Analysis of crack growth rate based on rotation at the crack tip plastic zone

The crack growth rate of a line crack is obtained from a linear elastic analysis of work required in the formation of a crack tip plastic zone. Equations of crack growth rate are derived from rigid body rotation at the root of Dugdale's plastic zone. The proposed relations are used to study the fracture behaviour of materials in tension tests and the three point bending tests. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the size of plastic zone ahead of crack tip

A method for the crack tip analysis of a tensile loaded crack (mode I) due to yielding of the material is developed. The stress/strain distribution within the plastic zone, as well as size of the plastic zone are presented. The development is based on the energy interpretation of the strain hardening exponent, and an analogy between mode III and mode I for the case of small scale yielding. Predictions of the proposed method are compared with the experimental results, and a fairly good agreement is observed. A number of proposed methods to estimate the plastic zone size for ductile materials are also discussed.     

Models of endurance under low-cycle loading

Moscow. Translated from Problemy Prochnosti, No. 4, pp. 8–13, April, 1989.     

Ⅰ型裂纹尖端塑性区和无位错区及其对裂纹扩展的影响

用裂纹与位错的相互作用模拟了刃型位错从Ⅰ型裂纹尖端沿多个滑移面的发射,得到了裂纹尖端周围塑性区和无位错区的形状和大小.结果表明,与宏观断裂力学算出的塑性区形状相比,本文给出的塑性区向裂纹前方倾斜;无位错区的形状与塑性区的相似.以应变能密度因子理论为判据,当存在明显的无位错区时,塑性区使裂纹扩展的潜力下降,但扩展方向不变;而当塑性区充分发展、无位错区的作用减小或消失后,裂纹扩展的方向可能发生变化.     

Large crack tip deformations and plastic crack advance during fatigue

Finite-deformation elastoplastic analysis of a crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip deformations is presented. Cyclic crack tip opening displacements agreed with predictions of simpler models, where available. Crack closure was not detected. Plastic crack advance was evidenced. Its rate per cycle reproduced common trends of the fatigue cracking dependence on loading range and overload.     

Effects of notch radius and anisotropy on the crack tip plastic zone

Factors which influence the shape and size of the plastic zone in the immediate vicinity of a crack tip in isotropic materials at small loads are investigated. The plastic zone dimensions for the opening mode (Mode I) have been calculated over a range of values for the crack tip radius. An increase in tip radius results in an increase in the plastic zone dimension. In anisotropic materials, the orientation of crack slit and the anisotropic yield constants are other factors that affect the plastic zone size and shape. In this paper, typical curves for the shape and size of plastic zone are given to illustrate the influence of normal or shear anisotropic yield constants. For sheet metals the effects of anisotropy on the plastic zone dimensions can be evaluated in terms of R values. Suggested values of constant b for isotropic materials are given if the “radius” approximation is employed for small applied stresses.     

Fracture at the crack tip in impact loading

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 4, pp. 75–77, July–August, 1988.     

Fatigue crack tip plastic zones in low carbon steel

Microscopic plastic zone parameters at the tips of fatigue cracks in low carbon steel, as derived by the X-ray microbeam technique, have been correlated with measurement of some of the same parameters by the electron channeling contrast technique. Good correlation has been obtained for the parameters common to both techniques. The results for low carbon steel are found to correlate well with fatigue crack plasticity in other metals.

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Résumé On met en corrélation les paramètres de la microdéformation plastique à l'extrémité des fissures de fatigue dans l'acier doux, tels qu'ils se déduisent d'une technique de microbombardement par des rayons X, et la mesure de certains de ces paramètres par une technique d'émission électronique à contraste renforcé.Une bonne corrélation a été obtenue pour les paramètres qui sont communs aux deux techniques et les résultats pour l'acier doux sont en corrélation satisfaisante avec les caractéristiques de plasticité des fissures de fatigue dans d'autres métaux.

     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Analysis of the stress-strained state in the zone of a semi-elliptical crack with low-cycle loading

Results are given for analysis of the stress-strained state in the zone of a surface semi-elliptical crack in plane specimens. Specimens prepared from steels 12Kh18N10T and 07Kh13N4AG20 were tested in a soft cyclic loading regime, maximum stresses in the cycle were in the range _max=(0.6-0.9)_0.2, and the temperature of the atmosphere T was 293 and 77 K. The analysis was carried out using an x-ray method for studying residual stresses and strains, and also by means of fractography. A correlation is established between the form of stress-strained state, the degree of its inhomogeneity and failure micromechanism, and also the microrelief of fatigue fractures corresponding to them. Differences are detected in the mechanisms for occurrence of plastic deformation and strengthening mechanisms for the two test steels with cyclic deformation. It is shown necessary to consider the effect of the body boundaries (specimen front and back) on the stress and strain fields in the zone of a surface fatigue crack.Translated from Problemy Prochnosti, No. 3, pp. 3–12, March, 1992.     

An experimental study of crack tip plastic flow in mild steel

The paper deals with an experimental study on the nature of plastic flow at the root of a crack in mild steel beams, for the non-valid $\text{K}{}_{\mathrm{IC}}$ test regime, under three point hending loads. Photoelastic coating technique has been used to measure the plasticity spread ahead of the tip in relation to the load-COD record. It is observed that in all cases there is a sudden increase in specimen compliance near the maximum linear load due to an abrupt increase in plastic zone size on some preferential planes ahead of the crack tip. This abrupt increase in plastic flow was seen to occur along the 45° planes (with respect to the plane of the crack) for thicker beams and/or with longer cracks. In contrast, the plastic zone extended more on the plane of the crack for thin section beams with relatively shorter cracks. The stress intensity factor required to cause this sudden loss of resistance to localized deformation is found to be remaining constant beyond a certain crack length for a given specimen thickness. These observations suggest that a critical stress intensity factor () concept can be introduced to describe the abrupt flow localization ahead of the crack tip. This () can be taken as a new parameter in addition to those commonly used in characterising the overall “fracture” behaviour of large scale yielding materials like mild steel, especially in the non-valid $\text{K}{}_{\mathrm{IC}}$ test regime.