, its machining were carried out through specialized machinery of cut under numerical command; its dimensions are presented in Figure 1.

Fig. 1: Specimen dimensions used on multiaxial fatigue tests with load control

The specimens had been inspected and manually polishing through sandpapers of decreasing grain since the 200 until a 1200. The monotonic and cyclical properties of 42CrMo4 [7] are presented in Table 1.

Table 1: Monotonic and Cyclic Properties of the 42CrMo4.

The fatigue tests had been carried out through a servo-hydraulic machine with biaxial capabilities of Instron mark, model 8874.In Figure 2, it is presented the experimental setup referred.

Fig. 2: Experimental Setup.

In order to study the different loading sequential effects, the specimens had been testedusing 5 types of trajectory under the combined loads, axial and torsion.In the first three cases, nominated cases 3, 3.1 and 3.2, the tests of multiaxial fatigue had

been lead with a constant ratio of amplitude of tension, aτ 1

=3

a

, differing between itself only in

the combination between half-reversions.In the cases 3.3A and 3.3B, the ratio of tensions leaves of being constant and starts to be

1

32for the case 3.3A, and

2

3for the case 3.3B.

The loading paths are shown from the Figure 3 until to the Figure 7.

Fig. 3: Stress time history and the respective loading path – Case 3

Fig. 4: Stress time history and the respective loading path – Case 3.1

Fig. 5: Stress time history and the respective loading path – Case 3.2

Fig. 6: Stress time history and the respective loading path – Case 3.3A

Fig. 7: Stress time history and the respective loading path – Case 3.3B

3 RESULTS AND DISCUSSION

3.1 Fatigue Life

The experimental analysis was implemented having in consideration related loads already presented as well as the axial and shear magnitudes represented in Table 2, in this table is also, presented the value of the equivalent tensions obtained for von Mises and Sines, andthe cycles of rupture verified for each case study. The equivalent tension MCE is applied to the Sines model.

Table 2: Applied loads, equivalent tensions and cycles at rupture for each case study

In order to analyze the behaviour of each approach in the prediction of the fatigue life in each model and case, it is applied the equivalent tension of von Mises and Sines to the S-Napproach.

´ ´2 2b c

vMS f f f fN E N (1.1)

´ ´2 2b c

Sines f f f fN G N

(1.2)

The Figure 8, represents the graphic of S-N curves for each case study and from which it will be able to achieve some conclusions about the effect of the relation enter the magnitude of axial and shear requests as well as its sequential of application.

Fig. 8: S-N curves for each case study

The type of the load trajectory history will influence the regimen of waste of the physical properties contained in the material, properties that establish or guarantee a certain life fatigue. This characteristic can be observed in Figure 8, when for the same material,42CrMo4, the equivalent tension that establishes the infinite life varies case to case.

To become this reasoning independent from the magnitudes of imposed loads we can fix, in Figure 8, the equivalent tension at the value 328 [MPa]. In this situation, we have a fixed equivalent tension that indicates different lives for the cases 3, 3.1 and 3.2, however in the cases 3.3A and 3.3B this same equivalent tension results in an infinite fatigue life, verifyingthat the load trajectory has influence in the prediction of the fatigue life.

3.2 Fractografic Analysis

The angles of the critical plan of crack initiation obtained experimentally had been compared with the theoretical results using the models of Findley, Brown-Miller, SWT, Fatemi-Socie, LIU I and LIU II. In Figure 9 is presented the results estimated of the critical plan of crack initiation using the method of Findley.It was become fulfilled for each model the same type of analysis used in the Findley model.Comparing the respective parameters of each model with the type of imposed load, in Table 4, is presented in summary the conclusions of the predictions achieved.The value of critical angle of crack initiation is established through the determination of the angle where the parameter of each model reaches its maximum value, for example, for the Findley model, Figure 9, the maximum value occurs when is equal to zero.

Fig. 9: Prediction of the critical angle of crack for the Findley model.

Table 3: Prediction of critical angles of each model

It is verified that this type of approach in the analysis of damage parameters only establishes the angle where occurs the request peak, not being sensible what it happens in other plans.This comment becomes pertinent when to observe that the angle where the crack evolves until the rupture is different of the angle were the fissuration was began. In Figure 10 is shown an example of that statement. The angle were the beginning of fissuration occur, that initiation is indicated by a white arrow, is different that adopted by the evolution of the fracture represented by a different plan of the considered one for the critical plan.

Fig.10: Macrograph of the V313 specimen, subject to the trajectory 3.1

The three-dimensional approach of damage surface allows to get much more information of what the one that would be gotten using only the method 2D. In Figure 11, it is presented surface of damage for case 3 using the Findley model.

Fig. 11: Surface of damage obtained by the Findley model for case 3.

In Table 4, is presented in summary the type of information that is possible to acquire fromthe damage surface, for case 3 of the Findley model is verified that the parameter of maximum damage occurs at 4º , however the value of the angle where the accumulation of the damage parameter is maximum occurs at 20º ; 70º .

Table 4: Interpretation of the damage surfaces.

4 CONCLUDING REMARKS

Fatigue damage of the 42CrMo4 steel is studied under 5 paths of sequential biaxial tension/torsion loading. Different cross-hardening levels were observed in axial/torsional loading sequence, and significant sequential loading effects were shown for both fatigue lives and fracture surfaces of the 42CrMo4 steel.

The ratio between normal stress and shear stress component has a strong influence to fatigue damage and consequently in fatigue life. The shear stress space used for the evaluation of the shear stress amplitude of multiaxial loading conditions should be appropriate for the material type.

The case that causes bigger damage in the material is the case 3, analyzing the cases 3, 3.3A and 3.3B, it is verified that the reduction for half of one of the magnitudes, axial or shear, increase the fatigue life of the material comparatively with case 3.

Comparing cases 3, 3.1 and 3.2 concludes that the complete reversions create greater damage in the structure of the material than the intercalated half-reversions.

For the cases 3, the 3.1 and 3.2 the critical plan models predict sufficiently well the criticalplans of crack initiation, the theoretical results are confirmed with the experimentally dataacquired.

In the case 3.3A is confirmed the fragility of the prediction of the critical plan models witch have a strong component in the estimation of the crack initiation through the predominance of the shear.

For a balanced contribution the 1/1 of the axial and shear component on the multiaxial effort the assertively of the critical plan models is observed however exist fragilities in all modelswhen the balance of the orthogonal components leaves to exist.

REFERENCES

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