共查询到19条相似文献,搜索用时 406 毫秒
1.
本文将条状分离区看作是位错连续分布区域,利用复变函数理论及切比雪夫多项式级数展开提出了一种统一的数学分析的方法,用以对均匀材料裂纹前方分离过程区的非线性效应进行有效的,精确的解析分析。避免以前各种模型一般都需要借助于有限元法或其他离散方法才能得到数值解答的难点。本文利用这一新方法,对断裂过程区是内聚力模型,条状屈服区模型的裂纹问题,受约束金属薄膜的裂纹问题,进行了分析计算,并与已有的结果进行了比较,得到了满意的结果。 相似文献
2.
裂纹扩展过程中线性内聚力模型计算的半解析有限元法 总被引:1,自引:0,他引:1
提出了求解基于线性内聚力模型的平面裂纹扩展问题的半解析有限元法,利用弹性平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,推导了一个环形和一个圆形奇异超级解析单元列式,组装这两个超级单元能准确地描述裂纹表面作用有双线性内聚力的平面裂纹尖端场。将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和载荷的基于线性内聚力模型的平面裂纹扩展问题。典型算例的计算结果表明本文方法简单有效,具有令人满意的精度。 相似文献
3.
4.
混凝土断裂过程区的虚拟裂纹粘聚力奇异性 总被引:4,自引:0,他引:4
混凝土断裂过程区视为具有粘聚阻力作用的虚拟裂纹,其非线性断裂和尺寸效应特性是与该虚拟裂纹粘聚力分布规律密切相关的。通过得到的粘聚应力分布函数解析结果,对该粘聚力分布特征的分析得知,在基于断裂过程区之外用线弹性场的力学模型上,该粘聚力随距离虚拟裂纹尖点的靠近,仍具有平方根奇异性。从而本文提出一个能够反映裂纹发展状态的粘聚应力奇异性强度参数,它是无粘聚力的线弹性裂纹应力强度因子和表征裂纹张开位移分布多项式参数的函数;因此,该参数可以作为混凝土非线性断裂的一个参量。文中就已有断裂试验测试结果进行了算例分析和相应的讨论。 相似文献
5.
一种建筑材料细观力学数值模拟的新方法 总被引:1,自引:0,他引:1
数值流形方法通过数学和物理双重网格,分析连续和非连续问题,已应用于模拟节理岩体裂隙的开裂与闭合问题.但对于裂纹尖端的局部化问题,数值流形方法需要像有限元那样在裂纹尖端设置细密单元.本文利用裂纹尖端解析解将数值流形方法的基函数进行扩展,推导了相应的试函数.从最小势能原理出发提出了断裂力学的数值流形方法,推导了相应的求解方程,将其应用于建筑材料细观力学数值模拟.最后给出两个数值算例,将计算结果与解析解对比,说明该方法的正确性和可行性. 相似文献
6.
内聚力模型的形状对胶接结构断裂过程的影响 总被引:1,自引:0,他引:1
内聚力模型被广泛应用于粘接结构的断裂数值模拟过程中,为深入分析不同形状内聚力模型与胶黏剂性质和粘接结构断裂之间的关系,本文分别采用脆性和延展性两种类型胶黏剂,对其粘接的对接试件进行了单轴拉伸、剪切实验,以及其粘接的双臂梁试件进行了断裂实验.3种类型的内聚力模型(抛物线型、双线型和三线型)分别模拟了以上粘接结构的断裂过程,并与实验结果进行对比.结果发现:双线型的内聚力模型适用计算脆性胶黏剂的拉伸与剪切的断裂过程;指数型内聚力模型较适合计算延展性胶黏剂的拉伸和剪切的断裂过程,临界应力、断裂能和模型的形状参数是分析拉伸和剪切的重要参数;双臂梁试件的断裂过程模拟结果发现,断裂曲线与胶黏剂性质有关,内聚力模型形状参数也有影响.通过实验与计算结果分析,双线型内聚力模型更适合脆性胶黏剂粘接的双臂梁断裂计算,而三线型更适合计算延展性胶黏剂粘接的双臂梁断裂过程,此研究结果对胶黏剂的使用和粘接结构的断裂分析有很重要意义. 相似文献
7.
扩展有限元法是基于常规有限元框架分析裂纹等不连续力学问题的一种有效数值方法,在常规的有限元位移表达式中,增加了能够反映位移不连续性的跳跃函数和渐进缝尖位移场函数来对不连续结构附近的节点自由度进行局部加强。本文介绍了扩展有限元法及粘聚力模型的基本原理,给出了基于扩展有限元法的地质聚合物混凝土断裂过程分析方法。分别采用四种不同的软化曲线对I型缺口地质聚合物混凝土梁从裂纹萌生、扩展直至断裂破坏的全过程进行了模拟,并基于双K断裂准则分析了其断裂韧性。结果表明,Petersson模型与试验结果吻合较好,最后基于模拟结果进一步揭示了断裂过程区的演化过程。 相似文献
8.
采用单边直裂纹三点弯曲梁(SC3PB)对鲁灰花岗岩I型裂纹的断裂特性进行了实验研究,得到其断裂韧度为0.9~1.4MN/m1.5。基于数字图像相关方法(DIC)分析了峰值载荷前试件断裂位移场及应变场的演化过程,根据位移场的不连续性给出过程区的扩展轨迹,由应变场得到了高应变区域的变化规律。当局部水平位移梯度发生剧烈变化时,鲁灰花岗岩I型断裂进入过程区;且以水平方向应变达到0.11%~0.20%时作为进入过程区的门槛值;并进一步给出了过程区尖端沿竖直方向的扩展速率与过程区长度呈三次多项式递增关系。 相似文献
9.
PZT-4紧凑拉伸试样的断裂分析 总被引:1,自引:1,他引:0
基于线性压电材料的复势理论,通过解析分析,导出了一种分析有限压电板裂纹问题的解析数值方法. 首先,计算了含中心裂纹有限板的断裂参数,与Woo和Wang的解析数值法(Int J Fract, 1993, 62: 203$\sim$218)相比较,表明该方法具有很高的精度和很好的计算效率. 随后,采用该方法和有限元法计算了PZT-4紧凑拉伸试样在绝缘裂纹面边界条件下断裂时的断裂参数,发现各断裂参数的临界值分散性很大,不能作为压电材料的单参数断裂准则. 进而,针对试样真实的裂隙形状,采用有限元法计算了裂隙尖端的应力、电位移场,比较了裂隙内介质的介电性能对裂隙尖端场的影响,计算了带微裂纹的真实裂隙模型的断裂参数并进行了理论分析. 相似文献
10.
11.
I.IntroductionCrazingdamageisacommonphenon1enonoffractureofpolymericmaterials.Theformationofcrazezoneisamid-stateinthefractureprocessofthematerialsfromperfectstatetofaiIurc.Microscopically,inthisregionthereexistssomefibrilslinkingthetwocracksurfacesandres… 相似文献
12.
Todd W Bjerke 《Journal of the mechanics and physics of solids》2003,51(6):1147-1170
A thermally dissipative cohesive zone model is developed for predicting the temperature increase at the tip of a crack propagating dynamically in a nominally brittle material exhibiting a cohesive-type failure such as crazing. The model assumes that fracture energy supplied to the crack tip region that is in excess of that needed for the creation of new free surfaces during crack advance is converted to heat within the cohesive zone. Bulk dissipation mechanisms, such as plasticity, are not accounted for. Several cohesive traction laws are examined, and the model is then used to make predictions of crack tip heating at various crack propagation speeds in the nominally brittle amorphous polymer PMMA, observed to fail by a crazing-type mechanism. The heating predictions are compared to experimental data where the temperature field surrounding a high speed crack in PMMA was measured. Measurements are made in real time using a multi-point high speed HgCdTe infrared radiation detector array. At the same time as temperature, simultaneous measurement of fracture energy is made by a strain gauge technique, and crack tip speed is monitored through a resistance ladder method. Material strength can be estimated through uniaxial tension tests, thus minimizing the need for parameter fitting in the stress-opening traction law. Excellent agreement between experiments and theory is found for two of the cohesive traction law temperature predictions, but only for the case where a single craze is active during the dynamic fracture of PMMA, i.e. crack tip speed up to approximately 0.2cR. For higher speed fracture where subsurface damage becomes prominent, the line dissipation model of a cohesive zone is inadequate, and a distributed damage model is needed. 相似文献
13.
14.
Analytical representation of the non-square-root singular stress field at a finite angle sharp notch
《International Journal of Solids and Structures》2014,51(25-26):4485-4491
The stress field near the tip of a finite angle sharp notch is singular. However, unlike a crack, the order of the singularity at the notch tip is less than one-half. Under tensile loading, such a singularity is characterized by a generalized stress intensity factor which is analogous to the mode I stress intensity factor used in fracture mechanics, but which has order less than one-half. By using a cohesive zone model for a notional crack emanating from the notch tip, we relate the critical value of the generalized stress intensity factor to the fracture toughness. The results show that this relation depends not only on the notch angle, but also on the maximum stress of the cohesive zone model. As expected the dependence on that maximum stress vanishes as the notch angle approaches zero. The results of this analysis compare very well with a numerical (finite element) analysis in the literature. For mixed-mode loading the limits of applicability of using a mode I failure criterion are explored. 相似文献
15.
Georgios C. Georgiou Lorraine G. Olson William W. Schultz Susan Sagan 《国际流体数值方法杂志》1989,9(11):1353-1367
Abrupt changes in boundary conditions in viscous flow problems give rise to stress singularities. Ordinary finite element methods account effectively for the global solution but perform poorly near the singularity. In this paper we develop singular finite elements, similar in principle to the crack tip elements used in fracture mechanics, to improve the solution accuracy in the vicinity of the singular point and to speed up the rate of convergence. These special elements surround the singular point, and the corresponding field shape functions embody the form of the singularity. Because the pressure is singular, there is no pressure node at the singular point. The method performs well when applied to the stick–slip problem and gives more accurate results than those from refined ordinary finite element meshes. 相似文献
16.
《International Journal of Solids and Structures》2006,43(5):1047-1060
A mode III crack with a cohesive zone in a power-law hardening material is studied under small scale yielding conditions. The cohesive law follows a softening path with the peak traction at the start of separation process. The stress and strain fields in the plastic zone, and the cohesive traction and separation displacement in the cohesive zone are obtained. The results show that for a modest hardening material (with a hardening exponent N = 0.3), the stress distribution in a large portion of the plastic zone is significantly altered with the introduction of the cohesive zone if the peak cohesive traction is less than two times yield stress, which implies the disparity in terms of the fracture prediction between the classical approach of elastic–plastic fracture mechanics and the cohesive zone approach. The stress distributions with and without the cohesive zone converge when the peak cohesive traction becomes infinitely large. A qualitative study on the equivalency between the cohesive zone approach and the classical linear elastic fracture mechanics indicates that smaller cracks require a higher peak cohesive traction than that for longer cracks if similar fracture initiations are to be predicted by the two approaches. 相似文献
17.
《International Journal of Solids and Structures》2003,40(15):3853-3868
A comparative analysis of intrinsic and extrinsic cohesive models has been performed for the case of spontaneous and steady-state dynamic crack propagation. Spontaneous crack propagation was simulated using a spectral form of the elastodynamic boundary integral equation, while steady-state solutions were obtained by numerically integrating the governing Cauchy singular integral equation. Spontaneous crack propagation results showed that intrinsic models are less numerically stable than the extrinsic ones. Under steady-state propagation conditions, some intrinsic cohesive models lead to unrealistic results as the crack opening velocity becomes negative at the cohesive zone tip. By imposing a positive crack opening acceleration at the cohesive zone tip, the envelope of the required minimum initial strength has been calculated. 相似文献
18.
19.
数学网格和物理网格分离的有限单元法(II):粘聚裂纹扩展问题中的应用 总被引:3,自引:3,他引:0
强化有限单元法将物理网格与数学网格分离开来,可以方便地描述非连续变形;粘聚区域模型是模拟断裂过程区作用最简单有效的方法,且可以避免裂纹尖端的应力奇异性.本文以平面问题为例,将强化有限单元法与粘聚区域模型相结合,利用富集数学节点描述任意粘聚裂纹扩展过程中的非连续变形问题,提出了裂纹扩展过程中数学节点富集和数学单元定义的方法.本文还导出了与平面4~8节点平面等参单元对应的8~16节点粘聚裂纹单元列武.最后,通过三点弯梁的裂纹扩展过程模拟验证了本文提出的粘聚裂纹扩展模拟方法的有效性. 相似文献