Plastic Stress Singularity Research Articles

Evaluation method of plastic stress singularity for V-shaped notch under various loading conditions

Evaluation method of plastic stress singularity for V-shaped notch under various loading conditions

Analysis of plastic stress singularities of cracks and wedges under the plane stress conditions

The aim of this paper is to analyze the plastic stress singularities of the V-shaped notches and cracks under the plane stress conditions and mixed mode. Based on the formulation of assuming an asymptotic displacement field with respect to the radial coordinate centered at the notch tip, the stress components near the notch tip are expressed as the asymptotic series expansions in term of the radial coordinate by satisfying the plastic yield criterion and the nonlinear stress-strain relation. Then, the series expansions of the stress and displacement components are substituted into the governing differential equations of the plastic theory. Hence, the nonlinear second-order system of ordinary differential equations (ODEs) with the plastic stress singularity orders and the associated eigenfunctions are deduced. The interpolating matrix method is applied to solving the nonlinear eigenvalue problems of the ODEs by an iteration procedure. Thus, the leading plastic stress singularity orders and the associated eigenvectors of the displacement and stress fields in the notch tip region are achieved simultaneously. In addition, the numerical examples are given to demonstrate the accuracy and the effectiveness of the present approach to solve the plastic stress singularities of the plane V-shaped notches and cracks. Furthermore, some mechanical behaviors related to the plastic stress singularities in the notch tip region are investigated.

平面V形切口塑性应力奇异性分析

A higher-order analysis of the stress singularity of the plane V-notches and cracks in power law hardening materials is studied. First the asymptotic displacement field in terms of radial coordinates at the notch tip is adopted. When the material near the notch tips arises in plastic deformation, the Von Mises yield criterion and the plastic‘total strain’theory are used. By introducing the displacement expressions into the governing differential equations of the plastic theory, it results in a set of the eigenvalue problem of nonlinear ordinary differential equations with the stress singularity orders and the associated eigenfunctions. Then the interpolating matrix method established by the first author is used to solve the eigenvalue problem by an iteration process. The several leading plastic stress singularity orders of plane V-notches and cracks have been obtained. Simultaneously the associated eigenvectors of the displacement and stress fields in the notch tip region have been determined with the same degree of accuracy. Finally two numerical examples have been given to illustrate the accuracy and the effectiveness of the present method to determine the singularity orders of the plastic V-notch and crack. Based on the computed results, some characteristics related to the stress singularity of the plastic notches and cracks are discussed.

Plastic stress singularity near interface edge of elasto-plastic/elastic bi-material

Stress field near the interface edge of Cu/Si bi-material is numerically analyzed under the small and large scale yielding conditions. Fifteen two-dimensional models with the different surface–interface angles and hardening exponents are used to investigate. The obtained results reveal that the elastic stress singularity order λel increases with increasing of the plastic surface–interface angle θ1 and the elastic surface–interface angle θ2, while the plastic stress singularity order λpl only increases in the range of 45°⩽θ1<90° and approaches to a constant value in the remain range (90°⩽θ1⩽180°). At a specific plastic surface–interface angle θ1, the plastic stress singularity order λpl has the same magnitude regardless of the change of the elastic surface–interface angle θ2. Especially, the elastic stress singularity order λel revealed is not always larger than the plastic stress singularity order λpl. In addition, the plastic stress singular investigated increases with decreasing of the hardening exponent n of the elasto-plastic material.

Plastic Singular Stress Field for a Crack Normal to and Meeting a Bimaterial Interface.

In this paper, the plastic singular stress field for a crack normal to and meeting a bimaterial interface is studied by using FEM. In the analysis, it is assumed that both materials obey Ramberg-Osgood stress-strain formulation, and have different strain hardening exponent n. Detailed results for MODE I under plane strain are investigated. When n1 for the material with a crack is larger than n2 for the other material without the crack, the plastic singular stress field obtained by FEM is almost the same field obtained by asymptotic analysis. However, from the FEM result, it is found that a term which is independent of the distance r from the crack tip is included in the displacement field so as to satisfy the continuity of displacement along the interface. When n1 < n2, the plastic stress singularity exists near the crack tip, but the stress singularity cannot be described as a power-type singularity form.

A Method for Determining Elastic-Plastic Stress Singularity at the Interface Edge of Bonded Power Law Hardening Materials

A theoretical method for estimating the elastic-plastic stress singularity at the interface edge of bonded power-law materials is proposed, based on the iterative approach developed in this study. It is found that the elastic-plastic stress singularity depends on the bonding angle and the larger hardening exponent of the composed materials. The smaller the hardening exponent is, the stronger the stress singularity becomes. Moreover, the elastic plastic stress singularity disappears when the bonding angle is smaller than 45°. The singularity coincides with that of an interface crack when the bonding angle approaches to 180°. Through the comparison with numerical results obtained by the elastic-plastic boundary element analysis, it is proved that the iterative method proposed in this study is accurate enough and very efficient.

Plastic stress singularity near the tip of a V-notch

In this study, a new practical method is proposed to analyze the plastic stress singularity at a V-shaped notch tip. By dividing the domain around the notch tip into a number of wedge-shaped elements, the problem is reduced to determining the stress singularity in a wedge composed of multiple materials with different stiffness matrix. The results so obtained appear to be quite satisfactory. Based on the numerical results, the effects of the notch geometry and the hardening exponent on the singularity are discussed. In particular, an approximate expression is presented for the evaluation of the plastic stress singularity.

A Method for Determining Elastic-Plastic Stress Singularity at the Interface Edge of Bonded Power Law Hardening Materials.

A theoretical method to evaluate the elastic-plastic stress singularity at the interface edge of bonded power-law materials is proposed, based on the interative approach developed in this study. It is found that the elastic plastic stress singularity depends only on the bonding angle and the hardening exponent of the composed material which has the larger hardening exponent. The smaller the hardening exponent is, the stronger the stress singularity becomes, Moreover, the elastic plastic stress singularity disappears when the bonding angle is smaller than 45°. The singularity concides with that of an interface crack when the bonding angle approaches to 180° Through the comparison with numerical results obtained by the elastic-plastic boundary element analysis, it is proved that the interative method proposed in this study is accurate enough and very efficient.

Elastic-Plastic Stress Singularity at the Tip of V-Notch.

In the present study, the plastic stress singularity occurring in a V-notch is studied. A practical method is introduced to solve homogeneous differential equations obtained in the analysis. The results so obtained appear to be quite satisfactory. Based on the numerical results, the effects of the notch geometry and the hardening power on the singularity are discussed. In particular, an approximate expression is presented for the evaluation of the plastic stress singularity.

Free-Edge Stress Intensity Factor for a Bonded Ductile Layer Subjected to Shear

The stress state found in a thin, power-law hardening ductile layer bonded between a pair of rigid adherends and subjected to a shear loading is investigated. Within the context of a work-hardening plasticity theory, a stress singularity of type Krδ (δ &lt; 0) exists at the point where the interface between one of the rigid adherends and the ductile layer intersects the stress-free edge. The intensity of this singularity (i.e., K) has been calculated for a plane strain condition using a technique that combines results of an asymptotic analysis of the stress singularity with those of a detailed finite element analysis. A dead-soft aluminum layer is considered first with emphasis placed on an assessment of the region dominated by the plastic stress singularity. Results for a fully plastic layer with negligible elastic strains are presented next. The relation defining the fully plastic, free-edge stress intensity factor for a shear loading depends only on a characteristic shear stress, layer thickness, and the layer’s hardening exponent.

Fracture prediction based on plastic stress singularity strength

The objective of this study was to predict the fracture behavior of specimens of various cracked configurations and materials based on information from standard fracture specimens of the same thickness. A three-dimensional elastic-plastic finite-element analysis was used to determine the critical value of plastic stress singularity strength and thus characterize specimen fracture behavior. Fracture instability was predicted for specimens of the following structural materials: 7075-T651 and 2024-T351 Aluminum alloys; Type 304 Stainless Steel. This study was one of many contributed by participants in a fracture-predictive round-robin conducted by ASTM Task Group E24.06.02.

Fracture resistance of a structural steel as characterized by the strength of the plastic stress singularity

Fracture resistance, characterized by the strength of the plastic stress singularity, was determined at failure load and crack length using three-dimensional elastic-plastic finite-element analysis of 29 A36 steel fracture specimens that had been tested at −50°F. This measure of fracture resistance was insensitive to specimen size, geometry, parent plate, and heat, provided that the specimens were either of full plate thickness or were taken from the mid-thickness of parent plates. On the other hand, the fracture resistance of full-thickness plates was not reliably estimated from fracture specimens taken from the thickness 1/4 point or near the surface of the parent plates. The computed variation in crack-front through-thickness response at 10% of maximum load was confirmed by comparison with elastic results. Elastic-plastic response at maximum load, including the tendency to more extensive yielding in smaller specimens, was similar to that indicated by other authors. Several parameter studies demonstrated the insensitivity of the results to the finite-element mesh design.

A phenomenological theory of subcritical creep crack growth in a cylindrical vessel weakened by an axial part-through crack

A phenomenological theory of subcritical creep crack growth is formulated for materials with large creep exponent. The subcritical crack growth is shown to be mainly controlled by the average net section stress and the plastic deformations in the vicinity of the crack tip. Plastic zone size is evaluated by considering the effects of relaxation on the plastic stress singularity at the crack tip for a power hardening material. The theory has been applied to a cylindrical vessel weakened by an axial part-through crack. The predicted rupture behaviour compares favourably with published creep rupture tests on 9Cr 1Mo steel tubing pressurised at 550°C. The concept of flaw size stress is introduced and is used in failure mode prediction. Failure will be by breakage or leakage, depending on the relative values of flaw size stress and material yield stress.