Calibration of COD Gauge and Determination of Crack Profile for Prediction of Through by MMSE Journal

Mechanics, Materials Science & Engineering, September 2016

ISSN 2412-5954

Calibration of COD Gauge and Determination of Crack Profile for Prediction of Through the Thickness Fatigue Crack Growth in Pipes Using Exponential Function Pawan Kumar1, a, Hemendra Patel2, P.K.Ray2, B.B.Verma2 1

Institute for Frontier Materials Deakin University, Australia

National Institute of Technology, Rourkela

pkumar@deakin.edu.au DOI 10.13140/RG.2.2.23243.18724

Keywords: fatigue crack propagation, Crack opening displacement calibration, crack profile, exponential function

ABSTRACT. In present investigation the calibration of COD gauge and study of crack profile for part-through cracked pipes subjected to four-point bending has been done. The results show that crack profile is semi-elliptical in nature for lower crack depth and is flattened with the increase in crack depth. The linear relationship is obtained between crack depth and COD gauge. The COD calibration curve is used to study fatigue crack propagation by exponential function. The material of the pipes under investigation was TP316L grade stainless steel. The specimens were subjected to fourpoint bend fatigue load in air and at room temperature. The predicted results were compared with experimental crack growth data. It has been observed that the results obtained using exponential function is in good agreement with experimental data.

Introduction. In industries pipe installations are used to transport pressurized fluids. Therefore, it is possible that these pipes experience stresses developed by the pressurized fluid. They may also experience seismic vibration as well as fluctuating bending stresses. It is possible that these stresses may promote extension of an existing crack or initiate a new fatigue crack from a highly stressed region [1-6]. In several industries the pipe installations carry hazardous fluids. Therefore, monitoring of these crack propagation in pipes is important in terms of safety and stability [7-8]. The study of fatigue crack growth requires determination of crack length/depth and number of cycles. The number of cycles can be obtained from data acquisition system, integrated with the fatigue testing machine. For crack growth measurement various techniques are available like potential drop method, compliance method etc. To use compliance method the relation between COD gauge deflection and crack depth must be known. For some standard specimens like compact tension (CT), single edge notched (SEN) and others, the relationship between dimensionless compliance and normalized crack length are known. The relation between dimensionless compliance and normalized crack length are available for standard specimen given by ASTM standard data book; and this relationship can be used for the standard specimen and geometry for which they were developed. But in case of pipes there is no such a relation is available in the software supplied with the machine. In present investigation the calibration of cod gauge for straight notched pipe subjected to four point bending has been done. Different techniques like finite element method, numerical analysis, boundary integral have been used to address fatigue crack growth in pipes. Athanassiadis et al. [9] reported numerical solution to a near circular crack front problem. Nezu et al. [10] applied finite element method with experimental results and studied circular shape of crack front. There are also finite element simulation software like CASCA and FRANC2D used to study fatigue crack growth in pipes [11]. There are methods in which it is proposed to convert 3D problems into 2D problems like spring model used by Rice and Levi [12] and conformal transformation methods by Wall Brink et al. [13]. These models are able to analyze partial circumferential crack as well as complex circumferential cracks in pipes. Mohanty et al. [14MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, September 2016

ISSN 2412-5954

17] developed an exponential model for prediction of fatigue crack growth in SENT specimen under constant amplitude loading and variable amplitude loading. Pawan Kumar et al. recently developed a fatigue crack propagation model for pipes using gamma function [18]. In present work exponential function is used instead of gamma function to estimate the fatigue crack propagation life in pipes. Experimental procedure The material under investigation was TP316L stainless steel. The specimens were part-through cracked pipes having notch angle 45o. The notches were prepared by wire-EDM process. The fatigue crack growth tests were conducted in servo-hydraulic dynamic testing machine (Instron 8800) under load control mode. A four-point bend fixture as shown in Fig. 1 was fabricated for conducting fatigue crack growth tests. The Instron da/dN software is not calibrated for COD output and crack extension for pipe geometry. Therefore before conducting the test, COD gauge was calibrated using multiple specimens. The notch-geometry of the material is presented in Table 1. Test Condition Pipe test have been carried out at room temperature and air environment under load control mode using sinusoidal waveform loading. The constant amplitude method with stress ratios of 0.1 with frequency 4 Hz has been followed. The load range applied during the fatigue crack initiation and growth test was of the order of 40.5 KN, which is below the yield strength of the piping material which corresponds given notch dimensions. This is to ensure that the crack growth is under gross elastic conditions.

Fig. 1. Four-point bend fixture and specimen. Table 1. Specimen and notch dimension of pipe. Specimen parameters

Outer radius (R0)

Inner radius (Ri)

Crack depth

Crack length (L)

Length of the specimen

Angle

Dimension (mm)

2.28

505

45o

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Mechanics, Materials Science & Engineering, September 2016

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Calibration of cod gauge Pipes with straight notches were used for calibrating COD gauge. Multiple specimens were used for this purpose. The COD calibration curve ( COD vs. measured crack length along the pipe thickness) is shown in Fig. 2. The crack length was measured with the help of a travelling microscope.

Crack length,a (mm)

6 5

4 3 2 1 0 0

10 20 Del. COD (mm)

Fig. 2. Calibration of COD gauge. Determination of crack profile With the help of optical travelling microscope crack profile are measured. The crack profiles of all the fractured pipes are shown in fig 3. From the crack profile it is clear that the crack propagates along thickness direction first, than the crack propagates in circumferential direction. It is also clear that the crack front profile is semi-elliptical in nature for lower crack depth, but the crack front shape is flattened as the crack depth increases. After initial crack propagation, there is crack growth in the circumferential direction as well. This reduces the SIF at the main crack front. This is the probable cause of flattening of the main crack front after the crack has grown some distance in the throughthickness direction. The SEM image of fractured surface is shown in fig. 4 and no beach mark is observed.

Fig. 3. Crack profile.

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Fig. 4. SEM image of fractured surface shows no beach mark. Formulation and validation of model Fatigue crack propagation, is characterised by rate of increase of crack length (a) with number of cycles (N). It requires a discrete set of crack length vs. number of cycle data generated experimentally. Fig. 5 shows experimental a-N data.

Crack length, a (mm)

5.8 4.8 3.8 2.8 1.8 0.8 0

20000 40000 No. of cycles, N

60000

Fig. 5. Experimental a-N curve. Finally the validation has been done with experimental data in order to compare its accuracy in predicting fatigue life in part-through cracked pipes. Formulation of model This model is based on the exponential growth of fatigue crack with number of loading cycles. The modified exponential equation is given as [15-16] (1) And,

(2)

Here, Nj and Ni represent number of cycles in jth step and ith step respectively; MMSE Journal. Open Access www.mmse.xyz

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aj and ai are the crack lengths in jth step; ith step respectively; mij

is specific growth rate in the interval (i-j).

The specific growth rate m is calculated for each step from experimental result of fatigue test (a-N data) using equation (2). The exponent mij (known as specific growth rate) of the proposed exponential model has been correlated with various physical variables like crack driving parameters, crack resisting parameter, and material properties in non-dimensional forms. The specific growth rate is correlated with a parameter l, which takes into account two crack driving forces K and Kmax as well as material parameters KC, E, ys and is represented by equation:

(3)

The different m and l values are fitted by a polynomial equation. The predicted m values are calculated for seven specimens by a polynomial fit as follows: (4) where A, B, C, and D are curve fitting constants whose average value for seven specimens have been presented in the Table 3. The stress intensity factor K has been calculated by equation [19]:

(5)

Here

is bending stress; is axis-symmetrical stress which is zero in present case.

Validation of model The predicted number of cycles or fatigue life is given by:

(6)

The predicted values of specific growth rate (mij) of the tested specimen have been calculated by putting the average values of the curve fitting constants (for specimen no. 1, 2, 3, 4, 5, 6, 7) in equation (4). For validation of proposed exponential model; fatigue life is calculated (for specimen no. 8) by using the equation (6) .

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Discussion. An attempt has been made to develop a fatigue crack propagation model for part-through cracked pipe using exponential function. The specific growth rate (m) which relates crack growth to material properties is an important parameter for exponential model. The experimental a-N data of seven specimens were used for formulation of model, and its validation was checked for 8th specimen. Table 2 shows the average value of curve fitting constants. These constants have been used to predict fatigue life of a through wall cracked pipe specimen. A comparative study of a-N curve is made for proposed exponential model and experimental data (Fig. 6).The da/dN K curves are also compared (Fig. 7). It is found that the predicted results are conservative in nature. Table 2. Value of coefficients for exponential model. Material

TP316L

-359.484

+52.708

-2.578

0.0421

crack length, a (mm)

a ( experimental)

a ( predicted)

7 6 5 4 3 50000

70000

90000

110000

130000

No. of cycles, N

Fig. 6. a-N curves (experimental and predicted).

0.0001

da/dN (mm/cycle)

9E-05 8E-05

da/dN ( experimental)

7E-05

da/dN (predicted)

6E-05 5E-05 4E-05 3E-05 2E-05 17

19 K (MPa*m^1/2)

Fig. 7. da/dN- K curves (experimental and predicted). MMSE Journal. Open Access www.mmse.xyz

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Three different criteria have been followed to evaluate performance of exponential model by comparing the predicted results with experimental data for part-through cracked pipes under constant amplitude loading condition. These criteria are Percent deviation, Prediction ratio and Error bands In order to predict fatigue crack propagation in part-through cracked specimen, seven specimens were used; the validity of proposed exponential model is checked for specimen no. 8. The percentage deviations and the prediction ratio of exponential model are presented in Table 3 and Table 4. Table 3. Model Performances (for crack length). Test specimen

% Dev

Prediction ratio

TP316L stainless steel

5.80

0.94

Table 4. Model performances (for number of cycle). Test specimen TP316L stainless steel

% Dev model) 3.66

Prediction ratio 1.038

Performance of exponential model is evaluated by error band scatter, which is shown in Figs. 8 & 9. The error band lie within +0.0% to -0.09% of experimental number of cycles and + 0.0% to+0.06% of experimental crack length for exponential model.

Fig. 8. Error band scatter for number of cycle (exponential model).

Fig. 9. Error band scatter for crack length (exponential model). MMSE Journal. Open Access www.mmse.xyz

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Summary. The crack front profile is nearly semi elliptical in nature for lower crack depth, but the crack front shape is flattened as the crack depth increases. The calibration curve of COD gauge is found to be straight line, which shows linear relationship between COD gauge and crack depth of pipe specimens. Fatigue crack propagation in part-through cracked pipes can be determined by using exponential function of the form . Exponential function can be effectively used to predict the fatigue life of part-through cracked pipe. References [1] Beden S M, Abdullah S, Ariffin A K, Review of fatigue crack propagation models for metallic components, European Journal of Scientific Research 28.3 (2009) 364-397. [2] Wang G S, Blom A F, A strip model for fatigue crack growth predictions under general load conditions, Engineering Fracture Mechanics 40.3 (1991) 507-533, DOI: 10.1016/00137944(91)90148-T [3] Rice J R, Mechanics of crack tip deformation and extension by fatigue, fatigue crack propagation, ASTM, ASTM STP (1966) 415. [4] Paris P C, Erdogan F, A critical analysis of crack propagation laws, Journal of Fluids Engineering 85.4 (1963) 528-533, DOI: 10.1115/1.3656901 [5] Paris P C, Gomez M P, Anderson W E, A Rational Analytical Theory of Fatigue, The Trend in Engineering, U. of Washington, Seattle, Wa 13.1 (1961). [6] Walker E K, The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7076T6 aluminum. In: Effect of environment and complex load history on fatigue life, ASTM STP 462. Philadelphia: American Society for Testing and Materials, (1970) 1 14. [7] Shibata K, Results of reliability test program on light water reactor piping, Nuclear engineering and design, 153.1 (1994) 71-86. [8] Yeon-Sik Y, Ando K, Circumferential fatigue crack growth and crack opening behavior in pipe subjected to bending moment, SMIRT-15, Seoul, Korea 15.5 (1999) 343-350. [9] Athanassiadis A, Boissenot J M, Brevet P, Francois D, Raharinaivo A, Linear elastic fracture mechanics computations of cracked cylindrical tensioned bodies, International Journal of Fracture 17.6 (1981) 553-566. [10] Kikuo N, Machida S, Nakamura H, SIF of surface cracks and fatigue crack propagation behaviour in a cylindrical bar, Japan Congress on Materials Research, 25 th, Tokyo, Japan (1982). [11] Sharan A, Prediction of fatigue crack propagation in circumferentially cracked pipe specimen using casca and Franc2D, Diss. National Institute of Technology Rourkela, (2012). [12] Rice J R, and Nouri L, The part-through surface crack in an elastic plate, Journal of Applied Mechanics 39.1 (1972): 185-194. [13] Wallbrink C D, Peng D and Jones R, Assessment of partly circumferential cracks in pipes, International Journal of Fracture (2005): 167-181 [14] Mohanty J R, Verma B B, and Ray P K, Prediction of fatigue crack growth and residual life using an exponential model: Part II (mode-I overload induced retardation), International Journal of Fatigue 31.3 (2009): 425-432, DOI: 10.1016/j.ijfatigue.2008.07.018 [15] Mohanty J R, Verma B B, and Ray P K, Evaluation of overload-induced fatigue crack growth retardation parameters using an exponential model, Engineering Fracture Mechanics 75.13 (2008): 3941-3951. [16] Mohanty J R, Verma B B, and Ray P K, Prediction of fatigue life with interspersed mode-I and mixed-mode (I and II) overloads by an exponential model: extensions and improvements, Engineering Fracture Mechanics 76.3 (2009): 454-468. MMSE Journal. Open Access www.mmse.xyz

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[17] Mohanty J R, Verma B B, and Ray P K, Determination of fatigue crack growth rate from experimental data: a new approach, International Journal of Microstructure and Materials Properties 5.1 (2010): 79-87. [18] Pawan Kumar, Vaneshwar Kumar Sahu, P.K.Ray and B.B.Verma , Modelling of Fatigue Crack Propagation in Part-Through Cracked Pipes Using Gamma Function, Mechanics, Materials Science & Engineering, Vol. 6 (2016), DOI: 10.13140/RG.2.2.16973.03043 Al Laham S, Structural Integrity Branch. Stress intensity factor and limit load handbook. British Energy Generation Limited, (1998).

Cite the paper Pawan Kumar, Hemendra Patel, P.K.Ray & B.B. Verma (2016). Calibration of COD Gauge and Determination of Crack Profile for Prediction of Through the Thickness Fatigue Crack Growth in Pipes Using Exponential Function. Mechanics, Materials Science & Engineering Vol.6, doi: 10.13140/RG.2.2.23243.18724

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