Idea Transcript
MECHANICAL BEHAVIOR OF AN ALUMINUM ALLOY AND A STRUCTURAL STEEL UNDER MULTIAXIAL LOW CYCLE FATIGUE
F. Miranda Department of Mechanical Engineering, Instituto Superior Técnico Av. Rovisco Pais, 1 – 1049-001 Lisboa, Portugal ABSTRACT Under service fatigue loading, cyclic plastic strain occurs and consequently fatigue cracks nucleate, the mechanical resistance of the material will decrease. The simulation of the cyclic stress/strain evolution and its distribution plays a fundamental role on fatigue life prediction of mechanical components. The objective of this dissertation is to study the Finite Element Method based algorithms for improved fatigue life prediction under multiaxial loading conditions. Two distinct materials (a structural steel AISI 303 and an Aluminum alloy 6060-T5) are studied and compared experimentally and numerically under typical proportional and non-proportional loading paths. Finite Element Code ABAQUS is applied to simulate the cyclic elastic-plastic stress/strain behavior; two element types (element type Pipe31 and C3D20R) are selected and compared. To improve the simulation results, studies are also carried out on different mesh methods, different hardening laws including the isotropic hardening, kinematic hardening, combined hardening, etc. Based on the simulated local cyclic stress/strain results, various critical plane models are applied for fatigue life prediction. By comparisons with experimental results, satisfactory agreements are shown between the numerical simulations and experimental results.
KEYWORDS MUTIAXIAL FATIGUE; LOADING PATHS; PROPORTIONAL AND NON-PROPORTIONAL LOADINGS; FATIGUE LIFE PREDICTION; FINITE ELEMENT METHOD; CRITICAL PLANES
INTRODUCTION Age hardened Aluminium alloys are of great technological importance, in particular for ground transport systems. When relatively high strength, good corrosion resistance and high toughness are required in conjunction with good formability and weldability, Aluminum alloys with Mg and Si as alloying elements (Al–Mg–Si, 6xxx Aluminium series alloys) are used. The comparison of experimental and theoretical results under biaxial fatigue between high strength steels and Aluminum alloys has an important role to choose which material would be better to a certain end. [1]
The investigation of early crack growth due to multiaxial fatigue is one branch of the wide field of research in multiaxial fatigue since most of fatigue accidents occur due to this kind of loads.
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Several methods to predict multiaxial fatigue loads have been developed in the last forty years and mainly due to change of directions and ratio variations of the principal stresses, classic approaches are not always conservative under multiaxial loads. As a result in the last decades, several multiaxial fatigue criteria based on critical plane and also on integral, invariant and energy approaches have been proposed. However the existing multiaxial fatigue models were developed to specific load conditions and the application to more general projects require more study. A few examples of applicable and promising critical plane methods on low cycle multiaxial fatigue are the Brown-Miller and Fatemi-Socie methods which are able to determinate the damage plane strain and stress levels. [2-3]
The ABAQUS program is used to evaluate the numerical results of the cyclic stress and strain evolution under proportional and nonproportional biaxial loading. The cyclic elasto-plastic response and local deformations are analyzed using the F.E.M. program ABAQUS, with two main objectives, complementing the experimental results of the cyclic behavior under certain loading situation of the material, and in other way to use the F.E. potential to determine when stress and strain values stabilize in a way to include those values in predicting models under multiaxial fatigue. In this research an Aluminium alloy is tested, and so, the life of the components can be predicted/estimated using multiaxial fatigue criteria. A usual procedure on fatigue design is to initiate the study with the calculations of the local elastic stress-time history so critical zones can be detected on a component or structure, using the finite element method. Next an evaluation on a critical zone is carried out under a certain number of cyclic loads, and the existence of cracks can be evaluated by the application of an appropriated multiaxial fatigue criterion. [3]
The objective of this work is to evaluate the mechanical behavior, in particular the proportional and non-proportional fatigue parameters, on 6060-T5 aluminum alloy and their comparison with similar results obtained for structural steels AISI 303, suitable for estimating non-proportional low cycle fatigue lives. Since the stabilized cyclic stress/strain fields are essential for fatigue life predictions, local elasto-plastic behavior of the material are studied first. The additional hardening coefficient, (), based on the stabilized cyclic stress/strain cycle is evaluated for correlating the fatigue lives obtained in the tests.
Materials may have very different additional hardening behavior, under multiaxial cyclic loading paths. Depending on the loading amplitude and loading level, stress relaxations occur and the stabilized cyclic stress/strain state may be very different from the initial one. Elasto-plastic FEM analysis, using ABAQUS Code, were carried out in order to predict the stabilized cyclic stress/strain state, under the same multiaxial loading paths used on the experimental tests. Two models were used; a linear beam element pipe31 with 4 integration points and an Isoparametric solid element with 20 nodes were used on the mesh modeling.
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Results show that metallic materials present different behavior concerning additional hardening which is of prime importance for predicting fatigue life.
MATERIALS, SPECIMEN FORM AND TEST PROCEDURE In order to compare the sensitivity of different materials to proportional and non-proportional loadings, two materials are studied. The materials studied are the stainless steel X10CrNiS 18 9 (AISI 303) and an Aluminum alloy 6060-T5. The monotonic and cyclic mechanical properties are shown in Table I Table I - Monotonic and cyclic mechanical properties of the materials studied
Al 6060 T5
AISI 303
(MPa) % , (MPa)
216
625
197
---
(MPa) A (%) (GPa) , cyclic (MPa) % ′ (MPa) ′ ′ (MPa)
--8 79 187 503 0.156 376.5 -0.084 0.157 -0.537
330 58 178 310 2450 0.35 534 -0.07 0.052 -0.292
Tensile strength Yield strength Yield strenght Elongation Young’s modulus Cyclic Yield strength Strength coefficient Strain hardening exponent Fatigue strength coefficient Fatigue strength exponent Fatigue ductility coefficient Fatigue ductility exponent
.
.
εf´
The geometries and dimensions of the structural steel and the Aluminum alloy specimens used are shown in Figure 1.
a)
b)
Figure 1 Geometries and dimensions of the specimens: a) AISI 303 [3], b) Al6060-T5
In order to characterize and to study the effects of the loading paths on the additional hardening and consequently on the cyclic stress-strain behavior of the studied materials, a series of low cycle fatigue tests, under proportional and non-proportional axial/torsional paths, (Figure 2, Blue lines), were carried out using a biaxial servo-hydraulic machine (8800 Instron) and a data acquisition system. [3]
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Case 1
Case 2
Case 3
Case 4
Figure 2 - Biaxial fatigue loading paths
Additional Hardening Coefficient α For non-proportional straining, a rotation of the principal strain axes leads to an additional cyclic strain hardening and higher than that obtained under stable conditions for proportional stressing. In the later case, dislocations glide on a fixed set of slip planes, whereas for continuously rotating principal axes, many slip systems are activated. Therefore, an additional factor must be introduced to represent this extra hardening. The additional hardening coefficient is a constant of a material, which is defined as the ratio of equivalent stress under 90º out-ofphase loading and the equivalent stress under proportional loading at high plastic strains in the flat portion of the stress-strain curve [3].
Finite Element Properties The used C3D20R mesh was carefully chosen, to diminish undesired distortions on the mesh elements, which could lead to serious errors, such as: simulation crashes or the solution didn’t converge to any result.
The model is axisymmetric and the mesh generation was semi-
automatic. [3]
The mesh of the pipe31 model is simpler than the C3D20R model, since each element already represents a partition of a tube, the number of elements used was decided to be five, since the results were considered basically the same for every element. Both tubular specimen meshes have 10mm of outer diameter and 1mm thickness Figure 3 a) C3D20R is more refined on the specimen center. The model has 2 elements thickness. The final model C3D20R has a total of 1656 elements and 9396 nodes; b) the pipe31 model has 5 elements with the same length.
Figure 3 - Boundary conditions of the models: a) c3d20r model b) pipe31 model
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Multiaxial Fatigue Models for Crack Initiation Life Prediction Using the maximum results of the finite element method and the material properties of the Table I, it is possible to determine the fatigue life
using the relations given by Fatemi-Socie (1) and
Findley (2). [3,4] ′
2
+
′
2
∆ + 2
= =
1+
∆ 2
1+
,
′
(1) (2)
RESULTS AND DISCUSSIONS Test Results The proportional cyclic tests were conducted in one direction out of phase 90º. Non-proportional cyclic tests were conducted with the circular, cross and square paths, respectively (see Figure 2). As an example, Figure 4 shows the cyclic stress evolution during strain control low cycle fatigue loading for AISI 303 and Al6060-T5, for case 2, respectively:
Figure 4 - Cyclic stress evolution for an equivalent strain=0.60%: a) AISI 303; b) Al6060-T5. Comparing all the results, it is observed that the AISI 303 steel is a very sensitive material to non-proportional loading paths. During non-proportional loading, the planes of maximum shear stress rotate, thus initiating plastic deformation along several different slip systems. Stresses are continuously increasing during the first 10-15 cycles until stabilization is reached. For the Aluminum alloy the experimental results were not enough to give a precise correlation, since the applied equivalent strain is near the beginning of the plastic region. The experimental tests proved that the proportional tests under biaxial fatigue cause less hardening than the biaxial nonproportional tests; the local cyclic stress/strain states are influenced by the multiaxial loading paths, due to the interactions between the normal stress and shear stress during cyclic plastic deformation. At the same equivalent strain amplitude, the nonproportional loading paths can cause much more hardening than the proportional paths.
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Additional Hardening Results In this study, the experimentally observed data of the additional hardening under nonproportional loading paths of the three materials studied were determined as: αAISI303=0.9 [3] and αAl6060-T5=0.4. The additional hardening coefficient is highly dependent on the microstructure and development of slip systems in a material. AISI 303 steel is a very sensitive material under nonproportional paths. [3] The same behavior was not observed on the Al6060-T5, which is lower sensitive to nonproportional paths. Since the additional hardening effect counts the effects of the rotation of the principal axis during an out-phased solicitation this coefficient, should be taken in account in the life prediction models to multiaxial fatigue.
Simulation Results The simulation results showed that the stress strain responses reached a stabilized cyclic state after 2 loading cycles for both materials, Figure 5b), 6a) and 6b). It is illustrated that very few transient cycles happened before the stabilized cycles were reached. Although in the case of AISI 303, the simulated results are not in agreement with experiments, due to the previous reasons, if using the combined hardening type with the multiaxial stabilized cyclic hardening data, the maximum stresses are approximately the same as the experimental results. The material Al6060-T5 also presents very few transient cycles until the stabilized cycles were reached. Although the experimental results are in agreement with the simulations results, it requires further development since to an equivalent strain of 0.60% the Aluminum alloy is near the beginning of the plastic region and therefore the results are not totally agreeable.
a)
b)
Figure 5 - a) Case 2 path history with an equivalent strain=0.60%; b) Axial Stress-Strain evolution, with an equivalent Strain=0.60%; Material=Al6060-T5; Element Type: Pipe31; Modeling properties: Combined Hardening – Stabilized; Cyclic hardening - monotonic data.
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a)
b)
Figure 6 - Case 2: Stress-Torsion evolution; Equivalent Strain=0.60%; Material=AISI 303; Element Type: Pipe31; Modeling properties: Combined Hardening a) monotonic cyclic hardening data, b) multiaxial cyclic hardening data Nonproportional cases 2, 3 and 4: For the structural steel when using the multiaxial data for nonproportional cases is roughly 2 times more than the stress of the kinematic and monotonic combined data of the other models, the behavior of the models can be explained by the values of the equivalent stress for the equivalent strain of 0.60%. The finite element analysis proved that the local stress-strain cyclic responses are different to different loading path. The graphics through different time have an important part when studying the evolution and redistribution of the cyclic stress-strain fields. Between the models: combined using monotonic data, kinematic and isotropic, the differences between the shear stress-axial stress graphics are mainly due to the use of linear data on the kinematic model, and therefore this is the least accurate model because it neglects large portion of the material behavior.
Crack Initiation Life Prediction Results Failure life is defined as the number of cycles at which a 10% drop from the maximum value occurs in either the tensile or shear stress range [3]. The predicted number of cycles for the Aluminum alloy and the structural steel using the parameters Findley and Fatemi-Socie values for an equivalent strain of 0.60% and using the combined hardening type are given on the table II for both materials
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Table II - Resume of the fatigue life results for AISI303 and the Al6060-T5 using the element type Pipe31 with an equivalent Strain=0.60% and combined hardening type.
Data Type
Case
Nf Cycles Findley
Nf Cycles Fatemi-Socie
Stabilized & Monotonic Cyclic Hardening Stabilized & Multiaxial Cyclic Hardening Stabilized & Monotonic Cyclic Hardening
1 4 1 4 1 4
57 1 7 1 469 9
3524 2776 3143 1170 780 656
Material
AISI 303
Al6060-T5
The number of cycles using the Findley model is clearly lower than using the Fatemi Socie. This difference can be explained by the fact that the Findley model is more accurate for high cycle fatigue.
CONCLUSIONS -
Using the kinematic hardening law with linear data reveals to be less accurate than isotropic and combined hardening, since this approximation neglects the behavior of the material during a large portion of the monotonic curve.
-
The effects of the non proportionality was quantified using the additional hardening coefficient , for the AISI303 the final result was 0.9 [3] for the Aluminum alloy the result was approximately 0.37;
-
To predict life using the critical plane models the Findley model reveals to be less accurate than the Fatemi Socie model, since the models were under low cycle fatigue conditions;
-
The nonproportional case 4 is more damaging to both materials than the proportional case 1.
REFERENCES [1]
Borrego, L. P. A., L. M.; Costa, J. M.; Ferreira, J.M. (2004). "Analysis of Low Cycle Fatigue in Al-Mg-Si Aluminium Alloys." Engineering failure Analysis 11: 715-725.
[2]
Zhang, L., Wang, G., Cheng, J. e Jiang, L. Y. (2003). "Investigation of the Low-Cycle Fatigue under Multiaxial NonProportional Loading." Materials Science and Engineering a - Structural Materials Properties Microstructure and Processing 355(1-2): 18-23.
[3]
Reis, L. F. G. d. (2004). "Comportamento Mecânico de Aços em Fadiga Multiaxial a Amplitude de Carga Constante e Sincrona." Tese de Doutoramento em Engenharia Mecânica. Instituto Superior Técnico. 2004
[4]
Socie, D. F. and Marquis, G. B. “Multiaxial Fatigue”, Society of Automotive Engineers, Warrendale, (2000) PA 15096-0001.
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