An energy approach to fatigue tests and crack initiation stage determination

The paper deals with the strain energy consumed in fatigue failure under sinusoidal loading. The damage stress is considered, and it is shown that an energy formulation can be given for the traditional interpretation of the fatigue test results. That approach is used in determining the position of the French line, which it is suggested should be taken as the end of the crack initiation stage. The French line is constructed from the same data as used for constructing the fatigue curve.Translated from Problemy Prochnosti, No. 2, pp. 19–27, February. 1994.     

Effect of frequency and environment on fatigue-crack propagation of SA533B-1 steel

The effects of a decrease in the frequency of cyclic loading on the fatigue-crack propagation characteristics of SA533B-1 steel in various environments were investigated. Frequency levels of 10 Hz, 1.0 Hz and 0.1 Hz were employed in laboratory air, distilled water and a 3.5% NaCl solution. As the loading frequency was decreased, statistically significant increases in the fatigue-crack growth rates (da/dN) for the distilled water and salt water environments, as compared to those measured in laboratory air, were observed. These increases in growth rates were limited to certain ranges of stress intensity range (ΔK) values depending upon the frequency level being tested. A hydrogen embrittlement mechanism is proposed to explain the increase in growth rates based upon a fractographic analysis.     

A comparison between the elastic strain energy and the plastic work at the crack tip

For ductile fractures it becomes progressively imperative to include the plastic components of the quantities defining each particular fracture criterion, in order to derive a relationship, which not only fits the experimental data but also satisfies some appropriate physical principle. In this paper the plastic components of stresses entering in the experessions for the specific plastic work were derived from the plastic singular solution described by the HRR stress field. In order to ascertain the accuracy of such approximate solutions for criteria based on energy balance, a comparison between the components of elastic strain energy density, and its total value, with the specific plastic work (W_p) was undertaken, in order to derive certain conclusions about the importance of the contribution of energy component and the specific plastic work. The analysis was based on the typical case of a transverse internal crack in plate under plane-stress conditions, which is submitted to a mode I deformation. While the dilatational (T_v) and the distortional (T_D) components of elastic SED were calculated for impending plasticity the specific plastic work (W_p) was evaluated by assuming ssy conditions and the theory of HRR field using the plastic singular solution for mode I. It was shown that the contributions of T_v, T_D, T_e (T_e = t_v + T_D) and W_P for different strain hardening exponents were varying with ductile materials, presenting a strong influence of W_p. The conclusion was that for highly strain-hardened materials the contribution of the elastic SED and particularly of T_v is important to the mode of fracture of the plate.     

A thermodynamic approach to the influence of plastic deformation on crack instability

It is argued that the role of plastic deformation in crack growth has been widely misinterpreted. In particular the notion that the work of plastic deformation contributes to the energy balance in such a way as to give rise to an increased effective surface energy is shown to be physically incorrect. A fundamental reappraisal of the role of plastic deformation on the instability of cracks is undertaken and a thermodynamic formulation of the problem of the energetics of crack extension is developed. This is capable of treating both moving cracks and the dislocations producing plastic deformation in a unified manner and provides a powerful tool for the study of combined crack extension and plastic deformation. A rigorous definition of plastic work is also given and it is shown that the crack extension force is the only physically meaningful parameter which can be used in the formulation of a crack instability criterion. The work of plastic deformation is not a part of the crack extension force and should not be included in the criterion for crack instability. It is found that one of the important effects of plastic deformation on crack instability is the shielding effect or the reduction it causes in the magnitude of the stress at the crack tip resulting in a smaller crack extension force. Other possible effects of plastic deformation on crack propagation are briefly discussed.     

Strain-based approach to fatigue crack initiation and propagation in welded steel joints with arbitrary notch shape

In this paper, a novel strain-based approach for the fatigue strength modelling of welded steel joints is introduced. The actual weld notch geometry and the variation in the microstructure characteristics of the material are considered, and thus, the approach enables the fatigue crack growth simulation from the crack initiation to the critical crack length before the final fracture. The predicted fatigue strength is in line with the experimental results. By considering the crack tip plasticity and stress triaxiality, the approach is able to describe the different crack growth periods of the fatigue life: the short crack, long crack, and tearing-related long crack growth periods. For a welded joint with a smooth notch shape, the short crack growth period is observed to be dominant and to have a significant influence on fatigue life.     

A method of determining the critical brittleness temperature of steel from the energy of crack initiation in the specimen

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 5, pp. 51–54, September–October, 1989.     

Small crack growth in combined bending–torsion fatigue of A533B steel

Crack growth rate data from bending, torsional and in-plane and 90° out-of-phase combined bending–torsional fatigue tests of A533B steel are presented. Crack growth was monitored from initial sizes generally in the range of 50–300  μm to final sizes of several millimetres. Crack growth rate was found to vary linearly with crack size. Two approaches for correlating the A533B crack growth rate were evaluated, an effective strain-based intensity factor range and a method based on total cyclic strain energy density. The approaches were also evaluated using small crack growth data from the literature for SAE 1045 steel and Inconel 718 specimens tested under axial–torsional loadings. Predicted crack growth lives using both approaches were found to agree within a factor of two of observed lives for nearly all of the data examined.     

Structure of the plastic zone at the crack tip and the endurance of steel during low-cycle loading

From microhardness, metallographic, and also layered and sight x-ray analyses, the mechanisms controlling changes in the phase composition, structure, and size of the plastic zone at the crack tip during low-cycle loading of steels 12Kh18N10T and Kh11N10M2T have been established. These steels had various initial structures due to directional changes in their strength and ductility. It was shown that with increase in the maximum uniform elongation, there is an increase in the amount of intense structural changes in the plastic zone, an increase in the number of load cycles to failure, and a decrease in the rate of stable crack growth. These mechanical effects can be explained by the positive influence of the martensitic transformation and of dislocation mobility on the energy intensity of failure activation in the plastic zone. In particular, dislocation mobility leads to a partial relaxation of microdistortion in the crystallographic lattice of the matrix phase.Translated from Problemy Prochnosti, No. 8, pp. 23–31, August, 1993.     

钢纤维对水泥基复合材料抗起裂特性的影响

通过不同钢纤维体积分数及不同试件尺寸的预制缺口三点弯曲梁断裂试验,研究了普通乱向及定向钢纤维增强水泥基复合材料的抗起裂特性。利用试验测得的荷载-裂缝口张开位移曲线,分析了钢纤维对水泥基复合材料断裂性能的影响,并基于线性相关系数陡降法计算了起裂韧度。结果表明,定向钢纤维增强水泥基复合材料的起裂韧度明显高于普通乱向钢纤维增强水泥基复合材料;起裂韧度随钢纤维体积分数的增加而逐渐增大,当钢纤维体积分数达到0.9%左右时,定向钢纤维增强水泥基复合材料的起裂韧度值趋于稳定;在本试件高度范围内(40~100mm),起裂韧度随试件尺寸增加而逐渐增大,且定向钢纤维增强水泥基复合材料的增长趋势较为平缓。此外,从裂缝尖端夹杂改变其应力强度因子的角度解释了钢纤维的掺入及定向对起裂韧度的提高作用。     

抑制预裂缝端部翼裂纹起裂动焦散实验研究

为了抑制预裂缝尖端产生翼裂纹,保护保留岩体,采用爆炸加载式动焦散系统对空孔影响预裂缝端部翼裂纹起裂规律开展研究。结果表明:空孔不仅可以引导裂纹扩展,而且可以抑制裂纹尖端产生新的翼裂纹向保留岩体扩展;在爆炸荷载作用下空孔周围形成复杂应力场,出现应力集中现象,随着空孔半径增大,主应力差的峰值逐渐减小,特征点连线与水平线夹角逐渐增大,空孔壁更难断裂产生新翼裂纹。研究成果为实际工程控制翼裂纹向保留岩体扩展提供了可靠依据。     

抑制预裂缝端部翼裂纹起裂动焦散实验研究

为了抑制预裂缝尖端产生翼裂纹,保护保留岩体,采用爆炸加载式动焦散系统对空孔影响预裂缝端部翼裂纹起裂规律开展研究。结果表明:空孔不仅可以引导裂纹扩展,而且可以抑制裂纹尖端产生新的翼裂纹向保留岩体扩展;在爆炸荷载作用下空孔周围形成复杂应力场,出现应力集中现象,随着空孔半径增大,主应力差的峰值逐渐减小,特征点连线与水平线夹角逐渐增大,空孔壁更难断裂产生新翼裂纹。研究成果为实际工程控制翼裂纹向保留岩体扩展提供了可靠依据。     

Comparison of virtual crack extension and strain energy density methods applied to contact surface crack growth

The paper is concerned with comparison of two crack propagation methods applied to a two-dimensional computational model of the surface initiated crack growth in the lubricated contact area of meshing gears. The virtual crack extension method and the minimum strain energy density criterion are used for simulation of the crack propagation in the framework of the finite element analysis. The discretised equivalent contact model, with the assumed size and orientation of the initial crack, is subjected to contact loading conditions, accounting for the elasto-hydro-dynamic lubrication effects, tangential loading due to sliding and the influence of lubricating fluid, driven into the crack by hydraulic mechanism. The computational results show that both crack propagation methods give comparable results, although the virtual crack extension method has some clear advantages due to its theoretical superiority in dealing with mixed-mode short crack propagation close to the loading boundary.     

The effect of temperature and loading rate on the crack initiation and propagation energy in carbon steel charpy specimens

The Charpy impact tests were carried out at different temperatures and loading rates. The temperature dependences of crack initiation and propagation in carbon steels 45 and St. 3 under impact testing were determined from the obtained force variation plots. The effect of the impact velocity in the range from 1 to 4.4 m/s on the fracture toughness temperature dependence is estimated. __________ Translated from Problemy Prochnosti, No. 5, pp. 120–127, September–October, 2006.     

Relation between fatigue crack initiation and propagation,toughness and microstructure in large steel blooms for automotive plastic molds

Molds for plastic automotive components such as bumpers and dashboards are usually machined from large pre-hardened steel blocks. Due to their dimensions, the heat treatment produces mixed microstructures, continuously varying with the distance from the quenched surface, at which fracture toughness and fatigue behavior are not well known; fracture toughness is generally lower than that corresponding to a fully quenched and tempered condition. The response of the mold to defects and stresses applied during service depends on steel properties, that in turn depend upon the heat treatment and the microstructure.A survey of the mechanical properties of some commercial blooms was carried out by using three point fatigue bending tests on notched samples to evaluate the threshold behavior and the crack growth behavior by ΔK-decreasing and ΔK-increasing methods. The samples were obtained from different depths of the blooms. The relationship between mechanical properties, fracture surfaces and microstructure was also investigated.     

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.     

An energy analysis of crack initiation and arrest in epoxy

The objective of this work is to study fracture processes such as crack initiation and arrest in epoxy. A compact tension specimen with displacement-controlled loading is employed to observe multiple crack initiations and arrests. The energy release rate at crack initiation is significantly higher than that at crack arrest, as has been observed elsewhere. In this study the difference between these energy release rates is found to depend on specimen size (scale effect), and is quantitatively related to the fracture surface morphology. The scale effect, similar to that in strength theory, is conventionally attributed to the statistics of defects which control the fracture process. Triangular shaped ripples, deltoids, are formed on the fracture surface of the epoxy during the slow sub-critical crack growth, prior to the smooth mirror-like surface characteristic of fast cracks. The deltoids are complimentary on the two crack faces which excludes any inelastic deformation from consideration. The deltoids are analogous to the ripples created on a river surface downstream from a small obstacle. However, in spite of our expectation based on this analogy and the observed scale effect, there are no defects at the apex of the deltoids detectable down to the 0.1 micron level. This suggests that the formation of deltoids during the slow process of sub-critical crack growth is an intrinsic feature of the fracture process itself, triggered by inhomogeneity of material on a sub-micron scale. This inhomogeneity may be related to a fluctuation in the cross-link density of the epoxy.     

A study of COD and crack initiation by a replication technique

A silicone rubber has been used to infiltrate cracks created during slow bend tests on notched HY 100 and HY 130 steel specimens at room temperature. Crack opening displacements have been measured directly from the hardened rubber replicas of the crack. The growth of the stretch zone is in agreement with that predicted by slip line analysis. Crack initiation is seen to be a nebulous process occurring irregularly along the slot front. The initial growth of a fibrous crack has also been studied.     

A note on plastic deformation at the tip of an edge crack

Summary An integral transform solution is given for the problem of an edgecrack forming at the free boundary of a half-plane. The plastic zone is taken in precisely the form as it appears experimentally in such materials as low-C steels. The method used is a further extension of the work of Sneddon and Das [1]. Using Dugdales hypothesis, the length of plastic zone is obtained. When the plastic zone tends of zero length, the solution of the stretching of an elastic half-plane with an edge crack is obtained.With 3 Figures     

Quasi-static extension of cohesive crack described by the energy partition technique

Nonlinear differential equation governing mode I fracture under small scale yielding condition has been derived on the basis of the energy partition concept. This technique is associated with a cohesive crack model. The nonlinear zone which precedes a propagating crack has been assumed to have a structured nature. In addition to this microstructural assumption, it has been postulated that the energy dissipated within the process zone (), embedded in a larger nonlinear zone (R), remains invariant to the extent of crack growth.Upper and lower bounds of the tearing modulus have been related to the material ductility via closed form expressions. It has been demonstrated that the energy screening, measured by the ratio of the true fracture energy () to the total work expended in the cohesive zone during the process of irreversible deformation, is a monotonic function of the crack growth increment, resembling a reciprocal of the apparent material resistance to cracking described by an R-curve.