A numerical analysis of flat internal cracks under mixed mode loading

A numerical/analytical approach is proposed to determine the stress intensity factors K_I, K_II, and K_III of a 3D internal crack. The main point of this approach is the meshing technique that can model very sharp crack fronts. The meshing technique is based on an elliptical coordinate transformation that starts from a circular crack. It allows the obtainment of a curved crack front with elements normal to the crack front. Remarkable accuracy can be obtained for elliptical crack fronts with axes ratio smaller that 0.01. Accuracy demonstration is provided for cylindrical element with an inclined internal crack subjected to uni-axial tension. This case corresponds to crack propagation for all three modes of loading, the solution of which can checked with references’ results.     

Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading

Fracture phenomenon was investigated both experimentally and theoretically for a type of coarse-grained polycrystalline graphite weakened by a U-shaped notch under mixed mode loading. First, 36 disc-type graphite specimens containing a central U-notch, so called in literature as the U-notched Brazilian disc (UNBD), were prepared for four different notch tip radii and the fracture tests were performed under mode I and mixed mode I/II loading conditions. Then, the experimentally obtained fracture loads and the fracture initiation angles were predicted by using the U-notched maximum tangential stress (UMTS) and the newly formulated U-notched mean stress (UMS) fracture criteria. Both the criteria were developed in the form of the fracture curves and the curves of fracture initiation angle, in terms of the notch stress intensity factors (NSIFs). The results showed that while the criteria could predict successfully the experimental notch fracture toughness values, the UMS criterion provides slightly better predictions than the UMTS criterion, particularly for shear-dominant deformations. Also, found in this research was that the curves of fracture initiation angle were almost identical for the two criteria which both could predict well the experimental results.     

柱形和球形壳体内爆界面不稳定性数值分析

为了更好地研究柱形和球形构型下果冻界面不稳定性发展,避免内爆聚心反弹前后直角坐标网格计算导致的误差,提高对流场和界面位置的计算精度,通过应用考虑了MVFT程序的网格适应性,使其能够适用于柱形网格和球形网格下的界面不稳定性数值模拟,特别是能够保证内爆聚心反弹前后流场和界面计算的稳定性。应用改进的计算程序对两种构型下的界面不稳定性进行了数值模拟,并对二者界面演化规律进行了详细讨论和归纳。结果表明:对于内外半径相同的柱形和球形果冻,聚心反弹时前者半径较小,而后者反弹时刻早于前者,其向内聚心和向外运动的速度最大值大于前者,对内部气体的压缩强度强于前者。对于外边界带有正弦扰动情况,除遵循上述规律外,计算还给出了峰谷转换现象。该项研究结果为进一步深入进行复杂构型下界面不稳定性高精度数值模拟研究提供了一种分析工具。     

Fatigue crack propagaion under mixed mode loading

Mixed model fatigue crack propagation is analyzed in this paper, using a centre cracked plate geometry, loaded under un-iaxial cyclic tension. Based on maximum principal stress criterion, a modified Paris expression of fatigue crack growth rate is derived in terms of ΔK and crack angle β_α for an inclined crack. It is also shown that it is more convenient to express the Paris equation by means of crack length projected on the x -axis, α_x rather than the actual length, α itself. The crack trajectory due to cyclic loading is predicted, β is varied from 29° to 90°. Experimental data on Type L3 aluminium agree fairly well with predicted values when β_α exceeds 30°.     

Numerical analysis of large elastic-plastic deformation of beams due to dynamic loading

Numerical calculations were performed for two examples of the response of elastic-plastic beams subjected to dynamic loads. These were a simply supported, axially restrained beam under suddenly applied uniform pressure, and an axially restrained, clamped beam with a central mass that is impacted by a projectile. Large elastic-plastic deflections were considered, and the method of finite differences was used. Two different constitutive equations were assumed: the elástic-perfectly plastic relation, and a special elastic-viscoplastic, strain hardening model. Analysis of the results included examining the interaction between the bending moment and the axial force, the variation of the axial force, bending moment and deflection with time, and the propagation velocities of the various phenomena during motion. Experiments were carried out in which a rifle projectile hit a central mass which had been fastened to a clamped beam. Comparison between the theoretical and experimental dynamic deflections shows good agreement for relatively short response times.     

DYNAMIC ANALYSIS OF A SPATIAL COUPLED TIMOSHENKO ROTATING SHAFT WITH LARGE DISPLACEMENTS

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Micro-crack tip fracture of commercial grade aluminum under mixed mode loading

In situ tensile tests were made in a scanning electron microscope (SEM) to investigate the deformation and micro-fracture in the immediate vicinity of a micro-crack tip in commercial pure aluminum with large-size crystal. Examined are the slip line field, stress intensity factor, strain energy density factor and crack tip opening displacement (CTOD) for mixed mode loading. Blunting and sharpening effects are observed. The latter is controlled by localized slip while the former by uniformed slip of the operating slip system with the highest crack tip Schmid factor. The operating slip system depends on the crystallographic orientation of crystal containing micro-cracks.The damage and fracture take place in the blunted region and depend on the coarsening and spacing of uniformed slip lines. The mixed mode micro-crack propagates along the direction where the voids grow and coalesce into the micro-crack. The direction also depends on the orientation of the applied loading. This suggests that the formation of macro-fracture mechanics could be applied. In particular, the minimum strain energy density criterion is suitable for determining the direction of micro-crack instability in the mixed mode. The in situ data were used to yield a nearly constant critical, minimum strain energy density factor for onset of micro-cracking.     

Numerical analysis of axisymmetric buckling of conical shells

Nonlinear boundaryvalue problems of axisymmetric buckling of conical shells under a uniformly distributed normal pressure are solved by the shooting method. The problems are formulated for a system of six firstorder ordinary differential equations with independent rotation and displacement fields. Simply supported and clamped cases are considered. Branching solutions of the boundaryvalue problems are studied for different pressures and geometrical parameters of the shells. The nonmonotonic and discontinuous curves of equilibrium states obtained show that collapse, i.e., snapthrough instability is possible. For a simply supported shell, multivalued solutions are obtained for both external and internal pressure. For a clamped thinwalled shell, theoretical results are compared with experimental data.     

Relationships of the Timoshenko-type theory of thin shells with arbitrary displacements and strains

A new modified version of the Timoshenko theory of thin shells is proposed to describe the process of deformation of thin shells with arbitrary displacements and strains. The new version is based on introducing an unknown function in the form of a rotation vector whose components in the basis fitted to the deformed mid-surface of the shell are the components of the transverse shear vector and the extensibility in the transverse direction according to Chernykh. For the case with the shell mid-surface fitted to an arbitrary non-orthogonal system of curvilinear coordinates, relationships based on the use of true stresses and true strains in accordance with Novozhilov are obtained for internal forces and moments. Based on these relationships, a problem of static instability of an isotropic spherical shell experiencing internal pressure is solved. The shell is considered to be made either of a linear elastic material or of an elastomer (rubber), which is described by Chernykh’s relationships.