Characterisation of crack tip stresses in elastic-perfectly plastic material under mode-I loading

Asymptotic crack tip stress fields are developed for a stationary plane strain crack in incompressible elastic-perfectly plastic material under mode-I loading. Detailed investigations have revealed that in between the two extreme conditions of crack tip constraint, that is, between the fully plastic Prandtl [1] field and the uniform stress field the most general elastic-plastic crack tip fields can be completely described by the 5-sector stress solution proposed in this article. The 3-sector stress field proposed by Li and Hancock [2] and the 4-sector field proposed by Zhu and Chao [3] are subsets of the general elastic-plastic field proposed in this work. This study has revealed that cases arise where the severe loss of crack tip constraint can lead to compressive yielding of crack flank. This particular situation leads to 5-sector stress field. Detailed studies have revealed that, in the most general case of elastic-plastic crack tip fields, the T_π parameter proposed by Zhu and Chao [3] cannot be used as a constraint parameter to represent a unique state of stress at the crack tip. A new constraint-indexing parameter T_CS-2 is proposed, which along with T_p is capable of representing the entire elastic-plastic crack tip stress fields over all angles around a crack tip. Excellent agreement is obtained between the proposed asymptotic crack tip stress field and the full-field finite element results for constraint levels ranging from high to low. It is demonstrated that the proposed constraint parameters are adequate to represent the crack tip constraint arising due to specimen geometry and loading conditions as well as the additional constraint that arises due to weld strength mismatch.     

Analysis of a crack approaching a circular hole in cross-ply laminates under biaxial loading

The problem of a crack approaching a circular hole in cross-ply laminates under uniaxial and biaxial loading is investigated in this paper. The effects of material orthotropy, geometry [R/d and a/d], and loading conditions on crack tip singularity are investigated. The stress intensity factors are obtained by the modified mapping collocation method. The present results for an isotropic infinite plate show good agreement with existing solutions. The results for cross-ply laminates show that the stress intensity factors strongly depend on material orthotropy, geometry, and loading condition. The stress intensity factors for cross-ply laminates exist between those for θ=0° and those for θ=90° in the whole range of crack length and decrease as the percentage of 0° plies increases. In the range of small crack length the stress intensity factors for biaxial tension are higher than those for uniaxial tension. In the range of large crack length the stress intensity factors for uniaxial tension are higher than those for biaxial tension.     

The role of plastic anisotropy deformation in fretting wear predictions

The deformation occurring under fretting conditions occurs over length scales of the same order as the grain size, so the plastic anisotropy plays a significant role in the very local region near the contact edge during fretting process. The present study first describes plastic anisotropy by unified anisotropy plastic model coupling with Archard's wear law on the fretting behavior incorporating the effect of wear debris into such a quantitative model. The finite element method, utilizing this model, is used to analyze gross slip fretting conditions. The implementation of the wear simulation tool together with anisotropy cyclic plasticity analysis during fretting process is applied to the wear depth simulation. The present study validates the experiment phenomena from numerical simulation that failure location of the specimens under the flat-on-flat configuration is very close to the trailing edge. The scar at the trailing edge is much deeper than any other locations and the larger relative slip range resulted in considerably deeper surface damage. Another interesting discovery is that when material with different orientations the degree of wear also develops differently and the quantitative prediction is given.     

Identification of sheet metal plastic anisotropy using heterogeneous biaxial tensile tests

The plastic behavior of anisotropic steel and aluminum sheets is identified by combining the results of classical uniaxial tensile tests and heterogeneous biaxial tensile tests on non-standard cruciform specimens specifically designed for obtaining a high sensitivity of strain fields to material anisotropy. The strain fields are measured on the surface of the specimens by means of an image correlation method. The 8-parameter anisotropic yield function proposed by Ferron et al. [1] is adopted for identification. On the one hand, the results of uniaxial tensile tests are analyzed to determine the strain-hardening parameters and yield function parameters related to transverse strain-anisotropy (angular variation of the anisotropy coefficient R) and stress-anisotropy (angular variation of the yield stress σ). On the other hand, strain fields measured in the biaxial tests are used as input data in an optimization procedure that consists of fitting simulated fields with experimental ones in order to determine the material parameters describing the shape of the yield surface in the biaxial stretching range. The identified yield function is validated using experimental data issued from biaxial tests that were not considered during the optimization process.     

Contact friction in the deformation zone during ultrasonic surface plastic deformation

It is shown that the introduction of torsional ultrasonic oscillations in the deformation source reduces the work of the frictional forces in comparison with the application of radial and longitudinal ultrasound or the absence of ultrasound. The application of torsional ultrasound to the deforming element reduces the contact-friction coefficient by a factor of 20–60, as against a factor of two or less when radial and longitudinal ultrasound is applied to the contact zone. With increase in the rolling rate and decrease in oscillation amplitude of the deforming element, the effectiveness of ultrasound application declines.     

The buckling and post-buckling behaviour of composite plates under biaxial loading

The response to applied load of general composite plates exhibits a coupling between the bending and extensional modes of deformation which may be significant when shear or compressive loads are applied in-plane. The additional deformation modes may affect the nature of the buckling behaviour, reduce the buckling load or change the post-buckled stiffness. This paper considers the stiffness immediately after buckling of a rectangular panel of angle-ply type in which coupling effects occur and which undergoes bifurcational buckling when biaxial load is applied in directions parallel to the panel edges. Expressions are derived for the buckling loads and for the in-plane stiffness of the panel immediately after the instant of buckling, it being found that the coupling terms affect the stiffness at buckling mainly via the associated change in buckling mode shape.     

Analysis of a flat annular crack under shear loading

An annular crack in an infinite isotropic elastic solid under shear loading is analyzed. General solution to the Navier's equilibrium equation is expressed in terms of three harmonic functions. Employing the Hankel transform the harmonic functions are represented by the solution of a pair of triple integral equations. The triple integral equations are reduced to a pair of mixed Volterra-Fredholm integral equations, which are numerically solved. The stress intensity factors of the annular crack under various shear loadings such as uniform radial shear, linearly varying radial shear, uniform shear and linearly varying shear are calculated as the Poisson's ratio ν anda/b (a; inner radius,b; outer radius) vary.     

Eccentric crack in a piezoelectric strip under electro-mechanical loading

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing a Griffith eccentric crack off the center line under anti-plane shear loading with the theory of linear piezoelectricity. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate are obtained, and the influences of the electric fields for piezoelectric ceramics are discussed.     

The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading

The goal of this paper is to provide the foundation for an analysis of contact between elastic-plastic solids, whose surface roughness is idealized with a Weierstrass profile. To this end, we conduct a parametric study of the plastic deformation and residual stress developed by the two-dimensional contact between a flat, rigid platen and an elastic-perfectly plastic solid with a sinusoidal surface. Our analysis shows that the general characteristics of the deformation can be characterized approximately by two parameters: α = a/λ, where a is the half-width of the contact and λ is the period of the surface waviness; ψ = E^*g/σ_Yλ, where E^* and σ_Y are the effective modulus and yield stress of the substrate, respectively, and g is the amplitude of the surface roughness. Depending on the values of these parameters, we identify eight general types of behavior for the asperity contacts: (a) elastic, elastic-plastic or fully plastic isolated Hertz type contacts; (b) elastic, or elastic-plastic non-Hertzian isolated contacts; and (c) elastic, elastic-plastic or fully plastic, interacting contacts. Relationships between contact pressure, contact size, effective indentation depth and residual stress are explored in detail in each regime of behavior. Implications on rough surface contacts are discussed.     

Fatigue crack propagation behavior at a notch for needled C/SiC composite under tension-tension loading

Fatigue test of a needled C/SiC composite with a notch under tension-tension cyclic loading was completed, and the main fatigue crack propagation curve of the needled composite was obtained by the in situ observation of the fatigue process. By analyzing the influence of the failure number and distribution on the tensile loading subjected by 0° fiber bundles, the relationship between the main fatigue crack propagation and the distribution of 0° fiber bundles in the needled composite was established. By observing the fracture microstructure (especially the distribution of 0° fiber bundles) of the needled composite through scanning electron microscopy, the reasons for the varying fatigue resistance of different notched specimens were also explained. In addition, acoustic emission (AE) was also used to analyze the AE energy characteristics during the fatigue crack propagation process of the needled composite.

     

Damage of plastic cylinders under localized pressure loading

The purpose of this paper is to develop a general methodology of converting a two-dimensional boundary value problem for a cylindrical shell to an equivalent one-dimensional problem of a plastic string on a non-linear plastic foundation. The shell is subjected to a localized pressure loading, thereby producing large plastic displacements and rotations. The equivalence parameter is defined and evaluated by making assumptions about the shape of the displacement and velocity field in the cross-sectional plane of the cylinder. Closed-form solutions for the deformation and velocity profile in the axial direction of the shell are obtained for two types of pressure loading, a rectangular pressure load and a Gaussian pressure load. The strain distribution and the maximum strains are also calculated for each load case and the possibility of predicting shell fracture is briefly discussed.     

Plastic deformation modes of regular hexagonal honeycombs under in-plane biaxial compression

A limit analysis approach is employed to identify the plastic deformation modes of regular hexagonal honeycombs with relatively large wall-thickness-to-length ratios under in-plane biaxial compression. An infinite block of honeycomb material is considered and a representative block consisting of four hexagonal cells is defined when assuming the kinematic admissibility of the modes and a periodic repeatability of the representative block in both spatial directions. In general, three plastic collapse modes are found to be preferable depending on the direction of loading, and in some particular cases they are similar to the modes that occur elastically under stress or strain controlled in-plane biaxial compression. It is shown that the critical forces at the onset of the plastic collapse depend on the assumed constraints for the deformation of the representative block. The results obtained from the theoretical analysis and the numerical simulations are compared and discussed.     

Dynamic plastic deformation of rings under impulsive load

A study of the plastic response of rings of different materials to different types of dynamic load is presented.

Inertial loading of rings was obtained by allowing heavy lead rings to fall freely on to flat and pointed rigid anvils and impulsive loading was obtained by subjecting stationary lead, copper and aluminium rings to a high-speed bullet or to contact explosives. Heavy mass, low velocity impact loading was obtained by allowing a large tup to freely fall on to the ring. Collision loading was obtained by allowing one ring to fall on to one or two stationary rings.

Two types of approach are employed to analytically investigate the loading of rings. The first is a numerical one which assumes a simple approximate model for the structure of the ring; it reduces the ring to small masses concentrated around the circumference, connected to each other by weightless links possessing the strength properties of the material of the ring. The problem is then reduced to solving the dynamical equations of each mass around the ring with the help of a digital computer. The second is an energy method which utilizes Lagrange's equations for the motion of approximated links within the ring.

Results of each of these approaches are compared with experiments presented in terms of instantaneous deformation obtained from high-speed photographs.     

Explicit solution to the large deformation of a cantilever beam under point load at the free tip using the variational iteration method-II

This study focuses on a new analytical method called the variational iteration method-II (VIM-II) for the differential equation of the large deformation of a cantilever beam under point load at the free tip. The rotation angles as well as the horizontal and vertical displacements of a cantilever beam with large deformation are calculated in an explicit analytical form. A comparison of the results with those of some numerical and analytical methods shows the simplicity and effectiveness of VIM-II. VIM-II is proven to be a powerful technique that can be used to obtain accurate solutions that cannot be provided otherwise by perturbation and other methods. The accuracy and convergence of the method are also investigated and compared with those of other methods. The results showed good agreement between VIM-II and other methods.     

Numerical analysis of the components of the three-dimensional non-singular stress field at a mixed-type crack tip

A program was developed that allows one to automate the process of calculating the three-dimensional stress field at a mixed-type crack tip within the ANSYS software. The calculation results are given for the stress intensity factors and components of the non-singular T-stress for the disk model with an inclined crack under compression with a varying thickness of the sample and an approximately constant parameter of mixing of the types of stress (I + II). We note the significant influence of the thickness of the sample on the nonsingular T _zz -stress when the value of the T _xx stress changes negligibly.     

Analysis of a kinked crack in an anisotropic material under antiplane deformation

This paper analyzes the asymptotic problem of a kinked crack in an anisotropic material under antiplane deformation. Using the linear transformation method proposed in this paper, a solution to the asymptotic problem of a kinked crack in an anisotropic material can be obtained from the solution of the corresponding isotropic kinked crack problem. The exact solution of the stress intensity factor for the kinked crack in the anisotropic material is obtained from the solution of the isotropic problem. The effect of the kink angle and two anisotropic parameters on the stress intensity factor is discussed for the inclined orthotropic material as well as the anisotropic material. In order to verify the exact solution of the stress intensity factor, numerical calculations are performed by using finite element analysis.     

The effect of anisotropy on wrinkling of tube under rotary draw bending

Rotary draw tube bending is one of the most complex tube forming processes subject to different process parameters such as material properties and geometry. This process is being practiced in more and more applications in industry due to its high efficiency, high forming precision and quality. However, improper process parameters can lead to wrinkling which restrict the thin walled tube bending. Therefore, the prediction and prevention of wrinkling is very important. Despite its importance, the effect of anisotropy on the occurrence of wrinkling was not considered in the literature up to now. In this investigation, a quantitative study on the wrinkling of thin walled tube bending is carried out through a finite element model of the process using velocity integral parameter, which is used for the detection of wrinkles. The other methods usually warn the wrinkling initiation with no precise location prediction. In addition, the effects of some process parameters, specially normal and planar anisotropy on the tube wrinkling are investigated. It is shown that increasing normal and planar anisotropy (increasing r0 and r90 values) result in a decrease in tube wrinkling.     

Estimation of fully plastic crack tip stresses from equilibrium of least upper bound circular arcs

This paper presents a simple method to estimate fully plastic crack tip stresses based on the equilibrium condition of the least upper bounds for plane strain deformation fields consisting of rigid-body rotation across a circular arc extending from a crack tip across the remaining ligament. The method is applied to deep, single-edge-cracked specimens under combined bending and tension. For various bending-to-tension ratios, the limit loads and crack tip stresses are estimated from the present method and compared with results from finite element limit analyses. The present method gives impressive results.     

Regularities of the change in the coercive force under biaxial asymmetric deformation of steel 3

The change in the coercive force under biaxial asymmetric (tension and compression in mutually perpendicular directions) cyclic deformation of cross-shaped steel 3 specimens in the elastic region of deformations was studied. Specimens were deformed beforehand under biaxial asymmetric loading to various degrees of plastic deformation. It was demonstrated that the elastic-deformation dependences of the coercive force measured along the tension and compression directions are qualitatively similar to those under uniaxial tension or compression. It was also shown that, under cyclic elastic loading, these dependences are reversible for well-annealed steel and have a hysteresis that expands with increasing degree of plastic deformation for plastically deformed steel. The possible causes of the hysteresis in the dependence of the coercive force on the elastic cyclic deformations under biaxial loading are discussed. It was supposed that the hysteresis of the coercive force was caused by the appearance of free (not bound in carbide phases) carbon atoms playing the role of interstitial impurity atoms for the α-iron lattice in plastically deformed carbon steels. The possibility of estimating the stressed-strained state of steel under biaxial loading using a magnetic method was discussed.     

Evaluation on interaction surface of plastic resistance for exposed-type steel column bases under biaxial bending

Exposed-type steel column bases are used widely in low-rise building construction Numerous researchers have examined methods to identify their stiffness and strength, but those studies have heretofore been restricted to in-plane behaviors This paper presents an experimental investigation of inelastic behaviors of square hollow section (SHS) steel column bases under biaxial bending Two types of failure modes are considered anchor bolt yielding and base plate yielding Different pinching effects and interaction surfaces for biaxial bending are observed for these two modes during bi-directional quasi-static cyclic loading tests Differences are elucidated using limit analyses based on a simple analytical model