Shear Stress-strain Curves Research Articles

Effect of Surface Finish on the Shear Properties of SnAgCu-Based Solder Alloys

The reliability of an electronic assembly is typically limited by the failure of one of the solder interconnections. One of the key factors that define the quality of solder interconnections is the strength of the solder joint attachment to the printed circuit board (PCB). The ball shear testing is commonly used as a quantitative approach to evaluate the integrity of the solder. Several factors control the shear strength and failure mechanism of solder joints, including the surface finish, solder alloy composition, and speed of shearing (shear strain rate). In this paper, the effect of surface finish on the shear properties of various “microalloyed” SnAgCu-based solder materials was investigated. Individual solder joints were fabricated on a PCB with a solder mask defined configuration. A series of shear testing was conducted at four different strain rates of 0.001, 0.01, 0.1, and 1 s−1. Shear stress–strain curves were recorded for each test, and both shear strength and shear energy were measured. Following the shear testing, fractured top surfaces and cross sections were inspected using SEM/EDS microscopy to characterize the failure mechanism. The results showed that both shear strength and shear energy increase with increasing shear strain rate due to the viscoplasticity of the solder materials. Failure mode analysis indicated the existence of three failure mechanisms, including ductile failure, brittle failure, and mixed failure. Higher occurrence of brittle failure was observed when the shear strain rate is high regardless of surface finish. It was also found that the combination of solder alloy with high silver (Ag) and bismuth (Bi) content and electroless Ni/immersion Au (ENIG) surface finish is more susceptible to brittle failure compared to the rest of solder alloy-surface finish combinations.

A New S-Shape Specimen for Studying the Dynamic Shear Behavior of Metals

A new S-shaped specimen geometry is developed in this study to investigate the shear behavior of materials under dynamic shear condition. Traditionally, hat-shaped geometry is used to study the dynamic shear of materials by a conventional split Hopkinson pressure bar apparatus. However, in this geometry, the force equilibrium on the two sides of the sample is difficult to fulfill, and the stress field in the shear region is not homogeneous. Hence, the calculated shear stress–strain curve from this geometry is not precise. To overcome this problem, the new S-shaped specimen is designed to achieve accurate shear stress–strain curve. This geometry can be used in a wide range of strain rates and does not require additional machining process for microstructure observation. The new S-shaped specimen is successfully coupled with digital image correlation method because of the flat surface. Digital image correlation results indicate that the fracture patterns of the new S-shaped specimen occur with maximum shear strains in the shear region in the middle of the sample. This result is also validated by finite element model simulation. The new S-shaped specimen geometry can be used to study the dynamic shear behavior of various metals.

The impact of CIP content on the field-dependent dynamic viscoelastic properties of MR gels

Magnetorheological (MR) gels are one of the categories of magnetic smart materials, whose mechanical properties changed significantly in the presence of a magnetic field. This paper present dynamic viscoelastic properties of MR gel under various of magnetic flux density and Carbonyl iron powders (CIPs) weight fraction. The test to understand the dynamic rheological properties are carried out using oscillatory shear. Firstly, the MR gels are prepared by dispersing the CIPs into polyurethane (PU) matrix with a mechanical stirrer. Experimental data are obtained by changing the magnetic flux density from 0 mT to 480 mT at room temperature of 25 ℃. The elastic stress of MR gels with different CIPs content was studied under different magnetic flux density in oscillating test environment. The study results display that the elastic stress increases with strengthening extra magnetic flux density and the shape of elastic stress—strain curves are different under various magnetic flux density. Initial modulus, magneto-induced modulus and MR effect of MR gels with different contents of CIPs were obtained by magnetic field scanning. The results show that a higher magnetic-induced storage modulus can be obtained at higher CIPs weight fraction. The critical values and static elastic yield stress of MR gels with different CIPs content are also obtained by shear stress vs shear strain curves at the different magnetic flux density.

Shear behavior of ultrafine magnetite tailings subjected to freeze-thaw cycles

To study the shear behavior of the ultrafine magnetite tailings subjected to freeze-thaw cycles, unconsolidated-undrained shear tests were conducted on ultrafine-grained tailings that were subjected to 1–11 cycles of freeze-thaw and defined as a type of clayey silt under confining pressures of 100, 200, and 300 kPa. Taking the number of freeze-thaw cycles, cooling temperature, initial dry density, and moisture content as the four main influencing factors of shear behavior of the tailings samples, the shear stress-strain curve, compression modulus, failure strength, cohesion, and internal friction angle were measured. The results show that the freeze-thaw cycle has an obvious weakening effect on the shear behavior of the tailings material, and the shear mechanical parameters are affected by a combination of confining pressure, freeze-thaw cycle condition, and initial physical-mechanical properties of the tailings samples. Through the microstructural analysis of the tailings samples subjected to freeze-thaw cycles, it shows that the freeze-thaw cycle mainly affects the porosity, bound water, and arrangement of the tailings particles. Subsequently, the macroscopic changes in shear strength indexes emerge, and then the stability of the tailings dam will decrease.

Mechanical response of a novel composite Y-frame core sandwich panel under shear loading

The hot-press molding method was developed to fabricate a novel composite Y-frame core sandwich panel in this paper. The shear experiments were conducted to investigate the shear mechanical response of the composite Y-frame core sandwich panels with different relative densities. The impact of relative density on the failure behavior, shear stress-strain curves and shear properties were discussed. The shear tests indicated that the shear mechanical response of the composite Y-frame core sandwich panels was significantly influenced by the relative density. It was observed from the tests that the delamination failure at the web of the Y-frame core was the dominant failure mode. The shear stress-strain curves of the composite Y-frame core sandwich panels with different relative densities were featured by three typical stages and two peak stresses. The shear strength and stiffness of the composite Y-frame core sandwich panels were predicted, which were in good agreement with the experimental results.

Shear behavior of three types of recycled aggregate concrete

This paper studied the shear behavior of three types of recycled aggregate concrete with different replacement levels of recycled coarse aggregate. Sixty cube specimens and thirty beam specimens with uniform depth and varying width were designed to test their mechanical parameters including cube compressive strength, splitting tensile strength, shear strength, peak shear strain, shear stress-strain curves, and shear modulus. We analyzed how these parameters are influenced by the type of recycled coarse aggregate and by recycled coarse aggregate replacement level. We established the strength conversion equations, one-parameter polynomial non-dimensional shear stress-strain equations, and shear modulus calculation formulas of three types of recycled aggregate concrete. It is found that the strength of recycled aggregate concrete I isslightly lower than that of conventional concrete and decrease with the increase of recycled coarse aggregate replacement level. However, the strength of recycled aggregate concrete II and recycled aggregate concrete III is slightly higher than that of conventional concrete when the recycled coarse aggregate replacement ratio is less than 70%. As the recycled coarse aggregate replacement ratio increase, the peak shear strain of three types of recycled aggregate concrete gradually decreases. The shear strength and peak scant shear modulus of three types of recycled aggregate concrete show the rule of recycled aggregate concrete III > recycled aggregate concrete II > recycled aggregate concrete I. Furthermore, the calculated values of several equations established by the authors agree well with the test values.

Oxygen impurity effects on the mechanical properties of SiC studied by first principles calculations

First principle calculations are performed to study the oxygen doping effects on the mechanical properties of SiC. Both interstitial and substitutional oxygen atoms decrease the shear and tensile modulus and strength of SiC. The substitutional oxygen atoms decrease the shear and tensile modulus and strength more than the interstitial oxygen atoms do. Local distortions around the oxygen doping atoms are found in both of tensile and shear stress strain curve calculations in the elastic region. The shear strength of SiC decreases linearly with the increase of the oxygen concentration. The tensile strength of SiC also decreases with the oxygen concentration and it drops dramatically at low concentration region.

Effect of Particle Breakage and Shape on the Mechanical Behaviors of Granular Materials

The particle breakage property under loading is an important factor affecting the nonlinearity of the shear strength and stress‐strain curves of coarse‐grained soils. The macromechanical behaviors of coarse granular materials under consolidation and drainage shearing were tested by using a large true triaxial apparatus. The particle breakage mechanism has been analyzed by the fluctuation change of stress‐strain curve and particle composition change. It was shown that the particle shape is an extremely important microproperty of the influence of granular material breakage. The variation rules of the internal friction angle and interlocking strength with the index of fine‐grained breakage were sorted out, and the critical particle size for measuring the two friction modes under the given gradation was determined to be 1 mm. In addition, the numerical analysis was conducted by simulating the microshape parameters of particles. The conclusion is as follows: (1) The effect of shape parameters on shear strength can be simulated using the smoothness index Fd. (2) Compared with spherical particles, irregular‐shaped particles lead to a decrease in the number of strong force chains. Moreover, more coordination numbers are needed to maintain a stable configuration, and the shear strength is improved.

Susceptibility of shear banding to chemical short-range order in metallic glasses

To clarify the critical role of chemical short-range order on the formation of shear bands in metallic glasses, atomistic simulations are performed on Pd82Si18 and Cu50Zr50 with different cooling history. It is found that shear bands are prone to form in samples with higher level of chemical short-range order. The magnitude of stress overshoot in shear stress-strain curve and the spatial fluctuation of short-range chemical composition are proposed to characterize shear banding susceptibility and chemical short-range order, respectively. A quantitative correlation is therefore established between shear banding and chemical short-range order. The microstructural origin of the correlation is discussed.

A modified direct measurement of shear moduli of two-dimensional materials

A direct measurement of shear moduli of two-dimensional (2D) materials is still a challenge in experiments. A commonly used method is to apply a tangential displacement on one side of a square specimen sheet for each 2D material, while its opposite side is fixed. Afterwards, the shear modulus can be obtained by fitting a linear stage of its total shear stress-strain curve. However, the obtained shear modulus can be defined as the nominal shear modulus which is much lower than that of its true value. The difference between the two shear moduli is independent of the 2D isotropic material and strongly depends on aspect ratios of the specimens. In this work, explicit equations of the nominal shear moduli of 2D materials for different aspect ratios are derived by continuum modeling. The analytical model is then verified by the finite element method and molecular dynamics simulation as well as experiments. It suggests that the true shear moduli of 2D materials can be directly and accurately measured using the specimens with high aspect ratios (≥3.6) in experiments. The present study provides key insights into a direct measurement of shear moduli for 2D materials.

Mechanical characterization of thin injection-moulded polypropylene specimens under large in-plane shear deformations

The methodology to extract in-plane shear properties has been standardised for polymer-based composite materials. However, no standards have been designed to extract reliable test data that can be used to calibrate material models in numerical simulations for non-fibre reinforced polymers. The quality of the results from three widely used experimental techniques was examined in this study for mineral-filled polypropylene in terms of shear strain distribution, out-of-plane deformations and shear stress-strain curves with the aid of the digital image correlation method. The V-Notched Rail test (ASTM D7078) exhibited ultimate fracture of the specimen, but valid shear strain was only obtained for small deformations. For relatively large strains, more reliable shear test data were obtained from a modified version of ASTM B831: a standard test designed for aluminium but modified and implemented for polymers. Although out-of-plane deformations were avoided using aluminium holders, large variability was found in the strain distribution along the shear path. In contrast, the modified Wyoming Iosipescu test (ASTM D5379) exhibited the most robust shear stress-strain results due to consistent shear strain uniformity and low variability during the entire duration of the test.

Surface Characterization and Frictional Energy Dissipation Characteristics of Deep Granite Under High Stress Conditions

Rockbursts are one of the most violent dynamic disasters in deep mining. New research has suggested that an energy theory-based approach may be useful for solving deep rockburst problems, and energy theory has been recognized as the most reasonable and effective method for understanding rock mechanics. Considerable efforts have focused on characterizing energy storage, energy dissipation and the energy of motion. However, existing research has not accurately represented frictional dissipated energy. In this paper, a shearing friction test was designed, and the frictional dissipated energy at different vertical stress levels was determined by calculating the area under the shear stress–strain curves. Fractal dimensions were used to express the roughness and waviness of the structural surfaces. In addition, to better understand the mechanisms producing this frictional dissipated energy, structural surfaces were examined using a binocular laser scanner before and after shearing friction tests. Analysis of the results indicates that frictional dissipated energy is controlled primarily by the macroscopic waviness. The mode of energy consumption changes from climbing to shearing with an increase in vertical stress, considering the simulated results.

Considering nonlinear properties of concrete in the design of reinforced concrete structures for torsion

Restoration and maintenance of cultural heritage concrete and reinforced objects always require accounting for the torsional stress in the elements, as well as the tensile, compressive and shearing stress. It should be considered, that torsion always develops in the elements of spatial structures, including cross-ribbed systems, bridges and overlaps, elements of shells and domes, stairs, etc. This paper briefly systematizes substantive results of the last studies of an urgent problem of torsional stiffness of reinforced concrete elements, including theoretical investigations, experimental studies and numerical research. Stress redistribution in the statically indeterminate reinforced concrete structures’ elements depends on both torsional and bending stiffness. However, while bending stiffness is considered in the design practice, the torsional stiffness is not aknowledged by engineers, nor used in building standards and software packages. This paper aims to substantiate the necessity of considering the torsional stiffness of reinforced concrete elements in design practice. This article is the result of numerous investigations conducted in the scientific school of professor Taliat Azizov. They certify that reduction of the torsional stiffness must be considered along with the bending stiffness in different stages of behaviour of concrete structures. Moreover, the research conducted for this paper proved that a change in the shear modulus of concrete also affects the deflected mode of structures and should be accounted for as the component of torsional stiffness. In order to provide engineers with specialized design techniques, they have been developed for the calculation of torsional stiffness of reinforced concrete elements with normal cracks of rectangular, triangular, t-sections, box-sections, and other cross-sections. The engineering bilinear shear stress-strain curve for concrete has also been proposed on the basis of experimental studies.

Shear modulus reduction of saturated sand under large liquefaction-induced deformation in cyclic torsional shear tests

Nanjing sand as a typical kind of natural schistous quartz sand is extensively deposited along the middle and lower Yangtze River valley in China. The engineering properties of the schistous sand are quite different from those of siliceous sands. Several cyclic torsional shear tests are completed in this research to investigate the shear modulus reduction of post-liquefaction Nanjing sand under different loading states. In these tests, the maximum double-amplitude shear strain should reach 100% for each soil specimen. The effect of rubber membrane force on the strength of the soil sample is demonstrated and studied by a special water sample. The results show that the shear stress–strain curves should be corrected on the strength of post-liquefaction sand in a cyclic torsional shear test to alleviate the effect of the rubber membrane. The effective confining pressure, initial static shear stress, and cyclic shear stress have a remarkably small effect on the shear modulus reduction of saturated post-liquefaction Nanjing sand in the “zero effective stress” and dilative stage after the phase transformation. However, these factors considerably affect the shear modulus reduction of saturated Nanjing sand in the reversal contractive stage. Meanwhile, the shear modulus and single-amplitude shear strain amplitude have a better correlation than that between the shear modulus and the double-amplitude shear strain. Accordingly, the modulus decay functions for post-liquefaction Nanjing sand in different loading stages are formulated by the test results.

Shear Strength of Square Graphene Nanoribbons beyond Wrinkling

Atomistic modeling of armchair and zigzag graphene nanoribbons (GNRs) has been performed to investigate the post-wrinkling behavior under in-plane (x–y) shear deformation. Simulations were performed at 300 K for square GNRs with size ranging from 2.5 nm to 20 nm. Shear stresses led only to diagonal tension, and wrinkling was not accompanied by any diagonal compressive force. Once the diagonal tension reached its ultimate elastic level, three major stress-relaxing phenomena were observed. The type of stress-relaxing phenomenon involved greatly affected the mechanical behavior in terms of the slope of the stress–strain diagram beyond the elastic range. The results showed that the average slope of the stress–strain relation beyond the ultimate elastic stress decreased with the increase of the GNR size. Moreover, the slope of the shear stress–strain curve beyond the ultimate elastic stress was always greater for armchair than for zigzag GNRs. GNRs can sustain very high plastic shear strains beyond 100% before failure. The ultimate elastic stress can range from 20 GPa to 50 GPa, occurring at shear strain ranging from 52% to 19%. The ultimate elastic stress and strain were inversely proportional to the size of the GNR with a power factor ranging from 0.261 for armchair GNRs to 0.354 for zigzag GNRs due to the decrease in the effective width for diagonal tension.

Shearing single crystal magnesium in the close-packed basal plane at different temperatures

Shear behaviors of single crystal magnesium (Mg) in close-packed (0001) basal plane along the [1¯21¯0], [12¯10], [101¯0] and [1¯010] directions were studied using molecular dynamics simulations via EAM potential. The results show that both shear stress-strain curves along the four directions and the motion path of free atoms during shearing behave periodic characteristics. It reveals that the periodic shear displacement is inherently related to the crystallographic orientation in single crystal Mg. Moreover, different temperatures in a range from 10 to 750 K were considered, demonstrating that shear modulus decreases with increasing temperatures. The results agree well with the MTS model. It is manifested that the modulus is independent with the shear direction and the size of the atomic model. This work also demonstrates that the classical description of shear modulus is still effective at the nanoscale.

Experimental Study on Bond Performances of Track Slab and Mortar Based on DIC Technology

In order to guarantee the normal long-time service performance of CRST II slab track, it is necessary to study the interface parameters between track slab and CA mortar layer of CRTS II slab track. Thus the splitting and shearing model test of concrete and mortar bonded composite specimens were conducted. Based on the Digital Image Correlation (DIC) technology, the stress-strain relationship and cohesion model parameters were obtained from the interface displacement and distribution of strain. The results showed that: The displacement and the strain field distribution of the composite specimens as well as the whole interlaminar cracking process of initiation, propagation and failure can be well described with DIC. The bond failure between the track slab and the CA mortar layer is part of the brittle failure, and the normal and tangent interface tension-displacements are both bilinear. The shear strength between the track slab and the CA mortar layer is 1.82 MPa with the peak strain of 2.49 × 10−4 and the secant modulus of 7.30 × 103 MPa; While the shear strength is 2.40 MPa with the peak strain of 6.17 × 10−3 and the secant modulus of 3.89 × 102 MPa. When the shear strain is about 7.5×10-4, the shear stress-strain curve tends to remain stable. At this point, the shear strain is 0.12 times of the peak strain. Parameters of the cohesive zone model between the track slab and the CA mortar layer are suggested as follows: the normal cohesive strength is 1.792 MPa with the interface stiffness of 708.485 MPa/mm and the critical fracture energy of 0.0252 mJ/mm2; the tangential cohesive strength is 0.956 MPa with the interface stiffness of 63.039 MPa/mm and the critical fracture of 0.018 mJ/mm2.

Nonlinear deformation and failure analysis of laminated composites

An approach to the characterization of different types of nonlinearity in the behavior of composite materials is proposed. One of them is concerned usually observed in experimental studies the dependence of deformation properties of composite materials on the type of external forces. Another type of nonlinearity lies in the fact that the shear stress-strain curves are nonlinear, though they are linear ones when the load is applied along the reinforcement. To describe these effects, the additional matrix is introduced into the proposed constitutive relations. There are different mechanisms of deformation of these materials, which are dependent on the type of reinforcement, matrix properties, loading conditions, directions of loads with respect to reinforcement and some others. These mechanisms and their interactions determine the stress-strain behavior of materials that influence the damage evolution and fracture properties of composite materials. To describe the damage accumulation process, the system of general failure model assumptions is formulated that include the choice of first ply failure criterion, constitutive relations for damaged materials with the use of corresponding damage parameters, the dependence of first ply failure criterion and elastic properties on the damage rate parameters and others. Some particular models are considered taking into account different types of nonlinearities, Lomakin et al. (1981, 2007, 2014, 2015 and 2017). This approach is verified using complex loading experiments. The theoretical dependencies obtained on the base of proposed models are compared with the results of experimental studies and good correspondence of them is shown. The proposed approach to the formulations of constitutive models from simple to more complex ones allows to describe adequately the behavior of composite materials under different loading conditions with the necessary precision.

An Experimental Study on Mechanical Behavior of Parallel Joint Specimens under Compression Shear

In order to investigate the influence of the joint on the failure mode, peak shear strength, and shear stress‐strain curve of rock mass, the compression shear test loading on the parallel jointed specimens was carried out, and the acoustic emission system was used to monitor the loading process. The joint spacing and joint overlap were varied to alter the relative positions of parallel joints in geometry. Under compression‐shear loading, the failure mode of the joint specimen can be classified into four types: coplanar shear failure, shear failure along the joint plane, shear failure along the shear stress plane, and similar integrity shear failure. The joint dip angle has a decisive effect on the failure mode of the specimen. The joint overlap affects the crack development of the specimen but does not change the failure mode of the specimen. The joint spacing can change the failure mode of the specimen. The shear strength of the specimen firstly increases and then decreases with the increase of the dip angle and reaches the maximum at 45°. The shear strength decreases with the increase of the joint overlap and increases with the increase of the joint spacing. The shear stress‐displacement curves of different joint inclination samples have differences which mainly reflect in the postrupture stage. From monitoring results of the AE system, the variation regular of the AE count corresponds to the failure mode, and the peak value of the AE count decreases with the increase of joint overlap and increases with the increase of joint spacing.

Loading direction-dependent shear behavior at different temperatures of single-layer chiral graphene sheets

The loading direction-dependent shear behavior of single-layer chiral graphene sheets at different temperatures is studied by molecular dynamics (MD) simulations. Our results show that the shear properties (such as shear stress–strain curves, buckling strains, and failure strains) of chiral graphene sheets strongly depend on the loading direction due to the structural asymmetry. The maximum values of both the critical buckling shear strain and the failure strain under positive shear deformation can be around 1.4 times higher than those under negative shear deformation. For a given chiral graphene sheet, both its failure strain and failure stress decrease with increasing temperature. In particular, the amplitude to wavelength ratio of wrinkles for different chiral graphene sheets under shear deformation using present MD simulations agrees well with that from the existing theory. These findings provide physical insights into the origins of the loading direction-dependent shear behavior of chiral graphene sheets and their potential applications in nanodevices.