Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.     

An improved experimental method for the determination of the critical stress intensity factor KIc of brittle materials

The critical stress intensity factor K_Ic is determined by a simple and accurate method, using small test specimens and a simple procedure in this paper.Single edge V-notched tension specimens made of PMMA are subjected to a load which is slowly increased until the crack begins to move from the notch tip. During the crack propagation event shadow patterns at the tip of the crack are recorded in a video recorder. Under these loading conditions, the creating real crack propagate slowly until the crack propagation velocity take an abrupt increase and the entire fracture of the specimen takes place. The stress intensity factor which correspond to the transition from the slow to fast crack speed, is the critical stress intensity factor K_Ic and it can be the fracture toughness of the material.The results are accurate and in good agreement with those values of K_Ic which are calculated by approximate theoretical expressions.The purpose of this paper is to introduce an improved, simple and accurate experimental method for the determination of fracture toughness of brittle materials.     

Unsteady Dynamic Crack Propagation in a Brittle Polymer

Dynamic crack propagation in a brittle polymer, poly(methyl-methacrylate) (PMMA), was studied using the method of caustics in combination with a Cranz–Schardin high-speed camera. Four different types of specimen geometry and loading method were employed to achieve the crack acceleration, deceleration, and/or reacceleration processes in one fracture event. The dynamic stress intensity factor K _ID and crack velocity were obtained in the course of the crack propagation and the corresponding relationship was determined. The effect of the crack acceleration and deceleration on the K _ID-velocity relationships was as follows: (1) the variations of K _ID and the velocity were strongly influenced by the specimen geometry and loading method; (2) the velocity change was qualitatively in accord with K _ID; (3) K _ID for a constant crack velocity was larger when the crack decelerated than it was when the crack accelerated or reaccelerated; (4) K _ID for an acceleration-free crack was uniquely related to the velocity; and (5) K _ID could be expressed as two parametric functions of the velocity and acceleration.     

Fatigue crack growth through residual stress fields—theoretical and experimental studies on thick-walled cylinders

Experiments are described which determined the effects of various residual stress distributions on the growth rate of fatigue cracks. For each stress distribution, the contribution (K_RS) to the net stress intensity at the crack tip is determined, and a comparison is then made with the behaviour predicted using a fracture mechanics approach based on a weight function analysis and a simple crack closure model. The example studied is a thickwalled pressure vessel containing a longitudinal crack which grows radially from the inner surface; fatigue cracks were grown under laboratory conditions in ring test specimens. sectioned from vessels which had been cold-expanded by different amounts to increase their pressure limits, and so contained various complex residual stress distributions. The experiments provide direct evidence that the effects of residual stress (and by extension, thermal stress) on the crack tip stress intensity may be modelled conveniently using weight function techniques, and can be incorporated satisfactorily in fatigue crack growth analyses.     

The effect of contact stress intensity factors on fatigue crack propagation

Using the technique of Dimensional Analysis the phenomenon of crack closure is modelled using the concept of a contact stress intensity factor Kc. For constant amplitude loading, a simple expression, Kc_max = g(R) ΔK, is obtained without making idealized assumptions concerning crack tip behaviour. Further, by assuming that crack closure arises from the interaction of residual plasticity in the wake of the crack and crack tip compressive stresses, the function g(R) is shown to be constant for non-workhardening materials. This implies that any dependency of Kc_max on R must be attributed to the workhardening characteristic of the material. With Kc known, an “effective” stress intensity factor Ke may be calculated and incorporated into a crack growth law of the form da/dn = f(ΔKe). From analysis, it can be deduced that for a workhardening material, Kc_max will decrease as R increases and the effective stress intensity factor will increase. This means that the fatigue crack propagation rate will increase with R, in accordance with experimental observations.     

Near threshold fatigue behaviour of flake graphite cast irons microstructures

This paper describes the influence of material toughness degradation, through reversed temper embrittlement (RTE) and mean stress on the near threshold fatigue crack growth characteristics of a CrMoV turbine bolting steel at ambient and elevated temperatures. It was established at ambient temperatures that strong effects of R-ratio and material condition (toughness) were observed on near threshold fatigue crack growth characteristics. At elevated temperatures it was shown that for the non-embrittled material that only under low R-ratio conditions did increased temperature increase the level of threshold stress intensity ΔK_th, by some 20%. In the case of embrittled material, increasing the temperature increased ΔK_th levels by around 30% and decreased near threshold growth rates by an order of magnitude at low to intermediate R-ratio levels.The effects of R-ratio on ΔK_th for all material and mechanical testing conditions could be simply expressed by the difference between ΔK_th at R = O and a constant B multiplied by R.Quantitative fractographic observations indicated that, generally, the incidence of intergranular failure prevalent in embrittled and non-embrittled steels exhibited a maximum at some specific ΔK level. Also in embrittled steels large effects of environmental assisted crack (EAC) growth were observed at near threshold fatigue crack growth rates. It was suggested that this was the result of the much reduced material cohesive strength which was caused by the presence of both impurity and hydrogen atoms.     

Fatigue crack growth rate in ferrite-martensite dual-phase steel

An empirical study is made on the fatigue crack growth rate in ferrite-martensite dual-phase (FMDP) steel. Particular attention is given to the effect of ferrite content in the range of 24.2% to 41.5% where good fatigue resistance was found at 33.8%. Variations in ferrite content did not affect the crack growth rate da/dN when plotted against the effective stress intensity factor range ΔK_eff which was assumed to follow a linear relation with the crack tip stress intensity factor range ΔK. A high ΔK_eff corresponds to uniformly distributed small size ferrite and martensite. No other appreciable correlation could be ralated to the microstructure morphology of the FMDP steel. The closure stress intensity factor K_cl, however, is affected by the ferrite content with K_cl/Kmax reaching a maximum value of 0.7. In general, crack growth followed the interphase between the martensite and ferrite.Dividing the fatigue crack growth process into Stage I and II where the former would be highly sensitive to changes in ΔK and the latter would increase with ΔK depending on the R = σ_min/σ_max ratio. The same data when correlated with the strain energy density factor range ΔS showed negligible dependence on mean stress or R ratio for Stage I crack growth. A parameter α involving the ratio of ultimate stress to yield stress, percent reduction of area and R is introduced for Stage II crack growth so that the da/dN data for different R would collapse onto a single curve with a narrow scatter band when plotted against αΔS.     

Thermoelastic investigations for fatigue life assessment

An investigation is presented on the suitability and accuracy of a thermoelastic technique for the analysis of fatigue cracks. The stress intensity factor ranges ΔK _I and ΔK _II are determined from thermoelastic data recorded from around the tip of a sharp slot in a steel specimen under biaxial load, in order to assess the accuracy of the technique. ΔK _I and ΔK _II are determined to within 4% and 9% of a theoretical prediction, respectively. The results from a similar test on a fatigue crack under biaxial load are also presented. These show that thermoelastic stress analysis is a rapid and accurate way of analyzing mixed-mode fatigue cracks. A discussion is given on the potential of thermoelastic stress analysis of propagating cracks.     

Fatigue crack extension behaviour in porous plasma spray 80%Ni---20%Cr material: The influence of R-ratio

This paper attempts to describe the fatigue crack growth response of a plasma spray 80%---20%Cr material, utilised in the corrosion protection of engineering components, whose microstructure consisted of (i) an austenitic matrix, (ii) a secondary dispersion of a chromite non-metallic inclusion phase and (iii) regions of closed and connected porosity.It was demonstrated that little or no effect of R-ratio was observed on the threshold stress intensity range ΔK_th, which was attributed to both the materials fine to intermediate grain size and probable plain stress testing conditions which significantly decrease crack closure effects. At intermediate fatigue crack growth rates high ratio results were an order of magnitude faster than the low R-ratio data. This was the result of the high R-ratio case seeking out more regions of porosity which then increased the local ΔK on the remaining ligaments leading to accelerated crack growth rates.Porosity was shown to significantly decrease the value of ΔK_th and the extent of porosity observed on fatigue fracture surfaces increased with ΔK level and was well in excess of that of 5% recorded by metallography. Hence the growing fatigue crack preferentially sought out regions of porosity as they represented locations of low fracture energy.     

Stress state in the vicinity of an inclined elliptical defect and stress intensity factors for biaxial loading of a plate

The problem of determining the stress state of a plate with an inclined elliptical notch under biaxial loading is considered. The Kolosov-Muskhelishvili method is used to obtain an expression for the stress near the vertex of an inclined ellipse, whose particular case are expressions for the stress in the case of an inclined crack. The stress intensity factors K _I and K _II were determined experimentally by holographic interferometry in the case of extension of a plate with an inclined crack-like defect. The calculation results are compared with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 118–127, January–February, 2009.     

Stress intensity factors of an oblique edge crack subjected to normal and shear tractions

Stress intensity factors (SIFs) were obtained for an oblique crack under normal and shear traction and remote extension loads. The oblique crack was modeled as the pseudodislocation. The stress field due to tractions was solved by the Flamant solution. The SIR of Mode I and Mode II (K_Iand K_II) were then obtained. Finite element analysis was performed with ABAQUS and compared with the analytical solutions. The analytical solutions were in good agreement with the results of FEM. From investigating SIFs and their ranges, the following results were obtained. The growth rate of an oblique edge crack decreased due to the reduction in the SIF ranges. The crack driving force depended on the obliquity, the normal traction and the ratio of crack to traction length. The peak value of shear traction was found as a key parameter to accelerate the crack growth.     

Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

钢轨表面剥离掉块路径预测研究

轮轨滚动接触下,钢轨表面会产生典型的鱼钩形剥离掉块,其形成机理目前暂未明确.为了探究轮轨滚动接触下钢轨表面裂纹扩展机理,基于最大周向拉应力准则,建立轮轨滚动接触疲劳计算模型,提出裂尖扩展路径预测方法,并对不同初始角度裂纹的扩展路径进行预测.结果表明,钢轨表面微裂纹为Ⅰ-Ⅱ复合型裂纹,随着裂纹长度增加,KⅠ先增加后减小,...     

Determination of the dynamic stress intensity factorsK I d andK II d,for a mixed-mode propagating crack

In this paper, the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics. The initial curve and caustic equations were derived under the mixed-mode dynamic condition. A multi-point measurement method for determining the dynamic stress intensity factors,K _I ^d , andK _II ^d , and the position of the crack tip was developed. Several other methods were adopted to check this method, and showed that it has a good precision. Finally, the dynamic propagating process of a mixed-mode crack in the three-point bending beam specimen was investigated with our method.     

Effect of stress ratio and specimen thickness on fatigue crack growth of CK45 steel

Presented are the effect of stress ratio and thickness on the fatigue crack growth rate of CK45 steel according to DIN 17200. Test results are obtained for constant amplitude load in tension with three stress ratios of R=0, 0.2 and 0.4 and three specimen thicknesses of B=6, 12 and 24 mm. Microgauge crack opening values were used to calculate ΔK_eff values from which the da/dN − ΔK_eff curves are obtained. Crack closure can be applied to explain the influence of mean stress and specimen thickness on the fatigue crack growth rate in the second regime of the two-parameter crack growth rate relation. An empirical model is chosen for calculating the normalized load ratio parameter U as a function of R, B and ΔK and, for correlating the test data.     

Effects of surface diffusion and resolved shear stress intensity factor on environmentally assisted cracking

Hydrogen induced crack-tip plastic deformation has been known as the primary mechanism of hydrogen assisted cracking and stress corrosion cracking. It has been systematically shown that the same mechanism of environmentally assisted crack-tip dislocation emission causes hydrogen assisted cracking, stress corrosion cracking, and liquid metal embrittlement cracking.An embrittling chemical species has to reach a crack tip in order to accelerate crack growth. Very close to a sharp crack tip, surface diffusion is shown to be the dominant transport process of embrittling species for stage-II crack growth. The role of surface diffusion in stage II crack growth is analyzed. The constant cracking velocity is proportional to the surface diffusion coefficient of an embrittling species and inversely proportional to a length parameter, , which is related to the transport process upstream.Dislocation emission at a crack tip is driven by crack-tip resolved shear stress. Crack-tip resolved shear stress field is characterized by resolved shear stress intensity factor, K_RSS·K_RSS is defined, the procedure for its calculation outlined, and its applications to crack-tip dislocation emission and environmentally assisted cracking discussed.     

Stress intensity factor range and propagation mode of surface cracks under rolling–sliding contact

Finite element analyses were conducted in order to evaluate the mode I and mode II stress intensity factors for inclined edge cracks under cyclic contact load under rolling and rolling–sliding condition. The SIF range depends on crack orientation, crack length to Hertzian contact zone half-width ratio, friction between the crack faces and friction on the contact surface. The results were combined in two compact functions that determine the ΔK_I and ΔK_II values. The crack propagation mode and direction were investigated using both the maximum stress criterion and the minimum strain energy density criterion. The results are displayed in graph form, which allows a fast evaluation of the crack growth condition.     

Plane-strain state of an elastoplastic body with a crack under mixed-mode loading

A mixed-mode (I + II) crack model with a plastic strip on its continuation under plane strain is proposed. The stress components within the strip are determined from the yield conditions, stress limitation, and relationship between the normal stress components defined via the principal stress state. The crack parameters are analyzed for the Mises yield condition. In the quasibrittle case, the governing system of equations includes stress intensity factors K _I, K _II, and T-stresses     

Stress intensification in cracked shank of tightened bolt

Defects or cracks in the shank of bolts can degrade their load carrying capacity. The ways with which loading and residual stress intensify the crack border stress field can be reflected through the stress intensity factor quantity as defined in the linear elastic fracture mechanics theory. Use is made of the stiffness derivative method where quarter-point singular finite elements are used in the numerical calculation. Improved accuracy is achieved by considering the displacements not only of the main nodes but also of those quarter-point nodes in plane normal and adjacent to the crack.Numerical results are obtained for a semi-elliptical shaped crack in the bolt shank owing to tension, bending, residual stress and stress caused by tightening of the bolt. Maximum value of the Mode I stress intensity factor K_a due to tension or bending could prevail either at the deepest point on the crack border or at the root of the shank where the crack border terminates depending on the aspect ratio of the ellipse. In general, K₁ at the deepest point of crack penetration is larger than that at the free surface for tension and bending for a fixed crack depth with reference to the bolt diameter. Tightening of the bolt tends to increase K₁ at the free surface if the crack depth is small. The opposite is obtained for deeper cracks. Assumed residual stress effect obtained from experimental data is found to have negligible influence on the stress intensity factor when compared with that arising from tensile load.     

A photoelastic study of crack repair

Birefringent coatings have been employed to study the effectiveness of an adhesively bonded repair of a center-cracked tension panel. The repair was one sided, with photoelastic coatings applied to the opposite side. Photoelastic coatings were also applied over the patch. Analysis methods are presented to permit the stress intensity factor to be determined from the isochromatic fringe patterns recorded from both continuous andX- andY-edged coatings. The results showed that the one-sided adhesively bonded patch reduced the stress intensity factor; however, the repair did not markedly change the character of stress distributions. Fringe loops formed near the crack tips for both the cracked and repaired tension panels. The primary difference was in the size of the loops. The reduction inK _I due to repair was smaller than anticipated, but even small improvements in ΔK _I markedly enhance the life of a repaired panel. The Paris power law is used to show the relation between the reduction in ΔK _I and the improvement in the crack growth rateda/dN. Fringe patterns from the birefringent coatings applied to the patch provided a means not only to investigate the stresses in the patch but also to detect the initiation of the local debonding of the adhesive in the neighborhood of the crack. The birefringent coating on the patch is an approach for producing an optically “smart” repair.