Anisotropic Deformation Behavior of Al 2024 T 351 Aluminum Alloy

The objective of this work was to investigate the effects of material anisotropy on the yielding and hardening behavior of 2024T351 aluminum alloy using isotropic and anisotropic yield criteria. Anisotropy may be induced in a material during the manufacturing through processes like rolling or forging. This induced anisotropy gives rise to the concept of orientation-dependent material properties such as yield strength, ductility, strain hardening, fracture strength, or fatigue resistance. Inclusion of the effects of anisotropy is essential in correctly predicting the deformation behavior of a material. In this study, uniaxial tensile tests were first performed in all three rolling directions, L, T and S, for smooth bar specimens made from hot rolled plate of Al2024 alloy. The experimental results showed that the Land T-directions yielded higher yield strengths and a greater percentage of elongation before fracture than the S-direction. Subsequently, finite element analysis of tensile specimens was performed using isotropic (von Mises) and anisotropic (Hill) yield criteria to predict the onset of yielding and hardening behaviors during the course of deformation. Hill's criterion perfectly fitted with the test data in the S-direction, but slightly underestimated the yield strength in L-direction. The results indicated that the Hill yield criterion is the most suitable one to predict the onset of yielding and hardening behaviors for 2024T351 aluminum alloy in all directions.


Introduction
Aluminum alloys are well-known for their excellent mechanical properties such as a high strength-toweight ratio, resistance to corrosion, and strength integrity at low temperatures.These properties have led to its extensive use in aerospace and cryogenic applications.For decades, thin rolled sheets of aluminum alloy 2024T351 have been used for aircraft applications (Starke 1996;Nakai 2000).Like other aluminum alloys, the 2024 alloy exhibits anisotropy in its deformation and fracture behaviors.Although extensive experimental work, along with analytical and numerical analyses, has been performed (Lam 2010;Lee 1999;Mimaroglu 2003;Schmitt 1998) for predicting the isotropic and anisotropic deformation behaviors of aluminum 2024 alloys, so far its deformation-induced anisotropy has not been completely understood.Anisotropy is induced in a material during manufacturing through processes like rolling or forging.The induced anisotropy results in directionaldependent material properties such as yield strength, ductility, strain hardening, fracture strength, and fatigue resistance.Numerous studies have been done to evaluate the material properties of 2024 aluminum alloys (Bron 2006(Bron , 2004b;;Srivatsan 2007;Shanmuga 2010).A thorough understanding of the effects of induced anisotropy is essential to correctly predicting the deformation behavior of a material.In thin plates made of 2024 alloy, the properties are strongly dependent on the rolling direction (Steglich 2008), while the other two orientations (ie.thickness and width) are not critical in predicting the deformation behavior.However, for thick plates the anisotropy along thickness and width directions cannot be neglected in estimating the deformation behavior under different loading conditions.The onset of yielding, the progression of plastic deformation, and work hardening are not the same in all directions.
Researchers have carried out numerous studies and developed various yield criteria, plastic flow rules, and work/strain hardening hypotheses to predict deformation-induced anisotropy for ferrous alloys.These same criteria, rules, and hypotheses are assumed to be equally applicable for aluminum alloys with some modifications.However, the yield criterion which is most applicable for 2024 alloy for all directions, and which agrees well with experimental results, remains a topic of research.There is no reported literature on this subject and filling this void is the main objective of the current study.
Downhole tubular expansion technology in the oil and gas industry has demonstrated its enormous influence on the overall drilling cost of wells (Campo 2003).Many issues remain unresolved in spite of its successful implementation.One of these issues is related to induced anisotropy in downhole tubular material during the cold expansion process.In the expansion process, the tube might not become deformed uniformly due to the presence of non-homogeneities as a result of the manufacturing process.The non-uniform expansion process results in the anisotropic behavior of downhole tubes and ultimately affects their structural integrity.Therefore, a careful analysis of induced anisotropy is necessary to estimate its effects on the structural integrity of downhole tubes.This work focused on analyzing an induced anisotropy in a material during deformation, while the relation between an induced anisotropy in a downhole tube with its structural integrity will be included in future work.Also, this research is an addition to the work reported by Pervez (2008), where the postexpansion properties of downhole tubular materials like expansion force, thickness reduction, length shortening, and contact pressure were compared in two different types of materials steel and aluminum.The authors concluded that aluminum is a better option for downhole tubular construction due to its lower energy requirement for expansion, high formability, and good corrosion resistance.This work contains the effects of anisotropy on the deformation behavior of downhole tubular materials, while assuming that the downhole tube is made up of Al2024 aluminum alloy.
A law defining the onset of yield under a combined state of stress is known as yield criterion.The generalized von Mises yield criterion for isotropic materials (1913) accurately predicts the onset of yielding for most polycrystalline metals as compared to the criterion of (Tresca 1864).An extension of von Mises's yield function was first proposed by Hershey (1954), and then was generalized by Hosford (1972).The loci of yield surface of isotropic yield function by Hosford lies between that proposed by von Mises and Tresca.The equivalent stress by Hosford is given as: where, R ij is defined as The current work is aimed at the prediction of yielding and hardening behaviors, resulting from different loading conditions and specimen geometries for the Al2024T351 alloy using different yield criteria.Uniaxial tensile tests were performed on smooth bar specimens.FE simulations were done in FE code Abaqus for smooth bar specimen using different yield criteria to find out which single yield criterion could be used to fit the hardening curve in all three directions.The numerical results were validated using experimental data.

Experimental Study
Uniaxial tensile tests were performed on smooth bar specimens made from a hot rolled plate of 2024 alloy in L-, T-and S-directions.The material orientations with respect to rolling and loading directions are shown in Figures 1a and b.Before cutting the sample, the plate was solution heat treated, air quenched, and stress relieved by cold stretching.All samples had a uniform thickness of 100 mm.The gauge length of the smooth bar specimen was 50 mm with a diameter of 10 mm.The main alloying element in 2XXX series of aluminum alloy was copper, while magnesium and manganese were added to improve the quenching properties.The composition of the Al2024 alloy is given in Table 1.

Results and Discussions
The experimental results for the uniaxial tensile tests of smooth bar are shown in Fig. 2. For smooth bar, the yield point remained the same in L-and Tdirections, but was of a lower value in the S-direction.For smooth bar, the percentage elongations in L, T and S-directions were 22,19.6,and 9,respectively. This (4e) means that the material exhibited less ductility in the thickness direction as compared to the rolling and width directions.The given coefficients in Eqn. ( 5) are a clear indication of the presence of anisotropy along the x and z axes only, but not along the y axis, which is the loading direction in S-material orientation.It indicates that only planar anisotropy is present.Also, no anisotropic effect on shearing was considered (R 12 =1, R 13 =1, R 23 =1).The comparison between simulation and experimental results for this case is shown in Fig. 4(a).

Smooth Bar Specimen
It is evident from Fig. 4(a) that the Hill's criterion resulted in a close match with experimental results for the S-direction but overestimated force at onset of yield by approximately for the L-direction.Based on tensile strengths in and L-directions, the anisotropic coefficients for Hill's yield criterion are in Eqn. ( 6): (6) It is obvious from 4(b) that the results perfectly fit the experimental hardening behavior in the L-direction while underestimating the onset of yielding.It can be concluded that using Hill's yield criterion, both the onset of yielding and hardening behaviors in the L-direction cannot be accurately predicted.Therefore, the choice of anisotropic coefficients in Hill's yield criterion is mainly dependent on the application's need.For designing products involving plastic deformation, hardening behavior is more important as compared to the onset of yielding, while the reverse is true in the case of designing within the elastic limit.The results prove that there is no isotropic effect in shear for smooth bar.

Conclusions
Isotropic and anisotropic yield criteria were used to predict the yielding and hardening behaviors for S-and L-directions in smooth bar using uniaxial tensile test specimens.Hardening behavior was determined only for S-direction.Three dimention finite element analyses for smooth bar were performed using isotropic and anisotropic yield criteria.Anisotropic parameters for Hill's criterion were determined using mechanical test data of smooth bar in the L-direction.Hill yield criterion slightly overestimated the hardening curve for the S-direction, while the effect was more pronounced in the L-direction.It can be concluded that by using Hill's yield criterion, yielding and hardening behaviors in the L-direction cannot be predicted precisely.Therefore, the selection of Hill's anisotropic coefficients is mainly dependent on application.The present work could be extended by including other anisotropic yield criteria to predict deformation behavior more accurately.Furthermore, the analysis of notched bar specimens could also be included to investigate the effects of notch radius on the anisotropy of materials.