Plastic Shear Strain Research Articles

Optimal heating control of thermosensitive bodies under plastic deformation of material

A mathematical statement has been formulated and algorithms for solving one- and two-dimensional problems on fast operation optimal heating control of homogeneous thermosensitive canonical form bodies has been developed. We have determined the control (the surrounding temperature at one of the boundary surfaces or heat flux at one of the boundary surfaces) which in a minimal time carries the body from the initial thermal state to the final one, characterized by the given mean-integral temperature. In addition, restrictions on the control function and the maximal tangential stress intensity or accumulated plastic shear strain have been considered. The elastoplastic deformation of the material has been studied within the framework of general plasticity theory proposed by Il’yushin.

Simulated extreme value fatigue sensitivity to inclusions and pores in martensitic gear steels

The objective of this work is to model the sensitivity of high cycle fatigue resistance of secondary hardening martensitic gear steels to variability in extrinsic inhomogeneities such as primary inclusions, and pores, coupled with intrinsic microstructure variability. A simplified approach is presented to quantify the variability in the driving force for fatigue crack formation in the matrix at non-metallic inclusions and pores in lath martensitic gear steels using a three-dimensional crystal plasticity constitutive model. The utility of a simulation-based strategy for exploring sensitivity of minimum fatigue lifetime (low probability of failure) to microstructure lies in its inherent capability to consider parametric simulations of hundreds of inclusions and microstructures in contrast to limited numbers of physical experiments. Experiments are used to calibrate the polycrystalline cyclic stress–strain response and mean (50% probability) fatigue crack formation life. Several remote loading conditions are considered in the high cycle fatigue (HCF) regime relevant to typical gear applications. Idealized inhomogenieties (spherical) in the form of hard (Al 2O 3), soft inclusions (La 2O 2S), and pores are systematically investigated in this parametric computational study. Relations between remote loading conditions and local plasticity are discussed as a function of stress amplitude and microstructure. The maximum plastic shear strain range is used in the modified form of Fatemi–Socie parameter evaluated at the grain scale as a measure of the driving force for fatigue crack formation (nucleation and early growth to lengths on the order of several times the average grain size). Multiple realizations of the polycrystal microstructure are considered to obtain a statistical distribution of this fatigue indicator parameter (FIP). The results are used to construct an extreme value Gumbel distribution of the FIPs for the selected microstructures. Subsequently, a computational micromechanics based minimum life estimate that corresponds to 1% fatigue crack formation probability is calculated.

The growth and mechanical properties of paratellurite single crystals at high temperatures

α-TeO2 single crystals have been grown by the Czochralski method on specially developed systems with automatic growth control. The mechanical properties of crystals under compression in the [100], [110], and [221] directions at a constant strain rate of about 10−4 s−1 in the temperature range T = 733−993 K have been investigated. The distribution of plastic shear strain in deformed samples is has been experimentally studied. Manifestations of localized strain in covalent paratellurite crystals at T > 900 K are revealed for the first time. The active slip systems along which localized shear band are oriented are determined. The temperature dependence of the critical stress of transition to localized flow is investigated.

On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization

The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e., an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid–solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress–strain response in good agreement with that of a rank-one convexification method, while showing the same numerical efficiency as a classical Taylor-type approximation. Consequently, it combines the advantages of both limiting cases. The model is calibrated for single crystal magnesium by means of the channel die test and finally applied to the analysis of texture evolution in a polycrystal. Comparisons of the predicted numerical results to their experimental counterparts show that the novel model is able to capture the characteristic mechanical response of magnesium very well.

Design of ultrahard materials: Go nano!

Intrinsically super- (H ∼ 40–70 GPa) and ultrahard (H ≥ 70 GPa) materials attain high hardness through their large intrinsic strength, whereas extrinsically super- and ultrahard materials reach such hardness through their nanostructure. The recent search for intrinsically super- and ultrahard materials has concentrated on those with high elastic moduli. Several examples are presented of materials with high zero-pressure elastic moduli but relatively low hardness, because, upon imposing a large lattice distortion or substantial plastic shear strain, they undergo an instability of their electronic structure. Recent progress is then elucidated in the understanding of the origin of ultrahardness of nc-TmN/a-Si3N4 nanocomposites (Tm = transition metal that forms hard and stable nitrides), in which 3–4 nm size TmN nanocrystals are joined together by about a monolayer thick SiN x interface material layer. A combined ab initio DFT calculation of the ideal shear strength of the interfaces between the plastically non-deformable randomly oriented TmN grains, followed by Sachs-type averaging of these shear resistances in space to obtain a uniaxial yield strength, Y, employing a proper pressure enhancement of Y and considering the Tabor relation between the hardness H and yield strength Y, shows that these materials can reach hardness significantly larger than diamond, when correctly prepared and essentially free of defects. Such superhard nanocomposites are already available on an industrial scale as protective coatings on tools for machining, such as for drilling, milling, turning, forming, stamping and the like.

Influence of partial slip and direction of traction on wear rate in wheel-rail contact

Abstract The ‘dynarat’ computer model is used to simulate accumulation of plastic shear strain (ratcheting) in rails and to predict wear and crack initiation. Recent developments have focussed on models of microstructure and strain hardening characteristics, based on twin-disc tests with British normal grade (Grade 220) rail steel. In Europe, and increasingly in Britain, the harder Grade 260 rail steel is more common. A set of twin-disc tests using Grade 260 rail steel has been performed, providing wear rates, micro-hardness data and shear strain estimates in order to select a new strain-hardening model. Calibration has led to developments in the core ratcheting model, including the ratcheting equation, the criterion for material failure and the influence of surface micro-roughness. Having calibrated the model against twin-disc data, wear rates are predicted for a set of generic wheel-rail contacts. The ratcheting model is developed here to simulate transverse traction, and a new quasi-static partial slip model for wheel-rail contact is presented. For the range of contact conditions studied, wear rate is found to vary linearly with peak contact pressure, and an equation for estimating wear rate as a function of peak pressure and traction coefficient is fitted to the simulation data.

Numerical modeling of crack formation in powder forming processes

This paper presents a constitutive model describing the mechanical behavior of metal powders during (uniaxial) cold die compaction processes, placing special emphasis on the modeling of cracks formed during the ejection stage. The constitutive relationships are derived within the general framework of rate-independent, isotropic, finite strain elastoplasticity. The yield condition is determined by three surfaces intersecting non-smoothly in stress space, namely, an elliptical cap and the classical Von Mises and Drucker–Prager yield surfaces. The distinct irreversible processes are described in terms of two internal variables: an internal hardening variable, associated with accumulated compressive (plastic) strains, and an internal softening variable, linked with accumulated (plastic) shear strains. Motivated by both numerical and physical reasons, a parabolic plastic potential function is introduced to characterize the plastic flow on the linear Drucker–Prager failure surface. A thermodynamically consistent calibration procedure is employed to relate the softening modulus to fracture energy values obtained experimentally on Distaloy AE powder specimens. The predictive capability of the constitutive model is checked by simulating three representative cases: a diametral compression test, the ejection of an over-densified thin cylindrical part and the compaction of an axially symmetric multilevel part in an advanced CNC press machine. These simulations demonstrate the ability of the model to detect evidence of macroscopic cracks, clarify and provide reasons for the formation of such cracks, and evaluate, at least qualitatively, the influence of variations in the input variables on their propagation through the green compact.

Effects of recrystallization on texture, microstructure and mechanical properties in HPT-deformed pure Mg

Mg of purity 99.8 wt% was deformed by High Pressure-Torsion at hydrostatic pressures 1 to 4 GPa and RT, up to plastic shear strains of 120. X-ray texture analysis showed up deviations from expected shear texture, which increased with increasing shear strain and hydrostatic pressure. According to TEM and SEM investigations these deviations can be understood in terms of recrystallization. The current paper aimed at the differences of the recrystallization processes which occur during HPT deformation and unloading (dynamic recrystallization, DRX), and those after deformation (static recrystallization, SRX). For this purpose, two sorts of samples were investigated: (i) such being stored at RT immediately after HPT deformation, and (ii) such being stored at 77 K immediately after HPT deformation, and stored at RT for a minimum and constant time needed for preparation. The results show that SRX brings the texture closer to the ideal shear texture and to higher strength values, but to smaller ductilities than DRX does. The mechanical properties can be attributed to changes of texture rather than to those of grain size.

Influence of plastic shear strain and confinement-dependent rock dilation on rock failure and displacement near an excavation boundary

Excavation-induced rock failure and displacement near an underground opening boundary is closely associated with rock mass dilation. A better understanding of rock mass dilation around the excavation helps us to predict or anticipate displacements and extent and shape of the failed zone, and subsequently assist design of proper ground support systems. A calibrated cohesion weakening and frictional strengthening (CWFS) model with a constant dilation angle can capture the stress-induced brittle failure shape in hard rocks. However, the use of a constant dilation angle, in either CWFS, Mohr–Coulomb perfectly elasto-plastic, or Mohr–Coulomb strain-softening models, cannot simulate the displacement distribution near the excavation reasonably. In the present study, numerical simulations are performed to study excavation-induced displacement around tunnels located in different rock mass types, i.e., coarse-grained hard rock, medium-grained hard rock, fine–medium-grained soft rock, and fine-grained soft rock, using a mobilized dilation angle model that depends on both confining stress and plastic shear strain. It is illustrated from a few examples that displacement distributions obtained from the dilation angle model are more reasonable when compared with the general trend measured underground.

An analysis to plastic deformation behavior of AZ31 alloys during accumulative roll bonding process

In present investigation, the plastic deformation behavior of an AZ31 alloy during accumulative roll bonding (ARB) process was analyzed by the rigid-plastic finite element method (FEM). The finite element simulations were performed relying on the true stress–true strain behavior of the experimental alloy obtained through hot-compression testing. The equivalent plastic strain and shear strain were predicted throughout the sheet thickness. Moreover, the influence of the friction between roller/sheet and sheet/sheet on the strain distribution was analyzed. The effect of temperature on the equivalent plastic strain was also characterized. The results indicated that any increase in friction coefficient ended to an increase in equivalent plastic strain and strain gradient. Furthermore, it was found that as the temperature increased the accumulated strain decreased. This was resulted in more homogeneous deformation throughout the sheet thickness.

Accelerated mechanical fatigue testing and lifetime of interconnects in microelectronics

Due to the rapid development of packaging industry accelerated reliability testing for evaluation of lifetime of electronic components are increasingly utilized. In addition to common active thermal cycling procedures, accelerated mechanical fatigue testing provides a new possibility to assess the reliability of microelectronic components, mainly due to the significantly shorter duration of testing time. In this investigation we have used an ultrasonic fatigue testing system in combination with a special experimental set-up for qualification and lifetime determination of microelectronic interconnects. Using this technique, fatigue life of Al wire bonded interconnects were determined and S-N curves (shear stress as a function of loading cycles) up to N=109 were plotted. Three dimensional elasto-plastic FEM simulations were performed to determine the distributions of shear stress and plastic strain generated during cyclic fatigue in the bond area. Furthermore, the FEM model was employed to predict the lifetime of wire-bonds. The results were correlated to the lifetime curves of similar bonds obtained by power cycling tests. Detailed microstructural investigations were performed by means of EBSD -SEM to study the evolution of microstructure of the interconnects subjected to thermal and mechanical fatigue loading. This study demonstrates the applicability of accelerated mechanical fatigue testing as an alternative to time consuming thermal cycling for qualification of microelectronic interconnects.

Micromechanical simulations for fatigue damage incubation mechanisms of [formula omitted] processed steel

A Laser Engineered Net Shaping (LENSTM) processed AISI 316L-grade stainless steel possesses unique microstructural features that affect its fatigue damage incubation mechanisms and fatigue life. As observed experimentally, fatigue damage was incubated almost exclusively at a relatively large pore located at or near the specimen surface, or at an incompletely melted powder particle on the surface in some rare cases. Micromechanical simulations were conducted on a series of representative volume elements to probe the micromechanism of fatigue damage incubation. A non-local plastic shear strain range-based fatigue manage parameter was introduced to represent the micronotch plasticity accumulation state under a large deformation gradient region. This microplasticity parameter was found to correlate to the fatigue endurance limit and transition between high cycle and low cycle fatigue regimes quite well. In the high strain amplitude regime (>0.3%), the spatial distribution extends no or little effect on fatigue damage incubation. The scatter in fatigue life is primarily dominated by small crack growth. In the low strain amplitude regime, the void on the edge of the specimen induced two times higher microplasticity compared to void inside the specimen. Due to the high population of the voids inside the alloy, the fatigue strength is limited by the voids on the surface. The microplasticity threshold is approximately 0.15% which corresponds to the fatigue endurance limit of 30.8 MPa.Micromechanical simulation demonstrated that the microplasticity induced by the unmelted powder particle is significantly lower than that generated by the void in the microplasticity threshold regime. Therefore, there must be an interactive effect between unmelted powder particles and the surround porosity in the alloy that incubated the fatigue damage.

Residual strain evolution in steel samples: tension versus torsion

Torsion provides a unique opportunity to probe mechanical behavior of materials subjected to pure state of shear stress. In this research, identical steel alloy (12L14) hollow cylinder samples are subjected to predetermined amounts of plastic axial and shear strain such that their octahedral shear strain (an invariant) are identical for comparison. Measurements were made at the residual stress measuring facility at the High Flux Isotope Reactor in Oak Ridge (NRSF2), using a small gauge area in the direction of strain gradients (0.5 mm×0.5 mm) through the hollow cylinder wall thickness. These orthogonal strains are obtained for BCC Fe for three hkl’s. Three normal strains in the hoop, radial, and axial directions are obtained as a function of centroid position of the gauge volume through the 2 mm wall thickness. Significant differences in measured residual strains are noted between the torsion and the tension samples. The largest differences are found for the Fe (200) planes while the smallest differences are observed for the Fe (211) planes. This research demonstrates the need for a systematic study of residual strain as a function of applied stress path moving beyond tensile testing for solving real world problems.

Micromechanics Study of Fatigue Damage Incubation Following an Initial Overstrain

Understanding and quantifying the effects of overloads/overstrains on the cyclic damage accumulation at a microscale discontinuity is essential for the development of a multistage fatigue model under variable amplitude loading. Micromechanical simulations are conducted on a 7075-T651 Al alloy to quantify the cyclic microplasticity in the matrix adjacent to intact or cracked, life-limiting intermetallic particles. An initial overstrain followed by constant amplitude cyclic straining is simulated considering minimum to maximum strain ratios of 0 and −1. The nonlocal equivalent plastic strain at the cracked intermetallic particles reveals overload effects manifested in two forms: (1) the cyclic plastic shear strain range is greater in the cycles following an initial tensile overstrain than without the overstrain and (2) the initial overstrain causes the nonlocal cumulative equivalent plastic strain to double in subsequent tensile-going half cycles and triple in subsequent compressive-going half cycles, as compared with cases without an initial tensile overstrain. The cyclic plastic zone at the microdiscontinuity corresponds to that of the maximum strain during the initial overstrain and the nonlocal cyclic plastic shear strain range in the matrix near the intact or cracked inclusion is substantially increased for the same remote strain amplitude relative to the case without initial overstrain. These results differ completely from the effects of initial tensile overload on the response at a macroscopic notch root or at the tip of a long fatigue crack in which the driving forces for crack formation or growth, respectively, are reduced. The micromechanical simulation results support the incorporation of enhanced cyclic microplasticity and driving force to form fatigue cracks at cracked inclusions following an initial tensile overstrain in a fatigue incubation model.

Elasto-plastic analysis in conventional tunnelling excavation

A new, rigorous approach for calculating the distribution of stresses and displacements around a circular opening excavated in a strain-softening generalised Hoek–Brown rock mass is presented. As most of the current solutions are relevant to elastic-perfectly plastic and elastic-brittle plastic material, it is worth developing a new analytical-numerical approach to address this end. This paper presents an elasto-plastic solution for the axisymmetrical problem of excavating a circular opening in generalised Hoek–Brown material. In the plastic region it is assumed that all the strength parameters are linear functions of the plastic shear strain. By invoking the Runge–Kutta fourth-order method the problem is solved numerically, and states of stress and displacement in the plastic region are determined. The accuracy and practical application of the proposed approach are shown through several examples. For elastic-perfectly plastic and elastic-brittle plastic cases, the proposed approach shows excellent agreement with closed-form solutions. Similarly, for the strain-softening case, this method is in good agreement with current rigorous methods. The influence of the softening parameter, appearing in the evolution of strength parameters, is examined by the construction of different ground reaction curves, and the influence of different definitions for dilation angle in the plastic region is investigated.

A mobilized dilation angle model for rocks

Experimental and field observations of rock failure show that the failure process is closely associated with rock dilation, an indicator of volumetric increase during rock deformation. The most common concept used to describe dilation is the dilation angle. The conventional Mohr–Coulomb model considering strain-softening often makes an assumption of constant dilation, but it is observed that the approach is not successful in characterizing the nonlinear deformation behavior of rocks. In the present study, based on published data acquired from modified triaxial compression tests with volumetric strain measurement, a mobilized dilation angle model considering the influence of both confining stress and plastic shear strain is established. Based on the model response and in combination with the grain size description and the uniaxial compressive strength, the model parameters for four rock types (coarse-grained hard rock, medium-grained hard rock, fine-medium-grained soft rock, and fine-grained soft rock) are suggested. For coal and quartzite representing fine-grained soft rock, and coarse-grained hard rock, respectively, the dilation angle model is used to predict the volumetric-axial strain relationships, and the predictions are found to be in good agreement with experimental results.

HCP双結晶の塑性すべりによって生ずる回位型変形場と応力集中(<小特集>M&M2009材料力学カンファレンス)

Plastic slip deformation of a HCP bicrystal is analyzed by a crystal plasticity FE code and distribution of plastic shear strain on the primary and secondary slip systems, as well as some stress components are examined. The constituent crystal are idealized ones and slip deformation on basal, prismatic and pyramidal slip systems can take place, but twin deformation cannot. After a deformation of 1% nominal tensile strain, sharp stress concentrations are developed at the junctions of the grain boundary plane and specimen surfaces even though the crystal orientations of the two grains differ only a few degree. Results are compared with the case for FCC bicrystals and effects of the activation of secondary slip systems are discussed.

Effect of Inclusions on Machinability of Carbon Steels for Machine Structural Uses

The plunge cutting test was carried out on several structural steels, Fe-0.4%C-0.2%Si-1.5%Mn and one containing 0.16%Pb and 0.06%S. The cutting force was reduced by the addition of Pb and the presence of MnS particles, and the former was found to be more effective to lower the cutting resistance. The lead observed in the primary shear zone of a chip exhibited a thin string-like morphology, suggesting the ductile and very deformable characteristic of Pb. The microhardness distribution inside the chip was lower for the Pb-bearing steel than for the MnS containing steel. Those results indicate that at the primary shear zone of the chip the deformation is mainly concentrated on lead particles and plastic shear strain accumulated in the chip remains lower. This lower plastic work is likely to be the outcome of the reduced shear stress, which might be the major origin of the lower cutting force observed in the Pb-bearing steel.

1208 レール頭部における短いき裂進展と摩耗の競合シミュレーション(OS12. 破壊力学とき裂の解析・き裂進展シミュレーション(2),オーガナイズドセッション講演)

In this study. numerical models have been developed to simulate the competition between short crack propagation and wear in rail head. The locations of crack initiation are given by a random generator in the pro-eutectoid ferrite at the beginning of the simulation. The crack is assumed to initiate when the total accumulated plastic shear strain in the region reaches the critical shear strain value. The growth of Stage I short crack occurs along the ferrite and pearlite boundaries. If the crack becomes long enough to open its faces, Stage II short crack growth is assumed to occur. In these crack growth simulations, Hobson law is applied. With regard to wear, the Archard model is adopted as the basis. The wear depth can be calculated from the normal pressure distribution in the wheel-rail contact region, the sliding distance etc.

A method for calculating damage evolution in adiabatic shear band of titanium alloy

A method for calculating the evolution of the local damage variable at the adiabatic shear band (ASB) center was proposed. In the present method, the JOHNSON-COOK model and the nonlocal theory were adopted, and the damage variable formula applicable for the bilinear (linearly elastic and strain-softening) constitutive relation was further generalized to consider the plastic deformation occurring in the strain-hardening stage. Aiming at Ti-6Al-4V, the effect of strain rate on the evolution of the local damage variable at the ASB center was investigated. In addition, a parametric study was carried out, including the effects of strain-hardening exponent, strain rate sensitive coefficient, thermal-softening exponent, static shear strength, strain-hardening modulus, shear elastic modulus, work to heat conversion factor, melting temperature and initial temperature. The damage extent at the ASB center in the radial collapse experiment was assessed. It is found that at higher strain rates the damage in the ASB becomes more serious at the same average plastic shear strain of the ASB.