Evaluating the limiting state of materials with asymmetric cyclic loading and a complex stress state

Conclusion In order to construct models of the limiting state in asymmetric cyclic loading, it is best to use the representation of a unique limit curve that is invariant to the time to failure and type of stress state. Isotropic metallic materials were used as an example to show that such a curve does exist and is described satisfactorily by an exponential cosine function.The models constructed above were used to calculate the limiting state for several steels and alloys acted upon by the combinations of cyclic bending and cyclic torsion, static bending and cyclic torsion, and static torsion and cyclic bending. Results were also calculated for materials with stress raisers. The calculated data were compared with experimental findings and were shown to agree satisfactorily with the latter.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 2, pp. 67–79, February, 1995.     

Brittle fracture and spinnability of viscous materials

Ohne Zusammenfassung     

Flow field modelling near a well with a conductive fracture

In the technology of oil recovery the oil production rate can be increased by generation of a vertical sand-filld conductive fracture on the wall of the well. Oil diffuses through the conductive fracture to the well. In this paper the seepage flow and isothermal deformation fields in both the formation and fracture and the oil production rate at the well are studied by modelling the formation as an infinite poroelastic medium saturated with a one-phase compressible fluid. The fracture is treated as a one-dimensional poroelastic medium. Darcy flows are considered in both the formation and fracture. The plane strain condition is imposed. Our solution is obtained numerically by a finite element method based on a variational principle. The accuracy of the analysis is studied by comparison of the numerical solutions of some problems with their analytical solutions. Since we are dealing with the transient flow problem of an infinite region, an extrapolation technique is employed to find the finite element solution. The production rate of a well with the conductive fracture is compared with that of a well without the conductive fracture.     

Brittle fracture and spinnability of viscous materials

Conclusion In both cases, brittle fracture and dropping breakdown, only very little deformation or elongation was observed in the experiments mentioned above, and limiting conditions were obtained reproducibly with respect to rate of extension and temperature. The brittle limits give the condition where the viscous resistance due to locally concentrated stress, i. e. the grip effect (5) exceeds cohesion of the materials, and development of the surface of separation is followed. At the dropping limits, the viscosities of the liquids may be too small to resist shrinking by surface tension with respect to the rate of extension. Although the theory of spinnability proposed here may be only tentative, it can be pointed out that surface tension plays some important role in spinning of viscous liquids of lower molecules. Concerning higher molecules, rubber-like elasticity as well as viscosity may become more important (6).

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Zusammenfassung Für beide Fälle, spröden Bruch und stufenweiser Bruch, wurde nur sehr geringe Deformation oder Verlängerung beobachtet und Grenzbedingungen hinsichtlich Dehnungsgeschwindigkeit und Temperatur reproduzierbar erhalten. Die Bruchgrenzen geben die Bedingungen, bei denen der viskose Widerstand entsprechend den lokalen Spannungskonzentrationen, d. h. entsprechend den grip-Effekt die Kohäsion des Materials übersteigt, und die Entwickelung der Trennfläche wird verfolgt. Bei der Grenzbelastung für das Absinken der Spannung mag die Viskosität der Flüssigkeiten zu gering sein, um dem Schrumpfen durch Oberflächenspannung im Vergleich mit der Dehnungsgeschwindigkeit entgegen zu wirken. Obgleich die Theorie der Spinnbarkeit, hier vorgeschlagen, nur einen Versuch darstellt, kann behauptet werden, daß die Oberflächenspannung beim Spinnen viskoser Flüssigkeiten mit kleineren Molekülen eine wichtige Rolle spielt. Für höhermolekulare Substanzen wird neben der Viskosität auch die Gummielastizität ausschlaggebend.

     

Flow of granular materials modeled as a non-linear fluid

Recently, Massoudi (2011a) derived a generalized form of a constitutive relation related to Reiner's fluid model for wet sand, where not only the effects of volume fraction are incorporated in the rheological properties of the fluid, but also the shear viscosity depends on the shear rate. In this paper, we use this model to study the fully developed flow of granular-like materials down an inclined plane. The governing equations are made dimensionless and numerical solutions are presented for the various dimensionless parameters.     

Flow in a fractured medium with fractal fracture geometry

A model of a fractured porous medium in which the fracture system forms a fractal with Hausdorff-Bezikovich dimension d is proposed. The fractal is immersed in a saturated porous medium with the dimension D (D d, D=2, 3). The rock skeleton is assumed to be nondeformable. The system of flow equations is written out for cylindrically (D=2) and spherically (D=3) symmetrical flows. When D=d the model reduces to the well-known Barenblatt-Zheltov model. Certain particular solutions, which make it possible to determine the phenomenological parameters of the model experimentally, are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 66–70, September–October, 1990.     

Magnetoelastic fracture of soft ferromagnetic materials

Effects of magnetic field on fracture toughness of soft ferromagnetic materials were studied using experimental techniques and theoretical models. The manganese–zinc ferrite with a single-edge-notch-beam (SENB) were chosen to be the specimen and the Vickers’ indentation specimen subjected to a magnetic field were chosen to be the specimens. Results indicate that there is no significant variations of the measured fracture toughness of the manganese–zinc ferrite ceramic in the presence of the magnetic field. The theoretical model involves an anti-plane shear crack with finite length in an infinite magnetostrictive body where an in-plane magnetic field prevails at infinity. Magnetoelasticity is used. The crack-tip elastic field is different from that of the classical mode III fracture problem. Furthermore, the magnetoelastic fracture of the soft ferromagnetic material was studied by solving the stress field for a soft ferromagnetic plane with a center-through elliptical crack. The stress field at the tip of a slender elliptical crack is obtained for which only external magnetic field normal to the major axis of the ellipse is applied at infinity. The results indicate that the near field stresses are governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter for finding whether magnetostriction or magnetic-force-induced deformation is dominant near the front an elliptically-shaped crack. The influence of the magnetic field on the apparent toughness of a soft ferromagnetic material with a crack-like flaw can be regarded approximately in two ways: one possesses a large induction magnetostrictive modulus and the other has a small modulus. Finally, a small-scale magnetic-yielding model was developed on the basis of linear magnetization to interpret the experimental results related to the fracture of the manganese–zinc ferrite ceramics under magnetic field. Studied also is the fracture test of the soft ferromagnetic steel with compact tension specimens published in the existing literature.     

The ductile fracture of anisotropic materials

A theoretical solution is obtained which adapts the Dugdale model to anisotropic materials. The effect of anisotropy is shown to modify each isotropic field equation by amultiplicative constant which is a function of the anisotropic-material constants. A limit on the validity of a Dugdale-type solution is found using a von Mises' yield criterion which implies that the crack and plastic zone will extend along a direction other than the crack line. As long as the material is within pirescribed limits, the Dugdale finiteness condition is shown to be affected by material anisotropy only in the calculation of a yield stress. Experimental results on crack-opening displacements are presented which indicate that a large degree of anisotropy is necessary to cause significant deviations from isotropic theory. Results are presented which indicate that anisotropy does affect the direction of crack propagation.     

Dynamic fracture of idealized fiber-reinforced materials

Dynamic plane stress of sheets composed of two orthogonal families of inextensible fibers, with infinitesimal elastic shearing stress response, is considered. The fibers through the tip of a propagating tear or crack carry finite forces. Fracture criteria that can be expressed in terms of these tip forces are discussed. In a particular example it is shown that the maximum energy release rate criterion leads to a circular crack trajectory, while the so-called critical force and critical stress criteria imply that the crack is L-shaped, like cracks or tears in real fibrous materials.     

Flow of a fluid-solid mixture: Normal stress differences and slip boundary condition

In this paper, using mixture theory we study the flow of a dense suspension, composed of solid particles and a fluid; the emphasis is on the influence of the slip boundary condition and the effect of normal stress differences. Very little work has been done considering both the slip at the walls and the normal stress effects in the frame of a two-component flow. In this paper, the stress tensor for the solid component is modeled as a nonlinear fluid which not only includes the viscous effects but also the normal stress effects; the fluid constituent is modeled as a viscous fluid. We look at the flow between two flat plates.     

On the deformation and fracture of porous materials

The constitutive behavior of porous materials (including the yield loci, the void growth rate, the macro stress-strain relation and the strain to localization instability) is examined based on the lower bound approach proposed by the present authors. These results are then compared with the experimental and the finite element results as well as those predicted by Gurson's equations. Emphasis is placed on approaching the real behavior from the upper and the lower bound analysis. Calculation is also made on the influence of void nucleation on the critical strain to instability and a modified strain-controlled nucleation criterion is proposed. Finally the instability and fracture of AISI4340 steel in plane strain tension is examined and comparison is made between theoretical and experimental results.     

Structural approach to enhance the fracture resistance of high-strength metallic materials

The paper proposes an approach to form (by special heat treatment) a structure and phase composition of martensitic steel that would enhance its ductility in the high-strength state. A correlation is experimentally established between the stability of fracture resistance and ductility in linear and plane stress states. The behavior of the scatterband of the ultimate strength with increase in the degree of ductility is analyzed. The possibility of predicting the ultimate strength from the lower edge of its scatterband is demonstrated with an example of a circular cylindrical shell __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 68–78, August 2006.     

A limiting “viscosity” approach to the Riemann problem for materials exhibiting a change of phase(II)

Communicated by C. Dafermos     

一个考虑形变能影响的脆断强度条件

针对常用强度理论解决复杂应力状态生断裂存在的问题,分析了由形状改变比能引起的塑性变形对脆断的影响,给出了一个新的脆断强度条件,并通过铸铁破坏试验作了验证。     

功能梯度材料的平面断裂力学分析

针对材料参数在厚度方向可能按任意连续变化的梯度材料，给出了一个新的分层模型，利用该模型求解了面内加载下梯度界面层和涂层中的界面裂纹问题，借助Fburier积分技术和传递矩阵方法，将该问题化为一个Cauchy型奇异积分方程，通过数值求解，得到感兴趣的应力强度因子，对不同形式的杨氏模量和泊松比，计算了界面裂纹应力强度因子，结果表明泊松比的变化形式对应力强度因子影响不大，可当作常数处理，而杨氏模量的影响则很大。