Finite element simulation of drop-weight tear test of API X80 at ductile-brittle transition temperatures

doi:10.1016/j.ijmecsci.2020.106103

International Journal of Mechanical Sciences
国际机械科学杂志

Volume 191, 1 February 2021, 106103
第 191 卷，2021 年 2 月 1 日，106103

https://doi.org/10.1016/j.ijmecsci.2020.106103 Get rights and content 获得权利和内容

Full text access 全文访问

Highlights 亮点

•
Simultaneous ductile and cleavage fracture in DWTT (drop-weight tearing test) at ductile-brittle transition temperature can be simulated from presented method.
通过所提出的方法可以模拟在延性-脆性转变温度下 DWTT（落锤撕裂试验）中同时发生的延性断裂和解理断裂。
•
For simulating ductile fracture, the stress modified fracture strain damage model is used.
为了模拟延性断裂，采用应力修正的断裂应变损伤模型。
•
For simulating cleavage fracture, the maximum principal stress criterion is applied.
为了模拟解理断裂，采用最大主应力准则。
•
By incorporating the element size effect on the ductile and cleavage damage models, the numerical simulation method of interacting ductile and cleavage fracture behavior of DWTT for API X80 steel is constructed.
通过在延性损伤模型和解理损伤模型中引入单元尺寸效应，建立了 API X80 钢 DWTT 交互延性与解理断裂行为的数值模拟方法。

Abstract 抽象的

This paper proposes a method to simultaneously simulate interacting ductile and cleavage fracture in a DWTT (drop-weight tear test). The stress-modified fracture strain (SMFS) damage model is used to simulate ductile fracture and the maximum principal stress criterion is applied to simulate cleavage fracture. By incorporating the element size effect in the ductile and cleavage damage models, the numerical method to simulate the interacting ductile and cleavage fracture behavior in a DWTT is constructed. To validate the proposed method, the simulation results are compared with six API X80 data measurements at temperatures ranging between -97 °C to -20 °C. The comparison of the experimental load-displacement curve and fracture surface with the FE simulation results shows good agreement.
本文提出了一种同时模拟落锤撕裂试验（DWTT）中韧性断裂和解理断裂交互作用的方法。采用应力修正断裂应变（SMFS）损伤模型模拟韧性断裂，采用最大主应力准则模拟解理断裂。通过在韧性和解理损伤模型中引入单元尺寸效应，构建了 DWTT 中韧性断裂和解理断裂交互作用的数值模拟方法。为了验证所提方法的有效性，将模拟结果与-97 ℃至-20 ℃温度范围内的 6 个 API X80 钢种的测量数据进行了比较。实验载荷-位移曲线和断口形貌与有限元模拟结果的对比表明，两者吻合良好。

Graphical abstract 图解摘要

Keywords 关键词

API X80 drop-weight tear test

Ductile-brittle transition temperature

Interacting ductile and cleavage fracture

Numerical fracture simulation

API X80 落锤撕裂试验；韧脆转变温度；延性断裂与解理断裂交互作用；断裂数值模拟

Abbreviation 缩写

API

American Petroleum Institute

CTOA

crack tip opening angle

CMOD

crack mouth opening displacement

DWTT

drop-weight tear test

finite element

GTN

Gurson-Tvergaard-Needleman

pressed notch

shear area

SENT

single-edge notched tension

SMFS

stress-modified fracture strain

API 美国石油学会 CTO 裂纹尖端张开角 CMOD 裂纹口张开位移 DWTT 落锤撕裂试验 FE 有限元 GTNGurson-Tvergaard-NeedlemanPN 压制缺口 SA 剪切面积 SENT 单边缺口拉伸 SMFS 应力修正断裂应变

Nomenclature 命名法

A, B A、B

material constant in strain-based failure criteria
基于应变的失效准则中的材料常数

D_c

critical damage value 临界伤害值

E_exp

experimental drop-weight tear test energy

E_FE

simulated drop-weight tear test energy

material constant in the modified Johnson-Cook model, see Eq. (12)

volumetric energy density, see Eq. (8)

L_e

element size

exponent of the Weibull distribution

T, T_melt

temperature and melting temperature ( °C)

V, V₀

volume and its reference value in fracture process zone

V_D

total volume of damage elements, see Eq. (8)

ε_e^p

equivalent plastic strain

ε_f

fracture strain

σ_e

equivalent stress

σ_e,RT

equivalent stress at room temperature

σ₁, σ_m

maximum principal stress and hydrostatic stress

σ_y, σ_TS

yield and tensile strength

σ_w

Weibull stress

1. Introduction

To transport energy resources such as natural gas or crude oil over long distances, line-pipe steels with higher strengths are being required to endure higher pressures. However, at low temperatures, brittle fractures can gradually occur due to the ductile-brittle transition phenomenon. Because rapid crack propagation can be difficult to control, brittle fractures must be prevented during operation. Thus, sufficient toughness even at low temperatures is also required for safe operation in cold locations. To ensure that these requirements are met, tests must be performed. The drop-weight tear test (DWTT) is a widely used test to evaluate fracture resistance [1,2] and it is commonly known that fracture behavior is well characterized by the DWTT because the thickness of a DWTT specimen is the same as that of a pipe [3,4]. In place of an actual pipe test, the API requires the appearance of a minimum of 85% shear area on the evaluated fracture surface of a DWTT specimen [1,3]. Note that fully ductile tearing is expected in pipe fractures above the temperature showing the minimum 85% shear area from the DWTT test, according to the Battelle criterion [5].

With the continuous development of new materials with high toughness, which can exhibit various fracture characteristics, it is recommended to apply suitable experimental methods in performing DWTTs according to the properties of steel [6,7]. One example of these fracture characteristics is the so-called ‘inverse fracture’, which is defined as a cleavage fracture following an initial ductile fracture [7], [8], [9]. The inverse fracture phenomenon can be observed in high-strength and high-toughness steel. In particular, a DWTT specimen made of high-strength and high-toughness steel can be subject to large plastic deformations prior to crack initiation, and this large plastic deformation with compressive stress at the back side of a bend specimen can change the fracture behavior [10]. Thus, inverse fractures appear more frequently when high energy is required at the time of crack initiation such as in a pressed-notch DWTT specimen [7,9]. Hwang et al. [8] suggest that work hardening caused by the impact of a hammer can produce inverse fractures. Because it is preferable to prevent the occurrence of inverse fractures, the presence of which can reduce the evaluation accuracy of a DWTT [8], a DWTT was conducted with a chevron-notch to reduce the energy for fracture initiation [11,12]. However, it was determined that inverse fractures cannot be completely suppressed even with a chevron-notch DWTT specimen [8,10]. To understand and systematically analyze the inverse fracture phenomenon, numerical simulations of the complex fracture behaviors of a DWTT specimen including the occurrence of the inverse fracture phenomenon can be highly effective.

The finite element (FE) method is used not only to provide a powerful approach to predict deformations and fractures but also to simulate fracture behaviors of DWTT specimens at transition temperatures. Simulating the fracture behaviors of DWTT specimens at transition temperatures requires the simultaneous simulation of interacting ductile fracture and cleavage fracture, which has not been addressed up to now. Most of the works in the literature have considered either ductile tearing simulations or cleavage fracture simulations. For instance, using the crack tip opening angle (CTOA) concept, Fang et al. [4] and Zhen et al. [13] analyzed the ductile fracture behavior during a DWTT for various linepipe steels at room temperature. In other studies, the two-dimensional cohesive zone model was used to simulate stable ductile crack propagation in a DWTT and to determine the CTOA for pipeline steels [14,15]. Later, a similar study was performed using the three-dimensional model by Yu et al. [16] and the simulated absorption energy was compared with the experimental absorption energy. Paermentier et al. [17] simulated the ductile fracture propagation of a DWTT specimen using the Gurson-Tvergaard-Needleman (GTN) model [18], [19], [20]. The above studies performed ductile fracture simulations of DWTT specimens at upper shelf temperatures. In fact, there are many studies that provide an extension of the above ductile fracture simulation techniques that combine cleavage failure probabilities based on the Beremin model [21,22]. Hojo et al. [21] tried to find the temperature-independent Beremin parameters by combining GTN model to predict probability of failure of cracked specimens. Jang et al. [22] characterized ductile and cleavage fracture by combining the GTN and Beremin model. However, there has yet to be published a study that simultaneously simulates interacting ductile and cleavage fractures aside from our previous work. Existing studies have only calculated the cleavage failure probabilities after a certain amount of ductile fracture. Since the Weibull stress can be calculated only by post-processing of simulation results, detailed fracture surface classified by ductile or cleavage cannot be obtained from simulation. In addition, the Weibull stress approach only assumes complete cleavage fracture after exceeding a reference value, and thus cannot accommodate ductile fracture occurrence after cleavage fracture initiation.

In our previous work [23], a numerical method to simultaneously simulate interacting ductile and cleavage fractures has been proposed and applied to simulate API X80 Charpy impact tests at ductile-brittle transition temperatures. To simulate ductile tearing, the stress-modified fracture strain (SMFS) model was applied in which the fracture strain is assumed to be the inverse-exponential function of the stress triaxiality [23], [24], [25], [26], [27], [28], [29], [30]. Although the model is simple, a comparison of the simulation results with cracked pipe test data in our previous works shows that the model is quite effective and the predictions are sufficiently accurate [24,26,27,29,30]. To simulate cleavage fracture, the maximum principal stress criterion was used [23]. It should be noted that although the Weibull stress approach has been popularly used to quantify cleavage fracture [31,[42], [43], [44], [45], [46]], it can be calculated only from post-processing FE results [47], [48], [49], [50] and is, therefore, not suitable for an interacting ductile and cleavage fracture simulation. However, based on the FE analysis of the Charpy impact test, it was shown that the maximum principal stress criterion is equivalent to the Weibull stress [23]. By analyzing the Charpy impact test using FE analysis, the relationship between the Charpy impact test energy and the maximum principal stress was established as a criterion for cleavage fracture, for which the simulated fracture surfaces were in good agreement with the experimental Charpy impact test data at various temperatures, suggesting the validity of the proposed method. The cleavage fracture is also implemented by a user subroutine function when maximum principal stress in a gauss point reaches pre-defined critical value. The fracture is defined by same mechanism on ductile fracture simulation. One notable point is the element size. The element size effect on the FE damage simulation results is relatively well known [[24], [25], [26], [27],29]. This is simply because a damage model depends on the stress and strain states, which are dependent on the element size in the FE analysis. For example, for a given damage model, the predicted crack initiation and growth using a larger element size tend to be delayed. Thus, some parameters in damage models should be adjusted to compensate for the element size effect. Note that in the Charpy impact test simulation of our previous study, the element size of 0.1 mm was used without causing any numerical difficulties because the unnotched ligament size was only 8 mm for the Charpy specimen. However, it is difficult to maintain numerical stability with the use of such a small element when simulating fractures in a larger specimen with a much longer ligament. For this reason, we believe that the element size effect on a damage model is an important problem to solve when performing numerical crack growth modeling for long crack growths.

In this paper, the method to simultaneously simulate interacting ductile and cleavage fractures in our previous work is extended to simulate fractures in the DWTT of API X80. The unnotched ligament area of the present DWTT specimen is approximately 23.7 mm x 71.1 mm, whereas that of the Charpy specimen is 10 mm x 8 mm. Thus the unnotched area of the DWTT specimen is about twenty one times larger than that of the Charpy specimen. In our previous work [23], the 0.1 mm element size in a crack propagation region was used for simulating the Charpy test. The use of the same element size in simulating DWTT test is very difficult due to numerical instability, because twenty one times more elements must be failed in simulating DWTT test than in Charpy test simulation. Therefore the key point to simulate the DWTT test is to develop a damage model that incorporates the element size effect. The validity of the developed element-size-dependent damage model has to be checked by comparing with experiment data. For comparison, six DWTT tests are performed at temperatures ranging between −97 °C to −20 °C. The fracture surfaces, load-displacement curves, and energies obtained from the experimental tests are compared with those from the simulated results. Section 2 explains the materials, mechanical properties, and DWTT test results. The numerical damage models incorporating the element size effect are explained in Section 3. Section 4 compares the simulation results with the DWTT results and the conclusions are presented in Section 5.

2. Drop-weight tear test (DWTT)

2.1. Material and mechanical properties

The American Petroleum Institute (API) X80 grade steel used in our previous work [23] was used in this study as well. A tensile test was performed at room temperature (25 °C) according to the API 5 L standard [32] for a flat plate test specimen with a width of 38.1 mm, a thickness of 24.2 mm, and a gage length of 50.8 mm, taken from the plate in the hoop direction. The tensile test was loaded with a universal testing machine (UTM Zwick Roell, 1200 kN). The engineering stress-strain curve is shown in Fig. 1(a) with the tensile properties (yield stress, σ_y, tensile stress, σ_TS, and elastic modulus, E).

Charpy impact tests were also performed at various temperatures using standard specimens with a 10 mm x 10 mm cross-section and a central 45° V-notch of 2 mm depth according to API 5 L [32]. Total ninety-eight specimens were tested from −196 to 0 °C. Variations of the impact energies with temperature are shown in Fig. 1(b) and minimum, averaged and maximum impact energies are summarized in Table 1 for the given temperature, together with the number of tests.

Table 1. Charpy test data with temperature.

T [ °C]	−196	−150	−120	−90	−60	−30	0
Number of specimens	3	74	3	6	6	3	3
Averaged E_CVN [J]	4.35	10.70	82.27	221.80	297.80	446.63	485.43
Minimum E_CVN [J]	3.42	4.82	10.47	78.74	207.45	380.68	478.45
Maximum E_CVN [J]	5.16	39.03	221.5	334.84	344.67	472.32	492.89

To measure crack growth resistance, a single-edge notched tension (SENT) test was performed at room temperature according to the recommended practice in the DNV RP-F108 [33]. The relevant dimensions of the SENT specimen are shown in Fig. 2(a). The specimen was clamped using hydraulic grips and loaded in the controlled displacement mode and unloaded controlled load mode. The crack mouth opening displacement (CMOD) was measured by a clip gage. Detailed dimensions are shown in Fig. 2(a). After machining 7 mm crack with an EDM, fatigue pre crack was additionally inserted. The total initial crack size is measured by 10.03 mm. To measure the crack extension, the compliance method suggested in the BS 8571 [34] was used [35], [36], [37]. The resulting variations in the load and crack extension (Δa) with the CMOD (crack mouth opening displacement) are shown in Fig. 2(b). Later in Section 3.2, the Δa-CMOD curve is used to determine the damage model for ductile fracture. For this purpose, the experimental data are fitted using a power-law equation which is shown in Fig. 2(b).

2.2. Drop-weight tear test (DWTT)

A drop-weight tear test (DWTT) of API X80 steel was conducted at various temperatures according to the ASTM E436 [2]. The DWTT and specimen are schematically shown in Fig. 3(a) with the a central 45° pressed notch of 5.08 mm depth. A DWTT testing machine (DWTT-100F) with the maximum energy capacity of 100 kJ was used. To apply sufficient energy to split the DWTT specimen, the hammer fell from a height of 2 m giving ~6 m/s speed at the impact. The anvil was fixed on both sides, and a three point-bending load was applied to the DWTT specimen. Load-load line displacement curves were obtained from the instrumented DWTT system. Total six tests at various temperatures were carried out to observe various characteristics on the fracture surface. The data for the six tests, such as temperature, measured energy, and percentage shear area (SA), are given in Table 2. Note that the tests are numbered according to the temperature and the fracture energy.

Table 2. Summary of six drop-weight tear test data: temperature T, measured energy Eexp, and measured shear area. The presence of the inverse fracture surface is also indicated.

Test Number	1	2	3	4	5	6
T [ °C]	−97	−97	−80	−60	−20	−20
E_exp [kJ]	0.60	1.03	1.28	1.90	10.5	14.2
Inverse fracture	No	No	No	Yes	Yes	Yes
Shear Area [%]	8.5	11.4	19.5	40.6	77.9	69.6

Experimental load-load line displacement curves are shown in Fig. 3(b). Although it is difficult to identify the experimental data for the different conditions in this figure, each curve is compared with simulated results in the later Section 4.2. The fracture energy E_exp can be measured from the load-load line displacement curve and is summarized in Table 2. These values are used to predict the maximum principal stress criteria that cause cleavage fracture in the simulations of the DWTT in the later Section 4.2.

Fig. 4 shows the fracture surfaces from the six DWTTs. According to Hong et al. [3], fracture surfaces can be classified into four regions: (1) cleavage fracture; (2) ductile fracture; (3) delamination; and (4) inverse fracture. In the cases of Tests 1–3 at low temperatures, cleavage fracture is dominant in the central part of the surface, continuing from the initial notch tip to the end of the specimen. A small ductile fracture region is observed only near the surface. With increasing test temperatures, the fraction of cleavage fracture decreases, whereas the fractions of ductile fracture and delamination increase, as shown with Tests 4–6. According to the API RP 5L3 [1], delamination is defined as a cleavage fracture when it is wide because it appears almost in the surface fractured by the cleavage. In contrast, when delamination is deep and shallow, it can be defined as ductile fracture because it is included almost in the ductile fracture surface. According to this definition, the delamination shown in Fig. 4 can be classified mainly as ductile. Inverse (cleavage) fracture is also observed in Fig. 4 with Tests 4 to 6, in which the ductile fracture forming after the cleavage fracture changes back to cleavage fracture. It is located near the hammer impact region (which is classified as a ductile fracture [7]) and appears distinctly at relatively high temperatures. Sung et al. [7] and Hwang et al. [9] pointed out that, in the case of pressed notched DWTT specimens, a high energy is required at the notch to initiate the fracture, resulting in an inverse fracture. Because higher energy is also required to initiate the fracture at a relatively high temperature, the inverse fracture was more clearly observed in Tests 5–6 performed at −20 °C.

From the tested fracture surface, the shear area was calculated with the thickness according to the ASTM E436 [2] in the middle region excluding the initial notch tip and the end of the specimen. Note that if the thickness of the DWTT specimen exceeds 19 mm, the length of the section excluded when calculating the shear area should be set to 19 mm and not to the thickness value. Because the thickness of the DWTT specimen used in this study was 23.7 mm, 19 mm was excluded from both sides when calculating the shear area, as shown in Fig. 4. The fracture surface types were manually classified with the photographs and the percentage shear area was calculated by an image analyzer. The calculated shear areas are given in Table 2 and are compared with simulated results in the later Section 4.2.

3. Numerical damage model for simulating the DWTT

3.1. The importance of an element-size-dependent damage model

In our previous work [23] in which the same material was considered, the minimum element size of 0.1 mm was used in the FE model to simulate fractures in the Charpy test at ductile-brittle transition temperatures. The use of a 0.1-mm element size was possible because the ligament length in the Charpy specimen was only 8 mm. However, the fracture simulation of large-scale specimens or pipes can be of practical interest. For instance, the DWTT specimen considered in this paper has the ligament size of approximately 72 mm, which is approximately ten times larger than the Charpy specimen. The length scale of large-scale pipes can be much longer. One of the challenges in simulating fractures in large-scale components is the finite element size used in the simulation. Because the element deletion technique is generally used to simulate fractures, the use of a small element size such as 0.1 mm in the simulation of large-scale components can cause numerical instability. One possible way to improve numerical stability is to use a larger element size. Therefore, because calculated stresses, strains, and damage depend on the element size, the parameters in a damage model can also depend on the element size.

In the following sub-sections, the ductile fracture and cleavage damage models proposed in our previous work [23] are extended to incorporate the element size effect, which is then used to simulate fracture in the DWTT specimen.

3.2. Element-size-dependent ductile damage model

In our previous study [[23], [24], [25], [26],29,30], the stress-modified fracture strain (SMFS) model was used to simulate ductile fracture (tearing), in which the multi-axial fracture strain ε_f is given by the exponential function of the stress triaxiality [[23], [24], [25], [26],29,30].(1)

ε_{f} = A \cdot exp [- 1.5 \cdot \frac{σ_{m}}{σ_{e}}] + B

For API X80, the material constants A and B were determined by analyzing the tensile and single-edge-notched tension (SENT) test data using FE simulations and are A = 3.34 and B = 0.4 [23].

The incremental damage is defined as the ratio of increments of equivalent plastic strain to the multi-axial fracture strain as follows:(2)

Δ D = \frac{Δ ε_{e}^{p}}{ε_{f}}

When the accumulated damage reaches a critical damage value D_c(3)

\int Δ D = \int \frac{Δ ε_{e}^{p}}{ε_{f}} = D_{c}

the element is removed using ABAQUS [39] user subroutines to simulate local ductile fracture. In the simulation, when the accumulated damage reached the critical damage value, the equivalent stress was decreased with the slope of −5000 MPa to 10 MPa. The elastic modulus was also reduced to 100 MPa. Finally, to completely remove the element, the “ELEMENT DELETION” option in ABAQUS was applied.

In our model, the fracture strain locus given by Eq. (1) is regarded as one of the material properties and is, therefore, not dependent on the element size. However, the value of D_c is assumed to depend on the element size [[24], [25], [26], [27],29]. In our previous work [23], it was found that D_c=1 for the minimum element size of 0.1 mm to simulate fractures in the Charpy test. The FE mesh for simulating SENT test with L_e=0.1 mm in the crack propagation area is shown in Fig. 5 and the comparison between the simulated results and experimental results for the experimental load-CMOD, crack extension(Δa)-CMOD, and dΔa/dCMOD-CMOD curves is shown in Fig. 6(a). Note that for the dΔa/dCMOD-CMOD curve, two experimental data plots are shown: one is the direct differentiation of experimental data (showing large scatter) and the other is the fitted equation given in Fig. 2(b).

When a different size of the element is used, a proper D_c value must be chosen. The FE meshes with L_e=0.2 and 0.5 mm are also shown in Fig. 5. The effect of the element size (L_e) and D_c on simulated dΔa/dCMOD-CMOD results are compared with experimental data in Fig. 7(a) for L_e=0.2 mm and in Fig. 7(b) for L_e=0.5 mm. For L_e=0.2 mm in Fig. 7(a), it can be observed that the use of D_c=0.85 yields nearly similar results compared with the results for L_e=0.1 mm in Fig. 6(b), which was presented in our previous work [23]. Although the results using L_e=0.5 mm do not match experimental data as well as those using other element sizes, Fig. 7(b) shows that it may be advantageous to use D_c=0.65. Fig. 7(c) and (d) compare the results for the three different element sizes with different values of D_c. It can be observed that the choice of D_c=0.65 for L_e=0.5 mm yields a slightly delayed crack initiation and a faster crack growth rate than the other cases with different element sizes but is quite similar to the load-CMOD response, rendering it the most suitable. To further confirm whether such a choice is appropriate, the simulated fracture surface is also compared with experimental results in Fig. 8. For comparison, the simulation result using L_e=0.1 mm is also shown where it can be observed that both simulated fracture surfaces using L_e=0.1 mm and L_e=0.5 mm agree well with experimental data.

In the simulated DWTTs presented later in this paper, the element size of 0.5 mm was selected for computational efficiency; thus, the following SMFS model was used:(4)

ε_{f} = 3.34 \cdot exp [- 1.5 \cdot \frac{σ_{m}}{σ_{e}}] + 0.4, D_{c} = 0.65 for L_{e} = 0.5 m m

To further confirm whether the proposed damage model for the different element sizes is appropriate, the FE simulation for the Charpy V-notch test at 0 °C, performed in our previous work [23] using an element size of 0.1 m, was repeated using different element sizes (0.2 mm and 0.5 mm). The corresponding FE meshes are shown in Fig. 9(a), and the resulting simulation results are compared in Fig. 9(b), which shows that the simulated load-displacement curve and impact energy follow a similar trend, supporting the efficacy of the element-size-dependent ductile damage model used in this paper.

3.3. Element-size-dependent cleavage fracture model

In our previous work [23], to simulate cleavage fracture, we applied the maximum principal stress criterion, which is equivalent to the Weibull stress approach [31]. The definition of the Weibull stress is given by(5)

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

where σ₁ is the maximum principal stress distributed on a fracture process zone V, the Weibull parameter m is the material constant, and V₀ is an arbitrarily chosen reference volume. Although the Weibull stress is a widely-used criterion to characterize cleavage fracture, it can be calculated only by post-processing the finite element (FE) analysis. Thus, it is difficult to simulate the combined ductile and cleavage fracture behavior. To overcome this problem, the maximum principal stress criterion within an element was proposed and shown to be equivalent to the Weibull stress criterion(6)

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

where σ_1,max denotes the maximum principal stress over V. The Weibull stress is proportional to the largest maximum principal stress within the fracture process zone V. The reference volume can be conveniently assigned to satisfy V/V₀=1 [23], which makes the Weibull stress numerically equal to the largest maximum principal stress. Therefore, the maximum principal stress can be applied to verify the element-wise cleavage fracture.

In our previous paper [23], the following relationship between the maximum principal stress and the fracture energy of API X80 was suggested by the FE simulation of Charpy impact test data:(7)

\frac{σ_{1, m a x}}{σ_{y} (T)} = {\begin{matrix} 0.40 \cdot \ln (\frac{E}{E_{0}}) + 1.83 for \ln (\frac{E}{E_{0}}) \leq 2.07 \\ 0.10 \cdot \ln (\frac{E}{E_{0}}) + 2.45 for \ln (\frac{E}{E_{0}}) \geq 2.07 \end{matrix}

where E₀=4.82 J (the minimum Charpy energy tested at −150 °C). Eq. (7) is shown in Fig. 10(a). In Eq. (7), the temperature-dependent yield stress value should be used for σ_y. Note that the constants in Eq. (7) were determined for the element size of 0.1 mm.

To incorporate the element size effect on the maximum principal stress criterion to simulate cleavage fracture, E₀ in Eq. (7) is re-defined as(8)

E_{0} = K \cdot V_{D}

where K is the volumetric energy density [J/mm³] and V_D denotes the total volume of damage elements in the FE simulation. In the FE analysis, a fracture is simulated by removing the elements in the first layer in front of the notch tip, as shown in Fig. 11. The volume V_D is the total volume of the first layer elements. For instance, when the element size of L_e is used for the Charpy specimen, the volume V_D can be calculated as V_D=2*L_e*A where A is the un-notched (un-cracked) area. The factor 2 is introduced for the symmetry condition along the crack propagation line; two elements are removed as crack growth. For the Charpy specimen, A=(8 × 10) mm². Thus, with an element size of 0.1 mm, V_D=(2 × 0.1 × 8 × 10) mm³ and with an element size of 0.5 mm, V_D=(2 × 0.5 × 8 × 10) mm³. The constant K in Eq. (8) can be determined as K = 4.82 J/(2 × 0.1 × 8 × 10) mm³=0.30125 J/mm³. Note that E₀=4.82 J was assumed for L_e=0.1 mm in our previous paper [23].

Combining Eqs. (7) and (8) gives(9)

\frac{σ_{1, m a x} (E)}{σ_{y} (T)} = {\begin{matrix} 0.40 \cdot \ln (\frac{E}{K \cdot V_{D}}) + 1.83 for \ln (\frac{E}{K \cdot V_{D}}) \leq 2.07 \\ 0.10 \cdot \ln (\frac{E}{K \cdot V_{D}}) + 2.45 for \ln (\frac{E}{K \cdot V_{D}}) \geq 2.07 \end{matrix}

The simulation results of the Charpy test using different element sizes of L_e=0.1 mm, 0.2 mm, and 0.5 mm are compared with Eq. (9) as shown in Fig. 10. In Fig. 10(a), the constant value of E₀ (=4.82 J) is used, whereas in Fig. 10(b), the proposed value of E₀ (=K•V_D) is used. Note that the calculated E₀=4.82 J for L_e=0.1 mm, E₀=9.84 J for L_e=0.2 mm, and E₀=24.1 J for L_e=0.5 mm. These results show that the use of the proposed Eq. (8) gives predictions less sensitive to the element size, although the results using the largest element size L_e=0.5 mm consistently show less accuracy than those using smaller element sizes. This is because the 0.5-mm element size may be too large for the Charpy specimen where the unnotched ligament is only 8 mm. Therefore, to use an element size of 0.5 mm to predict fracture behavior in a DWTT, the constants in Eq. (9) should be slightly modified as follows:(10)

\frac{σ_{1, m a x} (E)}{σ_{y} (T)} = {\begin{matrix} 0.37 \cdot \ln (\frac{E}{K \cdot V_{D}}) + 1.66 for \ln (\frac{E}{K \cdot V_{D}}) \leq 1.89 \\ 0.10 \cdot \ln (\frac{E}{K \cdot V_{D}}) + 2.17 for \ln (\frac{E}{K \cdot V_{D}}) \geq 1.89 \end{matrix}

The two lines in Eq. (10) are shown in Fig. 10(b) as dotted lines. For the present purpose, determining Eq. (10) is sufficient, but, in principle, the constants in Eqs. (9) and (10) can be found as a function of the element size. Note that for the DWTT data considered in this work, only the first equation is relevant.

To further investigate the applicability of the 0.5-mm element size, two Charpy tests at 150 °C and −90 °C, producing the Charpy impact energies of E_CVN=13.0 J and 78.7 J, respectively, were simulated using two different element sizes, L_e=0.1 mm and 0.5 mm. The resulting fracture surface and calculated energies are compared with experimental data in Fig. 12, Fig. 13. The gray color in the figures indicates the simulated cleavage fracture surface. The locations and sizes of the cleavage fracture from the simulations using the two different element sizes are similar. As shown in Fig. 12(a), the calculated fracture energy is E_CVN=11.6 J for L_e=0.1 mm at −150 °C, which is approximately 11% lower than the measured value of E_CVN=13.0 J. In Fig. 12(b), the calculated value is E_CVN=13.9 J for L_e=0.5 mm, which is 7% higher than the measured value. The corresponding results at −90 °C are shown in Fig. 13.

4. Simulation of DWTT and comparison with test data

4.1. FE model and analysis of DWTT specimen

The DWTTs at various temperatures were simulated using the presented method incorporating the element size effect and compared with experimental data. For numerical stability and efficiency, the element size of 0.5 mm was used along the crack propagation surface in the FE model of the DWTT specimen. The calculations terminated when smaller sizes for the elements such as 0.1 mm or 0.2 mm were used. The quarter model consisting of eight-noded solid elements (C3D8 in ABAQUS) was used for all DWTT simulations. The FE mesh is shown in Fig. 14 with 19,312 elements and 22,951 nodes.

The numerical simulation of the DWTT at ductile-brittle transition temperatures was performed. For the tensile properties, the temperature-dependent properties proposed in Canada [38] were used and can be expressed as(11)

σ = σ_{e, R T} (1 - λ {| T |}^{* k}); λ = {\begin{matrix} 1 : T = T_{r o o m} \\ \frac{T^{*}}{{| T |}^{*}} : T \neq T_{r o o m} \end{matrix}, T^{*} = \frac{T - T_{r o o m}}{T_{m e l t} - T_{r o o m}}

where σ_e,RT indicates the equivalent stress at room temperature. The values of k and T_melt are assumed to be 0.81 and 1500 °C, respectively [38]. The strain rate effect on the tensile properties is not considered in this work.

To simulate the DWTT conditions, a hammer and anvil were modeled as a rigid shell constrained to a reference point, as shown in Fig. 14. The impact load was applied to the reference point using the velocity control option offered in ABAQUS/Implicit [39]. At impact, the experimental hammer speed of 6 m/s was used in the analysis with the large geometry change option. All degrees of freedom for the anvil were fixed, and the hammer could move only vertically. The increment in the dynamic analysis was limited to move the hammer by 60 mm after 0.01 s with the automatic adjustment of the time increment. The mass density of 7900 kg/m³ was assigned to the DWTT specimen.

During the analysis, ductile and brittle fractures were simulated as follows. To simulate ductile fracture, the incremental ductile damage is calculated at the Gauss point in an element by Eqs. (1) and (2), given in Section 2.1. When the accumulated damage reaches the critical damage value (for the element size of 0.5 mm, the critical value was D_c=0.65), the elastic modulus and equivalent stress are reduced to small values to simulate ductile fracture. Detailed information is provided in our previous paper [23]. To simulate cleavage fracture, the maximum principal stress σ_1,max should be calculated using Eq. (10) for the given experimentally-measured DWTT energy. Note that the unnotched ligament area of the DWTT specimen is A = 1685.5 mm², and thus E_o=K•V_D=507.77 J was used based on the element size of 0.5 mm. When the maximum principal stress calculated at the Gauss point in an element exceeds the criterion σ_1,max, the technique used to simulate ductile fracture is also applied to simulate cleavage fracture, namely, the elastic modulus and equivalent stress are reduced to small values. The flowchart of fracture simulation is shown in Fig. 15. In each increment, the maximum principal stress and the plastic damage according to Eq. (2) is calculated. If the maximum principal stress is greater than σ_1,max but the accumulated plastic damage does not satisfy the ductile fracture criterion, Eq. (3), this element is assumed to be failed by cleavage and the element is removed by reducing the stresses and elastic modulus to small values, as described above. On the other hand, if the maximum principal stress is less than σ_1,max and the accumulated plastic damage satisfies the ductile fracture criterion, this element is assumed to be failed by ductile and the element is removed by reducing the stresses and elastic modulus to small values. When the maximum principal stress is less than σ_1,max and the accumulated plastic damage does not satisfy the ductile fracture criterion, the accumulated plastic damage is updated and saved for the next increment. It should be noted that ductile and cleavage fracture is assumed to be independent, and thus the accumulated plastic damage does not affect the cleavage fracture.

From the FE simulation, the following data are obtained and compared with the experimental data. The first is the load-displacement curve, under which the calculated area is used to determine the DWTT energy, which is also compared with the experimental value (used as input for the FE analysis). The second is the fracture surface from which the shear area (percentage ductile fracture area) can be calculated and also compared with the experimental data. Finally, the occurrence of inverse fracture (or abnormal fracture) in the simulation is similarly evaluated.

4.2. Comparisons between the experimental results and simulations

Fig. 16 compares the fracture surface of the DWTT results at −97 °C with the simulation results. The experimentally-measured energy E_exp, given in the captions, is used to calculate the maximum principal stress with Eq. (10). The calculated σ_1,max is also given in the captions. In Fig. 16(a), the fracture surfaces from the experiment and FE simulation are compared. The experimental fracture surface is divided into two fracture modes: ductile and cleavage fracture, according to Sung et al. [7]. In the simulated surface, the black color indicates cleavage fracture, whereas the lighter color indicates ductile fracture. In both the experiment and simulation, cleavage fracture started and continued from the center of the notch tip to the end of the specimen. Ductile fracture only appears on the specimen surface due to the lower plastic constraint. The predicted load-load line displacement curve is compared with experimental data in Fig. 16(b), showing good agreement. Note that the experimental data contain oscillations due to the impact of the hammer. The calculated fracture energy for Test 1 was E_FE=0.66 kJ, which is only 10% greater than the measured fracture energy E_exp=0.6 kJ.

The corresponding results for Test 2 are shown in Fig. 17. This test was performed at −97 °C, similar to Test 1, but it produced a higher energy than Test 1 (E_exp=1.03 kJ compared with E_exp=0.60 kJ for Test 1). In the experiment, the fracture surface is quite similar to that of Test 1 but shows more ductile fracture area near the specimen surface. Tani et al. [51] investigated relationships between the Charpy energy and a distance triggering brittle fracture. They showed that the variable distribution of the distance of brittle fracture initiation factors caused the scatter of the Charpy impact energy. In the DWTT test, such brittle fracture initiation factors could exist, which in turn produce the scatter in DWTT energies and fracture surfaces. Thus it would be quite difficult to simulate fracture surfaces in cleavage-dominant cases. Fig. 18 compares the test data at −80 °C (E_exp=1.28 kJ) with the simulation results. Again, the fracture surface is similar but demonstrates more ductile fracture. It can be observed that for both the experimental and simulated cases, the fracture surfaces and load-displacement curves agree well. Additionally, the predicted fracture surfaces are similar to experimental fracture surfaces, and the predicted energies are close to the measured energies: E_FE=1.02 kJ for Test 2 and E_FE=1.21 kJ for Test 3.

Fig. 19 compares the simulation results with the experimental data at −60 °C (Test 4) with a measured energy of E_exp=1.9 kJ. It can be observed that the fracture surface from the experiment includes one more region (delamination) in the ductile fracture area. Babinsky et al. [40] suggested that delamination occurs as a result of brittle fracture, and Joo et al. [41] suggested that the maximum principal stress may promote delamination for API X80 steel. Thus, the delamination can be considered as cleavage fracture. In the simulation, both the cleavage fracture in the center region and the ductile fracture on the specimen surface can be simulated well. Furthermore, the delamination region inside the ductile fracture region can be successfully predicted as cleavage fracture, as shown in Fig. 19(a). The predicted load-load line displacement curve is compared with the experimental data in Fig. 19(b), showing good agreement. In addition, the predicted energy (E_FE=1.8 kJ) is very close to the measured energy E_exp=1.9 kJ.

The simulation results at −20 °C are compared with experimental data in Fig. 20 for Test 5 and in Fig. 21 for Test 6. Note that the measured energies are quite high: E_exp=10.5 kN for Test 5 and E_exp=14.2 kJ for Test 6. The experimental load-displacement curves show a rather smooth decrease from the maximum load due to the larger proportion of ductile fracture. The simulation can well predict not only the maximum load but also the slope of the load drop. The predicted energies are relatively close to the experimental values: E_FE=10.7 kJ for Test 5 and E_FE=12.2 kJ for Test 6. Due to the high absorbed energy, more ductile fracture surface can be observed compared with the previous cases. The cleavage fracture initiates from the notch tip, propagates for a short distance, and then changes to ductile fracture. The initial cleavage fracture surface in Fig. 20(a) shows a triangle shape in both experiment and simulation. Hong et al. [3] performed DWTT tests with various specimen thicknesses for API X70 and X80 steel, and observed a triangle shape for the initial cleavage fracture surface for the pressed notch DWTT tests. After ductile fracture propagation with small delamination and cleavage fracture surfaces, the fracture in the center of the specimen becomes cleavage fracture. This phenomenon is referred to as the “inverse fracture” in the literature (see for instance Hwang et al. [9]). As shown in Figs. 20(a) and 21(a), the inverse fracture pattern can be also predicted in the simulation.

Table 3 summarizes the main results of the experiment and FE simulation, which are also presented in Fig. 22 in graphical form. The DWTT energies predicted by the simulation are very close to those measured in the experiments, except in Test 6 where the predicted energy is approximately 14% lower than the experimental value, a difference of which is still small for predictions at ductile-brittle transition temperatures. Typically, for shear area predictions, differences tend to be larger. However, the maximum difference between experimental values and predicted values for the shear area is within 18% (observed in Test 6), which can be regarded as a good prediction since large shear area cases are usually more relevant.

Table 3. Comparison of experimental data with simulation results. The subscript “exp” denotes the experimental values, whereas “FE” denotes the simulation results.

Test Number	1	2	3	4	5	6
T [ °C]	−97	−97	−80	−60	−20	−20
E_exp [kJ]	0.60	1.03	1.28	1.9	10.5	14.2
E_FE [kJ]	0.66	1.02	1.21	1.8	10.7	12.2
Shear Area [%]	8.5	11.4	19.5	40.6	77.9	69.6
Simulated Shear Area [%]	6.2	18.1	21.0	29.9	81.1	82.6

5. Conclusion

This paper proposes a method to simultaneously simulate interacting ductile and cleavage fracture in which the simulation results are compared with six API X80 DWTT data at temperatures ranging between −97 °C to −20 °C. This method is an extension of our previous method for simulating the Charpy impact test [23] by incorporating the element size effect on the ductile and cleavage damage models, which is a crucial aspect in the present method for the fracture simulation of larger-scale structures. For the ductile damage model, the stress-modified fracture strain (SMFS) model that was used in our previous work is incorporated with the element size effect by introducing the element-size-dependent critical damage model in this work. For the cleavage damage model in our previous study, a maximum principal stress criterion was proposed and the relationship between the maximum principal stress and Charpy impact energy was established. In this work, the energy is re-defined using the element-size-dependent volume with the relationship determined to be a function of the element size.

From the DWTT, the load-displacement curve and absorbed energy are measured. Using the measured energy, the cleavage fracture criterion is determined and the DWTT simulation is performed. The simulated load-displacement curves and absorbed energies are in good agreement with all six test data. Furthermore, the simulation is shown to reproduce experimental fracture surfaces of not only ductile and cleavage fracture surfaces but also inverse fracture surfaces. The good agreement between experimental values and simulated values in this study indicates the effectiveness and accuracy of the proposed method in simultaneously simulating interacting ductile and cleavage fracture for large-scale specimens or pipes. The key point to make simulating interacting ductile and cleavage fracture for large-scale specimens or pipes possible is to properly incorporate the element size effect into a damage model. When the fracture area to be simulated becomes larger, the element size used in simulation needs to be adjusted because the use of a small element can cause numerical instability due to the fact that the number of elements to be failed increases substantially. Although there are some methods available to minimize the element size effect in damage analyses such as non-local approach, the method proposed in this paper is more straightforward and easily implemented. For ductile fracture simulation, for instance, the authors have already shown the effectiveness of the present approach in simulating long ductile tearing in full-scale piping components [26,27,29].

Finally, the proposed method can offer an effective tool to investigate the variables that contribute to the occurrence of inverse fractures in high-strength pipeline materials. For instance, the effects of the presence of a Chevron notch, material strength and ductility, specimen width, and loading conditions on the occurrence of inverse fractures can be evaluated using the method proposed in this work.

CRediT authorship contribution statement

Ji-Su Kim: Conceptualization, Methodology, Formal analysis, Writing - original draft, Visualization. Yun-Jae Kim: Validation, Writing - review & editing, Supervision, Project administration. Myeong-Woo Lee: Software, Formal analysis. Ki-Seok Kim: Investigation, Resources. Kazuki Shibanuma: Validation, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by POSCO [2017R240], and the Korea Agency for Infrastructure Technology Advancement [17IFIP-B067108-05].

References

[1]
API recommended practice 5L3
API, Washington, DC, USA (1996)
Google Scholar
[2]
ASTM
Standard test method for drop-weight tear tests of ferritic steels 1
(October 1997), 10.1520/E0436-03R14.2
Google Scholar
[3]
S. Hong, S.Y. Shin, S. Lee, N.J. Kim
Effects of specimen thickness and notch shape on fracture modes in the drop weight tear test of API X70 and X80 linepipe steels
Metall Mater Trans A, Phys Metall Mater Sci, 42 (2011), pp. 2619-2632, 10.1007/s11661-011-0697-9
View in Scopus Google Scholar
[4]
J. Fang, J. Zhang, L. Wang
Evaluation of cracking behavior and critical CTOA values of pipeline steel from DWTT specimens
Eng Fract Mech, 124-125 (2014), pp. 18-29, 10.1016/j.engfracmech.2014.04.031
View PDF View article View in Scopus Google Scholar
[5]
G. Mannucci, D. Harris
Fracture properties of API X100 gas pipeline steels, final report
European Commission, Brussels, Belgium (2002)
Google Scholar
[6]
D.L. Rudland, Y.Y. Wang, G. Wilkowski, D.J. Horsley
Characterizing dynamic fracture toughness of linepipe steels using the pressed-notch drop-weight-tear test specimen
Eng Fract Mech, 71 (2004), pp. 2533-2549, 10.1016/j.engfracmech.2003.12.007
View PDF View article View in Scopus Google Scholar
[7]
H.K. Sung, S.S. Sohn, S.Y. Shin, S. Lee, N.J. Kim, S.H. Chon, et al.
Effects of finish rolling temperature on inverse fracture occurring during drop weight tear test of API X80 pipeline steels
Mater Sci Eng A, 541 (2012), pp. 181-189, 10.1016/j.msea.2012.02.019
View PDF View article View in Scopus Google Scholar
[8]
Z. Yang, C.B. Kim, Y. Feng, C. Cho
Abnormal fracture appearance in drop-weight tear test specimens of pipeline steel
Mater Sci Eng A, 483-484 (2008), pp. 239-241, 10.1016/j.msea.2006.09.182
View PDF View article View in Scopus Google Scholar
[9]
B. Hwang, S. Lee, Y.M. Kim, N.J. Kim, J.Y. Yoo, C.S. Woo
Analysis of abnormal fracture occurring during drop-weight tear test of high-toughness line-pipe steel
Mater Sci Eng A, 368 (1–2) (2004), pp. 18-27, 10.1016/j.msea.2003.09.075
View PDF View article View in Scopus Google Scholar
[10]
Z. Yang
The fracture during drop-weight tear test of high-performance pipeline steel and its abnormal fracture appearance
Procedia Mater. Sci., 3 (2014), pp. 1591-1598, 10.1016/j.mspro.2014.06.257
View PDF View article Google Scholar
[11]
B. Hwang, Y.G. Kim, S. Lee, N.J. Kim, J.Y. Yoo
Effects of microstructure on inverse fracture occurring during drop-weight tear testing of high-toughness X70 pipeline steels
Metall Mater Trans A Phys Metall Mater Sci, 36 (2005), pp. 371-387, 10.1007/s11661-005-0309-7
View in Scopus Google Scholar
[12]
M. Kang, H. Kim, S. Lee, S.Y. Shin
Effects of dynamic strain hardening exponent on abnormal cleavage fracture occurring during drop weight tear test of API X70 and X80 linepipe steels
Metall Mater Trans A Phys Metall Mater Sci, 45 (2014), pp. 682-697, 10.1007/s11661-013-2046-7
View in Scopus Google Scholar
[13]
Y. Zhen, X. Li, Y. Cao, S. Zhang
A novel method to determine critical CTOA directly by load-displacement curve
Eng Fract Mech, 230 (2020), Article 107013, 10.1016/j.engfracmech.2020.107013
View PDF View article View in Scopus Google Scholar
[14]
A. Dunbar, X. Wang, W.R. Tyson, S. Xu
Simulation of ductile crack propagation and determination of CTOAs in pipeline steels using cohesive zone modelling
Fatigue Fract Eng Mater Struct, 37 (2014), pp. 592-602, 10.1111/ffe.12143
View in Scopus Google Scholar
[15]
S. Parmar, C. Bassindale, X. Wang, W.R. Tyson, S. Xu
Simulation of ductile fracture in pipeline steels under varying constraint conditions using cohesive zone modeling
Int J Press Vessel Pip, 162 (2018), pp. 86-97, 10.1016/j.ijpvp.2018.03.003
View PDF View article View in Scopus Google Scholar
[16]
P.S. Yu, C.Q. Ru
Analysis of energy absorptions in drop-weight tear tests of pipeline steel
Eng Fract Mech (2016), 10.1016/j.engfracmech.2016.04.007
Google Scholar
[17]
B. Paermentier, D. Debruyne, R. Talemi
Numerical modelling of dynamic ductile fracture propagation in different lab-scale experiments using GTN damage model
Frat Ed Integrita Strutt, 52 (2020), pp. 105-112, 10.3221/IGF-ESIS.52.09
View in Scopus Google Scholar
[18]
A.L. 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 in Scopus Google Scholar
[19]
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
[20]
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
[21]
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]
Y.Y. Jang, J.H. Moon, N.S. Huh, K.S. Kim, W.Y. Cho, M.W. Lee, Y.J. Kim
Evaluations of ductile and cleavage fracture using coupled GTN and Beremin model in API X70 pipelines steel
Proc. Int. Conf. Offshore Mech. Arct. Eng. - OMAE (2019), 10.1115/OMAE2019-96483
Google Scholar
[23]
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
[24]
M.W. Lee, J.S. Kim, J.Y. Jeon, Y.J. Kim, J.W. Kim, J.S. Kim
Comparison of numerical predictions with experimental burst pressures of tubes with multiple surface cracks
Eng Fract Mech, 201 (2018), pp. 176-195, 10.1016/j.engfracmech.2018.06.016
View PDF View article View in Scopus Google Scholar
[25]
G.G. Youn, H.S. Nam, Y.J. Kim, J.W. Kim
Numerical prediction of thermal aging and cyclic loading effects on fracture toughness of cast stainless steel CF8A: experimental and numerical study
Int J Mech Sci, 163 (2019), Article 105120, 10.1016/j.ijmecsci.2019.105120
View PDF View article View in Scopus Google Scholar
[26]
H.S. Nam, Y.R. Oh, Y.J. Kim, J.S. Kim, N. Miura
Application of engineering ductile tearing simulation method to CRIEPI pipe test
Eng Fract Mech, 153 (2016), pp. 128-142, 10.1016/j.engfracmech.2015.12.012
View PDF View article View in Scopus Google Scholar
[27]
H.S. Nam, J.M. Lee, Y.J. Kim, J.W. Kim
Numerical ductile fracture prediction of circumferential through-wall cracked pipes under very low cycle fatigue loading condition
Eng Fract Mech, 194 (2018), pp. 175-189, 10.1016/j.engfracmech.2018.02.025
View PDF View article View in Scopus Google Scholar
[28]
H.S. Nam, J.M. Lee, G.G. Youn, Y.J. Kim, J.W. Kim
Simulation of ductile fracture toughness test under monotonic and reverse cyclic loading
Int J Mech Sci, 135 (2018), pp. 609-620, 10.1016/j.ijmecsci.2017.11.037
View PDF View article View in Scopus Google Scholar
[29]
H.W. Ryu, K.D. Bae, Y.J. Kim, J.J. Han, J.S. Kim, P.J. Budden
Ductile tearing simulation of Battelle pipe test using simplified stress-modified fracture strain concept
Fatigue Fract Eng Mater Struct, 39 (11) (2016), pp. 1391-1406, 10.1111/ffe.12456
View in Scopus Google Scholar
[30]
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 (1) (2011), pp. 124-137, 10.1016/j.engfracmech.2010.10.004
View PDF View article View in Scopus Google Scholar
[31]
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 in Scopus Google Scholar
[32]
Institute AP
API 5 L Specification for line pipe
API Spec 5 L (2007), 10.1520/G0154-12A
Google Scholar
[33]
DNV
Fracture control for pipeline installation methods introducing cyclic plastic strain
Recomm Pract (2006)
DNV-RP-F108
Google Scholar
[34]
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
[35]
S. Cravero, C. Ruggieri
Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance
Eng Fract Mech, 74 (17) (2007), pp. 2735-2757, 10.1016/j.engfracmech.2007.01.012
View PDF View article View in Scopus Google Scholar
[36]
X.K. Zhu
Full-range stress intensity factor solutions for clamped SENT specimens
Int J Press Vessel Pip, 149 (2017), pp. 1-13, 10.1016/j.ijpvp.2016.11.004
View PDF View article Google Scholar
[37]
H.G. Pisarski
Determination of pipe girth weld fracture toughness using SENT specimens
Proc. Bienn. Int. Pipeline Conf. IPC (2010), pp. 217-224, 10.1115/IPC2010-31123
View in Scopus Google Scholar
[38]
S. Canada
Temperature effects on dynamic fracture of pipeline steel
Master of Science, University of Alberta (2015)
Google Scholar
[39]
Abaqus
ABAQUS Version 2016
Dessault Syst (2016)
Google Scholar
[40]
K. Babinsky, S. Primig, W. Knabl, A. Lorich, R. Stickler, H. Clemens
Fracture behavior and delamination toughening of molybdenum in charpy impact tests
JOM, 68 (2016), pp. 2854-2863, 10.1007/s11837-016-2075-y
View in Scopus Google Scholar
[41]
M.S. Joo, D.W. Suh, J.H. Bae, H.K.D.H. Bhadeshia
Role of delamination and crystallography on anisotropy of Charpy toughness in API-X80 steel
Mater Sci Eng, A, 546 (2012), pp. 314-322, 10.1016/j.msea.2012.03.079
View PDF View article View in Scopus Google Scholar
[42]
C. Ruggieri, R.H. Dodds
A local approach to cleavage fracture modeling: an overview of progress and challenges for engineering applications
Eng Fract Mech, 187 (2018), pp. 381-403, 10.1016/j.engfracmech.2017.12.021
View PDF View article View in Scopus Google Scholar
[43]
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
Proc Struct Integr, 2 (2016), pp. 1643-1651, 10.1016/j.prostr.2016.06.208
View PDF View article View in Scopus Google Scholar
[44]
Y. Li, Z. Wang, Y. Lei, G. Qian, M. Zhou, Z. Gao, et al.
Weibull stress analysis in local approach to fracture
Theor Appl Fract Mech, 104 (2019), Article 102379, 10.1016/j.tafmec.2019.102379
[1]
View PDF View article View in Scopus Google Scholar
[45]
T. Jin, Z. Wang, Q. Wang, D. Wang, Y. Li, M. Zhou
Weibull stress analysis for the corner crack in reactor pressure vessel nozzle
Adv Mech Eng, 11 (12) (2019), pp. 1-8, 10.1177/1687814019893567
Google Scholar
[46]
C. Ruggieri
A modified local approach including plastic strain effects to predict cleavage fracture toughness from subsize precracked Charpy specimens
Theor Appl Fract Mech, 105 (2020), Article 102421, 10.1016/j.tafmec.2019.102421
View PDF View article View in Scopus Google Scholar
[47]
A. Rossoll, C. Berdin, C. Prioul
Determination of the fracture toughness of a low alloy steel by the instrumented Charpy impact test
Int J Fract, 115 (2002), pp. 205-226, 10.1023/A:1016323522441
View in Scopus Google Scholar
[48]
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 (3) (2005), pp. 413-434, 10.1016/j.engfracmech.2004.03.011
View PDF View article View in Scopus Google Scholar
[49]
A.R. Shen, P.C. Li, G. Qian, Z.S. Yu, F. Berto, W. Wu
Study on cleavage fracture probability-load curves of ferritic steel 20MnMoNi55 by using the new local approach model
Int J Press Vessel Pip, 178 (2019), Article 103999, 10.1016/j.ijpvp.2019.103999
View PDF View article View in Scopus Google Scholar
[50]
K. Bhattacharyya, S. Acharyya, S. Dhar, J. Chattopadhyay
Variation of Beremin Model Parameters with temperature by Monte Carlo Simulation
J Press Vessel Technol Trans ASME, 141 (2) (2019), Article 021401, 10.1115/1.4042121
View in Scopus Google Scholar
[51]
T. Tani, M. Nagumo
Fracture process of a low carbon low alloy steel relevant to charpy toughness at ductile-brittle fracture transition region
Metall Mater Trans A, 26 (2) (1995), pp. 391-399, 10.1007/BF02664675
View in Scopus Google Scholar

Cited by (16)

Prediction of the irradiation effect on the fracture toughness for stainless steel using a stress-modified fracture strain model
2024, International Journal of Mechanical Sciences
Citation Excerpt :
To overcome these issues, a finite element analysis can be a useful alternative. Among currently available approaches, the stress-modified fracture strain model [24,25] has been applied to predict changes in the fracture behavior due to various factors [26–30]. The model was implemented as an ABAQUS user-defined function by Oh et al. [31] and was validated [31] through comparisons with experimental results and the Gurson-Tvergaard-Needleman (GTN) model [32–36].
This paper proposes a numerical method for predicting the reduction in the fracture toughness with neutron dose using the concept of an embrittlement constant. Tensile and fracture toughness test data for type 304 stainless steel in the literature [41,42] are used to validate the proposed method. Fracture toughness tests are simulated using a stress-modified fracture strain damage model implemented in an ABAQUS user-subroutine. The true stress-strain curve and one point of the fracture strain locus are obtained from the tensile test simulation. The remaining parameters of the fracture strain locus are determined by simulating a fracture toughness test. The fracture strain locus is modified to reflect the irradiation effect on the fracture toughness using the proposed irradiation embrittlement constant C_I. The function of the constant with the neutron dose is calculated from the tensile tests and simulations. Subsequently, the modified damage model is used to predict the reduction in the fracture toughness. The predicted simulation results are compared with experimental data, showing good agreement.
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
2022, Theoretical and Applied Fracture Mechanics
In this paper, a robust technique is presented to predict the peak load and crack initiation energy of dynamic brittle fracture in X70 steel pipes using an improved artificial neural network (IANN). The main objective is to investigate the behaviour of API X70 steel based on two experimental tests, namely Drop Weight Tear Test (DWTT) and the Charpy V-notch impact (CVN), for steel pipe specimens. The mechanical properties in the brittle fracture behaviour of API X70 steel pipes are predicted utilizing numerical approaches with different crack lengths. Next, to simulate the impact of API X70 steel pipes at lower temperatures through a numerical approach, a cohesive approach using the extended Finite Element Method (XFEM) is used. The data obtained are used as input for the proposed IANN using Balancing Composite Motion Optimization (BCMO), Particle Swarm Optimization (PSO) and Jaya optimization algorithms, to predict the peak load values and crack initiation energy of dynamic brittle fractures in API X70 steel with different crack lengths. The results show the effectiveness of ANN-PSO and ANN-BCMO based on the convergence of the results and the accuracy of the prediction of the peak load and crack initiation energy. Note that, the source codes are publicly available at https://github.com/Samir-Khatir/JAYA-ANN.git.
Quantification of notch type and specimen thickness effects on ductile and brittle fracture behaviour of drop weight tear test
2022, European Journal of Mechanics A Solids
Citation Excerpt :
For the experimental data, published DWTT data using two notch types (press and chevron notch) and two specimen thicknesses (19 mm and 25 mm) (Hong et al., 2011) were used for investigation. The fracture behaviours of the DWTTs are investigated using the ductile-brittle fracture simulation model previously used by the authors (Kim et al., 2020, 2021). For ductile fracture simulation, the stress modified fracture strain model is used, whereas for brittle fracture simulation, the maximum principal stress criterion.
In this paper, effects of the notch type and specimen thickness on fracture behaviour of DWTT for API X80 at transition temperatures are quantified via FE analysis. Two notch types (press and chevron notch) and two specimen thicknesses (19 mm and 25 mm) are considered for the DWTT specimen. Fracture behaviours of the DWTTs are investigated using a ductile-brittle fracture simulation model. The ductile-brittle fracture simulation model is validated by comparing simulation results with experimental data. From the simulation results, it is found that the effect of the notch type and specimen thickness on fracture behaviour of DWTT can be well reproduced. Finally, the experimental findings are quantitatively supported by using the ductile-brittle fracture simulation method.
Numerical investigation on fatigue life of aluminum brazing structure with fin-plate-side bar under the low temperature thermal-structure cyclic stress
2022, Engineering Failure Analysis
A stress analysis model was established to analyze the thermal and structural stress of aluminum brazing structure with fin-plate-side bar (ABS) in the LNG plate-fin heat exchanger. The fatigue life of ABS was evaluated based on the above stress analysis results by the different standard. The result shows that the thermal and structural stress concentration is generated at the brazed joint of ABS. Under the common action of thermal and structural stress, the equivalent stress is influenced mainly by the equivalent thermal stress. The equivalent alternating stress was calculated to be 153.5 MPa based on thermal and structural stress. The permissible cycle numbers at the brazed joint of ABS, which is calculated by the fatigue assessment procedure of ASME and JB4732, are 3311 and 2953, respectively. The fatigue assessment results based on the third strength theory is more conservative for the ABS. The influence of operation parameters is also analyzed for the fatigue life of ABS. The temperature difference between NG and MR, MR temperature and NG pressure will be the main factors to impact the fatigue life of that. And a method is proposed to predict the fatigue life of ABS according to the main factors. The error will be less than 10% between the prediction results and the simulation results.
From macro- to micro-experiments: Specimen-size independent identification of plasticity and fracture properties
2021, International Journal of Mechanical Sciences
The stress-strain response of most engineering materials can be conveniently determined using well-established macro-specimens with outer dimensions of several millimeters or even centimeters. However, in the case of curved thin-walled structures or structures with spatial material property gradients, it is often impossible to extract macro-specimens. For the first group of structures the specimen dimensions are greater than the structural dimensions, while for the second group, the assumption of statistically-homogeneous material properties is not valid throughout a volume as large as the specimen gage section. A frequently encountered example is material property gradients around welds in metallic structures or castings in automotive engineering. In view of characterizing the local plasticity and fracture properties at the millimeter scale, a micro-testing technique is discussed in this study. In addition, the microscopic experimental results of 100μm thick steel alloy API X52 are compared to standard macroscopic counterparts with 2mm thickness. A new custom-made micro-testing device is employed to load uniaxial tension, notched, central hole and in-plane shear micro-specimens with a quasi-static nominal actuator strain rate of less than 1μm/s. These micro-scale experiments on a pipeline steel are performed under an optical microscope; a planar digital image correlation is used to compute the surface strain fields. The plasticity and fracture initiation model are then derived using the conventional macro- and micro-experiments. It is concluded that micro-testing provides a powerful means to characterize materials whose properties are homogeneous over a few hundred microns only.
Measuring J-R curve under dynamic loading conditions using digital image correlation
2023, Fatigue and Fracture of Engineering Materials and Structures

View all citing articles on Scopus

View Abstract

[1] [1]
API recommended practice 5L3
API, Washington, DC, USA (1996)
Google Scholar

[2] [2]
ASTM
Standard test method for drop-weight tear tests of ferritic steels 1
(October 1997), 10.1520/E0436-03R14.2
Google Scholar

[3] [3]
S. Hong, S.Y. Shin, S. Lee, N.J. Kim
Effects of specimen thickness and notch shape on fracture modes in the drop weight tear test of API X70 and X80 linepipe steels
Metall Mater Trans A, Phys Metall Mater Sci, 42 (2011), pp. 2619-2632, 10.1007/s11661-011-0697-9
View in Scopus Google Scholar

[4] [4]
J. Fang, J. Zhang, L. Wang
Evaluation of cracking behavior and critical CTOA values of pipeline steel from DWTT specimens
Eng Fract Mech, 124-125 (2014), pp. 18-29, 10.1016/j.engfracmech.2014.04.031
View PDF View article View in Scopus Google Scholar

[5] [5]
G. Mannucci, D. Harris
Fracture properties of API X100 gas pipeline steels, final report
European Commission, Brussels, Belgium (2002)
Google Scholar

[6] [6]
D.L. Rudland, Y.Y. Wang, G. Wilkowski, D.J. Horsley
Characterizing dynamic fracture toughness of linepipe steels using the pressed-notch drop-weight-tear test specimen
Eng Fract Mech, 71 (2004), pp. 2533-2549, 10.1016/j.engfracmech.2003.12.007
View PDF View article View in Scopus Google Scholar

[7] [7]
H.K. Sung, S.S. Sohn, S.Y. Shin, S. Lee, N.J. Kim, S.H. Chon, et al.
Effects of finish rolling temperature on inverse fracture occurring during drop weight tear test of API X80 pipeline steels
Mater Sci Eng A, 541 (2012), pp. 181-189, 10.1016/j.msea.2012.02.019
View PDF View article View in Scopus Google Scholar

[8] [8]
Z. Yang, C.B. Kim, Y. Feng, C. Cho
Abnormal fracture appearance in drop-weight tear test specimens of pipeline steel
Mater Sci Eng A, 483-484 (2008), pp. 239-241, 10.1016/j.msea.2006.09.182
View PDF View article View in Scopus Google Scholar

[9] [9]
B. Hwang, S. Lee, Y.M. Kim, N.J. Kim, J.Y. Yoo, C.S. Woo
Analysis of abnormal fracture occurring during drop-weight tear test of high-toughness line-pipe steel
Mater Sci Eng A, 368 (1–2) (2004), pp. 18-27, 10.1016/j.msea.2003.09.075
View PDF View article View in Scopus Google Scholar

[10] [10]
Z. Yang
The fracture during drop-weight tear test of high-performance pipeline steel and its abnormal fracture appearance
Procedia Mater. Sci., 3 (2014), pp. 1591-1598, 10.1016/j.mspro.2014.06.257
View PDF View article Google Scholar

[11] [11]
B. Hwang, Y.G. Kim, S. Lee, N.J. Kim, J.Y. Yoo
Effects of microstructure on inverse fracture occurring during drop-weight tear testing of high-toughness X70 pipeline steels
Metall Mater Trans A Phys Metall Mater Sci, 36 (2005), pp. 371-387, 10.1007/s11661-005-0309-7
View in Scopus Google Scholar

[12] [12]
M. Kang, H. Kim, S. Lee, S.Y. Shin
Effects of dynamic strain hardening exponent on abnormal cleavage fracture occurring during drop weight tear test of API X70 and X80 linepipe steels
Metall Mater Trans A Phys Metall Mater Sci, 45 (2014), pp. 682-697, 10.1007/s11661-013-2046-7
View in Scopus Google Scholar

[13] [13]
Y. Zhen, X. Li, Y. Cao, S. Zhang
A novel method to determine critical CTOA directly by load-displacement curve
Eng Fract Mech, 230 (2020), Article 107013, 10.1016/j.engfracmech.2020.107013
View PDF View article View in Scopus Google Scholar

[14] [14]
A. Dunbar, X. Wang, W.R. Tyson, S. Xu
Simulation of ductile crack propagation and determination of CTOAs in pipeline steels using cohesive zone modelling
Fatigue Fract Eng Mater Struct, 37 (2014), pp. 592-602, 10.1111/ffe.12143
View in Scopus Google Scholar

[15] [15]
S. Parmar, C. Bassindale, X. Wang, W.R. Tyson, S. Xu
Simulation of ductile fracture in pipeline steels under varying constraint conditions using cohesive zone modeling
Int J Press Vessel Pip, 162 (2018), pp. 86-97, 10.1016/j.ijpvp.2018.03.003
View PDF View article View in Scopus Google Scholar

[16] [16]
P.S. Yu, C.Q. Ru
Analysis of energy absorptions in drop-weight tear tests of pipeline steel
Eng Fract Mech (2016), 10.1016/j.engfracmech.2016.04.007
Google Scholar

[17] [17]
B. Paermentier, D. Debruyne, R. Talemi
Numerical modelling of dynamic ductile fracture propagation in different lab-scale experiments using GTN damage model
Frat Ed Integrita Strutt, 52 (2020), pp. 105-112, 10.3221/IGF-ESIS.52.09
View in Scopus Google Scholar

[18] [18]
A.L. 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 in Scopus Google Scholar

[19] [19]
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

[20] [20]
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

[21] [21]
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] [22]
Y.Y. Jang, J.H. Moon, N.S. Huh, K.S. Kim, W.Y. Cho, M.W. Lee, Y.J. Kim
Evaluations of ductile and cleavage fracture using coupled GTN and Beremin model in API X70 pipelines steel
Proc. Int. Conf. Offshore Mech. Arct. Eng. - OMAE (2019), 10.1115/OMAE2019-96483
Google Scholar

[23] [23]
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

[24] [24]
M.W. Lee, J.S. Kim, J.Y. Jeon, Y.J. Kim, J.W. Kim, J.S. Kim
Comparison of numerical predictions with experimental burst pressures of tubes with multiple surface cracks
Eng Fract Mech, 201 (2018), pp. 176-195, 10.1016/j.engfracmech.2018.06.016
View PDF View article View in Scopus Google Scholar

[25] [25]
G.G. Youn, H.S. Nam, Y.J. Kim, J.W. Kim
Numerical prediction of thermal aging and cyclic loading effects on fracture toughness of cast stainless steel CF8A: experimental and numerical study
Int J Mech Sci, 163 (2019), Article 105120, 10.1016/j.ijmecsci.2019.105120
View PDF View article View in Scopus Google Scholar

[26] [26]
H.S. Nam, Y.R. Oh, Y.J. Kim, J.S. Kim, N. Miura
Application of engineering ductile tearing simulation method to CRIEPI pipe test
Eng Fract Mech, 153 (2016), pp. 128-142, 10.1016/j.engfracmech.2015.12.012
View PDF View article View in Scopus Google Scholar

[27] [27]
H.S. Nam, J.M. Lee, Y.J. Kim, J.W. Kim
Numerical ductile fracture prediction of circumferential through-wall cracked pipes under very low cycle fatigue loading condition
Eng Fract Mech, 194 (2018), pp. 175-189, 10.1016/j.engfracmech.2018.02.025
View PDF View article View in Scopus Google Scholar

[28] [28]
H.S. Nam, J.M. Lee, G.G. Youn, Y.J. Kim, J.W. Kim
Simulation of ductile fracture toughness test under monotonic and reverse cyclic loading
Int J Mech Sci, 135 (2018), pp. 609-620, 10.1016/j.ijmecsci.2017.11.037
View PDF View article View in Scopus Google Scholar

[29] [29]
H.W. Ryu, K.D. Bae, Y.J. Kim, J.J. Han, J.S. Kim, P.J. Budden
Ductile tearing simulation of Battelle pipe test using simplified stress-modified fracture strain concept
Fatigue Fract Eng Mater Struct, 39 (11) (2016), pp. 1391-1406, 10.1111/ffe.12456
View in Scopus Google Scholar

[30] [30]
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 (1) (2011), pp. 124-137, 10.1016/j.engfracmech.2010.10.004
View PDF View article View in Scopus Google Scholar

[31] [31]
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 in Scopus Google Scholar

[32] [32]
Institute AP
API 5 L Specification for line pipe
API Spec 5 L (2007), 10.1520/G0154-12A
Google Scholar

[33] [33]
DNV
Fracture control for pipeline installation methods introducing cyclic plastic strain
Recomm Pract (2006)
DNV-RP-F108
Google Scholar

[34] [34]
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

[35] [35]
S. Cravero, C. Ruggieri
Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance
Eng Fract Mech, 74 (17) (2007), pp. 2735-2757, 10.1016/j.engfracmech.2007.01.012
View PDF View article View in Scopus Google Scholar

[36] [36]
X.K. Zhu
Full-range stress intensity factor solutions for clamped SENT specimens
Int J Press Vessel Pip, 149 (2017), pp. 1-13, 10.1016/j.ijpvp.2016.11.004
View PDF View article Google Scholar

[37] [37]
H.G. Pisarski
Determination of pipe girth weld fracture toughness using SENT specimens
Proc. Bienn. Int. Pipeline Conf. IPC (2010), pp. 217-224, 10.1115/IPC2010-31123
View in Scopus Google Scholar

[38] [38]
S. Canada
Temperature effects on dynamic fracture of pipeline steel
Master of Science, University of Alberta (2015)
Google Scholar

[39] [39]
Abaqus
ABAQUS Version 2016
Dessault Syst (2016)
Google Scholar

[40] [40]
K. Babinsky, S. Primig, W. Knabl, A. Lorich, R. Stickler, H. Clemens
Fracture behavior and delamination toughening of molybdenum in charpy impact tests
JOM, 68 (2016), pp. 2854-2863, 10.1007/s11837-016-2075-y
View in Scopus Google Scholar

[41] [41]
M.S. Joo, D.W. Suh, J.H. Bae, H.K.D.H. Bhadeshia
Role of delamination and crystallography on anisotropy of Charpy toughness in API-X80 steel
Mater Sci Eng, A, 546 (2012), pp. 314-322, 10.1016/j.msea.2012.03.079
View PDF View article View in Scopus Google Scholar

[42] [42]
C. Ruggieri, R.H. Dodds
A local approach to cleavage fracture modeling: an overview of progress and challenges for engineering applications
Eng Fract Mech, 187 (2018), pp. 381-403, 10.1016/j.engfracmech.2017.12.021
View PDF View article View in Scopus Google Scholar

[43] [43]
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
Proc Struct Integr, 2 (2016), pp. 1643-1651, 10.1016/j.prostr.2016.06.208
View PDF View article View in Scopus Google Scholar

[44] [44]
Y. Li, Z. Wang, Y. Lei, G. Qian, M. Zhou, Z. Gao, et al.
Weibull stress analysis in local approach to fracture
Theor Appl Fract Mech, 104 (2019), Article 102379, 10.1016/j.tafmec.2019.102379
[1]
View PDF View article View in Scopus Google Scholar

[45] [45]
T. Jin, Z. Wang, Q. Wang, D. Wang, Y. Li, M. Zhou
Weibull stress analysis for the corner crack in reactor pressure vessel nozzle
Adv Mech Eng, 11 (12) (2019), pp. 1-8, 10.1177/1687814019893567
Google Scholar

[46] [46]
C. Ruggieri
A modified local approach including plastic strain effects to predict cleavage fracture toughness from subsize precracked Charpy specimens
Theor Appl Fract Mech, 105 (2020), Article 102421, 10.1016/j.tafmec.2019.102421
View PDF View article View in Scopus Google Scholar

[47] [47]
A. Rossoll, C. Berdin, C. Prioul
Determination of the fracture toughness of a low alloy steel by the instrumented Charpy impact test
Int J Fract, 115 (2002), pp. 205-226, 10.1023/A:1016323522441
View in Scopus Google Scholar

[48] [48]
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 (3) (2005), pp. 413-434, 10.1016/j.engfracmech.2004.03.011
View PDF View article View in Scopus Google Scholar

[49] [49]
A.R. Shen, P.C. Li, G. Qian, Z.S. Yu, F. Berto, W. Wu
Study on cleavage fracture probability-load curves of ferritic steel 20MnMoNi55 by using the new local approach model
Int J Press Vessel Pip, 178 (2019), Article 103999, 10.1016/j.ijpvp.2019.103999
View PDF View article View in Scopus Google Scholar

[50] [50]
K. Bhattacharyya, S. Acharyya, S. Dhar, J. Chattopadhyay
Variation of Beremin Model Parameters with temperature by Monte Carlo Simulation
J Press Vessel Technol Trans ASME, 141 (2) (2019), Article 021401, 10.1115/1.4042121
View in Scopus Google Scholar

[51] [51]
T. Tani, M. Nagumo
Fracture process of a low carbon low alloy steel relevant to charpy toughness at ductile-brittle fracture transition region
Metall Mater Trans A, 26 (2) (1995), pp. 391-399, 10.1007/BF02664675
View in Scopus Google Scholar

Outline 大纲

Cited by (16) 被引用 (16)

Figures (23) 图（23）

Tables (3) 表格（3）

International Journal of Mechanical Sciences
国际机械科学杂志

Highlights 亮点

Abstract 抽象的

Graphical abstract 图解摘要

Keywords 关键词

Abbreviation 缩写

Nomenclature 命名法

1. Introduction

2. Drop-weight tear test (DWTT)

2.1. Material and mechanical properties

2.2. Drop-weight tear test (DWTT)

3. Numerical damage model for simulating the DWTT

3.1. The importance of an element-size-dependent damage model

3.2. Element-size-dependent ductile damage model

3.3. Element-size-dependent cleavage fracture model

4. Simulation of DWTT and comparison with test data

4.1. FE model and analysis of DWTT specimen

4.2. Comparisons between the experimental results and simulations

5. Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgement

References

Cited by (16)

Prediction of the irradiation effect on the fracture toughness for stainless steel using a stress-modified fracture strain model

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

Quantification of notch type and specimen thickness effects on ductile and brittle fracture behaviour of drop weight tear test

Numerical investigation on fatigue life of aluminum brazing structure with fin-plate-side bar under the low temperature thermal-structure cyclic stress

From macro- to micro-experiments: Specimen-size independent identification of plasticity and fracture properties

Measuring J-R curve under dynamic loading conditions using digital image correlation

Finite element simulation of drop-weight tear test of API X80 at ductile-brittle transition temperaturesAPI X80 钢在韧脆转变温度下落锤撕裂试验的有限元模拟

Highlights 亮点

Abstract 抽象的

Graphical abstract 图解摘要

Keywords 关键词

Abbreviation 缩写

Nomenclature 命名法

1. Introduction

2. Drop-weight tear test (DWTT)

2.1. Material and mechanical properties

2.2. Drop-weight tear test (DWTT)

3. Numerical damage model for simulating the DWTT

3.1. The importance of an element-size-dependent damage model

3.2. Element-size-dependent ductile damage model

3.3. Element-size-dependent cleavage fracture model

4. Simulation of DWTT and comparison with test data

4.1. FE model and analysis of DWTT specimen

4.2. Comparisons between the experimental results and simulations

5. Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgement

References

Finite element simulation of drop-weight tear test of API X80 at ductile-brittle transition temperatures
API X80 钢在韧脆转变温度下落锤撕裂试验的有限元模拟