Ideal Plastic Behavior Research Articles

The Influence of Reverse Yielding on the Plastic Conditioning of Interference Fits in Power Transmission Engineering

Interference fits are very common shaft–hub connections due to their low manufacturing costs and excellent technical properties. The Plastic Conditioning of this machine element is a new and not very well-known method. During the development of this method, it was discovered that Reverse Yielding occurs in certain applications and has a negative impact on the result. This paper examines the effects of Reverse Yielding on the technology of Plastic Conditioning of interference fits in Power Transmission Engineering. Based on the Shear Stress Hypothesis (SH), the Plane Stress State (PSS), and the ideal plastic behavior of materials, established stress–mechanical relationships are used to find the influencing parameters of Reverse Yielding on the technology of Plastic Conditioning and their limits. As a result, a new computational concept is developed that allows the user to maximize Plastic Conditioning while avoiding Reverse Yielding. Analytical calculation suggestions and diagrams for practical application are provided. Furthermore, the deviations in the obtained results, taking into account other material models such as the Von Mises Yield Criterion (VMYC) and material hardening, as well as the Bauschinger effect, are examined in comparison with our own numerical results from the development of Plastic Conditioning, and the resulting need for further research is defined. In addition, the method of Plastic Conditioning of interference fits is introduced and its basic principles are briefly explained.

Ideal plasticity and shape memory of nanolamellar high-entropy alloys.

Understanding the relationship among elemental compositions, nanolamellar microstructures, and mechanical properties enables the rational design of high-entropy alloys (HEAs). Here, we construct nanolamellar AlxCoCuFeNi HEAs with alternating high- and low-Al concentration layers and explore their mechanical properties using a combination of molecular dynamic simulation and density functional theory calculation. Our results show that the HEAs with nanolamellar structures exhibit ideal plastic behavior during uniaxial tensile loading, a feature not observed in homogeneous HEAs. This remarkable ideal plasticity is attributed to the unique deformation mechanisms of phase transformation coupled with dislocation nucleation and propagation in the high-Al concentration layers and the confinement and slip-blocking effect of the low-Al concentration layers. Unexpectedly, this ideal plasticity is fully reversible upon unloading, leading to a remarkable shape memory effect. Our work highlights the importance of nanolamellar structures in controlling the mechanical and functional properties of HEAs and presents a fascinating route for the design of HEAs for both functional and structural applications.

A Multiple Length-Scales Nanoimprinting Approach on Nanocrystalline and Strongly Deformed CuZn30 Alloys

Metallic Nanoimprinting is a new approach to form robust surface structures on metals at various length scales. The shape and size of the formed structures not only depends on the dimensions of the Nanoimprinting die but also the mechanical behaviour of the imprinted material and its microstructure. To characterise the Nanoimprinting process, a multi length-scale-approach was used by varying the cavities (widths between 20 nm and 2.76 µm) as well as the microstructure of the alloy. CuZn30 was used in different cold-worked and heat-treated conditions, with grain sizes from 100 nm up to 277 µm, thus, covering a wide range of hardening behaviours and grain size to cavity width ratios. Experimental results show that the work hardening behaviour as well as the subgrain or grain size have a major influence on the forming characteristics during Nanoimprinting and a nearly ideal plastic behaviour (no work hardening) leads to the largest extrusion heights. For materials with a pronounced work hardening, low extrusion heights were measured for all cavity widths. This work demonstrates the potential of a simple imprinting process to generate surface features on metallic materials with a width <300 nm and an aspect ratio >1.

Impact of tungsten recrystallization on ITER-like components for lifetime estimation

For ITER divertor, plasma facing components are made with tungsten as armor material. In previous papers, it has been shown that plasma facing components are prone to crack, appearing in tungsten block during thermal cyclic heat loading. In order to predict component lifetime, a numerical simulation is proposed in this paper. With regard to previous studies, tungsten (raw and recrystallized) real mechanical behaviors are taken into account. To be used as inputs for numerical simulations, compressive tests at different temperatures and strain rates were realized on raw and recrystallized tungsten. Raw tungsten tests reveal a linear elastic and ideal plastic behavior that is sensitive to strain rate. Concerning recrystallized tungsten, an elastic-viscoplastic behavior is observed on the entire explored temperature range (up to 1150 °C), that can be described by an elastic-plastic model with kinematic hardening. Manson-Coffin relationships are used to estimate the lifetime. When taking into account real mechanical behaviors for raw tungsten and recrystallized tungsten, we show that lifetime estimation is mainly driven by recrystallized thickness in the component, by the ductile to brittle transition temperature and finally by strain rate.

The Occurrence of Ideal Plastic State in CP Titanium Processed by Twist Extrusion

This paper deals with the analysis of strength and plastic characteristics of commercially pure (CP) titanium as a function of equivalent plastic strain accumulated during Twist Extrusion (TE) process. It is shown experimentally that multipass TE leads to the saturation of the following characteristics of the material: yield stress, reduction in area, elongation to failure, and uniform elongation. This fact indicates the occurrence of an ideal plastic state in the processed material. The threshold value of accumulated plastic strain for ideal plastic behavior of CP titanium during TE is defined. The strain state and mechanical properties of CP titanium billets processed by TE are studied. An explanation for the hardening on the axis of a billet during TE is offered. The analysis of deformation modes on the billet axis during TE and High Pressure Torsion is carried out. It is shown that the differences in strain state on the axis are caused by the difference in symmetry of these processes.

Effect of In implantation and annealing on the lattice disorder and nano-mechanical properties of GaN

The effect of 700keV In implantation and subsequent annealing on GaN was studied by Rutherford Backscattering spectroscopy, Raman spectroscopy and nanο-indentation as a function of the ion fluence (F) ranging from 5×1013 to 1×1016cm−2. Symmetry allowed and disorder activated Raman scattering peaks were analyzed using the spatial correlation model, allowing their assignment to phonon branches of crystalline GaN or defects and the estimation of the corresponding phonon coherence length (L). The L values decrease abruptly at a critical fluence of approximately 2×1014cm−2. After a slight increase in the nano-hardness (H) and reduced elastic modulus (Er) values at low implantation fluences, they exhibit a steep reduction. These variations are accompanied by changes in the shape of the load–displacement curves, which are indicative of elasto-plastic behavior up to a critical F, whereas they approach the ideal plastic behavior at higher fluences. Annealing at 1000°C of the sample implanted with 1×1015ions/cm2 results in efficient recovery of its structural and nano-mechanical properties. However, annealing of specimens implanted at higher fluences causes partial recovery that starts mainly from the transition region between the heavily damaged and the underlying undamaged GaN. The highly correlated behavior of L, H and Er on the implantation fluence implies a common origin of the studied effects.

Elasto-plastic model for analysis of influence of imperfections on stiffness of fully anchored light-frame timber shear walls

In order to stabilize timber-framed buildings against lateral loads, the diaphragm action of roofs, floors and walls is often used. This paper deals with the influence of imperfections such as gaps and uplift on the stiffness and the horizontal displacement of fully anchored shear walls. The significance of analyzing the effects of imperfections is evident when evaluating the stiffness of shear walls; tests of walls show that the horizontal displacement is underestimated in calculations using the stiffness of sheathing-to-framing joints as obtained from experiments. Also, in real structures where hold-downs are used, the influence of gaps and uplift should be included in order to obtain realistic displacements in the serviceability limit state. The analytical model is based on ideal plastic behavior of the mechanical sheathing-to-timber joints with stresses parallel to the perimeter of the frame and on linear elastic behavior for stresses perpendicular to the bottom rail. Using this elasto-plastic model, the equations for the stiffness and the deflection versus the number of segments in the wall are derived. The fully anchored condition for the shear walls is simulated by applying a diagonal load to the shear wall. Three types of imperfections are evaluated: Walls with gaps at all studs, a gap only at the trailing stud, and gaps at all studs, except at the trailing stud. It is shown that the effect of imperfections on the stiffness of the wall in the initial stage is considerable. Depending on the distribution of the gaps and the number of segments included in the shear wall, the displacement of the shear wall is increased several times compared to that of a fully anchored wall diaphragm with no gaps; e.g. for a single segment wall more than four times. However, for walls with more than six segments the effect of imperfections can be neglected. Finally, the theoretical model is experimentally verified.

Failure Process and Stress-Strain Curve of Plane Strain Rock Specimen with Initially Random Material Imperfections

The failure process of heterogeneous rock specimen with initially random material imperfections in uniaxial plane strain compression and the macroscopically mechanical response are numerically modeled by using FLAC (Fast Lagrangian Analysis of Continua). A FISH function is generated to prescribe the initial imperfections within the heterogeneous specimen by using Matlab. The imperfection is weaker than the intact rock. Beyond the failure of the imperfection, it undergoes ideal plastic behavior, while intact rock exhibits linear strain-softening behavior and then ideal plastic behavior once failure occurs. The specimen with smooth ends is loaded at a constant strain rate and is divided into 3200 elements. The maximum numbers of the initial imperfections in five schemes are 100, 300, 500, 700 and 900. The effects of the number of the imperfections on the fracture process, the final fracture pattern and the complete stress-strain curve are investigated. Prior to the peak stress, some imperfections extend in the axial direction and then a part of them coalesce to form inclined shear bands. Beyond the peak stress, shear bands progressively intersect the specimen; in the process the number of the yielded elements approximately remains a constant. With an increase of the number of the initial imperfections, the spacing of shear fractures decreases, the peak stress and corresponding axial strain decrease; the post-peak branch of stress-strain curve becomes steeper; much more elements fail in tension; the number of the yielded elements in tension in the vicinity of the two lateral edges of the specimen remarkably increases.

Joint Inclination Effect on Strength, Stress-Strain Curve and Strain Localization of Rock in Plane Strain Compression

Peak strength, mechanical behavior, and shear band (SB) of anisotropic jointed rock (JR) were modeled by Fast Lagrangian Analysis of Continua (FLAC). The failure criterion of rock was a composite Mohr-Coulomb criterion with tension cut-off and the post-peak constitutive relation was linear strain-softening. An inclined joint was treated as square elements of ideal plastic material beyond the peak strength. A FISH function was written to find automatically elements in the joint. For the lower or higher joint inclination (JI), the higher peak strength and more apparent strain-softening behavior are observed; the failure of JR is due to the slip along the joint and the new generated SBs initiated at joint’s two ends. For the lower JI, the slope of softening branch of stress-strain curve is not concerned with JI since the new and longer SBs’s inclination is not dependent on JI, as can be qualitatively explained by previous analytical solution of post-peak slope of stress-strain curve for rock specimen subjected to shear failure in uniaxial compression based on gradient-dependent plasticity. For the higher JI, the post-peak stress-strain curve becomes steeper as JI increases since the contribution of the new SBs undergoing strain-softening behavior to axial strain of JR increases with JI. For the moderate JI, the lower strength and ideal plastic behavior beyond the elastic stage are found, reflecting that the inclined joint governs the deformation of JR. The present numerical prediction on anisotropic peak strength in plane strain compression qualitatively agrees with triaxial experimental tests of many kinds of rocks. Comparison of the present numerical prediction on JI corresponding to the minimum peak strength of JR and the oversimplified theoretical result by Jaeger shows that Jaeger’s formula has overestimated the value of JI.

A radial compression test for plastic flow studies

A hydraulic experimental setup and related instrumentation were developed for testing constitutive models of ideal plastic behavior at large deformations using slow, radial compression of short, hollow cylinders at constant height. At this preliminary stage of development, plasticine rings with initial inner diameters of 25.4 mm were reduced to a final diameter of 9 mm or less. Further development is needed to test first lead and then harder metals.

The simple shear oscillation and the restrictions to elastic-plastic constitutive relations

Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence of hardening and softening behavior of elastic-plastic materials, namely the oscillation of hardening behavior, by analyzing a simple model of rigid-plastic materials with kinematical hardening under simple shear deformation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its response stresses to any continuous plastic deformation must be non-oscillatory, and there is no oscillation of hardening behavior during the plastic deformation.

Plastic inhomogeneity and easy glide of aluminum and Al[sbnd]Al3Ni eutectic alloy with [111] fiber texture

An aluminum of commercial purity and a directionally solidified AlAl3Ni eutectic alloy were extruded to obtain [111] fiber texture. Tensile testings were then performed at room temperature and 500°C with the tensile direction parallel to the fiber axis. Similar to stage I tensile deformation of single crystals, the room temperature flow curve of the pure aluminum and that of the AlAl3Ni alloy with pure intergranular particles reveal plateau-like flow behavior at the initial stage of yielding. For the latter deformed at 500°C, the flow curve shows superior elongation with ideal plastic behavior following the initial work-hardening stage. The above results are associated with plastic inhomogeneity with which primary slip occurs in limited subgrains and dislocation activities in most subgrains are extremely low or absent. This plastic inhomogeneity can be rationalized by comparing the Taylor factors of primary slip and multiple slip for the subgrains of different misorientations. Also, as discussed in this paper, the influence of the Portevin-LeChatelier effect on the above results can be neglected if it exists.

Plastic work in the peeling of work hardening foils

The plastic work consumed by the flexible metallic foil during a peel test can contribute significantly to the measured load. It is thus important to be able to quantify it in order be able to make inferences about the adhesion at the interface. Several models have been previously proposed which allow the calculation of the plastic work, based on the modulus and yield stress of the flexible metallic foil, assuming ideal plastic behavior. When testing the adhesion of thermal spray coatings, for example, a stainless steel foil is used which work hardens during peeling. A method is proposed here which allows the calculation of the plastic work during peeling for a work hardening material with experimentally determined stress-strain relationship. The plastic work is calculated by integrating the stress-strain curve for the peeled material numerically. The prediction is then compared with experimentally measured plastic work values for several materials.

Solution for the Design of Reinforced Concrete Plates and Shells

The use of finite-element packages by practioners as a design tool for reinforced concrete structures has increased considerably in the last few decades. All structural codes of practice recognize the assumption of linear elastic behavior at a design stage. However, the problem remains of calculating the required reinforcement in plates and shells. The amount of reinforcement is determined locally, i.e., for each sampling point, from the equilibrium between applied and internal forces. The formulation of the method includes biaxial behavior of concrete and different lever arms for all the internal forces. Ideal plastic behavior is assumed for both materials. A reference is made to the absence of universally accepted solutions for the design of these structures and, therefore, scarcity of provisions in the structural concrete codes. To appraise the validity of the method, a comparison is made with experimental tests on slab and shell elements. Additional numerical results for practical structures are also ...

Lattice parameter and hardness variations resulting from precipitation and misfit accommodation in a particle-reinforced AlSiCuMg alloy

Precipitation processes occurring in ageing of AI-20at.%Si-l.5at.%Cu-l.lat.%Mg (ASCM) alloys with and without AI203 particle reinforcement were studied using X-ray diffraction and hardness measurements. During ageing at 453 K after solid quenching, the Q phase (AlsCu2MgsSi6) precipitates first, followed by the 0 phase (AI2Cu). An optimized heat treatment for the ASCM alloys consists of a short solution treatment at 779 K, followed by water quenching and ageing for 4 h at 453 K. After the peak in hardness has occurred, continued ageing decreases the hardness. This overageing results from coarsening of the Q phase. After heat treatment, the lattice parameters were affected by the misfit effects caused by the difference in the coefficients of thermal expansion between the Al-rich phase, Si-rich phase and Al203 particles if present. These misfits still existed at room temperature after precipitation was completed. A model assuming ideal plastic behaviour of the matrix describes fairly well the cooling-induced changes in the Si-rich phase lattice parameter. For the cooling-induced changes in the Al-rich phase lattice parameter, there remains a difference between model predictions and measurements.

Plastic relaxation of the transformation strain energy of a misfitting spherical precipitate: Ideal plastic behavior

Assuming ideal plastic behavior for an isotropic matrix containing a misfitting spherical precipitate, the total amount of work expended during elasto-plastic deformation is calculated and compared with the total strain energy in the corresponding pure elastic state. For precipitates larger than one micron (µm), the effective yield stress is taken as the macroscopic yield stress while for smaller precipitates, size-dependent yield stresses are obtained from the Ashby-Johnson model. In the case of coherent submicron precipitates, the effective yield stress becomes the theoretical yield strength and thus plastic relaxation is not possible unless the transformation stress is extremely large. For incoherent submicron precipitates, the effective yield stress is approximately inversely proportional to the precipitate radius,r. Hence plastic relaxation again is not possible whenr < 10 nm, but whenr ≃100 nm the strain energy can decrease by 10 ∼ 40 pct at a misfit of 3 pct. For supra-micron particles, however, the ratio of the effective yield stress to the shear modulus becomes 10−3 or less, and plastic relaxation can reduce the strain energy by factors of 3 to 15 at misfits of 1 to 3 pct. Under this circumstance, the plastic zone becomes wide, its radius ranging from 3 to 5r.

Tensile properties of directionally solidified Al-Al3Ni composites with off-eutectic compositions

Ingots (1/8 in. diameter) of Al-Al3Ni with off-eutectic compositions were directionally solidified at two growth rates. At 1 cm h−1 fibres exhibited a blade-like morphology, and at 11 cm h−1, a rod-like morphology. Speciments were mechanically evaluated in tension. The composite modulus at stresses above the yield strength of the aluminium matrix obeyed the rule of mixtures, assuming ideal plastic behaviour of the matrix. An extrapolation of these data for composites with rod fibres gave a value of 146 GN m−2 for the modulus of Al3Ni. Tensile strength of composites with rod-like fibres followed the rule of mixtures, whereas those with non-uniform blade fibres showed a lower strength. In composites with blade-like fibres the extrapolated aluminium matrix strength was 86.3 MN m−2, a high value attributed to dispersion hardening, and that of the fibres was 2.69 GN m−2. Composites with blade-like fibres failed at lower strains than did those with more uniform rod-like fibres.