## 单边缺口拉伸试件J积分塑性因子有限元分析研究1)

*中海油研究总院有限责任公司,北京100028

## FINITE ELEMENT ANALYSIS OF J-INTEGRAL PLASTIC FACTOR OF SINGLE EDGE NOTCH TENSION SPECIMEN1)

WU Xu,*,,2), SHUAI Jian, XIE Bin*, HAN Xuliang*, MA Chenbo*, DENG Xiaokang*

*CNOOC Research Institute, Beijing 100028, China

College of Safety and Ocean Engineering, China University of Petroleum, Beijing 102249, China

 基金资助: 1)国家自然科学基金(51874324)中海油研究总院科技项目资助(2020-GCZLKT-001)

Abstract

The fracture toughness test of pipeline girth weld is the basis of pipeline integrity assessment, and the accurate calculation of J-integral plastic factor is the premise of fracture toughness test. In this paper, aiming at the SENT (single edge notch tension) specimen with thickness-to-width ratio $B/W=2$, a three-dimensional finite element model of the SENT specimen of the pipe base metal with/without side grooves depth of 10% is established. The influence of crack length, specimen thickness, hardening index and specimen side groove on J-integral plasticity factor are studied. Through fitting the numerical analysis results after considering the factors such as crack length and material hardening performance, the J-integral plastic factor equations of SENT specimens are developed, which is suitable for pipe base metal with or without side groove of depth of 10%. The equations could be used to test the fracture toughness of SENT specimens.

Keywords： single edge notch tension specimen; plastic factor of J integral; J-R curve; Ramberg-Osgood model

WU Xu, SHUAI Jian, XIE Bin, HAN Xuliang, MA Chenbo, DENG Xiaokang. FINITE ELEMENT ANALYSIS OF J-INTEGRAL PLASTIC FACTOR OF SINGLE EDGE NOTCH TENSION SPECIMEN1). Mechanics in Engineering, 2022, 44(2): 344-350 DOI:10.6052/1000-0879-21-344

## 1 J积分塑性因子计算方法

$J_{{\rm el}} =\frac{K(1-\nu^{2})}{E}$

$J_{{\rm pl}} =J-J_{\rm el}$

$A_{{\rm pl}} =A-A_{{\rm el}} =A-\frac{P^{2}C_{0} }{2}$

$\eta_{{\rm pl}} =\frac{J_{{\rm pl}} Bb}{A_{{\rm pl}}}=\frac{{{J_{{\rm pl}} }/{(b\sigma_{0} )}}}{{{A_{{\rm pl}}}/{(b^{2}B\sigma_{0} )}}}=\frac{\bar{{J}}_{{\rm pl}}}{\bar{{A}}_{{\rm pl}} }$

## 2 有限元分析

### 图1

Fig.1   Finite element model of SENT specimen with side groove]

### 2.2 材料模型

$\varepsilon =\frac{\sigma }{E}+\alpha \frac{\sigma }{E}\left( {\frac{\left|\sigma \right|}{\sigma_{\rm Y} }} \right)^{n-1}$

## 3 结果分析

### 3.1 塑性因子计算

J积分塑性因子根据计算方式可以分为基于载荷线位移的J积分塑性因子($\eta_{\rm LLD}$)和基于裂纹嘴张开位移的J积分塑性因子($\eta_{\rm CMOD}$)。对于$a/W=0.5$,$n=10$的不含侧槽SENT试件,其标准化J积分($\bar{J}_{\rm pl}$)和基于载荷线位移与基于裂纹嘴张开位移的标准化塑性区面积($\bar{A}_{\rm pl}$)的关系如图2所示。可知,当$a/W$一定时,$\eta_{\rm LLD}$在初始阶段随载荷增加逐渐下降,随着载荷的提升,曲线斜率逐渐趋于常数。$\eta_{\rm CMOD}$在整个加载范围内均基本保证恒定,表明基于裂纹嘴张开位移的J积分塑性因子与加载水平无关。

### 图2

Fig.2   Schematic diagram of $\overline{J}_{\rm pl}$-$\overline{A}_{\rm pl}$ of SENT without side groove

Table 1  Results of J-integral plasticity factor of SENT specimens

### 3.2 裂纹长宽比影响分析

J积分塑性因子计算结果与文献[8,9]中结果对比见图3。可知,$\eta_{\rm LLD}$和$\eta_{\rm CMOD}$与$a/W$密切相关。$\eta_{\rm LLD}$初始随着$a/W$的增加而提升,直到$a/W$达到0.3~0.4,之后随着$a/W$的增加而逐渐下降。$\eta_{\rm CMOD}$随着$a/W$的增加而减小。该规律与文献[16]和文献[8]等方法结果基本一致。

### 图3

Fig.3   Variation of J-integral plastic factor with $a/W$ of SENT with side groove

### 图4

Fig.4   Variation of J-integral plastic factor with $n$ of SENT with side groove

### 3.4 J积分塑性因子公式

$\eta_{\rm LLD} =\sum\limits_{i=0}^3 {p_{i} \lt(\frac{a}{W})}^{i}$
$\eta_{\rm CMOD} =\sum\limits_{i=0}^3 {q_{i} \lt(\frac{a}{W})}^{i}$

$p_{i} =\sum\limits_{j=0}^3 {M_{ij} \lt(\frac{\sigma_{{\rm Y}} }{\sigma_{{\rm b}} })^{j}}$
$q_{i} =\sum\limits_{j=0}^3 {N_{ij} \lt(\frac{\sigma_{{\rm Y}} }{\sigma_{{\rm b}} })^{j}}$

Table 2  Coefficient of fitting equation

### 图5

Fig.5   The J-integral plastic factor of SENT specimen for $n=10$

## 4 结论

(1) 基于载荷线位移的J积分塑性因子初始随着裂纹长宽比的增加而提升,直到裂纹长宽比达到0.3~0.4,之后随着裂纹长宽比的增加而逐渐下降。基于裂纹嘴张开位移的J积分塑性因子随着裂纹长宽比的增加而减小。

(2) 当试件的裂纹长宽比、材料硬化指数相同时,含侧槽SENT试件J积分塑性因子远大于不含侧槽试件。

(3) 根据不同情况J积分塑性因子计算结果,提出考虑裂纹长宽比、材料硬化性能、侧槽影响的J积分塑性因子方程,填补SENT试件厚宽比$B/W=2$的J积分塑性因子研究空白,可用于试件厚宽比$B/W=2$的SENT试件断裂韧性测试。

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