Huber Von Mises Research Articles

Dissimilar subalgebras of symmetry algebra of plasticity equations

In this paper we construct the optimal sets of dissimilar subalgebras up to dimension three for the Lie algebra of point symmetries of the system of three-dimensional stationary equations of perfect plasticity with the Huber–von Mises yield condition. The obtained results can be used to solve the problem of determining all invariant solutions of this system. It was necessary to design algorithms to facilitate some steps of the classification of subalgebras. The computational algebraic system SageMath was chosen to implement these algorithms. The most used functions and procedures are listed. The developed algorithms can be adapted to classify subalgebras of higher dimensions.

Numerical and analytical models of the mechanism of torque and axial load transmission in a shock absorber for drilling oil, gas and geothermal wells

The paper proposes an improved design of a shock absorber used in drilling deep oil and gas and geothermal wells with polycrystalline diamond compact (PDC) bits. The proposed innovations successfully combat the dangerous phenomenon of self-excited vibrations, which can lead to malfunctions such as stick-slip and whirling of the drilling tool. Most conventional drill shock absorbers are designed to only absorb longitudinal vibrations, which was sufficient when using roller cutter bits for the drilling process. However, the design features of PDC bits and the phenomenon of interaction of their cutters with interlayered rocks during deep drilling impose new requirements on the properties of the drill shock absorber. To protect the downhole tool from abnormal torque values and torque oscillations, it is proposed to equip the shock absorber with a special torque transmission unit in the form of a fourteen-thread self-releasing screw pair. This unit is capable of transforming increases in external torque into increases in the force that loads the elastic element of the shock absorber. The numerical and analytical models of the mechanism of transferring external axial load and torque to the elastic element of the drill shock absorber are constructed. The distribution of contact pressures on the interacting surfaces of the screw pair and the distribution of equivalent stresses in the screw pair parts are analysed. The strength of the proposed drill shock absorber assembly was evaluated using the Huber-von Mises energy criterion. The dependence of the load transmitted to the elastic element of the shock absorber on changes in the external torque and external axial force is investigated. In general, it is determined that the external load is distributed evenly between all turns of the screw pair, and the limit state of the parts of the proposed assembly is not reached even under high-torque operating load. The obtained analytical dependencies will allow to effectively determine the required strength and stiffness of the elastic element of the drill shock absorber at the design stage. The obtained analytical results were verified using a finite element model.

DESIGN OF SHELL CONJUNCTION ZONES IN PRESSURE VESSELS

Separation forces occur in shell junctions of fuel tanks due to the change in its geometry. To compensate the forces, thrust rings are placed in these zones. Moreover, there is a necessity to determine a form and dimensions of the trust ring cross section with consideration of the operation conditions. Welding is used to join trust rings with a shell in case of conventional manufacturing. Nowadays, additive manufacturing technology is constantly being developed. Additive method allows to create objects with various geometry, in a layer-by-layer way of addition of the material in accordance with a computer model. These new technological capabilities make the task of determining of the geometry of the fuel tank in the shell’s junctions zone actual. 
 The following work provides a consideration of two approaches to the determination of the conversion geometry of shells in-between area instead of trust ring. The first approach is based on determination of a median surface with the use of rational cubic splines and membrane theory of shells. The second approach is based on the use of topology optimization of the initial design. The choice of the first approach relates to the fact that standard energy functional like potential energy of uniform bent rod or uniform sheet can be described with cubic splines. In the following work the use of rational cubical splines for build-up a transitive area in a junction zone of the spherical-conical vessel is considered. Spline parameters are determined based on the condition of median surface propagation of the transitive zone in its probable location. Thickness of the shell in the transitive area was evaluated due to the membrane theory of shells with the use of Huber von Mises Hencky theory of failure. Obtained solutions are tested in numerical models of spherical-conical vessel. Comparison of two approaches is carried out and practical recommendations are given.

On the Springback and Load in Three-Point Air Bending of the AW-2024 Aluminium Alloy Sheet with AW-1050A Aluminium Cladding.

This article presents the results of an analysis of the bending load characteristics and the springback phenomenon occurring during three-point bending of 1.0 and 2.0 mm thick AW-2024 aluminium alloy sheets with rolled AW-1050A cladding. A new proprietary equation was proposed for determining the bending angle as a function of deflection, which takes into account the influence of the tool radius and the sheet thickness. The experimentally determined springback and bending load characteristics were compared with the results of numerical modelling using different models: Model I, a 2D model for a plane deformation state, disregarding the material properties of the clad layers; Model II, a 2D model for a plane deformation state, taking into account the material properties of the cladding layers; Model III, a 3D shell model with the Huber-von Mises isotropic plasticity condition; Model IV, a 3D shell model with the Hill anisotropic plasticity condition; and Model V, a 3D shell model with the Barlat anisotropic plasticity condition. The effectiveness of these five tested FEM models in predicting the bending load and springback characteristics was demonstrated. Model II was the most effective in predicting bending load, while Model III was the most effective in predicting the amount of springback after bending.

Dieless bulging and nonlinear buckling of longan-shaped pressure hull

In this study, the dieless bulging and nonlinear buckling behaviours of a stainless longan-shaped pressure hull were investigated. According to the Cassini oval equation, the longan shape has a shape index of 0.1. The lengths of the major and minor axes of the designed longan-shaped pressure hull were approximately 400 and 396 mm, respectively. The wall thickness of this pressure hull was 1 mm. The Huber–von Mises stress and first yielding load of the designed longan-shaped shell and its inscribed polyhedral preform were investigated analytically and experimentally. Moreover, the dieless bulging of the designed longan-shaped pressure hull was investigated numerically and experimentally by using the nonlinear finite element method and a hydrostatic test, respectively. The analytical, experimental, and numerical results exhibited good agreement with each other.

Lifetime Assessment for Multiaxial High-Cycle Fatigue Using Twin-Shear Unified Yield Criteria

In this paper, a life prediction model associated with maximum principal stress and equivalent shear amplitude based on twin-shear unified yield criterion for multiaxial high-cycle fatigue is proposed. The equivalent shear amplitude is the normalized format of the equivalent shear amplitude based on clusters of yield criteria embodying Tresca and the linearization of Huber-von Mises, extending the application to metallic materials. Simultaneously, the effect of mean stress on multiaxial high-cycle fatigue is considered in the proposed model. As an assessment of the new prediction model, the criterion is compared with experimental data of aluminum alloy LY12CZ and carbon structural steel SM45C published in the relevant literature, which shows that most of the data are located within an error range of less than two times the data and are in good agreement with the experiment. Moreover, the proposed model is also compared with other models, such as McDiarmid, Liu, and Freitas, to validate its competitiveness.

Bone Density Micro-CT Assessment during Embedding of the Innovative Multi-Spiked Connecting Scaffold in Periarticular Bone to Elaborate a Validated Numerical Model for Designing Biomimetic Fixation of Resurfacing Endoprostheses.

Our team has been working for some time on designing a new kind of biomimetic fixation of resurfacing endoprostheses, in which the innovative multi-spiked connecting scaffold (MSC-Scaffold) that mimics the natural interface between articular cartilage and periarticular trabecular bone in human joints is the crucial element. This work aimed to develop a numerical model enabling the design of the considered joint replacement implant that would reflect the mechanics of interacting biomaterials. Thus, quantitative micro-CT analysis of density distribution in bone material during the embedding of MSC-Scaffold in periarticular bone was applied. The performed numerical studies and corresponding mechanical tests revealed, under the embedded MSC-Scaffold, the bone material densification affecting its mechanical properties. On the basis of these findings, the built numerical model was modified by applying a simulated insert of densified bone material. This modification led to a strong correlation between the re-simulation and experimental results (FVU = 0.02). The biomimetism of the MSC-Scaffold prototype that provided physiological load transfer from implant to bone was confirmed based on the Huber–von Mises–Hencky (HMH) stress maps obtained with the validated finite element (FE) model of the problem. The micro-CT bone density assessment performed during the embedding of the MSC-Scaffold prototype in periarticular bone provides insight into the mechanical behaviour of the investigated implant-bone system and validates the numerical model that can be used for the design of material and geometric features of a new kind of resurfacing endoprostheses fixation.

Application of new twin-shear unified strength criterion to frozen soil

A new twin-shear unified strength criterion is proposed in this study. This criterion reveals the relationship among single-shear, twin-shear, and triple-shear strength criteria. All known linear and nonlinear strength criteria—such as Huber–von Mises, Drucker–Prager, Mohr–Coulomb, Tresca, and twin-shear series—are special cases of the new twin-shear unified strength criterion. The proposed unified strength criterion was employed to study the strength characteristics in the compressed meridional plane (where the stress Lode angle,θσ = − 30°) of frozen soil, based on the soil's nonlinear and asymmetric properties. In the criterion, β and C, which denote the relationship between the shear stress τ and normal stress σ on the twin-shear stress acting plane, are deemed variable; they vary with the change in normal stress σ or mean stress p. Through a comparison of results, we found that the results obtained with the proposed strength criterion were in good agreement with the results of tests on frozen soil. On this basis, expressions for the cohesive force and the internal friction angle of frozen soil were derived and discussed.

Identification of a Segment of the Yield Surface of a Two-Layer Pa38/M2R Composite

The aim of this study was to identify the initial yield surface of a two-layer aluminum alloy-copper composite in the range of small elastic-plastic deformations. Experimental tests in a plane stress state were conducted by loading tubular composite specimens with various combinations of axial forces and torque. The metal layers were joined together by using an epoxy resin. Independent studies were carried out for component of the composite under identical conditions. The yield surfaces obtained were compared with those given by the Huber–von Mises–Hencky and Tresca–Guest yield criteria. The yield criterion for the tested composite found by using a modified form of the rule of mixtures is presented. The yield surfaces of a Pa38/M2R composite and its components demonstrated the isotropic hardening.

Constraints on the applicability range of Hill’s criterion: strong orthotropy or transverse isotropy

Commonly used orthotropic Hill’s criterion of plastic flow initiation (Hill in Proc R Soc Lond A 193:281–297, 1948) suffers from some constraints and inconsistencies, which are of two different origins. Firstly, in case of high orthotropy degree, the quadratic form corresponding to Hill’s criterion may change type from convex and closed elliptic to concave and open hyperbolic in the deviatoric stress space (Ottosen and Ristinmaa in the mechanics of constitutive modeling, Elsevier, Amsterdam, 2005). Secondly, application of classical Hill’s criterion to transversely isotropic materials shows a discrepancy between Hill’s limit curves in the transverse isotropy plane and the Huber-von Mises prediction for isotropic materials (Huber 1904; von Mises 1913). The basic result of the present paper is to propose the new transversely isotropic von Mises–Hu–Marin’s-type criterion of hexagonal symmetry that is free from both constraints. The new enhanced Hu–Marin’s-type limit surface represents an elliptic cylinder, the axis of which is proportional to stress/strength, in contrast to Hill’s-type limit surface possessing the hydrostatic axis. Hence, this condition does not exhibit the deviatoricity property, which is a price for coincidence with the Huber–von Mises condition in the transverse isotropy plane, but with cylindricity ensured for an arbitrarily high orthotropy degree. The hybrid-type transversely isotropic Hu–Marin’s criterion of mixed symmetry based on additional biaxial bulge test, capable of fitting experimental findings for some complex composites, is also proposed. Application of this criterion has been verified for a unidirectional SiC/Ti composite examined by Herakovich (Thermal stresses V, Lastran Corp. Publ. Division, pp 1–142, 1999).

Rice Local Phase Angle Study for a Delamination Problem Between a Shape Memory Alloy and an Elastic Material

The present study is an extension of a recent paper of Freed et al. (J Mech Phys Solids 56:3003–3020, 2008). The final aim is to describe the transformation toughening behavior of a static crack along an interface between a shape memory alloy (SMA) and a linear elastic isotropic material. With an SMA as an equivalent Huber–Von Mises stress model (hypothesis of symmetric behavior between tension and compression), Freed et al. determine the initiation (ending) phase transformation yield surfaces in terms of the local phase angle introduced by Rice et al. (Metal ceramic interfaces, Pergamon Press, New York, pp 269–294, 1990). In this paper we give the general framework to determine this angle for a model integrating the asymmetry between tension and compression (experimentally measured: Vacher and Lexcellent in Proc ICM 6:231–236, 1991; Orgéas and Favier in Acta Mater 46(15):5579–5591, 2000), the Huber–Von Mises model being only a particular case. We demonstrate the local phase angle existence in an appropriate framing domain and give a sufficient hypothesis for its uniqueness and an algorithm to obtain it. Estimates are obtained in terms of physical quantities such as the Young modulus ratio, the bimaterial Poisson modulus values and also the choice of the yield loading functions. Finally, we illustrate this theoretical study by an application linking the asymmetry intensity on the width and the shape on predicted phase transformation surfaces and by a comparison with the symmetric case.

ABOUT THE CHOICE OF A PLASTIC-LIKE MODEL FOR SHAPE MEMORY ALLOYS

The aim of this paper is to examine the impact of the choice of plasticity theory-inspired model in the prediction of the shape of phase transformation domains. In this field a comparison is made between Huber-Von Mises based model and an another integrating the non-symmetry between tension and compression. The yield surface of phase transformation initiation for an homogeneous body under proportional biaxial loading is discussed. A transport of these surfaces in the space of the "effective transformation strain of martensite tensor" is given. Key words: Shape memory alloys, phase change, elastic-plastic models, multiaxial behavior.

About the choice of a plastic-like model for shape memory alloys

The aim of this paper is to examine the impact of the choice of plasticity theory-inspired model in the prediction of the shape of phase transformation domains. In this field a comparison is made between Huber-Von Mises based model and an another integrating the non-symmetry between tension and compression. The yield surface of phase transformation initiation for a homogeneous body under proportional biaxial loading is discussed. A transport of these surfaces in the space of the "effective transformation strain of martensite tensor" is given.

Impact of the choice of a 3D thermomechanical model for shape memory alloys on the fracture and the delamination predictions

The aim of this paper is to examine the impact of the choice of “plasticity theory-inspired” SMA model in the prediction of the shape of phase transformation domains. In this field a comparison is made between Huber-Von Mises based model and an another integrating the asymmetry between tension and compression. Two situations are observed(i) A classical mode I loading on a plate with a crack. The effect of the asymmetry intensity is important for plane stress conditions, not for plane strain ones. (ii) A problem of delamination between a SMA (shape memory alloy) and an elastic solid, reveales that taking into account the asymmetry has negligible impact on the size and the shape of the phase transformation surface generated in SMAs.

Damageability of a material reinforced with unidirectional orthotropic fibers for an exponential function of long-term microstrength

UDC 539.3 The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite material with a stochastic structure. Equations of mechanics of microinhomogeneous media of this structure form the base of the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores. The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the short-term strength on the basis of the Huber–von Mises criterion accepted as an arbitrary function of coordinates. Efficient deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case of a bounded function of the long-term microstrength, which is approximated by an exponential law.

Damage and failure processes of hybrid joints: Adhesive bonded aluminium plates reinforced by rivets

The aim of this article was the analysis of the damage and failure behaviour of the hybrid joint consisted of: three aluminium plates (adherents), the polyurethane adhesive (two laps 40×40mm) and reinforced by five rivets. The ABAQUS programme was used to simulate the tensile strength in this type of joint. The 3D numerical analysis includes modelling of: the aluminium plates, the rivets and the cohesive layers. We used mass scaling and a half of the specimen model to increase the minimum time increment in the explicit analysis. The aluminium plates and the rivets were subjected to large plastic deformations, which were described by Huber–von Mises yield model with isotropic hardening. Modelling of damage process in the adhesive layers with a finite thickness was based on their cohesive behaviour with application of cohesive elements. A displacement – based damage parameter was introduced into the constitutive equation. Experiments carried out for three kinds of joints: the simple rivet joint, the simple adhesive bonded joint and the hybrid adhesive–riveted joint were confirmed by numerical results. Both the experimental tests and the computer simulations showed that the tensile strength of the hybrid joint was higher than the adhesive bonded joint or joint with the five rivets. Addition of the rivets to the adhesive bonded joint increases the energy absorption during the failure process in comparison to the riveted or the adhesive bonded joints.

Coupled processes of deformation and long-term damage of fibrous materials with the microdurability of the matrix described by an exponential power function

The theory of long-term damage is generalized to fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–von Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by an exponential power function

Deformation and short-term damage of physically nonlinear stochastic composites

The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized. A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations. The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed

The Maxwell stress tensor for magnetoelastic materials

The emergency states of the electromagnetic devices short-circuit currents get very high impulse intensity and are the source of the undesirable electrodynamics forces. Mechanical stresses in the wires may than cause the long-term plastic strains. Therefore in designing of the elements of the power grid (distribution stations and transformation stations) the technical protective norms are used in order to omit such mechanical effects [e.g. Poland – the Polish Norm is PN-EN 60865-1:2002(U)]. In our opinion the above problem demand the wider theoretical description from the mechanical point of view. In this paper, deformable continuous medium immersed in electromagnetic field is considered. Based on momentum balance, on the traditional way a stress tensor and a volume force were introduced. Every quantity consists of two parts: electromagnetic part and mechanical part. Electromagnetic stress tensor is called Maxwell stress tensor. In the case of linear material equations the electromagnetic volume force equals zero. In this paper, we show the analysis of the influence of primary magnetic field orientation on the property of Maxwell stress tensor for linear magnetoelasticity and static magnetoelasticity. While doing research on eigenvalues of this tensor, it was established that the primary magnetic field always generates three-dimensional state of stress, no matter what the orientation was. In order to introduce reduced stresses, classical failure criteria were used: Tresca’s–Guest’s criterion and Huber–von Mises criterion. Having tested the eigenvalues of Maxwell stress tensor in linear magnetoelasticity, we received results that put the usefulness of this approximation into question. The approximation of static magnetoelasticity seems more reliable.

Principles of the micromechanics of material damage. 1. Long-term damage

The principles of the theory of long-term damage based on the mechanics of stochastically inhomogeneous media are set out. The process of damage is modeled as randomly dispersed micropores resulting from the destruction of microvolumes. A failure criterion for a single microvolume is associated with its long-term strength dependent on the relationship of the time to brittle failure and the difference between the equivalent stress and the Huber-von Mises failure stress, which is assumed to be a random function of coordinates. The stochastic elasticity equations for porous media are used to determine the effective moduli and the stress-strain state of microdamaged materials. The porosity balance equation is derived in finite-time and differential-time forms for given macrostresses or macrostrains and arbitrary time using the properties of the distribution function and the ergodicity of the random field of short-term strength as well as the dependence of the time to brittle failure on the stress state and the short-term strength. The macrostress-macrostrain relationship and the porosity balance equation describe the coupled processes of deformation and long-term damage