Showing papers on "Stress concentration published in 2000"

Experimental analysis of deformation mechanisms in a closed-cell aluminum alloy foam

Abstract: The evolution of plastic deformation in a cellular Al alloy upon axial compression is monitored through a digital image correlation procedure. Three stages in the deformation response have been identified. The first involves localized plastic straining at cell nodes. It occurs uniformly and leads to a nominal loading modulus appreciably lower than the stiffness. The second comprises discrete bands of concentrated strain containing cell membranes that experience plastic buckling, elastically constrained by surrounding cells. In this phase, as the loading increases, previously formed bands harden, giving rise to new bands in neighboring regions. The localized bands exhibit a long-range correlation with neighboring bands separated by 3–4 cells along the loading direction. This length scale characterizes the continuum limit. Thirdly, coincident with a stress peak, σo, one of the bands exhibits complete plastic collapse. As the strain increases, this process repeats, subject to small stress oscillations around σo.

Progressive fatigue damage modeling of composite materials, Part I : Modeling

Abstract: In this research a modeling technique for simulating the fatigue behaviour of laminated composite materials, with or without stress concentrations, called progressive fatigue damage modeling, is es...

Modes of dynamic shear failure in solids

Abstract: The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented.

Micromechanical simulation of the failure of fiber reinforced composites

Abstract: The strength of unidirectionally reinforced fiber composites is simulated using the three dimensional shear lag model of Landis, C. M., McGlockton, M. A. and McMeeking, R. M. (1999) (An improved shear lag model for broken fibers in composites. J. Comp. Mat. 33, 667–680) and Weibull fiber statistics. The governing differential equations for the fiber displacements and stresses are solved exactly for any configuration of breaks using an influence superposition technique. The model predicts the tensile strength of well bonded, elastic fiber/matrix systems with fibers arranged in a square array. Length and strength scalings are used which are relevant for elastic, local load sharing composites. Several hundred Monte Carlo simulations were executed to determine the statistical strength distributions of the composite for three values of the fiber Weibull modulus, m =5, 10 and 20. Stress–strain behavior and the evolution of fiber damage are studied. Bundle sizes of 10×10, 15×15, 20×20, 25×25, 30×30 and 35×35 fibers of various lengths are investigated to determine the dependence of strength on the composite size. The validity of weakest link statistics for composite strength is examined as well.

Atomistic simulations on the tensile debonding of an aluminum-silicon interface

Abstract: In this paper we present Modified Embedded Atom Method (MEAM) simulations of the deformation and fracture characteristics of an incoherent interface between pure FCC aluminum and diamond cubic silicon. As a first approximation, the study only considers the normal tensile separation of a [100] interface with the principal crystallographic axis of the aluminum and the silicon aligned. The MEAM results show that the relaxed interface possesses a rippled structure, instead of a planar atomic interface, and such ripples act as local stress concentrators and initiation sites for interfacial failure. The stress–strain (traction–displacement) response of aluminum and silicon blocks attached at an interface depends on the distance from the interface that the boundary conditions are applied, i.e. the size of the atomic blocks, and the location of the measured opening displacement. Point vacancy defects near the interface are found to decrease the maximum normal tensile stress that the interface can support at a rate almost linearly proportional to the number fraction of the dispersed defects. A crack-like vacancy defect in the bulk aluminum or silicon must reach an area fraction (projected to the surface normal to the tensile axis) of about 50 or 30%, respectively, in order to shift the failure from the interface to the bulk materials. It is further demonstrated that the present results are consistent with continuum-based traction separation laws, provided that the opening displacement is measured near the physical boundary of the deforming cohesive zone (±10 A from the boundary of the Al–Si interface). As the opening displacements are measured farther from the interface, the traction–displacement response approaches that of classical linear elastic fracture mechanics.

A discrete dislocation analysis of mode I crack growth

Abstract: Small scale yielding around a plane strain mode I crack is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a complementary solution that enforces the boundary conditions. The latter is non-singular and obtained from a finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. A relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, so that crack growth emerges naturally from the boundary value problem solution. Material parameters representative of aluminum are employed. For a low density of dislocation sources, crack growth takes place in a brittle manner; for a low density of obstacles, the crack blunts continuously and does not grow. In the intermediate regime, the average near-tip stress fields are in qualitative accord with those predicted by classical continuum crystal plasticity, but with the local stress concentrations from discrete dislocations leading to opening stresses of the magnitude of the cohesive strength. The crack growth history is strongly affected by the dislocation activity in the vicinity of the growing crack tip.

The validation of some methods of notch fatigue analysis

Abstract: This paper is concerned with the testing and validation of certain methods of notch analysis which the authors have developed theoretically in earlier publications. These methods were developed for use with finite element (FE) analysis in order to predict the fatigue limits of components containing stress concentrations. In the present work we tested and compared these methods using data from standard notches taken from the literature, covering a range of notch geometries, loading types, R-ratios and materials: a total of 47 different data sets were analysed. The greatest predictive success was achieved with critical-distance methods known as the point, line and area methods: 94% of these predictions fell within 20% of the experimental fatigue limits. This was a significant improvement on previous methods of this kind, e.g. that of Klesnil and Lucas [(1980) Fatigue of Metallic Materials, Elsevier Science]. Methods based on the Smith and Miller [(1978) Int. J. Mech. Sci. 20, 201–206] concept of crack-like notches were successful in 42% of cases; they experienced difficulties dealing with very small notches, and could be improved by using an ElHaddad-type correction factor, giving 87% success. An approach known as ‘crack modelling’ allowed the Smith and Miller method to be used with non-standard stress concentrations, where notch geometry is ill defined; this modification, with the same short-crack correction, had 68% success. It was concluded that the critical-distance approach is more accurate and can be more easily used to analyse components of complex shape, however, the crack modelling approach is sometimes preferable because it can be used with less mesh refinement.

Fracture mechanics analysis of a crack in a residual stress field

Abstract: The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.

Controlling and Testing the Fracture Strength of Silicon on the Mesoscale

Abstract: Strength characterizations and supporting analysis of mesoscale biaxial flexure and radiused hub flexure single-crystal silicon specimens are presented. The Weibull reference strengths of planar biaxial flexure specimens were found to lie in the range 1.2 to 4.6 GPa. The local strength at stress concentrations was obtained by testing radiused hub flexure specimens. For the case of deep reactive ion-etched specimens the strength at fillet radii was found to be significantly lower than that measured on planar specimens. This result prompted the introduction of an additional isotropic etch after the deep reactive ion etch step to recover the strength in such regions. The mechanical test results reported herein have important implications for the development of highly stressed microfabricated structures. The sensitivity of the mechanical strength to etching technique must be accounted for in the structural design cycle, particularly with regard to the selection of fabrication processes. The scatter of data measured in the mechanical tests clearly illustrated the need to use a probabilistic design approach. Weibull statistics may be the appropriate means to describe the data, although a simple two-parameter Weibull model only provides a moderately good fit to the experimental data reported in this study.

Strain relaxation in AlGaN under tensile plane stress

Abstract: Relaxation of tensile strain in AlxGa1−xN layers of different compositions epitaxially grown on GaN/sapphire is investigated. Extended crack channels along 〈211¯0〉 directions are formed if the aluminum content exceeds a critical value, which decreases with increasing layer thickness. This process is found to limit the average strain energy density to a maximum value of 4 J/m2. By calculating the stress distribution between cracks and the strain energy release rate for crack propagation, the relaxed strain as measured by x-ray diffraction is correlated to the crack density, and the onsets of crack channeling and layer decohesion are fitted to a fracture toughness of 9 J/m2. Moreover, the crack opening at the surface is found to linearly increase with the stress. Annealing of samples above the growth temperature introduces additional tensile stress due to the mismatch in thermal expansion coefficients between the layer and substrate. This stress is shown to relieve not only by the formation of additional cr...

Crack propagation in flexural fatigue of concrete

Abstract: In this paper the behavior of concrete subjected to flexural fatigue loading is studied. Notched concrete beams were tested in a three-point bending configuration. Specimens were subjected to quasi-static cyclic and constant amplitude fatigue loading. The cyclic tests were performed by unloading the specimen at different points in the postpeak part of the quasi-static loading response. Low cycle, high amplitude fatigue tests were performed to failure using four different load ranges. The crack mouth opening displacement was continuously monitored throughout the loading process. Crack propagation caused by quasi-static and fatigue loads is described in terms of fracture mechanics. It is shown that the crack propagation in the postpeak part of the quasi-static load response is predicted using the critical value of the mode I stress intensity factor (\IK\DIC\N). The ultimate deformation of the specimen during the fatigue test is compared with that from the quasi-static test; it is demonstrated that the quasi-static deformation is insufficient as a fatigue failure criterion. It is observed that crack growth owing to constant-amplitude fatigue loading comprises two phases: a deceleration stage where there is a decrease in crack growth rate with increasing crack length, followed by an acceleration stage where the rate of crack growth increases at a steady rate. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the peak load of the quasi-static response. Analytical expressions for crack growth in the deceleration and acceleration stages are developed, wherein the expressions for crack growth rate in the deceleration stage are developed using the \iR-curve concept, and the acceleration stage is shown to follow the Paris law. It is observed that the crack length at failure for constant amplitude fatigue loading is comparable to that of the corresponding load in the postpeak part of the quasi-static response. Finally, a fracture-based fatigue failure criterion is proposed.

Linking Riveting Process Parameters to the Fatigue Performance of Riveted Aircraft Structures

Abstract: The onset of widespread fatigue damage in riveted aircraft structure has been linked to sharp gradients of stress arising from contact between rivets and rivet holes. In addition, the mechanics of load transfer in lap joint structure (and resulting damage) is influenced by the through-thickness restraint offered by the installed rivet. Finally, the propagation of fatigue cracks at and around the rivet/hole interface is tied to the residual stress field induced during the riveting process. In light of the influence that rivet installation has on the fatigue performance of riveted joints, the aim was to link details of a quasi-static, squeeze force-controlled riveting process as provided by finite element modeling to the resulting residual stress field in a single-lap joint structure. Supporting experiments provide insight into the inelastic response of the rivet material and validation of the model results. These results from the model reveal both a strong through-thickness gradient in residual stresses and a change in the distribution of residual hoop stress near the rivet/hole interface with squeeze force. Comments are also made regarding the relationship between riveting process parameters and trends in observed fatigue failures of riveted lap joint test articles.

Similarities of stress concentrations in contact at round punches and fatigue at notches : implications to fretting fatigue crack initiation

Abstract: A linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines. The asymptotic forms for the stress fields in the vicinity of a rounded punch-on-flat substrate are derived for both normal and tangential loading, using both analytical and finite element methods. Under the action of the normal load, P, the ensuing contact is of width 2b which includes an initial flat part of width 2a. The asymptotic stress fields for the sharply rounded flat punch contact have certain similarities with the asymptotic stress fields around the tip of a blunt crack. The analysis showed that the maximum tensile stress, which occurs at the contact boundary due to tangential load Q, is proportional to a mode II stress intensity factor of a sharp punch divided by the square root of the additional contact length due to the roundness of the punch, Q/(√(b − a)√πb). The fretting fatigue crack initiation can then be investigated by relating the maximum tensile stress with the fatigue endurance stress. The result is analogous to that of Barsom and McNicol where the notched fatigue endurance stress was correlated with the stress intensity factor and the square root of the notch-tip radius. The proposed methodology establishes a ‘notch analogue’ by making a connection between fretting fatigue at a rounded punch/flat contact and crack initiation at a notch tip and uses fracture mechanics concepts. Conditions of validity of the present model are established both to avoid yielding and to account for the finite thickness of the substrate. The predictions of the model are compared with fretting fatigue experiments on Ti–6Al–4V and shown to be in good agreement.

Linear Elastic Fracture Mechanics for Engineers: Theory and Applications

Abstract: Introduction: Summary References Fracture toughness: Introduction Energy approach to brittle fracture Stress intensity factors Some Mode I stress intensity factor solutions Limitations of the stress intensity factor approach Effects of small scale yielding Slant crack growth in thin sheets Effect of thickness on fracture toughness Effect of notch acuity on fracture toughness R-curves General yielding fracture mechanics Summary References. Plane strain fracture toughness testing: Introduction Specimen types Offset procedure Fatigue precracking Specimen size requirements Klc- Charpy correlations Chevron notch tests Summary References. Fatigue crack growth: Introduction Use of stress intensity factors Fatigue crack growth rate data Mechanisms of fatigue crack growth Threshold for fatigue crack growth Overall fatigue crack growth behaviour Crack closure Short cracks Fatigue crack growth under variable amplitude loading Weighted average stress range Cycle counting Summary References. Fatigue crack growth testing: Introduction Specimen types Specimen size requirement Fatigue precracking Crack path requirement Data reduction The threshold and near threshold crack growth rates Summary References. Fatigue crack paths: Introduction Crack path stability in two dimensions Crack growth from an initial mixed Modes I and II crack Constraints on crack paths in three dimensions Constraints on crack fronts in three dimensions Mode I crack growth in three dimensions Slant crack growth in thin sheets Summary References. Applications: Introduction Modelling of irregular cracks Static failure Constant amplitude fatigue crack growth Variable amplitude fatigue crack growth Proof test logic Leak-before-break Summary References.

Small-crack growth and fatigue life predictions for high-strength aluminium alloys. Part II : Crack closure and fatigue analyses

Abstract: Small-crack effects were investigated in two high-strength aluminium alloys: 7075-T6 bare and LC9cs clad aluminium alloys. Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks. In the experimental program, fatigue and small-crack tests were conducted on single-edge-notch tension (SENT) specimens and large-crack tests were conducted on middle-crack tension specimens under constant-amplitude and Mini-TWIST spectrum loading. A pronounced small-crack effect was observed in both materials, especially for the negative stress ratios. For all loading conditions, most of the fatigue life of the SENT specimens was shown to be crack propagation from initial material defects or from the cladding layer. In the analysis program, three-dimensional finite-element and weight-function methods were used to determine stress intensity factors, and to develop equations for surface and corner cracks at the notch in the SENT specimen. (Part I was on the experimental and fracture mechanics analyses and was published in Fatigue Fract. Engng Mater. Struct. 21, 1289-1306, 1998.) This part focuses on a crack closure and fatigue analysis of the data presented in Part I. A plasticity-induced crack-closure model was used to correlate large-crack growth rate data to develop the baseline effective stress intensity factor range (ΔK eff ) against rate relations for each material, ignoring the large-crack threshold. The model was then used with the ΔK eff rate relation and the stress intensity factors for surface or corner cracks to make fatigue life predictions. The initial defect sizes chosen in the fatigue analyses were similar to those that initiated failure in the specimens. Predicted small-crack growth rates and fatigue lives agreed well with experiments.

Long-life torsion fatigue with normal mean stresses

Abstract: Relatively simple fatigue tests have been performed on two common engineering materials, cast ductile iron and low-carbon steel, using two stress states, cyclic torsion and cyclic torsion with static axial and hoop stresses. Tests were designed to discriminate between normal stress and hydrostatic stress as the most suitable mean stress correction term for high cycle fatigue analysis. Microscopy shows that cracks in low-carbon steel nucleate and grow on maximum shear planes, while for cast iron pre-existing flaws grow on maximum normal stress planes. The data illustrate that tensile normal stress acting on a shear plane significantly reduced fatigue life and is an appropriate input for fatigue analysis of ductile materials. Static normal stresses did not significantly affect the fatigue life for the cast iron because the net mean stress on the maximum normal stress plane was zero. Mean torsion significantly reduced the fatigue strength of the cast iron. A critical plane long-life parameter for nodular iron which accounts for both stress state and mean stress is proposed, and is found to accurately correlate experimental data.

Role of Foreign-Object Damage on Thresholds for High- Cycle Fatigue in Ti-6Al-4V

Abstract: The increasing incidence of military aircraft engine failures that can be traced to high-cycle fatigue (HCF) has prompted a reassessment of the design methodologies for HCF-critical components, such as turbine blades and disks. Because of the high-frequency vibratory loading involved, damagetolerant design methodologies based on a threshold for no crack growth offer a preferred approach. As impact damage from ingested debris is a prime source of HCF-related failures, the current study is focused on the role of such foreign-object damage (FOD) in influencing fatigue crack-growth thresholds and early crack growth of both large and small cracks in a fan blade alloy, Ti-6Al-4V. FOD, which was simulated by the high-velocity (200 to 300 m/s) impact of steel spheres on a flat surface, was found to reduce markedly the fatigue strength, primarily due to earlier crack initiation. This is discussed in terms of four salient factors: (1) the stress concentration associated with the FOD indentation, (2) the presence of small microcracks in the damaged zone, (3) the localized presence of tensile residual hoop stresses at the base and rim of the indent sites, and (4) microstructural damage from FOD-induced plastic deformation. It was found that no crack growth occurred from FOD impact sites in this alloy at ΔK values below ∼ 2.9 MPa √m, i.e., over 50 pct higher than the “closure-free”, worst-case threshold value of ΔK TH = 1.9 MPa √m, defined for large cracks in bimodal Ti-6Al-4V alloys at the highest possible load ratio. It is, therefore, concluded that such worst-case, large fatigue crack thresholds can, thus, be used as a practical lower-bound to FOD-initiated cracking in this alloy.