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Ductile fracture of advanced pipeline steels: study of stress states and energies in dynamic impact specimens - CVN and DWTT
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Ductile fracture of advanced pipeline steels: study of stress states Ductile fracture of advanced pipeline steels: study of stress states energies in dynamic impact specimens - CVN anddeDWTT XVand Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço Arcos, Portugal and energies in dynamic impact specimens - CVN and DWTT a a* Letícia dos Santos Pereiraaa, Rodrygo Figueiredo Moço , Gustavo Henrique Bolognesi Donato Thermo-mechanical modeling of a high pressure turbine blade of a Letícia dos Santos Pereira , Rodrygo Figueiredo Moço , Gustavo Henrique Bolognesi Donatoa*an Centro Universitário FEI, Humberto de A. Castelo Branco Av., 3972, Sãoengine Bernardo do Campo, 09850-901, Brazil airplane gas turbine Centro Universitário FEI, Humberto de A. Castelo Branco Av., 3972, São Bernardo do Campo, 09850-901, Brazil a a
a
b
c
Abstract P. Brandão , V. Infante , A.M. Deus * Abstract a Department Mechanical Engineering, Instituto Técnico, Universidade de Lisboa, Av.paramount Rovisco Pais, 1, 1049-001 Lisboa, The development ofofrobust protocols for assessing theSuperior structural integrity of gas pipelines is of relevance, since failures Portugal The development of robust protocols for assessing the structural integrityability of gas to pipelines is of the paramount relevance, since failures can blead to financial and human losses. In this scenario, the material’s slow down propagation of a running crack IDMEC, Department Mechanical Engineering, Instituto Superior Técnico,ability Universidade dedown Lisboa,the Av.propagation Pais,of1, a1049-001 can lead to financial and human losses. In thisSeveral scenario, the material’s to slowcalibrated running crack (crack arrest) becomes aof design requirement. empirical models and criteria, by Rovisco real pipeline burst tests,Lisboa, have (crack arrest) becomes a design requirement. Several (BTCM) empiricalPortugal models and of criteria, calibrated byemployed real pipeline burst tests, With have been being the Battele Two Curve Method one example technique widely during decades. c developed, CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, been developed, being there the Battele Curveincrease Method of (BTCM) one of technique widely duringmodels decades. With the evolution of steels, was a Two significant ductility andexample toughness, in a way that suchemployed semi-empirical usually Portugal the evolution of steels, there was a significant increase ductility and toughness, a waytothat suchunsatisfactory semi-empiricalpredictions. models usually based on the energy absorbed in the Charpy impact testof(ISO 148-1, ASTM E-23)in began present This based onexplained the energyby absorbed the Charpy impact test (ISO 148-1, ASTM E-23) began to present unsatisfactory predictions. may be the factinthat in current high-ductility and high-toughness materials (e.g.: API-5L X65, X80, X100),This the may be explained by of thefracture fact that in currentishigh-ductility andConsequently, high-toughness API-5L X65, X80, the dominant mechanism propagation plastic collapse. thematerials energies (e.g.: involved in deforming andX100), fracturing Abstract mechanism propagation plastic collapse. Consequently, energies in deforming andcan fracturing adominant laboratory specimenof arefracture remarkably altered is and transferability to pipelines bythe means of theinvolved aforementioned models be lost. aTherefore, laboratory specimen remarkably altered and transferability pipelines by means of the aforementioned models can bework lost. for aoperation, betterare phenomenological comprehension of thetoare ductile fracture under such circumstances, this During their modern aircraft engine components subjected to process increasingly demanding operating conditions, Therefore, for a better phenomenological comprehension of the ductile fracture process under such circumstances, this work investigates Charpy and DWTT (ASTM E-436) dynamic tests assessing stress fields and respective energies involved in especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent investigates Charpy DWTT (ASTM E-436) dynamic tests assessing stress and energies involved in deformation and fracture. It is is creep. of great to evaluate the energy associated to fields steady staterespective ductile fracture andable thustotry to degradation, one of and which A interest model using the finite element method (FEM) was developed, in order to be predict deformation and fracture. It is of great interest to evaluate the energy associated to steady state ductile fracture and thus try to characterize the energy available to slow down an ongoing fracture. Pipelines are references for the developments and support the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation characterize the available slow down an ongoing fracture. Pipelines are flight references formodels theorder developments and support assumptions and energy some Based on these golas, numerical analyses including damage (XFEM andthe GTN) were company, were used conclusions. to obtain to thermal and mechanical data for three different cycles. In to create 3D model assumptions and some conclusions. Based on these golas, numerical analyses including damage models (XFEM and GTN) implemented, including parameters’ calibration and sensitivity analyses. The methodology closely reproduced available needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material propertieswere were implemented, including parameters’ calibration sensitivity The for methodology closely reproduced available experimental results. Besides that, stress fields andand energies be the studied geometries and such analyses3D obtained. The data that was gathered was fed into the FEM could modelanalyses. andquantified different simulations were run, first with a simplified experimental results.shape, Besides that, to stress fields and could for 3D thethe studied geometries such scrap. analyses indicated the potential and inlimitations of Charpy andenergies DWTT specimens to characterize energies required to describe steady rectangular block order better establish the model, and be thenquantified with the real mesh obtained from and the blade The indicated the potential and limitations of Charpy and DWTT specimens to characterize the energies required to describe steady state ductile crack propagation and crack arrestability. Results support further developments related to pipeline integrity overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a state ductile crack propagation andpredicting crack arrestability. support further developments related to pipeline integrity assessments. model can be useful in the goal of turbine bladeResults life, given a set of FDR data. assessments. ©© 2018 The Authors. Published byby Elsevier 2016 The Authors. Published Elsevier B.V. © 2018 Published by Elsevier B.V. B.V. © 2018The TheAuthors. Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. Peer-review under responsibility the Scientific Committee of PCF 2016. Peer-review under responsibility of the of ECF22 organizers. Peer-review under responsibility of the ECF22 organizers. Keywords: Gas pipelines; Crack arrest; Advanced assessment. Keywords: High Pressure Turbine Blade; Creep;steels; FiniteDamage Element models; Method;Energy 3D Model; Simulation. Keywords: Gas pipelines; Crack arrest; Advanced steels; Damage models; Energy assessment.
Nomenclature Nomenclature D D da da
XFEM damage parameter XFEMsize damage parameter crack variation crack size variation
2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby ECF22 organizers. Peer-review underauthor. responsibility the ECF22 organizers. * Corresponding Tel.: +351of 218419991. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.219
1986 2
f0 fc fN ly 𝑞𝑞� , 𝑞𝑞� , 𝑞𝑞� 𝜺𝜺𝑵𝑵 𝜅𝜅 𝛤𝛤� 𝜎𝜎� 𝜎𝜎� 𝜎𝜎� 𝜎𝜎�
Letícia dos Santos Pereira et al. / Procedia Structural Integrity 13 (2018) 1985–1992 Author name / Structural Integrity Procedia 00 (2018) 000–000
initial porosity critical porosity fraction of particles where new voids can nucleate element height coefficients obtained empirically mean strain damage acceleration factor cohesive energy maximum cohesive stress von Mises stress hydrostatic stress standard deviation
1. Introduction Accurate and safe structural integrity assessments of gas pipelines are of paramount relevance, since failures can lead to financial and human losses. Considering pipes containing crack-like defects, the unstable propagation is critical and, depending on the material’s toughness, the related fracture micromechanism can be from brittle to remarkably ductile. In this context, several design and integrity assessment protocols have been developed during the last decades, usually based on empirical or semi-empirical models calibrated by real full-scale pipeline burst tests (Leis, 2015; Scheider et al., 2014). Such models have been employed successfully for predicting crack arrestability in low-tomedium toughness steels. However, considering the interest of this work on modern, high-resistance and hightoughness steels (e.g.: API-5L X80), the quantification of materials’ ability to slow down the propagation of a running crack (crack arrest) is of central relevance, but is not always accurately predicted by available methods. Consequently, it is useful to briefly discuss the phenomenological basis and limitations of the available techniques to predict crack arrest in gas pipelines and how the increase in toughness of structural steels demands revisions and corrections to take larger amounts of plasticity into account. One of the most widely employed methods is the Battelle Two Curve Method (BTCM) formulated in 1970 at the Battelle Institute. This model computes the necessary energy to promote the crack arrest using two independent expressions: i) one to describe the material resistance, based on the speed of the propagating shear fracture; ii) and other to model the gas decompression speed in the vicinity of the growing crack (Leis, 2015). In simple terms, this model quantifies if the decompression speed is higher than the speed of the ductile crack propagation – if it happens, crack driving force is reduced and the desired crack arrest is predicted. For low toughness materials, predictions based on the original model present good experimental agreement and the relationship between this energy and the one obtained from Charpy impact tests (ISO 148-1, 2011, ASTM E23, 2013) is linear, making this small-scale test laboratory of high interest - once the BTCM model has been calibrated by full-scale burst tests, Charpy tests have been widely employed to assess the arrestability of varying steels and applications. However, for medium-to-high toughness steels (e.g.: whose absorbed Charpy energy is higher than ~ 90 J), the linear relationship is violated and several corrections emerged - additional details can be found in Maxey (1974), Zhu (2015) and Leis (2015). In the case of Leis, for example, a semi-empirical correction factor was proposed and extended the applicability of the BTCM. Nevertheless, the corrected model is not accurate to predict the arrestability of modern high toughness steels applicable to gas pipelines, as discussed below. The phenomenological reasons for such limitations can be discussed based on Fig. 1(a), despite several assumptions were considered by the author – here, the total Charpy energy obtained from several steels tested in instrumented impact pendulums were stratified in three energies: i) one for crack initiation; ii) one for the deformation of the specimen and; iii) one for crack propagation. It is possible to observe that until ~ 90 J, around 70% of total energy is related to crack propagation and less than 5% to deformation, making BTCM valid. For higher energies, the aforementioned corrections can help, but one can realize that around 250 J deformation energy becomes more pronounced than propagation, which represents less than 30% of the total energy. For ~ 350 J, all absorbed energy is consumed for initiation and deformation, which means that such impact test is not useful to characterize and quantify
Letícia dos Santos Pereira et al. / Procedia Structural Integrity 13 (2018) 1985–1992 Author name / Structural Integrity Procedia 00 (2018) 000–000
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1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0
deformation initiation propagate
σ [MPa]
Energy component fraction
ductile fracture process in such materials – the failure in this case is governed by plastic collapse rather than by the original fracture assumptions. As a step to better understand such phenomena and energies related to ductile fracture of high toughness steels, this work investigates Charpy and DWTT geometries in details considering a high toughness API-5L X80 steel. The main goal is to employ refined finite element models including damage and crack propagation to accurately describe the stress states and energy fractions with less simplifying assumptions than those considered in Fig. 1(a).
0
50
100 150 200 250 300 Charpy Plateu value [J]
350
950 900 850 800 750 700 650 600
400
API-5L X80
0
0,2
0,4
ε
0,6
0,8
1
(b) (a) Fig. 1. (a) Shift in Charpy dissipation for the initiation, plastic deformation and propagation components as total energy increases; (b) True stresslogarithm strain curve for API-5L X80 steel considered for the simulations. Source: (a) Leis (2015); (b) Scheider et al. (2014)
2. Theoretical background 2.1. Gurson-Tvergaard-Needleman model The GTN (Gurson-Tvergaard-Needleman) damage model is widely applied for ductile fracture simulation. It models the ductile fracture by the nucleation, growth and coalescence of microvoids that initiated in hard or second phase particles (Gurson, 1977; Tvergaard, 1982; Tvergaard and Needleman, 1984). This model is based on the von Mises yield criterion, and the damage evolution is evaluated by the parameter f*, known as modified void volume fraction, using equation (1). The 𝜎𝜎� is the von Mises stress, 𝜎𝜎� the hydrostatic stress, 𝑞𝑞� , 𝑞𝑞� and 𝑞𝑞� are coefficients obtained empirically (Tveergaard and Needleman, 1984). Other parameters of this model are the porosity at the onset of void coalescence (critical porosity - fc), damage acceleration factor 𝜅𝜅, initial porosity f0 and fraction of particles where new voids can nucleate fN (Nonn and Kalwa, 2013). These new voids are created based on a mean strain 𝜺𝜺𝑵𝑵 and standard deviation 𝜎𝜎� . These parameters are mesh dependent, thus the element height ly is important. The disadvantages of this model include the mesh dependency and the number of calibrated parameters needed. Nonn and Kalwa (2013) recommended parameters for the GTN model for materials used in pipelines, as shown in Table 1. 𝛷𝛷�𝜎𝜎� , 𝜎𝜎� , 𝑓𝑓 ∗ � �
3𝑞𝑞� 𝜎𝜎� 𝜎𝜎� � � 2𝑞𝑞� 𝑓𝑓 ∗ cosh � � � �� � 𝑞𝑞� 𝑓𝑓 ∗ � � � � � 𝜎𝜎 2𝜎𝜎
(1)
Table 1. Recommended parameters for GTN model
𝒇𝒇𝟎𝟎 [%] 0.01- 0.03
𝒇𝒇𝑵𝑵 (%) 0.1-0.5
Source: Nonn and Kalwa (2013)
𝜺𝜺𝑵𝑵 0.3
𝝈𝝈𝑵𝑵 0.1
𝒇𝒇𝒄𝒄 0,02
𝜿𝜿 4,0
𝒒𝒒𝟏𝟏 1,5
𝒒𝒒𝟐𝟐 1,0
𝒒𝒒𝟑𝟑 2,25
𝑰𝑰𝒙𝒙 (mm) 0,1-0,3
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2.2. Extended finite element model The XFEM (Extended Finite Element Method) was presented in 1999 (Campilho et al., 2011). This model is simpler than GTN model, since it is not based on the ductile fracture phenomenology, but also allows the simulation of crack extension. This model has only two parameters to be calibrated; the first parameter (the maximum cohesive stress 𝜎𝜎�) describes the onset of damage, that is, when the damage will initiate - this parameter can be related to the strength of the material. The second parameter (the damage evolution D) describes the evolution of the damage, respectively decreasing the stiffness of the affected elements. The most phenomenological quantity in this model is the cohesive energy 𝛤𝛤� , which is the energy spent for the separation (Parmar et al., 2015). The energy can be related with the toughness of the material. The separation, in its turn, is simulated employing phantom-nodes created when the first parameter is reached, based on which separation at failure can be configured (SIMULIA, 2013). Depending on the simulated material and the adopted methodology, the decay model can change - the most suitable model to describe ductile steels is the exponential. It means that, as damage evolves until fracture, the stress decrease as a function of the displacement is exponential. All details regarding XFEM and its application for ductile fracture simulations can be found in Fries and Belytschko (2010) and Campilho et al. (2001). 3. Methodology 3.1. Materials, geometries and loading modes The material considered for the simulations is the API-5L X80 steel, widely employed in gas pipelines. The analyses employed an elastic-plastic constitutive model with J2 flow theory and conventional Mises plasticity in Large Geometry Change (LGC) setting and including dynamic effects (considered density was 7,85 g/cm3). The elastic behavior followed Hooke’s law with E = 206 GPa and υ = 0.3, while the elastic-plastic response was informed to the codes based on the true stress-strain curve available for this material and presented by Fig. 1(b). The strain-rate sensitivity was implemented based on Johnson-Cook’s model (Pereira, 2017). Figure 2 presents the considered geometries for V-notched Charpy (based on ASTM E23, 2013 and EN ISO 1481, 2010) and DWTT (based on ASTM E436, 2014) specimens submitted to 3-point bending loading schemes. The thickness for the DWTT specimen is not enforced by the aforementioned standard and was adopted 27.7 mm based on some gas pipelines of interest for the research group.
(a)
(b)
Fig. 2. (a) Charpy V-notch geometry in accordance with ASTM E23 (2013) and EN ISO 148-1 (2010); (b) DWTT geometry in accordance with ASTM E-436 (2014) and dimensions in mm
3.2. Numerical procedures The developed 3D finite element models were based on previous refined modeling conducted and validated in the research group. For GTN, only one quarter of the specimens were modeled with appropriate boundary conditions to ensure symmetry, saving computational resources (illustrated by Fig. 3(a)). For XFEM, it was not appropriate to use X-symmetry, consequently, half specimen was modeled. The mass of the hammers were considered, respectively,
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with 0.1 and 2.8 tons respectively for the Charpy and DWTT. The impact speeds were 4.85 m/s for both cases. MSC Patran 2013 was used as pre-processor and Abaqus CAE 6.13 was used as processor and post-processor. The simulations employed 3D hexahedral elements of reduced integration and linear interpolation with a greater refinement of the mesh in the contact regions and where the crack propagation would occur (Fig. 3(a)). In average, elements in the remaining ligament are 0.25 x 0.50 x 1.0 mm.
(b)
(a)
Fig. 3. (a) GTN model, mesh and symmetry for the DWTT specimen; (b) illustrative stress fields and studied domains.
All the GTN parameters were calibrated using as a reference the recommended parameters showed in Tab. 1. The calibration was made changing one parameter at a time until the experimental load-displacement curves were well reproduced. Once calibrated, the same parameters (Tab. 2) were employed for both Charpy and DWTT specimens. The same was conducted for XFEM, however, the parameters were not the same for the two geometries – for both specimens the maximum cohesive stress was 1100 MPa, but cohesive energy was, respectively, 9 and 5,8 N/mm2 for Charpy and DWTT. The difference comes from the different stress triaxiality found in such specimens - the higher the triaxiality, the smaller is the cohesive energy. Table 2. Calibrated parameters for GTN model
𝒇𝒇𝟎𝟎 0.00015
𝒇𝒇𝑵𝑵 0.0015
3.3. Energy separation
𝜺𝜺𝑵𝑵 0.3
𝝈𝝈𝑵𝑵 0.1
𝒇𝒇𝒄𝒄 0,02
𝜿𝜿 4,0
𝒒𝒒𝟏𝟏 1,5
𝒒𝒒𝟐𝟐 1,0
𝒒𝒒𝟑𝟑 2,25
𝑰𝑰𝒙𝒙 (mm) 0.25
The basis for the energy separation methodology employed in this paper is to isolate domains where the stress field deviates from the hypothetical bending field that would occur if there were no hammer, support and propagating crack. The idea is that the energy absorbed by elements within this specific domain is associated with the different processes occurring in the specimen, such as deformation, crack initiation and crack propagation, as discussed previously. The criteria for determining such domains are stress-based (evaluating von Mises equivalent stresses) as explained earlier and Fig. 3(b) illustrates some domains considered for one DWTT geometry – in such domains, energies associated with crack initiation, crack propagation, contacts and specimen’s deformation can be computed. Essentially similar results in terms of domains’ geometries were found for Charpy geometry. All additional details can be found in the works of Moço (2017) and Pereira (2017). 4. Results 4.1. Stress state analyses The stress fields found in fracture specimens (e.g.: Charpy and DWTT) and real gas pipelines strongly differ. While in pipelines tensile membrane stresses prevail, in both specimens studied here a 3-point bending loading takes place. Even considering that equivalent stresses and strains can be easily computed, such results do not completely support
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the discussion regarding ductile fracture triggering and control. First, in the laboratory specimens, an interaction between the crack plane and the hammer takes place and needs to be corrected; Second, the different loading modes, and the different thicknesses between Charpy and DWTT, cause a strong difference in local (near the crack tip) stress fields and triaxiality. For example, DWTT presents, in average and considering the evaluated thicknesses, 50% more stress triaxiality than Charpy for the analysed X80 steel – it means less plasticity spread ahead of the crack for the DWTT and a different energy distribution in each geometry. Consequently, the ductile fracture micromechanism behaves in a different manner for varying geometries and such effect must be taken into account. In this context, stress fields were evaluated in details, including stress traxiality. Such analyses, whose details can be found in Moço (2017) and Pereira (2017), can support the discussion that follows regarding the limitations and potential of Charpy and DWTT specimens for the quantification and description of energies involved in ductile crack extension and crack arrest. 4.2. Steady state verification Crack extension in real pipelines usually reach a steady state before arrest can take place. Consequently, to be able to quantify energies associated with crack propagation (see. Fig. 1(a)), it is interesting to verify if Charpy and DWTT geometries are able to reach stable crack propagation before final failure. Figure 4 presents the variation of absorbed energy (dEnergy/da) versus crack size (a) for Charpy (Fig. 4(a)) and DWTT (Fig. 4(b)). After crack initiation takes place and the specimens bend, in both cases a stable propagation region can be identified. However, it can be realized that in the case of Charpy specimen the steady state crack propagation is very limited - it does not have enough remaining ligament and when the stable propagation is reached, the crack tip lies in the highly compressive region near the hammer-specimen contact. In the case of DWTT, in its turn, the steady-state propagation takes place along several millimeters of the remaining ligament, favoring the study of the energies related to the ductile fracture process related to a running crack. To support the energy analyses and favor comparability, the domains illustrated by Fig. 3(b) were evaluated during crack initiation and during steady-state propagation.
(a)
(b)
Fig. 4. evolution of the absorbed energy rate as a function of a (a) for the Charpy specimen, (b) for the DWTT specimen.
4.3. Energy analysis Based on the explained domains and understanding the difference between the energy for crack initiation and energy for stable crack propagation, the two geometries could be investigated using both GTN and XFEM damage models, providing the energies absorbed for each phenomenon for the GTN damage model. All details can be found in Moço (2017) and Pereira (2017) and selected results are presented here, since trends for XFEM are similar as explained below. It is useful to recall Fig. 1(a) for a better comprehension.
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Considering Charpy and X80 steel modeled using GTN, the total absorbed energy was ≈ 350 J, while the energy associated with steady state propagation was only ≈ 14 J, which means only ≈ 4 %. This means that only 4 % of the energy obtained from the test data represents steady state ductile fracture and would be suitable to be considered in crack arrest methods. The same analysis based on XFEM results provided 3.7 % of total energy, indicating that the methodologies considering both damage models are comparable. Considering DWTT and X80 steel modeled using GTN, the total absorbed energy was ≈ 25300 J, while the energy associated with steady state propagation was ≈ 4500 J, which means ≈ 18 %. This means that 18 % of the energy obtained from the test represents steady state ductile fracture and would be suitable to be considered in crack arrest methods. The same analysis based on XFEM results provided 16.6 % of total energy. One can realize that the percentage of energy related to ductile fracture for the case of DWTT is much larger than Charpy, but it is still reduced if compared to the total absorbed energy – less than one quarter of the total is in fact phenomenologically associated with the propagation of the ductile fracture that could be related and useful to existing methods for predicting arrestability, which support structural integrity assessments of real gas pipelines. Such data deserve experimental validation, but indicates the potential and limitations of these widely employed specimen geometries and loading modes. In addition, call the attention to the need for a better comprehension of such stresses and energies and how respective quantities and fields can be compared to analogous running cracks in gas pipelines made of modern high-toughness steels. 5. Concluding remarks It was possible to calibrate the damage parameters for both GTN and XFEM models. Load-displacement evolutions presented very good experimental agreement. The results for both models in terms of stress states and energies were close, indicating that both methodologies can be considered comparable for the desired analyses. It is interesting to mention that GTN is more phenomenological, while XFEM proved to be simpler and more pragmatic. The steadystate crack propagation analyzes for X80 steel indicate that it is limited or does not take place in the case of Charpy geometry; in contrast, it is more characteristic and pronounced in DWTT. One of the limitations in using the Charpy specimen is the size of the remaining ligament; low stress triaxiality is an additional concern. Such limitations lead to only approximately 4 % of the total absorbed energy associated to stable crack propagation in this geometry. The percentage for the DWTT war larger, around 17 %, but it is still considered small if compared to total absorbed energy. The results demonstrate that DWTT potentially presents some benefits if compared to Charpy, but both cases present limitations to characterize the crack propagation resistance for advanced steels presenting high toughness and large amounts of plasticity. Finally, the selected results presented here calls the attention to the need for a better comprehension of such stresses and energies and how respective quantities and fields can be compared to analogous running cracks in gas pipelines made of modern high-toughness steels. Acknowledgements This investigation is supported by the Brazilian Metallurgy and Mining Company (CBMM) and by Centro Universitário FEI, Brazil. References ASTM, 2014. ASTM E23-12c. Standard Test Method for Notched Bar Impact Testing of Metallic Materials. ASTM International, West Conshohocken, PA. ASTM, 2013. ASTM E23-12c. Standard Test Method for Drop-Weight Tear Test of Ferritic Steels. ASTM International, West Conshohocken, PA. Fries, T.; Belytschko, T. (2010), The extended/generalized finite element method: An overview of the method and its applications. International Journal for Numerical Methods in Engineering 84, 253-304. Campilho, R. D. S. G. et al., 2011. Strength prediction of single- and double-lap joints by standard and extended finite element modelling. International Journal of Adhesion and Adhesives 31, 362–372. Gurson, A. L., 1977. Continuum theory of ductile rupture by void nucleation and growth: part I - yield criteria and flow rules for porous ductile media. Journal of Engineering Materials Technology 99, 2–15. ISO, 2011. EM ISO 148-1. Metallic metals - Charpy pendulum impact test - Part:1. ISO. Geneva.
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Leis, B.N., 2015. Arresting Propagating Shear in Pipelines. Steel in Translation 45, 1–17. Nonn, A., Kalwa, C., 2013. Analysis of dynamic ductile fracture propagation in pipeline steels: a damage-mechanics’ approach., 6th International Pipeline Technology Conference. Ostend, Belgium, paper S34-01. Maxey W. A., 1974. Fracture initiation, propagation and arrest, 5th Symposium on Line Pipe Research, AGA. Moço, R. F., 2017. Correlação da fenomenologia da fratura dúctil de gasodutos e corpos de prova dinâmicos Charpy e DWTT empregando o modelo GTN a aços avançados classe API. Master thesis, Centro Universitário FEI. Parmar, S. et al., 2015. Simulation of ductile fracture in pipeline steels under varying constraint conditions using cohesive zone modeling., ASME 2015 Pressure Vessels and Piping Conference. Boston, Massachusetts, paper PVP2015-45873. Pereira, L. S., 2017. Avaliação do potencial dos modelos de zona coesiva e XFEM na descrição da fenomenologia da fratura dúctil de corpos de prova Charpy e DWTT fabricados de aço classe API. Master thesis, Centro Universitário FEI. Scheider et al., 2014. A damage mechanics based evaluation of dynamic fracture resistance in gas pipeline. Procedia Materials Science 3, 1956– 196 SIMULIA, 2013. Abaqus theory guide. Abaqus Software Documentation: v. 6.13-4. Tvergaard,T, 1982. Ductile fracture by cavity nucleation between larger voids. Journal of the Mechanics and Physics of Solids 30, 265–286. Tvergaard,T. Needleman, A., 1984. Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica Journal 32, 157–169. Zhu X. K., 2015. State-of the-art review of fracture control technology for modern and vintage gas transmission pipelines. Engineering Fracture Mechanics Journal 148, 260-280.
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ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
Ductile fracture of advanced pipeline steels: study of stress states Ductile fracture of advanced pipeline steels: study of stress states energies in dynamic impact specimens - CVN anddeDWTT XVand Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço Arcos, Portugal and energies in dynamic impact specimens - CVN and DWTT a a* Letícia dos Santos Pereiraaa, Rodrygo Figueiredo Moço , Gustavo Henrique Bolognesi Donato Thermo-mechanical modeling of a high pressure turbine blade of a Letícia dos Santos Pereira , Rodrygo Figueiredo Moço , Gustavo Henrique Bolognesi Donatoa*an Centro Universitário FEI, Humberto de A. Castelo Branco Av., 3972, Sãoengine Bernardo do Campo, 09850-901, Brazil airplane gas turbine Centro Universitário FEI, Humberto de A. Castelo Branco Av., 3972, São Bernardo do Campo, 09850-901, Brazil a a
a
b
c
Abstract P. Brandão , V. Infante , A.M. Deus * Abstract a Department Mechanical Engineering, Instituto Técnico, Universidade de Lisboa, Av.paramount Rovisco Pais, 1, 1049-001 Lisboa, The development ofofrobust protocols for assessing theSuperior structural integrity of gas pipelines is of relevance, since failures Portugal The development of robust protocols for assessing the structural integrityability of gas to pipelines is of the paramount relevance, since failures can blead to financial and human losses. In this scenario, the material’s slow down propagation of a running crack IDMEC, Department Mechanical Engineering, Instituto Superior Técnico,ability Universidade dedown Lisboa,the Av.propagation Pais,of1, a1049-001 can lead to financial and human losses. In thisSeveral scenario, the material’s to slowcalibrated running crack (crack arrest) becomes aof design requirement. empirical models and criteria, by Rovisco real pipeline burst tests,Lisboa, have (crack arrest) becomes a design requirement. Several (BTCM) empiricalPortugal models and of criteria, calibrated byemployed real pipeline burst tests, With have been being the Battele Two Curve Method one example technique widely during decades. c developed, CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, been developed, being there the Battele Curveincrease Method of (BTCM) one of technique widely duringmodels decades. With the evolution of steels, was a Two significant ductility andexample toughness, in a way that suchemployed semi-empirical usually Portugal the evolution of steels, there was a significant increase ductility and toughness, a waytothat suchunsatisfactory semi-empiricalpredictions. models usually based on the energy absorbed in the Charpy impact testof(ISO 148-1, ASTM E-23)in began present This based onexplained the energyby absorbed the Charpy impact test (ISO 148-1, ASTM E-23) began to present unsatisfactory predictions. may be the factinthat in current high-ductility and high-toughness materials (e.g.: API-5L X65, X80, X100),This the may be explained by of thefracture fact that in currentishigh-ductility andConsequently, high-toughness API-5L X65, X80, the dominant mechanism propagation plastic collapse. thematerials energies (e.g.: involved in deforming andX100), fracturing Abstract mechanism propagation plastic collapse. Consequently, energies in deforming andcan fracturing adominant laboratory specimenof arefracture remarkably altered is and transferability to pipelines bythe means of theinvolved aforementioned models be lost. aTherefore, laboratory specimen remarkably altered and transferability pipelines by means of the aforementioned models can bework lost. for aoperation, betterare phenomenological comprehension of thetoare ductile fracture under such circumstances, this During their modern aircraft engine components subjected to process increasingly demanding operating conditions, Therefore, for a better phenomenological comprehension of the ductile fracture process under such circumstances, this work investigates Charpy and DWTT (ASTM E-436) dynamic tests assessing stress fields and respective energies involved in especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent investigates Charpy DWTT (ASTM E-436) dynamic tests assessing stress and energies involved in deformation and fracture. It is is creep. of great to evaluate the energy associated to fields steady staterespective ductile fracture andable thustotry to degradation, one of and which A interest model using the finite element method (FEM) was developed, in order to be predict deformation and fracture. It is of great interest to evaluate the energy associated to steady state ductile fracture and thus try to characterize the energy available to slow down an ongoing fracture. Pipelines are references for the developments and support the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation characterize the available slow down an ongoing fracture. Pipelines are flight references formodels theorder developments and support assumptions and energy some Based on these golas, numerical analyses including damage (XFEM andthe GTN) were company, were used conclusions. to obtain to thermal and mechanical data for three different cycles. In to create 3D model assumptions and some conclusions. Based on these golas, numerical analyses including damage models (XFEM and GTN) implemented, including parameters’ calibration and sensitivity analyses. The methodology closely reproduced available needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material propertieswere were implemented, including parameters’ calibration sensitivity The for methodology closely reproduced available experimental results. Besides that, stress fields andand energies be the studied geometries and such analyses3D obtained. The data that was gathered was fed into the FEM could modelanalyses. andquantified different simulations were run, first with a simplified experimental results.shape, Besides that, to stress fields and could for 3D thethe studied geometries such scrap. analyses indicated the potential and inlimitations of Charpy andenergies DWTT specimens to characterize energies required to describe steady rectangular block order better establish the model, and be thenquantified with the real mesh obtained from and the blade The indicated the potential and limitations of Charpy and DWTT specimens to characterize the energies required to describe steady state ductile crack propagation and crack arrestability. Results support further developments related to pipeline integrity overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a state ductile crack propagation andpredicting crack arrestability. support further developments related to pipeline integrity assessments. model can be useful in the goal of turbine bladeResults life, given a set of FDR data. assessments. ©© 2018 The Authors. Published byby Elsevier 2016 The Authors. Published Elsevier B.V. © 2018 Published by Elsevier B.V. B.V. © 2018The TheAuthors. Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. Peer-review under responsibility the Scientific Committee of PCF 2016. Peer-review under responsibility of the of ECF22 organizers. Peer-review under responsibility of the ECF22 organizers. Keywords: Gas pipelines; Crack arrest; Advanced assessment. Keywords: High Pressure Turbine Blade; Creep;steels; FiniteDamage Element models; Method;Energy 3D Model; Simulation. Keywords: Gas pipelines; Crack arrest; Advanced steels; Damage models; Energy assessment.
Nomenclature Nomenclature D D da da
XFEM damage parameter XFEMsize damage parameter crack variation crack size variation
2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby ECF22 organizers. Peer-review underauthor. responsibility the ECF22 organizers. * Corresponding Tel.: +351of 218419991. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.219
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f0 fc fN ly 𝑞𝑞� , 𝑞𝑞� , 𝑞𝑞� 𝜺𝜺𝑵𝑵 𝜅𝜅 𝛤𝛤� 𝜎𝜎� 𝜎𝜎� 𝜎𝜎� 𝜎𝜎�
Letícia dos Santos Pereira et al. / Procedia Structural Integrity 13 (2018) 1985–1992 Author name / Structural Integrity Procedia 00 (2018) 000–000
initial porosity critical porosity fraction of particles where new voids can nucleate element height coefficients obtained empirically mean strain damage acceleration factor cohesive energy maximum cohesive stress von Mises stress hydrostatic stress standard deviation
1. Introduction Accurate and safe structural integrity assessments of gas pipelines are of paramount relevance, since failures can lead to financial and human losses. Considering pipes containing crack-like defects, the unstable propagation is critical and, depending on the material’s toughness, the related fracture micromechanism can be from brittle to remarkably ductile. In this context, several design and integrity assessment protocols have been developed during the last decades, usually based on empirical or semi-empirical models calibrated by real full-scale pipeline burst tests (Leis, 2015; Scheider et al., 2014). Such models have been employed successfully for predicting crack arrestability in low-tomedium toughness steels. However, considering the interest of this work on modern, high-resistance and hightoughness steels (e.g.: API-5L X80), the quantification of materials’ ability to slow down the propagation of a running crack (crack arrest) is of central relevance, but is not always accurately predicted by available methods. Consequently, it is useful to briefly discuss the phenomenological basis and limitations of the available techniques to predict crack arrest in gas pipelines and how the increase in toughness of structural steels demands revisions and corrections to take larger amounts of plasticity into account. One of the most widely employed methods is the Battelle Two Curve Method (BTCM) formulated in 1970 at the Battelle Institute. This model computes the necessary energy to promote the crack arrest using two independent expressions: i) one to describe the material resistance, based on the speed of the propagating shear fracture; ii) and other to model the gas decompression speed in the vicinity of the growing crack (Leis, 2015). In simple terms, this model quantifies if the decompression speed is higher than the speed of the ductile crack propagation – if it happens, crack driving force is reduced and the desired crack arrest is predicted. For low toughness materials, predictions based on the original model present good experimental agreement and the relationship between this energy and the one obtained from Charpy impact tests (ISO 148-1, 2011, ASTM E23, 2013) is linear, making this small-scale test laboratory of high interest - once the BTCM model has been calibrated by full-scale burst tests, Charpy tests have been widely employed to assess the arrestability of varying steels and applications. However, for medium-to-high toughness steels (e.g.: whose absorbed Charpy energy is higher than ~ 90 J), the linear relationship is violated and several corrections emerged - additional details can be found in Maxey (1974), Zhu (2015) and Leis (2015). In the case of Leis, for example, a semi-empirical correction factor was proposed and extended the applicability of the BTCM. Nevertheless, the corrected model is not accurate to predict the arrestability of modern high toughness steels applicable to gas pipelines, as discussed below. The phenomenological reasons for such limitations can be discussed based on Fig. 1(a), despite several assumptions were considered by the author – here, the total Charpy energy obtained from several steels tested in instrumented impact pendulums were stratified in three energies: i) one for crack initiation; ii) one for the deformation of the specimen and; iii) one for crack propagation. It is possible to observe that until ~ 90 J, around 70% of total energy is related to crack propagation and less than 5% to deformation, making BTCM valid. For higher energies, the aforementioned corrections can help, but one can realize that around 250 J deformation energy becomes more pronounced than propagation, which represents less than 30% of the total energy. For ~ 350 J, all absorbed energy is consumed for initiation and deformation, which means that such impact test is not useful to characterize and quantify
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1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0
deformation initiation propagate
σ [MPa]
Energy component fraction
ductile fracture process in such materials – the failure in this case is governed by plastic collapse rather than by the original fracture assumptions. As a step to better understand such phenomena and energies related to ductile fracture of high toughness steels, this work investigates Charpy and DWTT geometries in details considering a high toughness API-5L X80 steel. The main goal is to employ refined finite element models including damage and crack propagation to accurately describe the stress states and energy fractions with less simplifying assumptions than those considered in Fig. 1(a).
0
50
100 150 200 250 300 Charpy Plateu value [J]
350
950 900 850 800 750 700 650 600
400
API-5L X80
0
0,2
0,4
ε
0,6
0,8
1
(b) (a) Fig. 1. (a) Shift in Charpy dissipation for the initiation, plastic deformation and propagation components as total energy increases; (b) True stresslogarithm strain curve for API-5L X80 steel considered for the simulations. Source: (a) Leis (2015); (b) Scheider et al. (2014)
2. Theoretical background 2.1. Gurson-Tvergaard-Needleman model The GTN (Gurson-Tvergaard-Needleman) damage model is widely applied for ductile fracture simulation. It models the ductile fracture by the nucleation, growth and coalescence of microvoids that initiated in hard or second phase particles (Gurson, 1977; Tvergaard, 1982; Tvergaard and Needleman, 1984). This model is based on the von Mises yield criterion, and the damage evolution is evaluated by the parameter f*, known as modified void volume fraction, using equation (1). The 𝜎𝜎� is the von Mises stress, 𝜎𝜎� the hydrostatic stress, 𝑞𝑞� , 𝑞𝑞� and 𝑞𝑞� are coefficients obtained empirically (Tveergaard and Needleman, 1984). Other parameters of this model are the porosity at the onset of void coalescence (critical porosity - fc), damage acceleration factor 𝜅𝜅, initial porosity f0 and fraction of particles where new voids can nucleate fN (Nonn and Kalwa, 2013). These new voids are created based on a mean strain 𝜺𝜺𝑵𝑵 and standard deviation 𝜎𝜎� . These parameters are mesh dependent, thus the element height ly is important. The disadvantages of this model include the mesh dependency and the number of calibrated parameters needed. Nonn and Kalwa (2013) recommended parameters for the GTN model for materials used in pipelines, as shown in Table 1. 𝛷𝛷�𝜎𝜎� , 𝜎𝜎� , 𝑓𝑓 ∗ � �
3𝑞𝑞� 𝜎𝜎� 𝜎𝜎� � � 2𝑞𝑞� 𝑓𝑓 ∗ cosh � � � �� � 𝑞𝑞� 𝑓𝑓 ∗ � � � � � 𝜎𝜎 2𝜎𝜎
(1)
Table 1. Recommended parameters for GTN model
𝒇𝒇𝟎𝟎 [%] 0.01- 0.03
𝒇𝒇𝑵𝑵 (%) 0.1-0.5
Source: Nonn and Kalwa (2013)
𝜺𝜺𝑵𝑵 0.3
𝝈𝝈𝑵𝑵 0.1
𝒇𝒇𝒄𝒄 0,02
𝜿𝜿 4,0
𝒒𝒒𝟏𝟏 1,5
𝒒𝒒𝟐𝟐 1,0
𝒒𝒒𝟑𝟑 2,25
𝑰𝑰𝒙𝒙 (mm) 0,1-0,3
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2.2. Extended finite element model The XFEM (Extended Finite Element Method) was presented in 1999 (Campilho et al., 2011). This model is simpler than GTN model, since it is not based on the ductile fracture phenomenology, but also allows the simulation of crack extension. This model has only two parameters to be calibrated; the first parameter (the maximum cohesive stress 𝜎𝜎�) describes the onset of damage, that is, when the damage will initiate - this parameter can be related to the strength of the material. The second parameter (the damage evolution D) describes the evolution of the damage, respectively decreasing the stiffness of the affected elements. The most phenomenological quantity in this model is the cohesive energy 𝛤𝛤� , which is the energy spent for the separation (Parmar et al., 2015). The energy can be related with the toughness of the material. The separation, in its turn, is simulated employing phantom-nodes created when the first parameter is reached, based on which separation at failure can be configured (SIMULIA, 2013). Depending on the simulated material and the adopted methodology, the decay model can change - the most suitable model to describe ductile steels is the exponential. It means that, as damage evolves until fracture, the stress decrease as a function of the displacement is exponential. All details regarding XFEM and its application for ductile fracture simulations can be found in Fries and Belytschko (2010) and Campilho et al. (2001). 3. Methodology 3.1. Materials, geometries and loading modes The material considered for the simulations is the API-5L X80 steel, widely employed in gas pipelines. The analyses employed an elastic-plastic constitutive model with J2 flow theory and conventional Mises plasticity in Large Geometry Change (LGC) setting and including dynamic effects (considered density was 7,85 g/cm3). The elastic behavior followed Hooke’s law with E = 206 GPa and υ = 0.3, while the elastic-plastic response was informed to the codes based on the true stress-strain curve available for this material and presented by Fig. 1(b). The strain-rate sensitivity was implemented based on Johnson-Cook’s model (Pereira, 2017). Figure 2 presents the considered geometries for V-notched Charpy (based on ASTM E23, 2013 and EN ISO 1481, 2010) and DWTT (based on ASTM E436, 2014) specimens submitted to 3-point bending loading schemes. The thickness for the DWTT specimen is not enforced by the aforementioned standard and was adopted 27.7 mm based on some gas pipelines of interest for the research group.
(a)
(b)
Fig. 2. (a) Charpy V-notch geometry in accordance with ASTM E23 (2013) and EN ISO 148-1 (2010); (b) DWTT geometry in accordance with ASTM E-436 (2014) and dimensions in mm
3.2. Numerical procedures The developed 3D finite element models were based on previous refined modeling conducted and validated in the research group. For GTN, only one quarter of the specimens were modeled with appropriate boundary conditions to ensure symmetry, saving computational resources (illustrated by Fig. 3(a)). For XFEM, it was not appropriate to use X-symmetry, consequently, half specimen was modeled. The mass of the hammers were considered, respectively,
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with 0.1 and 2.8 tons respectively for the Charpy and DWTT. The impact speeds were 4.85 m/s for both cases. MSC Patran 2013 was used as pre-processor and Abaqus CAE 6.13 was used as processor and post-processor. The simulations employed 3D hexahedral elements of reduced integration and linear interpolation with a greater refinement of the mesh in the contact regions and where the crack propagation would occur (Fig. 3(a)). In average, elements in the remaining ligament are 0.25 x 0.50 x 1.0 mm.
(b)
(a)
Fig. 3. (a) GTN model, mesh and symmetry for the DWTT specimen; (b) illustrative stress fields and studied domains.
All the GTN parameters were calibrated using as a reference the recommended parameters showed in Tab. 1. The calibration was made changing one parameter at a time until the experimental load-displacement curves were well reproduced. Once calibrated, the same parameters (Tab. 2) were employed for both Charpy and DWTT specimens. The same was conducted for XFEM, however, the parameters were not the same for the two geometries – for both specimens the maximum cohesive stress was 1100 MPa, but cohesive energy was, respectively, 9 and 5,8 N/mm2 for Charpy and DWTT. The difference comes from the different stress triaxiality found in such specimens - the higher the triaxiality, the smaller is the cohesive energy. Table 2. Calibrated parameters for GTN model
𝒇𝒇𝟎𝟎 0.00015
𝒇𝒇𝑵𝑵 0.0015
3.3. Energy separation
𝜺𝜺𝑵𝑵 0.3
𝝈𝝈𝑵𝑵 0.1
𝒇𝒇𝒄𝒄 0,02
𝜿𝜿 4,0
𝒒𝒒𝟏𝟏 1,5
𝒒𝒒𝟐𝟐 1,0
𝒒𝒒𝟑𝟑 2,25
𝑰𝑰𝒙𝒙 (mm) 0.25
The basis for the energy separation methodology employed in this paper is to isolate domains where the stress field deviates from the hypothetical bending field that would occur if there were no hammer, support and propagating crack. The idea is that the energy absorbed by elements within this specific domain is associated with the different processes occurring in the specimen, such as deformation, crack initiation and crack propagation, as discussed previously. The criteria for determining such domains are stress-based (evaluating von Mises equivalent stresses) as explained earlier and Fig. 3(b) illustrates some domains considered for one DWTT geometry – in such domains, energies associated with crack initiation, crack propagation, contacts and specimen’s deformation can be computed. Essentially similar results in terms of domains’ geometries were found for Charpy geometry. All additional details can be found in the works of Moço (2017) and Pereira (2017). 4. Results 4.1. Stress state analyses The stress fields found in fracture specimens (e.g.: Charpy and DWTT) and real gas pipelines strongly differ. While in pipelines tensile membrane stresses prevail, in both specimens studied here a 3-point bending loading takes place. Even considering that equivalent stresses and strains can be easily computed, such results do not completely support
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the discussion regarding ductile fracture triggering and control. First, in the laboratory specimens, an interaction between the crack plane and the hammer takes place and needs to be corrected; Second, the different loading modes, and the different thicknesses between Charpy and DWTT, cause a strong difference in local (near the crack tip) stress fields and triaxiality. For example, DWTT presents, in average and considering the evaluated thicknesses, 50% more stress triaxiality than Charpy for the analysed X80 steel – it means less plasticity spread ahead of the crack for the DWTT and a different energy distribution in each geometry. Consequently, the ductile fracture micromechanism behaves in a different manner for varying geometries and such effect must be taken into account. In this context, stress fields were evaluated in details, including stress traxiality. Such analyses, whose details can be found in Moço (2017) and Pereira (2017), can support the discussion that follows regarding the limitations and potential of Charpy and DWTT specimens for the quantification and description of energies involved in ductile crack extension and crack arrest. 4.2. Steady state verification Crack extension in real pipelines usually reach a steady state before arrest can take place. Consequently, to be able to quantify energies associated with crack propagation (see. Fig. 1(a)), it is interesting to verify if Charpy and DWTT geometries are able to reach stable crack propagation before final failure. Figure 4 presents the variation of absorbed energy (dEnergy/da) versus crack size (a) for Charpy (Fig. 4(a)) and DWTT (Fig. 4(b)). After crack initiation takes place and the specimens bend, in both cases a stable propagation region can be identified. However, it can be realized that in the case of Charpy specimen the steady state crack propagation is very limited - it does not have enough remaining ligament and when the stable propagation is reached, the crack tip lies in the highly compressive region near the hammer-specimen contact. In the case of DWTT, in its turn, the steady-state propagation takes place along several millimeters of the remaining ligament, favoring the study of the energies related to the ductile fracture process related to a running crack. To support the energy analyses and favor comparability, the domains illustrated by Fig. 3(b) were evaluated during crack initiation and during steady-state propagation.
(a)
(b)
Fig. 4. evolution of the absorbed energy rate as a function of a (a) for the Charpy specimen, (b) for the DWTT specimen.
4.3. Energy analysis Based on the explained domains and understanding the difference between the energy for crack initiation and energy for stable crack propagation, the two geometries could be investigated using both GTN and XFEM damage models, providing the energies absorbed for each phenomenon for the GTN damage model. All details can be found in Moço (2017) and Pereira (2017) and selected results are presented here, since trends for XFEM are similar as explained below. It is useful to recall Fig. 1(a) for a better comprehension.
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Considering Charpy and X80 steel modeled using GTN, the total absorbed energy was ≈ 350 J, while the energy associated with steady state propagation was only ≈ 14 J, which means only ≈ 4 %. This means that only 4 % of the energy obtained from the test data represents steady state ductile fracture and would be suitable to be considered in crack arrest methods. The same analysis based on XFEM results provided 3.7 % of total energy, indicating that the methodologies considering both damage models are comparable. Considering DWTT and X80 steel modeled using GTN, the total absorbed energy was ≈ 25300 J, while the energy associated with steady state propagation was ≈ 4500 J, which means ≈ 18 %. This means that 18 % of the energy obtained from the test represents steady state ductile fracture and would be suitable to be considered in crack arrest methods. The same analysis based on XFEM results provided 16.6 % of total energy. One can realize that the percentage of energy related to ductile fracture for the case of DWTT is much larger than Charpy, but it is still reduced if compared to the total absorbed energy – less than one quarter of the total is in fact phenomenologically associated with the propagation of the ductile fracture that could be related and useful to existing methods for predicting arrestability, which support structural integrity assessments of real gas pipelines. Such data deserve experimental validation, but indicates the potential and limitations of these widely employed specimen geometries and loading modes. In addition, call the attention to the need for a better comprehension of such stresses and energies and how respective quantities and fields can be compared to analogous running cracks in gas pipelines made of modern high-toughness steels. 5. Concluding remarks It was possible to calibrate the damage parameters for both GTN and XFEM models. Load-displacement evolutions presented very good experimental agreement. The results for both models in terms of stress states and energies were close, indicating that both methodologies can be considered comparable for the desired analyses. It is interesting to mention that GTN is more phenomenological, while XFEM proved to be simpler and more pragmatic. The steadystate crack propagation analyzes for X80 steel indicate that it is limited or does not take place in the case of Charpy geometry; in contrast, it is more characteristic and pronounced in DWTT. One of the limitations in using the Charpy specimen is the size of the remaining ligament; low stress triaxiality is an additional concern. Such limitations lead to only approximately 4 % of the total absorbed energy associated to stable crack propagation in this geometry. The percentage for the DWTT war larger, around 17 %, but it is still considered small if compared to total absorbed energy. The results demonstrate that DWTT potentially presents some benefits if compared to Charpy, but both cases present limitations to characterize the crack propagation resistance for advanced steels presenting high toughness and large amounts of plasticity. Finally, the selected results presented here calls the attention to the need for a better comprehension of such stresses and energies and how respective quantities and fields can be compared to analogous running cracks in gas pipelines made of modern high-toughness steels. Acknowledgements This investigation is supported by the Brazilian Metallurgy and Mining Company (CBMM) and by Centro Universitário FEI, Brazil. References ASTM, 2014. ASTM E23-12c. Standard Test Method for Notched Bar Impact Testing of Metallic Materials. ASTM International, West Conshohocken, PA. ASTM, 2013. ASTM E23-12c. Standard Test Method for Drop-Weight Tear Test of Ferritic Steels. ASTM International, West Conshohocken, PA. Fries, T.; Belytschko, T. (2010), The extended/generalized finite element method: An overview of the method and its applications. International Journal for Numerical Methods in Engineering 84, 253-304. Campilho, R. D. S. G. et al., 2011. Strength prediction of single- and double-lap joints by standard and extended finite element modelling. International Journal of Adhesion and Adhesives 31, 362–372. Gurson, A. L., 1977. Continuum theory of ductile rupture by void nucleation and growth: part I - yield criteria and flow rules for porous ductile media. Journal of Engineering Materials Technology 99, 2–15. ISO, 2011. EM ISO 148-1. Metallic metals - Charpy pendulum impact test - Part:1. ISO. Geneva.
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Leis, B.N., 2015. Arresting Propagating Shear in Pipelines. Steel in Translation 45, 1–17. Nonn, A., Kalwa, C., 2013. Analysis of dynamic ductile fracture propagation in pipeline steels: a damage-mechanics’ approach., 6th International Pipeline Technology Conference. Ostend, Belgium, paper S34-01. Maxey W. A., 1974. Fracture initiation, propagation and arrest, 5th Symposium on Line Pipe Research, AGA. Moço, R. F., 2017. Correlação da fenomenologia da fratura dúctil de gasodutos e corpos de prova dinâmicos Charpy e DWTT empregando o modelo GTN a aços avançados classe API. Master thesis, Centro Universitário FEI. Parmar, S. et al., 2015. Simulation of ductile fracture in pipeline steels under varying constraint conditions using cohesive zone modeling., ASME 2015 Pressure Vessels and Piping Conference. Boston, Massachusetts, paper PVP2015-45873. Pereira, L. S., 2017. Avaliação do potencial dos modelos de zona coesiva e XFEM na descrição da fenomenologia da fratura dúctil de corpos de prova Charpy e DWTT fabricados de aço classe API. Master thesis, Centro Universitário FEI. Scheider et al., 2014. A damage mechanics based evaluation of dynamic fracture resistance in gas pipeline. Procedia Materials Science 3, 1956– 196 SIMULIA, 2013. Abaqus theory guide. Abaqus Software Documentation: v. 6.13-4. Tvergaard,T, 1982. Ductile fracture by cavity nucleation between larger voids. Journal of the Mechanics and Physics of Solids 30, 265–286. Tvergaard,T. Needleman, A., 1984. Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica Journal 32, 157–169. Zhu X. K., 2015. State-of the-art review of fracture control technology for modern and vintage gas transmission pipelines. Engineering Fracture Mechanics Journal 148, 260-280.