Zur Ermittlung verformungsbedingter Makro- und Mikroeigenspannungen durch mechanische und röntgenographische Eigenspannungsanalysen

Analysis of deformation induced residual macro-and microstresses by mechanical and X-ray methods Residual stress distributions in plastically deformed tensile and bending specimens of perlitic steel were analysed using X-ray diffraction technique and incremental holedrilling method. After tensile loading compressive residual stresses are measured by X-ray analysis in the ferrite phase. Consequently X-ray analysis detects compressive microstresses. In the case of bending specimens residual macrostresses are superposed with residual microstresses after unloading. In no case identical residual stress values were measured by X-ray and hole drilling methods. Microstresses can be separated combining both measurement methods. Microstresses after tensile loading were found to be greater than in surface layers of respective bending samples subjected to the same amount of plastic strain.     

Effect of pressure rolling on the residual stress state of a particulate-reinforced metal matrix composite

The large difference between the coefficients of thermal expansion of the matrix alloy and the particle in a metal matrix composite gives rise to residual stresses in the material. In the present work, the effect of pressure rolling on the residual stress state of a silicon carbide particle-reinforced 2014 aluminium alloy has been investigated. The three-dimensional stress state measured in both phases-matrix and reinforcement-has been determined using an X-ray diffraction technique. A twofold effect of pressure rolling on the residual stresses was observed. On the one hand, compressive macrostresses as large as - 250 MPa were induced. On the other hand a significant reduction in pseudo-macrostresses was measured where the plastic deformation reaches a maximum. A modified Eshelby model was used to predict quantitatively and qualitatively the residual microstresses after heat treatment and pressure rolling respectively.     

A numerical study of steady plane granular chute flows using the Jenkins–Savage model and its extension

The granular flow model proposed by Jenkins and Savage and extended by us is used here to construct numerical solutions of steady chute flows thought to be typical of granular flow behaviour. We present the governing differential equations and discuss the boundary conditions for two flow cases: (i) a fully fluidized layer of granules moving steadily under rapid shear and (ii) a fluidized bottom-near bed covered by a rigid slab of gravel in steady motion under its own weight. The boundary value problem is transformed into a dimensionless form and the emerging system of non-linear ordinary differential equations is numerically integrated. Singularities at the free surface and (in one case) also at an unknown point inside the solution interval make the problem unusual. Since the non-dimensionalization is performed with the maximum particle concentration and the maximum velocity, which are both unknown, these two parameters also enter the formulation of the problem through algebraic equations. The two-point boundary value problem is solved with the aid of the shooting method by satisfying the boundary conditions at the end of the soluton interval and these normalizing conditions by means of a minimization procedure. We outline the numerical scheme and report selective numerical results. The computations are the first performed with the exact equations of the Jenkins–Savage model; they permit delineation of the conditions of applicability of the model and thus prove to be a useful tool for the granular flow modeller.     

Residual stresses in surface layers of carbide tool tips after diamond grinding

X-ray diffraction measurements were used to study residual stresses in the surface layers of WC-Co specimens after diamond wheel grinding. The presence of compressive macrostresses was established and the mechanism of their formation was considered. Data relating to grinding with diamond and other abrasive wheels were compared.     

Particle finite element analysis of the granular column collapse problem

The problem of granular column collapse is investigated by means of an axisymmetric version of the particle finite element method (PFEM). The granular medium is represented by a simple rate-independent plasticity model and the frictional contact between the granular flow and its rigid basal surface is accounted for. In the version of the PFEM developed for this study, the governing equations of the boundary value problem are cast in terms of an optimization problem and solved using mathematical programming tools. The agreement between model and experiment is generally satisfactory, quantitatively as well as qualitatively. However, the friction angle of the granular material, as well as the exact interface conditions between the base and granular material, are shown to have a relatively significant influence on the results.     

On the energy dissipation and velocity discontinuities in granular materials and solution of a boundary value problem in geophysics

Summary Consider the plane-strain rigid-perfectly plastic deformation of a granular material which satisfies the stress equilibrium equations and the Coulomb yield criterion. An expression is derived which enables the rate of energy dissipation to be calculated for any pair of stress and velocity fields. This is specialised to the Spencer-Mehrabadi-Cowin model and a kinematic inequality is obtained. Jump conditions are derived for velocity discontinuities on the boundary and in the interior of the plastic region. A simple analytic solution of the equations of the Mehrabadi-Cowin model is presented for the deformation of a granular material filled joint or fracture separating two rock masses undergoing a shearing motion.With 5 Figures     

Parametric instability of functionally graded beams with an open edge crack under axial pulsating excitation

This paper studies the parametric instability of functionally graded beams with an open edge crack subjected to an axial pulsating excitation which is a combination of a static compressive force and a harmonic excitation force. It is assumed that the materials properties follow an exponential variation through the thickness direction. Theoretical formulations are based on Timoshenko beam theory and linear rotational spring model. The governing equations of motion are derived by using Hamilton’s principle and transformed into a set of Mathieu equations through Galerkin’s procedure. The natural frequencies with different end supports are obtained. The boundary points on the unstable regions are determined by using Bolotin’s method. Numerical results are presented to highlight the influences of crack location, crack depth, material property gradient, beam slenderness ratio, compressive load, and boundary conditions on both the free vibration and parametric instability behaviors of the cracked functionally graded beams.     

Free-surface granular flows down heaps

The present paper extends the granular-flow constitutive model of Savage (1998 J Fluid Mech 377:1–26) to treat spherical particles. Savage accounted for both quasi-static and collisional stresses by considering: (i) strain-rate fluctuations embodied in a critical state plasticity model, as well as, (ii) individual particle velocity fluctuations modelled by granular-flow kinetic theory. In the present work, the governing equations of the kinetic theory of Jenkins (1998 In: Hermann HJ, Luding S (eds) Physics of Dry Granular Media. Kluwer Academic pp. 353–370) for identical spherical, smooth, inelastic particles are supplemented with additional quasi-static terms that have forms patterned after the corresponding terms in the equations of Savage for two-dimensional disk-like particles. The resulting equations along with side-wall and free-surface boundary conditions are applied to examine free-surface granular flow down a heap contained between two frictional vertical side walls. Width-averaged equations of motion are integrated to obtain depth profiles of mean velocity, granular temperature, solids fraction and the Savage–Jeffrey parameter. Detailed comparisons are made with particle-tracking experiments. When the gap between the vertical side walls is fairly narrow, good agreement is found between the predicted and the measured profiles of mean velocity and granular temperature.     

Stability of a twisted and compressed clamped rod

We consider the problem of determining the stability boundary of an elastic rod clamped at both ends and loaded by a compressive force and a couple. The constitutive equations of the rod are such that both shear of the cross section and compressibility of the rod axis are considered. The stability boundary is given by the bifurcation points of a system of eight nonlinear first-order differential equations, obtained by using the first integrals. Depending on the parameter values the type of bifurcation is determined. The post-critical shape of the rod is obtained by the numerical integration of a system of 12 nonlinear first-order differential equations.     

Multiple-parameter reduced basis technique for bifurcation and post-buckling analyses of composite plates

A multiple-parameter reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analyses of composite plates subjected to combined loadings. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the stability boundary. The plate is discretized by using displacement finite element models and the analysis region is reduced by exploiting the special symmetries exhibited by the response of the plate. The vector of unknown nodal displacements is expressed as a linear combination of a small number of path derivatives (derivatives of the nodal displacements with respect to path parameters), and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the stability boundary of the plate. In the second stage, a nonllnear solution in the vicinity of the stability boundary is obtained by using a bifurcation buckling mode as a predictor, and a set of reduced equations is generated. In the third stage, the reduced equations are used to trace post-buckling paths corresponding to various combinations of the load parameters. The potential of the proposed approach is discussed and its effectiveness is demonstrated by means of a numerical example of laminated composite plate subjected to combined compressive and shear loadings.     

Thermomechanical postbuckling analysis of functionally graded plates and shallow cylindrical shells

Summary. In this paper, an analytic solution is provided for the postbuckling behavior of plates and shallow cylindrical shells made of functionally graded materials under edge compressive loads and a temperature field. The material properties of the functionally graded shells are assumed to vary continuously through the thickness of the shell according to a power law distribution of the volume fraction of the constituents. The fundamental equations for thin rectangular shallow shells of FGM are obtained using the von Karman theory for large transverse deflection, and the solution is obtained in terms of mixed Fourier series. The effect of material properties, boundary conditions and thermomechanical loading on the buckling behavior and stress field are determined and discussed. The results reveal that thermomechanical coupling effects and the boundary conditions play a major role in dictating the response of the functionally graded plates and shells under the action of edge compressive loads.     

A BEM-based meshless solution to buckling and vibration problems of orthotropicplates

In this paper a BEM-based meshless solution is presented to buckling and vibration problems of Kirchhoff orthotropic plates with arbitrary shape. The plate is subjected to compressive centrally applied load together with arbitrarily transverse distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting buckling and vibration problems are described by partial differential equations in terms of the deflection. Both problems are solved employing the Analog Equation Method (AEM). According to this method the fourth-order partial differential equation describing the response of the orthotropic plate is converted to an equivalent linear problem for an isotropic plate subjected only to a fictitious load under the same boundary conditions. The AEM is applied to the problem at hand as a boundary-only method by approximating the fictitious load with a radial basis function series. Thus, the method retains all the advantages of the pure BEM using a known simple fundamental solution. Example problems are presented for orthotropic plates, subjected to compressive or vibratory loading, to illustrate the method and demonstrate its efficiency and its accuracy.     

通电瞬时板内半无限长裂纹尖端域的应力场

以导电弹性体的麦克斯威尔方程为出发点,借助于边界条件和初始条件,推得了在向含半无限长直线裂纹的无限大导电薄板内通入电流的瞬时,裂纹尖端附近电流密度的表达式。在此基础上,得到了裂纹尖端区域处温度和应力的具体表达式。算例表明,在电流所产生的焦耳热源的作用下,裂尖区域处的温度将瞬时升高,并伴有压应力的产生,从而可达到阻止裂纹扩展的目的。     

Plane steady shear flow of a cohesionless granular material down an inclined plane: A model for flow avalanches Part I: Theory

Summary A continuum mechanical model describing rapid shear flow of granular materials as deduced by Jenkins and Savage (1983) [11] from considerations of statistical mechanics is applied to steady plane shear flows down an inclined chute. Depending on the type and form of the physically suggested boundary conditions that are imposed at the base and the free surface, respectively, the emerging boundary value problems permit or prohibit existence of mathematical solutions. For instance, the model does not permit incorporation of an aerodynamic drag and requires special sliding boundary conditions at the base. Cause for the singular behavior is the fact that granular pressure and fluctuation energy vanish simultaneously. Rectification is e.g. possible by including particle density gradients in the constitutive relation of granular stress, but this requires postulation of additional boundary conditions.We present the differential equations and boundary conditions and suggest a procedure of non-dimensionalization which yields the dimensionless parameters governing the problem. Construction of local solutions close to the boundaries by means of Frobenius expansions discloses the singular behavior and yields the basis for the non-existence proof under limiting conditions. Adding to the particle stress a Newtonian viscous contribution is not sufficient to regularize the problem and neither is the form of the stress tensor resulting from Lun et al.'s statistical model that incorporates kinetic terms. The stress tensor must have a term proportional to the dyadic product of the particle concentration gradient with itself. Numerical solution techniques and computational results are given in a companion paper (Hutter, Szidarovszky, Yakowitz, 1986 [9]).With 3 Figures     

Zum Mechanismus der Wechselfestigkeitssteigerung durch Werkstoffverfestigung und Druckeigenspannungen nach einer Oberflächenbehandlung

The Improvement of Fatigue Limit as a Result of Hardening and Macrostresses Due to a Surface Treatment Surface treatments, that increase the hardness as well as induce surface residual macrostresses, are universaly able to improve the fatigue limit. It is shown, that depending on the shape of specimens both effects together are responsible for the raise of the fatigue strength, which is in contrast to former opinions. The increase of hardness increases the stress required for crack initiation and is thus decident for unnotched specimens, whereas in this case the influence of permanent residual stresses is relatively smaller. Notched specimens of sufficient stress concentration factor k_t are determined by the crack propagation conditions, which can be controlled decisively by mean loads. The increase of hardness improves the resistance against crack initiation proportional to the 1/k_t portion of the unnotched fatigue limit, but cracks remain nonpropagating as long as a certain minimum alternative stress, which can be raised by compressive residual stresses, is not exceeded. Depending upon concentration factor, mean compressive load and hardness the transition from crack initiation to crack propagation as the criterion for fatigue fracture can be estimated by several fatigue-strength-diagrams, which are evaluated for specimens of constant hardness but are valid for surface hardened specimens as well.     

Weakly nonlinear analysis of two dimensional sheared granular flow

Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg–Landau equation of a disturbance amplitude starting from a set of granular hydrodynamic equations and discuss the bifurcation of the steady amplitude in the hydrodynamic limit.     

Failure of cemented granular materials under simple compression: experiments and numerical simulations

We investigate the strength and failure properties of a model cemented granular material under simple compressive deformation. The particles are lightweight expanded clay aggregate beads coated by a controlled volume fraction of silicone. The beads are mixed with a joint seal paste (the matrix) and molded to obtain dense cemented granular samples of cylindrical shape. Several samples are prepared for different volume fractions of the matrix, controlling the porosity, and silicone coating upon which depends the effective particle–matrix adhesion. Interestingly, the compressive strength is found to be an affine function of the product of the matrix volume fraction and effective particle–matrix adhesion. On the other hand, it is shown that particle damage occurs beyond a critical value of the contact debonding energy. The experiments suggest three regimes of crack propagation corresponding to no particle damage, particle abrasion and particle fragmentation, respectively, depending on the matrix volume fraction and effective particle–matrix adhesion. We also use a sub-particle lattice discretization method to simulate cemented granular materials in two dimensions. The numerical results for crack regimes and the compressive strength are in excellent agreement with the experiments.     

Compressive pressure dependent anisotropic effective thermal conductivity of granular beds

In situ planetary thermal conductivity measurements are typically made using a long needle-like probe, which measures effective thermal conductivity in the probe??s radial (horizontal) direction. The desired effective vertical thermal conductivity for heat flow calculations is assumed to be the same as the measured effective horizontal thermal conductivity. However, it is known that effective thermal conductivity increases with increasing compressive pressure on granular beds and the horizontal stress in a granular bed under gravity is related to the vertical stress through Jaky??s at rest earth pressure coefficient. The objectives of this study were to examine the validity of the isotropic property assumption and to develop a fundamental understanding of the effective thermal conductivity of a dry, noncohesive granular bed under uniaxial compression. A model was developed to predict the increase in effective vertical and horizontal thermal conductivity with increasing compressive vertical applied pressure. An experiment was developed to simultaneously measure the effective vertical and horizontal thermal conductivities of particle beds with needle probes. Measurements were made as compressive vertical pressure was increased to show the relationship between increasing pressure and effective vertical and horizontal thermal conductivity. The results of this experiment showed quantitatively the conductivity anisotropy for two different materials and validated the developed model. This model can be used to predict the anisotropic effective thermal conductivity of granular materials under uniaxial compressive pressures, and evaluate the uncertainties in lunar heat flow measurements.     

Neutron Strain measurement

The use of neutrons has extended the technique of diffraction strain measurement from an essentially two-dimensional, near-surface tool using X-rays to a true three-dimensional method. The depth scale has gone from micrometres to millimetres. This initially gave rise to subsurface measurements of type I residual macrostresses in weldments and type II residual microstresses in anisotropic and multiphase metals, and composites. Soon the possibilities of in situ applied stress measurements became apparent and today they represent a significant portion of the work being carried out. This perspective focuses on the current state of the art, the prospects and developments necessary for further progress. The transition from two- to three-dimensions raised the issues of stress free reference values, methodology for general tensor measurements, beam optics and experimental design. Workers invested great effort in resolving these issues. In addition, the development of pulsed source instruments has enabled in situ measurements of slip, fatigue, load partitioning, twinning, high T stress-strain response, thermal cycling and the shape memory effect. Most recently, the SNS instrument, VULCAN, has introduced torsion and continuous recording of data which can later be binned in the shortest statistically significant time intervals.