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Rate Dependent Hardening Model for Pure Titanium Considering the Effect of Deformation Twinning (쌍정의 영향을 고려한 티타늄의 변형률속도 의존 경화 모델)
This study is concerned with the effect of deformation twinning on the strain hardening behavior of commercially pure titanium at wide range of strain rates. The strain hardening of titanium during compressive deformation shows uncommon behavior due to the occurrence of deformation twinning. Deformation twinning is one of the two principal modes of plastic deformation together with slip, while it becomes prevalent only at high strain rates and low temperatures. It is reported that deformation twinning is also observed at quasi-static and at room temperature for large deformations in several HCP metals because of the lack of slip systems. Since general HCP metals including commercially pure titanium have three independent slip systems, which is insufficient to deform only by slip, deformation twinning should be accompanied by slip for the HCP metals to sustain large deformation without cracking.
The strain hardening rates of metallic materials generally decrease as the strain increases due to dynamic recovery. In accordance with many studies on titanium, however, the strain hardening behavior of titanium during compression has different characteristics from those of general metallic materials. The strain hardening rate of titanium during compression can be divided into three stages. In the first stage, the strain hardening rate decreases as the strain increases due to dynamic recovery. Following the first stage, however, a sudden increase in the strain hardening rate is observed in the second stage. It is well known that the occurrence of the second stage is due to the generation of deformation twinning. After the second stage, the strain hardening rate decreases again as the strain increases in the third stage.
In this study, the compressive tests of commercially pure titanium are conducted at various strain rates ranging from 0.001/s to 10/s to investigate the effect of the strain rate on the three stages strain hardening behavior caused by the generation of deformation twinning. The universal testing machine (INSTRON 5583) is utilized for the compressive tests at the strain rate ranging from 0.001/s to 0.1/s, and the Gleeble 3800 system is used for the strain rate ranging from 0.1/s to 10/s. The tensile tests are also conducted in the same strain rate condition of the compressive tests to compare the strain hardening behavior with and without deformation twinning since it is reported that deformation twinning of titanium is hardly generated during the tensile deformation. The strain rate effect on the three stages strain hardening behavior during the compressive deformation is quantitatively investigated from the test results at the various strain rates.
OIM (Orientation Imaging Microscopy) analyses based on the EBSD (Electron Backscatter Diffraction) are conducted to examine the three stages strain hardening behavior of titanium. The generation and evolution of deformation twins with increase of compressive plastic strain are quantitatively investigated. By observing the micro-structures of the deformed titanium, it is verified that the three stages strain hardening behavior of titanium is caused by the generation and evolution of deformation twinning during the compressive deformation. The strain rate effect on the three stages strain hardening behavior is also investigated by observing micro-structures of the deformed titanium at wide range of strain rates and quantifying the strain rate effect on the generation and evolution of deformation twinning.
Using the results of the compressive tests and microscopic investigations, a rate dependent strain hardening model is proposed. The model is developed based on the investigated effect of deformation twinning on the strain hardening behavior of titanium and its strain rate dependency. The model is capable of representing the three stages of strain hardening at wide range of strain rates ranging from 0.001 to thousands/s. Microscopic investigated results of the compressive titanium at wide range of strain rates provide fundamental frame of the hardening model for titanium. The proposed model can suggest suitable form for the phenomenological representation of the abnormal strain hardening behavior of commercially pure titanium. The material constants of the model can be perceived as the fitting parameters, although each form of the model is constituted based on the physical effect of deformation twinning on the strain hardening behavior. The purpose of the model is to suggest the applicable form of the strain hardening representation for commercially pure titanium that can be applied for the finite element analysis, and it is shown that the model can represent the accurate strain hardening behavior. The applicability of the model to the higher strain rate conditions and the other kinds of material is also verified by applying the model to the two cases of the examples.