In-plane Stress State Research Articles

Effect of residual stress and microstructure on mechanical properties of sputter-grown Cu/W nanomultilayers

The combination of the high wear resistance and mechanical strength of W with the high thermal conductivity of Cu makes the Cu/W system an attractive candidate material for heat sinks in plasma experiments and for radiation tolerance applications. However, the resulting mechanical properties of multilayers and coatings strongly depend on the microstructure of the layers. In this work, the mechanical properties of Cu/W nanomultilayers with different densities of internal interfaces are systematically investigated for two opposite in-plane stress states and critically discussed in comparison with the literature. Atomistic simulations with the state-of-the-art neural network potential are used to explain the experimental findings of Young’s modulus and hardness. The results suggest that the microstructure, specifically the excess free volume associated with porosity and interface disorder interconnected with the stress state, has a great impact on the mechanical properties, notably Young’s modulus of Cu/W nanomultilayers.

Realization of ferroelectricity in sputtered Al1-xScxN films with a wide range of Sc content

The ferroelectric properties of wurtzite-structured Al1-xScxN thin films are affected simultaneously by the Sc concentration and in-plane stress state, however, the interaction between these two factors remains unclear. In this work, a series of Al1-xScxN films were deposited on (111) Si substrate by dual-target co-sputtering. X-ray diffraction analyses show the films with a wide range of Sc content (x= 0.05–0.50) have the (0002)-textured wurtzite structure and are in compressive stress state. Ferroelectricity in all the films is confirmed by polarization hysteresis loop measurements at room temperature, and the coercive field exhibits an interesting non-monotonic transition due to the competition between in-plane stress and Sc incorporation. The results provide insight into the wurtzite-structure stability and the nature of ferroelectricity for Al1-xScxN thin films.

Study on Fatigue Cracking of Diaphragm's Arc Opening of OSD in Steel Bridges by Using Biaxial Stress Method.

Changes in loading position have a significant impact on the stress field of each vulnerable area of an orthotropic steel deck (OSD). The arc opening area of the diaphragm and the connecting area between the U-rib and the diaphragm under the moving load are prone to fatigue cracking. By comparing the stress responses under different methods, the hot spot stress (HSS) method is used as the main stress extraction method in fatigue performance evaluation. The control stress of fatigue cracking was analyzed by comparing the direction of the principal stress field with the crack direction in this experiment. According to the stress amplitude deviation under the biaxial stress state, a set of methods for evaluating the effects of in-plane biaxial fatigue was developed. An improved luffing fatigue assessment S-N curve was applied to analyze the fatigue life of the diaphragm's arc opening area. The results show that when the moving load is exactly above the connection of the deck and the web of the U-rib on one side, it is in the most unfavorable position in the transverse direction, and the diaphragm is mainly under the in-plane stress state. The longitudinal range of the stress influence line of the arc opening is approximately twice the diaphragm spacing. Two to three stress cycles are caused by one fatigue load. Fatigue crack control stress is the principal stress tangential to the arc opening's edge in this area. The normal direction of the principal stress in the model test is roughly consistent with the crack initiation direction. The variation in the stress amplitude deviation in this area is caused by changes in the action position of the moving load. When the moving load is at a certain distance from the involved diaphragm, it is reduced to zero, implying that the in-plane fatigue effect is the greatest in this area.

Numerical investigation on the mechanical behaviors of 2D woven composites under complex in-plane stress states

Using finite element method (FEM), the mechanical behaviors of 2D woven composites with different weave structures are investigated with considering the complex in-plane stress states. Periodic boundary conditions for arbitrary off-axis loading scenarios are established, and a progressive damage model based on Linde criterion is proposed, which is subsequently validated by the previous experiments. In addition, the failure envelopes predicted by classical failure criteria are compared to the results obtained by FEM. The effects of woven structures on elastic properties and failure behavior are also discussed, which demonstrates that the plain woven composites have inferior mechanical performance than twill and satin woven composites. Based on the assessment of the failure criteria, this study provides recommendations for selecting relevant failure criteria to anticipate mechanical properties under various loading conditions. The findings in this paper are expected to encourage the development of damage constitutive models and their engineering applications for 2D woven composites.

Energy absorbing multilayered self-recovering metamaterials with chiral topology

A novel energy absorbing material is proposed for the design of shock absorbers and vibrational dampers. A layered architectured microstructure is put forward consisting of the repetition of plane lattices having hexachiral topology with alternate chirality, each being designed as a periodic assembly of rigid disks connected by elastic ligaments. Because of the chiral topology of the single layer, the rotation of the rigid disks takes place when in-plane stress states are applied so implying a relative rotation between the disks of adjacent lattices with opposite chirality. Pins passing through for each stacking of disks impose them the same in-plane displacement. Moreover, frictional dissipative mechanisms at the interface between adjacent disks according to two different compression modes orthogonal to the layers make the metamaterial suitable for either reusing or self-recovering the initial configuration. In the first case the pre-tensioning of the pins implies the compression of plane frictional interfaces. The frictional sliding compatible with the disk relative rotation implies an overall hysteretic bilinear response with remarkable energy dissipation. The metamaterial may be reused once the pins are relaxed and re-tensioned. In the latter case no pre-tension is applied to the pins and the compressive force between the disks is obtained through saw-tooth shaped interfaces between adjacent disks to get elastically constrained transverse dilation when the relative rotations at the interfaces take place. The overall response turns out to be highly dissipative and self-recovering, i.e. able to return to the initial configuration when removing the applied stresses. As shown in the examples the quasi-static behavior of the proposed metamaterial makes it a candidate as an efficient vibration damper and a shock absorber characterized by i) hysteretic response with remarkable energy dissipation under biaxial stress states; ii) reuse or self-recovering after the energy absorption event; iii) bilateral response, i.e. equal behavior under both tension and compression.

Effects of nitrogen flux and RF sputtering power on the preparation of crystalline a-plane AlN films on r-plane sapphire substrates

A-plane aluminum nitride (AlN) with high quality is crucial to fabricate high-performance non-polar deep-ultraviolet optoelectronic devices. In this work, we prepared crystalline a-plane AlN films on r-plane sapphire substrates by combining reactive magnetron sputtering and high temperature annealing (HTA). The effects of N2 flux and radio frequency (RF) sputtering power on the crystal quality, the surface morphology and the in-plane stress state of a-plane AlN films were comprehensively investigated. The results suggest that the properties of high temperature annealed a-plane AlN (HTA-AlN) films positively depend on the initial states of the sputtered AlN (SP-AlN) films. Increasing the N2 flux or the RF sputtering power can improve the crystalline quality of SP-AlN films by reducing the kinetic energy of deposited particles, which facilitates a-plane AlN deposition. A higher N2 flux smoothens the surface morphology due to the relieved bombardment effect, which is confirmed by the enlarged in-plane tensile stress state. However, a higher sputtering power leads to a rougher surface because of the accelerated deposition rate. With optimized sputtering parameters, a high-quality a-plane HTA-AlN template was obtained with full width at half maximum values of (11–20) plane x-ray rocking curves as low as 1188 and 1224 arcsec along [0001] and [1–100] directions, respectively. The surface presents an ordered stripe-like morphology with a root-mean-square value of 0.79 nm. Our work provides a convenient and effective strategy to prepare high quality a-plane AlN templates and accelerate the versatile application of non-polar deep-ultraviolet light-emitting diode devices.

Pre-buckling vibration and buckling analyses of composite skew plate: An analytical investigation

In this work, the analytical investigation for pre-buckling vibration and buckling analyses of a composite skew plate subjected to parabolically and linearly varying in-plane edge load are presented. When the composite skew plate is subjected to parabolic (non-uniform) in-plane edge loading, the pre-buckling stresses within the composite skew plate are not known a priori. To estimate the pre-buckling stresses within the composite skew plate for which the in-plane elasticity problem is solved by minimizing the membrane strain energy using the Ritz method. It is observed that the rate of diffusion of applied parabolic in-plane edge load within the skew plate to a state of uniform in-plane stress is faster in the case of isotropic material than composite material. Using estimated pre-buckling stresses, the total energy functional is derived from the total strain energy, potential energy, and kinetic energy. The total energy functional is reduced into sets of an ordinary differential equation and algebraic equation, respectively for pre-buckling vibration and buckling problems using the Ritz method in conjunction with BCOPs. The associated linear eigenvalue problems are solved to compute the pre-buckling vibration frequency and buckling load of the stressed skew plate. The outcome of the study may provide crucial inputs in the design of skewed bridge decks, ship structures, and aircraft wing design.

Increased sheet-forming capability via controlling in-plane stress state of the sheet metal using hetero-structured flexible dies

Increased sheet-forming capability via controlling in-plane stress state of the sheet metal using hetero-structured flexible dies

Prediction of strength and fatigue life for 2D plain-woven high-alumina fiber reinforced alumina matrix composites under a complex in-plane stress state

This paper presents a strength criterion and fatigue life prediction method for 2D braided alumina matrix composites under a complex in-plane stress state. The static strength of the material was obtained by in-plane tensile, compression, and pure shear tests. Considering the difference between tensile and compressive properties of materials and the influence mechanism of in-plane tensile and shear coupling on material strength, a revised Hoffman strength theory was proposed. The predicted off-axis tensile strength is consistent with the test results, and the deviation is not more than 10%. Tensile fatigue tests were carried out with the off-axis angle θ=0°, 15°, 30°, 45°, the stress ratio R=0.1, and frequency f=10 Hz. The test results show that the fatigue life decreases with the increase of off-axis angle. Due to the in-plane shear stress component, the fatigue failure is gradually changed from fiber-dominated to fiber-matrix dominated mode. Based on a combination of the uniaxial tensile fatigue life curve, the Broutman-Sahu residual strength model, which is used to characterize the variation of the residual strength with the fatigue cycles, and the modified Hoffman strength theory, the paper proposes a fatigue life prediction model under complex in-plane loading conditions. The fatigue shear damage factor is defined to characterize the effect of the normal and shear stress interaction on fatigue life. The fatigue life prediction model is used to predict the fatigue life of specimens in the off-axis tensile fatigue tests. The predicted result agrees with the test result, and the deviation is within the 1-time life span. The results indicate that the proposed fatigue life prediction model can be used to predict the fatigue life of 2D braided alumina matrix composites under the complex in-plane stress condition with the given stress ratio, temperature, and fatigue load frequency.

Experimental and numerical investigation of progressive damage and failure behavior for 2.5D woven alumina fiber/silica matrix composites under a complex in-plane stress state

The focus of this work is to characterize the progressive damage and failure behavior of 2.5D woven alumina fiber reinforced silica ceramic matrix thin composite specimen under a planar tension-shear stress state. The tensile and shear stress–strain diagrams in the principal material coordinate system were obtained using the off-axis tension test with the digital image correlation technique. A mesoscale finite element model of the composite material was developed within the framework of continuum damage mechanics. The thickness effect on the macroscopic mechanical response was considered by removing the periodic boundary conditions along the thickness direction. The macroscopic stress–strain response given by the numerical model was validated by the experimental results. The interaction of the planar biaxial tension and shear stresses was taken into account in the model, quantified using a shear contribution coefficient in the modified 3D Hashin failure criterion. The results from the damage evolution analysis indicate that the linear tensile stress–strain response with a brittle fracture characteristic for the on-axis tension specimen is governed by the axial fiber bundle. The nonlinear tensile stress–strain response with the significantly reduced ultimate stress under biaxial tension and shear stress state results from multiple damages with evolution in both axial and transverse fiber bundles. Both the effective tensile modulus and the ultimate tensile strength increase with increasing the thickness of the specimen due to the increase of the fiber volume fraction. The strengthening induced by the size effect is less significant for the specimen under biaxial tension and shear stress state than that for the on-axis tension specimen owing to the involvement of shear response dominated by the matrix of the material. The results of this study provide new insight into the failure of 2.5D woven ceramic-based composite material, which contributes to the optimal design of the reusable thermal protection system structure.

Analytical model for the bending of parallel wire cables considering interactions among wires

Bending behaviors can be critical in simulating cables, such as the local effects close to cable end regions or dynamic properties of short cables. Wires form up the cable and tend to slip relative to each other under bending load. Complex interactions among wires make the modeling of cables challenging. In this work, we propose an analytical model for bending parallel wire cables in which the cable cross section with layered wires is idealized as a composite section of the laminated beam. The slips and interactive forces among wires are modeled by the interfacial slips and the resulting interactive forces at the interfaces of the composite section. In this way, the bending cable can transform into an in-plane stress state laminated beam. The state space method is then applied to solve the problem, and the numerical results agree well with the experimental results and analytical formulations in the literature. Bending stiffness of the cable differs from lower bound to upper bound according to the anti-slip ability among wires, from full-slip state to no-slip state. The overall deflection, as well as the local deformations and stresses of the bending cable, can be simultaneously obtained. These results show that the present model is efficient and accurate in simulating bending cables, which is capable of extending to more cable studies.

Predicting the available work from deformation-induced α′′ martensite formation in metastable β Ti alloys

Deformation-induced α′′ martensite formation is essential to the mechanical properties of a variety of metastable β Ti alloys by extending elasticity or contributing to work-hardening during plastic deformation. Nevertheless, to date, a comprehensive analysis of the effect of β texture and applied stress state on the martensitic transformation to α′′ is still lacking. The present study therefore provides a detailed analysis of the work which is made available from the shape strain of the martensitic transformation under a variety of in-plane stress states and as a function of β crystal orientation. The available work was found to strongly depend on the applied stress state and the parent grain orientation. The shape strain of the martensitic transformation was obtained from applying the phenomenological theory of martensite crystallography. In cases where this theory was not applicable, an approximation of the shape strain by the Bain strain was found to provide a good approximation of the available work. Analysis of three different metastable β Ti alloys showed no strong effect of the alloy composition on the available work. Martensite formation from typical cold- and warm-rolling β texture components under different stress states is discussed. Cases are highlighted to show how the cold- and warm-rolling β textures can be tailored to hinder martensite formation upon subsequent industrial forming operations.

Computational micromechanics-based prediction of the failure of unidirectional composite lamina subjected to transverse and in-plane shear stress states

This paper presents a micromechanics-based 3D finite element model for predicting the damage initiation, propagation, and failure strength of TC33/Epoxy carbon fiber reinforced polymer (CFRP) unidirectional lamina under biaxial loadings. The finite element model is generated by introducing representative volume element (RVE) with a random distribution of fibers and a non-zero thickness, numerically identified interface phase via cohesive elements. In the finite element model, the carbon fibers are considered as elastic, while the elasto-plastic behavior and damage of the matrix are governed by extended Drucker–Prager plastic yielding model and ductile damage criterion. By imposing periodic boundary conditions to the RVEs, various cases subjected to uniaxial and biaxial loading conditions are carried out. During the combined transverse and in-plane shear stress states, a failure transition from compression- or tension-dominated to shear-dominated is captured, and the effects of the interfacial strength on the transition damage mechanisms are discussed. The corresponding failure locus is compared with the upper bound and lower bound predictions of three phenomenological failure criteria (Hashin, Tasi–Wu, and Puck failure criteria) for composites. It was found that in the interface-dominated failure of a CFRP lamina with a weak interface, the Hashin failure criterion performs best among the currently popular failure criteria. However, in the matrix-dominated failure with a strong interface, the Puck failure criterion performs best. Comparing these three criteria, it can be seen the Tsai–Wu may be generally better than both of others as it presents more neutral predictions in both of the examined cases.

Three-phase parabolic inhomogeneities with internal uniform stresses in plane and anti-plane elasticity

We examine the in-plane and anti-plane stress states inside a parabolic inhomogeneity which is bonded to an infinite matrix through an intermediate coating. The interfaces of the three-phase parabolic inhomogeneity are two confocal parabolas. The corresponding boundary value problems are studied in the physical plane rather than in the image plane. A simple condition is found that ensures that the internal stress state inside the parabolic inhomogeneity is uniform and hydrostatic. Furthermore, this condition is independent of the elastic properties of the coating and the two geometric parameters of the composite: in fact, the condition depends only on the elastic constants of the inhomogeneity and the matrix and the ratio between the two remote principal stresses. Once this condition is met, the mean stress in the coating is constant and the hoop stress on the coating side is also uniform along the entire inhomogeneity-coating interface. The unconditional uniformity of stresses inside a three-phase parabolic inhomogeneity is achieved when the matrix is subjected to uniform remote anti-plane shear stresses. The internal uniform anti-plane shear stresses inside the inhomogeneity are independent of the shear modulus of the coating and the two geometric parameters of the composite.

Prestress Effect on the Thermomechanical Response of Viscoelastic Plate Under Harmonic Loading

A statement of the coupled thermomechanical problem on forced resonant vibrations and dissipative heating of hinged viscoelastic elastomeric plate is given with account of prestresses present in the plate. It is assumed the prestress is generated as a result of the manufacturing process or preliminary plate service. The problem statement is based on the standard Kirchhoff-Love hypotheses and concept of complex moduli that are used to describe the viscoelastic material response to harmonic loading. Under these circumstances, the prestress manifests itself as a membrane forces applied in the plane of the rectangular plate. Therefore, the problem of in-plane stress state and problem of forced transverse vibration of the plate can be solved separately. Both steady-state and transient thermal response is investigated. Influence of the prestress is studied in details. Dissipative heating temperature histories are calculated for the variety of the prestress and loading parameters. Temperature criterion is adopted to determine the critical state. The data obtained are used for the plate fatigue life prediction as well as for the investigation of prestress effect on the plate response. The reliability of the values of frequencies on the several lowest resonances was checked. For the most energy-intensive first mode of transverse vibrations, the influence of the preliminary tensile stress state, as well as the amplitude of the transverse distributed load on the amplitude–frequency characteristics and temperature evolution was studied.

Nano-scale residual stress depth profiling in Cu/W nano-multilayers as a function of magnetron sputtering pressure

Residual stresses in thin films and multi-layered coatings fabricated by physical vapour deposition largely affect their mechanical and thermal reliability during operation in numerous fields of applications. By changing the argon working pressure in between each multilayer planar DC magnetron sputter deposition step, it is possible to control the residual stress distribution within coatings. A combination of FIB-DIC ring-core strain analysis, synchrotron XRD analysis based on the sin2(Ψ) method and micro-cantilever deflection analysis is used to reconstruct the in-plane stress state of multilayer coatings at different deposition pressures, with a residual stress depth profile resolution of 50 nm. A clear transition from compressive to tensile residual stresses is observed with an increase of working pressure, with pronounced stress peaks near the substrate-coating interface. These peak stresses resolved by FIB-DIC ring-core analysis exceed the average XRD stress measurements significantly, thus providing a reasonable explanation for multilayer failure. Experimental results are presented and comprehensively discussed in the context of deposition conditions for different thin film applications.

Characterizing the constitutive response of plain-woven fibre reinforced aerogel matrix composites using digital image correlation

The paper presents an experimental investigation of the constitutive behavior for plain-woven fibre reinforced silica aerogel matrix composites under a complex in-plane stress state using digital image correlation technique. Specimens were subjected to in-plane on-axis, off-axis tension and shear loadings. The material exhibits significantly nonlinear stress-strain behaviour under off-axis tension and shear loadings. Deformation mechanism of the composite material has been proposed using FEM analysis of representative volume cell qualitatively. It is proposed that nonlinear couplings of the stress and strain components may result from a combination of stress-free surface, heterogeneity and interaction of the woven fibre bundles and aerogel matrix for thin specimen under a complex stress state, even though no damage initiates in the material. The experimental results were subsequently used to develop a constitutive model based on general formulation of complementary strain energy density. The material constitutive parameters were extracted from calculated stress and measured strain using multi-variable linear least square regression. The performance of the constitutive model has been demonstrated by comparison with the off-axis tensile experimental results.

Analysis of residual stress around a Berkovich nano-indentation by micro-Raman spectroscopy

Nano-indentation is a destructive measurement that introduces non-uniform residual stress around each nano-indentation. Herein, the residual stress distribution around a Berkovich nano-indentation on (001)- and (111)-plane silicon was studied by micro-Raman mapping. All of the in-plane stress state components around the indentation were obtained specifically for the (001)- and (111)-plane silicon based on the expanding cavity model and the Raman-mechanical relationship. Calculating the distribution regularity of the residual stress, the effect of different crystal planes and crystal orientations was further analyzed. Finally, the stress near the vertex of the indentation was revised owing to the crack.

Reliable in-plane shear modulus for pultruded-fibre-reinforced polymer sections

A simple test method to determine the in-plane shear properties of pultruded materials, where the mat reinforcement is of randomly oriented continuous fibres, is presented. Existing standard test methods have a number of weaknesses, but a number of them can be overcome by using the 10° off-axis tensile test method proposed by Chamis and Sinclair in 1976. Straight-sided specimens have unidirectional fibre reinforcement oriented at 10° to the direction of tensile load. Tension generates a biaxial in-plane stress state that, by employing stress and strain transformations, enables the shear modulus to be determined. The mean shear moduli of web material in four shapes, from 20 coupon tests in batches of five, were found to be consistent at 4·2–4·8 GPa. Given that 10° off-axis coupons are easy to prepare, with no technical difficulties, this non-standard method is recommended to characterise the in-plane shearing of pultruded materials having continuous-filament (or strand) mat reinforcement.

Numerical Biaxial Tensile and Tension-Compression Tests of Aluminum Alloy Sheet Using Crystal Plasticity Finite Element Method

This paper presents the results of the numerical multi-axial material tests for predicting elastoplastic deformation behavior of aluminum alloy sheets under equi-biaxial tension and in-plane tension-compression stress states. In this study, we have performed the numerical biaxial tensile and tension-compression tests of a 5000-series aluminum alloy sheet using the crystal plasticity finite element method based on the mathematical homogenization method which has been developed by the previous studies. We found that the true stress-logarithmic plastic strain (SS) curves calculated by the numerical biaxial tensile test slightly deviate from those measured by the biaxial tensile tests using a cruciform specimen. On the other hand, the results of the numerical tension-compression test demonstrated that the predicted SS curves shows a reasonable agreement with those obtained by the experiment using the biaxial stress-testing machine with comb-shaped dies.