循环加载条件下混凝土Ⅰ型裂缝扩展模拟的接触算法

沿裂缝可能开展路径设置接触点对,把求解接触问题的有限元混合法进行扩展,以实现循环加载条件下混凝土Ⅰ型裂缝扩展的数值模拟.根据荷载过程状态和缝面接触状态的不同,将循环荷载作用下的混凝土本构关系抽象为力学模型中的六种不同接触状态,不同的接触状态对应着不同的位移-应力曲线关系.以缝面张开位移和接触应力作为接触状态转变的判断参量,并给出了各状态的转变关系和数值判断条件,以接触算法实现了循环加载条件下混凝土Ⅰ型断裂扩展的数值模拟.首先给出了有限元混合法求解接触问题的基本思路,然后引入循环荷载下的混凝土本构关系,再对Ⅰ型裂缝扩展的数值实现方法进行了阐述,最后通过数值算例说明了数值实现方法的正确性和有效性.     

考虑混凝土应变率变化的高拱坝非线性动力响应研究

提出一种新的应变率相关的混凝土非线性弹塑性损伤模型。采用此模型对混凝土拱坝的非线性地震响应作了分析。在综合考虑坝-地基-库水动力相互作用和坝缝非线性接触的基础上，着重研究了混凝土应交率相关效应及加载历史对混凝土极限强度等重要参数及拱坝响应的影响，并与采用不考虑应交率影响的混凝土损伤模型计算结果进行了对比分析。结果表明，拱坝考虑横缝作用后的坝面应变率分布不同于整体拱坝。应交率分布形态不仅可以很好地表征拱坝的振动形态，而且对于高拱坝的动力响应的影响也不可忽略。     

复合射孔爆燃气体压裂裂缝起裂扩展研究

结合线弹性断裂力学的裂缝尖端应力强度因子判据,建立了复合射孔爆燃气体压裂裂缝的起裂扩展模型,通过建立与多个变量相关的缝内气体压力分布函数,利用迭代法实现了模型的数值求解,获得了缝内气体压力分布随时间的动态变化规律,并分析了不同特征参数对裂缝起裂扩展与止裂过程的影响。实例计算结果表明:(1)随着裂缝扩展的进行,爆燃气体流动尖端与裂缝尖端经历了由重合到不重合再到重合的过程;(2)地应力越大,裂缝起裂扩展越困难,爆燃气体有效致裂作用时间越短,最终得到的裂缝扩展长度也越小;(3)初始裂缝越长,裂缝更容易起裂扩展,爆燃气体能量利用率越高,裂缝扩展更长;(4)岩石断裂韧性的改变对裂缝起裂、止裂和裂缝扩展长度没有明显的影响;(5)升压速率越小,爆燃气体有效致裂作用时间越长,最终裂缝扩展也更长,但对裂缝起裂压力与止裂压力几乎没有影响。     

页岩气藏压裂缝网扩展数值模拟

为探究页岩气藏水力压裂复杂裂缝网络的形成机理,开展了缝网扩展的数值模拟研究.考虑应力阴影和天然裂缝作用,建立了井筒和裂缝中流体流动模型,利用位移不连续方法求解应力与位移不连续量,然后构建了压力与裂缝宽度的迭代方程,并采用牛顿迭代法求解.通过比较数值解经典模型解析解,验证了模型和迭代解法的正确性.多簇裂缝同步扩展时裂缝间距越小,压裂液分配到各条裂缝越不均匀,靠近井筒跟部的裂缝的分流量越大,从而裂缝宽度越大;考虑天然裂缝作用时,逼近角越小或者应力各向异性越弱,水力裂缝越容易发生转向扩展,裂缝网络越复杂.      

致密油藏动态裂缝扩展机理及应用

致密油藏采用注水吞吐补充地层能量取得了一定效果. 但多轮次注水吞吐后, 地层压力和产量降低快. 本文考虑了致密油藏复杂的裂缝形态, 根据艾尔文理论及弹性力学剖析I型裂缝尖端附近的应力场分布, 基于渗流力学、裂缝性致密油藏特征及动态裂缝渗流规律, 建立了多裂缝交叉裂缝扩展渗流模型, 结合注水诱导裂缝扩展机理及断裂力学能量守恒原理, 得到裂缝扩展长度. 依据致密油藏逆向渗吸原理, 提出将注水吞吐转为不稳定脉冲注水. 对比分析注水吞吐、脉冲注水2种能量补充发方式, 预测10年累计采油、压力及剩余油分布. 结果表明, 裂缝净内压随着注水量的增加而升高, 当应力场强度因子达到断裂韧度, 在裂缝尖端会发生扩展. 扩展及延伸的天然裂缝相互沟通, 呈现不规则复杂缝网, 在复杂缝网中主要发生逆向渗吸作用. 脉冲注水累计产油高、注水波及面积广、逆向渗吸作用强. 裂缝性致密油藏水平井注水吞吐转变为脉冲注水方式, 能够充分发挥动态缝网的逆向渗吸及线性驱替作用, 实现有效驱油的目的.      

分布式光纤裂缝检测的有限元分析及试验

对分布式光纤裂缝检测技术中光纤-混凝土复合体的微观力学行为进行了分析. 考虑了涂覆-护套、护套-混凝土双界面的状态非线性,混凝土采用双线性各向同性强化模型以消减局部应力集中,避免护套-混凝土之间的过度穿透. 采用试验确定的接触对力学参数,用ANSYS进行了数值模拟,得到了光纤-混凝土复合体的微观应力分布及光纤的曲率分布. 定量分析了缝宽与弯曲损耗的关系,计算结果与试验结果符合较好,从理论上验证了光纤布置方式、护套厚度对传感灵敏度和动态范围的影响,为分布式光纤裂缝检测技术提供了修正的微观力学分析理论和方法.      

三维压裂缝网不稳定压力半解析求解方法

受地应力及压裂工艺影响, 大斜度井水力压裂缝网展布复杂, 缝网中存在不同倾斜方向、不同展布形态及不同贯穿程度的压裂缝. 本文通过将裂缝面离散为若干矩形微元实现裂缝形态有效表征, 将渗流过程划分为基质向裂缝流动及裂缝向井筒流动两阶段, 采用有限差分方法构建离散裂缝面内不稳定渗流数值解, 结合封闭边界面源函数及叠加原理构建基质内不稳定渗流解析解, 耦合裂缝内流动数值解与基质内流动解析解, 求解了三维压裂缝网不稳定压力. 基于积分中值定理提出了点源、特殊线源代替面源求解基质内渗流的求解方法, 分析了该方法的可行性及适用条件, 在保证模型精度的同时提升了计算效率. 研究表明, 在基质内采用点源函数面积分求解面源的方法可准确求解三维压裂缝网井底压力动态但计算效率极低, 基于积分中值定理的点源、特殊线源近似面源求解方法可大大提升计算效率, 且在裂缝微元划分较为精细(微元无因次边长小于0.15)时可取得较高精度, 基于该模型分析了裂缝导流能力、裂缝倾角、裂缝高度及裂缝段间距对压裂大斜度井典型试井曲线的影响.      

考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法

混凝土结构在服役期间受外界载荷的影响容易产生裂缝, 导致结构刚度降低、构件承载性能衰退, 而采用准确的计算方法预测混凝土裂缝的发展是治理裂缝的基本前提, 也是保障结构安全的重要手段. 连续损伤力学方法(continuou damage method, CDM)能够描述微裂缝的扩展过程, 但不能表示离散的开裂面, 且存在网格诱导偏差及虚假应力传递的弊端, 扩展有限单元法(mechanics-extended finite element method, XFEM)能够描述宏观裂纹的扩展过程, 但不能反映微裂缝的动态扩展, 两者计算出的裂纹分布与实际差异均较大. 现有的CDM-XFEM方法已经能够模拟混凝土微裂缝及宏观裂缝发展的整个过程, 但忽略了宏观裂缝出现时混凝土产生的塑性应变, CDM与XFEM的能量转化过程欠缺平衡性. 因此, 本文重点考虑能量转化时的塑性耗散, 选取指数型函数为粘结裂缝的牵引-分离模式, 基于能量及应力等效的条件重新构建了CDM与XFEM之间的能量转化方程. 采用广义逆最小二乘法求解能量转化系数, 确定能量转化时的临界位移, 并给出了裂缝面水平集的更新算法及整体计算方法的程序流程. 以双切口混凝土受剪拉开裂试验为例, 采用多种裂缝计算方法与试验进行了对比. 结果表明, 采用考虑混凝土塑性耗散的CDM-XFEM方法算出的裂缝分布及拉力-张开位移曲线与试验结果差异最小, 说明采用考虑混凝土塑性耗散的CDM-XFEM计算方法能够更好地计算混凝土裂缝.      

不同地应力条件下切缝药包爆破的数值模拟

针对切缝药包定向爆破的特点,考虑岩石介质非均匀性的基础上,把岩石爆破视为爆炸应力波动态作用和爆生气体压力准静态作用的过程,基于损伤力学理论建立岩石爆破的力学模型,并对不同地应力条件下切缝药包爆破的裂纹演化规律进行数值模拟,分析不同地应力条件对切缝药包爆破效果的影响。模拟结果表明:采用切缝药包爆破时,裂纹主要萌生于切缝周边,沿切缝方向扩展,切缝对定向裂纹的控制作用明显;当考虑地应力作用,且最大地应力方向与切缝方向垂直时,不利于定向裂纹的扩展;最大地应力方向与切缝方向平行时,有利于定向裂纹的扩展。裂纹的扩展方向受控于切缝角度和最大地应力方向这2个条件,裂纹扩展规模则受到地应力的限制。     

考虑诱导缝多段压裂水平井非均质改造压力动态模型研究

为了准确模拟致密油藏水平井大规模压裂形成复杂裂缝网络系统和非均质储层井底压力变化,建立考虑诱导缝矩形非均质储层多段压裂水平井不稳定渗流数学模型,耦合裂缝模型与储层模型得到有限导流裂缝拉普拉斯空间井底压力解,对两种非均质储层模型分别利用数值解、边界元和已有模型验证其准确性.基于压力导数曲线特征进行流动阶段划分和参数敏感性分析,得到以下结果:和常规压裂水平井井底压力导数曲线相比较,理想模式下,考虑诱导缝影响时特有的流动阶段是综合线性流阶段、诱导缝向压裂裂缝“补充”阶段、储层线性流动阶段和拟边界控制流阶段.诱导缝条数的增加加剧了综合线性流阶段的持续时间,降低了流体渗流阻力,早期阶段压力曲线越低;当诱导缝与压裂裂缝导流能力一定时,裂缝导流能力越大,线性流持续时间越长;当所有压裂裂缝不在一个区域时,沿井筒方向两端区域低渗透率弱化了低渗区域诱导缝流体向压裂裂缝“补充”阶段,因此,沿井筒方向两端区域渗透率越低,早期阶段压力曲线越高;当所有压裂裂缝在一个区域时,渗透率变化只影响径向流阶段之后压力曲线形态,外区渗透率越低,早期径向流阶段之后压力曲线越高.通过实例验证,表明该模型和方法的实用性和准确性.     

Cracking simulation of a tubesheet under different loadings

For shell-and-tube heat exchangers, tubesheet cracking is a major failure form. Owing to complicated structures, loadings and environments, mechanisms for the crack nucleation and propagation often puzzle engineers and as a result, it is hard to take effective measures to prevent this kind of failure from happening again. In this paper, three dimensional finite element models were established to investigate a real tubesheet cracking with the emphasis on the driving forces for the crack propagation from a fracture mechanics point of view. Three different loadings, namely residual expansion stress, crack face pressure and transverse pressure, and three crack growth patterns were considered. In order to obtain the residual stresses, the hydraulic expanding process of tube-to-tubesheet joint was simulated. Residual contact pressures between the tube and tubesheet and the induced residual stress distributions in the tubesheet were computed. The possibility for crack propagation in the tubesheet under the action of the different loadings was investigated in terms of the strain energy density factor. Results show that surface crack propagation may be driven by all the three loadings especially the transverse pressure. But when surface cracks come into the interior of the tubesheet along the thickness, as acted along the whole tubesheet thickness, the residual expansion stress would play key roles in crack propagation.     

Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model

Nowadays, numerical simulation of 3D fatigue crack growth is easily handled using the eXtended Finite Element Method coupled with level set techniques. The finite element mesh does not need to conform to the crack geometry. Most difficulties associated to complex mesh generation around the crack and the re-meshing steps during the possible propagation are hence avoided. A 3D two-scale frictional contact fatigue crack model developed within the X-FEM framework is presented in this article. It allows the use of a refined discretization of the crack interface independent from the underlying finite element mesh and adapted to the frictional contact crack scale. A stabilized three-field weak formulation is also proposed to avoid possible oscillations in the local solution linked to the LBB condition when tangential slip is occurring. Two basic three-dimensional numerical examples are presented. They aim at illustrating the capacities and the high level of accuracy of the proposed X-FEM model. Stress intensity factors are computed along the crack front. Finally an experimental 3D ball/plate fretting fatigue test with running conditions inducing crack nucleation and propagation is modeled. 3D crack shapes defined from actual experimental ones and fretting loading cycle are considered. This latter numerical simulation demonstrates the model ability to deal with challenging actual complex problems and the possibility to achieve tribological fatigue prediction at a design stage based on the fatigue crack modeling.     

Analysis of power-law self-similar solutions to the problem of hydraulic fracture crack formation

The problem of hydraulic fracture crack propagation in a porous medium is studied in the approximation of small crack opening and the inertialess flow of an incompressible Newtonian hydraulic fracturing fluid inside the crack. A one-parameter family of power-law self-similar solutions is considered in order to determine the crack width evolution, the fluid velocity in the crack, and the seepage depth in the case of high and low seepage rates through the soil when a fluid flow rate is given at the crack inlet.     

岩石偏心圆孔单裂纹平台圆盘的动态裂纹扩展与止裂

针对平台圆环构型的优点, 提出偏心圆孔单裂纹平台圆盘(cracked eccentrically holed flattened disc, CEHFD), 该试样具有更长的断裂路径。利用霍普金森压杆加载系统, 径向冲击CEHFD试样, 完成Ⅰ型动态断裂实验。砂岩试样表面粘贴应变片和裂纹扩展计, 用于监测裂纹动态起裂、扩展和止裂的全过程。实验表明, 在整个断裂过程中, 裂纹非匀速扩展, 裂纹扩展速度在裂纹起裂后加速上升, 在裂纹止裂前有明显的减速, 与地震时断层的动态破裂全过程完全吻合。采用实验-数值-解析法得到动态应力强度因子, 其时间历程呈现先增大后减小的趋势。根据断裂过程不同时刻, 得到相应的动态起裂韧度、扩展韧度及止裂韧度。在动态断裂全过程中, 动态扩展韧度为速度的函数, 变化趋势与速度一致, 随着时间先增大后减小; 动态起裂韧度大于动态止裂韧度, 止裂韧度随着裂纹最大扩展速度的增大而降低, 并且有较大的离散性。     

基于有限断裂法和比例边界有限元法的裂纹扩展模拟

基于有限断裂法和比例边界有限元法提出了一种裂缝开裂过程模拟的数值模型。采用基于有限断裂法的混合断裂准则作为起裂及扩展的判断标准,当最大环向应力和能量释放率同时达到其临界值时,裂缝扩展。结合多边形比例边界有限元法,可以半解析地求解裂尖区域附近的应力场和位移场,在裂尖附近无需富集即可获得高精度的解。计算能量释放率时,只需将裂尖多边形内的裂尖位置局部调整,无需改变整体网格的分布,网格重剖分的工作量降至最少。裂缝扩展步长通过混合断裂准则确定,避免了人为假设的随意性,并可以实现裂缝变步长扩展的模拟,更符合实际情况。通过对四点剪切梁的复合型裂缝扩展过程的模拟,对本文模型进行了验证,并应用于重力坝模型的裂缝扩展模拟,计算结果表明,本文提出的模型简单易行且精度较高。     

Surface initiated crack growth simulation in moving lubricated contact

The paper describes a two-dimensional computational model for simulating surface initiated crack growth in the lubricated contact area that leads to surface pitting of mechanical components. The model assumes size and orientation of the initial crack which is subjected to contact loading conditions, accounting for the elasto-hydrodynamic-lubrication effects and tangential loading due to sliding. The influence of a lubricating fluid, driven into the crack by hydraulic mechanism, is also considered. The minimum strain energy density criterion is used to analyze crack propagation with the aim of the finite element analysis. The model is applied to a real pitting problem of a gear. The results for pit sizes correlate well with those observed in experimental testing.     

Vibrations of an ice sheet with crack under a time-periodic load

The analytic solution of the problem of vibrations of an ice sheet with a rectilinear crack floating on the surface of an ideal incompressible fluid of shallow depth under the action of a local zone of the time-periodic pressure is obtained. The ice sheet is simulated by two thin viscoelastic semiinfinite plates of different thickness. Various conditions on the crack edges are considered. Far field asymptotics are investigated and it is revealed that the predominant directions of wave propagation at an angle to the crack can be distinguished in the far field in the case of contact of two plates of different thickness. In the case of contact of identical plates, a waveguide mode propagating along the crack is excited. It is shown that the waveguide mode is the same for the plates with the free edges and the free overlap since the part of the solution symmetric about the crack is the same while the difference between the solutions is caused by the antisymmetric part of the solution.     

爆炸加载下混凝土表面的裂纹扩展

为深入研究内爆加载下岩土类材料的破坏机理，提出了一种新的爆炸裂纹检测算法，采用数字图像相关方法测量表面位移场和应变场，建立了裂纹扩展和扩张模型，并通过混凝土内爆试验观测裂纹扩展过程，研究了裂纹长度扩展与宽度扩张规律。结果表明，裂纹长度扩展是应力波和爆生气体共同作用的结果，裂纹最大扩展速度为225.95 m/s，平均速度为122.27 m/s，裂纹总长159.92 mm，长度扩展止于1.75 ms；裂纹的张开由气体主导，最大宽度1.59 mm，作用时间长达4.5 ms；拉应变集中区先于裂纹出现，其形状决定了裂纹的走向和趋势，爆炸加载下断裂过程区长度为骨料粒径的8～9倍。     

Modelling of crack growth under cyclic contact loading

The paper describes a general computational model for modelling of subsurface fatigue crack growth under cyclic contact loading of mechanical elements. The model assumes that the initial fatigue crack develops along the slip line in a single crystal grain at the point of the maximum equivalent stress. The position and magnitude of the maximum equivalent stress are determined with the Finite Element Analysis of the equivalent contact model, which is based on the Hertzian contact conditions with the addition of frictional forces. The Virtual Crack Extension method is then used for simulation of the fatigue crack propagation from the initial to the critical crack length, when the surface material layer breaks away and a pit appears on the surface. The pit shapes and relationships between the stress intensity factor and the crack length are determined for various combinations of contacting surface curvatures and contact loadings. The computational results show that the model reliably simulates the subsurface fatigue crack growth under contact loading and can be used for computational predictions of surface pitting for various contacting mechanical elements.