Limiting velocity of crack propagation in dynamically fractured materials

A model of a fractal crack is considered. It is found that the limiting velocity of crack propagation is determined by the fractal dimension of the crack contour. It is shown that for commercial steels, the limiting crack velocity is in the range V _lim = (0.155–0.537)c ₁ (c ₁ is the speed of sound).     

Stress-strain field near crack tip and calculation of critical stress of crack propagation in a pure bending beam of rectangular section with one-sided mode i crack

This paper studies the stress-strain field near crack tip in a pure bending beam of rectangular section with one-sided mode I crack by the analytic method of Ref. [1], then it gives the stress and strain components at the crack tip when the crack propagates and further it obtains the formulas of calculating the elastic deformed area width, the deformed intensity area width and the equation groups of calculating the critical stress of crack propagation, last the equation group of calculating critical stress of crack propagation is verified by calculating instance. The maximum error is 0.18%. First Received May 7, 1994.     

动载荷作用下裂隙岩体的止裂机理分析

为深层次了解裂隙岩体在动载荷作用下的动态断裂特性及止裂机理,采用TWSRC（tunnel with single radial crack）构型进行中低速冲击实验,选择砂岩作为原材料制作裂隙岩体试样,以落锤冲击试验装置与裂纹扩展计实验系统对裂纹的动态起裂、扩展及止裂过程进行全过程监测,重点研究动态破裂过程的破裂行为及止裂现象。使用有限差分法程序进行数值模拟,验证冲击实验结果的科学性与准确性。研究发现:裂隙岩体的动态断裂过程是由起裂加速-高速扩展-缓慢减速-止裂-再次起裂加速-再次高速扩展等多次循环的过程构成,且止裂区间尺寸为微秒量级;裂隙岩体止裂位置的穿晶断裂比例远小于初始起裂点,青砂岩动态断裂过程的穿晶断裂比例稍大于黑砂岩;裂隙岩体中止裂点再次起裂所需的能量,远小于预制裂纹初始起裂所需要的能量。     

非均匀弹性材料中反平面的运动裂纹

用解析方法研究了非均匀弹性材料中反平面运动裂纹问题。首先采用余弦变换求解非均匀材料的基本方程，然后根据混合边值条件建立裂纹运动的对偶积分方程，再把对偶积分方程化为第二类Fredholm积分方程。给出了数值算例，计算结果表明材料的非均匀性对动应力强度因子有较大的影响。     

Boundary element analysis of interaction between an elastic rectangular inclusion and a crack

The interaction between an elastic rectangular inclusion and a kinked crack inan infinite elastic body was considered by using boundary element method. The new complexboundary integral equations were derived. By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically. Only one complex boundaryintegral equation was obtained on interface and involves only singularity of order l/ r. Toverify the validity and effectiveness of the present boundary element method, some typicalexamples were calculated. The obtained results show that the crack stress intensity factorsdecrease as the shear modulus of inclusion increases. Thus, the crack propagation is easiernear a softer inclusion and the harder inclusion is helpful for crack arrest.     

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

Investigation on 3D fatigue crack propagation in surface-cracked specimens

In the present work the fatigue crack growth in AISI304 specimens is investigated experimentally. In 3D finite element analysis the virtual crack closure technique is applied to calculate distributions and variations of the stress intensity factor along the surface crack front. It is confirmed that the stress intensity factor along the surface crack front varies non-uniformly with crack growth. Crack growth rate is proportional to the stress intensity factor distribution in the 3D cracked specimen. The fatigue crack growth in surface cracked specimens can be described by the Forman model identified in conventional compact tension specimens. For crack growth in the free specimen surface the arc length seems more suitable to quantify crack progress. Geometry and loading configuration of the surface cracked specimen seem to not affect the fatigue crack growth substantially.     

考虑闭合效应和三维应力约束的表面裂纹扩展模拟

假定承受Ⅰ型常幅载荷下的表面裂纹在扩展中的形状保持为半椭圆,利用Newman半椭圆表面裂纹应力强度因子公式计算应力强度因子。提出了等效厚度的概念,利用穿透直裂纹的研究结果,考虑表面裂纹扩展中塑性致闭和三维应力约束效应。基于Elber模型建立了三维表面裂纹扩展模型。数值模拟了表面裂纹扩展过程,研究了裂纹形状变化及规律,计算了裂纹扩展寿命。将计算结果与有关试验结果进行了对比,吻合较好。     

Some possible alternative solutions of near-tip fields for steady crack growth in elastic perfectly-plastic media

Some possible alternative solutions of near-tip fields are studied for plane-strain Mode—I quasi-static steady crack growth in incompressible (ν=1/2) elastic perfectly-plastic media. A group of four-sector solutions and a three-sector solution in which the elastic-unloading region vanishes are given. Stress functions, plastic flow factors and plastic strains in each region are also given. Project supported by the State Education Commission under a funding program for Excellent University Young Faculties and National Natural Science Foundation of China.     

Unsteady problem of crack propagation in the beam approximation

Unsteady crack propagation is studied in the beam approximation. The Euler and Timoshenko models of beam theory are used. Crack propagation is described using an energy balance equation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 177–189, September–October, 2008.     

Effects of characteristic material lengths on mode III crack propagation in couple stress elastic–plastic materials

The asymptotic fields near the tip of a crack steadily propagating in a ductile material under Mode III loading conditions are investigated by adopting an incremental version of the indeterminate theory of couple stress plasticity displaying linear and isotropic strain hardening. The adopted constitutive model is able to account for the microstructure of the material by incorporating two distinct material characteristic lengths. It can also capture the strong size effects arising at small scales, which results from the underlying microstructures. According to the asymptotic crack tip fields for a stationary crack provided by the indeterminate theory of couple stress elasticity, the effects of microstructure mainly consist in a switch in the sign of tractions and displacement and in a substantial increase in the singularity of tractions ahead of the crack-tip, with respect to the classical solution of LEFM and EPFM. The increase in the stress singularity also occurs for small values of the strain hardening coefficient and is essentially due to the skew-symmetric stress field, since the symmetric stress field turns out to be non-singular. Moreover, the obtained results show that the ratio η introduced by Koiter has a limited effect on the strength of the stress singularity. However, it displays a strong influence on the angular distribution of the asymptotic crack tip fields.     

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

ＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＮＥＡＲＣＲＡＣＫＬＩＮＥＦＩＥＬＤＳＦＯＲＭＯＤＥＩＣＲＡＣＫＵＮＤＥＲＰＬＡＮＥＳＴＲＥＳＳＣＯＮＤＩＴＩＯＮＩＮＡＮＥＬＡＳＴＩＣ－ＰＥＲＦＥＣＴＬＹＰＬＡＳＴＩＣＳＯＬＩＤＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＮＥＡ...     

爆炸聚能作用下混凝土试件劈裂的高速3D DIC实验

为探寻非钻孔条件下露天爆破大块二次破碎形态的控制方法, 应用线性聚能射流对圆柱混凝土模型试件进行侵彻实验, 使用High-speed 3D DIC(高速三维数字图像相关方法)方法分析试件劈裂发展过程的全场三维形变特征。研究结果表明, 数据分析区内劈裂裂纹扩展速度在4个区间内呈阶梯式变化趋势, 峰值速度为235.52 m/s, 平均速度为140.89 m/s;线性聚能射流侵彻对劈裂裂纹扩展有明显导向作用, 应力集中作用使得劈裂裂纹围绕线性射流侵彻对称轴扩展, 扩展方向变化幅度较小;在劈裂裂纹扩展速度突变的3个时刻, 劈裂裂纹路径产生了3处明显拐点, 在拐点处伴随有支裂纹的产生, 支裂纹的扩展距离均未超过5 cm;主应变集中带形状及分布位置决定了裂纹扩展路径及趋势, 拉应变集中先于裂纹出现, 试件呈现准静态劈裂形态, 劈裂面平整度较高。     

Torsion of an elastic space with a semi-infinite conical crack

The axisymmetric problem of stress concentration near a conical crack in an infinite elastic space with a rotation center is addressed. The problem is reduced to an integro-differential equation. Its exact solution is obtained. An expression for the stress intensity factor in crack neighborhood is derived and numerically analyzed for different positions of the rotation center and the crack opening angles __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 99–107, February 2007. For the centenary of the birth of G. N. Savin.     

修正的拉应力裂纹扩展准则及裂隙\=水压对裂纹扩展的影响

对脆性材料的第一主应力--拉应力裂纹扩展准则进行了补充和修正,修正的裂纹扩展准则能确定裂纹扩展步长.以平面斜置裂纹扩展为例,利用无网格Galerkin方法,对不含裂隙水压的二维裂纹扩展进行数值模拟,计算结果与试验结果一致,表明最大周向拉应力准则的正确性.在不同裂隙水压条件下,研究了二维裂纹初始破裂,并在给定水压下对二维裂纹扩展路径进行了数值模拟跟踪.结果表明裂隙水压对裂纹初始破裂方向、破裂步长、破裂载荷和裂隙岩体破裂强度有显著影响.有水压和无水压的扩展迹线不同,但后续的扩展趋势相同.     

Stress field near interface crack tip of double dissimilar orthotropic composite materials

In this paper, double dissimilar orthotropic composite materials interfacial crack is studied by constructing new stress functions and employing the method of composite material complex. When the characteristic equations＇ discriminants △1 〉 0 and △2 〉0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and interembedding between the interfaces of the crack.     

Ⅰ型裂纹对薄壁偏心柱弹性挠度的影响

本文重点研究了裂纹对薄壁截面偏心受压柱弹性挠度的影响,分析模型假设偏心柱两墙铰支;截面绕强轴发生单向弯曲变形：I型裂纹位于受力最为严重的中间截面的受拉翼缘上,首先简单介绍了Rayleigh-Ritz变分法求得的弹性挠度三角函数级数解,该解的优点是可以在裂纹截面满足变形协调条件,适应于裂纹在薄壁截面上的沿弯矩面外方向扩展的情况,然后针对工字形,箱形两种双轴对称薄壁截面柱,具体地分析了在不同荷载,偏心距和长细比条件下裂纹长度对偏心柱挠度的影响规律和范围,理论分析和数值结果表明,在其它条件不变的情况下,柱的长细比越小或偏心距越大,裂纹引起的挠度增量越明显。,     

Scattering of harmonic elastic waves by a plane interface crack with linear adhesive tips in a layered half space

In this paper, the scattering of elastic waves by an interface crack with linear adhesive tips in a layered half space is considered. By use of integral transform and integral equation methods, the singular integral equations of this problem are derived, which are transformed into a set of algebraic equations by means of contour integration and Chebyshev polynomials expanding technique. The numerical results of the adhesive region and stress amplitudes are given in this paper.     

压应力场中爆生裂纹分布与扩展特征实验分析

采用动静组合加载实验装置和数字激光焦散线实验系统,进行了0、3、6、9 MPa等4种压应力场中PMMA试件的爆破致裂实验,分析了沿静态主应力方向扩展的裂纹运动学和力学行为。实验结果表明:首先,静态竖向载荷在预制炮孔周围产生应力集中,在炮孔壁上下端部处出现最大拉应力;随后,在动态爆炸载荷的叠加作用下,裂纹优先在炮孔壁上最大拉应力位置处起裂,并沿最大主应力方向扩展;裂纹扩展过程中,静态竖向载荷越大,裂纹扩展速度越大,且裂纹尖端应力强度因子值越大。