Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model

This paper deals with the concurrent multi-scale optimization design of frame structure composed of glass or carbon fiber reinforced polymer laminates. In the composite frame structure, the fiber winding angle at the micro-material scale and the geometrical parameter of components of the frame in the macro-structural scale are introduced as the inde-pendent variables on the two geometrical scales. Considering manufacturing requirements, discrete fiber winding angles are specified for the micro design variable. The improved Heaviside penalization discrete material optimization inter-polation scheme has been applied to achieve the discrete optimization design of the fiber winding angle. An optimiza-tion model based on the minimum structural compliance and the specified fiber material volume constraint has been estab-lished. The sensitivity information about the two geometrical scales design variables are also deduced considering the char-acteristics of discrete fiber winding angles. The optimization results of the fiber winding angle or the macro structural topology on the two single geometrical scales, together with the concurrent two-scale optimization, is separately studied and compared in the paper. Numerical examples in the paper show that the concurrent multi-scale optimization can fur-ther explore the coupling effect between the macro-structure and micro-material of the composite to achieve an ultra-light design of the composite frame structure. The novel two geometrical scales optimization model provides a new oppor-tunity for the design of composite structure in aerospace and other industries.     

基于吸力量测确定膨胀土活动带和裂隙深度

采用M itchell公式和裂隙扩展深度方程两种吸力法确定安康地区膨胀土大气影响深度和裂隙开展深度。其一通过对安康地区两处天然边坡开挖观测井,利用张力计进行不同深度处吸力值的现场量测,根据M itchell提出公式计算大气影响深度;其二根据非饱和土抗拉强度公式,建立膨胀土裂隙扩展深度方程,利用基质吸力量测结果求其理论解。结果表明,安康地区膨胀土吸力变化曲线随深度增加变幅减小,呈“波浪式”推移。M itchell公式确定安康地区膨胀土的大气影响深度为3.35m以内,裂隙深度方程确定裂隙开展深度为3.06³.14m。利用M itchell公式计算大气影响深度与膨胀土断裂理论公式确定的裂隙开展深度结果接近。     

Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials

This paper discusses electromagnetic boundary conditions on crack faces in magneto- electroelastic materials, where piezoelectric, piezomagnetic and magnetoelectric effects are coupled. A notch of finite thickness in these materials is also addressed. Four idealized electromagnetic boundary conditions assumed for the crack-faces are separately investigated, i.e. (a) electrically and magnetically impermeable (crack-face), (b) electrically impermeable and magnetically permeable, (c) electrically permeable and magnetically impermeable, and (d) electrically and magnetically permeable. The influence of the notch thickness on important parameters, such as the field intensity factors, the energy release rate at the notch tips and the electromagnetic fields inside the notch, are studied and the results are obtained in closed-form. Results under different idealized electromagnetic boundary conditions on the crack-face are compared, and the applicability of these idealized assumptions is discussed.The project supported by the National Natural Science Foundation of China (10102004) The English text was polished by Yunming Chen.     

Poroelastic toughening in polymer gels: A theoretical and numerical study

We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness through asymptotic analysis. We confirm our theoretical findings by means of numerical simulations concerning the case of a steadily propagating crack. In broad terms, our results explain the role of poroelasticity and of the processes occurring in the fracturing region in promoting toughening of polymer gels.     

Mixed-mode I/II fields around a crack with a cohesive zone ahead of the crack tip

Considering a cohesive zone ahead of the crack tip, the linear elastic crack problem under Mode I, Mode II or mixed-mode conditions is formulated in an elliptic coordinate system, so that the cohesive surfaces are conveniently represented by straight line segments. It is shown that the displacement and stress fields around the crack tip and the cohesive zone, expressed in terms of elliptic coordinates, have a simple mathematical form, which does not contain a stress singularity at the crack tip due to the existence of the cohesive zone.     

Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.     

Creep crack growth on spent fuel zircaloy cladding in interim storage

The effect of creep failure mechanisms on the creep crack growth is examined on spent fuel Zircaloy cladding in interim storage. Based on the creep fracture mechanics parameter C^* and the strain energy density criteria, the relationship between the creep crack growth rate and the fracture mechanics parameter C^* is established theoretically. The effects of initial crack lengths and storage temperature profiles on cladding failure are discussed in detail. The results show that the initial crack length and the storage temperature profile play an important role in the interim dry storage. When the storage temperature remains at a constant temperature of 400 °C, it will be safe for the cladding which stores in the interim dry storage. The results presented in this study provide a reliable cladding integrity evaluation for spent fuel in the interim dry storage.     

Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method

A new experimental technique has been developed to investigate the onset of fracture in metals at low and intermediate stress triaxialities. The gage section of a flat specimen has been designed such that cracks are most likely to initiate within the specimen center, remote from the specimen boundaries. Along with the specimen, a biaxial testing device has been built to apply a well-defined displacement field to the specimen shoulders. The stress state within the specimen is adjusted by changing the biaxial loading angle. Using this new experimental technique, the crack initiation in metals can be studied experimentally for stress triaxialities ranging from 0.0 to 0.6. The stress and strain fields within the specimen gage section are determined from finite element analysis. The reliability of the computational model of the test set-up has been verified by comparing the simulation results with laser speckle-interferometric displacement measurements during testing. Sample experiments have been performed on the Al-7Si-Mg gravity die casting alloy. A three-step hybrid experimental–numerical calibration procedure has been proposed and applied to determine a phenomenological crack formation criterion for the Al-7Si-Mg alloy.

Forced oscillations of a layer of a viscoelastic material under the action of a convective pressure wave

The longitudinal and transverse components of deformation of the surface of a flat layer of a viscoelastic material glued onto a solid base under the action of a traveling pressure wave are determined. The coating compliance is described by two components corresponding to two components of surface displacement. The dimensionless compliance components depend only on the viscoelastic properties of the material, the ratio of the wave length to the layer thickness λ/H, and the ratio of the wave velocity to the velocity of propagation of shear oscillations V/C _t ⁰ . Data on the dynamic compliance are presented for 0.3 < λ/H < 30 and 0.1 < V/C _t ⁰ < 10. The compliance is demonstrated to be determined by its absolute value and by the phase lag of strain from pressure. The effect of viscous losses in the material and compressibility of the latter on the dynamic compliance is analyzed. An anomalous behavior of the compliance with the wave velocity being greater than a certain critical value is explained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 90–97, March–April, 2007.     

Mechanics of rubber shear springs

FEA calculations have been carried out for a model rubber shear spring, consisting of a block of a highly elastic material, bonded between two rigid parallel plates and sheared by displacing one of the plates parallel to the other in its own plane. The block was prevented from deforming in the perpendicular direction, and thus was deformed in plane strain. Stress distributions along the bond-line and the center-line are reported and compared with those expected from the theory of large elastic deformations. Unexpected tensile stresses were found to develop in the interior of the sheared block. They are attributed to the absence on the end surfaces of the stresses needed to maintain a simple shear, causing a pronounced change in the reference pressure—a consequence that is usually overlooked. Because the internal stresses are governed by the boundary conditions, they were strongly affected by the shape of the end surfaces. In addition, they were reduced markedly by assigning values to Poisson's ratio slightly lower than 0.5, thus allowing some volume expansion of the rubber. Strain energy release rates were also evaluated for growth of a crack along the bond-line, starting at the edges, and compared with those reported previously by Lindley and Teo [Energy for crack growth at the bonds of rubber springs, Plast. Rubber Mat. Appl. 4 (1979) 29-37], Muhr et al. [A fracture mechanics study of natural rubber-to-metal bond failure, J. Adhes. Sci. Technol. 10 (1996) 593-616], Gregory and Muhr [Stiffness and fracture analysis of bonded rubber blocks in simple shear, in: D. Boast, V.A. Coveny (Eds.), Finite Element Analysis of Elastomers, Professional Engineering Publications, Bury St. Edmunds, UK, 1999, pp. 265-274] and Gough and Muhr [Initiation of failure of rubber close to bondlines, in: Proceedings of the International Rubber Conference, Maastricht, Netherlands, June 2005, IOM Communications Ltd., London, 2005, pp. 165-174]. They confirm that a long crack at the compression edge will grow faster than one at the tension edge, but the results for short cracks were inconclusive.