T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms

A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a “generalized isoparametric formulation” and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions.     

Effect of residual stresses on interface crack growth by void expansion mechanism

Crack growth along an interface between two adjacent elastic–plastic materials in a layered solid is analysed, using special interface elements to represent the fracture process ahead of the crack-tip. These interface elements account for ductile failure by the nucleation and growth of voids to coalescence. In these elements the stress components normal to the interface and the shear stresses are given by equilibrium with the surrounding material, and the stress component tangential to the interface is determined by the requirement of compatibility with the surrounding material in the tangential direction. It is assumed that the layers are sufficiently thick, so that the plastic regions around the crack-tip are much smaller than the thickness of the nearest layers. The analyses focus on the effect of initial residual stresses in the layered material, or on T-stress components induced during loading. The results show that the value of the T-stress component in the softer material adjacent to the interface crack plays the dominant role, such that a negative value of this stress component gives a significant increase of the interface fracture toughness.     

T应力对脆性材料初始裂纹起裂角影响研究

为检验和提高MTS准则对线弹性材料复合型裂纹扩展预测的精确性,考虑了T应力在脆性断裂中的作用,建立了广义MTS准则。该准则描述了变量Ⅰ型和Ⅱ型断裂应力强度因子、断裂韧性KⅠ和KⅡ、平行裂纹的应力分量T应力以及临界裂纹扩展区半径对裂纹扩展的影响,对裂纹尖端应力分布的描述更加精确。研究结果表明：考虑T应力后,初始起裂角随裂纹倾角增大呈现先增大后减小的趋势;相比于GMTS准则预测结果,在β>45°时MTS准则预测起裂角偏大,且起裂角对T应力变化更加敏感;而在β>45°时预测结果受T应力变化影响均偏小;对于复合型裂纹,由GMTS准则计算得到的断裂角与传统MTS计算得到的结果区别很大。脆性材料裂纹扩展受到裂纹尖端奇异应力K及常数项T应力的共同控制,通过考虑裂纹尖端Williams级数解高阶项的影响提高了对裂尖应力分布的描述精度。     

On the dependence of the Weibull exponent on geometry and loading conditions and its implications on the fracture toughness probability curve using a local approach criterion

In a previous paper the authors assessed the probability of failure of a three point bend specimen, SE(B), using a local approach criterion. In that paper the Weibull exponent, m, was derived from tests performed on round notch bars in traction, RNB(T), following the procedure suggested by Mudry. In the present study, it is addressed the issue of the dependence of the Weibull exponent m on geometry and loading conditions. It is shown that the amplitude and shape of the notch tip stress field and, in particular, the triaxiality characterising the stress state determines the value of the exponent m. Tests performed on RNB(T) specimens of carbon steel 22NiMoCr37, type A 508 Cl 3, at temperatures ranging from –18 °C to –196 °C actually indicate that m varies from 6 to 40, depending on the notch depth and root radius while for specimens carrying sharp cracks its value drops down to 4. This last result seems to be consistent with the Wallin hypothesis of a theoretical value equal to 4 for fracture mechanics specimens with high constraint, such as C(T) or SE(B), with positive values of the Q-stress or T-stress and triaxiality factor, TF, approaching 2.5. Temperature, in as long as it does not modify the stress state from plane strain to plane stress and the TF, has no effect on the value of m which is independent of the material as well.     

T-stress and its implications for crack growth

Some of the “irregular” crack growth behaviour observed in different specimen geometries may not be unrelated. Discrepancies in fatigue crack growth rate have been observed in different specimen geometries of the same material; crack front “tunnelling” and out-of-plane crack growth have been found in mode I tension at elevated temperature. The results presented in this paper seem to indicate the relevance of a crack tip constraint parameter, the elastic T-stress, to the irregular crack growth behaviour that conventional LEFM fails to explain.     

Determination of weight functions for elastic T-stress from reference T-stress solutions

ABSTRACT This paper presents the application of the weight function method for the calculation of elastic T -stress. First, the background of the weight function method for the calculation of T -stress is summarized. Then an analysis of known weight functions for T -stress revealed that it is possible to approximate them with one universal mathematical form with three unknown parameters with high accuracy. The existence of this weight function form significantly simplified the determination of weight functions for T -stress. For any particular crack geometry, the unknown parameters can be determined from reference T -stress solutions. The general weight function expression, with suitable reference T -stress solutions, was used to derive the weight functions for single edge cracked plate, double edge cracked plate and center cracked plate specimens. These weight functions were then further used to calculate the T -stress solutions for cracked specimens under several nonlinear stress fields and were compared to available numerical data.     

T-Stress of an Interface Macrocrack Induced by Near Tip Subinterface Microcracks

Determination of the T-stress of an interface macrocrack induced by near tip subinterface microcracks is performed. Based on the general solution of the macro-microcrack interaction, the induced T-stress can be evaluated by using the principle of superposition. Numerical examples of an interface macrocrack interacting with a single near tip subinterface microcrack are considered and the results are shown graphically. The induced T-stress is shown to be significantly dependent on the location and orientation of the near tip microcrack. The induced T-stresses of the upper crack face (Δ T+) and the lower crack face (Δ T-) are different. The difference disappears only when the microcrack is located and oriented definitely, for which both Δ T+ and Δ T- become zero. Δ T+ and Δ T- have the same sign, i.e., simultaneously positive or negative. The positive or negative value is dependent on the location and orientation of the microcrack. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computation of stress intensity factors (KI, KII) and T-stress for cracks reinforced by composite patching

To increase the operational life of defected structures, a repairing method using composite patches has been used to reinforce cracked components. Due to various advantages of composite materials, this method has received much attention from researchers and engineers. Considerable investigations have been performed to highlight the effect of bonded composite patches on the fracture parameters such as stress intensity factors (SIF) and J-integral. However the effect of composite patches on the T-stress, the constant stress term acting parallel to the crack, has not been investigated in the past. In this paper, the finite element method is carried out to analyze the effect of bonded composite patches for repairing cracks in pure mode I and also mixed mode I/II conditions, by computing the stress intensity factors and the T-stress, as functions of the crack length, the crack inclination angle and the type of composite material. In pure mode I condition, the finite element analysis is carried out for three different specimens: centre crack, double edge crack and single edge crack specimens. For mixed mode I/II condition the analysis is conducted on an inclined central crack of various slant angles. For both pure mode I and mixed mode I/II, the numerical results show that composite patching has considerable effect on the T-stress.     

含裂纹损伤结构强度的多源数据融合方法研究

工程结构在制造工艺过程中或使用期间会产生裂纹,对结构断裂路径的预测和研究是防治工程安全问题发生的重要手段。在考虑裂纹尖端应力场常数项T应力的基础上对传统的最大周向应力准则(Maximum tangential stress criterion, MTS)和最小应变能密度因子准则(Minimum strain energy density criterion, SED)进行修正,采用Python语言对ABAQUS的前、后处理和有限元计算模块进行二次开发,通过计算最优解的粒子群算法(Particle swarm optimization, PSO)将修正后的准则编入裂纹自动扩展程序脚本中。利用上述二次开发程序对初始纯I型裂纹的扩展路径进行模拟,结果表明：采用ABAQUS脚本程序模拟结果与相关文献实验结果吻合,表明了程序的有效性,进而实现考虑T应力的多种断裂准则对裂纹扩展路径的预测;当T应力值处于一定范围内时,修正的MTS准则无法预测裂纹发生的偏转现象,扩展路径呈直线,此时可采用修正的SED准则进行预测。

     

Crack-tip fields in anisotropic shells

Asymptotic crack-tip fields including the effect of transverse shear deformation in an anisotropic shell are presented. The material anisotropy is defined here as a monoclinic material with a plane symmetry at x ₃=0. In general, the shell geometry near the local crack tip region can be considered as a shallow shell. Based on Reissner shallow shell theory, an asymptotic analysis is conducted in this local area. It can be verified that, up to the second order of the crack tip fields in anisotropic shells, the governing equations for bending, transverse shear and membrane deformation are mutually uncoupled. The forms of the solution for the first two terms are identical to those given by respectively the plane stress deformation and the antiplane deformation of anisotropic elasticity. Thus Stroh formalism can be used to characterize the crack tip fields in shells up to the second term and the energy release rate can be expressed in a very compact form in terms of stress intensity factors and Barnett–Lothe tensor L. The first two order terms of the crack-tip stress and displacement fields are derived. Several methods are proposed to determine the stress intensity factors and `T-stresses'. Three numerical examples of two circular cylindrical panels and a circular cylinder under symmetrical loading have demonstrated the validity of the approach.