Tensile fracture mechanism and constitutive models of V-5Cr-5Ti alloy under different strain rate deformation at room temperature

Author’s Accepted Manuscript Tensile Fracture Mechanism and Constitutive Models of V-5Cr-5Ti Alloy under Different Strain Rate Deformation at Room Temperature Jiangtao Zhang, Junkang Xia, Mei Zhang, Yanliang Qiao, Lisheng Liu, Pengcheng Zhai www.elsevier.com

PII: DOI: Reference:

S0167-577X(16)31135-1 http://dx.doi.org/10.1016/j.matlet.2016.07.040 MLBLUE21168

To appear in: Materials Letters Received date: 1 June 2016 Revised date: 30 June 2016 Accepted date: 10 July 2016 Cite this article as: Jiangtao Zhang, Junkang Xia, Mei Zhang, Yanliang Qiao, Lisheng Liu and Pengcheng Zhai, Tensile Fracture Mechanism and Constitutive Models of V-5Cr-5Ti Alloy under Different Strain Rate Deformation at Room Temperature, Materials Letters, http://dx.doi.org/10.1016/j.matlet.2016.07.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Tensile Fracture Mechanism and Constitutive Models of V-5Cr-5Ti Alloy under Different Strain Rate Deformation at Room Temperature Jiangtao Zhang*, Junkang Xia, Mei Zhang, Yanliang Qiao, Lisheng Liu, Pengcheng Zhai Department of Engineering Structure and Mechanics, School of Science, Wuhan University of Technology, Wuhan 430070, PR China *

Corresponding author: +86 27 87651820. [email protected]

Abstract The mechanical properties of V-5Cr-5Ti alloy were tested over the strain rate range of 10-4/s-10-1/s at room temperature, and the effect of strain rates on the fracture mechanisms was studied through the fracture surface analysis. The results show that the coalescence of intergranular microcracks and dimple rupture is the dominant fracture mechanism. Brittle fracture often occurred under the high strain rate deformation. Four different constitutive models were used to characterize the mechanical properties of V-5Cr-5Ti alloy. Their precisions were assessed by comparing the model predictions with the experimental results under different strain rates and a strain rate jump test. Keywords: Metals and alloys; Tensile; Deformation and fracture; Strain rate; Constitutive model; Microstructure

1. Introduction V-Cr-Ti alloys are important candidate materials for fusion reactor applications due to the high temperature strength, good compatibility with liquid metals and resistance to irradiation damage effects[1]. Previous studies have shown that the strengths of V-Cr-Ti alloys increase with the alloying element content[2]. When the total alloying element content exceeds 10%, the ductile-brittle transition temperature (DBTT) increases dramatically[3]. Thus, many researches have focused on vanadium alloys containing 4-5% Cr and 4-5% Ti, since they seem to be the optimal materials with high strength and low DBTT. The V-(4,5)Cr-(4,5)Ti alloys are typically ductile materials at the ambient temperature, and

the main fracture mechanisms are the growth and coalescence of microvoids [4-7]. Under a high strain rate deformation[8] or perpendicular to the rolling direction[10], the V-5Cr-5Ti alloy exhibits brittle fracture characteristics, including cleavage facets, inter-granular secondary cracks and river patterns in the fracture surface. The flow stress of V-(4,5)Cr-(4,5)Ti alloys increase with the increasing of strain rates and the decreasing of temperature[8,11]. The temperature and strain rate dependent constitutive equations for these alloys are seldom reported. Donahue et al[12] developed a dislocation-based constitutive model of V-4Cr-4Ti alloy for low-to-intermediate temperatures and strain rates. Cai et al[11] developed a modified Johnson-Cook model to describe the strain-rate sensitivity of the V-5Cr-5Ti alloy at room temperature. In this work, the effects of the tensile strain rate on flow stresses of V-5Cr-5Ti alloy were experimentally tested, and the effects of the strain rate on the fracture mechanisms were analyzed. Four different constitutive models were used to characterize the flow stresses of the V-5Cr-5Ti alloy, and their accuracy were compared. 2. Materials and Experimental Procedure The chemical compositions of the V-5Cr-5Ti alloy are 5.37wt.%Ti and 5.21 wt.% Cr. Dog-bone type specimens with gage length of 25 mm, width 6 mm and thickness 2 mm were cut from the bulk material along the rolling direction. Tensile tests were carried out under the strain rates of 1.0×10-1/s, 5.5×10-3/s, 5.5×10-4/s and 1.1×10-4/s at room temperature, and 3 specimens were tested for each strain rate. The test results showed that all the three stress-strain curves were very similar for each strain rate, and therefor only one of them was analyzed in the following. 3. Results and Discussions 3.1 Fracture mechanics A SEM micrograph of the fracture surface of the V-5Cr-5Ti alloy is shown in Fig. 1. The numerous short intergranular microcracks shown in the fracture surface suggest that the grain boundary (GB) strength of the alloy is weak. The possible reason is that the impurities (such as S, P etc.) and the second phases precipitation have been separated to the GBs [6,13]. Some long secondary cracks are formed through the coalescence of the intergranular microcracks. The equiaxed dimples with the sizes less than 1µm can be observed on the fracture surface at high magnification. These features indicate that the coalescence of intergranular microcracks

and dimple rupture lead to the fracture of the alloy.

Figure 1. The fracture surface of V-5Cr-5Ti alloy (𝜀̇ =1.0×10-1/s)

(a)

(c)

(b)

(d)

B B C A B B B A A

B

C

Figure 2. SEM micrographs of the fracture surface. (a) 𝜀̇ =1.1×10-4/s, (b) 𝜀̇ =5.5×10-4/s, (c) 𝜀̇ =1.0×10-1/s and (d) 𝜀̇ =5.5×10-3/s. In Fig. 2(d), the fracture is featured by intergranular separation (A), cleavage facets (B) and river patterns (C)

Fig. 2(a)–(d) illustrate the fractographies of the V-5Cr-5Ti alloy fractured under the strain rates ranging from 10-4/s to 10-1/s. Fig. 2(d) shows the brittle fracture surface under the strain rate of 5.5×10-3/s. For Fig. 2(a)-(c), the variation of the applied strain rates doesn't lead to obvious change in the fracture mode. But the grain deformation, the intergranular microcrack density and slip bands on intergranular facets in the ductile fracture surfaces are gradually changed with the applied strain rates. Under the strain rate of 1.1×10-4/s, few long transverse secondary cracks appear in the fracture surface, whereas the short intergranular microcracks seem to be isolated with each other as shown in Fig. 2(a). The obvious slip bands are shown on the intergranular facets at high magnification. This is because under the slow strain rate deformation, there is sufficient time for the development of GB sliding and dislocation pileups at GB. This can lead to the premature coalescence of intergranular microcracks in the weak regions to form a main crack, while the intergranular microcracks and microvoids far from the main cracks can't fully expand. Under the strain rate of 5.5×10-4/s, the short intergranular microcrack density is high in the fracture surface. The fractured grains with wedge shape can be observed in Fig, 2(b), which results from the slip plane splitted by shear stress[7]. The possible reason is that the increased strain rate causes the quick development of the nucleation of intergranular microcracks at the weak GBs in the initial stage of deformation. Then their propagations are restrained by the interlocked grains, and the grain deformation is improved in the following deformation. This causes the increase of dislocation sliding in the grains and the stress concentrations at GBs, which can promote the nucleation and propagation of intergranular microcracks and microvoids [6,7,13]. If the shear stress in the grains is high enough, the grains can be splitted from the slip planes. The coalescence of intergranular microcracks, microvoids and splitted grains result in the final fracture of the specimen. Consequently, the high density of intergranular microcracks is obtained under this strain rate deformation. Under the strain rate of 1.0×10-1/s, the short intergranular microcracks tend to coalesce to form long secondary cracks by tearing the grains or GBs. The slip bands on intergranular facets are not clear, and a few transgranular facets can be observed in fractography as shown in Fig. 2(c). This is because the high stress is developed in the grains, whereas the time for

GB sliding is inadequate due to the high strain rate. These factors promote the microvoid fracture on the GBs and even transgranular fracture [11]. As a result, some long secondary cracks were formed due to the coalescence of transgranular and intergranular microcracks, and caused the final fracture. Brittle fracture often occurred under the strain rates of 1.0×10-1/s and 5.5×10-3/s due to the high notch sensitivity of V-5Cr-5Ti alloy[7,9]. Under the high strain rate deformation, the high stress level in the specimens may induce the brittle fracture. The fractograph in Fig. 2(d) exhibits intergranular separation (A), cleavage facets (B) and river patterns (C). 3.2 Constitutive models The Johnson-Cook(J-C) model, modified J-C model[11], V-A model[14] and Z-A model[15] were used to characterize the flow stresses of the V-5Cr-5Ti alloy. At room temperature, the Johnson-Cook(J-C) model is given by 𝜀̇

𝜎 = (𝐴 + 𝐵𝜀𝑝𝑛 ) (1 + 𝐶𝑙𝑛 𝑝 )

(1)

𝜀̇ 0

Where 𝜀𝑝 , 𝜀̇𝑝 and 𝜀̇0 is plastic strain, strain rate and reference strain rate respectively, 𝐴, 𝐵, 𝑛 and C are model parameters. Since the original J-C model can’t correctly describe the correlation between the strain-rate sensitivity and the plastic strain of the V-5Cr-5Ti alloy, Cai et al[11] introduced a plastic strain-dependent modification for parameter C in Eq. (1): 𝜀̇

𝜎 = (𝐴 + 𝐵𝜀𝑝𝑛 ) (1 + (𝐶0 + 𝐶1 𝑒 −𝐶2 εp )𝑙𝑛 𝑝 )

(2)

𝜀̇ 0

Where C0, C1 and C2 are model parameters. At room temperature, the V-A model and Z-A model is given by V-A model: 𝜎 = ̂ 1

(

Z-A model: 𝜎 = 𝐶0

(

1

1⁄

𝑙𝑛𝜀̇𝑝 )

1⁄ 𝑝

+ 𝐵𝜀𝑝𝑛 +

𝑙𝑛𝜀̇𝑝 ) + 𝐵𝜀𝑝𝑛 +

(3) (4)

Where ̂ is the threshold yield stress of the Peierls barrier. B and n are the plastic hardening constants,

represents the temperature-independent stress.

parameters. p and q are assumed to be 1/2 and 3/2 respectively.

Table 1 Parameters of the constitutive models for V-5Cr-5Ti alloy J-C model

𝐴(MPa)

𝐵(MPa)

n

𝜀̇0 (/s)

𝐶

1,

, 𝐶0 and 𝐶 are model

454.92 revised J-C model

𝐴(MPa) 492.14

384.26

0.4596

1.0

0.0223

𝐵(MPa)

𝑛

𝜀̇0 (/s)

𝐶0

𝐶1

𝐶

244.46

0.4832

1.0

0.018

0.01252

25.7

̂ (MPa)

1

V-A model 0.305 (MPa)

1.065×10-2

1250

B(MPa)

n

Z-A model 80.3

395.7

0.5074

(MPa) 98.3

B(MPa)

n

p

395.7

0.5074 0.5

q 1.5

𝐶0 (MPa) 𝐶 402.1

0.04278

The fitted model parameters are listed in Table 1. The complete tensile stress/strain curve including post-peak response under the strain rate of 5.5×10-3/s was not obtained due to the brittle fracture of all 3 specimens. As shown in Fig. 3(b), the prediction accuracy of the modified J-C model is the best among these models. The two physically based constitutive models also can give very close predictions. The original J-C model underestimates the strain hardening at slow strain rate and overestimates the strain hardening at high strain rate. Since the effect of damage is not considered in the models, they overestimate the flow stresses for the plastic strain higher than 0.09, when necking deformation starts and the microstructure damage occurs in the necked region.

Figure 3.Comparison between experimental data and model predictions. (a) stress-strain curves at different strain rates (b) the strain rate jump test. In order to assess the applicability of the constitutive models, a strain rate jump test has been conducted[16]. The specimen firstly underwent an engineering strain of 0.025 at the strain rate of 1.0×10-4/s, then followed by another engineering strain increment of 0.025 at the enhanced strain rate 2.0×10-4/s. Finally, the specimen was loaded at the strain rate of

4.0×10-4/s until failure. The comparison of the model predictions with the experimental results of the strain rate jump test is shown in Fig.3(b). The revised J-C model and the two physically based constitutive models can precisely predict the flow stresses before necking deformation. The original J-C model overestimates the flow stress for the strain lower than 0.04, and underestimates the flow stress for the strain higher than 0.04. 4. Conclusions The tensile properties of V-5Cr-5Ti alloy over the strain rate range of 10-4/s - 10-1/s were experimentally tested at room temperature. The coalescence of intergranular microcracks and dimple rupture are the main fracture mechanisms, and the variation of the applied strain rates doesn't lead to obvious change in the fracture mode of V-5Cr-5Ti alloy. The transgranular microcracks increase with the increasing of strain rate. Two empirical constitutive models and two physically based constitutive models were used to characterize the strain rate-dependent mechanical properties of the V-5Cr-5Ti alloy at room temperature. The revised J-C model and the two physically based constitutive models can precisely predict the strain rate-dependent flow stresses before necking deformation.

Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities of China under Grant No. 2016IA007.

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Highlights 

The tensile properties of V-5Cr-5Ti alloy under the different strain rate were tested



The effect of strain rate on the fracture mechanisms of V-5Cr-5Ti were analyzed



Four constitutive models were used to characterized the strain rate dependent mechanical properties and their precision were accessed