Showing papers on "Stress concentration published in 1987"

A Progressive Damage Model for Laminated Composites Containing Stress Concentrations

Abstract: A progressive damage model is presented for notched laminated composites subjected to tensile loading. The model is capable of assessing damage in laminates with arbitrary ply-orientations and of predicting the ultimate tensile strength of the notched laminates. The model consists of two parts, namely, the stress analysis and the failure analysis. Stresses and strains in laminates were analyzed on the basis of classical lamination theory with the consideration of material nonlinearity. Damage accumulation in laminates was evaluated by proposed failure criteria combined with a proposed property degradation model. A nonlinear finite element program, based on the model, was developed for lami nates containing a circular hole. Numerical results were compared with the experimental data on laminates containing an open circular hole. An excellent agreement was found be tween the analytical prediction and the experimental data.

The growth of short cracks under cyclic compression

Abstract: The fatigue crack growth behaviour, the length of the arrested cracks and the shape of the crack front were investigated for cyclic compression. Specimens with deep sharp notches were used. The experiments were performed for different load amplitudes and load ratios under conditions of small scale yielding. The material used was ARMCO-iron. The growth rate and length of the arrested cracks were estimated and compared with the experimental results. The crack growth rate of very short cracks is determined by the stress intensity and is independent of the stress ratio. The length of the arrested cracks depends on the stress ratio and is bounded by the size of the cyclic and the monotonic plastic zones.

A model for short fatigue crack propagation with an interpretation of the short‐long crack transition

Abstract: The behaviour of short cracks approaching growth barriers (eg grain boundaries) is considered The crack model of Bilby, Cottrell and Swinden is applied to simulate the blocking of the plastic zone at the grain boundary and to obtain the stress concentration ahead of the crack as it approaches the barrier The idea of the Hall-Petch type relationship that the transmission of slip across grain boundaries needs the previous achievement of a critical stress has been used By making the crack growth rate proportional to the plastic displacement at the root of the crack the deceleration behaviour of short cracks and the existence of non-propagating cracks may be explained The fatigue limit is related to the stress below which a crack growing in a single grain is unable to promote slip in the neighbouring grain The different behaviour in the so-called long crack period has been rationalized in terms of the plastic zone exceeding the grain size For this case, and in the grain completely included within the plastic zone, the Hall-Petch analysis must be applied Hence the maximum back-stress sustained by this grain cannot exceed the yield stress After this point the Bilby et al model is used with uy as a friction stress (ie the Dugdale model) Finally use is made of Fracture Mechanics to correlate the results in the long crack phase

On mechanical stresses at cracks in dielectrics with application to dielectric breakdown

Abstract: The problem of an electric field applied to an isotropic dielectric containing a crack is considered as far as induced distortions and mechanical stresses are concerned. Near‐tip distortions occur when the crack contains a conducting fluid or the surfaces are lined by a conducting layer. Previous treatments of the problem failed to distinguish between material and Maxwell stresses and an unphysical singularity in stress, which was divergent in elastic strain energy, was permitted. In this work, the material stress is identified, and a model is developed in which only physically realistic stress singularities are present. These results are obtained by treating the crack as a narrow but open ellipse rather than a slit crack as in previous models. A conventional crack‐tip stress intensity factor KI characterizes the near‐tip mechanical fields in the results obtained in this paper. The magnitude of KI due to an electrostatic field is deduced for a conducting central through crack in plane strain. The results ...

The effect of residual stresses induced by shot‐peening on fatigue crack propagation in two high strength aluminium alloys

Abstract: — The crack initiation lives of peened specimens of aluminium alloys 7010 and 8090 are shorter than those of unpeened specimens. This is caused by the acceleration of crack initiation due to stress concentration in the rough peened surface, especially at fold-like defects. The crack growth rate in peened specimens is significantly reduced with increasing ΔK, i.e. with increasing crack length. At a crack length of approximately 0.3 mm this trend is reversed and the crack growth rate rapidly increases and attains the same level of crack growth rate as that in unpeened specimens. The point of smallest crack growth rate roughly corresponds to the point of maximum residual stress. The crack growth rate in a peened specimen has been modelled by assuming the effect of residual stress reduces to the equivalent stress ratio. The predicted results agree well with the experimental data.

The relationship between toughness and microstructure in Fe-high Mn binary alloys

Abstract: The influence of Mn content on the ductile-brittle transition in 16 to 36 wt pct Mn steels was investigated and interpreted in light of the evolving microstructure. It was found that when hcp e martensite is present in the as-quenched condition or forms during deformation, it lowers the toughness. In 25Mn steel, the stress concentrations at e plate intersections result in the formation of planar void sheets along the {111}γ planes. The deformation-induced α’ martensite in 16 to 20 pct Mn alloys enhances the toughness, but leads to a ductile-to-brittle transition at low temperatures that is due to the intrusion of an intergranular fracture mode. Binary alloys with greater than 31 pct Mn also fracture in an intergranular mode at 77 K although the impact energy remains quite high. Auger spectroscopy of the fracture surfaces shows no evidence of significant impurity segregation, which suggests the importance of slip heterogeneity in controlling intergranular fracture in these alloys.

Mechanisms of fatigue fracture in short glass fibre-reinforced polymers

Abstract: Fatigue-crack profiles and fracture surfaces of several short glass fibre-reinforced polymers were examined to gain insight into the mechanisms of cyclic damage and fatigue-crack propagation in these materials. Several distinctly different features were noted between fracture surfaces generated by stable fatigue crack growth and those produced by monotonic or unstable fracture. Among the most significant differences were the higher degree of single and multiple fibre fracture generally observed on stable fatigue-crack growth fracture surfaces, and the variations in the interfacial failure site in well-bonded systems. While the former effect is attributed to the occurrence of crack closure and the build-up of compressive stresses in the crack-tip damage zone during unloading, the differences in the interfacial failure mode are related to the adverse effect of fatigue loading on the interfacial bond strength. No features could be identified that would allow a quantitative correlation between the applied stress intensity factor level or the crack growth rates and characteristic fracture surface details.

Fatigue crack growth in MAR-M200 single crystals

Abstract: The effects of crystallographic orientation on the fatigue crack growth behavior of MAR-M200* single crystals were examined. Using compact-tension specimens tested at 20 Hz, fatigue crack growth rates were determined at ambient temperature at minimum stress to maximum stress ratios,R, of 0.1 and 0.5. In most cases, subcritical crack growth occurred either along a single {111} slip plane or a combination of {111} planes. The mode of cracking was generally mixed and contained mode I, II, and III components. Considerable crack deflection and branching were also observed. Some fracture surfaces were found to contain a significant amount of asperities and, in some specimens, black debris. Based on Auger spectroscopic analyses and the fracture surface appearance, it appears that the black debris represented oxides formed due to rubbing of the fracture surfaces. Using stress intensity solutions obtained based on the Boundary-Integral-Equation technique, an effective ΔK was successfully used for correlating the crack growth rate data. The results indicate that the effect of crystallographic orientation on crack growth rate can be explained on the basis of crack deflection, branching, and roughness-induced crack closure.

An analysis of crack tip shielding in aluminum alloy 2124: a comparison of large, small, through-thickness and surface fatigue cracks

Abstract: — The development of crack closure during the plane strain extension of large and small fatigue cracks has been investigated in a 2124 aluminum alloy using both experimental and numerical procedures. Specifically, the growth rate and crack closure behavior of long (∼17–38 mm) cracks, through-thickness physically-short (50–400 μm) cracks, and naturally-occurring microstructurally-small (2–400 μm) surface cracks have been examined experimentally from threshold levels to instability (over the range 10–12–10–6m/cycle). Results are compared with those predicted numerically using an elastic-plastic finite element analysis of fatigue crack advance and closure under both plane stress and plane strain conditions. It is shown that both the short through-thickness and small surface cracks propagate below the long crack threshold at rates considerably in excess of long cracks, consistent with the reduced levels of closure developed in their limited wake. Numerical analysis, however, is found consistently to underpredict the magnitude of crack closure for both large and small cracks, particularly at near-threshold levels; an observation attributed to the fact that the numerical procedures can only model contributions from cyclic plasticity, whereas in reality significant additional closure arises from the wedging action of fracture surface asperities and corrosion debris. Although such shielding mechanisms are considered to provide a prominent mechanism for differences in the growth rate behavior of large and small cracks, other factors such as the nature of the stress and strain singularity and the extent of local plasticity are shown to play an important role.

The Shadow Optical Method of Caustics

Abstract: The shadow optical method of caustics is a relatively new experimental technique in stress strain analysis. It was originally introduced by Manogg (1964) for investigating crack tip stress intensifications. The method is sensitive to stress gradients and therefore is an appropriate tool for quantifying stress concentration problems. The technique was extended later by Theocaris (1971–1981), Rosakis (1982, 1983) and the author and his colleagues (1976–1986) to different conditions of loading, material behavior, in static as well as dynamic situations. This summarizing article reviews the basic physical principles and the mathematical analyses of the method and gives applications to various problems of practical relevance.

The influence of crack length on fatigue crack growth in deep sharp notches

Abstract: The fatigue crack growth rateda/dN of short cracks and the transition to long crack behavior were investigated for ARMCO-iron. Deep notched specimens with very small notch radius (between 1.5 and 4 μm) were used. The experiments were performed with constant stress intensity ranges for various stress ratios; the fatigue crack growth rate was measured as a function of the crack length. The results permit a discussion of the mechanisms responsible for the different behavior of “short” and “long” cracks.

The effects of crack surface friction and roughness on crack tip stress fields

Abstract: A model is presented which can be used to incorporate the effects of friction and tortuosity along crack surfaces through a constitutive law applied to the interface between opposing crack surfaces. The problem of a crack with a saw-tooth surface in an infinite medium subjected to a far-field shear stress is solved and the ratios of mode I stress intensity to mode II stress intensity are calculated for various coefficients of friction and material properties. The results show that tortuosity and friction lead to an increase in fracture loads and alter the direction of crack propagation.

Constitutive behavior of a microcracking brittle solid in cyclic compression

Abstract: A constitutive formulation is presented to determine the “driving force” for Mode I fatigue crack growth in notched plates of brittle solids stressed in uniaxial cyclic compression. For the particular case of a microcracking medium, it is demonstrated that residual tensile stresses are induced ahead of the notch during unloading from the maximum far-field compressive stress. We propose that it is this region of residual tensile stresses at the notch-tip which promotes fatigue crack growth in ceramics along the notch plane in a direction normal to the compression axis. The predictions of the analysis are compared with new experimental results on compression fatigue in brittle solids. Specifically, it is shown that the numerical estimates of the near-tip tensile zone size for microcracking ceramics compare favorably with the experimentally measured distance of stable Mode I fatigue crack growth after the first compression cycle. Experimental information on the threshold stress for microcracking, transition stress for the inducement of residual tension during unloading, and the effect of mean stress on fracture, as well as direct observations of microcracks and crack growth in compression fatigue, corroborate the assumptions and implications of the analysis.

Dynamic Fatigue of Treated High‐Silica Glass: Explanation by Crack Tip Blunting

Abstract: In previous papers, it was shown that when abraded high-silica glass is soaked in hot water or annealed in air, its crack tip becomes blunt. The dynamic fatigue characteristics in various liquids of high-silica glass with different treatments were examined. The stress rate dependence of fracture strength was determined for freshly abraded samples and for abraded and soaked (in hot water) or heat-treated samples, in water, hydrazine, formamide, and acetonitrile. The stress rate susceptibility of the fracture strength was represented by the commonly used n value. Freshly abraded samples exhibited approximately the same low n values for all the liquids, which is consistent with the slope of the slow crack growth data. Treated samples, on the other hand, showed a slightly larger n value in water and extremely large n values in nonaqueous liquids. When the crack tip is sharp, only slow crack growth is involved in the fatigue. When the crack tip is blunt, crack initiation is involved in addition to the crack growth. The equation of dynamic fatigue based upon slow crack growth was modified to incorporate this effect of crack initiation and was applied to the present experimental results. The analysis showed that the crack initiation stress is stress rate dependent in water and is stress rate independent in nonaqueous liquids. This conclusion was supported by the crack initiation behavior observed using the microhardness indenter.

role of crack tip shielding in the initiation and growth of long and small fatigue cracks in composite microstructures

Abstract: The role of crack tip shielding in retarding the initiation and growth of fatigue cracks has been examined in metallic composite microstructures (consisting of hard and soft phases), with the objective of achieving maximum resistance to fatigue. Specifically, duplex ferritic-martensitic structures have been developed in AISI 1008 and 1015 mild steels to promote shielding without loss in strength. The shielding is developed primarily from crack deflection and resultant crack closure, such that unusually high long crack propagation resistance is obtained. It is found that the fatigue threshold ΔK TH in AISI 1008 can be increased by more than 100 Pct to over 20 MPa Vm, without sacrifice in strength, representing the highest ambient temperature threshold reported for a metallic alloy to date. Similar but smaller increases are found in AISI 1015. The effect of the dual-phase microstructures on crack initiation and small crack (10 to 1000 ώm) growth, however, is markedly different, characteristic of behavior influenced by the mutual comPctition of intrinsic and extrinsic (shielding) “toughening” mechanisms. Accordingly, the composite microstructures which appear to show the highest resistance to the growth of long cracks, show the lowest resistance to crack initiation and small crack growth. In general, dual-phase steels are found to display remarkable fatigue properties, with fatigue limits as high as 58 Pct of the tensile strengths and fatigue thresholds in the range of 13 to 20 MPaVm.

Elevated-temperature fatigue crack growth

Abstract: The fatigue crack growth behavior of MAR-M200 single crystals was examined at 982 °C. Using tubular specimens, fatigue crack growth rates were determined as functions of crystallographic orientation and the stress state by varying the applied shear stress range-to-normal stress range ratio. Neither crystallographic orientation nor stress state was found to have a significant effect on crack growth rate when correlated with an effective ΔK which accounted for mixed-mode loading and elastic anisotropy. For both uniaxial and multiaxial fatigue, crack growth generally occurred normal to the principal stress direction and in a direction along which ΔK II vanished. Consequently, the effective ΔK was reduced to ΔKI and the rate of propagation was controlled by ΔK I only. The through-thickness fatigue cracks were generally noncrystallographic with fracture surfaces exhibiting striations in the [010], [011], and [111] crystals, but striation-covered ridges in the [211] specimen. These fracture modes are contrasted to crystallographic cracking along slip bands observed at ambient temperature. The difference in cracking behavior at 25 and 982 °C is explained on the basis of the propensity for homogeneous, multiple slip at the crack tip at 982 °C. The overall fracture mechanism is discussed in conjunction with Koss and Chan’s coplanar slip model.

High-strength filter with improved fatigue rating

Abstract: A high-strength spin-on filter (10) of improved fatigue strength comprises a cylindrical housing (12), a unitary cover (28) and an internal filter element assembly (18). The open end of the housing (12) is folded inwardly over the periphery of the cover (28) and into deformable engagement with radial projections (54) thereon to secure the cover and housing against both relative rotation and separation without stress concentrations that would otherwise decrease fatigue life of the filter (10) in high-pressure pulsatile hydraulic systems.

Low stress intensity fatique crack growth in 2024-T3 and T351

Abstract: Constant amplitude fatigue crack growth properties of five batches of aluminium alloy 2024 in the naturally aged T3 and T351 conditions are compared. Particular attention is paid to crack growth curve transitions in the near-threshold regime. These transitions correspond to monotonie or cyclic plane strain plastic zone dimensions becoming equal to characteristic microstructural dimensions. Changes in fracture surface topography are associated with the transitions also. From the observations an explanation of the shape of the low stress intensity fatigue crack growth curve and the transitions is given.

Fatigue life prediction in bending from axial fatigue information

Abstract: Bending fatigue in the low cyclic life range differs from axial fatigue due to the plastic flow which alters the linear stress-strain relation normally used to determine the nominal stresses. An approach is presented to take into account the plastic flow in calculating nominal bending stress (S sub bending) based on true surface stress. These functions are derived in closed form for rectangular and circular cross sections. The nominal bending stress and the axial fatigue stress are plotted as a function of life (N sub S) and these curves are shown for several materials of engineering interest.

Stress and field dependence of critical current in Ba2YCu3O7−δ superconductors

Abstract: Superconductors in practical applications are subjected to large stresses such as caused by coil winding, thermal contraction, and the Lorentz force generated by magnetic field. In this letter, the stress and field dependence of the critical current density ( JC) of the high‐temperature superconductor (Ba2YCu3O7−δ) has been investigated. It has been found that the JC value is essentially independent of the applied stress, tensile or compressive, up to the level of fracture stress. This observation suggests that the grain boundary stress concentration is not likely to be one of the major causes of the ‘‘weak links’’ responsible for the relatively poor JC values in polycrystalline Ba2YCu3O7−δ. The rapid deterioration of JC in applied magnetic field does not seem to be affected by the co‐presence of applied stress.

J-shaped stress/strain curves and crack resistance of biological materials

Abstract: The influence of the stress/strain curve shape on the cracking of a brittle elastic material is analysed in terms of the energy balance theory of fracture mechanics. Both r-shaped and J-shaped elastic curves are investigated. For some cracking tests, for example the trouser tear and lubricated cutting tests, the shape of the stress/strain curve is found to have little effect on the crack extension force; this is determined mainly by the fracture surface energy of the material. However, in other tests such as tension, the shape of the stress/strain curve does influence the fracture stress, but not by a large amount when compared with the effect of reinforcement. Whether an r-shaped or J-shaped curve leads to a higher fracture stress depends on such factors as the fracture energy and the size of the pre-existing crack. It thus appears that no general statement can be made about the effect of the shape of the stress/strain curve upon the crack resistance of materials, contrary to views expressed previously in the literature.

fracture behavior of intercritically treated complex structure in medium-carbon 6Ni steel

Abstract: The fracture behavior of complex structure in 6Ni-0.3C steel in which the intercritical treatment in the range of 630 °C to 670 °C from the initial microstructure of coarse-grained martensite can control the amount and distribution of fibrous martensite has been investigated. The hardness increases, but the impact toughness decreases with increasing the temperature and time of the intercritical treatment. As the amount of martensite increases and the martensite coarsens with increasing the temperature and time, the fracture along the prior austenite grain boundaries becomes predominant and the fracture mode is changed from dimple type to low energy tear type. This fracture behavior is attributed to the increase in stress concentration susceptibility at the ferrite-coarser martensite interfaces along the prior austenite grain boundaries.

Fretting fatigue analysis using fracture mechanics.

Abstract: Fretting fatigue cracks appear very early in the fatigue life of metals. Fretting fatigue life is dominated by the propagation process of small cracks. Characteristics of fretting fatigue cracks are analysed using stress intensity factors which are obtained at the tip of cracks growing from contact edges. Stress intensity factors are calculated using contact pressure and tangential stress distributions across contact surfaces. Contact pressure and tangential stress distributions are anaysed using the Finite Element Method. Fretting fatigue limits are estimated by comparing the above mentioned calculated results of stress intensity factor ranges with the threshold stress intensity factor range of the material. These calculated results are compared with experimental results of fretting fatigue tests.