Application of the GTN model to ductile crack growth simulation in through-wall cracked pipes
Introduction
Ductile failure simulation using finite element (FE) methods can be efficiently used to predict fracture behaviour of cracked piping components. Various damage models to simulate ductile crack growth have been developed for ductile fracture simulation, such as the Gurson-Tvergaard-Needleman (GTN) model [1], [2], [3], [4], the Roussellier model [5], [6], [7] and the cohesive zone model [8], [9], [10]. Among these damage models, the GTN model has been wieldy used. It has been extensively applied to simulate ductile fracture of small-scale experiments such as tensile and fracture toughness test. As there are vast number of papers published in literature, no reference is given here. Despite its popularity, one difficulty in application of the GTN model is to determine its parameters from limited mechanical test data. There may be several ways to determine the parameters but detailed procedures may depend on researchers [11], [12], [13], [14], [15], [16]. The GTN model has been also applied to simulate ductile crack growth in cracked pipes [17], [18], [19], [20], [21], but simulation is typically limited to small amount of crack growth. It is partly because a small element size of 50–200 μm has been often used in crack growth simulation of metallic structures, which corresponds to a microstructural length scale for dimple fracture. The use of such small elements makes long stable ductile crack growth simulation computationally difficult and unstable. A simple way to solve this problem would be to increase the element size, but the damage parameters should be determined for the element size used in damage analysis, as they are known to be dependent on the element size [22], [23], [24], [25]. For instance, in Refs. [22], [24], the effect of the element size on damage simulation of tensile and cracked pipe tests was confirmed. Kiran et al. [25] investigated the relationship between the element size and the GTN parameter (one parameter related to void volume fraction) based on notch tensile test results. Although existing works have suggested that the GTN parameters are dependent on the element size, no systematic investigation on how to quantify the element-size-dependency of the GTN parameters to simulate long stable crack growth in cracked pipes.
In this paper, the GTN model is applied to simulate ductile crack growth in through-wall cracked STPT410 carbon steel pipes under pure bending and simulation results are compared with experimental data. Three issues related to practical application of the GTN model to ductile crack growth simulation in cracked pipes are addressed. The first one is how to determine the GTN parameters from fracture toughness data. The second issue is how to incorporate the element-size effect on the GTN model parameters. The third one is the effect of the crack-tip mesh design on determination of the GTN model parameters. In Section 2, the GTN model used in this work is summarized with typical values of the GTN model parameters used in literature. Section 3 explains how to determine the GTN model parameters from fracture toughness (J-R) data. The effects of the element size and crack-tip mesh design on the GTN parameters are also presented. Ductile crack growth simulation of the cracked pipe is performed using the determined GTN model and simulation results are compared with experimental data in Section 4. Section 5 concludes the presented work.
Section snippets
Summary of the model
In this paper, ductile tearing simulation was performed using the general purpose FE program ABAQUS [26] with the embedded GTN model. In ABAQUS, the following GTN model is used:where Φ is the yield function; is the von-Mises equivalent stress; is the yield strength; is the mean normal stress; and (i = 1-2) are Tvergaard coefficients. The function modeling the rapid loss of stress carrying capacity that accompanies void coalescence is
Mechanical test results
This paper considers a series of test data performed at Central Research Institute of Electric Power Industry (CRIEPI) in Japan. The material was STPT410 carbon steel in Japanese Industrial Standard, of which chemical composition is shown in Table 1. Two tensile test specimens with the 5 mm diameter and 25 mm gauge length were taken from 12B Schedule 40 pipes. Tensile test were conducted at 300 °C and resulting engineering and true stress strain curves are shown in Fig. 1. More information can
Description of pipe test
Circumferential through-wall cracked pipe fracture test was conducted at 300 °C under four-point bending (Fig. 13) [30]. The pipe material was STPT410 carbon steel and a through-wall crack was fabricated by fatigue pre-cracking after electric discharge machining. The pipe specimens had the outer radius of 318.5 mm and the thickness of 10.3 mm (Fig. 13). For the through-wall crack, two lengths were considered; one with a total circumferential angle of 63.6° (designated as TW-01 in this paper)
Discussion
Comparison of simulation results with circumferential through-wall cracked pipe test data in the previous sub-section suggests three issues related to application of the GTN model to predict ductile fracture in cracked pipes. The first one is transferability from a small specimen to a large-scale pipe. Although the parameters in the GTN model were determined from the C(T) test results such that the C(T) test results can be accurately reproduced, the model fails to correctly predict crack
Conclusion
In this paper, ductile crack growth in through-wall cracked STPT410 carbon steel pipes under pure bending are simulated via FE damage analysis. The damage model is based on the GTN model and three issues related to practical application of the GTN model to ductile crack growth simulation in cracked pipes are addressed. The first one is how to determine the parameters in the GTN model from fracture toughness (J-R curve) data. The second aspect is how to incorporate the element-size effect to the
Acknowledgement
This research was supported by National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2017R1A2B2009759) and by the Nuclear Power Core Technology Development Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20141520100860).
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