Shear Strain Components Research Articles

Self-organization of plastic shears in localized deformation macrobands in the neck of high-strength polycrystals, its role in material fracture under uniaxial tension

Based on the television-optical measurements of displacement vector fields, we study the distribution of shear and linear strain components as well as plastic flow intensity in the neck of flat high-strength polycrystals of steel VKS-12, submicrocrystalline armco-iron and titanium under uniaxial tension. The leading deformation mechanism in the neck is related to the development of two stationary localized plastic flow macrobands in it. The macrobands are self-organized as a cross along the conjugate directions of maximum tangential stresses. The self-consistency of plastic shears in these macrobands governs the specific character of material deformation and fracture in the neck.

Free vibration of higher-order sandwich and composite arches, Part I: Formulation

A higher-order refined model with seven degrees of freedom per node is presented in this paper for the free vibration analysis of composite and sandwich arches. The strain field is modeled through cubic axial, cubic transverse shear and linear transverse normal strain components. As the cross-sectional warping is accurately modeled by this theory, it does not require any shear correction factor. The stress–strain relationship is derived from an orthotropic lamina in a three-dimensional state of stress. The proposed higher-order formulation is validated, in this first part, through arches with various curvatures, aspect ratios, boundary conditions and materials.

Quasistatic propagation of steps along a phase boundary

We study quasistatic propagation of steps along a phase boundary in a two-dimensional lattice model of martensitic phase transitions. For analytical simplicity, the formulation is restricted to antiplane shear deformation of a cubic lattice with bi-stable interactions along one component of shear strain and harmonic interactions along the other. Energy landscapes connecting equilibrium configurations with periodic and non-periodic arrangements of steps are constructed, and the energy barriers separating metastable states are calculated. We show that a sequential one-by-one step propagation along a phase boundary requires smaller energy barriers than simultaneous motion of several steps.

Effect of Austenite as a Harder Second Phase on Ferrite Substructure Evolution by Intercritical Rolling

Effect of austenite as a harder second phase on ferrite substructure evolution by intercritical rolling has been investigated using 0.12C-0.3Si-1.35Mn steel. Slab was reheated at 780°C (ferrite; α + austenite; γ phase region) and rolled with 90% reduction down to 12mm in thickness using laboratory mill. 700°C (ferrite; α + cementite; θ phase region) rolled plate was also prepared to compare with 780°C rolled plate. Microstructure distribution along the plate thickness has been observed in detail by SEM and EBSD. Microstructure showed mixed structure of fine-grained ferrite and elongated ferrite for both of the plates. The ratio of fine-grained ferrite region was around 50% at the plate surface, however, fine-grained ferrite formation hardly occurred at mid thickness for 700°C rolled plate. FEM analysis revealed that fine-grained ferrite distribution along the thickness can be well explained by equivalent plastic strain distribution along the plate thickness for 700°C rolled plate. Equivalent plastic strain showed maximum value near the plate surface due to shear strain component, and it could help substructure evolution and fine grained ferrite formation. On the other hand, the ratio of fine-grained ferrite region reached to 50% all through the thickness for 780°C rolled plate. Austenite as a harder second phase seems to promote ferrite substructure evolution even at mid thickness of the plate.

Localized strain effects on photoluminescence of quantum dots induced by nanoprobe indentation

We report localized strain effects on the low temperature (10 K) photoluminescence (PL) of self-assembled InGaAs/GaAs quantum dots (QDs), measured through an optical fiber nanoprobe (metal coated, aperture approximately 850 nm, flat apex). The localized strain is generated by the indentation of the nanoprobe onto the sample surface within elastic limit. The simultaneous measurement of the indentation force (typically<3 mN) and PL spectra enables us to perform the quantitative analysis of the strain effects through numerical model calculations. The energy-band shift calculated with 6×6 strain Hamiltonian for QDs and GaAs matrix figures out the accumulation of photoexcited holes at the edge region of the nanoprobe-indented area, which should be the mechanism of PL enhancement evoked by the nanoprobe indentation. The hole accumulation is caused by the shear strain components and thus not realized by the conventional hydrostatic experiments. The mechanism must be related closely to the emission enhancement reported for a p-type modulation doped laser.

Low-Temperature Phase Transformations ofPbZr1−xTixO3in the Morphotropic Phase-Boundary Region

We present anelastic and dielectric spectroscopy measurements of PbZr(1-x)Ti(x)O(3) with 0.455 < or = x < or = 0.53, which provide new information on the low-temperature phase transitions. The tetragonal-to-monoclinic transformation is first order for x < 0.48 and causes a softening of the polycrystal Young's modulus whose amplitude may exceed the one at the cubic-to-tetragonal transformation; this is explainable in terms of linear coupling between shear strain components and tilting angle of polarization in the monoclinic phase. The transition involving rotations of the octahedra below 200 K is visible both in the dielectric and anelastic losses, and it extends within the tetragonal phase, as predicted by recent first-principle calculations.

Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution

We study the motion of steps along a martensitic phase boundary in a cubic lattice. To enable analytical calculations, we assume antiplane shear deformation and consider a phase-transforming material with a stress–strain law that is piecewise linear with respect to one component of shear strain and linear with respect to another. Under these assumptions we derive a semi-analytical solution describing a steady sequential motion of the steps under an external loading. Our analysis yields kinetic relations between the driving force, the velocity of the steps and other characteristic parameters of the motion. These are studied in detail for one, two and three-step configurations. We show that the kinetic relations are significantly affected by the material anisotropy. Our results indicate the existence of multiple solutions exhibiting sequential step motion.

Whole-field optical strain sensor using a microlens array

We discuss a novel whole-field optical strain sensor termed the moire interferometric strain sensor (MISS) for simultaneous measuring of multipoint strains and whole-field contours of in-plane displacement. A high-frequency grating, attached to the surface of a specimen, is used as the displacement and strain-sensing unit. When illuminated by two collimated beams at a prescribed angle, the interference of the diffracted beams gives the whole-field deformation contours. If, on the other hand, each of the individual beams is separately imaged using a multilens CCD sensor similar to a wavefront sensor, the separation between the spot centroids for each microlens is directly proportional to the normal or shear strain component at the corresponding position on the specimen. Applications are demonstrated for uniform rotation and simulated in-plane strains.

Numerical simulation of rheological processes in hardening plastics under stress control

The paper concerns the simulation of rheological processes in hardening plastics (resins) under stress control. It is assumed that the resins work in the glassy state, under normal conditions, and the rheological processes are quasi-static and isothermal. The reduced stress levels do not exceed 30% of the instantaneous tensile strength. A resin is modelled as a homogeneous, isotropic, linearly viscoelastic material. The HWKK/H rheological model, developed recently by the author, is used. Short-term, medium-term, and long-term shear strain components are considered and described by one fractional and two normal exponential functions as the stress history (memory) functions. A novel algorithm for the numerical simulation of rheological processes in resins has been developed, which is unified for all stress history functions in the HWKK/H model. The algorithm employs the Boltzmann superposition principle, a virtual table for the classic creep process, and a high-rank Gaussian quadrature. The stress function is approximated with a stair case function. The constitutive equations governing the HWKK/H model are trans formed into an algebraic form suitable for algorithmization. The problem of quasi-exact calculation of the double-improper integral resulting from the fractional exponential function is solved effectively. The algorithm has been tested successfully on selected loading programs of unidirectional tension of epoxide.

Precipitation and grain refinement in a 2195 Al friction stir weld

The microstructure across a friction stir weld in aluminum alloy 2195 was analyzed to reveal the precipitation processes, grain evolution mechanisms, and crystallographic texture within that weld. The complex microhardness variations across the weld are explained by the observed precipitation sequence, in which the original precipitates coarsen and dissolve during welding, and are then replaced by different precipitates, which form during cooling. The grain development from the thermomechanically affected zone (TMAZ) into the weld nugget reveals that subgrains form within the TMAZ grains and develop increasing boundary misorientations through continuous dynamic recrystallization by subgrain rotation to eventually form the refined grains observed within the weld nugget. Within the weld nugget, a {112}〈110〉 texture is observed, corresponding to a high strain/high temperature shear strain component.

An energy-based fatigue life assessment model for various metallic materials under proportional and non-proportional loading conditions

The present study examines the capability of a lately developed energy-based fatigue damage parameter [Jahed H, Varvani-Farahani A. Upper and lower fatigue life limits model using energy-based fatigue properties. Int J Fatigue 2006;28:467–73] to assess fatigue life of various metallic materials subjected to proportional and non-proportional loading conditions. The proposed damage is defined based on (i) shear and axial stress and strain components responsible for cracking/modes of failure dominantly Case A and Case B, (ii) energy-based fatigue coefficients analogous to Coffin–Manson’s coefficients, (iii) corresponding fatigue lives of components failed under axial and torsional loading conditions, and (iv) total elastic–plastic energy calculated from stress–strain hysteresis loops. For the latter, the modified Mroz cyclic plasticity model has been employed to calculate the hysteresis energy. Using this model in conjunction with the proposed damage parameter, fatigue lives of different materials have been predicted and then compared with reported experimental data in the literature. The predicted fatigue lives based on the proposed damage model were found in very good agreement as compared with experimental fatigue data of various metallic materials of Al 7075-T6, AISI 304, SAE 1045, 1% Cr–Mo–V steel, Inc 718 and Haynes 188 tested under both proportional and non-proportional loading conditions.

An improved discrete Kirchhoff quadrilateral element based on third‐order zigzag theory for static analysis of composite and sandwich plates

AbstractA new improved discrete Kirchhoff quadrilateral element based on the third‐order zigzag theory is developed for the static analysis of composite and sandwich plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid‐surface. The usual requirement of C1 continuity of interpolation functions of the deflection in the third‐order zigzag theory is circumvented by employing the improved discrete Kirchhoff constraint technique. The element is free from the shear locking. The finite element formulation and the computer program are validated by comparing the results for simply supported plate with the analytical Navier solution of the zigzag theory. Comparison of the present results with those using other available elements based on zigzag theories for composite and sandwich plates establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The accuracy of the zigzag theory is assessed by comparing the finite element results of the square all‐round clamped composite plates with the converged three‐dimensional finite element solution obtained using ABAQUS. The comparisons also establish the superiority of the zigzag theory over the smeared third‐order theory having the same number of degrees of freedom. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Shear locking reduction in eight-noded tri-linear solid finite elements

A new quadrature rule for eight-noded solid finite elements is suggested. The formulation reduces those locking problems associated with the classical full and selectively-reduced Gauss integration schemes and it is based on an element local coordinate system where the shear strain components are averaged in groups of four integration points. This work is mainly interesting in contexts of plasticity and explicit time integration, where low order elements often are preferable.

Microscopic Evaluation of Strain Distribution in Granular Materials during Shear

The evolution of local strains during shear of particles of a granular material is presented in this paper. A cylindrical specimen composed of 6.5-mm spherical plastic particles was loaded under an axisymmetric triaxial loading condition. Computed tomography (CT) was used to acquire three-dimensional images of the specimen at three shearing stages. The high-resolution CT images were used to identify the 3D coordinates of 400 particles. Nine strain components (normal, shear, and rotation), rotation angles, and local dilatancy angles for particle groups were calculated, and their frequency distribution histograms are presented and discussed. It was found that there is no preferred shear direction, and the standard deviation values for shear strain components (εxy, εxz, and εyz) were almost equal for the specific test shearing stage. Shear strains as high as 25.6% were recorded for some particle groups. Furthermore, granular particle groups rotated in the 3D space with almost equal amounts of rotation strains when loaded under axisymmetric triaxial condition. Rotation strain values are very close to the corresponding shear strains. Compared to particle sliding, rotation plays a major role in the shearing resistance of granular materials. The cumulative vertical rotation angles can be as high as 38° and the horizontal rotation angles have values as high as 60°. The statistical distributions of the local dilatancy angle (ψ1) of particle groups were calculated and found to be increasing as shearing continues. The “global” dilatancy angle value is very close to the mean local ψ1 during the first stage of shearing (i.e, when global εz=−7.3%)

A new discrete Kirchhoff quadrilateral element based on the third-order theory for composite plates

A new discrete Kirchhoff quadrilateral element based on the refined third-order theory is developed for the analysis of composite plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid-surface. The inplane displacements and the shear strains are interpolated using bilinear interpolation functions and the mid-surface rotations are interpolated using bi-quadratic functions based on the discrete Kirchhoff technique. The element stiffness matrix and the consistent load vector are developed using the principle of virtual work. The finite element formulation is validated by comparing the results for simply-supported plate with the analytical Navier solution. Comparison of the present results with those using other available elements based on the TOT establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The element is free from shear locking

Thermal deformation analysis of BGA package by digital image correlation technique

PurposeThe mismatch of the thermal expansion coefficients of the materials in multiplayer structure may induce serious stress concentrations in electronic packaging. Experimental evaluation of the thermal stresses and strains in those electronic composites is becoming significantly important for optimizing design and failure prediction of the electronic devices.Design/methodology/approachDigital image correlation (DIC) technique was utilized to obtain thermal deformation filed of a BGA package. With the help of white light to illuminate the cross section of the BGA package, the gray images were taken from the rough surface of the specimen, that offer a kid of carrier pattern for the DIC processing with statistical resemblance in gray distributions. By using the algorithm of correlation computation, the DIC searched the matching spots in a pair of those images in which the spot displacements were involved in between, to obtain the deformation fields of the package specimen caused by temperature changes.FindingsThe results show interesting strain distributions in the assembly. Both the horizontal displacement component and its normal derivative are strongly related to the arrangement of the solder joints in the bonding medium between the die and the ceramic substrate. The strain components in the middle region of the package are larger than those in the side regions where the strain relaxation may exist near the stress‐free boundaries. The shear strain components show special bands of parallel lines with identical amount over the chip‐package to sustain the shearing of the packed structure under thermal loading.Originality/valueThe DIC technique shows to be a useful tool for the thermal strain analysis of the electronic packaging devices. Not only provides it the whole field deformation of the assembly, but also maintains the surface pictures of the package without covering any fringes, which is important to compare the deformation field with the specimen surface to reveal the stain distribution related to the failure prediction of the materials.

A Numerical Analysis on the Dissimilar Channel Angular Pressing Process by Rolling

The dissimilar channel angular pressing (DCAP) process by rolling was numerically modeled and analyzed by the rigid-plastic two-dimensional finite element method in order to optimize the strain state of the DCAP process. Three distinct deformation mechanics during DCAP by rolling includes rolling, bending, and shearing. AA 1100 aluminum alloy was selected as a model material for the analysis of DCAP process. Difference in the friction conditions between the upper and lower roll surfaces led to large variation of shear strain component throughout the thickness of sample. Strain accompanying bending turned out to be negligible because of a large radius of curvature by relatively large roll diameter. The concentrated shear deformation was monitored at the corner of the DCAP-channel where the abrupt change in the direction of material flow occurred. The strain state at the upper and lower surfaces was observed to vary strongly from that of the center layer of the sheet.

熱間加工されたNi-30Fe合金の内部組織におよぼすせん断変形の影響

Electron backscattered diffraction analysis has been used to investigate the effect of shear deformation on the microstructural evolution of a Ni-30Fe alloy during hot deformation. The alloy was compressed by 50% or 75% in thickness at a strain rate of 1/s in a single pass at 1023 K using a hot compression simulator. An explicit finite element analysis was carried out to evaluate the inhomogeneous strain distribution introduced in the specimens by hot compression simulator. As the equivalent strain increased, the fraction of high angle grain boundaries with misorientaions between 15° and 30° increased almost in the similar way regardless of the presence of shear strain. The fraction of high angle grain boundaries having misorientations in excess of 30° increased mainly at the expense of low angle grain boundaries with misorientations smaller than 15°. Such the expense occurred at much higher rate with shear strain than without shear strain. The compressive direction changed continuously in the areas with shear strain component during deformation, which was thought to accelerate the subdivision of austenite grain interiors with increased misorientations between subdivided local areas.

AN EFFICIENT TECHNIQUE TO INCLUDE SHEAR DEFORMATION IN SPLINE FINITE STRIP ANALYSIS OF COMPOSITE PLATES

An efficient technique for the incorporation of transverse shear deformation in the analysis of laminated composite plates by spline finite strip method has been proposed. The Reissner-Mindlin's plate theory has been used to perform the formulation where transverse displacement and transverse shear strain components are the independent field variables. The interpolation function used for the transverse displacement is cubic whereas the shear strains are linear. To validate the proposed model and study its performance, numerical examples of composite plates have been solved and the results obtained have been compared with the published ones. Examples of isotropic plates have also been included as the model has not been tested with isotropic plates. A very thin plate has been analyzed to show that the proposed model is free from shear locking problems.

Numerical Analysis on the Dissimilar Channel Angular Pressing by Multi-Pass Rolling

The dissimilar channel angular pressing (DCAP or CCSS) based on the equal channel angular pressing (ECAP) was numerically modeled and analyzed by means of a rigid-plastic two-dimensional finite element method. Multi-pass rolling is performed in two different manners; the feeding direction of samples into the DCAP-channel is maintained in Route A and the feeding direction is reversed in the Route B. The deformation of AA1100 sheets during the DCAP process comprises three distinct processes of rolling, bending and shearing. The shear deformation of an amount of 0.5 was concentrated at the corner of the DCAP-channel where the abrupt change in the direction of material flow occurred. Because differences in the shear deformation in Route A and Route B led to the different strain states throughout the thickness of the aluminum sheet, the strain history in the DCAP-channel was analyzed in various thickness layers by the shear and effective strain components.