200,529 research outputs found
Mechanics of Interfacial Cracks between dissimilar Quasicrystals
No full textWe analize the steady propagation of a straight interfacial crack between two dissimilar planar quasicrystals in pure elastic setting and infinitesimal deformation regime. A closed form solution to the balance equations is furnished. Inertia is attributed only to the macroscopic motio
M- and L-integrals enclosing two circular holes in an infinite plate
No full textAn analytic solution is presented for stresses induced in an infinite plate with two unequal circular holes by remote uniform loadings and arbitrary internal pressures in the holes. The solution has been obtained by using the general expression for a biharmonic function in bipolar coordinates provided by Jeffery (1921). The Airy stress function is decomposed in the sum of a fundamental stress function for an infinite plate remotely loaded, which gives non vanishing tractions on the circular boundaries, and an auxiliary stress function required to satisfy the boundary conditions on the pressures at the edges of the holes, which produces vanishing stresses at infinity. By using the Jeffery solution, the problem of a circular disk containing a sliding eccentric circular inclusion has been recently solved by Radi and Strozzi (2009).Once the stress and displacement fields are obtained in closed form, the path independent Jk- (k = 1, 2), M- and L-integrals introduced by Knowles and Sternberg (1972) and Budiansky and Rice (1973) are analytically calculated on a closed contour encircling both holes by considering traction free hole surfaces. These integrals play an important role in the description of multiple defects damaged brittle materials. Physically, the Jk-, M- and L-integrals can be interpreted as the energy release rate for uniform movements, expansion, and rotation of the defects, respectively. Results are here presented for varying loading orientation angle ζ and holes geometry. The J1- and J2-integrals calculated for a closed contour enclosing both holes are found to vanish, whatever be the remote loading orientation and holes geometry. These results confirm the conservation laws proposed by Chen and Hasabe (1998) and then proved by Chen (2001) for multiple discontinuities, such as cracks, voids and inclusions, subject to remote uniform loading conditions, when the integration contour encloses all the discontinuities. Differently from the J1- and J2-integrals, the M- and L-integrals do not vanish when the integration contour encloses both holes. In particular, the M-integral attains a maximum for a certain loading orientation angle ζ0, and, correspondingly, the L-integral becomes vanishing small. For ζ ζ0 it assumes positive values. Chen (2001) and Hu and Chen (2009, 2011) observed that an implicit relation exists between the M-integral and the reduction in the effective elastic modulus. These authors showed that the loading direction along which the M-integral becomes maximum coincides with the direction corresponding to the minimum of the effective elastic modulus, due to the presence of the holes. Conversely, the loading direction along which the M-integral becomes minimum is just the direction of the maximum effective elastic modulus. This occurrence allowed these authors to conjecture the possiblity of formulating the effective elastic properties and describing the damage level induced by interacting holes in terms of the M-integral, although the proper mathematical formulation has not been adequately investigated yet.The purpose of the present contribution is to provide some basic understanding for the role played by conservation laws in multiple defects analysis
Mode III crack growth in linear hardening materials with strain gradient effects
No full textThe flow-theory version of couple stress strain gradient plasticity is adopted for investigating the asymptotic fields near a steadily propagating crack-tip, under Mode III loading conditions. By incorporating a material characteristic length, typically of the order of few microns for ductile metals, the adopted constitutive model accounts for the microstructure of the material and can capture the strong size effects arising at small scales. The effects of microstructure result in a substantial increase in the singularities of the skew-symmetric stress and couple stress fields, which occurs also for a small hardening coefficient. The symmetric stress field turns out to be non-singular according to the asymptotic solution for the stationary crack problem in linear elastic couple stress materials. The performed asymptotic analysis can provide useful predictions about the increase of the traction level ahead of the crack-tip due to the sole contribution of the rotation gradient, which has been found relevant and non-negligible at the micron scale
Mode III crack growth in elastic-plastic strain gradient solids
No full textThe flow-theory version of couple stress plasticity developed by Fleck and Hutchinson is employed to investigate the asymptotic fields near a crack-tip steadily propagating under mode III loading condition
Near-tip fields for quasi-static crack growth along the interface between a porous-ductile material and a rigid substrate
No full textA numerical asymptotic solution is provided for stress and velocity fields near the tip of an interface crack steadily propagating between a porous elastic-plastic material and a rigid substrate, under plane strain conditions. The constitutive description of the ductile material is defined by the Gurson model with constant and uniform porosity, both for isotropic hardening and for perfectly plastic behavior as a limit case. Solutions are obtained by numerically integrating the field equations within elastic and plastic asymptotic sectors and by imposing full stress and velocity continuity. If the hardening coefficient is lower than a critical value two distinct kinds of solution can be found in variable-separable form, corresponding to predominantly tensile or shear mixed mode. The elastic-perfectly plastic solution is constructed by means of an appropriate assembly of generalized centered fan and non-singular plastic sectors and an elastic unloading sector. The results show that the porosity mainly influences the stress fields of the tensile mode rather than the shear mode, due to the higher hydrostatic stress level. In particular, for high porosities the maximum of the hoop stress deviates from the interface line ahead of the crack-tip, causing possible kinking of the crack trajectory. The performed analysis of the debonding process of this kind of interface is essential for the determination of the overall strength, toughness and reliability of many advanced composite materials and structural components
Effects of microstructure on ductile crack growth
No full textThe flow-theory version of couple stress plasticity is employed to investigate the asymptotic fields near a steadily propagating crack-tip, under Mode III loading conditions. By incorporating a material characteristic length, typically of the order of few microns for ductile metals, the adopted constitutive model accounts for the microstructure of the material and can capture the strong size effects arising at small scales. Due to the effects of microstructure, the singularities of the stress and couple stress fields increase substantially, also for small hardening. The skew-symmetric stress field is found to be more singular then couple stress fields, whereas the symmetric stress components are regular at the crack-tip. The performed asymptotic analysis can provide useful predictions about the increase of the traction level ahead of the crack-tip due to the strain gradient effects, which have been found relevant and non negligible at the micron scale
Path-independent integrals around two circular holes in an infinite plate under biaxial loading conditions
No full textAn analytic solution is presented for stresses induced in an infinite plate with two unequal circular holes by remote uniform loadings and arbitrary internal pressures in the holes. The solution has been obtained by using the general expression for a biharmonic function in bipolar coordinates. The Airy stress function is decomposed in the sum of a fundamental stress function for an infinite plate remotely loaded, which gives non vanishing tractions on the circular boundaries, and an auxiliary stress function required to satisfy the boundary conditions on the pressures at the edges of the holes, which produces vanishing stresses at infinity. Correspondingly, the variations of the stress concentration factor are determined in terms of the holes geometry and loading conditions. The path independent Jk- (k = 1, 2), M- and L-integrals are analytically calculated on a closed contour encircling the two holes, under remote loading, in order to evaluate the energy release rates accompanying unit translation, self similar expansion and rotation of the holes, respectively. Results are then presented for varying loading orientation angle, biaxial loading ratio and holes geometry
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