The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading

As part of a programme to investigate the mixed mode fatigue crack growth threshold behaviour of mild steel, tests were carried out on three-point bend specimens with spark machined initial slits inclined to give mixed Mode I and III displacements. Overall the expected tendency to Mode I crack growth showed as an initial directional discontinuity followed by a smooth rotation of the crack front until it was almost perpendicular to the specimen sides. At a smaller scale, initial crack growth was by the formation of Mode I branch cracks which developed into a ‘twist’ fracture surface consisting of narrow Mode I facets separated by cliffs. The facets eventually grew out and the fracture surface became smooth. The result in the initiation it was necessary to distinguish between the threshold conditions which result in the initiation of crack growth, specimen failure and crack arrest. An envelope based on Mode I branch crack growth provides a reasonable lower bound to the results for crack initiation and specimen failure. The crack arrest threshold results and some of the crack growth threshold results could not be analysed in detail because of lack of appropriate stress intensity factors.     

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.     

Acoustic emission source characterization in concrete under biaxial loading

The results are reported of a mode identification study on cracks produced during mixed mode loading of concrete. The locations of cracks were found to agree very well with the surface crack patterns for a variety of loading paths. The classification of cracks into mode I and mode II were conducted using a simplified moment tensor analysis. The results indicated that, in general, cracking occurs in mode I, even when the loading is pure shear. Mode II deformations generally follow the mode I cracks, as the crack interface is subjected to shear.     

Experimental study of I + III mixed mode fatigue crack transformation propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the mode transformation process. It is found that with the crack growth, I + III mixed mode changes to Mode I. Crack mode transformation is governed by the Mode III component and the transformation rate is a function of the relative magnitude of the Mode III stress intensity factor. However, even in the process of the crack mode transformation the fatigue crack propagation is controlled by the Mode I deformation.     

Mixed mode fatigue crack propagation in a ferritic–perlitic cold drawn tube

Previous work by the authors has shown that torsional fatigue tests on cold drawn tube specimens with a longitudinal micronotch present both Mode III ahead of the crack tip (throughout the tube thickness) and Mode I at the defect edges. The co-planar Mode III propagation was prevalent and is followed by Mode II crack propagation along the cold drawn direction.In this work, this behaviour is further investigated by a new series of experimental tests together with a finite element analysis. The mechanisms behind this competition between Mode I and Mode III cracks are analysed and some fractographies were performed on run-outs, broken and interrupted tests.Indeed, pure Mode I and pure Mode II crack propagation rates along with mixed mode crack propagation rates are analysed. Finally, the conditions in order to get Mode I crack growth or shear driven propagation are discussed.     

Sustained Mode I and Mode II fatigue crack growth in flat plates

This study was conducted to contribute to the understanding of fatigue crack growth under mixed mode loading. This was accomplished by developing and analyzing a flat plate specimen capable of maintaining crack growth on a plane oblique to the direction of the applied load. Several specimens were built and exposed to controlled fatigue loading in the laboratory. These specimens were then modeled using finite elements to determine the stress intensity factors (SIF). For the “Mode I/Mode II” specimens developed, the crack was forced to grow in a direction other than perpendicular to the load. The resulting crack front did not remain straight and flat, but stabilized into a curved or warped shape. Based on finite element analyses of these curved specimen cracks, it is concluded that the SIR were predominantly Mode I, with the Mode II and III SIR being negligible.     

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.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

裂纹面动摩擦作用对脆性材料动力破坏的影响EI北大核心CSCD

基于岩石类材料的I型裂纹模型,提出了一种考虑裂纹密度、裂纹相互作用以及裂纹面动摩擦作用的脆性材料动力模型。以正方形阵列分布的裂纹为例,定量分析了不同裂纹密度及不同摩擦行为对试件的裂纹扩展过程、试件受力和破坏的影响。数值计算结果表明:随着裂纹密度增大,裂纹间的相互作用增强,试件破坏时的加载应力降低,惯性效应引起试件轴向附加应力增大。裂纹面的滑动会降低裂纹面的动摩擦系数,促进裂纹发展,并降低试件的强度。相对于常数摩擦系数,考虑速度及状态依赖型摩擦模型对裂纹面的滑动过程更为合理。动强度因子对比结果显示出试件明显的应变率效应和尺寸效应。     

Dynamic steady-state crack propagation in a transversely isotropic viscoelastic body

The problem considered herein is the dynamic, subsonic, steady-state propagation of a semi-infinite, generalized plane strain crack in an infinite, transversely isotropic, linear viscoelastic body. The corresponding boundary value problem is considered initially for a general anisotropic, linear viscoelastic body and reduced via transform methods to a matrix Riemann–Hilbert problem. The general problem does not readily yield explicit closed form solutions, so attention is addressed to the special case of a transversely isotropic viscoelastic body whose principal axis of material symmetry is parallel to the crack edge. For this special case, the out-of-plane shear (Mode III), in-plane shear (Mode II) and in-plane opening (Mode I) modes uncouple. Explicit expressions are then constructed for all three Stress Intensity Factors (SIF). The analysis is valid for quite general forms for the relevant viscoelastic relaxation functions subject only to the thermodynamic restriction that work done in closed cycles be non-negative. As a special case, an analytical solution of the Mode I problem for a general isotropic linear viscoelastic material is obtained without the usual assumption of a constant Poissons ratio or exponential decay of the bulk and shear relaxation functions. The Mode I SIF is then calculated for a generalized standard linear solid with unequal mean relaxation times in bulk and shear leading to a non-constant Poissons ratio. Numerical simulations are performed for both point loading on the crack faces and for a uniform traction applied to a compact portion of the crack faces. In both cases, it is observed that the SIF can vanish for crack speeds well below the glassy Rayleigh wave speed. This phenomenon is not seen for Mode I cracks in elastic material or for Mode III cracks in viscoelastic material.     

Interaction between tensile strength failure and mixed mode crack propagation in concrete

Crack size and structure size transitions are illustrated which connect the two limit-cases of ultimate tensile strength failure (small cracks and small structures) and mixed-mode crack propagation (large cracks and large structures). The problem of mixed-mode crack propagation in concrete is then faced. By increasing the size-scale of the element the influences of heterogeneity and cohesive crack tip forces disappear and crack branching is governed only by the linear elastic stress-singularity in the crack tip region. It is proved in this way that the fracture toughness of the material is measured by a unique parameter (G_IF, G_IC or K_IC) even for the mixed-mode condition. The ratio of the sliding or Mode II fracture toughness (G_IIF, G_IIC or K_IIC) to the opening or Mode I fracture toughness depends only on the crack branching criterion adopted and not on the material features. Eventually, very controversial experimental results recently obtained on the shear fracture of concrete are explained on the basis of the above-mentioned size-scale transition.     

Analysis of crack propagation due to rebar corrosion using RBSM

Cracking behavior due to rebar corrosion in concrete specimens having a single rebar is evaluated experimentally and analytically. In the experiments, in which corrosion was induced electronically, the propagation of cracks (including internal crack patterns and surface crack widths) was monitored. In addition, deformation of the specimen surface was measured using a laser displacement meter. In the analysis, a three-dimensional Rigid-Body-Spring Method (RBSM), combined with a three-phase material corrosion–expansion model, is proposed to simulate crack propagation due to rebar corrosion. The effects of the properties of corrosion products such as elastic modulus, penetration of corrosion products into cracks, and local corrosion after cracking of the concrete are investigated. Cracking behavior due to rebar corrosion is simulated reasonably well. The simulations using RBSM provide insight into the mechanisms of crack initiation and propagation due to rebar corrosion.     

Effects of the transient Mode II on the steady state crack growth in Mode I

Turbo-generator shafts in power plant systems are often subjected to transient torques due to electric faults and high-speed reclosures. These transient torques cause the initiation and growth of cracks in Modes II and III. However, these cracks are further subjected to cyclic bending (Mode I crack growth) due to the turbine shaft weight or possible misalignments. Such load histories are also very common in railroad tracks. An existing crack may be subjected to a sudden Mode II, followed by a steady state Mode I. In order to predict the fatigue life, the effect of the transient Mode II on a subsequent Mode I crack growth must be understood. In this paper the effects of the Modes I and II overloads on a subsequent Mode I crack growth are studied on the AISI 4340 and spherodized AISI 1090 steels using three- and four-point bending specimens. The results show that in contrast to Mode I overloads, where the crack is either arrested or retarded for a distance of the order of magnitude of the transient plastic zone size, Mode II overloads give rise to the crack growth acceleration (for a very short distance, much smaller than the Mode II transient plastic zone size with no retardation afterwards). The three known mechanisms of the crack closure in Mode I (plasticity-, roughness- and oxide-induced crack closures) were examined for the Mode II overloads and were found not to be applicable for that Mode.

Fractography analysis of 1090 steel at the point of Mode II overload showed a significant amount of shear cracks and cavities. Such cavities could contribute to the crack growth acceleration in the subsequent Mode I crack growth.     

FATIGUE AT NOTCHES SUBJECTED TO REVERSED TORSION AND STATIC AXIAL LOADS

Reversed torsion with and without a superimposed end load has been applied to 1% Cr-Mo-V steel specimens containing sharp notches. Crack propagation was monitored by a sensitive d.c. potential drop system that measured crack depths between 25 μm and 0.6 mm from the root of the notch. Stress intensity factors do not satisfactorily correlate all the crack growth data but a strain intensity factor which is a function of material properties and notch plastic zone size shows a significant improvement and provides a single upper bound solution for both ambient and elevated temperatures. This solution permits designers to make safe lifetime assessments. At room temperature cracks initially propagate by mode II along the surface, and mode III radially but at low stresses crack growth is continued by mode I propagation. At higher stresses a transition to mode I cracking is avoided. Elevated temperature causes a brittle layer to form and in this case cracks initially propagate by mode I which then translates to mode III cracking at high stresses. Mode III thresholds are significantly higher than mode I thresholds but a constrained shear strain zone, as found at the root of notches subjected to torsion, permits the initiation and generation of a mode III crack. The application of an axial load enhances the mode III crack propagation rate since this increases the effective crack tip intensification factor.     

Design and analysis of the crack rail shear specimen for mode III interlaminar fracture

The crack rail shear (CRS) specimen is a proposed test method to characterize the Mode III interlaminar fracture toughness of continuous-fiber-reinforced composite materials. The specimen utilizes the two-rail shear test fixture, and contains embedded Kapton film placed symmetrically about the midplane to provide starter cracks for subsequent characterization. Otherwise, specimen length and width are identical to the ASTM shear test specimen geometry. An analytical expression for the strain energy release rate is developed based on a strength of materials approach. The model illustrates the important material and geometric parameters of the test, and provides a simple data reduction scheme for experiments. A quasi three-dimensional, linear elastic finite element code, CCMQ3D, is employed to verify the pure Mode III fracture state and to determine admissible crack lengths. Deformation of the model shows that only the out-of-plane displacement is non-zero, indicating that a pure Mode III fracture state does indeed exist within the constraints of the Q3D assumption. Compliance and strain energy release rate predictions are in good agreement with the strength of materials model over the range of crack lengths, 0·15<a/w<0·85. A fully three-dimensional, linear elastic finite element analysis of the CRS is employed to quantify the effect of finite length on the fracture state. Only intermediate crack lengths are investigated. Crack closure techniques are utilized to determine the components of the strain energy release rate present. Results indicate that a small boundary layer of mixed mode behavior exists at the free edges that diminishes to a pure Mode III fracture state. Compliance and strain energy release rate predictions by the 3D model show good agreement with the Q3D and strength of materials models.     

Why are crack paths in concrete and mortar different from those in PMMA?

Experiments by Bazant and Pfeiffer on concrete and mortar seem to indicate that crack growth does not necessarily take place under Mode I conditions. In order to investigate the influence of the material, experiments were carried out in PMMA with similar geometry to that used by Bazant and Pfeiffer and a numerical simulation was made assuming Mode I crack growth. The experimental results for PMMA differ significantly from those in concrete and mortar, but agree closely with the result from the numerical simulations. The difference is believed to be explained by the fact that small-scale yielding conditions are not realized well enough in concrete and mortar. A fairly large region of small cracks probably influences the crack growth direction.     

Study of Fatigue Behavior of Epoxy‐Carbon Composites under Mixed Mode I/II Loading

This paper presents an experimental assessment of the initiation and propagation of interlaminar cracks under mixed mode I/II dynamic fracture loading of a composite material with an MTM45‐1 epoxy matrix and unidirectional IM7 carbon‐fiber reinforcement. The aims of the experimental program developed for this purpose are to determine, on the one hand, the initiation curves of the fatigue delamination process, understood as the number of load cycles needed to generate a fatigue crack, and on the other, the crack growth rate (delamination rate) for different percentages of static Gc, in both cases for two mode mixities (0.2 and 0.4) and for a tensile ratio R = 0.1. All this with the goal of quantifying the influence of the degree of mode mixity on the overall behavior of the laminate under fatigue loading. The results show that the energy release rate increases with increasing loading levels for both degrees of mode mixity and that the fatigue limit is located around the same percentages. However, crack growth rate behavior differs from one degree of mode mixity to the other. This difference in the behavior of the material may be due to the varying influence of mode I loading on the delamination process.

     

A study of fatigue crack growth with changing loading direction

Round compact specimens made of 1070 steel were experimentally tested under cyclic loading for crack growth. The specimen was first subjected to Mode I loading. After the crack reached a certain length, the external loading direction was changed 50° from the original loading direction. Right after the change of the loading direction, the specimen experienced the combined Mode I/II loading condition. Following a short transient period, the fatigue crack was found to grow in the direction approximately perpendicular to the external loading direction, indicating the recovery of Mode I cracking. A recently developed approach was used to predict the cracking behavior of the specimens. Detailed elastic-plastic stress analysis was conducted using the finite element (FE) method. Both crack growth rate and cracking direction were predicted by employing a critical plane multiaxial fatigue criterion based on the stress-strain response outputted from the FE analysis. The predictions made by using the approach were in excellent agreement with the experimental observations in terms of both crack growth rate and cracking direction. The material constants used in the approach were obtained from testing smooth specimens for crack initiation.     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.