Fracture under initial stresses acting along cracks: Approach, concept and results

The problems of fracture under initial stresses acting along cracks in [A.N. Guz’, Mechanics of Brittle Fracture of Materials with Initial Stresses, Naukova Dumka, Kiev, 1983 (in Russian)] is studied. Other approaches and concepts are also briefly discussed. Results for isolated and near-the-surface cracks are given.     

ON PROBLEMS OF FRACTURE OF MATERIALS IN COMPRESSION ALONG TWO INTERNAL PARALLEL CRACKS

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A simple testing technique for fracture under biaxial stresses

Evidence is accumulating to suggest that the fracture toughness of and cyclic crack-propagation rates in a material may be affected by stresses acting parallel to the crack plane. This effect contradicts the justifiable assumption, implicit in fracture-mechanics theory, that only loads causing a stress singularity at the tip of a crack can affect its behavior. More extensive investigation of this important problem involves the development of special testing equipment and specimens. This article offers a simple design for such a system, which has proved in practice to be highly reliable and of adequate accuracy. Preliminary tests on polymethylmethacrylate (PMMA) under biaxial fatigue and ramp loading are described, to demonstrate the technique itself and the phenomena under investigation. The results suggest that, for this material at least, the effects of transverse stresses are indeed slight.     

冲击作用下含预制裂纹梁柱试件的动态断裂

利用焦散线实验系统,进行了冲击加载下含预制裂纹梁柱试件的断裂实验,研究了梁柱试件的梁柱节点、梁上和柱端裂纹的扩展轨迹、扩展速度和应力强度因子的变化规律。实验结果表明:受冲击后,试件首先在梁柱节点处开裂,并在裂纹扩展过程中发生明显的曲裂运动,证明梁柱节点处最容易受到破坏。预制裂纹条数越多,梁柱节点处开裂越晚,说明裂纹条数少,能量可以在裂纹尖端积聚得更集中、更快。含柱端预制裂纹的试件,2条裂纹的开裂相隔时间要长于含梁上预制裂纹的试件;同时,试件的第2条裂纹优先在梁上裂纹处开裂,说明固端支座比简支梁断裂需要更多的能量。随着预制裂纹的增多,梁上裂纹在扩展过程中的曲裂现象减弱, 由于部分能量在柱端裂纹处积聚,用于推动梁上裂纹扩展的能量相应地减少。并且由于柱端裂纹的存在,梁上裂纹受到的拉应力分量减小,导致裂纹尖端受到弯矩变小,影响了裂纹的曲裂运动。     

Stability and fracture of plates with two edge cracks under tension

The paper presents experimental results on the deformation, local buckling, and fracture of D16AT plates with two parallel edge cracks under tension. The distribution of strains and deflections over typical cross-sections and buckling modes are determined. The influence of the crack length and the distance between the cracks on the local buckling stresses and breaking stresses is studied. The effect of local buckling on the strength of the plate is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 121–125, November 2006.     

Electromechanical fracture analysis for corners and cracks in piezoelectric materials

Corners and cracks are usually studied separately in the literature. To build a bridge connecting these two different but similar topics, in this paper the solutions for piezoelectric multi-wedges, which cover corners and interface corners, are used to study the cracks and interface cracks in piezoelectric materials. Moreover, the stress/electric intensity factors defined for cracks, interface cracks and interface corners are also extended to the general corners. By taking the special feature of Stroh formalism for anisotropic elasticity, all the solutions presented in this paper for piezoelectric materials preserve the same matrix form as those of the corresponding anisotropic problems. To see more clearly about the piezoeffects on the corners and cracks, most of the complex matrix form solutions are expanded in real component form for two typical piezoelectric ceramics with different poling directions.     

Fracture mechanics of materials under compression along cracks (survey). Structural materials

Conclusions The results elucidated in this paper and in [A. N. Guz' and V. M. Nazarenko, Fracture mechanics of materials under compression along cracks (Survey). Highly-elastic material, Prikl. Mekh.,25, No. 9, 3–32 (1989)] of investigations on compression of materials along defects of crack type are exact since they are obtained within the framework of rigorous three-dimensional linearized formulations. Let us note that the fact that the mentioned result are standards for approximate approaches is of independent value.The investigations performed whose survey is represented above should be considered the beginning of a study of problems of material fracture under compression along cracks in a rigorous formulation (within the framework of the linearized mechanics of deformable bodies).The present paper continues the survey [A. N. Guz' and V. M. Nazarenko, Fracture mechanics of materials under compression along cracks (survey). Highly-elastic materials, Prikl. Mekh.,25, No. 9, 3–32 (1989)] of investigations of questions for fracture under compression along cracks as applied to extensively utilized structural materials, composites with elastic components and elastic-plastic bodies. In the interest of convenience in the exposition, a single system of numbering the sections and formulas, figures, tables, as well as the bibliographic references is used (the references in this paper are given in conformity with the bibliographic listing in the above-mentioned citation).Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 10, pp. 3–19, October, 1989.     

Calculation of near-tip non-singular stresses for pressurized cracks

When the crack surfaces are traction-free, there is only one constant term T in the near-tip stress field, which contributes uniformly to the stress component acting in the direction parallel to the crack flank. As to pressurized cracks, the non-singular part of the asymptotic stresses appears to be more complicated and is no longer characterized only by the constant T. In this work, an effective numerical approach is developed for calculation of the non-singular parts of the asymptotic near-tip stresses under the action of nonuniform crack surface pressures. With this approach, the near-tip non-singular stress field can be accurately evaluated by direct use of regular numerical methods such as finite elements.     

On the statistical analysis of local fracture stresses in notched bars

Test results for critical local fracture stresses are analysed statistically for both “as-received” and “degraded” pressure-vessel weld metal. The values were determined from the fracture loads of blunt-notch four-point-bend specimens fractured over a range of low test temperatures, making use of results from a finite-element stress analysis of the stress-strain distributions ahead of the notch root. The “degraded” material tested in this work has been austenitized at a high temperature, followed by both prestraining and temper embrittlement. This has led to a situation in which the fracture stress for the “degraded” material is reduced significantly below that for the “as-received” material. The fracture mechanisms are different in that the “degraded” material shows evidence of intergranular fracture as well as cleavage fracture (in coarse grain size) whereas the “as-received” material shows only cleavage fracture (in fine grain size). The critical stress (σ_F) distributions plotted on normal probability paper show that the experimental cumulative distribution function (CDF) is linear for each condition with different mean values: for “as-received” material and for “degraded” material. The values of standard deviation are small and almost identical (33-). The decrease of the local fracture stress after degradation is related to the local fracture micro-mechanisms. Statistical analysis of the results for the two conditions supports the hypothesis that the values of σ_F are essentially single valued, within random experimental errors. A similar analysis of the data treating both conditions as a single population reveals some interesting points relating to statistical modelling and lower-bound estimation for mechanical properties. Comparisons are made with Weibull analysis of the data. A further conclusion is that it is extremely important to base any statistical model on inferences drawn from micro-mechanical modelling of processes, and that examination of “normal” CDFs can often provide good indications of when it is necessary to subject data to further statistical and physical analysis.     

General case of the plane problem of the mechanics of fracture of solids in compression along cracks

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 6, pp. 22–27, June, 1989.     

Formation of a plastic zone in an anisotropic body under loads acting along a crack

The effects of tension and compression along a crack on the plastic zone in a finite anisotropic body under plane strain are studied. The formation pattern for the plastic zone with increasing load is established by numerically solving a boundary-value problem for each of the cases. In particular, a new plastic zone is revealed. It occurs at the crack face under a compressive load of certain magnitude. How this plastic zone interacts with that at the crack tip is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 3–19, May 2007.