Construction of the Equivalent Plastic Strain Increment

Strain hardening plastic deformation of a material possessing a yield locus (f(σ_ij)) which may be written as a homogeneous function of the stress components (σ_ij), and which obeys the classical associated flow rule for metals (e.g. Bishop and Hill, 1951) is considered. The material may be anisotropic and may display plastic dilatation. A method is given for constructing the equivalent plastic strain increment in such a way that the increment of plastic work is always equal to the product of the equivalent plastic strain increment and the equivalent yield stress. Construction of the equivalent plastic strain at a corner in the yield locus is given. The method given here is implied in classical treatments of hardening (e.g. Hill, 1950) but seems not to have been given explicitly heretofore.     

Inconsistencies in Plane-strain Elasto-plastic Rolling Simulations

Plane strain conditions are frequently used as model assumptions for the approximate calculation of flat rolling processes for sufficiently wide strips. This means that during the entire forming process, the strain rate in strip width direction (z-direction) remains zero. In the case of elasto-plastic material, the transitions from elastic to plastic states and vice versa are of particular interest. If we accept the flow rule of Levy-Mises, the normal stress σ_zz equals the average value of the normal stresses σ_xx and σ_yy inside plastic domains. Using Hooke's law we obtain a different relation for σ_zz in elastic domains. At transition points from elastic to plastic domains and vice versa, above relations for σ_zz have to be fulfilled simultaneously. Generally, this yields a discontinuous behaviour of σ_zz at the transition points and consequently to discontinuities of the stress σ_yy as well as the strains ε_zz and ε_yy, provided a continuous behaviour of σ_xx in rolling direction is postulated. The resulting discontinuity of ε_zz indicates therefore an inconsistency of such a plane strain model. Some key aspects of the underlying theory and consequences of such model assumptions will be pointed out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A physically motivated model for filled elastomers including strain rate and amplitude dependency in finite viscoelasticity

A microstructure-based model of rubber reinforcement, the so-called dynamic flocculation model (DFM), is presented describing filler-induced stress softening and hysteresis by the breakdown and reaggregation of strained filler clusters [1]. An extension of this model allows to consider incomplete deformation cycles that occur in the simulation of arbitrary deformation histories [2]. Good agreement between measurement and the model is obtained for CB-filled elastomers like NR, SBR or EPDM, loaded along various deformation histories. One very important aspect is that the model parameters can be directly referred to the physical properties. This benefit is used to extend the model to further essential effects like time- and rate-dependent material behavior. In the limit range above the glass transition temperature these viscoelastic effects originate mainly from the filler-filler interactions. In the material model these interactions are characterized by two material parameters s_v and s_d, respectively. The parameter s_v defines the strength of the virgin filler cluster, whereas s_d represents the strength according to the broken or damaged filler clusters. Both parameters can be defined as functions of time s_v,d = ŝ_v,d(t), which can be motivated by physical meaning [3]. Due to this extension it is possible to capture the very complex strain rate and amplitude dependency during loading and relaxation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of Structural Curvings on the Stress Distribution in a Rigidly Fixed Composite Plate under Forced Vibration

Based on the exact three-dimensional equations of continuum mechanics and the Akbarov-Guz' continuum theory, the problem on forced vibrations of a rectangular plate made of a composite material with a periodically curved structure is formulated. The plate is rigidly fixed along the Ox ₁ axis. Using the semi-analytic method of finite elements, a numerical procedure is elaborated for investigating this problem. The numerical results on the effect of structural curvings on the stress distribution in the plate under forced vibrations are analyzed. It is shown that the disturbances of the stress ₂₂ in a hinge-supported plate are greater than in a rigidly fixed one. Also, it is found that the structural curvings considerably affect the stress distribution in plates both under static and dynamic loading.     

Micromechanical Simulation of the Hall-Petch Effect with a Crystal Gradient Theory including a Grain Boundary Yield Criterion

A viscoplastic strain gradient crystal plasticity theory based on the gradient of the equivalent plastic strain ∇γ_eq is proposed. A grain boundary yield condition is introduced. The microstructural explanation of the Hall-Petch effect, accounting for notch-like stress concentrations at the grain boundary as a result of discrete slip bands, is reviewed. Periodic tensile test FEM simulation results illustrate the prediction of the numerical model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of possible combinations of local stresses in local strain theory

In determining the strain tensor e_ij instead of all the components of the local stress deviator, it is possible to use only the shear stress _xz acting on a small local area. This fact makes it easy to establish the incremental loading conditions in solving complex loading problems for a plastic material. It is shown that in the local strain theory, distinct from the deformation theory, at degrees of nonlinearity n>3 the effect of the third, as well as the second, invariant of the stress deviator is taken into account.Mekhanika Polimerov, Vol. 3, No. 4, pp. 636–644, 1967     

Mixed Micromechanics and Continuum Damage Mechanics Approach to Transverse Cracking in [S, 90n]s Laminates

The stiffness reduction in [S, 90 _n ] _s laminates due to transverse cracking in 90-layers is analyzed using the synergistic continuum damage mechanics (SCDM) and a micromechanics approach. The material constants involved in the SCDM model are determined using the stiffness reduction data for a reference cross-ply laminate. The constraint efficiency factor, which depends on the stiffness and geometry of neighboring layers, is assumed to be proportional to the average crack opening displacement (COD). The COD as a function of the constraint effect of adjacent layers and crack spacing is described by a simple power law. The crack closure technique and Monte Carlo simulations are used to model the damage evolution: the 90-layer is divided into a large number of elements and the critical strain energy rate G _c having the Weibull distribution is randomly assigned to each element. The crack density data for a [0₂/90₄] _s cross-ply laminate are used to determine the Weibull parameters. The simulated crack density curves are combined with the CDM stiffness reduction predictions to obtain the stiffness versus strain. The methodology developed is successfully used to predict the stiffness reduction as a function of crack density in [±/90₄] _s laminates.     

Investigations of shear free turbulent diffusion in a rotating frame

We reconsider the problem of shear free turbulent diffusion in a rotating frame, rotating about x₁. Shear free turbulence is generated at a vibrating grid in the x₂–x₃ plane and diffuses away from the grid in x₁ direction. An important property of this flow case is that there is no mean flow‐velocity. With the help of Lie‐group methods Reynolds‐stress transport models can be analyzed for this kind of flow in a rotating frame. From the analysis it can be found, that the turbulent diffusion only influences a finite domain. Implicating this solution in the model equations shows that even fully nonlinear Reynolds‐stress transport models (non‐linear in the Reynolds‐stresses for the pressure‐strain model) are insensitive to rotation for this type of flow. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage behavior of laminated E-glass/epoxy beams with an initial delamination subjected to an axial impact

The damage behavior of laminated E-glass/epoxy beams, with and without an initial delamination, subjected to an axial impact by a moving bullet has been investigated experimentally and numerically. The specimens were made from a unidirectional fiber fabric stacked in the sequences [0₆] _s , [±45₃] _s , and [90₆] _s , and a delamination was created in them by locating a copper foil at a specified position. The data on the bullet speed and strain history were recorded by a laser setup, a high-speed dynamic strain indicator, and a TDS420A oscilloscope. It is shown that the delamination and the ply stacking sequence play a significant role in the dynamic response and damage behavior of laminated beams. A numerical simulation is performed by using the commercial finite-element software ABAQUS/Explicit, and the results obtained are in a good agreement with experimental observations. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 49–64, January–February, 2009.     

Predicting the Deformability of Expanded Polystyrene in Long-Term Compression

The interval prediction of creep strain on the basis of 15 years is carried out for slabs of expanded polystyrene (EPS) subjected to a compressive load. The expansion of the confidence interval caused by the discounted prediction information is allowed for by an additional factor. The creep compliance _c (t = 15) of the EPS is determined based on empirically estimating the long-term creep of this material subjected to a compressive stress σ _c = 0.3σ_10% for 15 years. A relationship between _c (t = 15) and EPS density in the slabs is established. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 607–618, September–October, 2005.     

Plastic deformation of rough surfaces

Friction forces are only transferred within the the real area of contact A_real, which is usually smaller than the apparent area of contact A_o. The maximum friction stress τ_fric is therefore determined by the shear limit τ_max in the area of real contact and the fraction of the real area of contact (τ_fric = τ_max (A_real/A_o)). For rough surfaces the size of A_real is governed o by the plastic deformation of the surface roughness. We present a fully elasto-plastic halfspace contact formulation based on the work of Jacq et al. [1]. Linear elastic-plastic material behavior is modeled based on v. Mises plasticity with isotropic hardening. The algorithm gives the residual stress as well as the full plastic deformation field due to a frictionless normal contact. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of chip formation during machining for different value of failure strain

Grinding is a very complicated processing. To increase quality of product and minimize the cost of abrasive machining, we should know physical phenomena which exist during the process. The first step to solution of this problem is analysis of machining process with a single abrasive grain. In the papers [1, 2] the thermo-mechanical models of this process are presented, but in this work attention is concentrated on chip formation and his separation from object. The influence of failure strain ε_f on states of strain and stress in surface layer during machining is explained. The phenomena on a typical incremental step were described using step-by-step incremental procedure, with updated Lagrangian formulation. Then, the Finite Element Method (FEM) and Dynamic Explicit Method (DEM) were used to obtain the solution. Application was developed in the ANSYS system, which makes possible a complex time analysis of the physical phenomena: states of displacements, strains and stress. Numerical computations of the strain have been conducted with the use of two methodologies. The first one requires an introduction of boundary conditions for displacements in the contact area determined in modeling investigation, while the second – a proper definition of the contact zone through the introduction of finite elements of TARGET and CONTACT types, without the necessity to introduce boundary conditions. This model includes variational equations of the object's motion and deformation. Examples of calculations for the displacement, strain and stress field in the surface layer zones were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal fracture of functionally gradient ceramics

An edge crack in a strip of functionally gradient ceramics (FGC) is studied under thermal loading conditions. Two FGC materials are considered, i.e., one with a spatial variation of shear modulus and the other with a spatial variation of thermal conductivity. Thermal stress intensity factors (TSIF) are numerically calculated based on singular integral equations derived for the dislocation density along the crack faces. It is shown that: (a) for the FGC with a graded shear modulus, the TSIF are reduced for crack lengths longer thanl _c b and remain approximately the same as those of a homogeneous material for shorter crack lengths, wherel _c is about 0.065 andb is the width of the strip; and (b) for the FGC with a thermal conductivity gradient, the TSIF are generally lower compared with those for the bonded two-layer material.     

Joint application of time — Temperature and time — Stress analogies to constructing unified curves

The possibility of constructing unified curves by joint application of time—temperature and time—stress analogies has been examined. It has been shown that by using this method the time scale can be expanded in constructing the unified curves that serve as models of long-time creep of material on the basis of short-time tests. The dependence of the influencing factorsa _T anda _σ on stress and temperature has been studied.

     

Une interprétation du théorème de colonnetti

Summary Considering an elastic-plastic continuum, the plastic deformations of which are given, it is prooved in a general way thatColonnetti's function (4), where ( _x , ..., _xy , ...) is the stress tensor, ( ) the plastic-strain tensor and the elastic potential energy, differs only by a constant value from the fictitious strain energy evaluated from the total strain as if it were purely elastic. Consequently, both functions are simultaneously minima andColonnetti's theorem can be rephrased in terms of fictitious (elastic) strain energy.     

On the piezoelectric shear effect in ultrasonic motors

A new actuator for piezoelectric ultrasonic motors (USM) using the d₁₅ effect was conceived. Whereas the piezoelectric d₃₃ and d₃₁ effects are normally used in commercial motors, there exist hardly any USM based on shear actuation. The actuator is a piezoelectric block polarized in axial direction and electroded circumferentially with four electrodes. The suitable superposition of two standing waves generates ultrasonic traveling waves in the actuator, which drives the rotor. The dimensions of the actuator are optimized with respect to the dynamic piezoelectric coupling factor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of the friction of rubber under constant compressive strain conditions at low pressure

A vacuum tribometer was developed which was used to investigate the maximum friction force occurring at the initial instant of slipping in rubber-metal friction pairs under conditions of a given (from 5 to 40%) compressive strain at a low pressure in the temperature range from +100 to –100°C. Filled rubbers on a base of nitrile-butadiene rubbers were studied. Up to the glass transition temperature T_g the vacuum had practically no effect on the maximum friction frocef _m; at temperatures T_g and lower the values off _m obtained in a vacuum were 10–15% higher than those obtained in the atmosphere. It is shown that with a decrease of temperature from 20°C to the glass transition temperature T_g the slope of the dependence of the maximum friction force on the degree of deformation increases, and below T_g decreases. The effect of the slipping speed v on the maximum friction forcef _m was also studied.Laboratory of Polymer Physics, V. I. Lenin Moscow State Pedagogical Institute. Leningrad Branch, Scientific Research Institute of the Rubber Industry. Translated from Mekhanika Polimerov, No. 3, pp. 486–492, May–June, 1970.     

Stress Intensity Factors near the Cracks on the Edges of Openings in Composite Plates

Based on the photoelasticity method, the behavior of stress intensity factors (SIFs) near cracks propagating from the edges of openings in plates made of elastic and linearly viscoelastic fibrous composite materials is studied. It is found that the relative value of the SIF, K ₁/K ₁ ⁰ (K ₁ ⁰=₀c), near the crack tips on the edges of openings in composite plates is a function of the ratio c/R, whose numerical values depend on the mechanical properties of materials of the plates. Using the quasi-elastic method for solving the viscoelastic problems, the effect of viscoelastic properties of the plate material on the value of K ₁/K ₁ ⁰ is estimated. It is shown that the values of the function K ₁(t)/>/K ₁ ⁰ near the cracks on the opening edges in plates made of linearly viscoelastic fibrous composites grow under creep.     

Dynamical effects at material instability phenomena

In a phenomenon called the Portevin-Le Chatelier (PLC) effect negative rate dependence is coupled with the appearance of a self-sustained oscillatory behavior in solid bodies. When PLC is treated as a type of dynamic material instability, the tools of the theory of dynamical system can be applied. The results of such investigation lead to an interpretation of PLC as a flutter type of loss of stability. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)