International Journal of Fracture 123: 1–14, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.

Crack arrest in rupturing steel gas pipelines X.C. YOU1 , Z. ZHUANG1,∗, C.Y. HUO2 , C.J. ZHUANG2 and Y.R FENG2

1 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China; 2 Tubular Goods Research Center of China National Petroleum Corp., Xi’an 710065, China; ∗ Author for correspondence:

[email protected] Received 14 February 2003; accepted in revised form 8 September 2003 Abstract. Failure incident investigations and full-scale experiments of pipelines rupturing indicate that the original methods in predicting arrest are no longer reliable when applied to high toughness pipelines. The cause of the phenomenon is analyzed in this paper through a macroscopic and phenomenological method by referring to the energy balance equation, by that is established the iterative algorithm used in finite element method (FEM) simulation of crack deceleration. This simulation, in combination with the two-specimen drop weight tear test (DWTT), provides a broad prediction of the dynamic fracture process. In addition, the crack tip opening angle (CTOA) criterion is consummated through the comparison between CTOA in FEM calculation and the critical value of (CTOA)C obtained in the two-specimen DWTT. Thus, the avoidance of both the dimensional effect and the dissipation of irrelevant energy common in small-scale tests are achieved. Key words: CTOA criterion, dynamic fracture mechanics, finite element, pipeline, toughness test.

1. Introduction Defects and micro-cracks introduced by steel pipe manufacturing and pipeline construction are the primary reasons of pipeline rupturing. Preventing pipeline from rapid crack propagation is a critical issue to avoid casualty and disaster. However, it would be difficult to completely diminish the possibility of crack propagation. In cases of important structures where the load case or the environment is complicated, and where regular crack inspection fails to be implemented, as a result of which, the cracking process cannot be controlled effectively. A study in this paper is to seek out the mechanism of avoiding crack propagation in high pressure steel gas pipeline, so as to set up a second defense line against the rupture. In the arrest study of ductile fracture, it is important to find out the material toughness of pipeline with enough arrest capability. Earlier work mainly adopts the approach of simulating a section of pressured pipeline to conduct full-scale blast tests, and by studying the results concluding how to control the dynamic ductile fracture. This test method becomes a standard method in determining arrest toughness. As full-scale tests are expensive, time-consuming, and the applicability of which is greatly limited by factors like the specific size of pipelines, the components and pressure of gas, there arises the need to establish a relation between these factors and corresponding critical arrest toughness. Hence, small-scale tests are needed to describe the dynamic fracture toughness of pipelines. CVN (Charpy V-Notch) impact test is the most commonly used in this aspect. The commonly used model predicting the critical value of arrest toughness is the twocurve method established in 1974 (Maxey, 1974). In this method, on the supposition that the decompression of gas and the dynamic crack propagation are two separate processes that can

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be linked together by crack tip speed, a relation between crack tip speed and decompression pressure or hoop stress is established. The two-curve method analyzes the criterion of decompression wave speed based on crack propagation, and comes up with an effective arithmetic solution, deducing directly through pipeline operation parameters the critical CVN impact toughness needed in arrest. Later, a series of handy empirical formulae have been summarized (Kanninen et al., 1992a). In those days when the CVN impact toughness of pipelines used in full-scale rupturing experiments was normally not over 100 J, the CVN impact toughness was enough to describe the fracture resistance capability of pipelines, and the two-curve model as well as empirical patterns fits in well with the results of full-scale rupturing experiments (Eiber and Maxey, 1977). With the development of gas transportation system, high-pressure and high-toughness pipelines come into use (Kanninen et al., 1992b). As an alternative to correct the test errors in CVN, DWTT (Drop Weight Tear Test) is used to measure the effective energy in crack propagation, and determine the arrest toughness with the two-curve method. Studies show that for high-toughness pipelines, the arrest prediction based upon DWTT is closer to testobtained values than CVN test (Wilkowski et al., 1980), but still cannot fundamentally solve the gap between arrest toughness predictions of the pipelines and the actual results. On the other hand, full-scale test observations on high-toughness-pipelines show that in pieces with similar toughness even within the same piece, deceleration and arrest unmistakably take place (Eiber et al., 2000). That is to say, if the test piece is long enough, arrest can happen to cracks on pipelines with toughness lower than the critical one. It indicates that in addition to critical toughness, other parameters are needed to describe the arrest capability of pipelines, for example, the crack propagation length with certain toughness and in certain environment. Against this background, this paper, relying on FEM computation, tries to solve the arrest prediction on high-toughness pipelines in two ways: one is through theoretical derivation to establish the iterative algorithm of crack deceleration obtained in small-scale tests in FEM model of pipeline fracture, simulate the entire arrest process of pipelines, and compare it with full-scale tests; the second is to compare the CTOA computational value in FEM model with the (CTOA)C obtained in two-specimen DWTT, and predict the critical toughness of crack propagation of gas pipelines from the angle of geometric criterion. 2. The energy balance equation of cracked steel pipelines The overall energy balance of cracked pipelines means that within a certain period of time the sum of the variation of kinetic energy
K and the variation of strain energy
U equates the sum of the heat transfer through pipelines δQ and the entire work by forces and couples δW , namely:
K +
U = δW + δQ.

(1)

The kinetic energy and strain energy here are both addable status functions, and only have relations with initial and final status. But work and heat also are related with the process, for which purpose, two increment signs
and δ are adopted. If the increment infinitely approximates zero and the variable in the equation is a function that can be differentiated with respect to time, then Equation (1) can be written in the differential form corresponding to time t:

Crack arrest in rupturing steel gas pipelines ˙ K˙ + U˙ = W˙ + Q.

3 (2)

As kinetic energy and strain energy are addable functions, we therefore have: ˙ ∗ ) + K(S ˙ F ), U˙ (V ) = U˙ (V ∗ ) + U˙ (SF ), ˙ ) = K(V K(V

(3)

where V and SF are the space occupied by pipelines and the new surface caused by crack ∗ propagation respectively, V is the difference between the two. Provided that the energy variation rate of the new crack surface is ˙ F ) + U˙ (SF ). ˙ F ) = K(S (S

(4)

So the following equation can be obtained: ˙ ∗ ) = U˙ (V ∗ ) = W˙ + Q˙ − . ˙ K(V

(5)

The above equation when put in differential form is ∗

∗

dW − dU (V ) − dK(V ) = d − dQ,

(6)

where W is the external work, U is strain energy, K is kinetic energy,  is surface energy, Q ∗ is the loss of energy caused by heat. (V ) is the value of the part excluding the new surface formed by crack propagation. Make  = −Q to represent the heat dissipation caused by plastic work unloading, and  and  can be written respectively as the rate of plastic work δ and the density of surface energy ρs multiplied by the newly formed surface area caused by crack propagation:  = 2ahλ,

 = 2ahρS ,

(7)

where a is the propagation length of the crack, h is the thickness of the pipe wall. Define the crack driving force G:
 ∗ ∗ dU (V ) dK(V ) 1 dW − − . (8) G= h da da da Normally the surface energy density of steel ρs can be assumed to be a material constant. At the same time, attention should be paid to the fact that both λ and Gd are related to crack propagation speed v. For instantaneous propagation, the fracture toughness at some point Gd can be denoted as:   dλ 1 d∧ d + = 2λ + 2γ + 2a . (9) Gd = h da da da For metal materials, λ is usually thousands times of ρs , therefore ρs can be neglected (Li, 1998). During the process of crack propagation, energy conservation is not tenable in every part. The tip of the pipeline crack at this juncture can be seen as a source of heat, which accumulates and provides energy for crack propagation, and which conforms to the relation G = Gd . With Equations (2), (8) and (9), the energy balance equation of crack propagation can finally be obtained: dU dK da dW = + + hGd . dt dt dt dt

(10)

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In Equation (10), da/dt = vt indicates the instantaneous propagation speed of pipeline crack at the time of t. From above derivation it can be seen that when dW/dt is fixed, heat dissipation rate λ plays the function of restricting kinetic energy K. The process of crack propagation is definitely accompanied by heat transmission and the generation of entropy. For dissipating materials, like high-toughness steel, the effect of heat dissipation cannot be neglected. 3. FEM simulation on fracture propagation of pipeline 3.1. N UMERICAL MODEL IN THE SIMULATION OF CRACKED PIPE The computation of G and CTOA is one of the critical steps in the analysis process. Due to the complexities of crack propagation event, e.g., gas escaping from the opening breech, the calculation of G and CTOA is a non-trivial task. Fortunately this can be accomplished using a unique finite element code PFRAC (O’Donoghue et al., 1991; Zhuang and O’Donoghue, 2000a). There are three basic segments to this code: a structural mechanics unit; a fluid mechanics unit; and a fracture mechanics unit. These three models are fully coupled together and are used to analyze the crack propagation in a pipeline. The primary requirements structural dynamics program are that the model must simulate the large deformations of the pipe wall. The code incorporates a Lagrangian finite element description with four-node quadrilateral elements that allow for geometric non-linearity. An explicit finite difference scheme is used to march forward in time. This code is ideally suited to shell-like structures undergoing large deformations, for example, the flap opening experienced in ruptured pipes. A three-dimensional finite difference scheme is used to model the complex highly transient flow that takes place when the pipeline is cracked and the gas is escaping. The modification of PFRAC, described in this paper, is developing FE simulation and experiment data to estimate the deceleration of fracture propagation in high-strength and hightoughness steel gas pipelines. 3.2. N ODE RELEASE METHOD In the generation mode, the input information includes the position of the crack tip as the time function, and the distance of crack advance within every time interval is given. As the crack propagates along the elements, the element node force is released step by step. The energy release rate G, namely, the energy change per unit area caused by crack propagation, can be represented approximately in the form of the work by node force:  2 t+
t F νn dt, (11) G= hL t where h is the thickness of a pipeline wall, L is the element length in the direction of crack propagation,
t is the time taken per element for crack propagation, νn is the displacement speed of node at right angles to the direction of crack propagation pipelines, and the coefficient 2 arises from the symmetry of the two parts of the pipelines, as shown in Figure 1. In Equation (11), F is the constraint force released, whose magnitude changes linearly in relation to the position along the boundary of elements, and is represented as:   a(t) , (12) F (t) = F0 1 − L

Crack arrest in rupturing steel gas pipelines

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Figure 1. Computing crack driving force with node release method.

where F0 is the constraint force released, a(t) is the length of crack propagation per element. 3.3. G AS DECOMPRESSION BEHAVIOR Gas-decompression calculations are used to determine the pressure at the tip of a propagating fracture. Gas decompression refers to the pressure decay in the pipe as time passes, which is related to the flow phenomenon occurring inside the pipeline in the vicinity of the pipe rupture and at the crack tip. After a significant opening has developed following rupture, gas starts to flow rapidly out of the rupture. This outflow locally lowers the pressure inside the pipe and initiates a decompression or expansion wave in the gas. Due to the computational expense of the fully coupled simulations, a simplification is to replace the gas dynamic analysis by a curve fit pressure distribution on the pipe walls obtained from experimented data. Maxey et al., from Battelle, found that the ideal gas law is an adequate equation of state for compressed air, nitrogen, and natural gas, for which theoretical models existed to characterize the decompression behavior (Maxey, 1974). These models assume that the expansion process is isentropic, a sudden full pipe cross-sectional opening occurs, and the fluid mixture is and remains homogeneous. The local pressure was related to its propagation speed in the form:     γ − 1 ν 2γ /(γ −1) 2 + , (13) p1 = p0 γ +1 γ + 1 νa where p1 is the crack tip pressure, p0 is the initial line pressure prior to rupture, v is the pressure wave speed (propagation speed for a given decompressed pressure level), va is the acoustic speed in the gas at its initial pressure and temperature, and γ is the initial specific heat ratio of the gas.

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Linear decay model is used in computation, namely, linear decay behind the crack tip is assumed from the crack tip pressure, p1 , to atmospheric pressure over a decay length L. The decay function is:  z , z < L, (14) p(z) = p1 1 − L where z is the position of the cross section to be calculated, L is usually assumed as 1.5 to 2.0 times of pipe diameter. 3.4. C RACK DECELERATING ITERATION Suppose time step is n, iteration step is k, and for any variable ,
n,k is used to represent n,k − n−1 , then the expression of the external work should be:

Fext (dn − dn−1 ), (15) W0 = 0, Wn = Wn−1 + where d is the displacement component on the node, Fext is the external force acting on the node. The expression of the kinetic energy should he:

1 [(Mi νn2 ) + (I, ωn2 )], (16) Kn = 2 where i is the node number, M is the mass gathered on the node, I is the rotating inertia gathered on the node, νn is the linear speed component of the node, ωn is the angular speed component of the node. The expression of the strain energy should be:

1 (σn εAh), (17) Un = Un−1 + 2 where h is element thickness, A is element area, σ and ε are stress and strain in the element. In accordance with Equation (10), decelerating mechanism is introduced into FEM computation. For any time step and iteration step (n, k), check the following formula: |
Wn,k −
Kn,k −
Un,k − 0.5hGgn
an,k | η
Wn,k ,

(18)

where η represents the precision demanded by energy balance iteration, and 0 < η < 1. The closer η is to zero, the higher is the precision. If inequality (18) is tenable, computation enters time step n + 1; if it is untenable, computation enters iteration step l + 1: 
Wn,k −
Un,k − 0.5hGdn
an,k . (19) νn,k+1 = νn,k
kn,k Use the obtained νn,k+1 as the new attempt speed for iteration till inequality (18) is tenable. Formula (18) has definite physical significance, namely: If (1 − η)
Wn,k >
Kn,k +
Un,k + 0.5hGdn
an,k , it means there is a surplus of external work, which will transform into kinetic energy through formula (18). If (1 − η)
Wn,k <
Kn,k +
Un,k + 0.5hGdn
an,k , it means the external work is not enough to counteract the fracture toughness and the change of strain energy, at the time of which kinetic energy is sacrificed to guarantee the crack propagation.

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Figure 2. Flow chart of speed feedback realization.

In formula (19), the replacement of the entire pipeline’s average speed rate by the speed rate of the crack tip reflects the influence of kinetic energy. The assumption is made out of the consideration that coherence is found in the tendency of both, and νn,k+1 at the left end of the equation is an attempt value, which only affects computation speed and convergence, instead of computation precision. The convergence of the speed feedback mechanism is related to the spacing of mesh, time step, attempt initial speed, etc. Its realization in program is demonstrated in Figure 2. 3.5. M EASURED TOUGHNESS FROM SMALL SCALE IMPACT TEST The purpose of this section is to determine the expression of the key value Gd , which represents the crack driving force in the crack deceleration mechanism, by means of design parameters and the absorbing work obtained in small-size impact tests. Besides the properties of materials, dynamic fracture toughness Gd is also intimately related to test temperature, stress status, specimen thickness, and fracture speed especially. Because of the similarity between small-size impact tests and full-scale crack propagation tests, the influence of stress status upon fracture toughness can be neglected. Suppose the specific parameters in small-size impact tests are respectively thickness h0 , impact speed v0 , test temperature T0 , ligament width, namely, crack propagation length a0 , and the obtained absorbing external work W0 . From Equation (9), in which surface energy is neglected, the dynamic fracture toughness Gd0 in small-size crack propagation can be represented as: dλ(h0 , T0 , ν) , (20) Gd0 (h0 , T0 , ν) = 2λ(h0 , T0 , ν) + 2a da where λ is the plastic work rate of material, ν is the instant propagation speed rate, a is the instant crack length, and 0 < a < a0 . Mark that with every da the crack propagates, the area of crack surface expands by 2h da. Considering the minute time increment dt in crack propagation, we apply the energy balance Equation (10) to small-size impact test, and integrate the whole process of crack propagation in terms of time:

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X.C. You et al. 
W = W0 − Wc (h0 , T0 , v0 ) =
U +
K + h0

a0

Gd0 (h0 , T0 , ν) da,

(21)

0

where
W,
U,
K are the external work consumed in crack propagation, the increment of strain energy, and the increment of kinetic energy, respectively; Wc is the work of crack starting in the process of cracking. For high-toughness steel,
U and
K can be neglected. Because the sample fracture time in small-size tests is short, it can be assumed that the fracture speed after cracking equates the impact speed of pendulum ν0 . Besides, considering that Gd will lose certain value at the end of the sample as a result of the shortening of the plastic deformation sphere at the tip of crack, suppose the loss of energy is P (h0 , T0 , ν0 ), then we have: Gd (h0 , T0 , ν0 ) =

W0 − Wc (h0 , T0 , ν0 ) + P (h0 , T0 , ν0 ) . h0 a0

(22)

Equation (22) can be taken as the basis upon which Gd (h, T , ν) from Equation (18) and Equation (19) is determined. Equation (22) leaves two parameters Wc and P for determination. According to their physical significance, we can diminish the influence of Wc with methods like prefabricating cracks and embrittling notches. Two-specimen method can achieve double purposes. By testing on specimens with different ligament widths a1 and a2 (the other conditions are the same), we get absorbed energy W1 , W2 , and their difference, by which we can obtain Gd0 directly: Gd0 (h0 , T0 , ν0 ) =

W2 (a2 ) − W1 (a1 ) . h0 (a2 − a1 )

(23)

Because the parameters influencing toughness are complicated, the most reliable method is to adopt specimens with the same thickness as that of real pipelines, and determine dynamic fracture toughness with two-specimen method under a series of temperatures and impact velocities for later computational purposes. 4. Simulation and toughness evaluation for steel pipelines 4.1. M ESH PARTITION AND BOUNDRY CONDITIONS Normally the crack on the pipeline propagates in opposite directions at the same time from the crack starting point. As the geometric shape of the pipeline as well as the distribution of load is symmetrical, half of the pipeline on one side, namely, one quarter of the model, is taken for analysis and computation, as shown in Figure 3. Four-node shell elements are taken to plot out mesh in axial and circular directions, and to present the air pressure distribution upon the inner wall of the pipeline. In Figure 3, C represents the position of the crack tip; A represents the initial position of the crack. The crack propagates along line AE. AD, DC and CE represent the opened crack, decompression zone, and pre-cracking zone, respectively. They are changing with time. The boundary conditions are designated below based upon symmetry: Point B and F are fixed. Point C changes with time and line AC is free side. On the boundary curve AB (including point A) and curve EF, the displacement in z direction and the rotating along axis x and y are constrained.

Crack arrest in rupturing steel gas pipelines

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Figure 3. Mesh partition of the pipeline.

On the boundary line BF, the displacement in the direction of x and y, and the rotating along axis x and z are constrained. 4.2. CTOA APPROACH Another common thread that links the main technical thrusts in this research is the use of an inelastic-dynamic crack tip characterizing parameter. This parameter is the crack tip opening angle, typically denoted by the acronym CTOA. The conditions under which a crack propagates in a gas pipeline are such that the motive force for crack propagation, here expressed in terms of the calculated value of CTOA, (CTOA)max , must be greater than or equal to the dynamic fracture toughness of material, in terms of (CTOA)C , to sustain propagation. This is given by: (CTOA)max (a, p, D, SDR, E) ≥ (CTOA)C (T , ν, h)

(24)

where (CTOA)max is a function of the crack length, a, the gas pressure, p, the outer diameter of the pipe, D, the standard dimension ratio of the pipe size, SDR = D/ h, and the stiffness of the pipe material, E. In turn, (CTOA)C is a material property dependent on the temperature, T , the crack speed, v, and the thickness of the pipe wall, h. Otherwise, if (CTOA)max <(CTOA)C , then the crack will arrest. Figure 4 shows the method to get (CTOA)max in finite element program. To complement the computation, a laboratory test procedure established for estimating (CTOA)C is also necessary. 4.3. E VALUATE Gd AND (CTOA)C WITH TWO - SPECIMEN METHOD The two-specimen DWTT is not only a suitable method in determining dynamic fracture toughness Gd as expounded in Section 3.5, but also a major method in determining (CTOA)C through test. The formula is shown as below (Kanninen et al., 1992b): 180 · 2571 · (dca1 − dca2 ) , (25) (CTOA)C π · σf d · (a2 − a1 )

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Figure 4. CTOA calculation in FEM.

where dCa is the absorbed energy per section area (J mm−2 ) of a V notch with a depth of a; a1 and a2 are the depths of the V notch (mm); σf d is the dynamic yielding stress (MPa). Table 1 shows the values of (CTOA)C and Gd obtained from Equation (25) and Equation (23) by the two-specimen DWTT on the same material (X70 steel). 4.4. S IMULATION BASED UPON CRACK DECELERATION MECHANISM The application of crack deceleration mechanism in FEM computation makes it easy to designate at will the initial crack speed of pipeline ν0 within computational sphere, and in combination with the dynamic fracture toughness Gd obtained by small-scale tests in Section 4.3, simulate the entire process of cracking including-the speed variation. Used the above mentioned method, the fracture speed curve obtained in full-scale tests of Alliance Pipelines (Eiber et al., 2000) is proofread, which achieves consistent results. Now take section in the test pipelines as an example, and suppose the initial speed of propagation is 330 m s−1 , the comparison between the speed variation in computation and in the test is shown in Figure 5. According to Mises stress distribution in Figure 6, the area of plastic sphere at the crack tip can be estimated. With the deceleration during crack propagation, the area of plastic sphere will dwindle. The parameters of pipelines are given in Figure 7 with X70 steel specially designed for the project of transporting gas for 4000 km from the west to east in China. Use the deceleration mechanism to calculate the variable of opening angle at the crack tip CTOA. In the simulation, the values of CTOA are decayed distinctly after reaching a peak value. However, the determined toughness (CTOA)C through tests are among 9.29 to 13.7. Arrest quickly occurs in the pipeline when CTOA drops below (CTOA)C , as shown in Figure 7, which is an encouraged information to us for the crack only to propagate a few or ten meters after initiation in the gas pipeline. This crack deceleration phenomenon has been evidenced by the full-scale blast tests of Alliance Pipelines (Eiber et al., 2000). The crack arrest length of 12 m obtained by the CTOA criterion is consistent with that estimated from Figure 5. With the deceleration of

Crack arrest in rupturing steel gas pipelines

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Table 1. Results of the two-specimen DWTT on 1550 × 14.7 mm X70 plates. Notch dept

Temperature ◦C

Head part Absorbed Average energy (J) (J)

Middle part Absorbed Average energy (J) (J)

Aft part Absorbed Average energy (J) (J)

20

5120 5070 5050

5080

4310 4400 4650

4453

5520 5360 5330

5403

−10

4730 3820 4490

4347

3820 3300 4020

3713

4900 4290 5000

4730

10 mm

36 mm

20

−10

2300 2240 2130 1880 1620 1820

2223

1773

1760 1890 1930 1180 1310 1400

1860

1297

2230 2100 2420 1540 1830 1680

2250

1683

(CTOA)C (◦ )

20 −10

9.57 9.69

9.29 10.6

11.8 13.7

Gd (kN m−1 )

20 −10

7.48 7.57

7.26 8.29

9.22 10.7

Figure 5. The comparison between the speed variation in computation and the full-scale test.

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Figure 6. The Mises stress distribution in the process of decelerating propagation.

Figure 7. Variation of CTOA in the computation of toughness deceleration.

crack caused by the toughness (CTOA)C in computation, the decay of CTOA remains obvious till arrest. 5. Discussions and conclusions By using crack deceleration mechanism to calculate the variable of crack tip opening angle CTOA with different design parameters, whether the crack will continue to propagate can be predicted. For X70 steel used in the simulation, the values of CTOA are decayed distinctly after reaching a peak value. Arrest quickly occurs in the pipeline when CTOA drops below

Crack arrest in rupturing steel gas pipelines

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(CTOA)C , which is an encouraged information to us for the crack only to propagate a few or ten meters after initiation in the gas pipeline. The crack arrest length of 12 m. obtained by the CTOA criterion, as shown in Figure 7, is consistent with that estimated from Alliance Pipeline in Figure 5. Though numerical simulation, the value of all stresses and displacements can be obtained, which has referential significance for the analysis of pipeline variation and intensity performance. Through comparison between numerical analysis and test results, it is found that for hightoughness pipelines, the reduction of kinetic energy caused by the dissipation of plastic work cannot be neglected. This paper, based upon the energy balance equation under the condition of instant crack propagation, establishes iteration method in solving instant speed in FEM. The material toughness Gd (ν), which is the parameter representing the driving force, is substituted in the computation as a given function, by which iterative deceleration model based upon the deceleration mechanism is established. The study on the dynamic fracture propagation and arrest of gas pipelines is still in its developing stage. The presently used method in determining the arrest toughness is to induce empirical criterion equations from limited full-scale tests, and then draw conclusions from the fracture toughness obtained from small-size tests. This kind of method can only produce simple critical toughness parameters, and cannot simulate the other variables intimately related to crack propagation. On the other hand, with the development of pipeline transportation technology, hightoughness pipes are more and more widely used. The traditional dynamic test methods will lead to conspicuous energy dissipation irrelevant to fracture. Finite element method is used in computing the CTOA of instant crack propagation. In combination with test results of (CTOA)C , it forms the geometric criterion of arrest and opens another way for the estimation of pipeline arrest toughness. References Eiber, R.J. and Maxey, W.A. (1977). Full-scale experimental investigation of ductile fracture behavior in simulated arctic pipeline. ASME Grey Rocks Symposium, Materials Engineering in the Arctic ASM, Metals Park, Ohio, 306–310. Eiber, B., Eiber, R., Carlson, L. et al. (2000). Fracture propagation control for the alliance pipeline. In: Proceedings of the Special Party of ASME, Langfang, China, 1–34. Kanninen, M.F., Leung, C.P., O’Donoghue, P.E. et al. (1992). Joint final report on the development of a ductile pipe fracture model. In: Proceeding of Pipeline Technology Conference, Virginia, 38–66. Kanninen, M.F., Leung, C.P., O’Donoghue, P.E., Morrow, T.B., Popelar, C.F., Buzzichelli, G., Demofonti, G., Hadley, I., Rizzi, L. and Venzi, S. (1992). Joint Final Report on the Development of a Ductile Pipe Fracture Model, American Gas Association, Arlington, Virginia. Li, Q.F. (1998). Fracture Mechanics and Its Engineering Application, Harbin Institute of Technology Press, Harbin. Maxey, W.A. (1974). Fracture initiation, propagation and arrest. In: Proceedings of the 5th Symposium in Line Pipe Research, American Gas Association, Houston, J1–J31. O’Donoghue, P.E. and Zhuang, Z. (1999). A finite element model for crack arrestor design in gas pipelines. Fatigue and Fracture of Engineering Materials and Structures 22, 59–66. O’Donoghue, P.E., Green, S.T., Kanninen, M.F. and Bowles, P.K. (1991). The development of fluid/structure interaction model for flawed fluid containment boundaries with applications to gas transmission and distribution piping. Computers & Structures 38, 501–513. Wilkowski, G.M., Maxey, W.A. and Eiber, R.J. (1980). Use of the DWTT energy for predicting ductile fracture behavior in Control-Rolled Steel Line Pipes. Can. Met. Quart. 19, 59–77.

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Zhuang, Z. and Guo, Y.J. (1999). The analysis for dynamic fracture mechanism in pipelines. Engineering Fracture Mechanics 64, 271–289. Zhuang, Z. and O’Donoghue, P.E. (2000a). The recent development of analysis methodology for crack propagation and arrest in the gas pipelines. International Journal of Fracture 101, 269–290. Zhuang, Z. and O’Donoghue, P.E. (2000b). Determination of material fracture toughness by a computational/experimental approach for rapid crack propagation in PE pipes. International Journal of Fracture 101, 251–268.