Unloading Deformation Research Articles

A Study on the Impact of Structure Plane on Unloading Rock Mass Deformation

The rock mass deformation properties of unloading is very different from loading.The physical and mechanical properties of structural plane can bring a very great influence to rock’s unloading behavior. The lower the strength parameter of joint plane and the greater the angle of joint, the lower the unloading modulus of deformation. The greater the connectivity of joint,the faster the unloading modulus of deformation descend. In any case unloading amount is near linear relation with descend amount of unloading deformation modulus.

Complex unloading behavior: Nature of the deformation and its consistent constitutive representation

Complex (nonlinear) unloading behavior following plastic straining has been reported as a significant challenge to accurate springback prediction. More fundamentally, the nature of the unloading deformation has not been resolved, being variously attributed to nonlinear/reduced modulus elasticity or to inelastic/“microplastic” effects. Unloading-and-reloading experiments following tensile deformation showed that a special component of strain, deemed here “Quasi-Plastic-Elastic” (“QPE”) strain, has four characteristics. (1) It is recoverable, like elastic deformation. (2) It dissipates work, like plastic deformation. (3) It is rate-independent, in the strain rate range 10 −4–10 −2/s, contrary to some models of anelasticity to which the unloading modulus effect has been attributed. (4) To first order, the evolution of plastic properties occurs during QPE deformation. These characteristics are as expected for a mechanism of dislocation pile-up and relaxation. A consistent, general, continuum constitutive model was derived incorporating elastic, plastic, and QPE deformation. Using some aspects of two-yield-function approaches with unique modifications to incorporate QPE, the model was implemented in a finite element program with parameters determined for dual-phase steel and applied to draw-bend springback. Significant differences were found compared with standard simulations or ones incorporating modulus reduction. The proposed constitutive approach can be used with a variety of elastic and plastic models to treat the nonlinear unloading and reloading of metals consistently for general three-dimensional problems.

Duality in process of noncommutative deformation and topological nature of Cherepanov-Rice integral

In t his paper it is showed, that for the noncommutative deformation simultaneously there exist also loading deformation H, and unloading deformation \(H^v\). The real deformation is a combination of these types of deformations. The criterion of destruction J reflects topological character of medium, i.e. it defines properties of symmetry of medium at destruction. It is possible to tell, that during destruction the energy is released not continuously but and discretely. This situation is reflected through topological number Q or number of unloading, connected to him.

A nonlinear fractional derivative model for large uni-axial deformation behavior of polyurethane foam

In uni-axial quasi-static tests, flexible polyurethane foam undergoing large compressive loading and unloading deformation exhibits highly nonlinear and viscoelastic behavior. In particular, the response in the first cycle is observed to be significantly different from the response in subsequent cycles. In addition, the stresses in the loading paths are higher than those in unloading paths. This quasi-static response is modeled as an additive sum of a nonlinear elastic and a linear viscoelastic response. The nonlinear elastic behavior is modeled as a polynomial function of compressive strain, while the viscoelastic behavior is modeled as a parallel combination of five-parameter fractional derivative models. The focus of this paper is to develop a multi-element fractional derivative model that can capture the multi-cycle behavior. A parameter estimation procedure based on separating the contributions of the viscoelastic elements and the nonlinear elastic component is developed. This approach is applied to both simulation and experimental data. The combination of a nonlinear elastic component and a two-element fractional derivative model is found to predict the observed responses reasonably well. The results for two distinct foams from tests with different compression rates are compared and discussed.

A middle surface concept (MSC) model for saturated sands in general stress space

An elastoplastic constitutive model is proposed for saturated sands in general stress space using the middle surface concept (MSC). In MSC, different features of stress–strain response of a material are divided into different pseudo-yield surfaces. The true-yield surface representing the true response is established by using various links between the yield surfaces. In this MSC sand model, several well-known features of sand response are represented by three different pseudo-yield surfaces, which are developed in a simple and straightforward way. These features include the critical state behaviour, the effects of state parameter, unloading and reloading plastic deformation, the influence of fabric anisotropy, and phase transformation line related behaviour. Finally, the model predictions and test results are compared for two different types of sands under a variety of loading conditions and good comparisons are obtained. The application of MSC to saturated sand modelling shows the versatility of MSC as a general concept for modelling stress–strain response of materials. Copyright © 2006 John Wiley & Sons, Ltd.

M. Yu. Bal'shin, A Founder in the Science of Powder Consolidation

The collection of analytical and experimental data makes it possible to consider the existence of three common scientific principles for solid body consolidation to be proved. One of them, the identity principle, formulates the degree of generality between properties and the behavior of a porous, consolidating or consolidated body, and a normal body; two others, i.e. the principle of self-regulation and the transmission principle, formulate features of the properties and behavior of powder bodies. The identity principle may be formulated as follows. The properties and behavior of any compact element of a porous body are the same as for the substance of a compact pore-free body with the condition of an identical chemical composition, degree of strain hardening, and test conditions. The self-regulation principle may be formulated as follows. During consolidation there are processes of non-self-regulation (intraparticle, consolidating, increasing and fixing the contacts and equilibrium) loading deformation and self-regulating (intraparticle, deconsolidating, reducing and breaking contacts and body equilibrium) unloading deformation; non-self-regulation consolidating deformation increases, and self-regulation deconsolidating deformation reduces compaction resistance; flow of particles substance is intermediate in nature between entirely continuous and entirely localized flow in contact areas. The greater the degree of consolidation, the lower is the level of self-regulation for its processes. The transmission principle may be formulated as follows. Consolidating stresses applied to a consolidating self-regulating body are transmitted by their elastic balancing in a continuous critical zone lying entirely within the solid phase of a body with equally large interparticle (contact) and intraparticle (critical) sections normal to the loading direction. These stresses and elastic loading are only transmitted through fixed, and not through broken, contact sections at this instant of consolidation, and consequently through fixed critical sections in a fixed critical zone.

Large deflection analysis of elastoplastic plate in steady continuous four-roll bending process

This paper presents a mathematical model to simulate the mechanics in a steady continuous bending mode for four-roll thin plate bending process. The differential equations governing the large deflection bending of elastic-perfectly plastic thin plate are derived by modelling the loading and unloading deformation of the operational process. Through a semi-analytical solution of the system equations, the physical quantities of (i) the deformation and stress resultants of bend plate, (ii) the springback, (iii) the shift of contact-angle of bend plate with rolls, (iv) the applied forces on rolls, (v) the bending torque and power, and (vi) the position of the operative side roll, etc., associated with bending of a plate to an anticipated curvature, for single-pass bending operation, are predicted and discussed.

Structure and strain hardening of metals with a complex stressed state

Strain hardening features for steels of the austenitic, martensitic, and maraging classes in stable and metastable states in relation to structural parameters in complex biaxial loading conditions have been studied, including prior and repeated (with intermediate unloading) deformation with different principal stress ratios. The structural sensitivity of the Bauschinger effect is studied, structural dependences for yield stress with compression after prior tension are obtained, and generalization of the yield stress under repeated biaxial loading is substantiated by experiment. In the relationships presented there is quantitative consideration of the regularities revealed for the change in structural parameters of deformed metal during repeated loading in relation to the principal stress ratio. Classification of the test steels is suggested according to structural state characteristics caused by preferred isotropic and anisotropic strain hardening.

Peel mechanics of adhesive strips with constraints

The peel force as a function of displacement was determined for debonding inextensible adhesive strips with an extensible boundary constraint. Using differential energy balance methods, a closed form expression for the peel force was obtained and found to be in excellent agreement with experimental studies. A solution was obtained in terms of the adhesive fracture energy and a modulus parameter for the constraint. The analysis was applied to both loading and unloading deformation modes. Recovery phenomena in the rest state was discussed.

Analysis of Unloading on a Thin Cirular Plate of Mild Steel Using Actual Unloading Stress‐Strain Relation

AbstractThe actual stress‐strain relation of mild steel in the unloading and subsequent inverse loading processes from plastic state shows a continuous curve without discrete yield point, and its configuration depends on the value of plastic prestrain. In the present paper, in formulating the relation, effective stress in the processes was expressed as a polynomial of the corresponding effective strain in which each coefficient was expressed again as a polynomial of plastic pre‐strain. Then, precise fundamental equations analysing the unloading deformation of a thin circular plate of mild steel are derived by using the above mentioned unloading stress‐strain relation. To examine the validity and applicable range of the derived equations, they are applied to analyse the case of a supported thin circular plate bent by uniform lateral pressure, and the analytical result is compared with that obtained by the corresponding experiment.