Discontinuity waves of orderr≧1 in an inhomogeneous anisotropic linear elastic solid

Summary In the present paper we study the propagation of discontinuity waves of orderr (r=fixed integer 1) travelling through an inhomogeneous anisotropic linear elastic solid. By means of the theory of singular surfaces and the ray-theory we determine the evolution law of ther-th discontinuity vector along the rays associated with the wave front. We find that, even if the solid is linear and contrary to the homogeneous case, the behaviour of the discontinuities depends on the orderr of the wave through the normal speed of propagation of the wave front.     

Surface Yielding of Metals by X-ray Diffraction

Surface yielding of metallic material was measured with strain gage and X-ray diffraction methods.The results show that.when the residual stress in the transverse direction is involved,the surface yieldstrength should be evaluated with biaxial Mises criterion.For a medium carbon high strength steel,the yield strength of the bulk material is 581 MPa and the surface yield strengths for 0.05% and0.1%plastic strain are about 436 MPa and 463 MPa respectively.The 0.05% yield strength willapproximately increase to 788 MPa after shot peening.In the early stage of plastic deformation,strain hardening in the surface layer is quite different from that of the bulk sample.     

The strengthening effect caused by an elastic contrast��part II: stratification by a thin stiff layer

To quantify the gain in strength of a layered heterogeneous structure caused by the elastic contrast between the layers, especially if no crack deflection is observed at the interface, two original mechanisms baptized ??step-over?? and ??jump-through?? were proposed in Part I. They addressed the ability of a crack to pass through an interface and were applied to a bimaterial structure; whereas part II is dedicated to a homogeneous beam embedding a thin stiff film. The asymptotic expansions differ significantly since the small parameter is now the layer thickness. Unlike the first part where it was difficult to evidence the gain in toughness due to the superposition of two effects: a simultaneous increase in stiffness and in toughness, here it is possible to characterize the strength enhancement in using a single parameter. A discussion of the possibility to repeat the effect by multiplying the thin films is presented at the end.     

Dynamics of an elastic multibody chain: Part B—Global dynamics

In this the second paper in a series describing the dynamics of an arbitrary multibody system, the global dynamics of a topological chain of elasticbodies is considered in detail. The direct-path approach is used in the assignment of coordinate systems, interbody position vectors, connection matrices, and in the handling of mass properties, all in conjunction with a Newton-Euler, finite-element formulation. Nonlinear inertial effects, which can be important during rapid manoeuvres, are also identified.

The equations are first collected in a form appropriate to a chain with unconstrained joints—a full six degrees of freedom are permitted at each interbody joint. Constraints are then selectively introduced and the associated constraint forces calculated using the concept of projection matrices. The associated control forces (to carry out robotics tasks, for example) are also calculated. Finally, a compact form of the motion equations is presented for a multibody chain with constrained-controlled interbody joints.     

Dynamic buckling of elastic–plastic beams including effects of axial stress waves

Buckling of axially compressed elastic–plastic beams is discussed. The load is applied instantaneously and remains unaltered during the motion. The effect of stress waves travelling along the beam is taken into account. It is assumed that the material of the beam has linear-strain hardening. A method of solution, based on the Galerkin technique, is proposed; this method is applicable to an arbitrary number of degrees of freedom. Numerical examples are presented.     

Dynamics of an elastic multibody chain: part a—body motion equations

In this paper—the first of a series describing the dynamics of an arbitrary multibody system—motion equations governing a set of individual bodies in a chain configuration are discussed. A chain consisting entirely of rigid bodies is considered first. Motion equations for a typical body of arbitrary shape and arbitrary mass distribution are then briefly summarized. Finally, the geometrical constraints necessary to connect the individual bodies into a chain are derived.

Large translational and rotational motions are permitted at the joints connecting contiguous bodies. In other words, both prismatic and revolute joints are included, alone and in combination. As well, the interbody force constraints required to ensure that equal but opposite forces and torques exist at each joint are developed. The resulting expressions are amenable to the introduction of constraint and control forces at the chain joints. This permits the number of actively controlled degrees of freedom at any specific joint to be arbitrarily specified. The equations are fully nonlinear in the ‘rigid’ velocities for all individual chain bodies.

The analysis is then extended to the case of a chain consisting of an arbitrary number of elastic bodies. Each elastic body is assumed to possess an arbitrary stiffness distribution, although structural deformations are assumed to be small.     

On a more generalized theory of the pull-out test from an elastic matrix Part II—Application to a polypropylene-cement system

The theoretical treatment presented in Part I of this work is applied to a system which consists of polypropylene (PP) yarns embedded in a cement matrix. The maximum pull-out force values, obtained from specimens produced with different embedment lengths, normal stresses and yarn thicknesses are analyzed by using the formulae deduced in Part I. The results show that increasing the above three parameters brought about an increase of the maximum pull-out forces. When comparison is made with the theoretical formulae, the interfacial shear strength of the PP-cement system is calculated to possess values between 0·8 and 1·2 MPa, according to the amount of pressure applied on the system. The hexagonal close-packed array is employed to describe the way the PP fibers are arranged in the yarn, and found suitable to estimate the effective area of contact of the fiber-matrix interface.     

Investigations of fracture instability in crack growth for several metals—Part II: An energy approach for fracture instability analysis of crack growth

An energy approach is presented to predict fracture instability using elastic-plastic internal energy in structures, the physical behaviour of crack growth, dynamic effects in the process of unstable crack growth and intense strain region near the crack tip are considered. The practical forms of the approach have predicted correctly fracture instability of tests with three-point bending specimens (3PB specimen) and compact specimens (CT specimen) under highly stiff supporting system, but tearing modulus criterion gave incorrect estimations which were shown in part I [1].     

Normal penetration of an eroding projectile into an elastic–plastic target

The main objective of the present work is to describe normal penetration of a deformable projectile into an elastic–plastic target. The force imposed on the projectile by the target is generally a complex function of the strength of the target material, the projectile velocity, its diameter and shape, as well as the instantaneous penetration depth. When this force exceeds a certain critical value the projectile begins to deform. At moderate-to-high values of the impact velocity, the projectile's tip material flows plastically with large deformations causing the formation of a mushroom-like configuration. This process is accompanied by erosion of the projectile material. In the rear (“elastic”) part of the projectile the deformations remain small and the region can be approximated as a rigid body being decelerated by the projectile's yield stress. The general model allows one to predict the penetration depth, the projectile's eroded length and the crater diameter. It has been shown that in the limit of very high impact velocities the present model reduces to the well-known form of the hydrodynamic theory of shaped-charge jets. Also, a simplified asymptotic formula for the crater radius has been derived which includes the effect of the target's yield stress and compares well with experimental data for very high impact velocities.     

The causal effective field approximation— Application to elastic waves in fibrous composites

A new version of the effective field approach is presented with application to random fibrous composites. The approach incorporates the causality of the response and the static results, which comply with the best bounds available. Extensive comparison with other methods is given.     

The analysis of elastic liner in a cylindrical tunnel subjected to sh‐waves

Abstract

In this paper, we investigate the dynamic stresses of an elastic liner around a cylindrical tunnel subjected to an incident plane SH‐wave in an infinitely extended elastic medium. The investigation is based on the anti‐plane strain approximation of the dynamic theory of elasticity. The solutions are obtained by applying the method of wave functions expansion. Numerical results of dynamic stress concentrations at the outer and inner boundaries of the liner for various parameters are discussed in detail.     

Effective properties of fiber-reinforced materials: II—Bounds on the effective elastic moduli of dispersions of fully penetrable cylinders

We evaluate third-order bounds on the effective transverse bulk and shear moduli of transversely isotropic fiber-reinforced materials for a distribution of fully penetrable cylinders in a matrix. The third-order bounds not only incorporate the simplest of statistical quantities, the fiber volume fraction φ₂, but also involve microstructural parameters which depend upon the threepoint matrix probability function of the model. The third-order bounds, for the fully penetrable-cylinder model and for a wide range of conditions, significantly improve upon second-order bounds on the effective transverse elastic moduli, due to Hill and to Hashin, which incorporate φ₂ only. In particular, when the fiber phase is as much as two orders of magnitude more rigid than the matrix phase, the Silnutzer bounds, for the model considered here, reduce the second-order bound widths by over 50% for 0 ≤ φ₂ ≤ 0.5.     

Dynamic buckling of elastic–plastic square tubes under axial impact—II: structural response

Dynamic elastic–plastic buckling of thin-walled square tubes is studied from the viewpoint of elastic–plastic stress wave propagation, which originates from an axial impact loading. The influence of the impact velocity and the striking mass on the development of the buckling shape is discussed when considering the transient deformation process. It is shown that the maximum load, which results from a high velocity impact load and occurs at t=0, is a function of the impact velocity and is related to the speed of the elastic–plastic stress waves propagating along the tube. The predictions for the initiation of buckling based on a numerical simulation of the axial impact of strain rate insensitive square tubes using the FE code ABAQUS show good agreement with the results from experiments on aluminium alloy tubes impacted at various initial velocities. A comparison between the buckling initiation in square tubes and geometrically equivalent circular tubes reveals differences in the response, which are attributed to the stress wave propagation phenomena and to the structural differences between the two structures.     

On fast fracture in an elastic-(plastic)-viscoplastic solid Part II – The motion of crack

The motion of a crack in an elastic-(plastic )-viscoplastic medium is studied in terms of an energetic analysis. Combined with the stress and velocity fields obtained in Part 1, Kishimoto's energy integral, , is used as a crack driving force to determine its motion. The major results obtained are: (1) dependence of crack speed on a modified near-field parameter, K _I tip, (or equivalently, a modified dynamic energy release, G _I tip), which is different from the usual stress intensity factor K _I of an elastic crack-tip field but is related to it; (2) influence of inelastic effect, such as the viscoplastic exponent n, on the motion of the crack; and (3) stability condition of crack motion. In particular, for the last point, it has been found that, for a given loading and material coefficients, there exist two possible motions of the crack: one is stable crack growth and the other is unstable fracture. The lower and upper bounds of crack motion are also discussed. It is finally shown that the maximum crack velocity is lower than the Rayleigh wave speed, and is dependent on the viscoplastic exponent of the material.     

Investigation of Peak Separation for X—ray Diffraction Profilesof Spinodal Decomposition by a Kind of Optimized Voigt Function

The intensity and position of sidebands (satellites) on both sides of main diffraction peak in a great number of X-ray diffraction profiles of alloys always change with progress of aging.The sidebands position is determined by a newly optimized Voigt function in present investigation.Furthermore,for Cu-4 wt pct Ti alloy aged at 400℃ for 720 min and 1080 min,after introducing the weight factor of above two satellites intensity,the relative error between the fitting curves and X-ray diffraction profiles is less than 0.185%,which is more precise than the previously calculating result.     

The semi-elliptical surface crack—A solution by the alternating method

A numerical solution to the three-dimensional equations of elasticity is presented for the problem of a semi-elliptical surface crack in the surface of a finite thickness solid. The alternating method is used to develop the numerical results which incorporate the effects on the stress intensity factor due to the presence of both the front and the back surfaces. The stress intensity factor is presented as a function of position along the crack border for a variety of crack shapes and crack depths. A comparison of the results of this study is made with previous theoretical and experimental work.

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Résumé Une solution numérique à équations tridimensionnelles d'élasticité est présentée pour le problème de la fissure de surface semi-elliptique située en surface ou en solide d'épaisseurs finies.La méthode proposée est utilisée pour développer des résultats numériques qui incorporent les effets des facteurs d'intensité des contraintes associée à la fois des surfaces recto et verso du solide. Le facteur d'intensité des contraintes est décrit pour diverses positions de la fissure et ce dans divers cas de formes et de profondeurs de fissuration. Une comparaison est faite entre les résultats de cette étude et des travaux théoriques et expérimentaux antérieurs.

     

The mode‐III fracture analysis of an inclined crack embedded in thin layer systems by analytical alternating methods

Abstract

This paper analyzes the mode‐III stress intensity factor of an inclined crack, embedded in a thin layer, bonded to a half plane, subjected to arbitrary distributed anti‐plane loads. Special alternating procedures are presented to evaluate the mode‐ III S.I.F. and the numerical results confirm the validity of the proposed alternating procedure. The solution of a bi‐material problem in an infinite plane with an inclined crack and the analytical solution of a thin layer, without crack, bonded to a half plane, subjected to an anti‐plane point force applied on the boundary are referred to as fundamental solutions. By using these fundamental solutions and alternating procedures, the stress intensity factors of a crack in a thin layer bonded to a half plane are evaluated. The numerical results of some reduced problems are computed and excellent agreements with existing solutions are obtained.     

Diffraction characterization of microstructure scale fatigue crack growth in a modern Al–Zn–Mg–Cu alloy

SEM-based electron backscattered diffraction (EBSD) measurements characterize constituent-particle nucleated fatigue crack path relative to local grain orientation and crack wake defect distribution for Al–Zn–Mg–Cu alloy 7050-T7451 stressed in moist air. Crack propagation is primarily transgranular; consisting of facets parallel to {1 0 0}, {1 1 0} and high-index planes with no evidence of {1 1 1} slip-based cracking; and is also inter-subgranular involving pre-existing or fatigue process zone generated subgrain boundaries. Dislocation substructure develops close to the fatigue crack surface due to dynamic recovery of crack tip cyclic plasticity. Crack growth through subgrain structure explains the broad occurrence of crack features without a low-index orientation and is justified based on trapped-hydrogen embrittlement. A failure criterion for environmental fatigue modeling must capture a failure mechanism based on: (a) formation of localized defect structure from cumulative cyclic plasticity (perhaps H sensitive), and (b) subsequent embrittlement due to interaction of H trapped at this defect structure with microstructure-sensitive local tensile stresses normal to this weakened interface. Crack interaction with subgrain (and grain) boundaries produces local deflections and branches that arrest over a short distance. Such features should cause a distribution of microstructure-sensitive growth rates.