MODE II STABLE CRACK GROWTH

Abstract Mode II stable crack extension has been examined for an aircraft grade aluminium alloy D16AT. Both theoretical and experimental results are presented. The experimental observations include load displacement diagrams, plastic wake, crack front tunnelling and scanning electron micrographs of the fracture surfaces. The crack shows a tendency for in-plane extension, and the fracture surface is very flat, smooth and free of any dimples. The crack front advances with neghgible tunnelling at all stages of extension. The span of mode II stable crack growth (SCG) is longer than in the case of mode I SCG reported earlier for the same material and there is also more extensive plastic deformation. In the presence of a slight mode I load, the crack grows out-of-plane and the fractured surface facets resemble that of a mode I or mixed-mode dimpled fracture. The theoretical study is based on a finite element analysis using small deformation theory and incremental plasticity. Some of the experimental results have been theoretically predicted using the COA criterion as the governing criterion. The theoretical results include load-displacement diagrams, crack edge displacement curves, plastic zones and the J resistance curves. There is good agreement between the load-displacement diagrams. The initiation and maximum loads differ by less than 15%. The J resistance curve has a constant slope over the whole span of stable crack growth.     

Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

Experimental and finite element studies on mode I and mixed mode (I and II) stable crack growth—II. finite element analysis

Finite element studies are presented on both mode I and mixed mode stable crack growth under static loadings through an aluminium (D16AT) alloy. A COD based criterion has been used to predict the load-displacement diagram from initiation to instability. The theoretical predictions are compared with experimental results presented in Part I. Results on computed crack profiles, stress-strain distribution ahead of the crack tip, J integrals, J resistance curves, plastic zones, etc., are included. The study indicates that the load-displacement diagram associated with a mixed mode stable crack growth in a compact tension type of specimen geometry can be predicted reasonably accurately using the criterion of a fixed crack opening displacement at a finite distance behind the crack tip provided the crack is allowed to grow in the direction of initial growth in the finite element analysis. The crack assumes a more blunted profile in a mixed mode than in the mode I at all the stages of stable extension. The distributions of normal stress and strain in the direction perpendicular to the crack extension line, ahead of the current crack tip, have similarities between the mode I and mixed mode, irrespective of loading angle. Both the stress and strain levels increase as the crack extension proceeds. In a mixed mode, the J integral at the onset of crack extension is the lowest compared with the values at the later stages of the extension. Further, the tearing modulus associated with initial kinking is very small; it becomes close to the mode I values at the later stages. The tearing modulus remained approximately constant during the whole mode I stable growth and it had a similar trend subsequent to kinking in a mixed mode. The specific work of crack extension is zero as Δa → 0 and it increases gradually with Δa irrespective of the mode of loading; the actual variation depends on the loading angle. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line.     

Experimental and finite element studies on mode I and mixed mode (I and II) stable crack growth—I. Experimental

Experimental results on mode I and mixed mode stable crack growth under static loadings through an aluminium alloy (D16AT) are presented. The compact tension type of geometry was employed for both the sets of tests. Data pertaining to load-deflection diagrams, crack opening displacements, crack front geometry, etc., are included. There is a greater spurt of crack growth at the initiation stage in a mixed mode than in mode I. The crack opening angle (COA) remained nearly constant during the whole stable growth. There is a substantial tunneling, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as the ratio a₀/W increases. Because of this tunneling, the COD at a point finite distance behind the crack tip and on the specimen surface is much more than expected. At the maximum load the tunneling is 2 to 3.5 mm in the case of mode I. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum to initiation load ratio varied in the range 1.50 to 1.75 for the whole range of tests.     

Experimental and finite element study on stable crack growth in three point bending

Experimental and finite element results are presented on mode I and mixed mode (involving I and II only) stable crack growth under static loading through an aircraft grade aluminium alloy (D16AT) in three point bending. The results include load-displacement diagrams, J-integrals, plastic zones, tunneling (or crack front curving), etc. During experiment a substantial amount of tunneling is observed, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as a_o/w increases. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum load is observed to be as high as 1.6 times the initiation load in the whole range examined. From the finite element study it is seen that, in a mixed mode, the J-integral at the onset of extension is the lowest compared with the values at the later stages. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line. The direction of initial crack extension in a mixed mode can be predicted through an elastic finite element analysis and using the criterion of maximum tangential principal stress. The study also indicates that the load-displacement diagram associated with a mixed mode stable crack growth can be predicted reasonably accurately using the criterion of crack opening angle.     

Creep crack growth laws in heat-resistant steels

The conditions of various fundamental fields' domination at the creep crack tip have been considered. The creep crack growth properties and criteria are discussed. The relation between the creep crack growth kinetics and mechanisms have been studied for heat-resistant turbine steels over a wide test temperature and load range. In recent years much attention has been paid to the theoretical analysis of creep crack growth, though experimental investigations were generally performed for a comparatively narrow temperature and test time interval. The paper is concerned with the criteria and basic laws of creep crack growth. The results of our experimental investigation of the crack kinetics and crack growth mechanisms in heat-resistant steels in wide temperature and test time ranges are also presented.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Crack growth analysis at adhesive–adherent interface in bonded joints under mixed mode I/II

The propagation of an interface crack subjected to mixed mode I/II was investigated for two 2024-T351 aluminum thin layers joined by means of DP760 epoxy adhesive produced by 3M^©. On the basis of beam theory, an analytical expression for computing the energy release rate is presented for the mixed-mode end loaded split (MMELS) test. The analytical strain energy release rate was compared by finite element (FE) analysis using the virtual crack closure technique (VCCT). Several fatigue crack growth tests were carried out in a plane bending machine to compare the experimental energy release rates to those of the analytical and FE solutions. Experimental results showed the relationship between the delamination modality and initial crack length rather than the applied load. The crack growth behavior showed stable crack growth followed by rapid propagation at the interface with the adhesive layer.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

无网格法模拟复合型疲劳裂纹的扩展

本文提出了用无网格Galerkin法模拟构件在复合变形作用下疲劳裂纹扩展路径并预估其疲劳寿命的方法。该法能够自然模拟疲劳裂纹的扩展,不需要网格重构,避免了裂纹扩展过程中的精度受损。应用无网格数值结果计算了J积分和应力强度因子IK和IIK;按照最大周向应力理论获得了裂纹扩展偏斜角。基于最小应变能密度因子理论,确定了裂纹扩展量aD,并能获得疲劳载荷的循环周数ND。文末对数值模拟结果和实验拟合结果进行了对照。     

Finite-element analysis of fatigue crack closure under plane strain conditions: stabilization behaviour and mesh size effect

An elastic–plastic finite‐element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behaviour of crack opening level and the effect of mesh size on the crack opening stress are investigated. It has been well reported that the crack opening level under plane stress conditions becomes stable after the crack advances beyond the initial monotonic plastic zone. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behaviour is influenced by the crack growth increment and discontinuous opening behaviour is observed.     

Mixed Mode Fracture of Concrete under Proportional and Nonproportional Loading

A novel testing procedure for mixed mode crack propagation in concrete is presented: four point bend of notched beams under the action of two independent force actuators. In contrast to classical procedures, this method allows nonproportional loading and crack trajectory modifications by changing the action of one actuator. Different experimental crack trajectories, under mixed mode and nonproportional loading, are presented together with the corresponding curves of load-CMOD and load-displacement. The tests were performed for three homotetic specimen sizes and two mixed mode loading conditions. The results are useful for checking the accuracy of mixed mode fracture analytical and numerical models. The models should predict the crack trajectory and a complete group of experimental records of load and displacements on several control points in the specimen. This revised version was published online in July 2006 with corrections to the Cover Date.     

The fracture behaviour of a welded tubular joint—an ESIS TC1.3 round robin on failure assessment methods: Part VI: application of WES 2805-1997

The Japanese flaw assessment method WES 2805-1997 is applied to the fracture tests on welded tubular T-joints presented in Engineering Fracture Mechanics (2002;69). The approach is shown to yield conservative results for small amounts of stable crack growth but it overestimates the load carrying capacity for larger amounts of stable crack growth. As a consequence it is proposed to restrict the application to ductile crack initiation and to brittle fracture below or at stable crack initiation.     

Ⅰ-Ⅱ复合型裂纹脆性断裂的最小J_2准则

实际工程的结构中,裂纹多处于复合型状态,因此复合型裂纹断裂的理论研究有着更为重要的理论意义和实用价值。本文以Ⅰ-Ⅱ复合型裂纹为研究对象,将偏应力张量的第二不变量2J作为判定依据,预测了裂纹起裂的角度以及开裂荷载,并与一些实验数据进行了比较,符合得也较好。计算结果进一步表明了在裂纹起裂引起的应变能转化过程中,起主要作用的是形状改变比能这一事实,由此得出了另一个结论是在裂纹尖端,平行于裂纹方向的应力级数展开式中非奇异项对裂纹的开裂角度以及开裂荷载是有影响的。     

Can pure mode III fatigue loading contribute to crack propagation in metallic materials?

The possibility of pure mode III crack growth is analysed on the background of theoretical and experimental results obtained in the last 20 years. Unlike for modes I and II, there is no plausible micromechanistic model explaining a pure mode III crack growth in ductile metals. In order to realize 'plain' mode III fracture surface, we propose the propagation of a series of pure mode II cracks along the crack front. Fractographical observations on crack initiation and propagation in a low alloy steel under cyclic torsion support such a model. The authors have not seen any clear indication of a pure mode III crack growth micromechanism in metals until now.     

Experimental and numerical investigations on the influence of the loading direction on the fatigue crack growth

During a service loading fatigue cracks can be subjected to a mixed mode loading if, due to the alteration of the loading direction, the basic crack modes (Modes I, II and III) are combined. An alteration of the loading direction, e.g. can occur either occasionally paired with an overload (mixed mode overload) or permanently in terms of a mixed mode block loading as a combination of normal and shear stresses.Within the scope of this paper, experimental investigations on both mixed mode overloads, which are interspersed into a Mode I baseline level loading, and mixed mode block loadings are presented. The experimental investigations show that the retardation effect decreases with an increasing amount of Mode II of the overload. Due to the block loading, the fatigue crack growth rate is retarded as well, and the crack is also deflected. The kinking angle depends on the fraction of shear stresses. Furthermore, a detailed elastic–plastic finite element analysis of the fatigue crack growth after mixed mode overloads is presented in order to understand the mechanism of the load interaction effects. By such numerical simulations, it can be shown that, due to mixed mode overloads, plastic deformations occur, which on the one hand reduce the near-tip closure and on the other hand cause a far-field closure. Also the stress distribution before and after the crack tip changes. A mixed mode overload causes lower closure and the crack tip deformations become asymmetrical, which is a reason for the smaller retardation effect of a mixed mode overload.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

Inverse End Loaded Split test configuration for stable mode II crack propagation in bonded joint: macroscopic analysis—effective crack length approach

Mode II crack propagation along a bonded joint is investigated using newly proposed Inverse-End Loaded Split experimental configurations. This test configuration allows stable crack propagation all along the crack propagation path. The specimen compliance and strain energy release rate for the new experimental arrangement are derived. An experimental data reduction procedure, based on the effective crack length approach, is also proposed. Two series of experiments are performed to assess the stable nature of the crack propagation and data reduction scheme associated to this new experimental arrangement. In addition to stable crack growth, the experiment may prove his worthiness in the study of crack onset under mode II loading.     

Crack growth in a mixed-mode loading on marble beams under three point bending

A combined theoretical and experimental study of a crack growth in a mixed-mode I–II loading is presented. A 160×40×20 mm marble beam, with an artificial crack 8 mm and 10 mm long each, was subjected to three point bending. The crack was located vertically to the beam's lower longitudinal fiber, through the whole width of the beam. The position of the crack was displaced from the center of the beam to one of the supporting points. The vertical force P, placed on the middle of the upper fiber of the beam, imposed the combination of the opening (mode I) and the sliding (mode II) modes on the crack mouth, creating the mixed-mode I–II loading case. The stress intensity factors K _I and K _II, which describe the local stress and strain field around the crack tip, were determined by a suitable finite element program. The crack growth was defined by two classical fracture criteria of LEFM; the minimum strain energy density and the maximum circumferential stress criteria. The initial crack growth angle () was calculated from both criteria and the critical load (P _c) from the minimum strain energy density (SED) criterion. These theoretical predictions were compared with some experimental results found from three marbles with different elastic constants; the Krystallina of Kavala, the Snow-white of Thassos and the White of Piges Drama. The theoretical results showed the same trend of and P _c as the experimental ones and they are in good agreement.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.