Combined Ductile-Brittle Fracture Simulation of API X80 Under Impact Loading

doi:10.1016/j.jpse.2025.100295

Journal of Pipeline Science and Engineering

Available online 8 May 2025, 100295

In Press, Journal Pre-proof

Journal of Pipeline Science and Engineering

https://doi.org/10.1016/j.jpse.2025.100295 Get rights and content

Under a Creative Commons license

Open access

ABSTRACT

This study explores finite element (FE) simulation of the combined ductile-brittle fracture behavior of API X80 steel under impact loading, incorporating the influences of strain rate and adiabatic heating. The Johnson-Cook (J-C) deformation model is employed for deformation analysis, while ductile fracture is modeled using the (J-C) fracture strain model, and brittle fracture is captured using a critical stress model. Temperature-dependent parameters for the J-C model were calibrated through smooth round bar (SRB) tests conducted at varying temperatures, while strain rate-dependent parameters were identified using the Charpy V-notch (CVN) impact test at room temperature (RT). Additionally, the critical stress model for brittle fracture was determined via FE simulation of CVN tests at RT. The calibrated deformation and combined fracture models were applied to simulate both CVN and drop-weight tear test (DWTT) over a temperature range of -120 to 0 °C. The simulations accurately captured deformation behavior, load-displacement curves, and fracture surfaces. Sensitivity analyses highlighted the roles of adiabatic heating and strain rate effects in fracture behavior.

Keywords

Adiabatic heating and strain rate effects

API X80 steel

Combined ductile-brittle fracture simulation under impact loading

Johnson-Cook deformation and fracture strain model

Critical stress brittle fracture model

Nomenclature

a₀

initial crack length [mm]

Δa

crack extension [mm]

C_p

specific heat [J/kg∙°C]

strain rate dependent Johnson-Cook (J-C) deformation parameter

D₁, D₂, D₃

Johnson-Cook fracture parameters at quasi-static strain rate and room temperature

D₄

strain rate dependent J-C fracture parameter

D₅

temperature dependent J-C fracture parameter

D_c

critical damage value

Young's modulus [GPa]

E₀

elastic energy absorption [J]

T, ΔT

temperature and its change [°C]

T_melt

melting temperature [°C]

V₀

reference volume [mm³]

V_E

total volume of one layer element in the unnotched ligament [mm³]

ε_f

multi-axial fracture strain in Eqs. (1, 2, 7, 9, 10) and (11)

\dot{ε}

\dot{ε_{0}}

strain rate and reference strain rate

ε_p, Δε_p

equivalent plastic strain and its increment

density [kg/m³]

σ₁

principal stress [MPa]

σ_1,max

maximum principal stress [MPa]

σ_c

critical stress for brittle fracture [MPa]

σ_y, σ_u

yield strength and ultimate tensile strength, respectively [MPa]

σ_e

equivalent stress [MPa]

σ_m

mean normal stress [MPa]

σ_w

Weibull stress [MPa]

ABBREVIATIONS

CMOD

crack mouth opening displacement

CVN

Charpy V notch

DWTT

drop-weight tear test

Finite element

J-C

Johnson-Cook

room temperature

SENT

single edge notched tension

SRB

smooth round bar

1. INTRODUCTION

Impact loading represents one of the most severe conditions leading to brittle fracture in steel structures and pipelines (Kristoffersen et al., 2013). While the Charpy V-notch (CVN) test provides insights into mechanical behavior under impact loading, including the ductile-brittle transition, it is recognized that the small specimen size can result in non-conservative evaluations of the ductile-brittle transition temperature (DBTT) (Eiber, 1965). To address this limitation, the drop weight tear test (DWTT) has been developed as a more reliable method for determining DBTT (Eiber, 1965). Finite element (FE) analysis is a powerful tool to investigate the deformation behavior and combined ductile-brittle fracture mechanisms under impact loading, offering deeper insights into these phenomena.

Numerous studies have focused on simulating ductile fracture under impact conditions (Wang and Ru, 2016, Yu and Ru, 2015, Gu and Wang, 2022, May et al., 2015, Chandran et al., 2022, Rousselier, 1987, Tanguy and Besson, 2002, Tanguy et al., 2005, Tanguy et al., 2005, Dey et al., 2004, Dey et al., 2006, Dey et al., 2007, Banerjee et al., 2015, Mirone et al., 2024, Seo et al., 2024, Chu et al., 2019, Samaniego et al., 2021, Zhang et al., 2024). For instance, Wang et al. (Wang and Ru, 2016) examined the relationship between the crack tip opening angle and impact hammer speed using a strain rate-dependent cohesive zone model (Yu and Ru, 2015). Similarly, Gu et al. (Gu and Wang, 2022) employed a cohesive zone model incorporating a strain rate-dependent traction-displacement law introduced by May et al. (May et al., 2015). The strain rate dependency is quantified through shear tests performed at varying strain rates (Gu and Wang, 2022). Chandran et al. (Chandran et al., 2022) extended these efforts by accounting for both Lode angle and strain rate effects using a model with nine parameters, which were calibrated through tensile and shear tests conducted across a range of strain rates. Notably, these studies (Wang and Ru, 2016, Yu and Ru, 2015, Gu and Wang, 2022, May et al., 2015, Chandran et al., 2022) did not consider the effects of adiabatic heating. The Rousselier model (Rousselier, 1987, Tanguy and Besson, 2002) has also been utilized to simulate ductile fracture under impact loading, incorporating temperature and strain rate effects (Tanguy et al., 2005, Tanguy et al., 2005). Tanguy et al. (Tanguy et al., 2005, Tanguy et al., 2005) quantified these influences through tensile tests conducted under both quasi-static and dynamic conditions at varying temperatures. Alternatively, the Johnson-Cook (J-C) deformation and fracture model has been widely adopted for simulating ductile fracture, as it accounts for adiabatic heating and strain rate effects. The parameters of the J-C model, dependent on strain rate and temperature, are typically determined through smooth and notched round bar tests performed at various temperatures and strain rates (Dey et al., 2004, Dey et al., 2006, Dey et al., 2007, Banerjee et al., 2015, Mirone et al., 2024), as well as split Hopkinson pressure bar tests. Recently, Seo et al. (Seo et al., 2024) proposed an efficient method for determining the J-C model parameters without requiring dynamic tensile tests.

All the aforementioned studies focused primarily on ductile fracture modeling, with limited attention to the combined ductile and brittle fracture behavior under impact loading. Since the ductile-brittle transition is prominent at low temperatures, a simulation methodology capable of addressing both ductile and brittle fracture mechanisms is essential for accurately simulating impact fracture behavior. In studies (Chu et al., 2019, Samaniego et al., 2021), both adiabatic heating and strain rate effects under dynamic loading were incorporated using the Johnson-Cook (J-C) deformation model alongside a phase-field model to simulate brittle fracture. For ductile fracture simulation, Chu et al. (Chu et al., 2019) employed an energy release rate corrected for stress triaxiality. However, as noted in their study (Chu et al., 2019), determining the critical energy release rate and validating it with experimental data proved challenging. To address these limitations, Zhang et al. (Zhang et al., 2024) introduced an additional ductile fracture criterion based on the critical storage energy density. While this methodology successfully simulated the crack shape under impact loading, the simulation results lacked experimental validation, highlighting an area requiring further investigation.

Although combined ductile and brittle fracture modeling under impact loading remains scarce, numerous studies have addressed combined ductile-brittle fracture under quasi-static loading conditions (Hojo et al., 2016, Beremin et al., 1983, Gurson, 1977, Tvergaard and Needleman, 1984, Koplik and Needleman, 1988, Batra and Lear, 2004, Lin et al., 2022, Chakraborty and Biner, 2014, Kim et al., 2022, Seo et al., 2023, Hwang et al., 2024, Camacho and Ortiz, 1997, Gerstgrasser et al., 2021, Borvik et al., 2001, Chanda, 2015, Gambirasio and Rizzi, 2016, Seo et al., 2022, Seo et al., 2024, Kim et al., 2011). In the works of Tanguy et al. (Tanguy et al., 2005) and Hojo et al. (Hojo et al., 2016), brittle fracture was modeled using the Beremin model (Beremin et al., 1983). For ductile fracture simulation, either the Rousselier model (Rousselier, 1987, Tanguy and Besson, 2002) or the Gurson-Tvergaard-Needleman (GTN) model (Gurson, 1977, Tvergaard and Needleman, 1984, Koplik and Needleman, 1988) was employed, as reported in Refs (Tanguy et al., 2005) and (Batra and Lear, 2004). Lin et al. (Lin et al., 2022) utilized a cohesive zone model for brittle fracture and the GTN model for ductile fracture to simulate combined ductile-brittle behavior in hydrogen-embrittled materials. However, their work lacked experimental validation. Chakraborty et al. (Chakraborty and Biner, 2014) adopted a unified cohesive zone model to simulate both ductile and brittle fracture, achieving fracture toughness predictions for 5% and 95% failure probabilities that aligned well with the experimental variations in fracture toughness and crack growth across a temperature range. The authors (Kim et al., 2022, Seo et al., 2023, Hwang et al., 2024) have proposed a simulation methodology for combined ductile and brittle fracture, utilizing a multi-axial fracture strain-based model for ductile fracture and a critical stress-based model for brittle fracture. While their approach successfully simulated impact tests such as the CVN test and DWTT, the phenomenological aspects of impact loading—particularly the effects of adiabatic heating and strain rate—were not fully considered. These effects are critical for accurately simulating impact fracture behavior.

This paper presents finite element (FE) simulations of combined ductile-brittle fracture in API X80 steel under impact loading, with a focus on incorporating strain rate and adiabatic heating effects. The Johnson-Cook (J-C) deformation and fracture strain models were employed for ductile fracture simulation, while brittle fracture was modeled using a critical stress approach. The simulation methodology is detailed in Section 2. 3 SUMMARY OF EXPERIMENTS FOR MODEL DETERMINATION, 4 DETERMINATION OF API X80 DEFORMATION AND FRACTURE MODELS discuss the experiments conducted for model parameter determination and the corresponding determination procedure. Validation experiments and the validation process are described in 5 EXPERIMENTS FOR VALIDATION, 6 COMPARISON WITH FE SIMULATION RESULTS FOR VALIDATION, respectively. Section 7 provides an analysis of the effects of adiabatic heating and strain rate on the combined ductile-brittle fracture simulation for impact tests. Finally, the conclusions are summarized in Section 8.

2. PROPOSED COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION MODEL

This section proposes a combined ductile-brittle fracture simulation model for impact loading scenarios. For deformation analysis, the Johnson-Cook (J-C) deformation model is employed (see Section 2.1). Ductile fracture simulation utilizes the Johnson-Cook fracture strain model, which incorporates both strain rate and adiabatic heating effects. Brittle fracture simulation, on the other hand, is performed using a critical stress model. The models used for ductile and brittle fracture simulations are detailed in 2.2 Johnson-Cook (J-C) Fracture Strain Model for Ductile Fracture Simulation, 2.3 Critical Stress Model for Brittle Fracture Simulation, respectively. The integration of these models to simulate combined ductile-brittle fracture is described in Section 2.4. Determination of model parameters specific to the material under investigation (API X80 steel in this study) requires experimental testing, which is discussed in Section 3. The parameter determination procedure for API X80 is provided in Section 4.

2.1. Johnson-Cook (J-C) Deformation Model under Impact Loading

The original form of the J-C deformation model is as follows:(1) $σ = σ_{e, RT} (1 - λ {| T^{*} |}^{k}) (1 + c \ln (\frac{\dot{ε}}{{\dot{ε}}_{0}})); T^{*} = \frac{T - T_{r o o m}}{T_{m e l t} - T_{r o o m}}, λ = \frac{T^{*}}{| T^{*} |}$

where σ_e_, RT denotes the flow stress at room temperature (RT) under quasi-static conditions, T_room and T_melt represent the room temperature and melting temperature, respectively, and

\dot{ε_{0}}

is the reference strain rate. For steels, T_room = 25 °C and T_melt = 1,500 °C are used (Chanda, 2015, Gambirasio and Rizzi, 2016). Notably, the strain rate dependent logarithmic term on the right-hand side of Eq. (1) causes numerical instability when the strain rate is lower than the reference strain rate. To mitigate this issue, the original form of the J-C deformation model was slightly modified, as proposed in (Camacho and Ortiz, 1997, Gerstgrasser et al., 2021).(2)

σ = σ_{e, RT} (1 - λ {| T^{*} |}^{k}) {(1 + \frac{\dot{ε}}{{\dot{ε}}_{0}})}^{c}; T^{*} = \frac{T - T_{r o o m}}{T_{m e l t} - T_{r o o m}}, λ = \frac{T^{*}}{| T^{*} |}

Under quasi-static conditions, this term approaches unity by setting the reference strain rate to

\dot{ε_{0}}

 = 100 /s (Gu and Wang, 2022). Tensile tests under high strain rates (up to 1,000/s) performed on high-strength ferritic steels in (Uenishi et al., 2011, Vaynman et al., 2006) showed significant strain rate hardening was observed when the strain rate exceeded 100/s. Based on these observations, Yu et al. (Yu and Ru, 2015) chose 100/s as the reference strain rate for simulating the DWTT test for API X80. In our previous work (Seo et al., 2024), the same choice of reference strain rate of 100/s could successfully simulate the CVN and DWTT tests for API X52 (Seo et al., 2024). Finally, two parameters, k and c, need to be determined. The parameter determination procedure for API X80 steel will be described in Section 4.1.

2.2. Johnson-Cook (J-C) Fracture Strain Model for Ductile Fracture Simulation

The Johnson-Cook (J-C) fracture strain model is employed to simulate ductile fracture in impact tests, incorporating both strain rate (

\dot{ε}

) and temperature (T) effects (Camacho and Ortiz, 1997, Gerstgrasser et al., 2021, Borvik et al., 2001):(3)

ε_{f} = (D_{1} \cdot \exp (D_{3} \cdot \frac{σ_{m}}{σ_{e}}) + D_{2}) {(1 + \frac{\dot{ε}}{{\dot{ε}}_{0}})}^{D 4} (1 - λ T^{* D 5})

Where σ_m and σ_e denote the hydrostatic stress and von Mises stress, respectively; D₁, D_2, and D₃ are the multi-axial fracture strain damage model parameters at room temperature (RT) under quasi-static conditions; and D₄ and D₅ are parameters associated with strain rate and temperature, respectively.

The accumulated damage (D) due to plastic strain is calculated as follows (Seo et al., 2022, Seo et al., 2024, Kim et al., 2011):(4)

D = \int Δ D = \int \frac{Δ ε_{p}}{ε_{f}}

where Δε_p represents the increment of equivalent plastic strain. In the simulation, ductile fracture was assumed to occur when D reaches the critical damage value (D_c). Once D_c is reached at an integration point, that point is excluded from further calculation. When all integration points in an element fail, the element is removed from the finite element (FE) simulation using the “DELETE” option in ABAQUS. It is important be note that the value of D_c can depend on the element size (Oh et al., 2011, Jeon et al., 2016). The determination of J-C fracture strain model parameters for API X80 steel is detailed in Section 4.2.

2.3. Critical Stress Model for Brittle Fracture Simulation

The critical stress model is employed to simulate brittle fracture under impact loading in this study, based on the Weibull stress concept (Beremin et al., 1983). The Weibull stress (σ_w) is defined as:(5)

σ_{w} = {(\frac{1}{V_{0}} \int_{V} {(σ_{1})}^{m} d V)}^{1 / m}

Where V₀ and V represent the reference volume and fracture process zone, respectively; σ₁ is the maximum principal stress, and m denotes the Weibull modulus. For finite element (FE) simulations, the Weibull stress criterion can be approximately implemented as:(6)

σ_{w} (V_{0}) \approx {(\frac{1}{V_{0}} \sum_{i = 1}^{n_{e}} {(σ_{1}^{i})}^{m} V^{i})}^{1 / m} \approx {(\frac{V}{V_{0}})}^{1 / m} σ_{1, \max}

where σ_1,max represents the maximum principal stress in the fracture process zone (V). The approximation σ_w = σ_1,max holds when the ratio V/V₀ = 1 (Kim et al., 2020). Brittle fracture is assumed to occur in an element when the maximum principal stress (σ_1,max) exceeds the critical stress value (σ_c). The parameter σ_c for API X80 steel will be determined based on impact energy, as detailed in Section 4.3.

2.4. Combined Ductile and Brittle Fracture Simulation

Combined ductile-brittle fracture under impact loading is simulated by integrating the Johnson-Cook (J-C) fracture strain model and the critical stress model into a finite element (FE) impact simulation. Prior to simulation, the fracture strain model parameters and the critical stress value (σ_c) must be determined for the specific material. Using these calibrated models, impact simulations are conducted. During the simulation, the maximum principal stress (σ_1,max) and accumulated damage (D) are calculated at each Gauss point within an element. These calculated values are then compared against their respective failure criteria, σ_c and D_c. If σ_1,max exceeds σ_c, brittle fracture is assumed to occur, Similarly if D reaches D_c, ductile fracture is assumed. When all Gauss points in an element fail, the element is removed from the FE simulation using the “DELETE” option in ABAQUS. The fracture simulation process is summarized in Fig. 1.

3. SUMMARY OF EXPERIMENTS FOR MODEL DETERMINATION

Determining material-specific parameters for deformation and fracture models is a crucial step in accurate simulation. To identify these parameters, basic experimental data are required. This section provides a summary of the experimental data for API X80 (pipeline steel) utilized in this study, from which the material-specific parameters for the deformation and fracture models are derived. The chemical composition of the API X80 are shown in Table 1 and the averaged grain size was 6 µm. The following experimental data are used in this work:

(1)
Smooth round bar (SRB) test data conducted over a temperature range of -100 °C to 60 °C,
(2)
Single edge notched tensile (SENT) test conducted at room temperature (RT), and
(3)
Instrumented Charpy V-notch (CVN) test conducted at RT.

Table 1. Chemical composition of API X80 (wt.%).

C	Si	Mn	Ni+Mo	Nb+Ti	Al
0.073	0.23	1.76	0.56	0.05	0.033

These tests are summarized in Table 2 and are detailed in the subsequent sub-sections. The procedure for determining the model parameters is explained in Section 4.

Table 2. Summary of test cases for determination of deformation and fracture model parameters.

Test	Temperature [°C]
SRB	60, RT, -50, -100
SENT	RT
CVN	RT

* RT: room temperature.

3.1. Tensile Test

In this study, smooth round bar (SRB) tests were conducted at temperatures ranging from -100 to 60 °C using specimens extracted from an API X80 plate. Each specimen had a minimum section diameter of 6 mm and a gauge length of 25 mm. Figure 2(a) presents selected engineering stress-strain curves at -100 °C, room temperature (RT), and 60 °C. Figure 2(b) illustrates the variation of the yield strength (σ_y, 0.2% proof strength) and tensile strength (σ_u) with temperature. Both the yield and tensile strength decrease as temperature increases. Figure 2(b) also shows the fracture strain calculated from the reduction of area (RA) using:(7)

ε_{f} = \ln (\frac{1}{1 - RA})

The fracture strain exhibits minimal sensitivity to temperature changes. These trends align with tensile test results for other API steels reported in the literature (Jung et al., 2014, Heier et al., June 2013, Akselsen et al., June 2012, Kim et al., 2024).

3.2. Single Edge Notched Tensile (SENT) Test

The Single Edge Notched Tensile (SENT) test was conducted at room temperature (RT) following the BS8571 standard (BSI 2014). A through-thickness notch was created using electro-discharge machining. After fatigue pre-cracking, the specimen had an initial crack length of a₀ = 10.2 mm. Figure 3(a) presents a schematic illustration of the SENT test specimen, which includes side grooves of 1.65 mm for each side. Figure 3(b) presents the experimental load-crack mouth opening displacement (CMOD) and crack extension (Δa-CMOD) curves. The crack length was determined using the unloading compliance method.

3.3. Charpy V Notched (CVN) Impact Test at Room Temperature

An instrumented Charpy V-Notched (CVN) impact test was conducted following the API 5L standard (Institute, 2007). The specimens had a cross-sectional area of 10 × 10 mm², a ligament length of 8 mm, and a 45 ° center V-notch. The test was performed at room temperature (RT) with an initial velocity of 5 m/s using a Zwickroell PSW 750 instrumented CVN testing machine. Note that the notch without the fatigue crack was introduced in the CVN specimen.

Figure 4 illustrates the measured load-displacement curves from the CVN test. The load increased to its maximum value as the specimen deformed and subsequently decreased due to crack initiation and propagation. Three repeated tests demonstrated consistent load-displacement responses and CVN impacts energy values.

4. DETERMINATION OF API X80 DEFORMATION AND FRACTURE MODELS

To simulate combined ductile-brittle fracture under impact loading, three models must be determined for the material under study (API X80 in this work), as outlined in Section 2: (1) the deformation model, (2) the ductile fracture model, and (3) the brittle fracture model. The parameters for these models are derived from the experimental data presented in Section 3. The determination of the parameters for the deformation model is described in Section 4.1. The parameters for the ductile and brittle fracture models are detailed in 4.2 Parameter Determination of Ductile Fracture Model, 4.3 Determination of Brittle Fracture Model, respectively.

4.1. Parameter Determination of Deformation Model

The strain rate and temperature-dependent Johnson-Cook (J-C) deformation model (see Eq. (2) was calibrated using the procedure proposed by Seo et al. (Seo et al., 2024). The steps for parameter determination are as follows:

(1)
The true stress-strain curve at room temperature (RT) under quasi-static conditions was obtained from the smooth round bar (SRB) testing at RT.
(2)
The temperature-dependent parameter (k) was determined based on the variation of yield strength with temperature.
(3)
The strain rate-dependent parameter (c) was calibrated by simulating the experimental maximum load from the Charpy V-notch (CVN) test at RT

The true stress-strain curve beyond the necking point was determined by simulating the experimental engineering stress-strain curve using the method proposed by Tu et al. (Tu et al., 2022). Simulations were performed using the commercial finite element (FE) analysis software ABAQUS (ABAQUS Version 2018). Figure 5(a) illustrates the half FE model of the SRB specimen, consisting of 280 to 1,230 axisymmetric elements with reduced integration (CAX8R). The minimum element size in the center of the specimen was set to 0.1, 0.2, and 0.3 mm for sensitivity analysis. The top surface of the FE model was constrained using the Multi-Point Constraints (MPC) option in ABAQUS, and the reaction force at the central node was obtained to calculate engineering stress. Engineering strain was calculated by dividing the nodal displacement at the gauge node by the gauge length (25 mm). Figure 5(b) shows the determined engineering and true stress-strain curves, along with the simulated engineering stress-strain curves obtained using three different element sizes (0.1, 0.2, and 0.3 mm) through elastic-plastic FE analysis. The results indicate that the simulated curves are not significantly affected by element size.

Figure 5(c) illustrates the variation of yield strength with temperature. Experimental data are represented by symbols, while the temperature-dependent term in the J-C model, calculated with a calibrated k value of 0.7, is shown as a line. The k value was derived using the data analysis software ORIGINPRO (Origin(Pro), Version 2020). Figure 5(d) compares the simulated engineering stress-strain curves, generated using the calibrated J-C model, with experimental data at 60 °C and -100 °C. It is important to note that the hardening exponent in the J-C model is assumed to be temperature-independent. As a result, the tensile strength was slightly underestimated by the determined J-C deformation model. However, achieving highly accurate predictions of tensile data at different temperatures is not the primary focus of this study. The current J-C model provides sufficient accuracy for the intended purpose of stimulating combined ductile-brittle fracture under impact loading.

After determining the true stress-strain curve at room temperature (RT), the parameters k and c were calibrated as follows. Figure 6 presents the quarter finite element (FE) model used to simulate the Charpy V-notch (CVN) test, comprising 11,112 to 38,740 eight-node brick elements with full integration (C3D8). To examine the effects of element size, the minimum element sizes in the notched section were set to 0.1, 0.2, and 0.3 mm.

For friction modeling, a friction coefficient of 0.1 was applied between the specimen and the apparatus (hammer and anvil) using the “CONTACT” option in ABAQUS. This value is commonly used for impact simulations (Seo et al., 2024, Talemi et al., 2019). Both the anvil and hammer were modeled as rigid bodies, with the anvil fixed in place. The hammer impacted the specimen with an initial velocity of 5.0 m/s, and the simulated load and displacement were obtained at the reference point of the hammer. Strain rate and adiabatic heating effects were incorporated into the simulation using the “adiabatic heating” option in dynamic implicit finite element (FE) analysis. The temperature rise due to adiabatic heating was calculated based on the equivalent plastic strain (ε_p) using the following relationship (Seo et al., 2024):(8)

Δ T = \frac{0.9}{ρ C_{p}} \int_{V} σ d ε_{p}

where ρ and C_p represent the material density and specific heat, respectively. A typical value of ρ = 7.9 g/mm³ was used, while the specific heat values for API X80 were taken from (Yan et al., 2014) and are provided in Table 3. It should be noted that the factor of 0.9 on the right-hand side of Eq. (8) represents the Taylor-Quinney (T-Q) coefficient. It has been found that the T-Q coefficient is the strain rate-dependent parameter (Soares and Hokka, 2021, Rittel et al., 2017). Soares and Hokka (Soares and Hokka, 2021) analyzed the effect of strain rate on the T-Q coefficient using pure metal materials, titanium, iron and copper under strain rate ranging from 500 to 3,100 /s. Similarly, Rittel et al. (Rittel et al., 2017) also measured the value of T-Q coefficients for many materials, including Ti6Al4V, Aluminum, stainless steel and 1020 steel under strain rate ranging from 1,000 to 6,000 /s. It should be noted that, although the exact strain rate when the adiabatic heating effect should be considered is not clear yet, this phenomenon has been considered when the strain rate is higher than 500 /s (Soares and Hokka, 2021, Rittel et al., 2017). Because the strain rate of CVN test and DWTT is higher than 1,000 /s, the adiabatic heating effect cannot be neglected.

Table 3. Temperature-dependent specific heat for API 5L X80 in (Yan et al., 2014).

Temperature [°C]	20	100	200	400	800	1,200
Specific heat [J/kg∙°C]	423	473	536	662	914	1,160

Figure 7(a) compares the experimental load-displacement curve from the CVN test with the finite element FE simulation results. The J-C model in Eq. (2) was used, with the calibrated k value of 0.7 and varying values of c. The simulated maximum load increases linearly with c, as shown in Figure 7(b). It is important to note that the crack initiated near the maximum load during the CVN test (Tronskar et al., 2002, Kobayashi, 1984, Oulad Brahim et al., 2022). Based on this observation, the final value of c = 0.18 was selected by matching the simulated maximum load with the experimental results, resulting in the final J-C deformation model:(9)

σ = σ_{e, RT} (1 - λ {| T^{*} |}^{0.7}) {(1 + \frac{\dot{ε}}{{\dot{ε}}_{0}})}^{0.18}

Using the determined value of c = 0.18, the effect of element size on the simulation was analyzed. The same element sizes as those used for the SRB simulation (0.1, 0.2, and 0.3 mm) were applied to the CVN simulation. The results, shown in Fig. 7(a), indicate that the simulation outcomes are not significantly affected by element size.

4.2. Parameter Determination of Ductile Fracture Model

The Johnson-Cook (J-C) fracture strain model described in Section 2.2 involves six parameters (from D₁ to D₅ and D_c) that need to be determined. The determination process follows these steps:

(1)
The multi-axial fracture strain damage model parameters (D₁, D_2, and D₃) and critical damage value D_c are determined by analyzing Smooth Round Bar (SRB) and Single Edge Notched Tensile (SENT) tests at room temperature (RT) under quasi-static conditions.
(2)
The temperature dependent parameter (D₅) is determined by fitting the variation of fracture strain with temperature.
(3)
Finally, the strain rate dependent parameter (D₄) is obtained by simulating the experimental Charpy V Notched (CVN) energy at RT.

Under quasi-static conditions at RT, the J-C fracture model in Eq. (3) simplifies to:(10)

ε_{f} = (D_{1} \exp (D_{3} \cdot \frac{σ_{m}}{σ_{e}}) + D_{2})

Initially, D₃ is typically assumed to be -1.5, following guidance from previous studies (Seo et al., 2022, Seo et al., 2024, Kim et al., 2011). One point on the fracture strain locus is determined through elastic-plastic FE analysis of the SRB test. Figure 8(a) shows the variation of the stress triaxiality with equivalent plastic strain, measured at the center of the SRB specimen under RT conditions (see Fig. 5(b)). The average stress triaxiality up to the failure point, combined with the fracture strain, provides a data point on the fracture strain locus, depicted in Figure 8(b) using a symbol.

Next, the single edge notched tensile (SENT) test is simulated using finite element (FE) damage analysis to establish the final fracture strain locus and critical damage value (D_c). Figure 9 illustrates the quarter FE model used for the SENT test stimulation, which consists of 10,320 to 58,432 eight-node brick elements with full integration (C3D8). Three different FE meshes were created, with the minimum element size in the cracked ligament set to 0.1, 0.2, and 0.3 mm. The top surface of the FE model was constrained using the multi-point constraint (MPC) option in ABAQUS. The reaction force was measured at the central node, while the crack mouth opening displacement (CMOD) was recorded at the gauge node using a clip-on gauge with a length of 3 mm. It should be noted that macroscopically straight crack propagation was observed in all tests. Accordingly, our model also assumed straight crack growth and failure was considered only for the elements on the symmetric surface.

Fracture toughness tests provide properties related to both crack initiation and crack growth rate. In previous studies (Seo et al., 2022, Seo et al., 2024, Kim et al., 2011), it was observed that D_c predominantly affects the crack initiation point, whereas D₂ primarily influences the crack growth rate. Accordingly, FE damage simulations were first conducted with D₂ set to zero, varying D_c to assess its effect. As shown in Figure 10(a), the crack initiation point was delayed as D_c increased. The value of D_c = 1 was chosen to match the experimental crack initiation point. Subsequently, FE damage simulations were performed with D_c fixed at 1, varying D₂ to analyze its impact on the crack growth rate (d(Δa)-d(CMOD)). Figure 10(b) illustrates that the final value of D₂ = 0.4 was selected to align the simulated crack growth rate with experimental data. The resulting fracture strain locus is represented by:(11)

ε_{f} = (3.37 \cdot \exp (- 1.5 \cdot \frac{σ_{m}}{σ_{e}}) + 0.4)

It is well-known that element size can significantly affect fracture simulation results. In this context, it is assumed that the determined fracture strain locus is independent of the element size. However, the critical damage value D_c is considered to be element size-dependent. Therefore, the influence of element size on D_c is analyzed using the established fracture strain locus. The FE meshes for various element sizes are shown in Figure 9. The values of D_c determined from FE damage analysis with different element sizes are presented in Figure 10(c), demonstrating that the FE damage simulation results correspond well with experimental data. Figure 10(d) shows the variation of the critical damage value D_c with element size L_e.

The temperature-dependent parameter (D₅) is determined based on the variation of fracture strain with temperature. The fracture strain data, obtained from the SRB test conducted at temperatures ranging from -50 to 60 °C, showed minimal variation regardless of temperature (see Fig. 2(b)). As a result, D₅ is assumed to be 0.

The strain rate-dependent parameter (D₄) is determined by simulating the experimental CVN energy at RT. The FE mesh for the CVN simulation, as shown in Fig. 6, is utilized. The simulation employs the J-C deformation model determined in Section 4.1 and the J-C fracture strain model from Eq. (11). Figure 11(a) displays the impact of D₄ on the simulated load-displacement curves using a minimum element size of 0.1 mm. As explained in Section 4.1, cracks typically start propagating at the maximum load. The result indicates that while D₄ does not affect the maximum load, a lower D₄ value leads to a decrease in the load after the maximum point. The final value of D₄ = -0.28 is selected to align the simulated CVN energy with the experimental data, as illustrated in Fig. 11(b). The finalized fracture strain locus, incorporating both temperature and strain rate effects, is given by Eq. (12)(12)

ε_{f} = (3.37 \cdot \exp (- 1.5 \cdot \frac{σ_{m}}{σ_{e}}) + 0.4) {(1 + \frac{\dot{ε}}{{\dot{ε}}_{0}})}^{- 0.28}

To evaluate the element size effect, Fig. 11(a) compares the simulated load-displacement curves using element sizes of 0.1, 0.2, and 0.3 mm. The results indicate that the J-C strain-based fracture model is relatively insensitive to element size variations. Validation of the determined J-C deformation and fracture strain model will be provided in Section 6 through simulations of CVN tests at other temperatures.

4.3. Determination of Brittle Fracture Model

In this section, the determination procedure for the critical stress of the brittle fracture model is outlined. This critical stress is identified through CVN simulation utilizing the J-C fracture strain ductile fracture model established in Section 4.2. During the simulations, both ductile and brittle fracture models are employed, with the critical stress value (σ_c) being varied. Ductile fracture is presumed to occur when the accumulated damage reaches the critical damage value (D_c), while brittle fracture is considered to occur when the maximum principal stress surpasses the assumed critical stress (σ_c), as detailed in Section 2.3. The CVN energy is then calculated based on the assumed critical stress.

For the CVN test simulations, the FE mesh from Fig. 6 with an element size of 0.1 mm is utilized. Given that combined ductile-brittle fractures typically occur at temperatures below -60 °C for API X80 (Kim et al., 2020), CVN simulations were conducted at temperatures ranging from -60 to -120 °C. Figure 12(a) illustrates the impact of the assumed σ_c on the simulated load-displacement curves. The solid line represents simulation results considering only the ductile fracture model from Section 4.2. The dotted and dashed lines depict the load-displacement curves when both ductile and brittle fracture models are applied, with different assumed σ_c values. The critical stress value normalized by the temperature-dependent yield strength (σ_c /σ_y) was assumed to be 2.8 and 3.0. A sudden drop in load is observed at a displacement of ∼12 mm for σ_c /σ_y = 3.0, while for σ_c /σ_y = 2.8, the drop occurs at ∼6 mm, indicating the occurrence of brittle fracture. \

The relationship between CVN energy (the area under the load-displacement curve) and critical stress is established by simulating the CVN test using the determined ductile fracture model while varying the critical stress value through parametric analysis. Elastic energy absorption is calculated as:(13)

E_{0} (T) = \frac{σ_{y} {(T)}^{2}}{2 E} \cdot V_{E}

where E denotes Young's modulus, and V_E represents the total volume of a single layer element in the unnotched ligament. Notably, only one layer of elements in the unnotched ligament is considered when calculating the total volume. For example, a CVN specimen with an unnotched ligament area of 80 mm² results in V_E = 2 × 80 × 0.1 mm³ for an element size of 0.1mm. The factor of 2 accounts for the symmetry condition, making V_E linearly dependent on the element size.

Figure 12(b) depicts the variation of normalized critical stress (σ_c/σ_y(T)) with normalized CVN energy (E_CVN/E₀(T)), where σ_y(T) is the temperature-dependent yield strength for a specific temperature T. The Figure shows that σ_c /σ_y(T) is nearly linearly related to ln (E_CVN/E₀(T)). Using the commercial data analysis program “ORIGIN PRO” (Origin(Pro), Version 2020), the following linear relationship is derived:(14)

\frac{σ_{c}}{σ_{y} (T)} = 1.67 + 0.38 \cdot \ln (\frac{E_{C V N}}{E_{0} (T)})

The effect of element size on the determination of critical stress is investigated using the FE model with element sizes of 0.2 and 0.3 mm. CVN simulations were conducted for a CVN test at -60 °C, applying the J-C fracture strain model determined in Section 4.2 while varying the critical stress values. The elastic energy absorption for the FE model with element sizes of 0.2 and 0.3 mm is calculated as V_E = 2 × 80 × 0.2 mm³ and V_E = 2 × 80 × 0.3 mm³, respectively. Figure 12(c) demonstrates the variation of σ_c /σ_y(T) with ln(E_CVN/E₀(T)), indicating that the curve remains consistent across different element sizes.

5. EXPERIMENTS FOR VALIDATION

To validate the proposed simulation method under impact loading, additional tests were conducted:

(1)
CVN test at temperatures ranging from -120 to -30 °C
(2)
Drop weight Tear Test (DWTT) at -40 and 0 °C.

Details of these tests are summarized in Table 4 and will be elaborated upon in the following subsections. A comparison with FE simulation results will be presented in Section 6.

Table 4. Summary of test cases for validation.

Test	Temperature [°C]
CVN	-30, -60, -90, -120
DWTT	0, -40

5.1. Charpy V Notched (CVN) Test

The CVN tests for validation were conducted using the same testing machine described in Section 3.3. Six tests were performed at -120°C, and three tests were conducted at each of the other temperatures (-30, -60, and -90°C). Figure 13 presents the load-displacement curves. The curve at -30°C in Fig. 13(a) shows a smooth decline after reaching the maximum load, indicating a ductile-dominant fracture. In contrast, the curves at -60, -90, and -120°C show a significant drop of around 10mm displacement, indicating a combined ductile-brittle fracture behavior.

5.2. Drop-Weight Tear Test (DWTT)

The Drop-Weight Tear Test (DWTT) was conducted following ASTM E436 (ASTM Standard E436-03 2021). A schematic of the DWTT specimen is shown in Fig. 14(a). The test was performed at -40 and 0 °C with an initial velocity of 5.15 m/s using Imatek DWTT-100F testing machine. One or two tests were conducted at each temperature. Figure 14(b) presents the load-displacement curve for the DWTT at 0 and -40 °C. The maximum load increases as the temperature decreases due to low-temperature hardening. After reaching the maximum load, the curve shows a decrease, with a sudden reduction occurring at a displacement of approximately 30 to 40 mm, indicative of combined ductile-brittle fracture. Figure 14(c) shows the fracture surfaces at 0 and -40 °C, respectively. Cleavage fracture, often referred to as “inverse fracture” (Kim et al., 2021, Kim et al., 2022), is observed on the fracture surface of the specimen. The load-displacement curves and fracture surfaces will be further analyzed in conjunction with the FE analysis results.

6. COMPARISON WITH FE SIMULATION RESULTS FOR VALIDATION

In this section, the CVN tests and DWTT are simulated using the proposed combined ductile and brittle fracture model, with the model parameters determined in Section 4. A comparison of the CVN test results with FE simulations will be presented in Section 6.1, while the comparison for the DWTT is provided in Section 6.2.

6.1. Comparison of CVN Test with Simulation Results

The CVN test at -30 °C was simulated using the FE mesh shown in Fig. 6, with an element size of 0.1 mm. Note that only ductile fracture mode was observed in the CVN test at -30 °C. The J-C deformation and fracture strain models in Equations (9) and (11) were used for the simulation. Figure 15 compares the simulated load-displacement curve and fracture surface of the CVN simulation at -30 °C with experimental data. The results show that the simulation aligns well with the experimental data at -30 °C. The simulated fracture surface is also compared with experimental data in Fig. 15(b), demonstrating that the shape of the deformation and ductile fracture surface is accurately simulated.

The CVN tests at temperatures ranging from -60 to -120 °C were also simulated using the FE mesh shown in Fig. 6 with a 0.1 mm element size. In the test, combined ductile and brittle fracture modes were observed for all cases. The J-C deformation and fracture strain models in Equations (9) and (11) were used for ductile fracture simulation, while the critical stress model in Eq. (14) was applied for brittle fracture simulation. The critical stress was calculated using the experimental CVN energy, resulting in a value of σ_c/σ_y = 3.05 for -60 °C, σ_c/σ_y = 3.01 for -90 °C, and σ_c/σ_y = 2.95 for -120 °C. The simulated load-displacement curves from the FE simulation are compared with the experimental data in Fig. 16. The simulation reproduced the experimental results very well using the determined combined ductile-brittle fracture model. The simulated fracture surface at -90 °C is also compared with experimental data in Fig. 16(d). The simulated load-displacement curve, considering only the ductile fracture model, is shown for comparison (indicated as “w/o σ_c”). The significant load drop at a displacement of 10 mm could not be reproduced without incorporating the brittle fracture criterion, σ_c. The results also show that the steep load decrease at a displacement of 10 mm is attributed to brittle fracture. The simulated ductile-brittle combined fracture surface agrees well with the experimental fracture surface.

6.2. Comparison of DWTT with Simulation Results

In this section, DWTT tests conducted at -40 and 0 °C, which exhibited a combined ductile-brittle fracture mode, are simulated using the proposed combined ductile and brittle fracture models determined in Section 4.

Figure 17 shows the quarter FE model for the DWTT simulation, consisting of 40,848 eight-node brick elements with full integration (C3D8). The minimal element size, L_e, at the unnotched ligament, was set to 0.3 mm. The friction coefficient between the apparatus, hammer anvil, and the specimen was set to 0.1, consistent with the value used in the CVN simulation, utilizing the “CONTACT” option in ABAQUS. Both apparatuses were modeled as rigid bodies using rigid elements (R3D4). The anvil was fixed, and the hammer impacted the specimen with an initial velocity of 5.15 m/s. The simulation was conducted via dynamic implicit analysis, considering the large geometric change. Both strain rate and adiabatic heating were considered during the simulation.

The DWTT tests performed at 0 and -40 °C were simulated using the J-C deformation and fracture strain model for ductile fracture and the critical stress model for brittle fracture. The FE mesh shown in Fig. 17 was used for the DWTT simulation. The critical stress for the DWTT simulation was calculated using the experimental DWTT energy from Eq. (14). The total volume of one layer element, E₀, in Eq. (13) was calculated for the element size of 0.3 mm, resulting in values of σ_c/σ_y = 2.92 for 0 °C and σ_c/σ_y = 2.81 for -40 °C.

Figure 18(a) compares the simulated load-displacement curve with experimental results. Note that the raw experimental curves, without any processing, are shown to highlight the effect of data scattering. The FE results closely follow the experimental load-displacement curves, and the simulated impact energies were within 5 % of the experimental data. The fracture behavior of BCC steels shows four different trends depending on temperature: upper shelf (ductile), upper transition (ductile-brittle), lower transition (ductile-brittle), and lower shelf (brittle). In the transition regions, data show large scatters due to the mixed contribution of ductile and brittle fracture mechanisms, making it difficult to provide the relative contribution of ductile versus brittle fracture energy to the overall fracture energy. The proposed methodology can predict the energy contribution from ductile and brittle fracture for the given total fracture energy in transition regions. For comparison, the simulated load-displacement curves considering only the ductile fracture model are also shown in Fig. 18(a) (indicated as “w/o σ_c”). Without considering σ_c, the load increases smoothly up to 20 mm of displacement. However, in both the experimental and simulation results, when brittle fracture is accounted for, the load decreases once the displacement exceeds 10 mm. Figure 18(b) compares the fracture surface from the experimental test at -40 °C with the FE simulation. The fracture surface of the DWTT specimen was analyzed after the test using an image analyzer. The central surface showed brittle fracture due to high stress triaxiality, whereas the side surface exhibited ductile fracture. A very similar fracture surface can be observed in the FE results. In particular, the triangular shape near the initial notch tip and the jaggedly propagating brittle fracture surface were well simulated using the deformation and fracture models determined from CVN tests.
图 18(a) 将模拟的载荷-位移曲线与实验结果进行了比较。需要注意的是，图中显示的是未经任何处理的原始实验曲线，以突出数据散布的影响。FE 结果紧密遵循实验载荷-位移曲线，模拟的冲击能量与实验数据的误差在 5% 以内。体心立方钢的断裂行为随温度变化呈现四种不同的趋势：上部架状（延性）、上部转变（延性-脆性）、下部转变（延性-脆性）和下部架状（脆性）。在过渡区，由于延性和脆性断裂机制的混合贡献，数据表现出很大的散布性，因此很难提供延性断裂能量与脆性断裂能量对总断裂能量的相对贡献。所提出的方法可以预测过渡区中给定总断裂能量时延性和脆性断裂的能量贡献。为了进行比较，图 18（a）还显示了仅考虑延性断裂模型的模拟载荷-位移曲线（表示为“w/o σ _c ”）。在不考虑σ _c 的情况下，载荷平稳增加至 20 mm 的位移。然而，在实验和模拟结果中，当考虑脆性断裂时，一旦位移超过 10 mm，载荷就会降低。图 18（b）比较了-40 °C 下实验测试的断裂表面与 FE 模拟的断裂表面。试验后，使用图像分析仪分析了 DWTT 试样的断裂表面。由于应力三轴性高，中心表面表现出脆性断裂，而侧面表现出延性断裂。在 FE 结果中可以观察到非常相似的断裂表面。特别是，使用从 CVN 测试确定的变形和断裂模型可以很好地模拟初始缺口尖端附近的三角形和锯齿状扩展的脆性断裂表面。

7. DISCUSSION: EFFECT OF ADIABATIC HEATING AND STRAIN RATE ON COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION FOR IMPACT TESTS
7. 讨论：绝热加热和应变速率对冲击试验韧脆性断裂模拟的影响

In this section, the effects of strain rate and adiabatic heating on CVN and DWTT simulations are discussed. Under impact loading conditions, characterized by high strain rates, the material's temperature rises due to adiabatic heating. Consequently, the material undergoes both strain rate hardening and adiabatic heating softening. To analyze the individual effect, three cases were considered: (Case 1) accounting for both strain rate and adiabatic heating effects, (Case 2) considering only the strain rate effect, and (Case 3) neglecting both strain rate and adiabatic heating effects. FE simulations were conducted for scenarios where combined ductile-brittle fracture was observed in tests, specifically at -90 °C for the CVN test and -40 °C for the DWTT.
本节将讨论应变率和绝热加热对 CVN 和 DWTT 模拟的影响。在高应变率的冲击载荷条件下，材料温度会因绝热加热而升高。因此，材料会同时经历应变率硬化和绝热加热软化。为了分析每种效应，我们考虑了三种情况：（情况 1）同时考虑应变率和绝热加热效应；（情况 2）仅考虑应变率效应；以及（情况 3）忽略应变率和绝热加热效应。我们针对在试验中观察到延性-脆性复合断裂的场景进行了 FE 模拟，具体而言，CVN 试验在 -90°C 下进行，DWTT 试验在 -40°C 下进行。

Figure 19(a) displays the CVN simulation results for the three cases described earlier. In our previous work (Seo et al., 2024), it was determined that the maximum load increases by about 10 % due to the strain rate effect but decreases by about 5 % due to the adiabatic heating effect in CVN test simulations for fully ductile fracture scenarios. For combined ductile-brittle fracture simulations, the maximum load decreases by 5 % due to the adiabatic heating effect, displaying a trend similar to that observed in ductile fracture. However, the strain rate effect on the maximum load is more pronounced, showing an increase of 15 %. The sudden load drop due to brittle fracture is accelerated when adiabatic heating is not considered (Cases 2 and 3 in Fig. 19(a)). This occurs because adiabatic heating softens the material and reduces the principal stress, aligning with findings from previous research (Petti and Dodds, 2005, Gao et al., 2006, Wasiluk et al., 2006). Notably, Petti et al. (Petti and Dodds, 2005), Gao et al. (Wasiluk et al., 2006), and Wasiluk et al. (Wasiluk et al., 2006) found that the Weibull stress σ_u increases with rising temperature under quasi-static conditions. Therefore, adiabatic heating contributes to delaying the initiation of brittle cracks.
图 19(a) 显示了前面描述的三种情况的 CVN 模拟结果。在我们之前的研究（Seo 等，2024）中，我们发现，在完全延性断裂场景的 CVN 试验模拟中，应变速率效应会使最大载荷增加约 10%，而绝热加热效应会使最大载荷降低约 5%。对于延性-脆性断裂组合模拟，绝热加热效应会使最大载荷降低 5%，呈现出与延性断裂中观察到的趋势类似的趋势。然而，应变速率对最大载荷的影响更为明显，增加了 15%。当不考虑绝热加热时，脆性断裂导致的载荷突然下降会加速（图 19(a) 中的情况 2 和 3）。这是因为绝热加热会使材料软化并降低主应力，这与先前研究的结果一致（Petti 和 Dodds，2005 年；Gao 等，2006 年；Wasiluk 等，2006 年）。值得注意的是，Petti 等（Petti 和 Dodds，2005 年）、Gao 等（Wasiluk 等，2006 年）和 Wasiluk 等（Wasiluk 等，2006 年）发现，在准静态条件下，威布尔应力 σ _u 会随着温度升高而增大。因此，绝热加热有助于延缓脆性裂纹的萌生。

Figure 19(b) shows the DWTT simulation results for the three cases. The maximum load increases by about 10 % due to the strain rate effect and decreases by 10 % due to the adiabatic heating effect. In the CVN simulation, brittle fracture was delayed due to the adiabatic heating effect. However, in the DWTT test, this delay was not observed. This discrepancy may be attributed to the difference in specimen size between the CVN and DWTT tests. In both tests, the impacted surface was compressed, and the compressive plastic strain raised the specimen's temperature due to the adiabatic heating effect. The temperature increase is more pronounced in CVN specimens compared to DWTT specimens, due to the smaller size of the CVN specimens, as shown in Fig. 20. However, the temperature rise at the crack tip is similar in both tests. During the impact simulation, the temperature increased by approximately 150 °C. The estimated temperature rise closely matches the measured value of 150 °C in CVN test, reported in (Tanguy et al., 2005). Similarly, our previous work also observed a similar temperature increase (Seo et al., 2024). The occurrence of brittle fracture is not affected by the temperature rise during the impact simulation. The difference becomes more noticeable as the displacement increases. Consequently, the adiabatic heating effect is less significant in the DWTT test simulation.
图 19(b)显示了三种情况下的 DWTT 模拟结果。由于应变速率效应，最大载荷增加了约 10%，而由于绝热加热效应，最大载荷降低了 10%。在 CVN 模拟中，由于绝热加热效应，脆性断裂被延迟。然而，在 DWTT 试验中，并未观察到这种延迟。这种差异可能归因于 CVN 和 DWTT 试验之间试样尺寸的差异。在两种试验中，受冲击表面都被压缩，压缩塑性应变由于绝热加热效应使试样的温度升高。由于 CVN 试样尺寸较小，CVN 试样的温度升高比 DWTT 试样更明显，如图 20 所示。然而，两种试验中裂纹尖端的温升相似。在冲击模拟过程中，温度升高了约 150℃。估算的温升与 CVN 试验中测量的 150°C 值非常接近，该值已在 Tanguy 等人，2005 年发表的论文中报道过。同样，我们之前的研究也观察到了类似的温升（Seo 等人，2024 年）。冲击模拟过程中的温升对脆性断裂的发生没有影响。随着位移的增加，这种差异变得更加明显。因此，在 DWTT 试验模拟中，绝热加热效应不太显著。

8. CONCLUSION

This paper presents the finite element (FE) impact simulation of combined ductile-brittle fracture for API X85 under impact loading. The simulation incorporates the effects of strain rate and adiabatic heating on deformation and fracture, which are crucial for accurately modeling fracture behavior under high strain rates. For the models, deformation and ductile fracture under impact loading are simulated using the J-C deformation and fracture strain models, respectively, while brittle fracture under impact load is simulated using the critical stress model. The parameters in the deformation and fracture models were determined through the following methods:

(1)
The temperature-dependent parameters in the J-C models are determined using smooth round bar (SRB) tests conducted at various temperatures under quasi-static conditions.
(2)
The strain rate-dependent parameters in the J-C models were obtained through a CVN test performed at room temperature (RT).
(3)
The critical stress fracture model was calibrated from CVN simulations using the determined J-C models.

The determined deformation and combined fracture models were applied to simulate CVN and Drop Weight Tear Test (DWTT) at various temperatures ranging from -120 °C to room temperature (RT). For the CVN test, the combined ductile-brittle fracture mode was observed at a temperature lower than -60 °C, while a purely ductile fracture mode was observed at higher temperatures. In contrast, for the DWTT, the combined ductile-brittle fracture mode was observed at temperatures below 0 °C. The simulation incorporated the effects of strain rate and adiabatic heating. The deformation behavior, load-displacement curves, and fractured surfaces obtained from the simulation were compared with experimental data, demonstrating good agreement across all cases.

The key contribution of this study, different from previous works (Kim et al., 2020, Kim et al., 2021), is the consideration of both strain rate and adiabatic heating effects. The strain rate in CVN and DWTT exceeds 1,000 /s, and the temperature can increase more than 150°C. By accounting for both effects, their influence on combined ductile-brittle fracture simulation is analyzed in this study. The effects of adiabatic heating and strain rate were also analyzed through sensitivity analysis. The adiabatic heating effect influences the occurrence of brittle fractures. In the CVN test, brittle fracture is delayed due to the thermal softening caused by adiabatic heating. This delay is found to be more significant in CVN simulations than in DWTT simulations, likely because the CVN specimen is much smaller than the DWTT specimen. In conclusion, the adiabatic heating effect plays a more significant role in smaller specimen tests. Finally, the effect of element size on key numerical parameters for simulating combined fracture under impact loading has been also analyzed. The critical stress for brittle fracture (σ_c) was dependent on element size and its dependence could be quantified using the proposed elastic energy absorption in Eq. (13).

CRediT authorship contribution statement

Ki-Wan Seo: Writing – original draft, Visualization, Formal analysis, Conceptualization. Jae-Yoon Kim: Resources, Formal analysis. Yun-Jae Kim: Writing – review & editing, Validation, Supervision, Project administration.

Declaration of competing interest

Please check the following as appropriate: All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version. - checked

This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.- checked

The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript - checked

The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:- None

References

Kristoffersen et al., 2013
M. Kristoffersen, T. Børvik, I. Westermann, M. Langseth, OS. Hopperstad
Impact against X65 steel pipes – An experimental investigation
Int J Solids Struct, 50 (2013), pp. 3430-3445, 10.1016/J.IJSOLSTR.2013.06.013
View PDF View article View in Scopus Google Scholar
Eiber, 1965
R J Eiber
Correlation of full-scale tests with laboratory tests
Proc. AGA Symposium on line-pipe research, American Gas Association, Dallas (1965), pp. 83-118
pp
Google Scholar
Wang and Ru, 2016
Y.J. Wang, CQ. Ru
Determination of two key parameters of a cohesive zone model for pipeline steels based on uniaxial stress-strain curve
Eng Fract Mech, 163 (2016), pp. 55-65, 10.1016/j.engfracmech.2016.06.017
View PDF View article Google Scholar
Yu and Ru, 2015
P.S. Yu, CQ. Ru
Strain rate effects on dynamic fracture of pipeline steels: finite element simulation
Int J Press Vessels Pip, 126–127 (2015), pp. 1-7
View PDF View article Crossref Google Scholar
Gu and Wang, 2022
T. Gu, Z. Wang
A strain rate-dependent cohesive zone model for shear failure of hat-shaped specimens under impact
Eng. Fract. Mech., 259 (2022), Article 108145, 10.1016/J.ENGFRACMECH.2021.108145
View PDF View article View in Scopus Google Scholar
May et al., 2015
M. May, O. Hesebeck, S. Marzi, W.B ̈ohme, J. Lienhard, S. Kilchert, M. Brede, S. Hiermaier
Rate dependent behavior of crash-optimized adhesives–experimental characterization, model development, and simulation
Eng. Fract. Mech., 133 (2015), pp. 112-137, 10.1016/J.ENGFRACMECH.2014.11.006
View PDF View article View in Scopus Google Scholar
Chandran et al., 2022
S. Chandran, W. Liu, J. Lian, S. Münstermann, P. Verleysen
Strain rate dependent plasticity and fracture of DP1000 steel under proportional and non-proportional loading
Eur J Mech - A/solids, 92 (2022), Article 104446, 10.1016/J.EUROMECHSOL.2021.104446
View PDF View article View in Scopus Google Scholar
Rousselier, 1987
G. Rousselier
Ductile fracture models and their potential in local approach of fracture
Nucl Eng Des, 105 (1987), pp. 97-111, 10.1016/0029-5493(87)90234-2
View PDF View article View in Scopus Google Scholar
Tanguy and Besson, 2002
B. Tanguy, J. Besson
An extension of the Rousselier model to viscoplastic temperature dependent materials
Int J of Fract, 116 (2002), pp. 81-101, 10.1023/A:1020192527733
View at publisher
View in Scopus Google Scholar
Tanguy et al., 2005
B. Tanguy, J. Besson, R. Piques, A. Pineau
Ductile to brittle transition of an A508 steel characterized by Charpy impact test: Part I: experimental results
Eng Fract Mech, 72 (2005), pp. 49-72, 10.1016/j.engfracmech.2004.03.010
View PDF View article View in Scopus Google Scholar
Tanguy et al., 2005
B. Tanguy, J. Besson, R. Piques, A. Pineau
Ductile to brittle transition of an A508 steel characterized by Charpy impact test: Part II: modeling of the Charpy transition curve
Eng Fract Mech, 72 (2005), pp. 413-434, 10.1016/j.engfracmech.2004.03.011
View PDF View article View in Scopus Google Scholar
Dey et al., 2004
S. Dey, T. Børvik, O.S. Hopperstad, J.R. Leinum, M. Langseth
The effect of target strength on the perforation of steel plates using three different projectile nose shapes
Int. J. Impact Eng, 30 (2004), pp. 1005-1038, 10.1016/J.IJIMPENG.2004.06.004
View PDF View article View in Scopus Google Scholar
Dey et al., 2006
S. Dey, T. Børvik, O.S. Hopperstad, M. Langseth
On the influence of fracture criterion in projectile impact of steel plates
Comput. Mater. Sci, 38 (2006), pp. 176-191, 10.1016/J.COMMATSCI.2006.02.003
View PDF View article View in Scopus Google Scholar
Dey et al., 2007
S. Dey, T. Børvik, O.S. Hopperstad, M. Langseth
On the influence of constitutive relation in projectile impact of steel plates
Int. J. Impact Eng, 34 (2007), pp. 464-486, 10.1016/J.IJIMPENG.2005.10.003
View PDF View article View in Scopus Google Scholar
Banerjee et al., 2015
A. Banerjee, S. Dhar, S. Acharyya, D. Datta, N. Nayak
Determination of Johnson cook material and failure model constants and numerical modelling of Charpy impact test of armour steel
Mater. Sci. Eng. A, 640 (2015), pp. 200-209, 10.1016/J.MSEA.2015.05.073
View PDF View article Google Scholar
Mirone et al., 2024
G. Mirone, R. Barbagallo, L. Corallo
Combined rate-temperature effects in postnecking plasticity of A2-70 stainless steel
Int J Mech Sci, 262 (2024), Article 108754, 10.1016/j.ijmecsci.2023.108754
View PDF View article View in Scopus Google Scholar
Seo et al., 2024
K.W. Seo, J.Y. Kim, Y.J. Kim, KS. Kim
Finite Element Ductile Fracture Simulation of Charpy and Drop Weight Tear Tests for API X52
Theor Appl Fract Mech, 133 (2024), Article 104629, 10.1016/j.tafmec.2024.104629
View PDF View article View in Scopus Google Scholar
Chu et al., 2019
D. Chu, X. Li, Z. Liu, et al.
A unified phase field damage model for modeling the brittle-ductile dynamic failure mode transition in metals
Eng Fract Mech, 212 (2019), pp. 197-209, 10.1016/j.engfracmech.2019.03.031
View PDF View article View in Scopus Google Scholar
Samaniego et al., 2021
C. Samaniego, J. Ulloa, P. Rodríguez, G. Houzeaux, M. Vázquez, E. Samaniego
A phase-field model for ductile fracture with shear bands: A parallel implementation
Int J Mech Sci, 200 (2021), Article 106424, 10.1016/j.ijmecsci.2021.106424
View PDF View article View in Scopus Google Scholar
Zhang et al., 2024
Y. Zhang, H. Han, G. Huang, T. Wang
A three-dimensional coupled thermo-elastic-plastic phase field model for the brittle-ductile failure mode transition of metals
Int J Impact Eng, 193 (2024), Article 105062, 10.1016/j.ijimpeng.2024.105062
View PDF View article View in Scopus Google Scholar
Hojo et al., 2016
K. Hojo, N. Ogawa, T. Hirota, K. Yoshimoto, Y. Nagoshi, S. Kawabata
Application of Coupled Damage and Beremin Model to Ductile-Brittle Transition Temperature Region Considering Constraint Effect
Procedia Struct Integr, 2 (2016), pp. 1643-1651, 10.1016/j.prostr.2016.06.208
View PDF View article View in Scopus Google Scholar
Beremin et al., 1983
F.M. Beremin, A. Pineau, F. Mudry, J-C Devaux, Y. D'Escatha, P. Ledermann
A local criterion for cleavage fracture of a nuclear pressure vessel steel
Metall Trans A, 14 (1983), pp. 2277-2287, 10.1007/BF02663302
View at publisher
View in Scopus Google Scholar
Gurson, 1977
AL. Gurson
Continuum theory of ductile rupture by void nucleation and growth: Part 1 - yield criteria and flow rules for porous ductile media
J. Eng. Mater. Technol. Trans. ASME., 99 (10) (1977), pp. 2-15, 10.1115/1.3443401
View at publisherView in Scopus Google Scholar
Tvergaard and Needleman, 1984
V. Tvergaard, A. Needleman
Analysis of the cup-cone fracture in a round tensile bar
Acta Metall, 32 (1) (1984), pp. 157-169, 10.1016/0001-6160(84)90213-X
View PDF View article View in Scopus Google Scholar
Koplik and Needleman, 1988
J. Koplik, A. Needleman
Void growth and coalescence in porous plastic solids
Int. J. Solids Struct., 24 (8) (1988), pp. 835-853, 10.1016/0020-7683(88)90051-0
View PDF View article View in Scopus Google Scholar
Batra and Lear, 2004
R.C. Batra, M.H. Lear
Simulation of brittle and ductile fracture in an impact loaded prenotched plate
Int. J. Fract., 126 (2004), pp. 179-203, 10.1023/B:FRAC.0000026364.13365.71
View at publisher
View in Scopus Google Scholar
Lin et al., 2022
M. Lin, H. Yu, Y. Ding, V. Olden, A. Alvaro, J. He, et al.
Simulation of ductile-to-brittle transition combining complete Gurson model and CZM with application to hydrogen embrittlement
Eng Fract Mech, 268 (2022), Article 108511, 10.1016/j.engfracmech.2022.108511
View PDF View article View in Scopus Google Scholar
Chakraborty and Biner, 2014
P. Chakraborty, SB. Biner
A unified cohesive zone approach to model the ductile to brittle transition of fracture toughness in reactor pressure vessel steels
Eng Fract Mech, 131 (2014), pp. 194-209, 10.1016/j.engfracmech.2014.07.029
View PDF View article View in Scopus Google Scholar
Kim et al., 2022
J-S Kim, J-H Jang, Y-J Kim, K-S. Kim
Quantification of notch type and specimen thickness effects on ductile and brittle fracture behaviour of drop weight tear test
Eur J Mech A Solids, 92 (2022), Article 104466, 10.1016/j.euromechsol.2021.104466
View PDF View article View in Scopus Google Scholar
Seo et al., 2023
K-W Seo, Y-J Kim, J-H Hwang, K-S. Kim
Finite element simulation method for combined Ductile-Brittle fracture of small punch test in hydrogen
Eng Fract Mech, 289 (2023), Article 109489, 10.1016/j.engfracmech.2023.109489
View PDF View article View in Scopus Google Scholar
Hwang et al., 2024
J-H Hwang, K-W Seo, Y-J Kim, K-S. Kim
Fracture-toughness estimation from small-punch test in hydrogen exhibiting ductile and ductile–brittle fracture modes
Eur J Mech A Solids, 103 (2024), Article 105193, 10.1016/j.euromechsol.2023.105193
View PDF View article View in Scopus Google Scholar
Camacho and Ortiz, 1997
G.T. Camacho, M. Ortiz
Adaptive Lagrangian modelling of ballistic penetration of metallic targets
Comput Methods Appl Mech Eng, 142 (1997), pp. 269-301, 10.1016/S0045-7825(96)01134-6
View PDF View article View in Scopus Google Scholar
Gerstgrasser et al., 2021
M. Gerstgrasser, D. Smolenicki, M. Akbari, H. Klippel, H. Roelofs, E. Cadoni, et al.
Analysis of two parameter identification methods for original and modified Johnson-Cook fracture strains, including numerical comparison and validation of a new blue-brittle dependent fracture model for free-cutting steel 50SiB8
Theor Appl Fract Mech, 112 (2021), Article 102905, 10.1016/J.TAFMEC.2021.102905
View PDF View article View in Scopus Google Scholar
Borvik et al., 2001
T. Borvik, O.S. Hopperstad, T. Berstad, M. Langseth
A computational model of viscoplasticity and ductile damage for impact and penetration
Eur J Mech - A/Solids, 20 (2001), pp. 685-712, 10.1016/S0997-7538(01)01157-3
View PDF View article View in Scopus Google Scholar
Chanda, 2015
Chanda, Sourayon. Temperature effects on dynamic fracture of pipeline steel. 2015. https://doi-org.ezproxy.lib.kyushu-u.ac.jp/10.7939/R3695Q
Google Scholar
Gambirasio and Rizzi, 2016
L. Gambirasio, E. Rizzi
An enhanced Johnson–Cook strength model for splitting strain rate and temperature effects on lower yield stress and plastic flow
Comput Mater Sci, 113 (2016), pp. 231-265, 10.1016/J.COMMATSCI.2015.11.034
View PDF View article View in Scopus Google Scholar
Seo et al., 2022
K-W Seo, J-H Hwang, Y-J Kim, K-S Kim, P-S. Lam
Fracture toughness prediction of hydrogen-embrittled materials using small punch test data in Hydrogen
Int J Mech Sci, 225 (2022), Article 107371, 10.1016/j.ijmecsci.2022.107371
View PDF View article View in Scopus Google Scholar
Seo et al., 2024
K-W Seo, Y-J Kim, K-S. Kim
Quantification of pre-strain effect on ductile fracture and application to irradiation embrittlement problems
Eng Fract Mech, 300 (2024), Article 109986, 10.1016/j.engfracmech.2024.109986
View PDF View article View in Scopus Google Scholar
Kim et al., 2011
N-H Kim, C-S Oh, Y-J Kim, K-B Yoon, Y-H. Ma
Comparison of fracture strain based ductile failure simulation with experimental results
Int J Press Vessels Pip, 88 (2011), pp. 434-447, 10.1016/j.ijpvp.2011.07.006
View PDF View article View in Scopus Google Scholar
Oh et al., 2011
C-S Oh, N-H Kim, Y-J Kim, J-H Baek, Y-P Kim, W-S. Kim
A finite element ductile failure simulation method using stress-modified fracture strain model
Eng Fract Mech, 78 (2011), pp. 124-137, 10.1016/j.engfracmech.2010.10.004
View PDF View article View in Scopus Google Scholar
Jeon et al., 2016
J-Y Jeon, Y-J Kim, S-Y Lee, J-W. Kim
Extracting ductile fracture toughness from small punch test data using numerical modeling
Int J Press Vessels Pip, 139–140 (2016), pp. 204-219, 10.1016/j.ijpvp.2016.02.011
View PDF View article View in Scopus Google Scholar
Kim et al., 2020
J-S Kim, Y-J Kim, M-W Lee, K-S Kim, K. Shibanuma
Fracture simulation model for API X80 Charpy test in Ductile-Brittle transition temperatures
Int J Mech Sci, 182 (2020), Article 105771, 10.1016/j.ijmecsci.2020.105771
View PDF View article View in Scopus Google Scholar
Jung et al., 2014
D-H Jung, J-K Kwon, N-S Woo, Y-J Kim, M. Goto, S. Kim
S–N Fatigue and Fatigue Crack Propagation Behaviors of X80 Steel at Room and Low Temperatures
Metall Mater Trans A, 45 (2014), pp. 654-662, 10.1007/s11661-013-2012-4
View at publisher
View in Scopus Google Scholar
Heier et al., June 2013
Espen Heier, Erling Østby, Odd M. Akselsen
Reeling Installation of Rigid Steel Pipelines at Low Temperature
Paper presented at the The Twenty-third International Offshore and Polar Engineering Conference, Anchorage, Alaska (June 2013)
Google Scholar
Akselsen et al., June 2012
Odd M. Akselsen, Erling Østby, Bård Nyhus
Low Temperature Fracture Toughness of X80 Girth Welds
Paper presented at the The Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece (June 2012)
Google Scholar
Kim et al., 2024
J-Y Kim, K-W Seo, Y-J Kim, K-S. Kim
Fracture analysis of hydrogen-embrittled API X52 pipes at low temperature
Int J Mech Sci, 276 (2024), Article 109374, 10.1016/j.ijmecsci.2024.109374
View PDF View article View in Scopus Google Scholar
BSI 2014
BSI
BS 8571 2014 - Method of test for determination of fracture toughness in metallic materials using single edge notched tension (SENT) specimens
BSI; (2014)
Google Scholar
Institute, 2007
AP. Institute
API 5L Specification for line pipe
Api Spec, 5L (2007)
Google Scholar
Tu et al., 2022
S. Tu, S. Suzuki, Z. Yu, K. Shibanuma
Hybrid experimental-numerical strategy for efficiently and accurately identifying post-necking hardening and ductility diagram parameters
Int J Mech Sci, 219 (2022), Article 107074, 10.1016/J.IJMECSCI.2022.107074
View PDF View article View in Scopus Google Scholar
ABAQUS Version 2018
ABAQUS Version
User's manual. Dassault Systems
Inc (2018), p. 2018
Google Scholar
Origin(Pro), Version 2020
Origin(Pro), Version 2020. OriginLab Corporation, Northampton, MA, USA.
Google Scholar
Talemi et al., 2019
R. Talemi, S. Cooreman, H. Mahgerefteh, S. Martynov, S. Brown
A fully coupled fluid-structure interaction simulation of three-dimensional dynamic ductile fracture in a steel pipeline
Theor. Appl. Fract. Mech., 101 (2019), pp. 224-235, 10.1016/J.TAFMEC.2019.02.005
View PDF View article View in Scopus Google Scholar
Yan et al., 2014
C. Yan, C. Liu, B. Yan
3D modeling of the hydrogen distribution in X80 pipeline steel welded joints
Comput Mater Sci, 83 (2014), pp. 158-163, 10.1016/J.COMMATSCI.2013.11.007
View PDF View article View in Scopus Google Scholar
Tronskar et al., 2002
J.P. Tronskar, M.A. Mannan, Lai MO
Measurement of fracture initiation toughness and crack resistance in instrumented Charpy impact testing
Eng Fract Mech, 69 (2002), pp. 321-338, 10.1016/S0013-7944(01)00077-7
View PDF View article View in Scopus Google Scholar
Kobayashi, 1984
T. Kobayashi
Analysis of impact properties of A533 steel for nuclear reactor pressure vessel by instrumented Charpy test
Eng Fract Mech, 19 (1984), pp. 49-65, 10.1016/0013-7944(84)90068-7
View PDF View article View in Scopus Google Scholar
Oulad Brahim et al., 2022
A. Oulad Brahim, I. Belaidi, N. Fahem, S. Khatir, S. Mirjalili, M. Abdel Wahab
Prediction of the peak load and crack initiation energy of dynamic brittle fracture in X70 steel pipes using an improved artificial neural network and extended Finite Element Method
Theor Appl Fract Mech, 122 (2022), Article 103627, 10.1016/J.TAFMEC.2022.103627
View PDF View article View in Scopus Google Scholar
Seo et al., 2022
K-W Seo, J-H Hwang, Y-J Kim, K-S Kim, P-S. Lam
Fracture toughness prediction of hydrogen-embrittled materials using small punch test data in Hydrogen
Int J Mech Sci, 225 (2022), Article 107371, 10.1016/j.ijmecsci.2022.107371
View PDF View article View in Scopus Google Scholar
Seo et al., 2024
K-W Seo, Y-J Kim, K-S. Kim
Quantification of pre-strain effect on ductile fracture and application to irradiation embrittlement problems
Eng Fract Mech, 300 (2024), Article 109986, 10.1016/j.engfracmech.2024.109986
View PDF View article View in Scopus Google Scholar
Kim et al., 2011
N-H Kim, C-S Oh, Y-J Kim, K-B Yoon, Y-H. Ma
Comparison of fracture strain based ductile failure simulation with experimental results
Int J Press Vessels Pip, 88 (2011), pp. 434-447, 10.1016/j.ijpvp.2011.07.006
View PDF View article View in Scopus Google Scholar
ASTM Standard E436-03 2021
ASTM Standard E436-03
Standard Test Method for Drop-Weight Tear Tests of Ferritic Steels
(2021)
Google Scholar
Kim et al., 2021
J-S Kim, Y-J Kim, M-W Lee, K-S Kim, K. Shibanuma
Finite element simulation of drop-weight tear test of API X80 at ductile-brittle transition temperatures
Int J Mech Sci, 191 (2021), Article 106103, 10.1016/j.ijmecsci.2020.106103
View PDF View article Google Scholar
Kim et al., 2022
J-S Kim, Y-J Kim, M-W Lee, K-S Kim, K. Shibanuma
Numerical method to characterize probabilistic energy distribution of drop weight tear test at Ductile-Brittle transition temperatures
Eng Fract Mech, 269 (2022), Article 108540, 10.1016/j.engfracmech.2022.108540
View PDF View article View in Scopus Google Scholar
Petti and Dodds, 2005
J.P. Petti, RH. Dodds
Calibration of the Weibull stress scale parameter, σu, using the Master Curve
Eng Fract Mech, 72 (2005), pp. 91-120, 10.1016/j.engfracmech.2004.03.009
View PDF View article View in Scopus Google Scholar
Gao et al., 2006
X. Gao, G. Zhang, TS. Srivatsan
A probabilistic model for prediction of cleavage fracture in the ductile-to-brittle transition region and the effect of temperature on model parameters
Mater Sci Eng, 415 (2006), pp. 264-272, 10.1016/j.msea.2005.09.098
View PDF View article View in Scopus Google Scholar
Wasiluk et al., 2006
B. Wasiluk, J.P. Petti, RH. Dodds
Temperature dependence of Weibull stress parameters: Studies using the Euro-material
Eng Fract Mech, 73 (2006), pp. 1046-1069, 10.1016/j.engfracmech.2005.11.006
View PDF View article View in Scopus Google Scholar
Uenishi et al., 2011
A. Uenishi, H. Yoshida, S. Yonemura, S. Hiwatashi, S. Hirose, N. Suzuki
High Strain Rate Properties of High Strength Steel Sheets
Int J Automot Eng, 2 (2011), pp. 109-113, 10.20485/jsaeijae.2.4_109
Google Scholar
Vaynman et al., 2006
S. Vaynman, M.E. Fine, S. Lee, HD. Espinosa
Effect of strain rate and temperature on mechanical properties and fracture mode of high strength precipitation hardened ferritic steels
Scr Mater, 55 (2006), pp. 351-354, 10.1016/J.SCRIPTAMAT.2006.04.029
View PDF View article View in Scopus Google Scholar
Soares and Hokka, 2021
G.C. Soares, M. Hokka
The Taylor–Quinney coefficients and strain hardening of commercially pure titanium, iron, copper, and tin in high rate compression
Int J Impact Eng, 156 (2021), Article 103940, 10.1016/J.IJIMPENG.2021.103940
View PDF View article View in Scopus Google Scholar
Rittel et al., 2017
D. Rittel, L.H. Zhang, S. Osovski
The dependence of the Taylor–Quinney coefficient on the dynamic loading mode
J Mech Phys Solids, 107 (2017), pp. 96-114, 10.1016/J.JMPS.2017.06.016
View PDF View article View in Scopus Google Scholar

Cited by (0)

[1] Kristoffersen et al., 2013
M. Kristoffersen, T. Børvik, I. Westermann, M. Langseth, OS. Hopperstad
Impact against X65 steel pipes – An experimental investigation
Int J Solids Struct, 50 (2013), pp. 3430-3445, 10.1016/J.IJSOLSTR.2013.06.013
View PDF View article View in Scopus Google Scholar

[2] Eiber, 1965
R J Eiber
Correlation of full-scale tests with laboratory tests
Proc. AGA Symposium on line-pipe research, American Gas Association, Dallas (1965), pp. 83-118
pp
Google Scholar

[3] Wang and Ru, 2016
Y.J. Wang, CQ. Ru
Determination of two key parameters of a cohesive zone model for pipeline steels based on uniaxial stress-strain curve
Eng Fract Mech, 163 (2016), pp. 55-65, 10.1016/j.engfracmech.2016.06.017
View PDF View article Google Scholar

[4] Yu and Ru, 2015
P.S. Yu, CQ. Ru
Strain rate effects on dynamic fracture of pipeline steels: finite element simulation
Int J Press Vessels Pip, 126–127 (2015), pp. 1-7
View PDF View article Crossref Google Scholar

[5] Gu and Wang, 2022
T. Gu, Z. Wang
A strain rate-dependent cohesive zone model for shear failure of hat-shaped specimens under impact
Eng. Fract. Mech., 259 (2022), Article 108145, 10.1016/J.ENGFRACMECH.2021.108145
View PDF View article View in Scopus Google Scholar

[6] May et al., 2015
M. May, O. Hesebeck, S. Marzi, W.B ̈ohme, J. Lienhard, S. Kilchert, M. Brede, S. Hiermaier
Rate dependent behavior of crash-optimized adhesives–experimental characterization, model development, and simulation
Eng. Fract. Mech., 133 (2015), pp. 112-137, 10.1016/J.ENGFRACMECH.2014.11.006
View PDF View article View in Scopus Google Scholar

[7] Chandran et al., 2022
S. Chandran, W. Liu, J. Lian, S. Münstermann, P. Verleysen
Strain rate dependent plasticity and fracture of DP1000 steel under proportional and non-proportional loading
Eur J Mech - A/solids, 92 (2022), Article 104446, 10.1016/J.EUROMECHSOL.2021.104446
View PDF View article View in Scopus Google Scholar

[8] Rousselier, 1987
G. Rousselier
Ductile fracture models and their potential in local approach of fracture
Nucl Eng Des, 105 (1987), pp. 97-111, 10.1016/0029-5493(87)90234-2
View PDF View article View in Scopus Google Scholar

[9] Tanguy and Besson, 2002
B. Tanguy, J. Besson
An extension of the Rousselier model to viscoplastic temperature dependent materials
Int J of Fract, 116 (2002), pp. 81-101, 10.1023/A:1020192527733
View at publisher
View in Scopus Google Scholar

[10] Tanguy et al., 2005
B. Tanguy, J. Besson, R. Piques, A. Pineau
Ductile to brittle transition of an A508 steel characterized by Charpy impact test: Part I: experimental results
Eng Fract Mech, 72 (2005), pp. 49-72, 10.1016/j.engfracmech.2004.03.010
View PDF View article View in Scopus Google Scholar

[11] Tanguy et al., 2005
B. Tanguy, J. Besson, R. Piques, A. Pineau
Ductile to brittle transition of an A508 steel characterized by Charpy impact test: Part II: modeling of the Charpy transition curve
Eng Fract Mech, 72 (2005), pp. 413-434, 10.1016/j.engfracmech.2004.03.011
View PDF View article View in Scopus Google Scholar

[12] Dey et al., 2004
S. Dey, T. Børvik, O.S. Hopperstad, J.R. Leinum, M. Langseth
The effect of target strength on the perforation of steel plates using three different projectile nose shapes
Int. J. Impact Eng, 30 (2004), pp. 1005-1038, 10.1016/J.IJIMPENG.2004.06.004
View PDF View article View in Scopus Google Scholar

[13] Dey et al., 2006
S. Dey, T. Børvik, O.S. Hopperstad, M. Langseth
On the influence of fracture criterion in projectile impact of steel plates
Comput. Mater. Sci, 38 (2006), pp. 176-191, 10.1016/J.COMMATSCI.2006.02.003
View PDF View article View in Scopus Google Scholar

[14] Dey et al., 2007
S. Dey, T. Børvik, O.S. Hopperstad, M. Langseth
On the influence of constitutive relation in projectile impact of steel plates
Int. J. Impact Eng, 34 (2007), pp. 464-486, 10.1016/J.IJIMPENG.2005.10.003
View PDF View article View in Scopus Google Scholar

[15] Banerjee et al., 2015
A. Banerjee, S. Dhar, S. Acharyya, D. Datta, N. Nayak
Determination of Johnson cook material and failure model constants and numerical modelling of Charpy impact test of armour steel
Mater. Sci. Eng. A, 640 (2015), pp. 200-209, 10.1016/J.MSEA.2015.05.073
View PDF View article Google Scholar

[16] Mirone et al., 2024
G. Mirone, R. Barbagallo, L. Corallo
Combined rate-temperature effects in postnecking plasticity of A2-70 stainless steel
Int J Mech Sci, 262 (2024), Article 108754, 10.1016/j.ijmecsci.2023.108754
View PDF View article View in Scopus Google Scholar

[17] Seo et al., 2024
K.W. Seo, J.Y. Kim, Y.J. Kim, KS. Kim
Finite Element Ductile Fracture Simulation of Charpy and Drop Weight Tear Tests for API X52
Theor Appl Fract Mech, 133 (2024), Article 104629, 10.1016/j.tafmec.2024.104629
View PDF View article View in Scopus Google Scholar

[18] Chu et al., 2019
D. Chu, X. Li, Z. Liu, et al.
A unified phase field damage model for modeling the brittle-ductile dynamic failure mode transition in metals
Eng Fract Mech, 212 (2019), pp. 197-209, 10.1016/j.engfracmech.2019.03.031
View PDF View article View in Scopus Google Scholar

[19] Samaniego et al., 2021
C. Samaniego, J. Ulloa, P. Rodríguez, G. Houzeaux, M. Vázquez, E. Samaniego
A phase-field model for ductile fracture with shear bands: A parallel implementation
Int J Mech Sci, 200 (2021), Article 106424, 10.1016/j.ijmecsci.2021.106424
View PDF View article View in Scopus Google Scholar

[20] Zhang et al., 2024
Y. Zhang, H. Han, G. Huang, T. Wang
A three-dimensional coupled thermo-elastic-plastic phase field model for the brittle-ductile failure mode transition of metals
Int J Impact Eng, 193 (2024), Article 105062, 10.1016/j.ijimpeng.2024.105062
View PDF View article View in Scopus Google Scholar

[21] Hojo et al., 2016
K. Hojo, N. Ogawa, T. Hirota, K. Yoshimoto, Y. Nagoshi, S. Kawabata
Application of Coupled Damage and Beremin Model to Ductile-Brittle Transition Temperature Region Considering Constraint Effect
Procedia Struct Integr, 2 (2016), pp. 1643-1651, 10.1016/j.prostr.2016.06.208
View PDF View article View in Scopus Google Scholar

[22] Beremin et al., 1983
F.M. Beremin, A. Pineau, F. Mudry, J-C Devaux, Y. D'Escatha, P. Ledermann
A local criterion for cleavage fracture of a nuclear pressure vessel steel
Metall Trans A, 14 (1983), pp. 2277-2287, 10.1007/BF02663302
View at publisher
View in Scopus Google Scholar

[23] Gurson, 1977
AL. Gurson
Continuum theory of ductile rupture by void nucleation and growth: Part 1 - yield criteria and flow rules for porous ductile media
J. Eng. Mater. Technol. Trans. ASME., 99 (10) (1977), pp. 2-15, 10.1115/1.3443401
View at publisherView in Scopus Google Scholar

[24] Tvergaard and Needleman, 1984
V. Tvergaard, A. Needleman
Analysis of the cup-cone fracture in a round tensile bar
Acta Metall, 32 (1) (1984), pp. 157-169, 10.1016/0001-6160(84)90213-X
View PDF View article View in Scopus Google Scholar

[25] Koplik and Needleman, 1988
J. Koplik, A. Needleman
Void growth and coalescence in porous plastic solids
Int. J. Solids Struct., 24 (8) (1988), pp. 835-853, 10.1016/0020-7683(88)90051-0
View PDF View article View in Scopus Google Scholar

[26] Batra and Lear, 2004
R.C. Batra, M.H. Lear
Simulation of brittle and ductile fracture in an impact loaded prenotched plate
Int. J. Fract., 126 (2004), pp. 179-203, 10.1023/B:FRAC.0000026364.13365.71
View at publisher
View in Scopus Google Scholar

[27] Lin et al., 2022
M. Lin, H. Yu, Y. Ding, V. Olden, A. Alvaro, J. He, et al.
Simulation of ductile-to-brittle transition combining complete Gurson model and CZM with application to hydrogen embrittlement
Eng Fract Mech, 268 (2022), Article 108511, 10.1016/j.engfracmech.2022.108511
View PDF View article View in Scopus Google Scholar

[28] Chakraborty and Biner, 2014
P. Chakraborty, SB. Biner
A unified cohesive zone approach to model the ductile to brittle transition of fracture toughness in reactor pressure vessel steels
Eng Fract Mech, 131 (2014), pp. 194-209, 10.1016/j.engfracmech.2014.07.029
View PDF View article View in Scopus Google Scholar

[29] Kim et al., 2022
J-S Kim, J-H Jang, Y-J Kim, K-S. Kim
Quantification of notch type and specimen thickness effects on ductile and brittle fracture behaviour of drop weight tear test
Eur J Mech A Solids, 92 (2022), Article 104466, 10.1016/j.euromechsol.2021.104466
View PDF View article View in Scopus Google Scholar

[30] Seo et al., 2023
K-W Seo, Y-J Kim, J-H Hwang, K-S. Kim
Finite element simulation method for combined Ductile-Brittle fracture of small punch test in hydrogen
Eng Fract Mech, 289 (2023), Article 109489, 10.1016/j.engfracmech.2023.109489
View PDF View article View in Scopus Google Scholar

[31] Hwang et al., 2024
J-H Hwang, K-W Seo, Y-J Kim, K-S. Kim
Fracture-toughness estimation from small-punch test in hydrogen exhibiting ductile and ductile–brittle fracture modes
Eur J Mech A Solids, 103 (2024), Article 105193, 10.1016/j.euromechsol.2023.105193
View PDF View article View in Scopus Google Scholar

[32] Camacho and Ortiz, 1997
G.T. Camacho, M. Ortiz
Adaptive Lagrangian modelling of ballistic penetration of metallic targets
Comput Methods Appl Mech Eng, 142 (1997), pp. 269-301, 10.1016/S0045-7825(96)01134-6
View PDF View article View in Scopus Google Scholar

[33] Gerstgrasser et al., 2021
M. Gerstgrasser, D. Smolenicki, M. Akbari, H. Klippel, H. Roelofs, E. Cadoni, et al.
Analysis of two parameter identification methods for original and modified Johnson-Cook fracture strains, including numerical comparison and validation of a new blue-brittle dependent fracture model for free-cutting steel 50SiB8
Theor Appl Fract Mech, 112 (2021), Article 102905, 10.1016/J.TAFMEC.2021.102905
View PDF View article View in Scopus Google Scholar

[34] Borvik et al., 2001
T. Borvik, O.S. Hopperstad, T. Berstad, M. Langseth
A computational model of viscoplasticity and ductile damage for impact and penetration
Eur J Mech - A/Solids, 20 (2001), pp. 685-712, 10.1016/S0997-7538(01)01157-3
View PDF View article View in Scopus Google Scholar

[35] Chanda, 2015
Chanda, Sourayon. Temperature effects on dynamic fracture of pipeline steel. 2015. https://doi-org.ezproxy.lib.kyushu-u.ac.jp/10.7939/R3695Q
Google Scholar

[36] Gambirasio and Rizzi, 2016
L. Gambirasio, E. Rizzi
An enhanced Johnson–Cook strength model for splitting strain rate and temperature effects on lower yield stress and plastic flow
Comput Mater Sci, 113 (2016), pp. 231-265, 10.1016/J.COMMATSCI.2015.11.034
View PDF View article View in Scopus Google Scholar

[37] Seo et al., 2022
K-W Seo, J-H Hwang, Y-J Kim, K-S Kim, P-S. Lam
Fracture toughness prediction of hydrogen-embrittled materials using small punch test data in Hydrogen
Int J Mech Sci, 225 (2022), Article 107371, 10.1016/j.ijmecsci.2022.107371
View PDF View article View in Scopus Google Scholar

[38] Seo et al., 2024
K-W Seo, Y-J Kim, K-S. Kim
Quantification of pre-strain effect on ductile fracture and application to irradiation embrittlement problems
Eng Fract Mech, 300 (2024), Article 109986, 10.1016/j.engfracmech.2024.109986
View PDF View article View in Scopus Google Scholar

[39] Kim et al., 2011
N-H Kim, C-S Oh, Y-J Kim, K-B Yoon, Y-H. Ma
Comparison of fracture strain based ductile failure simulation with experimental results
Int J Press Vessels Pip, 88 (2011), pp. 434-447, 10.1016/j.ijpvp.2011.07.006
View PDF View article View in Scopus Google Scholar

[40] Oh et al., 2011
C-S Oh, N-H Kim, Y-J Kim, J-H Baek, Y-P Kim, W-S. Kim
A finite element ductile failure simulation method using stress-modified fracture strain model
Eng Fract Mech, 78 (2011), pp. 124-137, 10.1016/j.engfracmech.2010.10.004
View PDF View article View in Scopus Google Scholar

[41] Jeon et al., 2016
J-Y Jeon, Y-J Kim, S-Y Lee, J-W. Kim
Extracting ductile fracture toughness from small punch test data using numerical modeling
Int J Press Vessels Pip, 139–140 (2016), pp. 204-219, 10.1016/j.ijpvp.2016.02.011
View PDF View article View in Scopus Google Scholar

[42] Kim et al., 2020
J-S Kim, Y-J Kim, M-W Lee, K-S Kim, K. Shibanuma
Fracture simulation model for API X80 Charpy test in Ductile-Brittle transition temperatures
Int J Mech Sci, 182 (2020), Article 105771, 10.1016/j.ijmecsci.2020.105771
View PDF View article View in Scopus Google Scholar

[43] Jung et al., 2014
D-H Jung, J-K Kwon, N-S Woo, Y-J Kim, M. Goto, S. Kim
S–N Fatigue and Fatigue Crack Propagation Behaviors of X80 Steel at Room and Low Temperatures
Metall Mater Trans A, 45 (2014), pp. 654-662, 10.1007/s11661-013-2012-4
View at publisher
View in Scopus Google Scholar

[44] Heier et al., June 2013
Espen Heier, Erling Østby, Odd M. Akselsen
Reeling Installation of Rigid Steel Pipelines at Low Temperature
Paper presented at the The Twenty-third International Offshore and Polar Engineering Conference, Anchorage, Alaska (June 2013)
Google Scholar

[45] Akselsen et al., June 2012
Odd M. Akselsen, Erling Østby, Bård Nyhus
Low Temperature Fracture Toughness of X80 Girth Welds
Paper presented at the The Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece (June 2012)
Google Scholar

[46] Kim et al., 2024
J-Y Kim, K-W Seo, Y-J Kim, K-S. Kim
Fracture analysis of hydrogen-embrittled API X52 pipes at low temperature
Int J Mech Sci, 276 (2024), Article 109374, 10.1016/j.ijmecsci.2024.109374
View PDF View article View in Scopus Google Scholar

[47] BSI 2014
BSI
BS 8571 2014 - Method of test for determination of fracture toughness in metallic materials using single edge notched tension (SENT) specimens
BSI; (2014)
Google Scholar

[48] Institute, 2007
AP. Institute
API 5L Specification for line pipe
Api Spec, 5L (2007)
Google Scholar

[49] Tu et al., 2022
S. Tu, S. Suzuki, Z. Yu, K. Shibanuma
Hybrid experimental-numerical strategy for efficiently and accurately identifying post-necking hardening and ductility diagram parameters
Int J Mech Sci, 219 (2022), Article 107074, 10.1016/J.IJMECSCI.2022.107074
View PDF View article View in Scopus Google Scholar

[50] ABAQUS Version 2018
ABAQUS Version
User's manual. Dassault Systems
Inc (2018), p. 2018
Google Scholar

[51] Origin(Pro), Version 2020
Origin(Pro), Version 2020. OriginLab Corporation, Northampton, MA, USA.
Google Scholar

[52] Talemi et al., 2019
R. Talemi, S. Cooreman, H. Mahgerefteh, S. Martynov, S. Brown
A fully coupled fluid-structure interaction simulation of three-dimensional dynamic ductile fracture in a steel pipeline
Theor. Appl. Fract. Mech., 101 (2019), pp. 224-235, 10.1016/J.TAFMEC.2019.02.005
View PDF View article View in Scopus Google Scholar

[53] Yan et al., 2014
C. Yan, C. Liu, B. Yan
3D modeling of the hydrogen distribution in X80 pipeline steel welded joints
Comput Mater Sci, 83 (2014), pp. 158-163, 10.1016/J.COMMATSCI.2013.11.007
View PDF View article View in Scopus Google Scholar

[54] Tronskar et al., 2002
J.P. Tronskar, M.A. Mannan, Lai MO
Measurement of fracture initiation toughness and crack resistance in instrumented Charpy impact testing
Eng Fract Mech, 69 (2002), pp. 321-338, 10.1016/S0013-7944(01)00077-7
View PDF View article View in Scopus Google Scholar

[55] Kobayashi, 1984
T. Kobayashi
Analysis of impact properties of A533 steel for nuclear reactor pressure vessel by instrumented Charpy test
Eng Fract Mech, 19 (1984), pp. 49-65, 10.1016/0013-7944(84)90068-7
View PDF View article View in Scopus Google Scholar

[56] Oulad Brahim et al., 2022
A. Oulad Brahim, I. Belaidi, N. Fahem, S. Khatir, S. Mirjalili, M. Abdel Wahab
Prediction of the peak load and crack initiation energy of dynamic brittle fracture in X70 steel pipes using an improved artificial neural network and extended Finite Element Method
Theor Appl Fract Mech, 122 (2022), Article 103627, 10.1016/J.TAFMEC.2022.103627
View PDF View article View in Scopus Google Scholar

[57] Seo et al., 2022
K-W Seo, J-H Hwang, Y-J Kim, K-S Kim, P-S. Lam
Fracture toughness prediction of hydrogen-embrittled materials using small punch test data in Hydrogen
Int J Mech Sci, 225 (2022), Article 107371, 10.1016/j.ijmecsci.2022.107371
View PDF View article View in Scopus Google Scholar

[58] Seo et al., 2024
K-W Seo, Y-J Kim, K-S. Kim
Quantification of pre-strain effect on ductile fracture and application to irradiation embrittlement problems
Eng Fract Mech, 300 (2024), Article 109986, 10.1016/j.engfracmech.2024.109986
View PDF View article View in Scopus Google Scholar

[59] Kim et al., 2011
N-H Kim, C-S Oh, Y-J Kim, K-B Yoon, Y-H. Ma
Comparison of fracture strain based ductile failure simulation with experimental results
Int J Press Vessels Pip, 88 (2011), pp. 434-447, 10.1016/j.ijpvp.2011.07.006
View PDF View article View in Scopus Google Scholar

[60] ASTM Standard E436-03 2021
ASTM Standard E436-03
Standard Test Method for Drop-Weight Tear Tests of Ferritic Steels
(2021)
Google Scholar

[61] Kim et al., 2021
J-S Kim, Y-J Kim, M-W Lee, K-S Kim, K. Shibanuma
Finite element simulation of drop-weight tear test of API X80 at ductile-brittle transition temperatures
Int J Mech Sci, 191 (2021), Article 106103, 10.1016/j.ijmecsci.2020.106103
View PDF View article Google Scholar

[62] Kim et al., 2022
J-S Kim, Y-J Kim, M-W Lee, K-S Kim, K. Shibanuma
Numerical method to characterize probabilistic energy distribution of drop weight tear test at Ductile-Brittle transition temperatures
Eng Fract Mech, 269 (2022), Article 108540, 10.1016/j.engfracmech.2022.108540
View PDF View article View in Scopus Google Scholar

[63] Petti and Dodds, 2005
J.P. Petti, RH. Dodds
Calibration of the Weibull stress scale parameter, σu, using the Master Curve
Eng Fract Mech, 72 (2005), pp. 91-120, 10.1016/j.engfracmech.2004.03.009
View PDF View article View in Scopus Google Scholar

[64] Gao et al., 2006
X. Gao, G. Zhang, TS. Srivatsan
A probabilistic model for prediction of cleavage fracture in the ductile-to-brittle transition region and the effect of temperature on model parameters
Mater Sci Eng, 415 (2006), pp. 264-272, 10.1016/j.msea.2005.09.098
View PDF View article View in Scopus Google Scholar

[65] Wasiluk et al., 2006
B. Wasiluk, J.P. Petti, RH. Dodds
Temperature dependence of Weibull stress parameters: Studies using the Euro-material
Eng Fract Mech, 73 (2006), pp. 1046-1069, 10.1016/j.engfracmech.2005.11.006
View PDF View article View in Scopus Google Scholar

[66] Uenishi et al., 2011
A. Uenishi, H. Yoshida, S. Yonemura, S. Hiwatashi, S. Hirose, N. Suzuki
High Strain Rate Properties of High Strength Steel Sheets
Int J Automot Eng, 2 (2011), pp. 109-113, 10.20485/jsaeijae.2.4_109
Google Scholar

[67] Vaynman et al., 2006
S. Vaynman, M.E. Fine, S. Lee, HD. Espinosa
Effect of strain rate and temperature on mechanical properties and fracture mode of high strength precipitation hardened ferritic steels
Scr Mater, 55 (2006), pp. 351-354, 10.1016/J.SCRIPTAMAT.2006.04.029
View PDF View article View in Scopus Google Scholar

[68] Soares and Hokka, 2021
G.C. Soares, M. Hokka
The Taylor–Quinney coefficients and strain hardening of commercially pure titanium, iron, copper, and tin in high rate compression
Int J Impact Eng, 156 (2021), Article 103940, 10.1016/J.IJIMPENG.2021.103940
View PDF View article View in Scopus Google Scholar

[69] Rittel et al., 2017
D. Rittel, L.H. Zhang, S. Osovski
The dependence of the Taylor–Quinney coefficient on the dynamic loading mode
J Mech Phys Solids, 107 (2017), pp. 96-114, 10.1016/J.JMPS.2017.06.016
View PDF View article View in Scopus Google Scholar

Outline

Figures (20) 图（20）

Tables (4) 表格（4）

Journal of Pipeline Science and Engineering

ABSTRACT

Keywords

Nomenclature

ABBREVIATIONS

1. INTRODUCTION

2. PROPOSED COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION MODEL

2.1. Johnson-Cook (J-C) Deformation Model under Impact Loading

2.2. Johnson-Cook (J-C) Fracture Strain Model for Ductile Fracture Simulation

2.3. Critical Stress Model for Brittle Fracture Simulation

2.4. Combined Ductile and Brittle Fracture Simulation

3. SUMMARY OF EXPERIMENTS FOR MODEL DETERMINATION

3.1. Tensile Test

3.2. Single Edge Notched Tensile (SENT) Test

3.3. Charpy V Notched (CVN) Impact Test at Room Temperature

4. DETERMINATION OF API X80 DEFORMATION AND FRACTURE MODELS

4.1. Parameter Determination of Deformation Model

4.2. Parameter Determination of Ductile Fracture Model

4.3. Determination of Brittle Fracture Model

5. EXPERIMENTS FOR VALIDATION

5.1. Charpy V Notched (CVN) Test

5.2. Drop-Weight Tear Test (DWTT)

6. COMPARISON WITH FE SIMULATION RESULTS FOR VALIDATION

6.1. Comparison of CVN Test with Simulation Results

6.2. Comparison of DWTT with Simulation Results

7. DISCUSSION: EFFECT OF ADIABATIC HEATING AND STRAIN RATE ON COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION FOR IMPACT TESTS
7. 讨论：绝热加热和应变速率对冲击试验韧脆性断裂模拟的影响

8. CONCLUSION

CRediT authorship contribution statement

Declaration of competing interest

References

Cited by (0)

Journal of Pipeline Science and Engineering

Combined Ductile-Brittle Fracture Simulation of API X80 Under Impact Loading

ABSTRACT

Keywords

Nomenclature

ABBREVIATIONS

1. INTRODUCTION

2. PROPOSED COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION MODEL

2.1. Johnson-Cook (J-C) Deformation Model under Impact Loading

2.2. Johnson-Cook (J-C) Fracture Strain Model for Ductile Fracture Simulation

2.3. Critical Stress Model for Brittle Fracture Simulation

2.4. Combined Ductile and Brittle Fracture Simulation

3. SUMMARY OF EXPERIMENTS FOR MODEL DETERMINATION

3.1. Tensile Test

3.2. Single Edge Notched Tensile (SENT) Test

3.3. Charpy V Notched (CVN) Impact Test at Room Temperature

4. DETERMINATION OF API X80 DEFORMATION AND FRACTURE MODELS

4.1. Parameter Determination of Deformation Model

4.2. Parameter Determination of Ductile Fracture Model

4.3. Determination of Brittle Fracture Model

5. EXPERIMENTS FOR VALIDATION

5.1. Charpy V Notched (CVN) Test

5.2. Drop-Weight Tear Test (DWTT)

6. COMPARISON WITH FE SIMULATION RESULTS FOR VALIDATION

6.1. Comparison of CVN Test with Simulation Results

6.2. Comparison of DWTT with Simulation Results

7. DISCUSSION: EFFECT OF ADIABATIC HEATING AND STRAIN RATE ON COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION FOR IMPACT TESTS7. 讨论：绝热加热和应变速率对冲击试验韧脆性断裂模拟的影响

8. CONCLUSION

CRediT authorship contribution statement

Declaration of competing interest

References

7. DISCUSSION: EFFECT OF ADIABATIC HEATING AND STRAIN RATE ON COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION FOR IMPACT TESTS
7. 讨论：绝热加热和应变速率对冲击试验韧脆性断裂模拟的影响