Scholarly article on topic 'Fracture toughness evaluation of 3Cr-1Mo steel from Vickers indentation and tensile test data'

Fracture toughness evaluation of 3Cr-1Mo steel from Vickers indentation and tensile test data Academic research paper on "Materials engineering"

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{"Fracture toughness" / "3Cr-1Mo steel" / "Vickers indentation test" / "tensile test" / "IEF model" / "CVN impact test"}

Abstract of research paper on Materials engineering, author of scientific article — A.H. Mohammadi, M. Naderi, M. Iranmanesh

Abstract The 3Cr–1Mo steels have a potential for hydrogen and temper embrittlement. In the current study a theoretical model is proposed to estimate the fracture toughness of 3Cr-1Mo steel from Vickers indentation and tensile test data using the indentation energy to fracture (IEF) model and substituting ball indenter for Vickers indenter. These predicted values were compared with KIc values obtained from Rolfe-Barsom equations based on Charpy V-Notch (CVN) impact test results. It was found that the relative error between estimated fracture toughness from theoretical model and one's calculated from CVN impact test have an admissible value equal to 17%.

Academic research paper on topic "Fracture toughness evaluation of 3Cr-1Mo steel from Vickers indentation and tensile test data"

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ScienceDirect

Procedia Engineering 10 (2011) 228-235

Engineering

Procedia

Fracture toughness evaluation of 3Cr-1Mo steel from Vickers indentation and tensile test data A.H. Mohammadia*, M. Naderia, M. Iranmaneshb

aDepartment of Mining and Metallurgy, Amirkabir University of Technology, Tehran, Iran bDepartment of Marine Sciences and Ship Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

The 3Cr-1Mo steels have a potential for hydrogen and temper embrittlement. In the current study a theoretical model is proposed to estimate the fracture toughness of 3Cr-1Mo steel from Vickers indentation and tensile test data using the indentation energy to fracture (IEF) model and substituting ball indenter for Vickers indenter. These predicted values were compared with KIc values obtained from Rolfe-Barsom equations based on Charpy V-Notch (CVN) impact test results. It was found that the relative error between estimated fracture toughness from theoretical model and one's calculated from CVN impact test have an admissible value equal to 17%.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of ICM11

Keywords: Fracture toughness; 3Cr-1Mo steel; Vickers indentation test; tensile test; IEF model; CVN impact test

1. Introduction

Low-carbon, low-alloy steels are often used in petrochemical industries and refineries. These steels mainly contain Cr, Mo or V as significant alloying elements [1]. The Cr-Mo pressure vessel steels have a potential for temper embrittlement that leads to toughness degradation and decrease of the critical flaw size for brittle fracture [2, 3]. With respect to this fact, there is a growing importance being attached to the assessment of the integrity of such structures that work at high pressure and elevated temperatures [4].

When assessing the integrity of structural materials, the indentation test is an attractive test technique to obtain material property data because it is in nature semi-nondestructive and requires a relatively small material volume.

Many theories and models have been developed to measure fracture toughness of materials by indentation techniques [5-9]. However, since indentation on ductile metals does not induce cracking even at very low temperatures, the estimation of fracture toughness using the indentation test has been rarely attempted for ductile metals [6].

* Corresponding author. Tel.: +98-912-215-3014; fax: +98-21-8888-2410. E-mail address: amir_hossein@aut.ac.ir.

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.04.041

One of well known model in this field is the indentation energy to fracture (IEF) model was proposed to estimate the fracture toughness of ferritic steels from ball indentation test data by Byun et al. [10].

The IEF model is based on the assumption that the indentation deformation energy per unit contact area up to a critical mean contact pressure is equal to the plastic energy portion of the fracture energy per unit area. In the model an imaginary fracture should be imposed to the indentation deformation. The criterion for the imaginary fracture is that fracture occurs when the maximum contact pressure reaches the fracture stress of the material [10].

This study is aimed at the development of IEF model by substituting ball indenter for Vickers indenter and proposing a new equation for evaluation fracture toughness from Vickers indentation and tensile test data. Eventually the predicted value of KIC for 3Cr-1Mo steel which calculated by theoretical model is compared with KIc values obtained from Rolfe-Barsom equations based on CVN impact test results.

2. Theoretical model

Byun et al. proposed an equation for calculating fracture toughness using ball indentation and tensile test data, as follows [10]:

2 E 1-v2

2A2D2 fnp.

2m-2> / \ m-2

Where E is Young's modulus, v is Poisson's ratio, W0 is the lower shelf fracture energy, A is the material yield parameter, m the Meyer index, D is the indenter diameter, S is the slope of the linear load - penetration depth and Pj is critical mean contact pressure.

By substituting the features of ball indenter for Vickers indenter, equation (1) becomes:

K,r —

2E A2D2fp^m~2

In this equation pj is calculated from:

= (tj,D+?)Ka»e-lntfD

Where K and n are the strength coefficient and work-hardening exponent of the Hollomon-type flow curve, A is a material constant determining the stress triaxiality-dependence of fracture strain, a is a temperature-dependent parameter and the values of A and a are determined by fitting the results of tensile test with equation (4):

£f = ae~Xtf (4)

Where ef is fracture strain and tf is stress triaxiality in tensile test.

In equation (3), tfD is the stress triaxiality for indentation deformation and expressed by:

zf ~ K 3 C5;

3. Experimental procedure

3.1. Material and metallography

The investigated material was obtained from an out of service hydro-processing reactor of Tehran oil refining company. This reactor was manufactured by JSW Co. in Japan. The composition of steel is listed in Table 1.

Table 1. Chemical analysis of the steel

Element C Si S P Mn Ni Cr Mo V Cu Ti Co Al

Wt% 0.1 0.28 0.013 0.011 0.49 0.3 2.7 0.86 0.01 0.22 0.004 0.02 0.004

The specimens for optical metallography were mechanically polished and etched in 2% nital solution and then observed by optical microscope.

3.2. Indentation tests

The sample for indentation test was grinded and polished by conventional metallographic methods and then tested by a universal hardness tester which was equipped with a LVDT, using a Vickers indenter with 2mm diameter and applying various forces on the surface ranging from 10 to 1200 N.

3.3. Tensile tests

To obtain the flow properties, which are needed for calculating the critical mean contact pressure and fracture toughness, tensile tests were performed using five smooth round bar specimen conducted at room temperature using an INSTRON model 6027 universal test machine according to BS 2832 standard [11] at a crosshead speed of 5 mm/min. The tensile test using three notched round bar specimen were also performed in room temperature according to the same standard procedure specified in [11], to obtain the relationships between mechanical properties and stress triaxiality. Also to determine yield stress in upper shelf temperature for using in Rolfe-Barsom equation, tensile test for three smooth round bar specimen was conducted in 200°C temperature (upper shelf temperature according to CVN impact test results).

3.4. CVN impact test

Standard CVN impact tests according to ASTM E-23 were performed at the temperature range 0 to 200°C, using an AMSLER model PW-750 test machine.

4. Results and discussion

4.1. Microstructure

Fig. 1 shows the microstructure of steel in two magnifications. According to micrographs, carbide distributions have been observed in the ferritic matrix.

Fig. 1. Microstructure of 3Cr-1Mo steel. 4.2. Indentation tests

Fig. 2 shows load - indentation diameter curve for Vickers indentation test. This figure illustrates that Vickers indentation obeys from Meyer law, which correlates the applied load P and the resulting indentation diameter d with each other:

P = kdm (6)

Where m is Meyer index and k is a material constant. These parameters are derived from the curve fitting of experimental results of indentations. In our study the m and k values were 1.758 and 946.6 respectively.

The value of m is consistent with other reports. According to Onitsch, m lies between 1 to 1.6 for hard materials, and for soft materials it is above 1.6 [12]. So, 3Cr-1Mo alloy studied in the current research can be accepted as soft materials.

d (mm)

Fig. 2. Load - indentation diameter curve for Vickers indentation test.

The relationship between indentation parameters (i.e.,

— versus-) is illustrated in Fig. 3.

Fig. 3. Relationship between indentation parameters.

By fitting the data to Meyer law [13]:

P (d\m~2

The value of A is derived as 800.5 MPa.

The linear load - penetration depth curve is shown in Fig. 4. From the plot, the S value is derived as 32.049 KN/mm.

h (mm)

Fig. 4. Load - penetration depth curve for Vickers indentation test.

4.3. Tensile tests

The mean values of flow coefficients are listed in Table 2.

Table 2. The mean values of flow coefficients for smooth specimens

Flow Coefficient K n E

Mean Value 586 MPa 0.049 205.6 GPa

The effect of stress triaxiality on fracture strain is illustrated in Fig. 5. As seen in the figure, the fracture strain decreases with increasing the stress triaxiality. As stated earlier, to evaluate the critical mean contact pressure as a criterion for fracture, the relationship between the fracture strain and the stress triaxiality, Eq. (4), should be known for the test materials. The coefficients of the relationship were obtained from the Fig.5. As seen in the figure, coefficients of A and a are 0.96 and 3.133, respectively.

1.6 1.4 1.2 1

w"0.8 0.6 0.4 0.2 0

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 tf

Fig. 5. Relationship between fracture strain and stress triaxiality.

4.4. Fracture toughness evaluation from Vickers indentation and tensile test data

Values of stress triaxility for indentation deformation and critical mean contact pressure are calculated by equations (5) and (3): tfID=2.29 pmf=1640 MPa

When stress triaxility for indentation compared to tensile test, much higher value is evaluated for the indentation, while this value is similar to one's ahead of the crack tip. The finite element simulation for RPV steels showed that the stress triaxility at the crack tip was about 2.8 [14-17]. This observation explains the reason of similar fracture toughness values obtained from the standard fracture mechanics test and the IEF model.

The calculated parameters are required for evaluating fracture toughness from IEF model is summarized in table

Table 3. The calculated parameters are required for evaluating fracture toughness

Parameter m pj A S W0 E v D

Value 1.758 1 640Mpa 800.5MPa 32.049KN/mm 1975 J/m2 206 GPa 0.28 2 mm

Eventually, fracture toughness of steel is calculated by equation (2): KIC=182 MPam1/2

4.5. Calculating fracture toughness by means of CVN impact test results

Values of impact energy at various temperatures are plotted in Fig. 6. The FATT is defined as the temperature at which the fracture face contains 50% shear fracture characteristics. The value of FATT measured in the current work is 75°C.

The upper-shelf CVN for pressure vessels has a correlation with KIC-us as Rolfe-Barsom equation [18]:

IK,c-us\ (CVNUS \

( ) = 0.64781-— — 0.0098) (8)

V a0,2 / V ffn? >

Where a02 is upper shelf yield stress and Tus is defined as the temperature at which the fracture face contains 100% shear fracture characteristics. For our study required parameters are as follows: Tus=200°C Go.2= 269.1 MPa CVNus=171.55 J

So the KIC-us is calculated by equation (8) as 171.59 MPam1/2.

For calculating KiC value with 99% certainty, Weibull distribution model [19] is used. According to the model, for -40 °C< T-FATT <350 °C:

= 0.623 + 0.406exp[—0.00286(T - FATT)]

So the KIC is calculated by equation (9): KIC=155.63 MPam1/2

0 50 100 150 200 250 Temprature (°C)

Fig. 6. Impact energy vs. Temperature for CVN impact test.

The relative error between estimated fracture toughness from theoretical model and one's calculated from CVN test have a value equal to 17%. The error is relative to material piled up around the indenter during indentation test. When this happens, more material is supporting the indenter and specimen appears harder than it really is. As a result, fracture toughness increases by increasing in hardness of specimen.

5. Conclusions

This paper proposed a methodology for estimating the fracture toughness of 3Cr-1Mo steel based on the IEF model and substituting ball indenter for Vickers indenter. Predicted value of KIC was compared with KIC value obtained from Rolfe-Barsom equations based on CVN test results. It was found that the relative error between estimated fracture toughness from theoretical model and one's calculated from CVN test have an admissible value equal to 17%. The error is relative to material piled up around the indenter during indentation test.

Finally, much higher stress triaxiality is evaluated for indentation test in regard to tensile test, but this value is similar to the value ahead of the crack tip. This observation explains the reason of similar fracture toughness values obtained from the standard fracture mechanics test and the IEF model.

Acknowledgements

The authors wish to thank to Eng. Yarandi of research institute of petroleum industry for supplying the material and Eng. Poshteban and Eng. Naderi of Hamyar Sanat Eghbal Co. for their supports in performing the hardness measurements.

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