Showing papers in "Journal of the mechanical behavior of materials in 1993"

On the Effective Young's Modulus of Elasticity for Porous Materials: Microstructure Modelling and Comparison Between Calculated and Experimental Values

Abstract: A model equation for the prediction of Young's modulus of elasticity of porous materials has been proposed on the basis of an earlier theoretical work on two-phased composite materials. The derivation assumes a definite microstructural spheroidal model and the effective Young's modulus can be given as a function of the volume fraction of closed porosity and the microstructural parameters: shape (axial ratio of the spheroidal pores) and orientation. The theoretical predictions for different pore geometries have been compared with experimental data on porous metals, ceramics and glasses. Good agreement between theory and experiment was found. The microstructural parameters involved in the equation can be obtained from real microstructural data via quantitative microstructural analysis and stereology, no fitting is involved. This fact makes the proposed equation substantial also for practical applications. * The present article is the second part of a comprehensive study under the same title« The first part has already been published and is quoted in ref, [2].

The Conversion of Plastic Work to Heat Around a Dynamically Propagating Crack in Metals

Abstract: Investigations of the temperature rise at a dynamically propagating crack tip using an infrared detector array are reported. Also, a measurement of the fraction of plastic work converted to heat using a split hopkinson bar apparatus in conjunction with an infrared detector array is summarized. For 4340 steel it is seen that ≈85% of the plastic work is converted to heat leading to a temperature rise of 300°C at a crack tip propagating 600 m/s in steel. This results is compared to earlier studies that report a 450°C temperature rise at a crack tip propagating 900 m/s in steel. In a titanium alloy the temperature rise is higher than that in steel for equal plastic work rate densities. The conditions at the crack tip are shown to be adiabatic, and, as a result, this effect is due to the difference in density, heat capacity and crack tip speed. Thermal conductivity has no effect.

The Eigenvalue Problem in Hemivariational Inequalities and its Application to Composite Plates

Abstract: The aim of the present paper is the mathematical study of a new type of eigenvalue problem for variational inequality expressions, the eigenvalue problem of hemivariational inequalities. This problem arises in the case of nonconvex energy functionals in several problems of Mechanics and Engineering. Due to the lack of monotonicity the study of this problem is based on compactness and average value arguments in contrast to the variational inequalities where monotonicity arguments are applied. After the formulation and the study of the mathematical problem concerning the existence and the approximation of its solution, the theory is applied to the study of the stability problem of composite von Karman plates which are connected with an adhesive material.

Dynamics of Rods with Interfacial Dry Friction

Abstract: Dynamics of elastic rods interacting with environment accordingly to the dry friction law is studied. Method of exact solution of this nonlinear problem is developed. As an example the problem of stationary forced vibrations of an elastic semiinfinite rod excited by a periodical triangular stress impulse is considered. The exact solution of this problem is applied to analysis of the structural damping.

An Experimental and Numerical Study of Mode I (Tensile) and Mode II (Shear) Fracture in Concrete

Abstract: In the paper tensile (mode I) and shear (mode Π) fracture experiments on concrete are analysed with a recently developed lattice model. In the mode I experiments, crack growth is correlated to the global load-displacement behaviour. In the mode II experiments on four point shear beams, the influence of boundary conditions is studied. In the model, the material is schematized as a regular lattice of brittle breaking beam elements. The lattice is projected on top of a generated grain structure of concrete, and different stiffness and strength values are assigned to the bar elements in different parts of the concrete. Cracking is simulated as a pure brittle process. The mode I experiments revealed that crack face bridging is the main explanation for softening of concrete. In the simulations, crack face bridging was observed, and was found to be a direct consequence of the heterogeneous structure of the material. Moreover it was found that the response of the four point shear tests, including effects caused by a variation of boundary conditions, could be simulated with a pure mode I criterion for the lattice elements. Because the aggregative structure of the material is modelled directly, a natural size effect follows from the analyses. The fracture law is extremely simple, and only information regarding the stiffness and strength of the lattice elements is needed. All the model parameters are single valued. This is in sharp contrast to the softening law needed in macroscopic fracture models, which is usually a function of global average crack opening, and which becomes path dependent under combined tension and shear.

Inelastic memory versus viscoplasticity of continuously damaged materials

Abstract: In the paper the principle of determinism based on inelastic (i.e. damage– plastic) deformation history is formulated. In the case of fading memory materials of integral (leading to a general endochronic theory) and differential type (leading to standard viscoplasticity with a non-associate flow rule) are obtained from a general functional representation. Rotations of natural state local reference configuration are discussed and issues concerning plastic spin and Drucker’s normality are discussed. INTRODUCTION The objective of this paper is to consider a relation between inelastic materials with internal variables and damaged inelastic materials with memory. If an evolution equation for plastic strain rate is given for the first class of materials, then its integration leads to the description represented by integrals whose kernels are responsible for a plastic memory. Here the opposite and more difficult way is aimed: to see how functionals appearing in a description of damaged inelastic materials with memory may be transformed into the corresponding evolution equations. For a correct constitutive theory a geometric description able to desribe properly most important microstructural changes during an inelastic deformation process is indispensable. This is done in the following section, whereas the last section is reserved for formulation of the theory. KINEMATICAL ISSUES Consider a crystalline body, B, in a real configuration (ψt) with defects (such as dislocations, voids, impurities) and an inhomogeneous temperature Published in Journal of the Mechanical Behavior of Materials, Vol.4, No.4, p.331–341, 1993.

Reverse Torsion Testing for Material Modeling

Abstract: The testing of metals to large strain using thin-walled tubular spev mens in torsion has been gaining in popularity in recent years. This pop larity has in large part stemmed from the predictions of the stress response to simple shear. This deformation mode has been shown to be able to discriminate between various material models, particularly the manner in which they handle the skew symmetric portion of the deformation. In this paper, the ability of the thin-walled specimen to successfully give simple shear behavior for a single strain reversal is analyzed using finite element simulation. The specimen is seen to sufficiently approximate reverse simple shear. Experimental results for the reverse torsion of 316 stainless steel and 1100 aluminum are presented. The stainless steel results are compared with the simple shear predictions for a variety of kinematic hardening theories. None of the theories considered here give good agreement with the experiment. The importance of reverse torsion tests are discussed in that light.

Thermodynamics of some viscoplastic material models with internal variables

Abstract: The thermodynamic restrictions for elastic-viscoplastic material models with evolution equations for the internal variables involving rates of external variables are derived. Compatibility with the Clausius-Duhem entropy inequality (Second Law) is required and this yields non-classical potential relations and a residual dissipation inequality. For two viscoplastic models (Robinson et al., Krempl et al.), which involve external variable rates in the evolution equations and which have not been embedded in a thermodynamic frame, the consistence with the non-classical potential relations is discussed. Further, the evaluation of the residual dissipation inequality is done for a thermodynamic extension of an early version of the Robinson model. Necessary and sufficient conditions for the material data are obtained to insure a non-negative mechanical dissipation. The results demonstrate that the model is formally consistent with the Second Law. 1. ON THE STRUCTURE OF EVOLUTION EQUATIONS FOR INTERNAL VARIABLES INVOLVING RATES OF EXTERNAL VARIABLES It is well known that thermodynamic restrictions for the constitutive equations derive from an evaluation of an entropy principle. Very often it is taken to be the Clausius-Duhem inequality. In its time and space integral form it reads where η is the specific entropy, qk are components of the heat flux, r is the external heat supply, Τ is the absolute temperature, ρ is the density, and V , A , nj, are the volume, the surface area of the body and the external unit vector on the surface. The usual summation convention applies to repeated subscripts. For sufficiently smooth fields the divergence theorem and localization in space and time yield the local instant Clausius-Duhem inequality V (1 .1)

Homogenized Model for Discretely Drained Soil Systems

Abstract: I N T R O D U C T I O N For the purposes of foundation improvement prior to construction and in decontamination of polluted sites it is often necessary to dewater large scale soil stratum by large arrays of discrete drains, e.g. wells, stone or sand columns, or wick drains. The number of discrete drains may number in the thousands. In many situations it is necessary to analyze the soil deposit containing the drains and any structure built on or within it in order to determine their behavior during the drainage process The modeling and analysis of such discretely drained systems is the subject of this paper. While the emphasis of this paper is on drainage of water from soil, the concepts are applicable to other physical problems such as heat or electrical conduction in a composite system consisting of a low conducting matrix and high conducting reinforcing elements such as metallic wires.

About Rotational and Translational Modes of Plasticity and Fracture Initiated by Dynamic Loading of Materials

Abstract: An approach based on the multiscale micromechanisms of dynamic deformation is developed. The coupling between kinetics of elementary carriers of deformation and macroscopic strength of materials is studied on example of three kind of ductile steel loaded within flyer velocities 100-500 m/s. Transition between mesoscopical (10 10 cm), superstructural (2-10 grain sizes), and macroscopical scale levels is found to take a translational or rotational form depending on the particle velocity distribut ion (PVDW) at the corresponding scale level. The main sense of that characteristic is reduced to ability of a material structure to rapid relaxation of internal stress at that level. The increasing of PVDW at the mesolevel leads to decreasing analogous value at the superstructural level, that is kinetic characteristics of adjacent scale levels are in opposite phase. The evidence is available that the greatest dynamic tensile and shear strength appears to be inherent to materials in which rotational mechanisms of deformation and fracture is realized, in distinction from materials with translational ones, where shear strength is the smallest.

Laminated Intermetallic Composites Based on NiAl

Abstract: Laminated intermetallic composites based on NiAI have been fabricated, and their mechanical properties and microstructures have been studied. Composites were prepared by hot isostatic pressing laminates consisting of NiAI powders, and either N13AI or IN718 sheets. The sheet materials were introduced as a toughening agent. The microstructures and mechanical properties of the composites were varied by heat treatment. Three-point bending tests at room temperature indicated a four-fold improvement in the strength compared to monolithic NiAI, as well as substantial toughness. The composites were significantly less dense than traditional nickel-base alloys, which makes them attractive as potential hi.^h temperature structural materials. The strength of the composites was controlled by the NiAI, but the toughness depended strongly on the properties of interfaces and the toughening phases.

Constitutive model for concrete under biaxial stress state

Abstract: A biaxial constitutive model for concrete based upon the incremental theory of plasticity with isotropic hardening is presented. In order to improve the accuracy of the model, the experimental results of Kupfer et al. are used by introducing them into a data base. The model is used in the finite element computer program \"RECOFIN\" for the in-plane nonlinear analysis of Reinforced Concrete (R/C) structural members up to failure which has been developed in the R/C Laboratory Aristotle Univ. of Thessaloniki. A very good agreement of the analytically predicted stress-strain curves with experimental ones is observed. The results from the analysis of three specimens of plain concrete up to failure under various loading conditions are also presented.

Numerical Simulations of Dislocation Density Evolutions During Finite Elastic Plastic Deformation of FCC Single Crystals

Abstract: A previously developped microstructural description of the single crystal hardening law at the dislocation density scale has been introduced into a simulation code of FCC crystal finite elastic plasticity. In addition to the usual phenomenological and crystallographic parameters of the crystal plasticity in the athermal range, such a microstructural plasticity modelling allows some evolution estimates, under various mixed, regular and uniform loading conditions, for different types of dislocations (primary ones from source activation and glissile or sessile interaction products) on each crystallographic system (either of easy glide or not) of the considered structure. The relations between microstructure evolutions and hardening characteristics can thus be analyzed for different loading situations, either for isolated or for collections of grains. For a global visualisation of the dislocation distribution evolution with plastic straining, mainly in statistical terms but including some spatial features too, the concept of microstructural pole figure is introduced.

Crack Initiation Under Stress-Assisted Diffusion

Abstract: A macroscopic study of the crack init iat ion under stress-assisted d i f fu sion was undertaken. The stress-assisted diffusion creates a br i t t le core-region around the crack-t ip, which depends on the sum of principal stresses (o i +o 2 ) . The distribution of the stress-assisted diffusion around the crack-t ip influences the init ial curve of the caustics as well as the size and the form of the caustics. The pridiction of the crack init iation angle and the cr i t ical stress of fracture under stress-assisted diffusion are determined by using the Det. -cr i terion of fracture. The init iation angles and the cr i t ica l stresses depends on the br i t t le core-region, which is developed by the stress-assisted diffusion around the crack-t ip, and the phenomenological coeff icients, which depends on the materials. INTRODUCTION The stress-assisted diffusion theory has been recently proposed by Aifant is [1-5]. According to the stress-assisted diffusion theory, the distribution of the concentration ρ around the crack-t ip is given by: ρ = po [1 + Β(σχ • o y ) ] A (1) where ρ denotes the concentration on the boundary and A, Β are phenomenologicaf coeff icients. In the case of stress-assisted diffusion, it turns out that A = M/N and Β = N/D with the coeff icients D, Μ, Ν having a precise physical interpretation. Relation (1) is valid for points which lie outside a small region (process zone) surrounding the crack-t ip and defined by a \"c r i t i cal distance\" determined by the particular constitut ive structure of the material . For perfectly materials the \"cr i t ical distance\" approaches zero [6]. According to Oriani theory [7], the stress-assisted diffusion creates a br i t t le region around the crack-t ip. This br i t t le region is defined by the relation (1). So, we suggest that a new core-region is developed around the crack-t ip. In the new core-region there are many microcracks and voids which are created by the moving of the crack-t ip. The direction of the crack init iat ion and the VoL 4, No. 2,1993 Crack Initiation Under Stress-Assisted Diffusion critical stress of fracture are depended on magnitude of the new core-region. Applying the Det.-criterion [8-13] along of the new core-region, the direction of the crack initiation and the critical stress of fracture are calculated. THE DET.-CRITERION FOR PLANE-STRESS CONDITION For the case under generalized plane-stress conditions, the stress components in the vicinity of the crack-tip for a Cartesian coordinate system (Fig.1) are: σ * 0 , σ * 0 , τ * 0 , σ = τ = τ = 0 χ y xy ζ xz yz (2) The elastic strain-energy density is expressed by [14]: dW _ _ dV = ν + D where Τ energy Γ and T D are the dilatational (T ) and the distortional (Tp) straindensity. The T v and T D are given by [15,16]: τ 1-2v , s2 Τ = 0 [(σ + σ ) ν 6Ε χ y 1+υ Τ η = [(σ + σ ) 2 3 (ο σ τ ) ] D 3Ε χ y χ y xy (3)

Development of Slip Concept in Theory of Plasticity of Materials and Rocks

Abstract: Advantages of applying a mesoscale approach to mathematical description of plastic deformation of metals and rocks based on slip concept are demonstrated. First, development of continual theory of dislocations for solving elastic-plastic boundary value problems with strainindependent yield criterion is considered both for the case when slips occur along a preexisting set of parallel planes (as in layer composites and rocks) and the case when the slip surfaces are stress induced. Then, work-hardening materials are discussed. It is shown how with the aid of accounting for the cooperative and direct interaction of plastic slip increments of different orientations in the frame of kinematics of BatdorfBudiansky's type one can obtain constitutive equations. They involve only few material constants (for metals with monotonously decreasing plastic compliance) and has been experimentally verified for a wide variety of complex loading paths.

Surface Effects Identified Through Strain Gage Tests in Brittle Materials

Abstract: Surface effects is a common feature in material behaviour, and have been reported theoretically and experimentally. In this paper, the experimental observations from strain gage tests are interpreted to identify the surface effects of a brittle material under uniaxial compression. In the experiments, strain gages were placed at characteristic locations on the free surface of prismatic samples, and the strain gage readings were recorded at each load step. It is seen that brittle materials experience heterogeneous deformation from the early straining stages, and relative large deformation is claimed on the free surface at low load levels. As stress reaches about 80 percent of the peak strength, material starts to slab or spall from the structure along the free surface(s) , and deformation far from the surface increases rapidly. Through a simple statistical analysis, the transf ormation of local deformation is shown and explained by the mechanics of surface effects .

Structural Characteristics and Mechanical Properties of Compositionally Modulated Metallic Multilayers

Abstract: Compositionally modulated metallic thin films were prepared by dualsource thermal evaporation with modulation periods containing a small number of atomic planes. The structure of these materials was studied by x-ray diffraction as well as conventional and cross-sectional transmission electron microscopy. It was found that the primary defect type was the twinning which also determined the various growth modes. The latter were observed to be characteristically depended on the extent of the modulation period as was the twinning character, also. Thus, depending on this period, the primary parameter for the structural properties could be either the coherency strains or the chemical modulation, as well as an interplay of the two. This model is considered in discussing the mechanical properties of such materials and especially the socalled "supermodulus effect".

An Analysis of Morphological Instabilities at the Initiation of the Eutectoid Transformation Using a Kinetic Analogue

Abstract: A large number of two component solids show a specific temperature and composition where three-phase equilibrium is possible. In many cases, this three-phase equilibrium consists of a high temperature phase in equilibrium with two low temperature phases at a specific temperature and composition. In these instances, this point of three phase equilibrium on the phase diagram is called a eutectoid point, being specified by the eutectoid composition and the eutectoid temperature. An example of a eutectoid point of extreme technological significance is shown on the Fe-C phase diagram in Figure la.

Kinetic Theory of Continuously Distributed Dislocations

Abstract: Chapter 1 is devoted to formulation of the 3D kinetic theory of continuously distributed dislocations which is considered to be the basis for the mesoscale formation In this theory, the formation of mesoscale is considered to be the dynamic polarisation and collectivization of single-sign dislocations The dislocation densities and flows are determined as averaged values of the dislocation velocity distribution function When applied to high-velocity deformation processes in solids, this theory takes into account: (i) the inertial properties of the ECD; (ii) the dissipative character of the dislocation motion; (iii) the long-range interaction of dislocations with each other and (iv) the collective features of dislocations The development of the kinetic theory of dislocations includes the following steps: (i) definition of the velocity distribution function; (ii) deduction of the kinetic equation for the velocity distribution function The convective and collision parts of the kinetic equation consider both the dissipative features of the medium in which the dislocations move and their mutual long-range interactions; (iii) deduction of the moment equations by using the successive procedure of averaging the kinetic equation for the dislocation velocity distribution function The moment equations coincide with the well-known 3D equations of the continuous dislocation theory Being locked with the constitutive equation for dislocation interaction with each other and with the medium where they move, the moment equations allow to describe the formation of mesoscale as totality of the short-living single-sing dislocation pile-ups

On the Fast Crack Motion in Elastic and Elastic-Plastic Materials

Abstract: In the paper the comparison between experimental and theoretical findings on fast crack motion has been made. The essential differences have been pointed out. It has been concluded that these differences are due to the inadequacy of the models to represent the actual physical processes taking place and to the improper equations of crack motion usually assumed in the analysis. Utilizing simple Dugdale model for mode III case the results obtained suggest that one should adopt the equation of crack motion in another shape, both for s.s.y. and l.s.y. situations. The equation introduced contains a new physical quantity that represents energy flux into plastic or process zone. The quantitative results and computer simulation of the fast crack growth indicate that postulated equation is reasonable one giving good qualitative agreement with experiment.

Aspects of a Multiple Slip Model for 2D Texture Development and Plastic Spin

Abstract: A recently proposed simple 2D model for plastic spin and texture development in polycrystalline materials due to multiple slip is briefly reviewed. Some features of the analytical solutions of the model available for initially isotropic materials are highlighted. These properties are then used to define a triad of texture vectors within a phenomenological constitutive framework and to partly derive/motivate their evolution equations.

Transfer of Shear Tractions Along Rough Cracks

Abstract: A constitutive model for transfer of shear tractions along rough cracks in strain softening composites like concrete, is presented. The model relates the normal and shearing stresses on the rough crack to the corresponding displacements in terms of the interface strength, contact areas, the contact angle of the rough crack surface, and the crack closing pressure. The initial angle of contact at zero normal stresses, a fundamental property of the rough crack surface, was established by means of statistical and numerical simulations. Using the concepts of critical state soil mechanics, conditions were stipulated for dilation and contraction of the rough crack. The deformability of the asperity was mathematically described in terms of the initial angle of contact and a progression of this angle to a minimum by means of an exponential model. Using idealizöi test results such as constant crack width experiments, a mathematical model was developed for contact area as a function of the crack width and tangential displacement. The performance of the constitutive model was verified by predicting experimental results with varying crack width and normal stress boundary conditions, as well as constant crack width and constant normal stress. The comparison between predicted and experimental results appear to be very satisfactory. INTRODUCTION With the advent of fast computers such as vector processor, nonlinear problems which were hitherto time consuming, can now be solved very quickly on computers. This feature has let researchers and designers to use more sophisticated mathematical models for material description. While a number of mathematical models for continuous media are available, there is a scarcity of constitutive models for media with discontinuities such as cracks, joints and interfaces. In the investigations conducted by Bazant and Gambarova (1,2), stress displacement relations were developed for a rough crack using some idealized test results. Other investigations (3,4,5,6,7) relate shear and normal stresses and displacements of the rough crack by using empirical relations. Most of these constitutive models are based on macroscopic considerations, and so far, there has not been any model which considers the internal structure of the material and nature of the rough crack surface.

Vibrations and Acoustical Emission in Media With Microstructure

Abstract: The mathematical models of nonlinear sound waves in continuous media with microstructure are considered. It is shown that introduction of high order time derivatives in rheological laws is corresponded to fragmentation and can explain the evolution of arbitrary vibrations to dominant frequencies. In nonlinear case kinematically independent rotation of particles corresponds to generation of ultrasound by vibrations typical for seismic waves. Creep flows of media with rotating microparticles are also treated as sources of acoustical noise with typical spectrum. The experimental evidence and numerical illustrations are given.

Hardening Mechanism in a MG 8.5 Wt.% Al Alloy

Abstract: The mechanical properties and the fracture behaviour of Mg Al alloys with discontinuous precipitation has been investigated. It is shown that this alloy presents a combination of composite hardening for the flow stress and of a modified Hall Petch hardening for the yield stress by lamellaes and Orowan hardening for g lobu lae .

The Interfacial Somigliana Ring Dislocation

Abstract: The concept of an interface ring dislocation in an infinite linearly elastic medium is analyzed. The solution is carried out using the Love stress function. The extended stress and displacement fields are formulated in integral form. Some characteristics of the stress components are calculated for different shear modulus ratios and Poisson ratios and their effect on the behavior of these components are analyzed. The results presented here are believed to be useful in determining the extent of deviation from the homogeneous case for bimaterial problems.

A General Shear Deformable Laminated Beam Theory Accounting for Interlaminar Continuity of Displacements and Shear Stress

Abstract: A general theory suitable for the static analysis of shear deformable laminated beams is presented. This is a displacement-based theory which accounts for interlaminar continuity of both displacements and shear stress. Moreover, the theory accounts for unlimited multiple choices of continuous displacement distributions, through the beam thickness, while, starting with the smallest possible number of independent displacement components (three, for a shear deformable theory), it enables further operation with as many degrees of freedom as desired. The derivation of its differential governing equations is based on the application of the minimum potential energy principle in conjuction with the method of Lagrange multipliers.

Synergetics of Dislocations

Abstract: Attempts to explain plastic behavior of solids within the frame-work of the conventional theory of dislocations have not been successful. It seems that physics of plasticity ought to be based on different grounds. It is proposed to treat the dislocation population in a deformed solid as a synergetic system represented by a nonlinear, nonlocal continuum driven far from thermodynamic equilibrium. In such model plastic behavior is governed by structural and geometrical instability. The structural instability arises from collective properties of dislocations and leads to the formation of dislocation structures which underlie work hardening. The geometrical instability is of the nonlinear continuum mechanics origin and results in a strain localization in a form of shear bands and/or dislocation cell misorientation.

A Numerical Approach for the Elastoplastic Unilateral Contact Between Adjacent Structures During Earthquakes

Abstract: The paper presents a numerical treatment for the proble of earthquake interaction among neighboring buildings whe unilateral elastoplastic contact under second-order geometr and other instabilizing effects can take place. The method based on formulating the problem by the finite element meth< as an inequality one and on solving this by the Houbolt tim< discretization scheme and nonlinear mathematical programmin« methods. Some results concerning a two-building system undei P-Delta effects are given in a numerical example.