The initiation of slow crack growth in linear polyethylene under single edge notch tension and plane strain

The kinetics and microstructural changes associated with the initiation of slow crack growth in PE were measured. The initiation process consists of an instantaneous deformation zone which grows at a constant velocity until the beginning of fracture. The velocity of the damaged zone accelerates when the fibril fracture begins at the root of the initial notch. It was found that the initial velocity of the deformation zone depended on stress to about the 4th power and had an activation energy of about 100 kJ mol^–1; these results are about the same as those found by Chan and Williams for the crack growth velocity. It is concluded that both crack initiation and crack growth are governed by the same fundamental process, notably fibril thinning.     

Maximum Average Tangential Stress Criterion for Prediction of the Crack Path

The concept of the average stress has been employed to propose the maximum average tangential stress (MATS) criterion for predicting the direction of fracture angle. This criterion states that a crack grows when the maximum average tangential stress in the fracture process zone ahead of the crack tip reaches its critical value and the crack growth direction coincides with the direction of the maximum average tangential stress along a constant radius around the crack tip. The tangential stress is described by the singular and non-singular (T-stress) terms in the Williams series solution. The predicted directions of fracture angle are consistent with the experimental data for the mixed mode I/II crack growth behavior of Guiting limestone.     

Influence of the constraint effect on the fatigue crack growth rate in S355 J2 steel using digital image correlation

Displacement fields around the fatigue crack tip for a constant value of stress intensity factor (SIF) range were measured using digital image correlation (DIC) technique on the S355 J2 steel grade. The data obtained were resolved into the T‐stress evaluation and quantification of its influence on the fatigue crack growth rate. The higher order terms of the Williams expansion (WE) were calculated as well. The displacements of a set of points outside of the plastic zone were selected for application of the over‐deterministic method (ODM) to obtain several initial WE terms. The computed values of T‐stress show good agreement with finite element analysis and literature. It was shown by collected experimental displacement, that the level of constraint influences the fatigue crack propagation rate.     

Asymptotic fields at the tip of a cohesive crack

Recently, the authors (Xiao and Karihaloo, J Mech Mater Struct 1:881–910, 2006) obtained universal asymptotic expansions at a cohesive crack tip, analogous to the Williams (ASME J Appl Mech 24:109–114, 1957) expansions at a traction-free crack tip for any normal cohesion-separation law (i.e. softening law) that can be expressed in a special polynomial. This special form ensures that the radial and angular variations of the asymptotic fields are separable as in the Williams expansions. The coefficients of the expansions of course depend nonlinearly on the softening law and the boundary conditions. They demonstrated that many commonly-used cohesion-separation laws, e.g., rectangular, linear, bilinear and exponential, can indeed be expressed very accurately in this special form. They also obtained universal asymptotic expansions when the cohesive crack faces are subjected to Coulomb friction. The special polynomial involves fractional powers which seem rather contrived. In this paper, we will show that the asymptotic expansions can be obtained in a separable form even when the cohesion-separation law is in a special polynomial form involving only integer powers.     

Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method

Coefficients of the Williams expansion of the linear elastic crack tip asymptotic field can only be evaluated analytically for a few simple cases. Numerical solution is necessary in the general case, and the presence of the singular term presents numerical difficulties. The scaled boundary finite element method is a new semi-analytical approach to computational mechanics developed by Wolf and Song. This paper shows that when the scaling centre is located at the crack tip, the scaled boundary finite element solution converges to the Williams expansion. Consequently the coefficients of the Williams expansion, including the stress intensity factor and the T-stress, can be determined directly without further processing. The technique is applied to several problems for which coefficients of the Williams expansion are available, and close agreement with existing results is obtained with very few degrees of freedom.     

Experimental investigations on the damage of Portland cement concrete made with natural aggregates

As part of research on the fracture behaviour of concrete, a series of tests on large (3.00 m×3.50 m×0.12 m) concrete slabs has been performed. The crack propagated under the action of a load applied to a crack notch placed in the centre of the largest side. The dimensions of the damaged zone in the neighbourhood of the crack tip have been determined using three different techniques: strain rosettes, acoustic emission and sonic testing. Computations based on the crack length must take account of this damaged zone. The tests have shown that this zone is approximately 10 cm long and about 10 mm wide, which corresponds to the maximum size of the aggregates.     

Direct evaluation of stress intensity factors for curved cracks using Irwin's integral and XFEM with high‐order enrichment functions

This paper presents a comprehensive study on the use of Irwin's crack closure integral for direct evaluation of mixed‐mode stress intensity factors (SIFs) in curved crack problems, within the extended finite element method. The approach employs high‐order enrichment functions derived from the standard Williams asymptotic solution, and SIFs are computed in closed form without any special post‐processing requirements. Linear triangular elements are used to discretize the domain, and the crack curvature within an element is represented explicitly. An improved quadrature scheme using high‐order isoparametric mapping together with a generalized Duffy transformation is proposed to integrate singular fields in tip elements with curved cracks. Furthermore, because the Williams asymptotic solution is derived for straight cracks, an appropriate definition of the angle in the enrichment functions is presented and discussed. This contribution is an important extension of our previous work on straight cracks and illustrates the applicability of the SIF extraction method to curved cracks. The performance of the method is studied on several circular and parabolic arc crack benchmark examples. With two layers of elements enriched in the vicinity of the crack tip, striking accuracy, even on relatively coarse meshes, is obtained, and the method converges to the reference SIFs for the circular arc crack problem with mesh refinement. Furthermore, while the popular interaction integral (a variant of the J‐integral method) requires special auxiliary fields for curved cracks and also needs cracks to be sufficiently apart from each other in multicracks systems, the proposed approach shows none of those limitations. Copyright © 2017 John Wiley & Sons, Ltd.     

Stretchable,strong and self-healing hydrogel by oxidized CNT-polymer composite

Acrylamide hydrogel made from poly-acryloyl-6-amino caproic acid (PAACA) was reinforced with functional carbon nanotubes which strengthen composite four times more compare to PAACA, pure hydrogel. Oscillatory rheological experiments improved the special strength and reversible behavior of composite. Structure features and internal cross linking density of the composite were observed by allowing swelling and deswelling of composite in different pH solutions. The crack damaged composite was first self-healed autonomically with in a period of less than 3 min to a same strength observed by mechanical tensile testing. Later pH solution was introduced into crack damaged zone which re-healed the crack in a period of 1 min and strengthen the composite 15% (an average) more than that which re-healed without pH solution. This enhanced reinforcement performance and healing of composite hydrogel with pH solution refers to strong hydrogen bonding of the terminal groups across the interface and hydrophobic, hydrophilic interactions.     

Compression induced shear damage in brittle solids by scattered microcracking

Failure observation and numerical analysis were conducted to understand how shear damage develops in brittle solids under biaxial compression. A biaxial compression often induces shear damaged in brittle solids, which is preceded by a formation of huge number of array cracks. Cracks in the array appeared gradually as applied compression increased. They were almost similar in shape; gently curved but were possible to approximate a troop of straight cracks almost parallel to each other without loss of essential characteristics. Under a uniaxial compression, a brittle material tends to fail exhibiting a crack growth almost parallel to the loading axis. In this situation, the crack propagates rather in a stable fashion since the stress intensity factor at crack tip generally decreases with crack extension. Under a biaxial compression, however, such a stable crack growth is strongly inhibited. Consequently, an array of microcracks often appears as a presage of the macroscopic shear failure. A mechanism of the appearance of damaged zone with increase of applied compression was discussed using a scattered cracking model. It was found that each crack composing the damaged zone has a possibility to open due to crack-to-crack interaction and a localized tensile stress appeared both in the interior and in the exterior of the damaged zone. The localized tension appeared in the interior of the damaged zone may increase a crack density, while that appeared in the exterior of the damaged zone would bring an enlargement of the damaged zone.     

The configuration of moving crack tip zones

The dynamic elasticity solution of a steady state crack is used for determination of the geometrical characteristics and of the displacement rates within the discrete crack zones which are formed as a result of the selective propagation of cleavage microcracks ahead of the tip of a running brittle crack in a mild steel plate. The zone length and the stress distribution in the zone are found to be strongly dependent on the assumed form of the stress-displacement relation for the progressively fracturing metal. On the other hand, the crack opening displacement rate is much less sensitive to the assumed form. The magnitudes of the nominal plastic strain rates, found by an approximate procedure, are of the order of 10⁵ to 10⁶ sec^?1. A comparison with the results of dynamic tension tests on similar steels indicates that the flow stress at these strain rates would exceed the twinning stress, and therefore, it is suggested in agreement with experimental observations, that twinning is the principal deformation mode in the crack zone. Accordingly, the crack tip boundary conditions considered in the solution of crack propagation problems can be assumed as independent of crack velocity. Also, their possible dependence on temperature would not be related to the deformation mode in the crack zone.     

The influence of higher order terms of Williams series on a more accurate description of stress fields around the crack tip

In this work, the crack tip stress field is investigated in two different configurations loaded in mode I as well as in mode I + II. The detailed two‐dimensional solution includes a conventional finite elements analysis that is compared to results obtained analytically from what is referred to as Williams expansion. The influence of consideration of various numbers of terms of the series expansion on the stress distribution is discussed, and the significance of the multi‐parameter fracture mechanics approach is emphasized for some engineering applications, for example, failure of quasi‐brittle materials and estimation of plastic zone extent.     

Prediction of the service life of pipeline elements subjected to the action of hydrogen-containing media

We study the process of crack propagation in a preliminarily hydrogenated pipe placed in a hydrogen-containing medium. The crack growth rate is mainly controlled by the mass transport of hydrogen into the prefracture zone. We obtain an approximate solution of the problem of diffusion of hydrogen in the vicinity of the crack tip and establish the dependence of the crack growth rate on the crack tip opening displacement. This dependence is used for the determination of the residual service life of damaged elements of the pipe. The pipe is made of 4147 steel and the defect is modeled by a semielliptic longitudinal crack on the internal surface of the pipe. We show that the initial concentration of hydrogen may significantly accelerate the fracture process. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 4, pp. 43–48, July–August, 1999.     

Influence of deformation anisotropy on the size of the plastic zone at the tip of an opening mode crack

The form and dimensions of the plastic zone at the tip of an opening mode crack in a plate made of a material with deformation anisotropy were investigated within the limits of the elastic solution. The anisotropy was caused by strengthening during plastic deformation until formation of cracks by loading in a straight trajectory located in the plane of the plate. It was shown that in the case of anisotropy caused by loading in a trajectory which is oriented on a normal to the crack edges the size of the plastic zone decreases and its boundaries are rotated in the direction opposite to the crack growth. Loading in a trajectory in the direction of crack growth leads to broadening of the plastic zone in the transverse direction.Translated from Problemy Prochnosti, No. 1, pp. 73–76, January, 1990.     

半刚性基层沥青路面反射裂缝扩展过程分析的Williams单元

该文对半刚性基层沥青路面结构采用弹性层状体系平面应变分析模型,利用改进的Williams级数,结合广义参数有限元法和常规等参元,建立了反射裂缝裂尖应力强度因子分析的广义参数Williams单元,并推导了Williams单元的刚度方程,据此研究了正对称荷载和偏载分别作用时,反射裂缝扩展过程中应力强度因子的变化规律;重点分析了偏载作用下路面结构层参数与应力强度因子之间的关系。Williams单元中含有与应力强度因子相关的参数,可以直接获得裂尖应力强度因子。算例分析表明:Williams单元与传统方法的计算结果吻合较好,且格式简单,计算精度高,适用于沥青路面反射裂缝扩展过程分析。     

Effect of Hydrogen on Plastic Deformation near Crack-tipof A537 Steel in 3.5%NaCl Solution

A computerized digital speckle-intederometry system was set up to study in-situ the influence of cathodic hydrogen charging on the crack opening displacement and on the plastic strain distribution at corrosion fatigue crack tip for the singIe-edge notched plate specimens of structural steel in 3.5%NaCl solution with an applied potential of -1400 mV (SCE). Meanwhile, the mono-directional tension tests with smooth specimens were pedermed in both air and 3.5%NaCl solution under the hydrogen charging conditions. The fracture sudece morphology from corrosion fatigue and tension was examined by SEM. The experimental results show that the existence of hydrogen in crack tip material caused an increase of both yield strength and hardening exponent and a decrease of plastic zone size at the corrosion fatigue crack tip.     

骨料级配对二维模型混凝土单轴抗拉强度影响的理论研究

混凝土尺寸效应及其宏观力学非线性根源于其材料细观组成的非均质性。结合混凝土细观结构形式,将混凝土看作由骨料颗粒、砂浆基质及界面过渡区组成的复合材料。采用双线性弹性损伤模型来描述砂浆基质及界面过渡区的力学行为,假定骨料颗粒为弹性体而不发生破坏,进而推导并获得了单轴拉伸条件下不同骨料颗粒级配混凝土断裂裂缝扩展路径长度及其抗拉强度的理论解。最后,对比了建立的理论公式结果与细观尺度数值模拟结果,验证了构建的关于裂缝长度及抗拉强度理论解的准确性和合理性。     

Analysis of a rate-dependent cohesive model for dynamic crack propagation

The effect of including rate-dependence in the cohesive zone modeling of steady-state and transient dynamic crack propagation is analyzed. Spontaneous crack propagation simulations are performed using a spectral form of the elastodynamic boundary integral equations, while the solution to the steady-state problem is obtained by solving the governing Cauchy singular equation on the crack plane. The steady-state analysis shows that the existing techniques for solving the Cauchy singular integral equation are not suitable. A solution technique for the underlying Riemann-Hilbert problem for the chosen rate and damage-dependent cohesive law is presented. Under spontaneous propagation conditions, quasi-steady-state speeds slower than the theoretically predicted shear wave speed are possible. Results also show that, due to the dissipation of energy inside the cohesive zone, the energy required for crack propagation increases with the crack speed.     

疲劳裂纹在奥氏体/铁素体异种钢焊接接头中的扩展行为

采用三点弯曲试样研究了疲劳裂纹在奥氏体/铁素体异种钢焊接接头中的扩展行为与显微组织的关系,测得疲劳裂纹在Cr25Ni13/13CrMo44异种钢焊接接头中的扩展速率da/dN,并且讨论了疲劳裂纹扩展与显微组织之间的关系。实验结果表明,疲劳裂纹在异种钢焊接接头熔合区中扩展的路径,是接头中韧性最低的热影响区过热区,裂纹在铁素体材料侧,跟随熔合线并平行于熔合线5～25μm扩展,而马氏体层对疲劳裂纹有较大的抗力,疲劳裂纹的扩展路径主要受组织韧性的控制。疲劳裂纹在Cr25Ni13/13CrMo44异种钢接头的扩展速率为：da/dN=7.07×10-13(△K)3.863。