力学学报, 2019, 51(6): 1830-1840 DOI: 10.6052/0459-1879-19-170

固体力学

基于声发射矩张量分析混凝土破坏的裂纹运动 1)

任会兰*, 宁建国,*,2), 宋水舟*, 王宗炼†

* 北京理工大学爆炸科学与技术国家重点实验室, 北京 100081

† 中国计量大学机电工程学院, 杭州 310018

INVESTIGATION ON CRACK GROWTH IN CONCRETE BY MOMENT TENSOR ANALYSIS OF ACOUSTIC EMISSION 1)

Ren Huilan*, Ning Jianguo,*,2), Song Shuizhou*, Wang Zonglian†

* State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

† College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, China

通讯作者: 2) 宁建国, 教授, 主要研究方向: 爆炸与冲击动力学. E-mail:jgning@bit.edu.cn

收稿日期: 2019-07-1   接受日期: 2019-09-30   网络出版日期: 2019-09-30

基金资助: 1) 国家自然科学基金资助项目.  11572049

Received: 2019-07-1   Accepted: 2019-09-30   Online: 2019-09-30

作者简介 About authors

摘要

从细观上看, 混凝土是一种由骨料、水泥浆基体、裂纹等组成的非均匀复合材料. 单轴准静态加载条件下, 应力应变曲线表现出明显的准脆性特征. 其变形破坏过程实质上是内部微裂纹产生、扩展和汇合的过程, 研究细观尺度的裂纹扩展演化将有助于深入了解混凝土的变形和破坏过程. 声发射作为一种物理检测方法可以获取材料内部细观损伤演化的物理信息. 本文基于声发射技术, 结合改进的时差定位算法和矩张量理论对声发射信号进行分析, 反演了混凝土巴西劈裂破坏中裂纹位置、裂纹类型以及裂纹面运动方向, 揭示了混凝土宏观拉伸破坏的细观裂纹扩展机制. 结果表明: 裂纹运动过程清晰地显示了混凝土内裂纹源首先在试件与载荷接触面附近产生, 之后聚集形成局部损伤区域, 并沿轴线向中心扩展(加载平面)以及裂纹从试件中间向表面扩展的动态过程(厚度方向); 裂纹运动体积可以作为裂纹形成、扩展过程中弹性能释放的度量, 初始裂纹成核时体积参数较小, 峰值载荷时, 裂纹运动体积最大达到$5.93\times10^{-4}$ mm$^{3}$; 混凝土宏观尺度的拉伸破坏在细观尺度上存在有拉伸裂纹、混合裂纹以及剪切裂纹; 拉伸裂纹最多, 占裂纹总数约为60%, 剪切裂纹最少, 约占裂纹总数的10%; 拉伸裂纹运动主导了试件的宏观劈裂破坏.

关键词： 声发射 ; 矩张量 ; 裂纹运动

Abstract

On meso-scale, concrete can be considered as a kind of non-homogeneous composite mainly composed of aggregates, cement paste and cracks. Under uniaxial quasi-static loading condition, quasi-brittle characteristics can be observed in the stress-strain curves. Failure process of concrete is essentially a process of nucleation, propagation and convergence of internal micro-cracks.Therefore, investigation on the crack growth process on meso-scale is beneficial to understand the deformation and failure process of concrete. Acoustic emission is a physical detection method which can be used to obtain the physical information of the mesoscopic damage evolution inside many kinds of materials. Acoustic emission technique, modified time of arrival approach and moment tensor theory were applied to analyze the AE sources obtained in the Brazilian test and the locations, types and orientations of cracks in the specimens were investigated. Relationship between the failure on macro-scale and the mechanisms of cracking on meso-scale of concrete was revealed. The results show that the micro-cracks generate near two contact surfaces between specimen and loading plates firstly. Then the nucleation of the micro-cracks occur at the local zone. Finally, cracks propagate from top and bottom to the center of specimen along the loading direction in the elevation view. In the side view, cracks propagated from the internal zone to the surface. Volume of micro-cracks could be regarded as a measure of elastic energy released from the nucleation of micro-cracks. The volume of micro-cracks is small at the early stage of nucleation. When the load reached its peak value, the maximum volume of the micro-crack was $5.93\times 10^{ - 4}$ mm$^{3}$. Tensile cracks, shear cracks and mixed-mode cracks on meso-scale could be observed in the tensile failure process of concrete on macro-scale. The failure process of the concrete was dominated by tensile cracks (nearly 60%) and the shear cracks had the minimum proportion (nearly 10%). The motion of tensile cracks dominate the macro-scale failure of specimen.

Keywords： acoustic emission ; moment tensor ; mechanism of cracking

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本文引用格式

任会兰, 宁建国, 宋水舟, 王宗炼. 基于声发射矩张量分析混凝土破坏的裂纹运动 1). 力学学报[J], 2019, 51(6): 1830-1840 DOI:10.6052/0459-1879-19-170

Ren Huilan, Ning Jianguo, Song Shuizhou, Wang Zonglian. INVESTIGATION ON CRACK GROWTH IN CONCRETE BY MOMENT TENSOR ANALYSIS OF ACOUSTIC EMISSION 1). Chinese Journal of Theoretical and Applied Mechanics[J], 2019, 51(6): 1830-1840 DOI:10.6052/0459-1879-19-170

引言

混凝土是一种非均质、不等向的复合材料, 其组构成分多样[1], 包括硬化水泥砂浆和骨料颗粒. 在外载荷作用下, 混凝土内基体开裂或骨料和基体弱界面处产生剥离, 形成微裂纹; 这些微裂纹继续扩展将形成宏观裂纹, 并最终导致材料失效破坏, 丧失承载能力. 在工程中, 这些损伤的累积将引发灾难性的事故[2]. 混凝土等准脆性材料裂纹的形成和扩展将裂纹表面能以瞬态弹性波的形式释放出来, 产生声发射现象. 声发射信号由材料内部微缺陷本身产生, 每一个声发射信号都反映了材料内部缺陷性质和状态变化. 因此, 开展混凝土声发射源运动机制的研究, 对于在役混凝土结构的健康监测和灾害预警具有非常重要的意义.

基于声发射技术, 对混凝土损伤破坏进行研究的前期工作主要集中在参数分析上. Sagar等[3-5]提出了$b$值理论, 用$b$值大小反映混凝土材料的损伤程度, 该理论以简单易实施的特点被广泛应用于混凝土损伤研究中. Carpinter等[6-7]基于分形理论, 计算混凝土损伤区域的分形维数, 定量表征了混凝土结构中损伤局部化程度. Wang等[8]基于小波变换对混凝土在单轴压缩和三点弯曲载荷作用下损伤的声发射信号进行分析与统计, 成功识别出了裂纹萌生、裂纹生长和裂纹汇合所对应的声发射信号.

此外, 基于声发射信号频率[9-11]以及Kaiser效应与Felicity比[12]的定性分析方法也被广泛用于混凝土损伤声发射研究中. 这些定性研究虽能提供关于混凝土损伤程度和破坏模式转变的信息, 但无法表征损伤源性质. 基于RA-AF分析法[13-17]虽然可以判别裂纹类型, 但两个参数之间的坐标比例选取目前没有固定的标准, 比例选取不同, 分类结果也会有一定的差异.日本学者Ohstu等[18]于1991年首次把矩张量反演方法引用到声发射无损检测中, 提出了SIGMA程序, 研究了切口梁、素混凝土梁在三点弯、四点弯等实验条件下破坏演化区(FPZ)的产生机理, 定量分析了材料中裂纹扩展机理[19-22]. Lassaad等[23]应用矩张量理论分析了大尺寸混凝土梁弯曲和剪切变形中的损伤机制.

近年来, 矩张量理论应用在岩石破裂机制的研究中较多, 如Chang等[24]应用矩张量理论研究岩石破裂过程, 结论显示出剪切破坏是岩石三轴压缩条件下微观损伤的主要机制, 而且随着围压的增大而更加明显. Grosse等[25]对岩石进行了巴西劈裂实验和拉拔实验, 充分证实了矩张量反演岩石破裂机制的可行性和正确性. Yu等[26]通过大尺度岩石破裂声发射实验对地震灾变的前兆现象进行研究, 基于矩张量分析法对岩石的破坏类型和趋势进行判断. Liu等[27-28]基于Ohtsu的SIGMA矩张量法模拟了岩石巷道中典型破坏面附近的裂纹分布特征.

巴西劈裂实验是应用广泛的岩石、混凝土等材料抗拉强度的间接测试方法[29]. 在压缩载荷下, 根据Griffith强度理论, 满足平面应力或平面应变条件下, 试件端面中心位置处拉伸应力最大, 巴西原盘试件破坏应从端面中心处起裂. 由于应力集中的存在, 理论分析和实验观测发现, 试件破坏是从加载点处起裂的[30]. 研究材料的损伤破坏从本质上需要了解内部裂纹的演化规律, 还需要了解裂纹的产生类型、运动方向以及时空演化规律, 才能更深入地了解微裂纹间的相互作用和扩展贯穿机制. 基于此, 本文采用声发射技术, 基于矩张量分析方法, 结合小波降噪改进的时差定位算法, 对混凝土巴西劈裂实验中的裂纹源运动过程进行研究, 揭示混凝土劈裂破坏过程中的细观损伤演化机制.

1 基于声发射信号的矩张量理论

1.1 矩张量理论

根据弹性波动力学理论, 由于裂纹扩展, 在$x$位置处$t$时刻产生的位移可表示成[31]

$\begin{eqnarray}\label{eq1}u_i ( x,t) = G_{ip,q}( x,y,t)M_{pq} * S( t)\end{eqnarray}$

式中, $G_{ip,q}(x,y,t)$为弹性动力学格林函数的空间导数, $S(t)$是震源$\!-\!$时间函数, $M_{pq} $为声发射源矩张量, 是对声发射源力学性质的描述. 依据地震学理论, 可以将矩张量定义为

$\begin{eqnarray}\label{eq2}M_{pq} = C_{pqkl} n_l l_k \Delta V\end{eqnarray}$

式中, $n_l $为裂纹面法线向量, $l_k $为裂纹面运动向量, $\Delta V$为微裂纹体积, $C_{pqkl}$为弹性常数. 图1所示为裂纹面微元体矩张量.

图1

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图1   裂纹面微元体矩张量矩张量

Fig.1   Element of the moment tensor


$M_{pq} $是对称张量, 9个分量中有6个独立分量, 因此需要至少6个传感器探测到同一裂纹源的声发射信号才能计算该声发射源的矩张量, 进而获得裂纹运动的信息.

如图2所示, 裂纹面法线方向为${{\ n}}$, 运动方向$\ l$, 弹性应力波经过传输介质传播到不同位置处的声发射传感器. 只考虑P波引起的传输介质运动, 同时考虑传感器位置处传输介质表面的反射效应, 并简化源$\!-\!$时间函数, 则传感器探测到的声发射信号的初动振幅$A(x)$可表示为[32]

$\begin{eqnarray}\label{eq3}A(x) = \frac{C_{\rm s} {\rm Ref}({{ t}},{{ r}})}{R}({\begin{array}{*{20}c} {r_1 } & {r_2 } & {r_3 } \\ \end{array} })\left( {{\begin{array}{*{20}c} {m_{11} } & {m_{12} } & {m_{13} } \\ {m_{21} } & {m_{22} } & {m_{23} } \\ {m_{31} } & {m_{32} } & {m_{33} } \\ \end{array} }} \right)\left( {{\begin{array}{*{20}c} {r_1 } \\ {r_2 } \\ {r_3 } \\\end{array} }} \right)\end{eqnarray}$

图2

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图2   传感器方向和裂纹源位置示意图

Fig.2   Diagram of the direction of AE sensor and position of crack


传感器的反射系数Ref$({{ t}},{{ r}})$, 可以表示为

$\begin{eqnarray}\label{eq4}&&{\rm Ref}({{ t}},{{ r}}) =\\&&\qquad \frac{2k^2a[ {k^2 - 2({1 - a^2} )} ]}{[ {k^2 - 2( {1 - a^2} )}]^2 + 4a( {1 - a^2} )\sqrt {k^2 - 1 + a^2} }\end{eqnarray}$

式中, $k = {v_{\rm p} }/{v_{\rm s} }$, $v_{\rm p} $为弹性纵波波速, $v_{\rm s} $为横波波速, $C_{\rm s} $为传感器的灵敏度系数, 用断铅实验进行标定, $a = {{ r}} \cdot {{t}}$.

采用Ohtsu提出的优势分类方法判断微裂纹类型, 主要依据最大特征值对所有特征值进行正则化

$\left. \begin{array}{l}{m_1 }/{m_1 } = X + Y + Z \\\\{m_2 }/{m_1 } = 0 - 0.5Y + Z \\\\{m_3 }/{m_1 } = - X - 0.5Y + Z\end{array} \right\}$

式中, $X$代表剪切部分比例, $Y$代表拉应力偏量部分比例, $Z$代表静水拉应力部分比例. 若$X\leqslant 40\%$, 判断为拉伸型裂纹, $X \geqslant 60\%$, 判断为剪切型裂纹, $40\% < X < 60\%$则为混合型裂纹[28].

矩张量$M$的3个特征值对应的特征向量分别为${{ e}}_{1}$, ${{ e}}_2 $, ${{ e}}_3 $, 和裂纹法线方向${{ n}}$及运动方向${{ l}}$之间的关系如下

$\begin{eqnarray}\label{eq6}{{ e}}_{1} = \frac{{{ l}} + {{ n}}}{|{{{ l}} + {{ n}}} |},\ \ {{ e}}_2 =\frac{{{ l}}\times {{ n}}}{|{{{ l}}\times {{ n}}} |},\ \ {{ e}}_3 = \frac{{{ l}} - {{ n}}}{| {{{ l}} - {{ n}}}|}\end{eqnarray}$

由此可以获得裂纹面的法线方向和运动方向. 裂纹的3种模式为拉伸裂纹, 剪切裂纹和混合裂纹, 示意图如图3所示. 三维显示中, 圆饼代表裂纹面, 其法线方向为${{ n}}$, 运动方向为$ l$, 圆饼的几何中心点位置则为声发射事件点的坐标.

图3

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图3   不同类型裂纹示意图

Fig.3   Models for tensile crack, mixed-mode crack and shear crack


1.2 声发射源的定位

由矩张量理论可知, 要判断声发射源的裂纹类型, 需要对声发射源进行准确的定位. 图4描述了三维空间中时差定位基本原理, 裂纹源发出的声发射信号传播到不同位置处的传感器, 根据声发射信号到达同一阵列内不同传感器的时间差, 计算获得裂纹源的具体位置坐标.

图4

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图4   三维空间时差定位法

Fig.4   The diagram of 3-dimensional localization


Geiger算法是假定一个初始的声发射源${{ S}}( {x_0 ,y_0 ,z_0 ,t_0 })$, 通过迭代不断修正$( {x_0 ,y_0 ,z_0 ,t_0 })$而接近最终结果. 每一次的迭代结果都要满足下式[33]

$\begin{eqnarray}\label{eq7}\sqrt {(x_i - x)^2 + (y_i - y)^2 + (z_i - z)^2} = v(t_i - t)\end{eqnarray}$

式中, $x$, $y$, $z$为声发射源的坐标, $t$为声发射事件发生时刻, $x_i $, $y_i $, $z_i $为第$i$个传感器的位置, $t_i $为P波到达第$i$个传感器的时刻, $v$为材料中P波波速.

定位算法中需要确定不同传感器接收声发射信号的时间差, 而传感器采集到的声发射信号中包含有大量的噪声信号, 这些噪声信号会使定位结果产生一定误差. 小波变换利用真实信号和噪声信号在小波分解尺度上的不同特点, 选择合适的小波基, 对采集到的声发射信号进行多层分解, 实现信噪分离, 从而可以精确读取信号到时, 提高对声发射源的定位精度[34].

声发射信号P波初动振幅的准确拾取是进行混凝土破裂源矩张量反演的基础与关键. 在确定声发射波初到时间后, 在初到时间之后的振幅中找到第一个到达最值的点, 此点的幅值即为P波的初动振幅, 如图5所示. 假设第$k$个点为P波初到时间, 设$A_i$表示波形幅值, 若

$\begin{eqnarray}\label{eq8}A_i (A_{i + 1} - A_i ) \leqslant 0\end{eqnarray}$

则初动波幅值为$A_i $, 其中, $k + 1 \leqslant i < n$ ($n$为一个信号波形里的采样点数).

图5

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图5   声发射信号P波初到时间与初动振幅

Fig.5   Typical acoustic emission signal waveform showing arrive time and amplitude of the first motion of P-wave


2 混凝土巴西劈裂实验

采用WDW-300型微机控制电子式万能试验机对混凝土试件进行加载, 轴向位移控制, 加载速率为0.05 mm/min. 混凝土圆盘试件尺寸为$\varPhi106~{\rm mm}\times 53~{\rm mm}$, 表面对称粘贴8个传感器进行实时监测, 各传感器与加载方向夹角为45$^\circ$, 距离圆心30 mm. 传感器谐振频率为150 KHz, 带宽为50$\sim $400 KHz, 声发射采样频率设为1 mHz, 噪声门槛值设为45~dB. 实验设置及传感器布置如图6所示.

图6

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图6   实验设置及传感器位置

Fig.6   Test setup and positions of sensors


加载开始前, 采用断铅实验模拟声发射信号, 检查传感器以及测试系统的可靠性; 通过在混凝土试件上进行多次断铅实验, 测定混凝土试件中的平均波速为3350 m/s. 计算中, 混凝土弹性模量为$2.657\times10^{4}$ MPa, 泊松比为0.19, 纵波与横波的波速比为1.61.

3 结果分析

3.1 裂纹运动参数

对于一个任意声发射源, 通过试件表面的传感器检测到声发射信号, 首先需要对声发射源位置进行定位, 再结合前面矩张量分析方法, 自行编制计算程序, 计算该声发射源的矩张量, 进而判断裂纹类型并获得裂纹运动参数. 表1给出了3组声发射源的矩张量反演结果. 依据$X$值的大小, 结合前文给出的裂纹类型判别方法, 将表中3个声发射源分别判定为拉伸型、剪切型及混合型裂纹. 本文所有的计算结果, 都采用相同的方式对裂纹类型进行判断.

表1   典型声发射源的矩张量反演结果

Table 1  Results of moment tensor inversion for three AE sources

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通过每一个声发射源的矩张量反演结果, 可以对裂纹运动体积以及裂纹法线方向${{ n}}$与运动方向${{ l}}$间的夹角$\alpha $进行计算.式(2)可以展开为

$\begin{eqnarray}\label{eq9}M_{pq} = [ {\lambda \delta _{pq} \delta _{kl} + \mu ( {\delta_{pk} \delta _{kl} + \delta _{pl} \delta _{qk} } )}]n_l l_k\Delta V\end{eqnarray}$

可得裂纹运动体积$\Delta V$

$\begin{eqnarray}\label{eq10}\Delta V = \frac{m_1 + m_2 + m_3 }{3\lambda + 2\mu }\end{eqnarray}$

式中, $m_1 ,m_2 ,m_3 $为矩张量的3个特征值, $\lambda $, $\mu $为Lam\'{e}常数.

裂纹法线方向${{ n}}$及运动方向${{ l}}$间的夹角$\alpha $可下式计算

$\begin{eqnarray}\label{eq11}\cos \alpha = \frac{l_k n_k }{|{{ l}}| \cdot | {{ n}} |}\end{eqnarray}$

由式(10)可看出, 裂纹体积是矩张量主值和弹性参数的函数, 因此, 裂纹运动体积可作为裂纹形成过程中弹性能释放的度量. 图7是试件1裂纹运动体积的计算结果. 当加载载荷到0$\sim$40%峰值载荷时, 单个裂纹扩展运动体积最大值为$2.53\times 10^{ - 5}$ mm$^{3}$; 40%$\sim$80%峰值载荷时, 该值约为$1.12\times10^{ - 4}$ mm$^{3}$. 80%$\sim$100%峰值载荷时, 出现多个体积较大的裂纹, 裂纹运动最大体积达$5.93\times10^{-4}$ mm$^{3}$. 这也反映出初始加载时材料内处于裂纹成核阶段, 释能较少; 随着载荷增大, 内部裂纹扩展汇合形成宏观裂纹, 释放较多的弹性能. Landis[35]研究了混凝土梁在三点弯载荷下内部裂纹的扩展, 接近混凝土梁的承载极限时裂纹体积最大, 其值约为$1.6\times 10^{ - 4}$ mm$^{3}$.

图7

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图7   载荷与裂纹运动体积(试件1)

Fig.7   Micro-crack volume (specimen 1)


表2列出了试件1中裂纹运动体积的计算结果, 可以看出, 单个拉伸裂纹与混合裂纹运动的体积相近, 而剪切裂纹比拉伸裂纹小一个数量级. 巴西劈裂实验中产生的裂纹是在拉伸及剪切应力共同作用下产生的. 矩张量分析中, 剪切裂纹是以剪切破裂为主, 也包含有张拉的成分.

表2   裂纹运动体积参数

Table 2  volumes of three types of cracks

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图8是剪切分量$X$值与裂纹运动方向和裂纹面法线方向夹角$\alpha $的关系曲线. 可以看出, 夹角与剪切分量的值呈现出非线性关系. 由图中可以看出, 拉伸裂纹对应的夹角$\alpha$范围在10$^\circ$$\sim$70$^\circ$之间, 混合型裂纹的夹角$\alpha$范围在60$^\circ$$\sim$90$^\circ$之间, 剪切型裂纹的夹角$\alpha $范围在80$^\circ$$\sim$90$^\circ$之间.

图8

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图8   剪切分量$X$的值与裂纹运动方向和法线夹角之间的关系

Fig.8   Angle between crack slip and crack normal vectors versus the shear ratio


3.2 裂纹运动的时空演化

图9中给出了试件1中声发射事件出现的时间顺序, 图中每一个声发射事件都对应一个微裂纹, 其所对应的裂纹类型由$X$的值确定,$X \leqslant 40\% $, 为拉伸型裂纹, 用红色圆点表示$X \geqslant 60\%$, 判断为剪切型裂纹, 用黑色正方形表示, $40\% < X < 60\% $, 判断为混合型裂纹, 用蓝色三角形表示. 在从图中可以看出, 在加载初期, 即0$\sim$293 s的时间范围内, 声发射事件数较少. 随着时间的推移, 在声发射事件总数逐渐增多的情况下, 每个加载阶段所对应的时间段内声发射事件的数量也在逐渐增加. 在884$\sim$1070 s的范围内, 声发射事件密度明显增大, 并在达到峰值载荷的瞬间密集出现.

图9

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图9   声发射事件出现的时间顺序

Fig.9   Events in chronological order


应用矩张量分析程序对混凝土试件中的声发射信号进行分析, 图10显示了试件1在整个加载过程中裂纹运动的空间演化过程(图中红色代表剪切型裂纹, 蓝色代表拉伸型裂,绿色代表混合型裂纹), 特点有:

(1)加载初期(0$\sim$20%峰值载荷水平), 沿$XOY$平面, 试件上下两端接触试验机压盘的附近位置处首先出现分散的声发射信号, 数量较少, 表明混凝土内部细观尺度上有裂纹的产生. $ZOY$平面上, 此时的裂纹多出现在试件内部.

(2)载荷水平达到峰值载荷的40%时, 裂纹数量增多, 聚集在初始裂纹源附近. $ZOY$平面上, 裂纹在轴向的分布范围逐渐从试件中部向试件表面扩展, 从如图10(b)所示.

(3)当载荷增大到峰值载荷的60%时, 裂纹数量继续增加, 并向试件中部扩展, 沿试件轴线方向形成上下两个明显的局部损伤区. $ZOY$平面上, 裂纹源进一步由试件内部向前后表面扩展.

(4)载荷达到峰值载荷的80%时, 试件内的裂纹之间产生汇合或贯通, 两个损伤区域逐步向试件中心位置扩展; 当应力达到100%时, 微裂纹数量急剧增长, 两个损伤区在试件中部发生汇合; 加载平面($XOY$)的轴线上, 几乎布满了定位出的裂纹, 且拉伸型裂纹数量多于混合型裂纹和剪切型裂纹. 试件1的实际破坏情况如图10(f)所示.

图10

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图10   不同应力水平下混凝土试件内裂纹演化(试件1)

Fig.10   Evolution of cracks in concrete specimens under different stress state (specimen 1)


图11和图12显示了试件2和试件3在不同峰值应力水平下试件内部裂纹源的动态演化, 与试件1中的特点类似, 不再赘述. 3组试件定位出的裂纹源均在试件沿加载轴线附近, 与试件实际破坏情况吻合良好. 同试件2和试件3的破坏相比, 试件1的破坏更为严重, 下方混凝土试件出现大量的碎块; 试件2沿加载轴线附近出现了两条明显的宏观裂纹, 上端比下端破坏严重; 下端裂纹在扩展过程中出现了弯折扩展. 试件3宏观破坏上可见一条长的贯穿裂纹, 此外, 试件底部有两条小的弯折裂纹.

图11

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图11   不同应力水平下混凝土试件内裂纹演化(试件2)

Fig.11   Evolution of cracks in concrete specimens under different stress state (specimen 2)


图12

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图12   不同应力水平下混凝土试件内裂纹演化(试件3)

Fig.12   Evolution of cracks in concrete specimens under different stress state (specimen 3)


需要注意的是, 矩张量分析中裂纹类型是基于裂纹面的运动方向进行划分的; 而线弹性断裂力学中, 破坏模式是按照裂纹尖端扩展方向进行分类的. Ohstu等[36]考虑了矩张量分析中裂纹面的运动, 研究了断裂力学中I型破坏; 矩张量分析结果表明, 该破坏模式中从细观尺度上有拉伸裂纹, 剪切裂纹和混合裂纹3种裂纹, 但拉伸裂纹的扩展主导了I型断裂. 因此, 可以将矩张量分析中拉伸裂纹和剪切裂纹(细观尺度)分别对应于线性断裂力学中张开型裂纹扩展模式(I型)和滑开型裂纹扩展模式(II型)(宏观尺度).

由此可见, 拉伸裂纹扩展为主导控制了混凝土巴西劈裂破坏, 由于混凝土试件的不均匀性而使裂纹在扩展过程会出现弯折扩展(图11), 少量的剪切裂纹导致了II型剪切断裂. 与弹性力学理论分析结果的不同之处在于, 试件破坏是从试件与载荷接触面附近最先产生裂纹源, 之后随着载荷增大, 裂纹源聚集并沿试件轴线向中心扩展, 最终导致了试件的宏观劈裂破坏, 并不是按照理论分析中的从试件中心进行起裂的.

3.3 不同类型裂纹统计

表3统计了3组试件中判别出的总裂纹数, 尽管3组试件中裂纹总数不同, 但3组试件在整个破坏过程中拉伸裂纹最多, 剪切裂纹最少. 在细观尺度上, 拉伸裂纹占所有有效裂纹总数的一半以上, 拉伸裂纹对试件的破坏起到了主导作用. 此外, 拉伸裂纹在宏观裂纹的贯穿过程中起着很重要的作用, 而剪切裂纹则产生较破碎的破坏形式. 结合试件的破坏特点, 试件1中剪切裂纹较多, 试件的宏观破坏也呈现出大量的剪切碎裂的特点. 而试件3中剪切裂纹较少, 拉伸裂纹占比78.8%, 整体呈现出明显的贯穿拉伸破坏.

表3   3种类型裂纹占比统计

Table 3  Statistics of the proportion of three types of cracks

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对3组试件中不同峰值应力水平范围内拉伸裂纹、剪切裂纹和混合裂纹数进行统计, 变化情况见图13所示. 初始加载时, 3种裂纹数量均较少, 40%$\sim$60%峰值应力水平阶段, 拉伸型裂纹增多, 占比约为50%左右; 60%$\sim$80%应力水平阶段, 拉伸裂纹仍占主导作用, 由于裂纹扩展处于相对稳定的阶段, 3种类型的裂纹数量增长都比较缓慢; 100%峰值应力水平时, 试件破坏, 拉伸裂纹数量剧烈增长, 混合裂纹和剪切裂纹数量增长缓慢.

图13

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图13   累计裂纹数

Fig.13   Accumulated number of different types of cracks


从前面矩张量计算中可知, 求解一个裂纹的矩张量信息, 需要至少有6个传感器采集到的声发射信号. 3组试件加载时声发射传感器采集到的数据中, 满足上述条件的声发射信号数占总数比例分别为30.66%, 27.71%, 41.60%. 提高用于矩张量分析的有效声发射信号数, 可以更准确地分析试件中裂纹的运动情况.v

4 结论

本文采用多通道声发射测试系统, 基于弹性波动力学的矩张量理论, 结合小波降噪的时差定位算法, 研究了混凝土巴西劈裂实验中的细观损伤机制, 得到了如下结论.

(1)反演获得了混凝土巴西劈裂实验中裂纹源的空间位置、裂纹类型以及裂纹面运动方向. 计算获得了混凝土试件损伤破坏过程中裂纹运动的体积参数, 最大约为$5.93\times 10^{-4}$ mm$^{3}$. 材料内裂纹成核时释能较小, 裂纹运动体积较小; 之后随着裂纹扩展汇合形成宏观裂纹, 试件破坏时释放大量的弹性能.

(2)矩张量分析结果清晰地显示了试件内裂纹源的时空演化过程, 揭示了混凝土试件的破坏是试件与载荷接触面附近裂纹源产生、聚集形成损伤区域并沿轴线向中心扩展的动态过程(加载平面)以及裂纹从试件内部向表面扩展的过程(试件厚度方向).

(3)混凝土试件的宏观劈裂破坏, 细观尺度上是由大量的拉伸裂纹、剪切裂纹和混合裂纹的形成和扩展引起的; 不同应力水平下, 拉伸裂纹、剪切裂纹和混合裂纹数随着载荷的增加而增加, 三组巴西劈裂实验中, 拉伸裂纹最多, 占裂纹总数约为60%, 拉伸裂纹的运动主导控制了混凝土试件的劈裂破坏, 而剪切型裂纹和混合型裂纹对材料的破坏起到了促进作用.

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Wang Z, Ning J, Ren HL.

Intelligent identification of cracking based on wavelet transform and artificial neural network analysis of acoustic emission signals

Insight-Non-Destructive Testing and Condition Monitoring, 2018,60(8):426-433

DOI      URL     [本文引用: 1]

Wang Z, Ning J, Ren H.

Frequency characteristics of the released stress wave by propagating cracks in brittle materials

Theoretical and Applied Fracture Mechanics, 2018,96:72-82

DOI      URL     [本文引用: 1]

Zitto ME, Piotrkowski R, Gallego A, et al.

Damage assessed by wavelet scale bands and b-value in dynamical tests of a reinforced concrete slab monitored with acoustic emission

Mechanical Systems and Signal Processing, 2015,60:75-89

王宗炼, 任会兰, 宁建国 .

基于小波变换的混凝土压缩损伤模式识别

兵工学报, 2017,38(9):84-92

[本文引用: 1]

( Wang Zonglian, Ren Huilan, Ning Jianguo.

Identification of damage modes of concrete under compressive loading based on wavelet transform

Acta Armamentarii, 2017(9):84-92 (in Chinese))

[本文引用: 1]

Sagar RV, Prasad BKR, Singh RK.

Kaiser effect observation in reinforced concrete structures and its use for damage assessment

Archives of Civil and Mechanical Engineering, 2015,15(2):548-557

DOI      URL     [本文引用: 1]

Committee RT.

Recommendation of RILEM TC 212-ACD: acoustic emission and related NDE techniques for crack detection and damage evaluation in concrete

Materials & Structures, 2010,43(9):1187-1189

DOI      URL     PMID      [本文引用: 1]

Nanometer zinc oxide has become a new hotspot in the research of tissue engineering materials due to its excellent antibacterial properties, biocompatibility, and anti-tumor properties. In this paper, the existing research results were summarized, generalized, and analyzed. The antibacterial mechanism of nanometer zinc oxide was discussed in depth. The antibacterial properties and advantages of the latest nanometer zinc oxide composite materials were introduced in detail. In this review, we made prospect of the future application of nanometer zinc oxide.

Prem PR, Murthy AR, Verma M.

Theoretical modelling and acoustic emission monitoring of RC beams strengthened with UHPC

Construction and Building Materials, 2018,158:670-682

DOI      URL    

Rasheed MA, Prakash SS, Raju G, et al.

Fracture studies on synthetic fiber reinforced cellular concrete using acoustic emission technique

Construction and Building Materials, 2018,169:100-112

DOI      URL    

Lacidogna G, Piana G, Carpinteri A.

Damage monitoring of three-point bending concrete specimens by acoustic emission and resonant frequency analysis

Engineering Fracture Mechanics, 2019,210:203-211

DOI      URL    

Han Q, Yang G, Xu J, et al.

Acoustic emission data analyses based on crumb rubber concrete beam bending tests

Engineering Fracture Mechanics, 2019,210:189-202

DOI      URL     [本文引用: 1]

Ohtsu M.

Simplified moment tensor analysis and unified decomposition of acoustic emission source: Application to in situ hydrofracturing test

Journal of Geophysical Research B, 1991,96(B4):1187-1189

[本文引用: 1]

Ohtsu M, Shigeishi M.

Virtual reality presentation of moment tensor analysis by SiGMA

J. Korean Soc. for NDT, 2003,23(3):189-199

[本文引用: 1]

Ohtsu M, Kaminaga Y, Munwam MC.

Experimental and numerical crack analysis of mixed-mode failure in concrete by acoustic emission and boundary element method

Construction and Building Materials, 1999,13(1-2):57-64

DOI      URL    

Ohno K, Uji K, Ueno A, et al.

Fracture process zone in notched concrete beam under three-point bending by acoustic emission

Construction and Building Materials, 2014,67:139-145

DOI      URL    

Investigation on fracture process zones in notched concrete beams under three-point bending is performed by applying acoustic emission (AE). The tests were conducted on beam specimens with different notch depths and the maximum sizes of aggregate in concrete to clarify the generation mechanisms of micro-cracks in the fracture process zone. SiGMA (simplified Green's functions for moment tensor analysis) procedure was applied to analyze AE signals. The experimental results show the fracture energy increases with increase in the maximum size of aggregate. It is found that dominant motions of microcracks vary with the notch depth, regardless of the maximum size of aggregate. The widths of the fracture process zone were estimated from results of AE source location. It is confirmed that the fracture energy correlates with the width of AE cluster, as the energy increase when the width of fracture process zone expands. (C) 2014 Elsevier Ltd.

Ohno K, Ohtsu M.

Crack classification in concrete based on acoustic emission

Construction and Building Materials, 2010,24(12):2339-2346

DOI      URL     [本文引用: 1]

Abstract

The fracture mode of cracking in concrete is normally changing from tensile mode to shear mode at impending failure. As for crack classification in concrete by acoustic emission (AE) techniques, two crack classification methods have been carried out. One of them is parameter-based method (parameter analysis) which has been carried out by employing two parameters of the average frequency and the RA value. The proportion of these two parameters, however, has not been determined yet. The other crack classification is simplified Green’s functions for moment tensor analysis (SiGMA) procedure which is known as signal-based method. The SiGMA analysis is based on the generalized theory of AE, while the parameter analysis results from an empirical relation. Therefore, an optimal proportion of the parameter analysis is in great demand. In this study, these crack classification methods are compared and discussed from results of three types of concrete failure tests. As a result, ratios of the shear crack which are identified by SiGMA analysis are good agreement with those by parameter analysis in the case that the proportion of the RA value and the average frequency is set to 1–200.

Lassaad M, Thomas S, Lindsay L.

Characterization of flexural and shear cracks in reinforced concrete beams using moment tensor inversion from acoustic emission signals

Journal of Structural Engineering, 2016,143(3):1-9

[本文引用: 1]

Chang SH, Lee CI.

Estimation of cracking and damage mechanisms in rock under triaxial compression by moment tensor analysis of acoustic emission

International Journal of Rock Mechanics & Mining Sciences, 2004,41(7):1069-1086

DOI      URL     PMID      [本文引用: 1]

Organic matter is responsible for the generation of hydrocarbons during the thermal maturation of source rock formation. This geochemical process engenders a network of organic hosted pores that governs the flow of hydrocarbons from the organic matter to fractures created during the stimulation of production wells. Therefore, it can be reasonably assumed that predictions of potentially recoverable confined hydrocarbons depend on the geometry of this pore network. Here, we analyze mesoscale structures of three organic porous networks at different thermal maturities. We use electron tomography with subnanometric resolution to characterize their morphology and topology. Our 3D reconstructions confirm the formation of nanopores and reveal increasingly tortuous and connected pore networks in the process of thermal maturation. We then turn the binarized reconstructions into lattice models including information from atomistic simulations to derive mechanical and confined fluid transport properties. Specifically, we highlight the influence of adsorbed fluids on the elastic response. The resulting elastic energy concentrations are localized at the vicinity of macropores at low maturity whereas these concentrations present more homogeneous distributions at higher thermal maturities, due to pores' topology. The lattice models finally allow us to capture the effect of sorption on diffusion mechanisms with a sole input of network geometry. Eventually, we corroborate the dominant impact of diffusion occurring within the connected nanopores, which constitute the limiting factor of confined hydrocarbon transport in source rocks.

Grosse CU, Finck F.

Quantitative evaluation of fracture processes in concrete using signal-based acoustic emission techniques

Cement & Concrete Composites, 2006,28(4):330-336

DOI      URL     PMID      [本文引用: 1]

To evaluate the three-dimensional fit of abutments fabricated by the industry to those either milled or cast by a commercial laboratory and to correlate the implant-abutment connection fit with stress at fatigue failure of prostheses. Probability of survival (reliability) and fractography to characterize failure modes were also performed for cemented and screw-retained prostheses.

Huaizhong YU, Zhu Q, Yin X, et al.

Moment tensor analysis of the acoustic emission source in the rock damage process

Progress in Natural Science: Materials International, 2005,15(7):609-613

DOI      URL     [本文引用: 1]

Liu JP, Li YH, Xu SD, et al.

Cracking mechanisms in granite rocks subjected to uniaxial compression by moment tensor analysis of acoustic emission

Theoretical and Applied Fracture Mechanics, 2015,75:151-159

DOI      URL     [本文引用: 1]

Liu JP, Li YH, Xu SD, et al.

Moment tensor analysis of acoustic emission for cracking mechanisms in rock with a pre-cut circular hole under uniaxial compression

Engineering Fracture Mechanics, 2015,135:206-218

DOI      URL     [本文引用: 2]

王启智, 李炼, 吴礼舟 等.

改进巴西试验: 从平台巴西圆盘到切口巴西圆盘

力学学报, 2017,49(4):793-801

[本文引用: 1]

( Wang Qizhi, Li lian, Wu Lizhou, et al.

Improvement of Brazilian test: from flattened Brazilian disc to grooved Brazilian disc

Chinese Journal of Theoretical and Applied Mechanics, 2017,49(4):793-801 (in Chinese))

[本文引用: 1]

喻勇 .

质疑岩石巴西原盘拉伸强度实验

岩石力学与工程学报, 2005,24(7):1150-1157

URL     [本文引用: 1]

指出人们使用了40多年的巴西圆盘试验拉伸强度公式是来自二维问题的弹性力学解答，而实际情况并不满足该公式所要求的平面应力或平面应力条件。分析指出，在三维条件下影响试样应力分布的因素有试样高径比和材料的泊松比。通过40次三维有限元分析，得到了高径比和泊松比对试样拉应力分布影响的规律。发现了试样中最大拉应力出现在试样端面的中心，并拟合出了最大拉应力的计算公式。根据Griffith强度理论和Mohr强度理论，计算了试样中的最大等效应力，发现试样的破坏不可能满足中心起裂条件。由于加载点应力集中的影响，试样必然从端面加载点处起裂破坏。因此认为巴西试验方法已不适合用于测试岩石类脆性材料的抗拉强度。

( Yu Yong,

Questioning the validity of the Brazalian test for determing tensile strength of rocks

Chinese Journal of Rock Mechanics and Engineering, 2005,24(7):1150-1157 (in Chinese))

URL     [本文引用: 1]

指出人们使用了40多年的巴西圆盘试验拉伸强度公式是来自二维问题的弹性力学解答，而实际情况并不满足该公式所要求的平面应力或平面应力条件。分析指出，在三维条件下影响试样应力分布的因素有试样高径比和材料的泊松比。通过40次三维有限元分析，得到了高径比和泊松比对试样拉应力分布影响的规律。发现了试样中最大拉应力出现在试样端面的中心，并拟合出了最大拉应力的计算公式。根据Griffith强度理论和Mohr强度理论，计算了试样中的最大等效应力，发现试样的破坏不可能满足中心起裂条件。由于加载点应力集中的影响，试样必然从端面加载点处起裂破坏。因此认为巴西试验方法已不适合用于测试岩石类脆性材料的抗拉强度。

Ohno K, Shimozono S, Sawada Y, et al.

Mechanisms of diagonal-shear failure in reinforced concrete beams analyzed by AE-SiGMA

Journal of Solid Mechanics and Materials Engineering, 2008,2(4):462-472

DOI      URL     [本文引用: 1]

Hampton J, Gutierrez M, Matzar L, et al.

Acoustic emission characterization of microcracking in laboratory-scale hydraulic fracturing tests

Journal of Rock Mechanics and Geotechnical Engineering, 2018,10(5):805-817

DOI      URL     [本文引用: 1]

Geiger L.

Probability method for the determination of earthquake epicenters from the arrival time only (translated from Geiger's 1910 German article)

Bulletin of St Louis University, 1912,8(1):56-71

[本文引用: 1]

王宗炼, 任会兰, 宁建国 .

基于小波变换降噪的声发射源定位方法

振动与冲击, 2018,37(4):226-232

[本文引用: 1]

( Wang Zonglian, Ren Huilan, Ning Jianguo,

Acoustic emission source location based on wavelet transform de-noising

Journal of Vibration and Shock, 2018,37(4):226-232 (in Chinese))

[本文引用: 1]

Landis EN.

Micro--macro fracture relationships and acoustic emissions in concrete

Construction and Building Materials, 1999,13(1-2):65-72

DOI      URL     [本文引用: 1]

Ohtsu M, Uddin FAKM.

Mechanisms of corrosion-induced cracks in concrete at meso-and macro-scales

Journal of Advanced Concrete Technology, 2008,6(3):419-429

DOI      URL     [本文引用: 1]

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