Determination of stress intensity factors at the tips of cracks growing from loaded holes in finite anisotropic plates

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 171–177, March–April, 1990.     

Mode III Stress-intensity factors in cracked orthotropic plates—An analogy with propagating cracks in isotropic media

In this paper, the method of reflected caustics—which was used to evaluate Mode III SIF's in stationary cracks in isotropic plates—was extended to deal with stationary cracks in orthotropic plates. Furthermore, a correspondence between the anisotropic stationary case and the case of a Mode III dynamic crack, traversing an isotropic plate, is developed by analyzing appropriately the governing equations of the two problems. For this purpose the singulardisplacement field for rectilinearly orthotropic cracked bodies was combined with either Yoffé's model for steady-state, or Broberg's model for transient-crack propagation. Graphs are given where the equivalence between these cases can be established. In this way, the dynamic problem of the propagating crack in an isotropic medium can be readily simulated by considering the experimentally easier anisotropic stationary case.     

Local weight functions for semi-elliptical surface cracks in finite thickness plates

Weight functions for any local point, 0 < Φ < π/2 along a semi-elliptical surface crack in finite thickness plates were derived from an assumed approximate general weight function and two reference stress intensity factors. The resulting weight functions were verified using available finite element results for two nonlinear stress fields and good agreement was achieved. When used together with weight functions for Φ = 0 and Φ = π/2 the weight functions are suitable for the calculation of stress intensity factors anywhere along the crack front for semi-elliptical surface cracks in complex stress fields with aspect ratios in the range 0 ≤ a/c ≤ 1 and relative depths 0 ≤ a/t ≤ 0.8.     

Stress wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 79–84, February 2006.     

Fracture instability of reinforced panel with cracks emanating from hole

Initiation of failure by yielding and/or fracture depends on the magnitude of the distortion and dilatation of material elements. According to the strain energy density theory (SED), failure is assumed to initiate at the site of the local maximum of maxima [(dW/dV)^max_max]_L by yielding and the maximum of minima [(dW/dV)^max_min]_L by fracture. The fracture is assumed to start from point L where [(dW/dV)^max_min]_L appears and tends toward G where the global maximum of dW/dV minima appears, denoted by [(dW/dV)^max_min]_G. The distance l between L and G along the anticipated crack trajectory is an indication of failure instability of the system by fracture. If l is sufficiently large and [(dW/dV)^max_min]_L exceeds the threshold, fracture initiation could lead to global failure. The local and global failure instability of a composite structural component is studied by application of the strain energy density theory. The depicted configuration is that of a panel with a circular hole reinforced by two side strips made of different material. The case of two symmetric cracks emanating from the hole and normal to the applied uniaxial tensile stress is also analyzed. Results are displayed graphically to illustrate the geometry and dissimilar material properties influence the fracture instability behavior of the two examples.     

Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method

In this paper, a new semi-analytical and semi-engineering method of the closed form solution of stress intensity factors (SIFs) of cracks emanating from a surface semi-spherical cavity in a finite body is derived using the energy release rate theory. A mode of crack opening displacements of a normal slice is established, and the normal slice relevant functions are introduced. The proposed method is both effective and accurate for the problem of three-dimensional cracks emanating from a surface cavity. A series of useful results of SIFs are obtained.     

Surface cracks in a plate of finite width under extension or bending

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.     

Subcritical growth of high-cycle fatigue cracks in finite thin isotropic plates

The problem of constructing a two-stage model of the motion of a fatigue crack in finite thin isotropic plates under symmetric tension-compression is formulated, and a method for its solution is considered. The two-stage nature is regarded as the presence of the incubation and propagation stages. The model is constructed by jointly considering the resolving equations of the theory of elasticity and the evolutionary equations of the mechanics of continuous damage. The damage function's attaining the critical value is considered as a criterion of initiation of local fracture and movement of a fatigue crack. Plates containing central and lateral cracks are considered. The effect of the level of stresses, the finiteness of the plate, the initial length of the crack, and the behavior of the length of the plastic zone on fracture kinetics is evaluated. The present work was carried out with financial support from the European Community in accordance with the INTAS-UA 95-0202 International Project. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 106–116, July, 2000.     

Closed-form solution for two collinear mode-III cracks in an orthotropic elastic strip of finite width

The problem of an orthotropic strip containing two collinear cracks normal to the strip boundaries is considered. The Fourier series method is used to reduce the associated boundary value problem to triple series equations, then to a singular integral equation, which can be solved analytically. Under remote uniform antiplane shear loading, the stress field and the crack sliding displacement are determined analytically and stress intensity factors are also given in a closed form.     

Fatigue growth modeling of cracks emanating from a circular hole in infinite plate

This paper presents a numerical approach of fatigue growth analysis of cracks emanating from a hole in infinite elastic plate subjected to remote loads. It involves a generation of Bueckner’s principle and a hybrid displacement discontinuity method (a boundary element method) proposed recently by the senior author of the paper. Because of an intrinsic feature of the boundary element method, a general crack growth problem can be solved in a single region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is modeled conveniently by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, fatigue growth process of an inclined crack in an infinite plate under uniaxial cycle load is modeled to illustrate the effectiveness of the numerical approach. In addition, fatigue growth of cracks emanating from a circular hole in infinite elastic plate subjected to remote loads is investigated by using the numerical approach. Many numerical results are given     

Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermomechanical loading

This paper describes the development and application of a general domain integral method to obtain J-values along crack fronts in three-dimensional configurations of isotropic, functionally graded materials (FGMs). The present work considers mode-I, linear-elastic response of cracked specimens subjected to thermomechanical loading, although the domain integral formulation accommodates elastic–plastic behavior in FGMs. Finite element solutions and domain integral J-values for a two-dimensional edge crack show good agreement with available analytical solutions for both tension loading and temperature gradients. A displacement correlation technique provides pointwise stress-intensity values along semi-elliptical surface cracks in FGMs for comparison with values derived from the proposed domain integral. Numerical implementation and mesh refinement issues to maintain path independent J-values are explored. The paper concludes with a parametric study that provides a set of stress-intensity factors for semi-elliptical surface cracks covering a practical range of crack sizes, aspect ratios and material property gradations under tension, bending and spatially-varying temperature loads.     

The mode III cracks emanating from an elliptical hole in the piezo-electro-magneto-elastic materials

The mode III crack problem in a medium possessing coupled electro-magneto-elastic is considered. Two asymmetrical edge cracks emanate from an elliptical hole. Combined stress, electric and magnetic loads are considered. The elliptical hole and cracks are assumed to be either magneto-electrically impermeable or permeable. The closed-form solution for stress, electric and magnetic intensity factors are derived explicitly. Also the solution for energy release rate is given in closed form. The solution is based on the complex variable method combined with the method of conformal mapping. Numerical computations are given to illustrate the effect of variable geometrical and material parameters on stress, electric and magnetic intensity factors and energy release rate.     

The evolution of caustics from holes to cracks

The method of caustics was used for the study of the evolution of stress concentration around a circular hole, which progressively changes in shape and becomes an elliptic hole, tending to an internal crack. The influence of the amount of ellipticity of the holes and their orientation relative to the axis of the applied external loads at infinity on the form of caustics created around the discontinuity was studied, as the elliptic holes tended to become internal cracks. A series of experiments with tension specimens containing small elliptic holes of any ellipticity and orientation was performed. Comparison of experimentally obtained caustics with theory yielded a good agreement of both results. Finally, the use of small elliptic holes drilled all over a biaxial stress field for the determination of the individual principal stresses and the principal directions at the area of the holes was outlined.     

Experimental investigation on the propagation of fatigue cracks emanating from sharp notches

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches is investigated by means of an experimental campaign performed on Al-7075-T651 specimens carrying notches with opening angles of 45°, 90°, and 135°. The samples were tested using a servohydraulic machine under different loading directions and at several loading levels. The crack deflection induced by the variation in loading direction was determined my measuring the kinking angle and by studying the crack propagation plane through fractographic analysis. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. The influence of K _II on the crack propagation was discussed on the basis of theoretical and semi empirical models.     

In-hole and mainflow velocity measurements of low-momentum jets in crossflow emanating from short holes

Discrete hole film cooling utilizes jet-in-crossflow geometry where the jet is supplied through a short hole which may be pitched relative to the main flow. Typically, the velocity ratio is near one. Under these conditions, the mean flow structure of the jet/mainstream interaction may be strongly affected by the characteristics of the flow within the hole. Magnetic resonance velocimetry (MRV) is used to measure the 3-dimensional mean velocity field for various jets in crossflow with short holes of varied inclination angles and blowing ratios typically of gas turbine applications. Novel measurements of the flow within inclined feed holes are captured using MRV. Secondary flows within the hole are found to be strongly dependent on the inclination of the hole. The traditional counter-rotating vortex pair is observed in the mainstream, as well as high levels of wall-normal vorticity. The 3D vorticity field is used to modify traditional jet-in-crossflow vortex ring theory to apply to low-momentum jets which remain attached to the ejection surface.     

任意多椭圆孔多裂纹无限大各向异性板应力强度因子求解的一种新方法

采用各向异性体平面弹性理论中的复势方法,应用保角变换技术,以F aber级数为工具,导出含任意多椭圆孔和裂纹群无限大各向异性板在远场载荷作用下其应力场和位移场的级数解,并在此基础上利用断裂力学方法确定裂纹尖端的应力强度因子,通过算例讨论了材料参数及裂纹、孔的尺寸等对应力强度因子的影响规律,得出了一些有益的结论。数值结果表明本文方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响。