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
2025 年 5 月 8 日在线发布，100295

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Journal of Pipeline Science and Engineering

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ABSTRACT 抽象的

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.
本研究探索了冲击载荷下 API X80 钢延性-脆性断裂行为的有限元 (FE) 模拟，其中考虑了应变率和绝热加热的影响。采用 Johnson-Cook (JC) 变形模型进行变形分析，采用 (JC) 断裂应变模型模拟延性断裂，并采用临界应力模型捕捉脆性断裂。通过在不同温度下进行的光圆棒 (SRB) 试验校准了 JC 模型的温度相关参数，而采用室温 (RT) 下的夏比 V 型缺口 (CVN) 冲击试验识别了应变率相关参数。此外，通过在室温下对 CVN 试验进行 FE 模拟，确定了脆性断裂的临界应力模型。校准后的变形模型和组合断裂模型用于模拟-120 至 0 °C 温度范围内的 CVN 和落锤撕裂试验 (DWTT)。模拟准确地捕捉了变形行为、载荷-位移曲线和断裂表面。敏感性分析强调了绝热加热和应变率效应在断裂行为中的作用。

Keywords 关键词

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

绝热加热及应变速率效应 API X80 钢冲击载荷下延脆性断裂模拟 Johnson-Cook 变形及断裂应变模型临界应力脆性断裂模型

Nomenclature 命名法

a₀

initial crack length [mm]
初始裂纹长度[mm]

Δa

crack extension [mm] 裂纹延伸[毫米]

C_p

specific heat [J/kg∙°C] 比热[J/kg∙°C]

strain rate dependent Johnson-Cook (J-C) deformation parameter
应变率相关的 Johnson-Cook（JC）变形参数

D₁, D₂, D₃
D ₁ 、D ₂ 、D ₃

Johnson-Cook fracture parameters at quasi-static strain rate and room temperature
准静态应变率和室温下的 Johnson-Cook 断裂参数

D₄

strain rate dependent J-C fracture parameter
应变率相关的 JC 断裂参数

D₅

temperature dependent J-C fracture parameter
温度相关的 JC 断裂参数

D_c

critical damage value 临界伤害值

Young's modulus [GPa] 杨氏模量[GPa]

E₀

elastic energy absorption [J]
弹性能量吸收[J]

T, ΔT T，ΔT

temperature and its change [°C]
温度及其变化[°C]

T_melt

melting temperature [°C] 熔化温度[°C]

V₀

reference volume [mm³]
参考体积 [mm ³ ]

V_E

total volume of one layer element in the unnotched ligament [mm³]
无缺口韧带中一层单元的总体积 [mm ³ ]

ε_f

multi-axial fracture strain in Eqs. (1, 2, 7, 9, 10) and (11)
公式（1、2、7、9、10）和公式（11）中的多轴断裂应变

\dot{ε}

\dot{ε_{0}}

strain rate and reference strain rate
应变率和参考应变率

ε_p, Δε_p
e _p ，德 _p

equivalent plastic strain and its increment
等效塑性应变及其增量

density [kg/m³] 密度[kg/m ³ ]

σ₁

principal stress [MPa] 主应力[MPa]

σ_1,max

maximum principal stress [MPa]
最大主应力[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.

7. DISCUSSION: EFFECT OF ADIABATIC HEATING AND STRAIN RATE ON COMBINED DUCTILE-BRITTLE FRACTURE SIMULATION FOR IMPACT TESTS

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.

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.

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.

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

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Outline 大纲

Figures (20) 图（20）

Tables (4)

Journal of Pipeline Science and Engineering

ABSTRACT 抽象的

Keywords 关键词

Nomenclature 命名法

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

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 LoadingAPI X80 在冲击载荷下的延性-脆性断裂模拟

ABSTRACT 抽象的

Keywords 关键词

Nomenclature 命名法

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

8. CONCLUSION

CRediT authorship contribution statement

Declaration of competing interest

References

Combined Ductile-Brittle Fracture Simulation of API X80 Under Impact Loading
API X80 在冲击载荷下的延性-脆性断裂模拟