Analytical and experimental evaluations of the influence of fracture surface roughness,its sliding actions and the associated plasticity on fatigue crack propagation

An investigation of fatigue crack propagation in rectangular AM60B magnesium alloy plates containing an inclined through crack is presented in this paper. The behavior of fatigue crack growth in the alloy is influenced by the fracture surface roughness. Therefore, in the present investigation, a new model is developed for estimating the magnitude of the frictional stress intensity factor, k_f, arising from the mismatch of fracture surface roughness during in-plane shear. Based on the concept of k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, the proposed model is applied to predict crack growth due to fatigue loads. Experiments for verifying the theoretical predictions were also conducted. The results obtained are compared with those predicted using other employed mixed mode fracture criteria and the experimental data.     

Macroscopic and microscopic examination of the relationship between crack velocity and path and Rayleigh surface wave speed in single crystal silicon

The speed of Rayleigh surface waves, denoted C_R, is the accepted upper limit for Mode I crack velocity in monolithic solids. In the current contribution, we discuss several critical issues associated with the velocity of Rayleigh surface waves and crack velocity in single crystal (SC) brittle solids, and the global and local influence of C_R on crack path selection in particular.Recent cleavage experiments in SC silicon showed that crack velocity at certain cleavage planes and crystallographic orientations cannot exceed a small fraction of C_R, and thereafter the crack deflects to other cleavage planes. Indeed, C_R defined by the continuum mechanics ignores atomistic phenomena occurring during rapid crack propagation, and therefore is limited in predicting the crack velocity. Examination of these anomalies shows that this limitation lies in microstructural lattice arrangement and in anisotropic phonon radiation during rapid crack propagation. Globally, C_R has no influence on the crack deflection phenomenon. However, the misfit in C_R between the original plane of propagation and the deflected plane generates local instabilities along the deflection zone.     

Fracture mechanics analysis of thin coatings under plane-strain indentation

A combined experimental/analytical work is carried out to elucidate the fracture resistance of a thin, hard coating bonded to a semi-infinite substrate due to indentation by a cylindrical surface. The bending of the coating under the softer substrate induces concentrated tensile stress regions at the lower and upper surfaces of the coating, from which cracks may ensue. The evolution of such damage in a model transparent system (glass/polycarbonate) is viewed in situ from below and from the side of the specimen. The critical load needed to initiate a crack on the lower coating surface generally increase proportionally to the coatings thickness, d. An interesting departure from this trend occurs for thin coatings, where the fracture load, although marred by a large scatter, increases somewhat with decreasing d. The fracture data for the upper coating surface are limited to relatively thick coatings due to the recurrence of premature failure from the coating edges. The behavior in this range is similar to that for the lower surface crack, albeit with an order of magnitude greater fracture resistance.A fracture mechanics analysis in conjunction with FEM is performed to elucidate the stress intensity factors responsible for crack propagation. A crack normal to the coating surface is assumed to emanate either from the lower or upper surface of the coating. A major feature of the solution is the occurrence of a bending-induced compression stress field over a region ahead of the crack tip. This effect, which become more dominant as the ratio between the contact length and the coating thickness is increased, tends to delay the onset of crack propagation, especially for the lower surface crack. Consequently, in applications associated with large indenters, thin and/or tough coatings and stiff substrates, cracking from the upper coating surface may precede that from the lower surface. An interesting feature of this crack shielding mechanism is that when the coating surface contains a distribution of flaws rather than a single crack, small flaws in this population may be more detrimental than large ones. Incorporation of these aspects into the analysis leads to a good correlation with the test results. In the special case of line loading, which constitutes a lower bound for the critical loads, a closed-form, approximate solution for the stress intensity factors or the critical loads are obtained.Plane-strain indentation, although less common than spherical indentation, allows for characterizing the fracture resistance of opaque films through observation from the specimen edge. This approach is not easily implemented to thin films (i.e., less than about a hundred microns), however.     

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.     

Theoretical and experimental studies in fracture mechanics of crack-like defects under biaxial loading

It is a common point of view in fracture mechanics that, for any geometry of the body with a crack and any boundary conditions for the loading acting in the body plane, the stress and displacement components near the crack tip can be approximated in the framework of the theory of elasticity by a one-parameter or one-term representation, i.e., strictly in terms of the stress intensity coefficients K _I and K _II for an arbitrary failure crack [1, 2]. The authors of [2] specified the Westergaard function of the singular solution for a central crack under the biaxial loading of a plate. This approximate two-component solution has satisfactory accuracy. It is clear from [2] that this method cannot be admitted as a general statement [1], although it has long been assumed to be correct. The cause is that one cannot reasonably justify neglecting the second term in the Williams representation of the stress components in the plane case in the form of eigenfunction series; the contribution of this term in the rectangular coordinate system x, y is independent of the distance from the crack tip. This method may result in a serious mistake, from both the qualitative and quantitative viewpoints, in the prediction of local stresses, displacements, and related variables that are of interest. Apparently, this can best be demonstrated by an example of biaxial loading of a plate with a crack [1]. The unfounded neglect of the second term (whose contribution is independent of the distance from the crack tip) in the series representing the stress components is the source of the above-mentioned difficulties. In this problem, the influence of the load applied in the direction parallel to the crack plane manifests itself only in the second term of the series [3]. Therefore, this term should be clearly determined and studied in detail in the case of technological welding defects (faulty fusions, incomplete fusions, undercuts, and slag inclusions) and crack-like defects (scratches and cuts) in the base metal. The influence of the stress σ _OX along the crack axis on the stress tensor σ _x , σ _y , τ _xy and on the displacements u _x and u _y is confirmed by experimental studies of cracks by the photoelasticity method [4].     

Toughening by Phase Boundary Propagation

Transformation toughening has enhanced the fracture toughness of certain Zirconia-Toughened Ceramics (ZTC) by factors of 2–4. The primary explanation of toughening, by McMeeking and Evans [1] and Budiansky et al. [2], suggests that the main source of toughening is the energy stored by the transformed inclusions in the wake of a propagating crack. In the case of supercritical ZTC where the boundary of the transformed zone is a phase boundary (surface of strain discontinuity), this paper suggests an additional source of toughening – that due to propagation of the phase boundary. By extending the J-integral to cracked bodies containing surfaces of strain discontinuity, the transformation toughening for a steady Mode I crack is evaluated.     

Effect of residual surface stress on the fracture of nanoscale materials

The problem of a mode I crack in nanomaterials under a remote mechanical load is investigated. The effect of the residual surface stress on the crack surface is considered and the solutions to the crack opening displacement (COD) and the stress intensity factor (K_I) are obtained. The results show that the surface effect on the crack deformation and crack tip field are prominent at nanoscale. Moreover, COD and K_I are influenced by the residual surface stress not only on the surface near the crack tip region but also on the entire crack surface.     

Analyses of steady quasistatic crack growth in plane strain tension in elastic-plastic materials with non-isotropic hardening

Steady state crack propagation problems of elastic-plastic materials in Mode I, plane strain under small scale yielding conditions were investigated with the aid of the finite element method. The elastic-perfectly plastic solution shows that elastic unloading wedges subtended by the crack tip in the plastic wake region do exist and that the stress state around the crack tip is similar to the modified Prandtl fan solution. To demonstrate the effects of a vertex on the yield surface, the small strain version of a phenomenological J₂, corner theory of plasticity (Christoffersen, J. and Hutchinson, J. W. J. Mech. Phys. Solids,27, 465 C 1979) with a power law stress strain relation was used to govern the strain hardening of the material. The results are compared with the conventional J₂ incremental plasticity solution. To take account of Bauschinger like effects caused by the stress history near the crack tip, a simple kinematic hardening rule with a bilinear stress strain relation was also studied. The results are again compared with the smooth yield surface isotropic hardening solution for the same stress strain curve. There appears to be more potential for steady state crack growth in the conventional J₂ incremental plasticity material than in the other two plasticity laws considered here if a crack opening displacement fracture criterion is used. However, a fracture criterion dependent on both stress and strain could lead to a contrary prediction.     

Angle cracks in two bonded functionally graded piezoelectric material under anti-plane shear

Consider two bonded functionally graded piezoelectric material (FGPM) with finite height. Each material contains an arbitrary oriented crack. The material properties are assumed in exponential forms in the direction normal to the interface. The crack surface condition is assumed to be electrically impermeable or permeable. Using the Fourier transform technique, the problem can be reduced to a system of singular integral equations, which are then solved numerically by applying the Gauss-Chebyshev integration formula to obtain the stress intensity factors at the crack tips. Numerical calculations are carried out to obtain the energy density factor S and the energy release rate G. In impermeable case, the energy release rate has been shown to be negative as the electric loads are applied. The positive definite characteristic of the energy density factor makes it possible for predicting the fracture behavior of the cracked structure. The influences of the non-homogeneous parameters and crack orientation on the energy density factors at the crack tips are discussed in detail. The results show that the energy density factor at the crack tip will be increased when the crack tip is located within the softer material.     

Simulation of partial closure of a crack-like cavity with cohesion between the faces in an isotropic medium

A mathematical model for the closure of a crack-like cavity with cohesive end zones in an isotropic medium is constructed using methods of elastic theory. It is assumed that the interaction between the surfaces of the crack-like cavity under the action of body and surface forces can lead to the formation of contact zones on their surfaces. Determination of the unknown parameters characterizing the closure of the crack-like cavity reduces to a system of singular integrodifferential equations. The integral equations are converted to a system of nonlinear algebraic equations which is solved by the method of successive approximations. The contact stresses, the interaction forces between the faces of the crack-like cavity, and the size of the contact zone in which the faces of the crack-like cavities are closed are determined.     

Transient crack growth under creep conditions

Transient crack growth in an elastic/power-law creeping material is investigated under antiplane shear loading and small-scale-yielding conditions. At time t = 0 the solid is suddenly loaded far from the crack by tractions that correspond to the elastic crack-tip stress distribution. At that time the crack begins to propagate at a constant velocity. The stress fields evolve in a complex manner as the crack propagates due to the competing effects of stress relaxation due to constrained creep and stress elevation due to the instantaneous elastic material response to crack growth. From detailed finite element calculations it is shown that these fields can be approximated by a simple matching of three asymptotic singular crack-tip solutions. A characteristic stress, distance and time are defined for this problem which provide a normalization that accounts for any crack velocity, loading and all material properties for a given creep exponent n. Results are presented for crack-tip stresses, strains, crack opening displacements and creep zones.     

Direction of crack growth initiation in roller contact: strain energy density criterion

Small defects or cracks near the surface of roller contact could spread and lead to failure at large. Their growth behavior depends on the rolling load, size and orientation of the initial defects, and material property in addition to friction at the contacting surfaces. Stress intensity factors K₁and K₂ are obtained for three different crack types near the surface between the roller and contacting solid. Various possible directions of crack growth initiation are obtained as the different roller loads are moved relative to the crack. The results are indicative of railway failure observed in service and are helpful to future studies on subcritical and/or critical crack growth.     

On fatigue crack growth in ductile materials by crack-tip blunting

One of the basic mechanisms for fatigue crack growth in ductile metals is that depending on crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading. In a standard numerical analysis accounting for finite strains it is not possible to follow this process during many cycles, as severe mesh distortion at the crack-tip results from the huge geometry changes developing during the cyclic plastic straining. In the present numerical studies, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 200 full cycles by using remeshing at several stages of the plastic deformation. Three different values of the load ratio R=K_min/K_max are considered. It is shown that the crack-tip opening displacement, CTOD, typically undergoes a transient behaviour, with no crack closure during many cycles, before a steady-state cycling with crack closure at the tip starts to gradually develop.     

A study of hysteresis in theK ID -å relation

A photoelastic study of high speed crack propagation in Homalite 100 was conducted to measure hysteresis in the constitutive relation forK _ID -å. The fracture specimen was designed to obtain both crack acceleration and deceleration during a single crack extension. Additional loads perpendicular to the cráck-propagation path were applied at secondary locations to accentuate the magnitude of acceleration-deceleration observed in this specimen. The photoelastic data were analyzed using dynamic stress field equations in conjunction with the least-squares over-deterministic method to obtain the crack-propagation fracture toughness,K _ID . Crack velocity, å, was determined numerically by differentiating a polynomial fitted to the crack length-time data in a leastsquares sense. Experimental results indicate that Homalite 100 does not exhibit significant hysteresis in theK _ID -å relation.     

A piezoelectric material strip with a crack perpendicular to its boundary surfaces

A cracked piezoelectric material strip under combining mechanical and electrical loads is considered. The crack is vertical to the top and bottom edges of the strip. The edges of the strip are parallel to the x-axis and perpendicular to the z-axis. When a piezoelectric ceramic is poled, it exhibits transversely isotropic behavior. Among many possible poled axis orientations, a particular orientation when the poling direction lies parallel to x-axis is examined in this paper. Both impermeable crack and permeable crack assumptions are considered. Numerical results are included for three kinds of fracture mechanics specimens, namely an edge-cracked strip, a double edge-cracked strip, and a center-cracked strip, subjected to uniform tensions and uniform electric displacement loads simultaneously, at the far ends. In addition, an edge-cracked strip under pure bending and uniform electric displacement loads at the far ends is also investigated in this paper.     

Properties of dynamic rupture and energy partition in a solid with a frictional interface

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. General considerations and observations suggest that the subshear pulse and supershear crack are, respectively, the most and least common modes of earthquake ruptures.     

Crack stabilization in a brittle body using stiffeners

The behavior of a crack under uniaxial tension in the presence of reinforcement is studied. The reinforcing members (riveted stiffeners) are modeled by point loads. Only four members nearest to the crack are taken into account. It is shown that stiffeners allow one to arrest a crack and prevent its catastrophic growth. Relations between the geometrical and force characteristics for which the crack is stabilized are obtained. The stabilization mechanism is discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 137–143, November–December, 2006.     

Development of a multiaxial fatigue theory by considering constraint effects on small mixed-mode cracks

The effects of the transverse strain (the normal strain in the crack-line direction) on the near-tip fields of small shallow surface cracks (Case A cracks) in power-law hardening materials are investigated by finite element analyses. The small Case A cracks are under plane stress, general yielding, and mixed mode I and II conditions. Constant effective stress contours representing the intense straining zones near the tip, deformed crack-tip profiles and near-tip mode mixity factors are presented for different transverse strains in the crack-line direction. Based on the concept of characterization of fatigue crack growth by the cyclic J-integral, the effects of the transverse strain on J are investigated. The results suggest that the fatigue life prediction based on multiaxial fatigue theories and the critical plane approach should include the constraint effects due to the transverse strain. Consequently, the concept of constant fatigue life contour on the Γ-plane in multiaxial fatigue theories is generalized to the constant fatigue life surface in the Γ-space where the shear strain and the two normal strains are the three axes. Finally, a damage parameter as a function of the shear strain and the two normal strains is proposed for evaluation of fatigue damage under multiaxial loading conditions.     

Tensile and compressive buckling of plates weakened by cracks

Plates are susceptible to buckling under compression when the thickness dimension becomes sufficiently small. Such mode of structure failure can prevail even if the plates were extended in tension. Wribkling of stretched thin sheets is a commonly observed phenomenon that leads to complex deflection patterns, particularly in regions close to crack-like imperfections. Predictions of the buckled displacement modes for plates weakened by cracks will be made on the basis of a theory formulated by application of variational calculus. Finite element method is used such that defects of other shapes can also be analyzed. Various buckled displacement modes of a center-cracked plate are determined and displayed graphically. The critical buckling loads are found to decrease with increasing crack size. Moreover, local wrinkling of the plate surface becomes less pronounced for the higher buckling modes. The method of solution applies equally well to plates that are initially curved.     

A moving-load controlled-displacement fracture-toughness testing machine

In conventional fracture-toughness testing, the line of application of the loads remains fixed with respect to specimen geometry. In this testing machine, the load moves with the advancing crack front, and displacement is used as the controlled variable to propagate and arrest a crack. The energy-release rate at the onset of crack propagation and, hence, the plane-strain fracture toughnessK _Ic can be measured directly without compliance calibration or stress-intensity evaluation. The specimen is in the form of a flat plat 25 by 50 cm which is simple to machine and provides about 30 values ofK _Ic. The versatility of the machine is demonstrated by making a statistical analysis ofK _Ic for 7075-T6 Al by showing the effect of plate thickness on the fracture toughnessK _c using a tapered specimen, and by evaluatingK _c in 7075 Al as a function of aging temperature in a thermal-gradient-treated specimen.