SINGULAR STRESS FIELD IN VISCOELASTIC CONTACT INTERFACE ENDS 1)
Peng Fan2), Xie Shuangshuang, Dai Hongliang3)State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China收稿日期:2018-08-9接受日期:2018-10-22网络出版日期:2019-03-18
基金资助: |
Received:2018-08-9Accepted:2018-10-22Online:2019-03-18
作者简介 About authors
2)彭凡,教授,主要研究方向:疲劳与断裂.E-mail:fanpeng@hnu.edu.cn
3)戴宏亮,教授,主要研究方向:多场耦合力学.E-mail:hldai@hnu.edu.cn
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/down.png)
摘要
研究蠕变加载条件下线黏弹性材料接触界面端附近的奇异应力场问题.考虑接触界面的摩擦,假设界面端的滑移方向不改变,相对滑移量微小,且其与位移同量级,由此线性化局部边界条件,根据对应原理得到Laplace变换域中的界面端应力场,导出时域中奇异应力场的卷积积分表达式.对卷积积分核函数进行数值反演,考虑接触材料的两类组合,一是持久模量具有量级上的差异,另一是持久模量接近相同.算例结果证实核函数可以用准弹性法求得的解析式较准确地近似.在此基础上,利用积分中值定理,并引入各应力分量的修正系数,得到黏弹性奇异应力场的简化式.结合核函数的数值反演结果分析修正系数表达式的取值范围,得到如下结论,若两相接触材料的持久模量相差很大,可以采用准弹性解的解析式较准确地描述界面端的奇异应力场;一般情况下,应力场不存在统一的奇异值和应力强度系数,当采用类似于准弹性解的表达式近似给出黏弹性应力场时,可以估计此近似描述的误差限.文中最后采用有限元分析黏弹性板端部嵌入部位的应力场,算例包括了黏弹性板与弹性金属支承、黏弹性板与黏弹性垫层所形成的滑移接触界面端,利用黏弹性有限元的数值结果验证理论分析所得结论的有效性.
关键词:
Abstract
The paper concerns the problem of singular stress filed in viscoelastic contact interface ends under creep loading. The local boundary conditions taking into account the contact friction are linearized by the assumptions of tiny relative slip and invariant slip direction between interfaces. The solution of stress field at the interface end in the Laplace transform domain is obtained based on the correspondence principle, and the convolution integral expressions of the singular stress field in the time domain is developed. The numerical inversion of convolution integral kernel is made by considering two types of combinations of contact materials. One is that the durable modulus has a difference in magnitude, and the other is that the durable modulus is nearly the same. The results of inversion show that kernel functions can be approximated by analytical expressions obtained by the quasi-elastic method with a good accuracy. On this basis, simplified formulas of the viscoelastic singular stress field are developed by using the integral mean value theorem and introducing the correction coefficient of each stress component. The value range of expressions for correction coefficient is investigated in combination with the examination the numerical inversion results of the kernel functions, following conclusions are drawn as follows. If the durable modulus of the two-phase contact material differs greatly, the quasi-elastic solution can be used to describe the singular stress fields near the interface end; in general, there is no uniform singular value and no uniform stress intensity factor for stress fields; when the solution of viscoelastic stress is approximated by formulas similar to the quasi-elastic solution, the error limit can be estimated. In the last part of the paper, the viscoelastic stress analysis of viscoelastic plate at support ends is performed by means of finite element simulation as plane strain problem. The example includes two types of contact interface ends, one is constructed by the viscoelastic plate and an elastic metal support, the other is formed by a viscoelastic plate and viscoelastic cushion layers. The theoretical conclusions obtained in the front part of the paper are validated by the simulation results.
Keywords:
PDF (919KB)元数据多维度评价相关文章导出EndNote|Ris|Bibtex收藏本文
本文引用格式
彭凡, 谢双双, 戴宏亮. 黏弹性接触界面端附近的奇异应力场 1). 力学学报[J], 2019, 51(2): 494-502 DOI:10.6052/0459-1879-18-264
Peng Fan, Xie Shuangshuang, Dai Hongliang.
引 言
工程中常见两物体呈现未粘接的接触,物体沿接触面产生相对滑移,此即所谓滑移接触,接触部位力学行为的分析一直是研究热点[1-4]. 在接触界面的端部附近存在奇异应力场[5-9],应力集中加速了材料磨损和开裂.Xu等[5-6]假设相对滑移量微小,与位移同量级,从而线性化界面端附近的局部边界条件,然后由Goursat应力函数获得线弹性材料接触界面端的奇异应力场及确定奇异性指数的特征方程.文献[10,11,12]采用接触界面端的奇异应力场强度定量评估微动疲劳寿命.实际应用中,存在界面端材料呈现出固体流变特性的情形,如航空飞行器与水下潜航器用到的有机玻璃透明结构件与支承形成的黏弹性接触界面[13-14]、高温环境中不同金属材料之间的接触界面蠕变问题.针对界面具有完全粘接,且材料具有与时间相关的力学行为的粘接界面端,已发表了下述应力奇异性分析及强度问题的研究结果.文献[15-17,19-20]分析了弹性/线黏弹性或双相线黏弹性粘接界面端应力场,作者们采用了一个基本相同的处理方法,直接将Laplace变换域中的Dunders参数反变换后代入相应线弹性解的特征方程,由此得到时域内的奇异指数;部分研究工作[15-16,18]还进一步假设黏弹性奇异应力场的数学表达式与弹性解相似.然而,以上所述的确定奇异指数的弹性-黏弹性对应方法在数学上并不成立;另一方面,当以弹性解的相似形式描述黏弹性奇异应力场时,缺乏理论依据,将产生方法误差,其范围也需估计.Kuo等[21]在Laplace变换域中采用Stroh公式求解双相各向异性黏弹性材料粘接界面端的位移场和奇异应力场,由Laplace数值逆变换得到时域中的数值解,显然,这种解法不能给出应力场的解析表达式.Kitamura等[22]研究了弹性材料/非线性蠕变材料组成的粘接界面端问题,蠕变相材料的变形服从Norton律,由于获得奇异应力场的解析式困难,假设沿界面的应力场表达式在形式上与弹性解相同,通过有限元分析结果外推得到时间相依的奇异指数和相应的应力强度系数,需要指出的是,应力场沿界面的分布假设同样缺乏严密的论证.Takahashi等[23]在文献[22]的基础上提出了弹性材料与非线性蠕变材料组成的界面端蠕变开裂的破坏条件.目前,对界面具有滑移接触的黏弹性界面端奇异应力场问题所开展的研究工作还未见报道.黏弹性变形过程中界面之间的相对滑移,以及滑移方向的变化引起摩擦力方向的改变等因素的出现,导致边界条件非线性,使得问题的理论分析难以进行.文中考虑蠕变加载,首先对问题进行一定简化,线性化边界条件,由对应原理得到Laplace变换域中的接触界面端应力场,以卷积积分形式给出时域中奇异应力场的表达式;通过数值算例指出应力场的卷积积分核函数可以利用准弹性求解所得解析式来近似;在此基础上讨论应力场的奇异性特征,得到采用准弹性解相似形式的表达式描述黏弹性应力场的误差估计.最后,采用有限元法分析黏弹性板端部嵌入部位的奇异应力场,以数值结果验证理论分析所得结论的有效性.
1 接触界面端附近的黏弹性应力场
考虑平面问题,如图1(a)所示,两种黏弹性材料1和材料2在材料2端部附近接触,取x轴沿接触界面.对问题进行以下简化,一是假设在整个黏弹性变形过程中,接触界面端的相对滑移量是微小的,与变形位移同量级,且相对滑移方向不变;另一方面,如图1(b)所示,以$O$为原点,假定存在一个$r_{0}$,在$r \le r_{0}$的局部区域内,两种材料始终保持接触,摩擦系数不随时间而变;外部区域对该局部区域内的应力分布与变形的影响通过后者周边的位移边界施加.由此,我们可以用变形及滑移前的几何形状为基准来研究黏弹性材料接触界面端的变形与相对滑移.图1
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_1.png)
图1接触界面端
Fig.1Contact interface ends
在$r \le r_{0}$的部区域内,与$O$相连边界的线性边界条件表示如下
式中,$\sigma _{r}$和$\sigma _{\theta}$分别为径向和环向正应力,$\tau$}$_{r\theta}$为剪切应力,$u_{\theta }$为环向位移,f为接触面的摩擦系数,下标1和2分别对应于材料1和材料2.
1.1 奇异应力场的黏弹性解
假设两种材料泊松比的时间相关性弱,近似为常量.各向同性平面应力问题的积分型线黏弹性本构关系可表示为式中,j=1,2代表两种接触材料,$v_{j}$是泊松比;$E_{j}(t)$表示松弛模量.分别用$E_j (t) / [1-\nu _j^2 ]$与$\nu _j / (1-\nu _j)$代替式(2)的$E_{j}(t)$和$v_{j}$即可得平面应变问题的本构关系.
$E_{j}(t)$用Prony级数表示如下式
式中,$E_{j0}$,$E_{jk}$和$\tau$}$_{jk}$ (k=1,2,$\cdots$,$n_{j})$为材料参数,其中,$E_{j}(\infty )=E_{j0}$为持久模量.
将式(1)、式(2)作Laplace变换,且在变换域中取 Goursat 应力函数为
式中,z =$r{\rm e}^{{\rm i}\theta}$,其中i为虚数单位,$s$为Laplace参数,$\lambda$}$^{\ast}$为指数,$A_{j}$与$B_{j}$为待定复系数.Laplace变换域中的应力和位移为
式中,等号左边各项的上标"*"表示变换域中的对应力学量,其中$u_{rj}^{\ast}$是径向位移. 常系数$\kappa$}j(j=1,2)在平面应力时为(3-$\nu$}j)/(1+$\nu$}j),平面应变时为(3$-$4$\nu$}$_{j})$;$\mu$}$_{j}^{\ast }$= sE}$_{j}^{\ast }$/[2(1+$\nu$}$_{j})$]为剪切模量,其中$E_{j}^{\ast}=L$[$E(t)$]为松弛模量的Laplace变换.类似文献[5,6]的推导,利用式(5)和Laplace变换后的齐次边界条件(1),可导出确定式(4)中奇异性指数$\lambda$}$^{\ast }$的特征方程如下
式中,$\alpha$}$^{\ast }$,$\beta$}$^{\ast}$为变换域中的Dundurs参数,分别为
$$\left.\begin{array}{lll} \alpha ^ * = \frac{\mu _1^ * (s)\left( {\kappa _2 + 1} \right)-\mu _2^ * (s)\left( {\kappa _1 + 1} \right)}{\mu _1^ * (s)\left( {\kappa _2 + 1} \right) + \mu _2^ * (s)\left( {\kappa _1 + 1} \right)}\\ \beta ^ * = \frac{\mu _1^ * (s)\left( {\kappa _2-1} \right)-\mu _2^ * (s)\left( {\kappa _1-1} \right)}{\mu _1^ * (s)\left( {\kappa _2 + 1} \right) + \mu _2^ * (s)\left( {\kappa _1 + 1} \right)}\end{array}\right\}$$
将变换域中的局部应力场写为以下向量形式
式中,$K_{V}^{\ast }(s)$为比例因子;$\varTheta _r^ *$,$\varTheta _\theta ^ *$和$\varTheta _{r\theta }^ *$是$\lambda$}$^{\ast }$与$\theta$}的函数,参见附录.由式(7)可知,当Re[$\lambda$}$^{\ast}$]$<$1时,应力场具有奇异性, 可将$K_{v}^{\ast}(s)$理解为应力强度系数. 令
将式(7)作Laplace逆变换后得到
式中,$\varGamma$}$_{r}$,$\varGamma$}$_{\theta}$和$\varGamma$}$_{r\theta }$为核函数,$K_{v}(t)$是$K_{v}^{\ast }$(s)的逆变换.式(9)和式(8)表明,奇异性隐含在卷积积分的核函数中,且具有"记忆"功能.
1.2 奇异应力场的准弹性解
将两种材料的本构关系式(2)由卷积形式简化为乘积形式,结合局部边界条件式(1),经时域中的Goursat应力函数法,可导出奇异应力场的准弹性解为式中,$K_{q}(t)$为准弹性解的强度系数,$\varGamma '_{r}$,$\varGamma '_{\theta }$和$\varGamma '_{r\theta }$以向量形式写为
式中,右端$\varTheta _r^q$,$\varTheta _\theta ^q$和$\varTheta_{r\theta }^q$的形式分别对应附录中的$\varTheta _r^ *$,$\varTheta _\theta ^ *$和$\varTheta _{r\theta }^ *$,只须将后者的$\lambda$}$^{\ast}$替换为准弹性解的奇异性指数$\lambda$}$_{q}$,其由下述特征方程解出
式中,$\alpha$},$\beta$}为准弹性法的Dunders参数,有
$$\left\{\begin{array}{ll} \alpha = \frac{\mu _1 (t)\left( {\kappa _2 + 1} \right)-\mu _2 (t)\left( {\kappa _1 + 1} \right)}{\mu _1 (t)\left( {\kappa _2 + 1} \right) + \mu _2 (t)\left( {\kappa _1 + 1} \right)}\\ \beta = \frac{\mu _1(t)\left( {\kappa _2-1} \right)-\mu _2 (t)\left( {\kappa _1-1} \right)}{\mu _1 (t)\left( {\kappa _2 + 1} \right) + \mu _2 (t)\left( {\kappa _1 + 1} \right)}\end{array}\right.$$
其中,$\mu$}$_{j}=E_{j}(t)$/[2(1+$\nu$}$_{j})$].
1.3 黏弹性奇异应力场的近似表示
将式(11)左端各项视为准弹性解(10)式的核函数,比较式(9)与式(10)可见,黏弹性解是核函数与强度系数的卷积,而准弹性解是相应核函数与强度系数的直接乘积,但两者所对应的强度系数分别在变换域和时域中定义,显然,应力强度系数的时间相关性依赖于图1中$r=r_{0}$的位移边界条件.下面通过数值算例来考察黏弹性解与准弹性解核函数的相近程度,式(8)的解析求逆困难,文中采用Bellman算法求其数值逆变换[24-26],由以下形式表示
式中,$n$是求积节点个数,$s$=1,2,\ldots ,$n$;{{$\varPhi$}}(r,$\theta$},$t_{i})$=[$\varGamma$}$_{r}$, $\varGamma$}$_{\theta }$, $\varGamma$}$_{r\theta }$]$^{\rm T}$,{{$\varPsi$}}$^{\ast }$($\theta$},$\lambda$}$^{\ast })$=[$\varTheta$}$^{\ast }_{r}$, $\varTheta$}$^{\ast }_{\theta }$, $\varTheta$}$^{\ast }_{r\theta }$]$^{\rm T}$;$X_{i}^{\ast }$=(1+$X_{i})$/2,$W_{i}^{\ast }=W_{i}$/2,其中$X_{i}$和$W_{i}$分别是$n$阶高斯积分点和权重系数;$X_{i}^{\ast }$和$W_{i}^{\ast }$是移位后的高斯积分点和相应的权重系数,$A_{0}$($>$0)是移轴系数,调整该系数可改变离散时间点的分布区间,$t_{i}$=$-A_{0}$ln($X_{i}^{\ast })$是时域内的离散时间点.
考虑表1所示三种黏弹性材料的组合,取两组算例,算例1中,图1所示材料1取参数组group 3,材料2取参数组group 1,可见材料1的持久模量等材料2大近两个量级;算例2中,材料2的参数不变,但材料1取参数组group 2,此时材料2的持久模量小于材料1. 统一取摩擦系数f=0.3,图2~图5给出了算例1的核函数计算结果,其中,图2和图3分别是给定极径r=0.005 mm,0.01 mm,0.1 mm, 1 mm, $\theta$}=$-${π}/2时剪应力核函数相对比值与径向应力核函数相对比值随时间变化的关系。
Table 1
表1
表1材料参数组合
Table 1
EVGPa | Eu/GPa | Ej/GPa | /h-1 | T2jf^~X | V | |
---|---|---|---|---|---|---|
Group 1 | 3 | 2 | 1 | 0.03 | 0.05 | 0.35 |
Group 2 | 1 | 2 | 1 | 0.04 | 0.03 | 0.40 |
Group 3 | 140 | 40 | 20 | 0.04 | 0.03 | 0.30 |
新窗口打开|下载CSV
图2
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_2.png)
图2算例1中剪应力核函数与时间的关系
Fig.2Kernel function of shear stress versus time for example 1
图3
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_3.png)
图3算例1中径向应力核函数与时间的关系
Fig.3Kernel function of radial stress versus time for example 1
图4
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_4.png)
图4算例1中剪应力核函数与极角的关系
Fig.4Kernel function of radial stress versus polar angle for example 1
图5
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_5.png)
图5算例1中剪应力核函数与极角的关系
Fig.5Kernel function of shear stress versus polar angle for example 1
其中,相对比值的基准是对应准弹性核函数在$t$=0时的取值,如图3中纵轴表示
图6
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_6.png)
图6算例2中剪应力核函数与时间的关系
Fig.6Kernel function of shear stress versus time for example 2
图7
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_7.png)
图7算例2中径向应力核函数与时间的关系
Fig.7Kernel function of radial stress versus time for example 2
图8
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_8.png)
图8算例2中剪应力核函数与极角的关系
Fig.8Kernel function of radial stress versus polar angle for example 2
图9
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_9.png)
图9算例2中剪应力核函数与极角的关系
Fig.9Kernel function of radial stress versus polar angle for example 2
由图2~图9可见,黏弹性解与准弹性解的核函数接近相同,尤其对算例1,两者基本吻合.算例2的差别略大,但相对于准弹性核函数的差值不超过4%.如前所述,两组算例中所取的材料1和材料2的黏弹性参数组合具有极端特点,更多的数值算例结果表明,对任选的黏弹性参数组合,两类核函数仍然是非常接近的.故可将准弹性解给出的核函数近似代替黏弹性解的核函数,由此,式(9)变化为
进一步,设$K_{V}(t)$的导数连续,则由积分中值定理,式(14)变为
式中,$ K'_{r}(r$, $\theta$},$t)$,$ K'_{\theta }(r$,$\theta$},$t)$和$K'_{r\theta }(r$,$\theta$},$t)$是各应力分量所对应的核函数比值系数,分别有
式中,0$ \le$$\xi$}$_{i} \le t$~(i=1,2,3)与时间$t$有关,也与坐标参数r,$\theta$}相关.式(15)、式(16)表明,一般情况下,在不同时刻,沿不同极角,各应力分量与极径r之间的奇异性特征是不同的,不存在统一的奇异指数和应力强度系数.数学上,式(15)是用类似于准弹性解的形式描述黏弹性应力场,其中的核函数比值系数可被解释成一种修正系数,
在图2~图5中进一步考察算例1的结果,核函数与时间的相关性弱,其随时间的相对变化范围很小,此时,式(16)所示修正系数略等于1,则式(15)可近似为
可见,如聚合物材料与金属材料,两种接触材料的持久模量相差悬殊,接触界面端端部的奇异应力场可以采用类似于准弹性解的形 式进行解析描述,此时的奇异指数是统一的,只与时间有关,且可以采用如式(12)所示的准弹性解法确定.
在图6~图9中考察算例2的结果,核函数其随时间的相对变化范围相对较大,则式(16)所给出的3个系数的变化范围增大,且受坐标参数r和$\theta$}的影响,表明此情形下的各应力分量的奇异指数不相同,与准弹性解给出的奇异性指数的差别较大.若采用式(17)描述黏弹性奇异应力场,将存在一定的误差.利用附录所列的解析式不难得到这种方法误差的误差限.
2 黏弹性板端部嵌入部位的奇异应力场
如图10所示,黏弹性板的端部被嵌入固定的金属支承,两者在搭接部位的接触问题用接触界面端模型描述,并简化为平面应变问题.分析两组算例,算例A的板直接与金属接触,即图中的垫层不存在;算例$B$是在板与金属支承之间存在不同的黏弹性垫层,后者相对板的材料要"柔"一些.三种材料的弹性或黏弹性力学参数列于表2,其中设金属为线弹性材料.Table 2
表2
表2算例材料参数
Table 2
E0j/GPa Eu/GPa Ej/GPa | 了1>-1 | /h-1 | V | |
---|---|---|---|---|
plate | 3.7 0.754 0.278 | 0.01 | 0.1 | 0.33 |
cushion | 121 | 0.04 | 0.03 | 0.40 |
metal support | 206 — — | — | — | 0.30 |
新窗口打开|下载CSV
图10
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_10.png)
图10黏弹性板嵌入端示意图
Fig.10Illustration of fixed end for viscoelastic plate
取板、垫层和金属支承厚度分别为55 mm,8 mm与25 mm. 剪力为恒载$F_{s}$=78$H(t)$ kN,弯矩是阶梯型加载M=$M_{0}$[0.5$H(t)$+0.25$H(t-$75)+0.25$H(t-$150)],其中,$M_{0}$=8.3 kN$\cdot$m;$H(t)$为单位阶梯函数,时间$t$的单位为分钟.在局部接触区域加密有限元网格,最小网格尺寸0.005 mm.首先由黏弹性有限元得到两个算例中位移和应力场随时间演化的历史,然后,由$\theta$ }=-π}/2的径向节点上的剪应力和径向应力计算结果讨论黏弹性应力场的奇异性和近似重构.
给定$t$ =50 h,图11给出时接触界面的垂直位移分布,可见两组算例中都存在$r_{0}$=0.8 mm左右的接触区;图12是接触界面的相对滑移量分布,可见两组算例中的界面滑移量大小与位移同量级,正负符号无变化,即相对滑移方向没有改变.两图结果综合说明,式(1)所给出的接触位移条件是满足的.可以验证,不同时刻也存在相似结论.
图11
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_11.png)
图11$t$=50 h时接触界面的竖向位移分布
Fig.11Illustration of fixed end for viscoelastic plate
图12
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_12.png)
图12$t$=50 h时接触界面的相对滑移分布
Fig.12Distribution of relative slip along contact interface when $t$ =50 h
由式(15),沿$\theta$ =-π/2方向的应力与极径r的关系可以近似表示为
利用式(18),结合有限元分析结果外推得到对应极角$\theta$ }=-π}/2的奇异指数. 表3给出了两组算例在时刻$t$=50 min和$t$=100 min的结果,分别由剪应力与径向应力外推和准弹性解预测得到.从表中可见,算例A中的3种途径确定的奇异性指数接近相同,最大相差约4%;而算例$B$的差值较大,最大约18%.这是由于算例A是黏弹性板与弹性金属支承直接接触,模量差近40倍,奇异特征值和核函数基本上与时间无关.第二组算例中,黏弹性板与黏弹性垫层材料接触,模量变化范围相近,各应力分量的核函数随时间的变化范围明显增大,根据式(15)和式(16)可知,故此时各应力分量的奇异性指数不相同,且与时间的相关性增加.
Table 3
表3
表3沿极角0=-n/2奇异特征值2
Table 3
50 | 0.578 | 0.549 | 0.555 | |
---|---|---|---|---|
example A | ||||
100 | 0.534 | 0.555 | 0.555 | |
50 | 0.683 | 0.582 | 0.675 | |
example B | ||||
100 | 0.602 | 0.562 | 0.681 |
新窗口打开|下载CSV
下面近似重构接触界面端的黏弹性奇异应力场,首先利用式(12)确定奇异性指数$\lambda$}$_{q}$,再由式(17)中的剪应力分布公式确定系数$K_{V}(t)$,再将此系数回代入式(17),获得其余应力分量的近似表示.对应算例A,图13和图14分别给出沿$\theta$ }=-π}/2方向在两个时刻的剪切应力与径向正应力分布;图中的黏弹性解是有限元数值解,近似解表示应力场重构的结果,此两图所示结果表明,数值解与近似解基本吻合,径向应力的最大相对误差约为5%.而针对算例B,图15和图16显示了数值解和近似解的较大差异,径向应力的相对误差达到18%.两组算例结果的区别实际上是由各自核函数的时间相关性强弱所决定的.
图13
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_13.png)
图13算例A中剪应力与极径的关系
Fig.13Shear stress versus polar radius for example A
图14
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_14.png)
图14算例A中径向应力与极径的关系
Fig.14Radial stress versus polar radius for example A
图15
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_15.png)
图15算例B中剪应力与极径的关系
Fig.15Shear stress versus polar radius for example B
图16
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-2-494/thumbnail/img_16.png)
图16算例B中径向应力与极径的关系
Fig.16Radial stress versus polar radius for example B
3 结论
基于相对滑移量非常微小、滑移方向不变,以及存在局部的不变接触区域的简化假定,分析蠕变载荷作用下的线黏弹性接触界面端奇异应力场.数值算例中分别考虑接触材料的模量相差悬殊和模量接近这两种情形,得到以下结论.(1)奇异应力场卷积积分解与准弹性解的核函数接近相同,可以用具有解析表达的准弹性解核函数代替卷积积分解中的核函数.
(2)在给定时刻,黏弹性应力场的奇异性与应力分量、极角有关.严格意义上,不存在统一的奇异值和应力强度系数.
(3)采用类似于准弹性解的解析式描述黏弹性奇异应力场将产生一定的误差,依据文中方法可以得到相应的误差限估计.若接触材料的持久模量相差悬殊,因核函数随时间的变化范围小,故能利用类似准弹性解的解析式较准确地表示奇异应力场,此时有统一的奇异指数和应力强度系数.
附录
$$ \varTheta _r^ * =-\{(3-\lambda ^ * )(F^ * + \lambda ^ *-\cos 2\lambda ^ * π)\cos (\lambda ^ *-1)\theta +$$$$[F^ * (\lambda ^ * + \cos 2\lambda ^ * π) + \lambda ^ {* 2}-1]\cos (\lambda ^ * + 1)\theta\}/$$$$[(F^ * + \lambda ^ *-1)\sin 2\lambda ^ * π]-$$
$$ \frac{(3-\lambda ^ * )\sin (\lambda ^ *-1)\theta-F^ * \sin (\lambda ^ * + 1)\theta }{(F^ * + \lambda ^ *-1)} ~~~$$
$$ \varTheta _\theta ^ * =-\{(1 + \lambda ^ * )(F^ * + \lambda ^ *-\cos 2\lambda ^ * π)\cos (\lambda ^ *-1)\theta-$$
$$ [F^ * (\lambda ^ * + \cos 2\lambda ^ * π) + \lambda ^ {* 2}-1]\cos (\lambda ^ * + 1)\theta\}/~~~$$
$$[(F^ *+ \lambda ^ *-1)\sin 2\lambda ^ * π]-$$
$$ \frac{(1 + \lambda ^ * )\sin (\lambda ^ *-1)\theta + F^ * \sin (\lambda ^ * + 1)\theta }{(F^ * + \lambda ^ *-1)}$$
$$\varTheta _{r\theta }^ * =-\{(1 + \lambda ^ * )(F^ * + \lambda ^ *-\cos 2\lambda ^ * π)\sin (\lambda ^ *-1)\theta-$$
$$[F^ * (\lambda ^ * + \cos 2\lambda ^ * π) + \lambda ^ {* 2}-1]\sin (\lambda ^ * + 1)\theta\}/$$$$[(F^ * + \lambda ^ *-1)\sin 2\lambda ^ * π]+$$
$$ \frac{(\lambda ^ *-1)\cos (\lambda ^ *-1)\theta + F^ * \cos (\lambda ^ * + 1)\theta }{(F^ * + \lambda ^ *-1)}$$
$$F^ * =-\lambda ^ *-1 + \frac{2\cos \lambda ^ * π }{f\sin \lambda ^ * π + \cos \lambda ^ * π }$$
参考文献 原文顺序
文献年度倒序
文中引用次数倒序
被引期刊影响因子
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
为了克服基于统计学参数的接触模型的尺度依赖性以及现有接触分形模型推导过程中初始轮廓表征受控于接触面积或取样长度的不足,基于粗糙表面轮廓分形维数D、尺度系数G和最大微凸体轮廓基底尺寸l,建立了新的粗糙表面接触分形模型,探讨了微凸体变形机制、粗糙表面的真实接触面积和接触载荷的关系,揭示了接触界面的孔隙率和真实接触面积随端面形貌、表面接触压力等参数变化的规律,给出了不同形貌界面被压实的最大变形量.结果表明:微凸体变形从弹性变形开始,并随着平均接触压力pm的增大逐步向弹塑性变形和完全塑性变形转变;接触界面的初始孔隙率0随D的增大而增大,压实孔隙所需要的最大变形量也随之增大;接触压力pc增大,孔隙率减小,并随着D的增大和G减小,快速减小,直至填实,变为零;D较小时,G的增大对真实接触面积的增大影响较小;D较大时,G的增大对真实接触面积的增大作用明显.研究成果为端面摩擦副的润滑与密封设计提供了理论基础.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
为了克服基于统计学参数的接触模型的尺度依赖性以及现有接触分形模型推导过程中初始轮廓表征受控于接触面积或取样长度的不足,基于粗糙表面轮廓分形维数D、尺度系数G和最大微凸体轮廓基底尺寸l,建立了新的粗糙表面接触分形模型,探讨了微凸体变形机制、粗糙表面的真实接触面积和接触载荷的关系,揭示了接触界面的孔隙率和真实接触面积随端面形貌、表面接触压力等参数变化的规律,给出了不同形貌界面被压实的最大变形量.结果表明:微凸体变形从弹性变形开始,并随着平均接触压力pm的增大逐步向弹塑性变形和完全塑性变形转变;接触界面的初始孔隙率0随D的增大而增大,压实孔隙所需要的最大变形量也随之增大;接触压力pc增大,孔隙率减小,并随着D的增大和G减小,快速减小,直至填实,变为零;D较小时,G的增大对真实接触面积的增大影响较小;D较大时,G的增大对真实接触面积的增大作用明显.研究成果为端面摩擦副的润滑与密封设计提供了理论基础.
DOIURL
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
针对两粗糙表面在法向力和切向力共同作用下相互接触时结合面切向阻尼的问题进行了研究。首先,根据KE模型对单个微凸体在弹性、弹塑性、塑性变形阶段的切向接触行为进行了分析,获得了微凸体在三个变形阶段的黏滑特性;然后,基于GW统计模型建立了一种在微凸体法向弹性、弹塑性和塑性变形机制基础上,考虑微凸体黏滑摩擦行为的机械结合面切向接触阻尼统计模型;最后,分别讨论了机械结合面的法向预载荷、切向激振频率和切向动态位移幅值对机械结合面切向阻尼的影响。研究表明:结合面切向接触阻尼系数随着结合面法向载荷的增大而增大,随着切向激振频率和切向动态位移幅值的增大而减小;在高频率、大幅值下,结合面切向接触阻尼系数几乎与动态位移幅值和激振频率无关。为了验证模型的准确性,构建了动态切向力作用下的结合面切向阻尼试验,其试验结果与理论仿真变化规律与量级基本一致,从而证明了本文所提出的切向阻尼模型的有效性。
DOIURL
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
针对两粗糙表面在法向力和切向力共同作用下相互接触时结合面切向阻尼的问题进行了研究。首先,根据KE模型对单个微凸体在弹性、弹塑性、塑性变形阶段的切向接触行为进行了分析,获得了微凸体在三个变形阶段的黏滑特性;然后,基于GW统计模型建立了一种在微凸体法向弹性、弹塑性和塑性变形机制基础上,考虑微凸体黏滑摩擦行为的机械结合面切向接触阻尼统计模型;最后,分别讨论了机械结合面的法向预载荷、切向激振频率和切向动态位移幅值对机械结合面切向阻尼的影响。研究表明:结合面切向接触阻尼系数随着结合面法向载荷的增大而增大,随着切向激振频率和切向动态位移幅值的增大而减小;在高频率、大幅值下,结合面切向接触阻尼系数几乎与动态位移幅值和激振频率无关。为了验证模型的准确性,构建了动态切向力作用下的结合面切向阻尼试验,其试验结果与理论仿真变化规律与量级基本一致,从而证明了本文所提出的切向阻尼模型的有效性。
DOIURLMagsci
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
<p>摩擦接触问题是计算力学领域最具挑战性的问题之一,接触系统的泛函具有非线性、非光滑的特点,导致接触算法的收敛性与精确性难以保证.因此将比例边界等几何分析(scaled boundary isogeometric analysis,SBIGA)与B可微方程组(B dierential equation,BDE)相结合,提出了求解二维摩擦接触问题的比例边界等几何B可微方程组方法.在比例边界等几何坐标变换的基础上,通过虚功原理推导了关于边界控制点变量的接触平衡方程,表示成B可微方程组形式的接触条件可被严格满足,求解B可微方程组的算法的收敛性有理论保证.此比例边界等几何B可微方程组方法(SBIGA-BDE)只需在接触体边界进行等几何离散,使问题降低一维,能精确描述接触边界,并可通过节点插入算法进行真实接触区域的识别.此外,由于几何建模和数值分析使用相同的基函数,节约了划分网格的时间.以赫兹接触问题和悬臂梁摩擦接触问题为例,通过与解析解及数值计算软件ANSYS计算结果进行对比,验证了该方法求解二维摩擦接触问题的有效性及高精度等特点.</p>
DOIURLMagsci
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
<p>摩擦接触问题是计算力学领域最具挑战性的问题之一,接触系统的泛函具有非线性、非光滑的特点,导致接触算法的收敛性与精确性难以保证.因此将比例边界等几何分析(scaled boundary isogeometric analysis,SBIGA)与B可微方程组(B dierential equation,BDE)相结合,提出了求解二维摩擦接触问题的比例边界等几何B可微方程组方法.在比例边界等几何坐标变换的基础上,通过虚功原理推导了关于边界控制点变量的接触平衡方程,表示成B可微方程组形式的接触条件可被严格满足,求解B可微方程组的算法的收敛性有理论保证.此比例边界等几何B可微方程组方法(SBIGA-BDE)只需在接触体边界进行等几何离散,使问题降低一维,能精确描述接触边界,并可通过节点插入算法进行真实接触区域的识别.此外,由于几何建模和数值分析使用相同的基函数,节约了划分网格的时间.以赫兹接触问题和悬臂梁摩擦接触问题为例,通过与解析解及数值计算软件ANSYS计算结果进行对比,验证了该方法求解二维摩擦接触问题的有效性及高精度等特点.</p>
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
由于功能梯度材料在改善表面接触损伤方面的潜在应用,其接触力学问题受到越来越广泛关注,许多****开展了大量的研究工作.本文结合作者近些年来在功能梯度材料接触力学方面开展的研究工作,综述了功能梯度材料接触力学若干基本问题的最新理论研究进展,包括功能梯度材料的无摩擦和滑动摩擦接触、微动接触、热弹性接触及失稳、力电磁多场耦合接触和黏附接触.最后对未来功能梯度材料接触力学研究进行了展望.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
由于功能梯度材料在改善表面接触损伤方面的潜在应用,其接触力学问题受到越来越广泛关注,许多****开展了大量的研究工作.本文结合作者近些年来在功能梯度材料接触力学方面开展的研究工作,综述了功能梯度材料接触力学若干基本问题的最新理论研究进展,包括功能梯度材料的无摩擦和滑动摩擦接触、微动接触、热弹性接触及失稳、力电磁多场耦合接触和黏附接触.最后对未来功能梯度材料接触力学研究进行了展望.
[本文引用: 3]
[本文引用: 3]
[本文引用: 2]
DOIURL
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
Singular stresses arising in the neighborhood of contact surfaces introduced in laminated orthotropic plates by mechanical joining with clamp-up were investigated by using local asymptotic solutions and full-field numerical analysis. Three-dimensional B-spline approximation of the displacements and a penalty function-based contact solution was used in the numerical analysis. Recent work has shown that fracture in bolted composite joints may initiate near the outer edge of the bolt head or washer away from the hole edge, particularly if the joint is preloaded. Material and geometric discontinuities exist in these regions, resulting in singular stress behavior. Asymptotic stress analysis was performed to obtain the power of singularity in these regions as a function of the bolt-head (washer) stiffness. Frictionless contact conditions were assumed. It was found that the characteristics of the stress singularity for such practically important combinations as titanium bolt-head and carbon fiber composite plate are similar to a crack in terms of the power of singularity and uniqueness of the singular term. Coefficients of the singular terms of the asymptotic expansion were determined by comparison with the numerical solution in the close vicinity of the singular contour. Good agreement between the asymptotic and numerical solution in the transition regions was observed.
DOIURL
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
This paper develops an effective approach to analyse the asymptotic displacement and stress fields near the singular points in laminated anisotropic composite joints with a fictional contact along the interface. The Ting's theory, extended from the Stroh's formulation for anisotropic elasticity problems, is employed to represent the asymptotic fields near the singular points of the contact problems. The characteristic equations of the contact problems are constructed from the boundary conditions, where the continuity conditions at the frictional interface governed by the Coulomb's law of friction are considered. The order of stress singularities and the asymptotic fields near the singular points are determined by solving the developed non-linear coupled characteristic equations for the general contact problems of friction in anisotropic bimaterials from an iterative procedure. Only real values of root representing the order of stress singularities are found for the general frictional contact problems. In the special case when the frictional contact exists in two half plane composite laminates, stress singularities may appear if the material constants satisfy certain requirements. Explicit solutions for the root of the characteristic equations and the asymptotic fields for the special case can be directly obtained without requiring the iterative procedure. The theoretical and numerical results show that both the friction coefficient within the slip interface and the wedge angle of anisotropic materials have significant effects on the stress singularities for the frictional contact problems. Further investigations are undertaken for several special cases, including studies for isotropic materials that are confirmed by existing theoretical results and experimental data available.
[本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
针对铆接结构的特点,应用特征函数扩展技术分析柱坐标下接触界面端的应力奇异性问题。建立了柱坐标下圆柱体端面接触边缘附近的三维渐近位移场和应力场渐近表达式,并根据铆钉/被铆接件接触界面端的位移和应力边界条件,建立一个非线性特征方程组。据此方程组可求解界面端邻域的应力奇异性指数、位移和应力角分布函数的数值解。通过与有限元方法计算结果相对比,验证了该方法的有效性。分析了平头、沉头以及半圆头铆钉构成的铆接结构的应力奇异性问题,考察了铆钉材料、几何形式和摩擦系数对接触界面端应力奇异性指数和应力场角分布的影响。
[本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
针对铆接结构的特点,应用特征函数扩展技术分析柱坐标下接触界面端的应力奇异性问题。建立了柱坐标下圆柱体端面接触边缘附近的三维渐近位移场和应力场渐近表达式,并根据铆钉/被铆接件接触界面端的位移和应力边界条件,建立一个非线性特征方程组。据此方程组可求解界面端邻域的应力奇异性指数、位移和应力角分布函数的数值解。通过与有限元方法计算结果相对比,验证了该方法的有效性。分析了平头、沉头以及半圆头铆钉构成的铆接结构的应力奇异性问题,考察了铆钉材料、几何形式和摩擦系数对接触界面端应力奇异性指数和应力场角分布的影响。
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
Fretting-fatigue cracks start very early in a fretting-fatigue life. The fretting-fatigue life is dominated by the propagation of small cracks. Therefore, predicting the start of fretting-fatigue cracking and the propagation of the cracks is a very important part of estimating fretting-fatigue strength and fretting-fatigue life. The start of a fretting-fatigue crack was estimated by using the stress-singularity parameters at the contact edges. The way in which the crack propagates was then estimated by using fracture-mechanics analysis, in which the wear on the contact surfaces and the direction of crack propagation were taken into account.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
Fretting fatigue tests have been carried out on 7075-T6 aluminium alloy and En24 steel as a pad material to study the crack initiation behaviour. An asymptotic analysis is carried out to study the equivalence of stress state at the edge of a rectangular pad for complete contact for the Dundur’s parameters, α, β and at notch root of an associated internal angle, 2γ and subsequently a model is developed giving the stress singularity, λ611 for the complete contact for dissimilar materials with friction. Further, a theoretical formulation is developed to predict the crack initiation angle using the stress singularity, λ611 and the strain energy density failure criteria. The crack initiation angle experimentally obtained through the scanning electron micrographs of the failed fretting fatigue specimens are compared with the predicted crack initiation angle using the strain energy density failure criteria. The experimental observations and the theoretical results suggest that the strain energy density failure criteria can be successfully used to predict the crack initiation angle under fretting fatigue loading conditions for the complete contact case with friction. Also it is observed that the crack initiation angle in general decreases with increase in coefficient of friction at the interface.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
采用ABAQUS有限元软件对微动桥平面/平面试样接触状态进行三维有限元分析,详细计算了接触边缘应力变化,分析了不完全接触区应力场,讨论了不同半径R(0.3mm,0.6mm,0.9mm)和不同的摩擦系数f(0.3,0.6,0.8)对微动区接触应力集中的影响,分析其应力奇异性的变化。根据界面力学接触界面奇异应力场和应力强度参数来计算应力奇异性特征值λ,进而计算微动疲劳强度系数K,对微动疲劳强度进行评估。从理论计算出发,研究分析接触边缘的微动疲劳强度,以及各参数对微动疲劳强度系数K的影响。
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
采用ABAQUS有限元软件对微动桥平面/平面试样接触状态进行三维有限元分析,详细计算了接触边缘应力变化,分析了不完全接触区应力场,讨论了不同半径R(0.3mm,0.6mm,0.9mm)和不同的摩擦系数f(0.3,0.6,0.8)对微动区接触应力集中的影响,分析其应力奇异性的变化。根据界面力学接触界面奇异应力场和应力强度参数来计算应力奇异性特征值λ,进而计算微动疲劳强度系数K,对微动疲劳强度进行评估。从理论计算出发,研究分析接触边缘的微动疲劳强度,以及各参数对微动疲劳强度系数K的影响。
[本文引用: 1]
[本文引用: 1]
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
载人球是深海载人潜水器最为关键的部件。在设计过程中,要准确了解观察窗在使用工况下的蠕变变形过程和强度变化过程,据此开展窗座设计,否则可能出现观察窗挤出窗座或者在蠕变过程中变形不协调使得密封失效,或者载人球整体抗压能力的降低。文章通过计算分析和试验两种手段,对深海观察窗的强度、蠕变、边界条件的影响进行了研究。观察窗与窗座之间的相对位移,文中认为由两部分构成:一部分是观察窗玻璃随时间的蠕变变形,另一部分为观察窗与窗座在海水压力作用下发生的挤压变形。文中采用有限元方法进行接触分析,了解在不同边界摩擦系数下,观察窗因海水压力产生的挤压变形。从加工出来的观察窗产品中,任意抽取了两套侧观察窗和两套主观察窗进行试验研究。对理论计算与试验结果进行了对比分析,相关结果可供工程设计参考。
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
载人球是深海载人潜水器最为关键的部件。在设计过程中,要准确了解观察窗在使用工况下的蠕变变形过程和强度变化过程,据此开展窗座设计,否则可能出现观察窗挤出窗座或者在蠕变过程中变形不协调使得密封失效,或者载人球整体抗压能力的降低。文章通过计算分析和试验两种手段,对深海观察窗的强度、蠕变、边界条件的影响进行了研究。观察窗与窗座之间的相对位移,文中认为由两部分构成:一部分是观察窗玻璃随时间的蠕变变形,另一部分为观察窗与窗座在海水压力作用下发生的挤压变形。文中采用有限元方法进行接触分析,了解在不同边界摩擦系数下,观察窗因海水压力产生的挤压变形。从加工出来的观察窗产品中,任意抽取了两套侧观察窗和两套主观察窗进行试验研究。对理论计算与试验结果进行了对比分析,相关结果可供工程设计参考。
DOIURL [本文引用: 2]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
Abstract This paper concerns the stress singularity at the interface corner between the adhesive layer and the rigid adherend subjected to a uniform transverse tensile strain. The adhesive is assumed to be a linear viscoelastic material. The standard Laplace transform technique is employed to get the characteristic equation and the order of the singularity is obtained numerically for given viscoelastic models. The time-domain boundary element method is used to investigate the behavior of stresses for the whole interface. For the viscoelastic models considered, it is shown that the free-edge stress intensity factors are relaxed with time, while the order of the singularity increases with time or remains constant.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
The stress and displacement solutions are obtained for an elastic/viscoelastic joint subjected to a surface traction in the vicinity of an interface corner using elastic iscoelastic correspondence principles and existing corresponding solutions for elastic/elastic joints. The intensity of the resulting stress singularity is determined by a combination of asymptotic analysis and the finite element method. A quasi-static assumption is used to investigate the effects of sliding and rolling contact loads near the interface corner on failure initiation. The results suggest the interface may experience stress reversal as the contact load (normal or shear) moves from one side of an interface corner to the other, leading to the possibility of fatigue failure. Further a relaxation or an increase of the interfacial stresses occurs depending on whether the edge load near the interface corner is on the elastic or viscoelastic side of the joint. The implications of the results in predicting the deformation and failure of asphalt concrete used in highway bridges are discussed.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
Traditional finite element analyses of the stress state in regions with dissimilar viscoelastic materials are incapable of correctly resolving the stress state because of the unbounded nature of the stresses. A hybrid formulation is developed utilizing the exact solution for the stress and displacement fields based on the eigenfunction expansion method under general loading. The region has two dissimilar viscoelastic material wedges with perfect bonding, and is not limited to a particular geometric configuration. The solution method is based on the principle of work in conjunction with the use of Laplace transformation to eliminate time dependency. The strength of the singularity is obtained in the time space without resorting to approximate Laplace inversion techniques. However, the intensification of the stress components is obtained by employing an approximate inversion technique.
URL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
在电子封装等结构中存在大量的粘弹性界面问题,其破坏一般均始于界面端,但目前尚无关于粘弹性界面端奇异场的解。粘弹性问题在拉普拉斯域内与弹性问题有对应关系,理论上可以利用对应性原理由弹性解经拉氏逆变换得到粘弹性问题的解。但是,对于粘弹性界面端,由于奇异场的奇异指数也是与时间有关的,因此进行严密的拉氏逆变换是非常困难的。本文借鉴弹性界面端奇异场,近似地给出了线性粘弹性体界面端奇异场的具体形式,并通过数值计算验证了近似理论解的有效性。
URL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
在电子封装等结构中存在大量的粘弹性界面问题,其破坏一般均始于界面端,但目前尚无关于粘弹性界面端奇异场的解。粘弹性问题在拉普拉斯域内与弹性问题有对应关系,理论上可以利用对应性原理由弹性解经拉氏逆变换得到粘弹性问题的解。但是,对于粘弹性界面端,由于奇异场的奇异指数也是与时间有关的,因此进行严密的拉氏逆变换是非常困难的。本文借鉴弹性界面端奇异场,近似地给出了线性粘弹性体界面端奇异场的具体形式,并通过数值计算验证了近似理论解的有效性。
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
AbstractMeasurements of interface bonding strengths are necessary for predicting the failure behavior of structures and materials with bi-material interfaces. However, it is well known that due to the discontinuity of material properties, stress singularity may exist at the edges of the interface. For accurate determination of the bonding strength of bi-material interface, the elimination of the stress singularity is necessary. This paper presents an analytical solution for the determination of the stress singularity and the critical bonding angle of a bonded joint between elastic and viscoelastic materials. This solution is based on the analytical solution available for an elastic–elastic bonded joint via the elastic–viscoelastic corresponding principle. For the viscoelastic material, both time-independent and time-dependent Poisson’s ratios are considered to find its effect on the stress singularity. As an example, the developed solution is applied to a simulated aluminum-epoxy bonded joint with a spherical interface. It is found that the critical bonding angle and the order of the stress singularity are different for assuming a time-independent or time-dependent Poisson’s ratio of the idealized viscoelastic epoxy. With the analytical solution developed, it is possible to design an optimal interface geometry that can eliminate the stress singularity from the interface corner.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
从界面防护的角度出发,研究了温度载荷下固体发动机中弹性-粘弹 性轴对称界面端的奇异应力场。依据对应原理,由弹性-弹性界面端的特征方程获得了弹性-粘弹性界面端的应力奇异性指数。根据应变匹配模型,推导了温度载荷 下轴对称界面端中的常应力项。针对现有的应力释放罩/推进剂界面端,分析了材料参数和结合角对其应力奇异性指数的影响规律,在不改变装药量的前提下,提出 了弱奇异性或无奇异性界面端的设计。结果表明,自由边呈平角时界面端至多存在-0.1的弱奇异性,界面端应力集中水平显著降低。
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
从界面防护的角度出发,研究了温度载荷下固体发动机中弹性-粘弹 性轴对称界面端的奇异应力场。依据对应原理,由弹性-弹性界面端的特征方程获得了弹性-粘弹性界面端的应力奇异性指数。根据应变匹配模型,推导了温度载荷 下轴对称界面端中的常应力项。针对现有的应力释放罩/推进剂界面端,分析了材料参数和结合角对其应力奇异性指数的影响规律,在不改变装药量的前提下,提出 了弱奇异性或无奇异性界面端的设计。结果表明,自由边呈平角时界面端至多存在-0.1的弱奇异性,界面端应力集中水平显著降低。
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
In this study, an extended Stroh formalism for two-dimensional linear anisotropic viscoelasticity is developed for the problems of interface corners between two dissimilar viscoelastic materials. In this formalism, the solutions for the displacements and stress functions in the time domain can be written in the form of a matrix function using complex variables. The correspondence relations for viscoelastic analysis are then obtained and verified for material eigenvectors, displacement and stress eigenfunctions, singularity orders of stresses, and stress intensity factors. Explicit solutions for the material eigenvector matrices in the Laplace domain are also obtained for standard linear and isotropic linear viscoelastic solids. To calculate the singularity orders and stress intensity factors of the interface corners, four different approaches are proposed. Through numerical examples on cracks, interface cracks, and interface corners, an approach using the path-independent H-integral in the Laplace domain with an elastic near-tip solution, which takes the correspondence relations for singularity orders and stress intensity factors, is demonstrated to be better than the other three approaches. (c) 2012 Elsevier Ltd. All rights reserved.
DOIURL [本文引用: 2]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
Stress fields on elastic-creep bi-material interfaces with different geometry of the interface edge are analyzed by finite element method. The results reveal that the stress highly concentrates near the interface edge at the loading instant and it gradually decreases as the creep-dominated zone expands from the small-scale creep to the large-scale creep. The stress singularity due to creep which resembles the HRR stress singularity appears near the interface edge in all cases. The stress intensity near the interface edge time-dependently decreases and becomes constant when the transition reaches the steady state. The magnitude is scarcely influenced by the edge shape of elastic material, though it depends on the edge shape of creep material. The stress intensity during the transition can be approximately predicted by the -integral at the loading instant.
DOIURL [本文引用: 1]
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
The time-dependent crack initiation from the interface free-edge of adhesively bonded axisymmetric columnar butt joints (epoxy/SUS, edge shape: 90°/90°) was investigated in detail. With the change of applied stress level, , the butt joints exhibited crack initiation life,, that varied about four orders of seconds (10∼ 10s). Such a clear time-dependent life property was then studied in terms of the fracture mechanics. The near-edge stress/strain field at the crack initiation was numerically evaluated with the finite element method (FEM) by applying the time-hardening creep law to the epoxy resin. It was found that the critical asymptotic stress field along the interface represented by the combination of two parameters,(creep stress singularity index) and(creep stress intensity factor), satisfies a unique relation irrespective of ( ,) sets. The same tendency was also confirmed when the near-edgestrain field parameters were employed. These results indicate that the- criterion, originally developed for static fracture problems, still holds its validity in the time domain.
DOIURL
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
Not Available
DOIURLMagsci
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
<p>针对组分材料体积含量任意分布的黏弹性功能梯度材料裂纹问题建立有限元分析途径. 通过Laplace变换,将黏弹性问题转化到象空间中求解,基于反映材料非均匀的梯度单元和裂纹尖端奇异特性的奇异单元计算象空间中的位移、应力和应变场,应用虚拟裂纹闭合方法得到应变能释放率,分别由应力和应变能释放率确定应力强度因子. 给出这些断裂参量在物理空间和象空间之间的对应关系,由数值逆变换求出其在物理空间的相应值. 文中分析两端均匀受拉的黏弹性边裂纹板条,首先针对松弛模量表示为空间函数和时间函数乘积的特殊梯度材料进行计算,结合对应原理验证方法的有效性. 然后分析组分材料体积含量具有任意梯度分布的情形,由Mori-Tanaka方法预测象空间中的等效松弛模量. 计算结果表明,蠕变加载条件下,应变能释放率随时间增加,其增大程度与黏弹性组分材料体积含量相关. 由于梯度材料的非均匀黏弹性性质,产生应力重新分布,导致应力强度因子随时间变化,其变化范围与组分材料的体积含量分布方式有关.</p>
DOIURLMagsci
![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/richHtml_jats1_1/images/more.jpg)
<p>针对组分材料体积含量任意分布的黏弹性功能梯度材料裂纹问题建立有限元分析途径. 通过Laplace变换,将黏弹性问题转化到象空间中求解,基于反映材料非均匀的梯度单元和裂纹尖端奇异特性的奇异单元计算象空间中的位移、应力和应变场,应用虚拟裂纹闭合方法得到应变能释放率,分别由应力和应变能释放率确定应力强度因子. 给出这些断裂参量在物理空间和象空间之间的对应关系,由数值逆变换求出其在物理空间的相应值. 文中分析两端均匀受拉的黏弹性边裂纹板条,首先针对松弛模量表示为空间函数和时间函数乘积的特殊梯度材料进行计算,结合对应原理验证方法的有效性. 然后分析组分材料体积含量具有任意梯度分布的情形,由Mori-Tanaka方法预测象空间中的等效松弛模量. 计算结果表明,蠕变加载条件下,应变能释放率随时间增加,其增大程度与黏弹性组分材料体积含量相关. 由于梯度材料的非均匀黏弹性性质,产生应力重新分布,导致应力强度因子随时间变化,其变化范围与组分材料的体积含量分布方式有关.</p>