Electric Current-Induced Stresses at the Crack Tip in Conductors

The electromagnetic and thermal effects on the stress distribution around the crack tip in conducting materials due to electric current are investigated. Emphases are placed on quantifying the crack growth behavior affected by the interplay between these effects. A two-dimensional finite element analysis is conducted to examine the coupled problems. The results show that the compressive stress state around the crack tip plays a decisive role in preventing the crack from further growth. The resulting normal stress in front of the crack tip caused by the Joule heat generation tends to suppress the crack growth, while the stress induced by the electromagnetic forces provides a tensile normal stress with smaller magnitude in the vicinity of the crack tip, hence promotes the crack growth. Favorable agreements between numerical analysis results and existing experimental results are achieved. By utilizing these phenomena, the electric current may be used to actively control the damage propagation, hence catastrophic failure can be prevented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Calculation of crack tip phase transformation zones with the weight function method

Stabilized Zirconia ceramics can undergo a stress-induced tetragonal-to-monoclinic phase transformation. This way, a transformation zone with compressive stresses develops around crack tips, leading to an increase in fracture toughness. The increase in fracture toughness depends on the size of the transformation zone. Therefore, the ability to compute the phase transformation zone at a crack tip is crucial to determine the transformation toughening due to phase transformation. In the case of subcritical phase transformation, the crack tip phase transformation zone has been calculated using the finite element method. In some Zirconia ceramics, such as ceria-stabilized TZP Zirconia ceramics, an autocatalytic phase transformation takes place, leading to large, elongated transformation zones. As this supercritical phase transformation cannot be computed with finite elements, several methods for investigating supercritical phase transformation have been developed. In this paper, a method based on the weight function method will be described.     

Fatigue crack growth testing at negative stress ratios: discussion on the comparability of testing results

It is an accepted fact in fatigue community that compressive loads contribute to fatigue crack growth. Evidences range from fatigue crack growth under fully compressive loads to effects of compressive underloads to negative stress ratio loading. Because the crack closes under compression and the crack flanks transmit compressive stresses, the loading situation is completely different to those of tensile loading. The present paper addresses the comparability of crack growth testing procedures at negative stress ratios. It reveals that compressive loading at the crack tip differs in different specimens for an equal maximum stress intensity factor K_max and negative stress ratio R. Furthermore, the crack length can significantly influence the loading conditions at the crack tip for tension–compression loading. Depending on the specimen type and crack length, a negative force ratio may lead to a change of algebraic sign of the stresses at the crack tip or not. As a consequence, the comparability of available literature results for R ≤ 0 tests is not ensured. Proposals to improve the comparability of tension–compression crack growth testing will be given.     

CRACK GROWTH ARRESTING PROPERTY OF A HOLE AND BRINELL-TYPE DIMPLE

Abstract— Fatigue tests of sheet specimens having a central crack were carried out to study the effects of holes and dimples on the arrest of fatigue crack propagation. Two holes were drilled at some distance from, and at either side of, a crack tip, and the dimple of a certain diameter was introduced by pressing steel balls in the specimen at a crack tip. Results showed that the two holes produced an increase in crack propagation life (about 3 times) when the holes were drilled at an appropriate distance. On the other hand, the effect of a dimple on the fatigue strength was remarkably large, i.e. in the greatest case a 2.2 times increase in the fatigue endurance limit of cracked specimens and about a 50 times increase in the crack propagation life, at stresses above the fatigue limit. The main reason for the remarkable recovery of fatigue strength was the residual compressive stresses produced by the dimple. To evaluate the effect of residual compressive stresses on the da/dN vs. δK relation, a simple model is proposed. By using this model, the effect of residual stresses on crack propagation can be estimated quantitatively. Furthermore, the fatigue life of dimpled specimens was estimated based on the model.     

金属构件中裂纹的电磁热效应局部跨越止裂

采用理论分析和实验研究的方法讨论了应用电磁热效应对金属构件中裂纹实施局部跨越止裂的技术。在带有裂纹的模具钢构件上取样,对裂纹处通过点电极进行局部跨越脉冲放电。实验研究和理论分析结果均表明:跨越止裂可以使导体中局部裂纹在裂纹尖端处很小的范围内熔化形成微小的焊口,实现了钝化止裂,遏制了裂纹的扩展。通过对止裂后裂尖的金相组织观察和力学性能测试发现:超细化的条状马氏体、极少量残余奥氏体和细颗粒碳化物的出现极大地提高了裂纹尖端的硬度、韧性和耐磨性。     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

Influence of macroscopic residual stress fields on fatigue crack growth measurement in SiC particulate reinforced 8090 aluminium alloy

Abstract

The effect of residual stresses, induced by cold water quenching, on the morphology of fatigue crack fronts has been investigated in a powder metallurgy 8090 aluminium alloy, with and without reinforcement in the form of 20 wt-%SiC particles. Residual stress measurements reveal that the surface compressive stresses developed in these materials are significantly greater than in conventional metallurgy ingot 8090, because surface yielding occurs on quenching. The yield stresses of the powder route materials are greater than those of ingot produced 8090 and hence greater surface stresses can be maintained. In fatigue, severe crack front bowing is observed in the powder formed materials as a result of the reduction of the R ratio (minimum load/maximum load) by the compressive residual stresses at the sides of the specimen, causing premature crack closure and hence reducing the local driving force for fatigue crack growth ?K_eff. This distortion of the crack fronts introduces large errors into measurements of crack growth rate and threshold values of ?K.

MST/1370     

Molecular dynamics simulation and in situ TEM study of crack healing

Abstract

In situ TEM observation of crack healing during heating was carried out in an α-Fe crystal, and the results indicated that a crack in α-Fe could completely heal when the temperature increased to a critical value. The molecular dynamics method was used to simulate crack healing during heating and/or under compressive stress in a Cu crystal. The simulation results showed that a centre crack in a Cu crystal would close under a compressive stress or by heating. The roles of compressive stress and heating in crack healing were additive. During crack healing, dislocations generation and motion occurred. If there were pre-existing dislocations around the crack, the critical temperature or compressive stress necessary for crack healing would decrease, and the higher the number of dislocations, the lower the critical temperature or compressive stress. The critical temperature necessary for a crack to heal depended upon the orientation of the crack plane.     

RESIDUAL STRESS FIELDS DURING FATIGUE CRACK GROWTH

This study outlines the distinction between (1) residual stresses at an ideal crack tip, undergoing reversed deformation in the absence of crack closure, and (2) additional residual stresses generated due to plasticity induced closure upon fatigue crack growth. Residual stresses resulting from reversed deformation in plane strain were higher compared to the plane stress case, while residual stresses generated behind the crack tip were more significant in plane stress compared to plane strain. The origin of these residual stresses was studied for two specimen geometries over a wide range of loading conditions. We define a new crack tip parameter, S_tt as the applied stress level that corresponds to the development of tensile stresses immediately ahead of crack tips. The S_tt levels were significantly higher for a fatigue crack than for an ideal crack. We attribute the difference in S_tt levels between these two cases to plasticity induced closure. The results demonstrate the importance of the S_tt parameter, since the stresses ahead of crack tips could remain compressive even when the crack surfaces are open. Moreover, the study emphasizes the need, when describing fatigue crack growth, to incorporate both the closure concept and residual stress field ahead of a crack tip.     

Modelling ferroelastic domain switching at a stationary crack tip in a single crystal with account of transformation stresses due to domain reorientation

The present paper deals with ferroelastic domain switching around a stationary crack tip in a single crystal for potential applications in the context of crack toughening. The main focus is directed towards the effect of transformation stresses on the domain. The transformation stresses themselves are coupled to the extent and the shape of the domain. Therefore, they and the domain are unknown a-priori and have to be determined simultaneously. The model is applied to a crack in barium titanate and indicates a major effect of the transformation stresses on the observed needle-like domain shapes. Comparison with experimental observations shows a reasonable agreement although essential properties of barium titanate as ferroelectricity and piezoelectricity are neglected yet.     

An estimate of the residual stress distribution in the vicinity of a propagating fatigue crack

Experiments have been performed on a series of 2024-T351 Aluminum alloy uniaxial, tension specimens loaded under $\text{R = 0}$ conditions to grow a low cycle fatigue crack to a predetermined length. One half of the specimens were given a 33% single pulse overload at the conclusion of the test.All specimens were sectioned along the plane of the crack and measurements made of the residual displacements occurring at this location due to the relief of the internal stresses produced during crack propagation and overload. The data was used as the boundary condition in a Displacement Boundary Value Problem solving an Airy Stress Function for the residual stress distribution in the vicinity of the crack.The results indicate a significant degree of tensile stress ahead of the crack tip and compressive stresses both at the crack tip and in the wake of the crack reaching magnitudes as high as 36% of the yield stress. The results are consistent in both the overload and no overload cases however the magnitude and extent of the compressive stress region appears to be increased by the action of the overload. These results are consistent with the concept of crack closure as proposed by Elber.     

Modellierung des Ermüdungsrisswachstums in Schweißverbindungen unter Berücksichtigung von Schweißeigenspannungen

The present paper contains research results determined within the framework of a project called IBESS (?Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“) by the Materials Mechanics Group of the Technische Universität Darmstadt [1]. Aim is to calculate the fatigue life of welded joints by taking into account the effect of residual stresses and the influence of the weld toe geometry. Here, the fatigue life is regarded as period of short fatigue crack growth. Two and three dimensional finite element models, with cracks as initial defects, are constructed for this purpose. Fatigue crack growth analyses are performed by using the node release technique together with the finite element program ABAQUS. The welding residual stresses as well as the plasticity induced crack closure effects are considered. Structural calculations are performed in order to introduce residual stress fields in finite element models. The calculated compressive residual stress field matches the measured one especially in the weld notch area. The effective cyclic J‐integral (ΔJ_eff) is used as crack tip parameter in a relation similar to the Paris equation for the calculation of the fatigue life. For this purpose, a Python code was written for the determination of ΔJ_eff at every crack length phase. The calculated fatigue lives were compared with experimental data and a good accordance between both results was achieved. The impact of welding residual stresses on ΔJ_eff as well as on the fatigue life during short crack growth was investigated. As expected, results revealed that at lower stress amplitude, a compressive residual stress field is favorable to the fatigue life, whilst a tensile residual stress field is unfavorable. The influence of residual stresses can be neglected only for large load amplitudes.     

Analysis of an edge crack in a semi-infinite composite with a long reinforced phase

For the purpose of clarifying the micro fracture of continuous fiber unidirectionally reinforced composite materials, the problem of an edge crack perpendicular to a long reinforced phase is considered on the basis of the plane strain theory of elasticity. The stress intensity factor at the tip of the crack, and the stresses on the interface between the matrix and the reinforced phase and in the reinforced phase are discussed. In the analysis, the method of continuous distributions of dislocations is used. Then, a singular integral equation is derived and is solved by the technique developed by Erdogan and Gupta. From the numerical results it was concluded that:

1. The stress intensity factor decreases monotonically as the crack tip approaches the reinforced phase. That is, the presence of the reinforced phase can result in crack arrest.
2. When the crack tip exists near the reinforced phase, the normal stress on the interface between the matrix and the reinforced phase has a maximum at the intersection of the extension of the edge crack and the reinforced phase, while the shear stress on the interface and the normal stress in the reinforced phase take, respectively, maxima at symmetric points with respect to the crack surface in the immediate vicinity of the intersection.
3. The maximum values of the stresses on the interface and in the reinforced phase increase monotonically as the crack tip approaches the reinforced phase.

     

TIME-DEPENDENT FATIGUE CRACK GROWTH IN TITANIUM METAL MATRIX COMPOSITES

Abstract The interaction of fatigue and creep in a titanium metal matrix composite was studied by employing loading frequencies of 10 Hz (in both air and vacuum environment) and 0.1 Hz with and without hold times (in air) at 500°C. It was shown that, for the same loading frequency, the crack growth rate is lower in vacuum than in air. In an air environment, however, where the influence of load-related creep and environmental effects exist, it was shown that a decrease in the loading frequency leads to a decrease in the crack growth rate. This behavior is interpreted in terms of the redistribution of fiber and matrix stresses occurring in response to the creep-related relaxation of matrix stresses. The result of this stress redistribution is the generation of a compressive axial residual stress in the matrix phase in the region of the composite ahead of the crack tip. As the crack bridges the fibers in this region, the release of the matrix residual compressive stress leads to the closure of the matrix fractured surfaces at the crack tip, thus leading to a decrease in the crack tip driving force. To support this concept, experimental measurements of the crack opening displacement at different loading frequencies are presented. In addition, a simple model is proposed to describe the nature of the residual stresses developed in the matrix phase during cyclic loading. Results of this model have been examined using finite element analysis. The influence of time-dependent effects during a fatigue cycle was, furthermore, investigated by carrying out high frequency fatigue tests on specimens which have been previously subjected to creep deformation. Results of these tests in terms of the crack growth rate and associated crack closure, support the conclusion that a predeformed matrix produces a decrease in the crack growth rate of the corresponding composite.     

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach (CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.     

Compressive maximum shear crack initiation and propagation

A maximum shear crack γ (a Mode II shear crack along the maximum shear direction associated with the crack tip shear displacement) was produced successfully in a so-called compressive maximum shear (CMS) specimen. This specimen was specificially designed to produce a compressive maximum shear failure which is one of two mechanisms widely believed to be responsible for limiting bearing fatigue life in rolling contact. The fracture initiation stress (or crack nucleation stress) σ_c and the upward crack propagation rate (toward the loading surface) $\text{dli}\text{dσi}$ per unit cyclic compressive stress increment were determined for the 52100 steel. These parameters were measured at two cleanness levels (DE and CEVM) [DE: basic electric arc furnace melted plus vacuum degassed. CEVM: Consumable electrode vacuum melted] and two tempered hardness levels, RC61 and 51. The possibility of determining K₁₁ for ith cycle was also elucidated. The formation of tail cracks and parallel multiple cracks as fine structure of CMS cracks can be well expounded by the concept of restoring tensile stresses and the residual shear stress relaxation at the CMS crack tip. The fracture mechanism advanced here can explain the formation of similar tail cracks and parallel multiple cracks frequently observed along the inclined shear cracks existing in the subsurface regions of rolling     

Interpretation of effects at the static fatigue limit of soda-lime-silicate glass

Crack growth in soda-lime-silicate glass near the static fatigue limit is rationalized by a fracture mechanics model of the crack tip, in which a stressed layer is built up on the crack surface as a consequence of ion exchange at the crack tip. This model extends the one presented earlier by Bunker and Michalske. Ion exchange, between hydronium (H₃O⁺) ions in the solution and sodium (Na⁺) ions in the glass, gives rise to compressive stresses at the tips of cracks in soda-lime-silicate glasses. These compressive stresses are responsible for (1) the occurrence of a fatigue limit in glass, (2) for the fact that crack tips remain sharp at the fatigue limit even though the walls of the crack are corroded by the basic solutions that form as a consequence of ion exchange, (3) for the crack tip bifurcation often observed when cracks are held at the fatigue limit for a while and then restarted at higher loads, and (4) for the fact that a delay time to restart the crack is often observed after the crack is held under load at the static fatigue limit. Most of the predictions are in quantitative agreement with experimental observations on crack growth and crack tip structure for soda-lime-silicate glass. The prediction of the time required to restart the crack is, however, only qualitatively correct, as experimental data report a sharp peak centered at the fatigue limit in the plot of restart time versus hold stress intensity factor, whereas the model gives a broad maximum on such a plot. Clearly, further development of the model will be needed for a better representation of the experimental data.     

Fatigue crack propagation into the residual stress field along and perpendicular to laser beam butt‐weld in aluminium alloy AA6056

Laser beam butt welds in Al‐alloys are very narrow and are accompanied by steep residual stress gradients. In such a case, how the initial crack orientation and the distance of the notch tip relative to the weld affect fatigue crack propagation has not been investigated. Therefore, this investigation was undertaken with two different crack orientations: along the mid‐weld and perpendicular to the weld. Fatigue crack propagation ‘along the mid‐weld’ was found to be faster in middle crack tension specimens than in compact tension specimens. For the crack orientation ‘perpendicular to the weld’, the relative distance between the notch tip and the weld was varied using compact tension specimens to generate either tensile or compressive residual stresses near the notch tip. When tensile residual stresses were generated near the notch tip, fatigue crack propagation was found to be faster than that in the base material, irrespective of the difference in the initial residual stress level and whether the crack propagated along the mid‐weld or perpendicular to the weld. In contrast, when compressive weld residual stresses were generated near the notch tip, fatigue crack arrest, slow crack propagation, multiple crack branching and out of plane deviation occurred. The results are discussed by considering the superposition principle and possible practical implications are mentioned.     

Residual stresses in two laser surface melted stainless steels

Abstract

Residual stresses were studied in two laser surface melted stainless steels: one martensitic, Fe–12Cr–0·2C, and the other austenitic, Fe–17Cr–11Ni–2·5Mo (compositions in wt-%). Stresses were measured by X-ray diffractometry over a range of depths, processing conditions, and stress relieving heat treatments. The volume increase associated with the martensitic transformation develops compressive stresses in single tracks of the martensitic steel and modifies the subsurface stresses of the laser surface melted steel. However, interactions between tracks offset the compressive surface stresses at all but the slightest overlaps. Residual stresses in the martensitic steel are minimized by increasing the advance between tracks and are reduced to a lesser extent by increasing the beam diameter and decreasing the traverse velocity. The austenitic steel, undergoing no solid state phase transformation on cooling, develops tensile residual stresses of the order of the yield stress for all the processing conditions evaluated. Suitable stress relieving heat treatments were identified for each steel.

MST/422