Stress field near interface edge of elastic-creep bi-material

Stress fields on elastic-creep bi-material interfaces with different geometry of the interface edge are analyzed by finite element method. The results reveal that the stress highly concentrates near the interface edge at the loading instant and it gradually decreases as the creep-dominated zone expands from the small-scale creep to the large-scale creep. The stress singularity due to creep which resembles the HRR stress singularity appears near the interface edge in all cases. The stress intensity near the interface edge time-dependently decreases and becomes constant when the transition reaches the steady state. The magnitude is scarcely influenced by the edge shape of elastic material, though it depends on the edge shape of creep material. The stress intensity during the transition can be approximately predicted by the J-integral at the loading instant.     

Increase of stress intensity near interface edge of elastic-creep Bi-material under a sustained load

The transition from small-scale creep to large-scale creep ahead of a crack tip or an interface edge with strong elastic stress singularity at the loading instant causes stress relaxation and the decrease of stress intensity in general. However, this study shows that the stress near the interface edge of bi-material with no or weak elastic stress singularity increases after the loading instant and brings about the stress concentration during the transition. In addition, the creep strain distribution of this bi-material after the loading instant is different from that occurred in the transition of an interface edge with strong elastic stress singularity or a crack tip (notch root). The criterion for the increase or decrease of stress intensity near the interface edge proved by the finite element method is proposed in this study. The stress intensity near the interface edge increases when the elastic stress singularity is lower than the creep stress singularity (λ^el < λ^cr) and vice versa.     

Stress intensity factors of a surface crack near an interface end

Due to the singular behavior of the stress field near the interface edge of bonded dissimilar materials, fracture generally initiates near the interface edge, or just from the interface edge point. In this paper, an edge crack near the interface, which can be considered as being induced by the edge singularity and satisfying two conditions, is analyzed theoretically, based on the singular stress field near the interface edge and the superposition principle. It is found that the stress intensity factor can be expressed by the stress intensity coefficient of the edge singular stress field, the crack length, the distance between the interface and the crack, as well as the material combination. Boundary element method analysis is also carried out. It is found that the theoretical result coincides well with the numerical result when the crack length is small. Therefore, the theoretical representation obtained by this study can be used to simply evaluate the stress intensity factor of an edge singularity induced crack for this case. However, when the crack length becomes larger than a certain value, a significant difference appears, especially for the case with large edge singularity.     

An eigenfunction expansion solution for three-dimensional stress field in the vicinity of the circumferential line of intersection of a bimaterial interface and a hole

An asymptotic solution pertaining to the stress field in the neighborhood of the circumferential line of intersection of an interface of a two-layer plate made of dissimilar isotropic materials and a through-hole, subjected to far-field extension/bending (mode I), inplane shear-twisting (mode II) and torsional (mode III) loadings, is presented. A local orthogonal curvilinear coordinate system (, , ), is selected to describe the local deformation behavior of the afore-mentioned plate in the vicinity of the afore-mentioned circumferential line of intersection. One of the components of the Euclidean metric tensor, namely g ₃₃, is approximated (/a1) in the derivation of the kinematic relations and the ensuing governing system of three partial differential equations. Four different combinations of boundary conditions are considered: (i) open hole (free-free), (ii) hole fully filled with an infinitely rigid plug (clamped-clamped), (iii) hole partially (i.e., in the layer 2) filled with an infinitely rigid plug (free-clamped), and (iv) hole partially (i.e., in the layer 1) filled with an infinitely rigid plug (clamped-free). The computed eigenvalues for the clamped-free boundary condition can be obtained from their free-clamped counterparts by replacing G ₂ by G ₁ and ₂ by ₁, and vice versa. These two boundary conditions are then equivalent in the complementary sense. Numerical results presented include the effect of the ratio of the shear moduli of the layer materials, and also Poisson's ratios on the computed lowest eigenvalues.     

On three-dimensional singular stress/residual stress fields at the front of a crack/anticrack in an orthotropic/orthorhombic plate under anti-plane shear loading

A novel eigenfunction expansion technique, based in part on separation of the thickness-variable, is developed to derive three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness crack/anticrack weakening/reinforcing an infinite orthotropic/orthorhombic plate, of finite thickness and subjected to far-field anti-plane shear loading. Crack/anticrack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed and lubricated) surfaces of the orthotropic plate are exactly satisfied. Five different through-thickness crack/anticrack-face boundary conditions are considered: (i) slit crack, (ii) anticrack or perfectly bonded rigid inclusion, (iii) transversely rigid inclusion (longitudinal slip permitted), (iv) rigid inclusion in part perfectly bonded, the remainder with slip, and (v) rigid inclusion located alongside a crack. Explicit expressions for the singular stress fields in the vicinity of the fronts of the through-thickness cracks, anticracks or mixed crack–anticrack type discontinuities, weakening/reinforcing orthotropic/orthorhombic plates, subjected to far-field anti-plane shear (mode III) loadings, are presented. In addition, singular residual stress fields in the vicinity of the fronts of these cracks, anticracks and similar discontinuities are also discussed.     

Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material

On the basis of general solutions of two-dimensional linear elasticity, displacement and singular stress fields near the singular point in orthotropic materials are derived in closed form expressions. According to the presented expressions, analysis formulas of displacement and singular stress fields near the tip of a V-notch under the symmetric and the anti-symmetric modes are obtained subsequently. The open literatures devoted to developing stress singularity near the tip of the V-notch in anisotropic or orthotropic materials. In this study, however, not only direct eigenequations were derived, but also the explicit solutions of displacement and singular stress fields were obtained. At the end, the correctness of the formulas of the singular stress field near the tip of the V-notch has been verified by FEM analysis.     

Transverse shear stress distribution through thickness near an internal part-through elliptical hole in a stretched plate

A semi-analytical post-processing method, termed the equilibrium/compatibility method here, is used for computation of hitherto unavailable through-thickness variation of transverse shear stresses in the vicinity of the circumferential re-entrant corner line of an internal part-through elliptical cylindrical hole weakening an edge-loaded rectangular plate. A C⁰-type triangular “composite” plate element, based on the assumptions of transverse inextensibility and piece (“layer”)-wise constant shear-angle theory (LCST), is employed to first compute the inplane stresses and “layer”-wise through-thickness average transverse shear stresses. These serve as the starting point for computation of through-thickness distribution of transverse shear stresses in the vicinity of the circumferential re-entrant corner line of the internal part-through elliptical hole. As in the case of its circular counterpart, the transverse shear stresses computed by the conventional equilibrium method (EM) are, in contrast, in serious error in the presence of the circumferential re-entrant corner line singularity arising out of the internal part-through elliptical hole, and are found to violate the compatibility condition. The computed maximum transverse shear stress can be high enough to cause catastrophic transverse shear fracture in the shape of a cone, of elliptical cross-section starting from the circumferential re-entrant corner line of the internal part-through hole. The results computed by the present analysis are in line with a three-dimensional asymptotic analysis.     

Three-dimensional asymptotic stress field in the vicinity of the circumference of a bimaterial penny-shaped interfacial discontinuity

An eigenfunction expansion method is presented to obtain three-dimensional asymptotic stress fields in the vicinity of the circumference of a bimaterial penny-shaped interfacial discontinuity, e.g., crack, anticrack (infinitely rigid lamella), etc., located at the center, edge or corner, and subjected to the far-field torsion (mode III), extension/bending (mode I), and sliding shear/twisting (mode II) loadings. Five different discontinuity-surface boundary conditions are considered: (1) bimaterial penny-shaped interface anticrack or perfectly bonded thin rigid inclusion, (2) bimaterial penny-shaped interfacial jammed contact, (3) bimaterial penny-shaped interface crack, (4) bimaterial penny-shaped interface crack with partial axisymmetric frictionless slip, and (5) bimaterial penny-shaped interface thin rigid inclusion alongside penny-shaped crack. Solutions to these cases except (3) are hitherto unavailable in the literature. Closed-form expressions for stress intensity factors subjected to various far-field loadings are also presented. Numerical results presented include the effect of the ratio of the shear moduli of the layer materials, and also Poisson’s ratios on the computed lowest real parts of eigenvalues for the case (5). Interesting and physically meaningful conclusions are also presented, especially with regard to cases (1) and (2).     

A method for the evaluation of regular components of the stress field in the plastic zone near the tip of a mode-I crack

We propose a method aimed at the evaluation of the amplitude of singularity and dimensionless angular distributions of the second terms in the expansions of stresses, strains, and displacements in the plastic zone in the vicinity of the crack tip. The method is based on the combination the Hutchinson-Rice-Rosengren-type analytic solution and a numerical solution obtained by using a modified method of boundary layer. The presented results enable us to analyze the effects of constraints in broad ranges of conditions of biaxial loading. __________ Translated from Problemy Prochnosti, No. 3, pp. 43–59, May–June, 2006.