Decrease In Stress Intensity Factor Research Articles

Fracture mechanics approach to penetration of surface crevasses on glaciers

In linear elastic fracture mechanics, the stress intensity factor is used to describe elastic stresses near the tip of a crack. Crack growth occurs when the stress intensity factor is larger than a critical value, the fracture toughness, which is a material parameter that applies to cracks of any size. For surface crevasses on glaciers, the net stress intensity factor can be calculated by superimposing the effects of a tensile stress, the weight of the ice, and water pressure if the crevasse is filled with water. The analysis is applied to individual and multiple crevasses to investigate the important factors determining crevasse depth. The model indicates that a single crevasse can only exist if the tensile stress is larger than 30–80 kPa, depending on the fracture toughness of glacier ice. Multiple crevasses result in a decrease in stress intensity factor for any crevasse, thus reducing their depth (all other factors being equal). Consequently, in a field of crevasses, a larger tensile stress is needed compared to an individual crevasse, to allow crevasse formation. Further, a water-filled crevasse or field of crevasses can reach the bottom of a glacier provided that the water level is about 15 m below the surface, or higher, and the tensile stress is larger than ∼150 kPa. Compared to earlier studies, it is shown that accounting for the finite thickness of the glacier has a small effect on the calculated stress intensity factor only if the ratio of crevasse depth to ice thickness is larger than ∼0.3. However, such deep crevasses can only exist if filled with water, in which case the crevasse may penetrate the ice completely and the small error introduced by approximating the glacier as a semi-infinite plane is unimportant. It is more important to account for the lower density of the upper firn layers: this effect increases the maximum depth of crevasses by almost a factor of two compared to the solution of Weertman (1973) [Weertman, J., 1973. Can a water-filled crevasse reach the bottom surface of a glacier? IASH Publ. 95, 139–145.].

Determination of stress intensity factor for embedded elliptical crack in turbine rotor

The stress intensity factor (SIF) for an embedded elliptical crack in a turbine rotor and the thermal shock stress intensity factor for a semi-elliptical surface crack in a finite plate are determined by means of Vainshtok's weight function method. The solution for the semi-elliptical surface crack is in good agreement with the previous one. The value of the SIF for the embedded elliptical crack in the turbine rotor under centrifugal and thermal loading is larger at the crack contour near the inner radius surface and almost constant at the opposite crack contour. The SIF decreases by increasing the crack ratio, and the distance between the inner radius surface and the crack center.

Dependence of the threshold stress intensity factor on hydrogen concentration during delayed hydride cracking in zirconium alloys

The theoretical work on the criterion for fracture initiation at hydrides at sharp crack tips in zirconium alloys is extended to include the effect of hydrogen concentration in solid solution on the threshold stress intensity factor, K IH. The analysis shows that the crack-tip hydride can only grow to a certain maximum length which depends on hydrogen concentration in solution and the stress intensity factor. Analytical and numerical solutions of the critical hydride length for fracture show that it increases as temperature increases and as the stress intensity factor decreases. These results are used to develop the relationship between the hydrogen concentration in solution and K IH. This shows that K IH increases as the hydrogen concentration in solution decreases. The variation of the crack-tip critical hydride length with temperature, yield strength and applied K I is also derived and the results compared with striation spacing data obtained from fracture surfaces.

耐応力腐食割れ性に優れた高力Ａｌ‐Ｚｎ‐Ｍｇ‐Ｃｕ‐Ｌａ系押出合金の疲労き裂伝ぱ特性

Fatigue crack growth tests on an extruded Al-8wt.% Zn-2.5wt.% Mg-1.2wt.% Cu-4wt.% La alloy were carried out using CT specimens (TL orientation). Crack closure was examined by the unloading elastic compliance technique. The main results are as follows;(1) The effect of stress ratio was observed on the crack growth rate, da/dN, vs. stress intensity factor range, ΔK, diagram. A higher stress ratio gives a faster crack growth rate at same ΔK.(2) Crack closure was observed under the stress ratio=0.1, and its degree was increasing with decreasing stress intensity factor range. On the other hand, it was not at the stress ratio=0.5.(3) The effect of stress ratio on the second region of da/dN vs. ΔK diagram disappeared when the effective stress intesity factor range, ΔKeff, was used instead ofΔK.(4) The second region of da/dN vs. ΔKeff diagram for the extruded Al-8wt.% Zn-2.5wt.% Mg-1.2wt.% Cu-4wt.% La alloy was in agreement with that for the commercial 7075T6 alloy. So, the fatigue crack growth resistance of the extruded Al-8wt.% Zn-2.5wt.% Mg-1.2wt.% Cu-4wt.% La alloy is nearly equal to that of the commercial 7075T6 alloy.

Analysis of crack-dislocation interaction: crack closure, crack opening

The decrease in stress intensity factor, expected from dislocation emission at a crack tip, can be achieved either through a change in crack tip radius (blunting) or through a crack closure induced by the dislocation (shielding) opposite to the opening imposed by the external stress field. So an apparent contradiction arises between the shielding concept and the crack opening displacement (COD) concept. In this paper a relation linking the COD to the stress intensity factor K is demostrated. The explicit crack opening displacements induced by a dislocation are derived from this equation. Opposite to modes II and III for which positive or negative displacement (or K) are allowed, physical limitations in mode I lead to changes in crack length: full or partial closure can be noticed. Special attention is paid to the latter case arising from dislocations whose Burgers' vectors are parallel to the crack plane, dislocations which have been observed experimentally under mode I loading: it is shown that these dislocations can account for both the crack shielding and the crack opening. The evaluation of the closed crack length with the applied K is discussed and the minimum stress intensity factor for crack opening as well.

Cracked composite laminates least prone to delamination

In [( ± θ ) n 2 /(90°) n 1 /( ǂ θ ) n 2 ] fibre-reinforced composites, the outer (± θ ) n 2 sublaminates are known to act as crack arrestors, i. e. to reduce the stress intensity factors at the tips of a crack in the central (90°) n 1 layer in all three modes of loading. The degree of reduction depends on the stiffness of the plies, the ply angle θ and the thickness of the outer sublaminates. However, although the stress intensity factor decreases, the crack-induced largest interfacial principal tensile stress increases. The situation is particularly severe under transverse mode II loading, inevitably resulting in interfacial delamination. The aim of this paper is to choose the design variables of the laminate, namely the ply angle θ , relative ply stiffness and thickness, in such a way as to minimize the stress intensity factor at a crack tip in the (90°) n 1 layer without exceeding the interfacial bond strength. A constraint is also placed on the minimum flexural stiffness of the laminate. An alternative optimization problem in which the largest interfacial principal tensile stress is minimized subject to a limit on the stress intensity factor is also formulated and solved. The above optimization problem is solved in two stages. First, an analysis of the non-homogeneous, anisotropic medium containing a flaw is performed within the bounds of the classical lamination theory and fracture mechanics. This allows development of mathematical expressions relating the stress intensity factor in the central (90°) n 1 layer and the interfacial tensile stress to the sublaminate thickness and stiffness and the ply angle θ . These expressions are highly complicated, precluding a completely analytical approach to the calculation of design sensitivities. In the next stage the optimization problem is reduced to a nonlinear mathematical programming one, whose solution is attempted by several techniques. The sensitivities with respect to the design variables required in these techniques are calculated by a mixed analytical/numerical approach.

Growth of shear lips in surface cracked shafts subjected to fatigue loading

Shear lip growth was monitored on the fracture surfaces of notched and plain surface cracked shafts subjected to constant amplitude axial fatigue loads. Results showed that shear lip growth in the plain specimens was slightly slower than predictions based on equations derived from through cracked plate data. This is in contrast to shear lip growth in the notched shafts, which was much slower than predicted. The reduced rate of shear lip growth in the shaft geometries is attributed to the decreasing stress intensity factor along the surface crack front and the tensile circumferential stress in the notch shafts. It was also seen that the formation of shear lips had a significant effect on the shape of the crack front. Overall specimen fatigue life, however, was relatively unaffected by shear lip growth.

The influence of applied stress, crack length, and stress intensity factor on crack closure

Experimental and analytical evidence for the influence of applied stress, crack length, and stress intensity factor on crack closure is critically compared and evaluated. Fatigue crack opening behaviors are broadly catalogued into three classes. Class I comprises “near-threshold” behavior, where crack closure levels increase with decreasing stress intensity factor. In class II, the “stable” regime, the crack opening level is independent of the stress intensity factor and crack length but is influenced by the applied stress. Class III is characterized by the loss of elastic constraint accompanying extensive yielding at the crack tip or in the remaining ligament, especially with further crack growth. Here, the crack opening level decreases with increasing crack length until little or no closure occurs. These three different classes of closure behavior are extensively illustrated with both experimental data and the results of numerical closure simulations, particularly original finite element (FE) analyses. No single relationship between crack opening levels and the fundamental fatigue parameters is found to hold universally, due to the wide range of mechanisms which cause or influence closure.

On the mechanism of fatigue crack growth in silicon nitride

The mechanism of fatigue crack growth in silicon nitride under the experimental conditions utilized is found to be of a cyclic nature, as contrasted to a form of static fatigue observed in some other ceramic systems. Conventional methods of analysis of the rate of fatigue crack growth in terms of ΔKeff are not applicable, because the results of the experimental portion of this investigation show that ΔKeff can decrease as the rate of fatigue crack growth increases. A mechanism which involves the formation of microcracks caused by a wedge effect which develops during the unloading portion of a cycle is discussed and evaluated. The wedge effect results from crack closure, which arises due to the roughness of the intergranular fracture surface as well as to debris trapped between the opposing fracture surfaces. In the proposed mechanism, the extent of crack advance per cycle is limited because of the decrease in stress intensity factor with crack advance in a given cycle associated with the wedge effect. The quantitative results of a semiempirical analysis of tests carried out in either air or vacuum are in agreement with some unusual experimental trends.

Transformation toughening in ceramic with martensites or micro-cracks

In certain ceramics, the high stress in the tip of a macroscopic crack induces martensitic type transformation of the second phase particles (e.g. Zirconia, ZrO 2). The transformation changes the near-tip stress by decreasing the net stress intensity factor and the toughness of the material is thereby enhanced. To evaluate the decrease of the stress intensity factor, one needs to know the distribution of the transformation strain around the crack tip. Therefore, an incremental analysis of plasticity, which takes into account the microstructural properties and mechanism of the particle transformation, is generally required. In this paper, we present a method of calculating the decrease of stress intensity factor without considering the microstructural details or performing an incremental analysis. Regardless of the history of loading and unloading, the current crack opening displacement is all the information needed for the calculation. It is proven that under a given distribution of crack opening displacement, there are infinite numbers of possible configurations of transformation zone with transformation strain inside. Identifying the actual transformation strain and transformation zone is impossible unless additional information is provided. However, all these transformation strains inside the corresponding transformation zones induce the same decrease of stress intensity factor. In this sense, they are all equivalent. If we can obtain any of these transformation strains with the corresponding transformation zone, the decrease of stress intensity factor is then determined. The problem is formulated as a system of integral equations of the first kind with transformation strain as unknown and crack opening displacement as input data. The regularization method is employed to obtain a stable solution of these ill-posed integral equations. The stress intensity factor is then computed by using Bueckner's weight function.

Thermal shock fracture experiments on large size plates of A533-B steel

The paper gives a complete report on a five-year research program concerning the fracture behaviour of the pressure vessel steel A533-B under thermal shock conditions. Five tests on 140-mm thick plates carrying a surface through-thickness crack were performed with different material conditions and thermal histories. The results confirmed the applicability of the Linear Elastic Fracture Mechanics approach and of the arrest toughness criterion. Moreover, the confidence limits achievable by a material characterization procedure based on Charpy-V tests were assessed. The prevention of crack initiation under a decreasing stress intensity factor and crack-tip temperature (‘simple’ warm pre-stressing effect) was largely confirmed, while reinitiation prevention after thermal-mechanical histories including complete unloading could not be demonstrated.

Considerations of grain orientation and work hardening on short-fatigue-crack modelling: de los Rios, E.R. and Navarro, A. Philos. Mag. A Mar. 1990 61, (3), 435–449

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/dn, and the stress intensity threshold levels, ΔKth were measured over the range of stress ratio, R, from −1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔKth was well represented as |ΔKth/2|R=(1−R)γ|ΔKth/2|R=0; and the propagation rate, as da/dn = A(1−R)γm[(ΔK/2)m − {(1 − R)γ|ΔKth/2|R=0}m] for −1≦R≦0.33 or da/dn = A(1 − 0.33)−γm [(ΔK/2)m {(1 − R)γ |ΔKth/2|R=0}m] for 0.33 < ≦ 0.8.

Evaluation of actual fatigue stress by using striation spacing and hardness: Ishida, S., Tokumasu, M., Nakasa, K. and Ishihara, H. J. Soc. Mater. Sci., Japan Jan. 1990 39, (436), 63–69 (in Japanese)

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/dn, and the stress intensity threshold levels, ΔKth were measured over the range of stress ratio, R, from −1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔKth was well represented as |ΔKth/2|R=(1−R)γ|ΔKth/2|R=0; and the propagation rate, as da/dn = A(1−R)γm[(ΔK/2)m − {(1 − R)γ|ΔKth/2|R=0}m] for −1≦R≦0.33 or da/dn = A(1 − 0.33)−γm [(ΔK/2)m {(1 − R)γ |ΔKth/2|R=0}m] for 0.33 < ≦ 0.8.

FATSYS, a computer controlled system for fatigue crack growth data collection using an Amsler Vibrophore

A system of hardware and software developed for collecting fatigue crack growth data from an Amsler Vibrophore fatigue machine is described. The system allows testing at constant, increasing and decreasing stress intensity factor ranges ( ΔK), and it generally complies with the proposed ASTM standards on fatigue crack growth testing. The system has proven to be extremely beneficial particularly for work at growth rates approaching threshold, where manual methods are tedious and time consuming.

THERMAL SHOCK FRACTURE IN AN EDGE-CRACKED PLATE

Abstract In this paper the transient thermal stress problem for an elastic strip with an edge crack is investigated. The elastic medium is assumed to be insulated on one face and cooled by surface convection on the face contaning the edge crack. Using the principle of superposition, the formulation results in a mixed boundary value problem, with the thermal stresses calculated from the thermoelasticity solution for an uncracked strip utilized as the necessary crack surface tractions. The resulting singular integral equation is of a well-known type and is solved numerically. In this paper, inertia effects are assumed negligible and possible temperature dependence of thermoelastic constants is not considered. The numerical results presented, include the stress intensity factor as a function of nondimensional time (Fourier number) and crack length, for various values of the dimensionless Biot number. The temperature distribution and the thermal stresses in the uncracked strip are also included. The time lag, which occurs between the time at which the stress on the surface of the strip is a maximum and the time when a maximum occurs in the stress intensity factor, is clearly shown to be a function of the Biot number for any given ratio of crack length to strip thickness. A result of particular interest is the degree with which the maximum stress intensity factor decreases, as a function of crack length, for decreasing values of the Biot number.

Influence of stress ratio on the threshold level for fatigue crack propagation in high strength steels

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/ dn, and the stress intensity threshold levels, ΔK th were measured over the range of stress ratio, R, from −1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔK th was well represented as | ΔK th /2| R =(1− R) γ| ΔK th /2| R=0 ; and the propagation rate, as d a/d n = A(1− R) γm [( ΔK/2) m − {(1 − R) γ | ΔK th /2| R=0} m ] for −1≦ R≦0.33 or d a/d n = A(1 − 0.33) − γm [( ΔK/2) m {(1 − R) γ | ΔK th /2| R=0} m ] for 0.33 < ≦ 0.8.

Effect of cryogenic temperatures on mechanical properties of experimental alloys of the AMg6N type

1. The mechanical properties of AMg6N alloys and welded joints vary mainly with the testing temperature. When the temperature is lowered to −269° the strength characteristics increase, the toughness decreases, and the ductility remains at practically the same level as at standard temperature, reaching a maximum value at the temperature of liquid nitrogen. The ultimate tensile strength and the yield strength of the base metal increase 40% in this case, and those of welded joints by 20%. The toughness decreases by a factor of three to four. 2. For all the alloys investigated the stress intensity factor decreases (10–15%) in tests of samples with a sharp notch in the temperature range from +20 to −269°. 3. The elevated notch sensitivity of the base metal and welded joints and the sharp reduction of the toughness of AMg6N alloys cooled to the temperature of liquid helium can be taken as an indication that the metal is transformed to the quasibrittle condition. 4. For alloys of high purity the ultimate tensile strength of the base metal and of welded joints is 5–7 kg/mm2 higher (and the ductility and toughness are 1.5–2 times higher) than that of standard alloy AMg6N.

Interaction of a rapidly moving crack with a small hole in polymethylmethacrylate

The behaviour of a rapidly moving crack around a small hole in p.m.m.a. (polymethylmethacrylate) has been investigated, by the use of ultra-high-speed photographic techniques, to measure the changes in dynamic stressintensity factor and crack velocity. Cracks were initiated by explosively driven wedge impact, and penetrated holes of diameters of 1/16 in (1.56 mm) and 1/8 in (3.12 mm). The cracks propagating after the hole show a higher velocity than those prior to the hole, though the dynamic stress-intensity factor decreases. There is no general relation between the dynamic stress-intensity factor and the surface roughness for the higher-velocity crack.