Shear Stress-strain Curves Research Articles

Mechanical behavior and microstructural evolution in rolled Mg-3Al-1Zn-0.5Mn alloy under large strain simple shear

Mechanical behavior and microstructural evolution in rolled Mg-3Al-1Zn-0.5Mn (AZ31B) magnesium alloy under in-plane shear (IPS) and through-thickness shear (TTS) were investigated. The newly designed butterfly-shaped specimens were sheared along the rolling direction, and a full field strain analysis was performed by digital image correlation (DIC). The shear stress-strain curves show that the shear strength and strain hardening rate are significantly different between the IPS and TTS. The electron backscatter diffraction (EBSD) observation shows that extension twinning is the dominant twinning mechanism under shear deformations. Moreover, a certain volume of {10-12}-{10-12} double twins appears throughout the deformation process in the TTS, while a few compression twins and {10-11}-{10-12} double twins occur at the early stage in the IPS. The results suggest that crystal orientation plays an important role in determining the twin types and twin volume fraction in the shear deformations. The visco-plastic self-consistent (VPSC) model is also applied to predict the activity of slip/twinning under shear deformations. The VPSC results confirm that the mechanical discrepancy at early shear deformation is mainly due to the activation of extension twin and prismatic slip.

Basic mechanical properties of ultra-high ductility cementitious composites: From 40 MPa to 120 MPa

A systematic study of the basic mechanical properties of ultra-high ductility cementitous composites (UHDCC), including the compressive, tensile and shear properties from normal strength to high strength were investigated in present research. The compressive strength of cylinder specimens with diameter of 100 mm and height of 200 mm were in the range of 43–115 MPa. The compressive strain corresponding to the peak stress, the Young’s modulus and the Poisson’s ratio were calculated. The tensile properties including the peak stress, the strain capacity and the strain energy were obtained as well as the relationships between the aforementioned parameters and the compressive strength. The peak tensile stress and the strain capacity of UHDCC were ranged from 6.2 MPa to 16.5 MPa, and 8.0% to 11.1%, respectively. Additionally, the shear stress-strain curves and the relationship between the shear strength and the corresponding compressive strength were also established. During the whole loading process of direct tensile and shear tests, the crack patterns were monitored by digital image correlation method.

Experimental Research on the Shear Behavior of Laminated Glass with PVB Film Under Different Temperature

The shear modulus of PVB film with different thickness used in different temperatures has been investigated by shearing test. The results indicate that shear stress-strain curve has been changed with different thickness of PVB film. The bigger of thickness, the smaller of shearing modulus will be. Change of Temperature leads obvious variation of the shear modulus which decreases quickly with the increasing of temperature.

Dynamic shear characteristics of titanium alloy Ti-6Al-4V at large strain rates by the split Hopkinson pressure bar test

The focus of this paper is the dynamic shear characteristics of titanium alloy Ti-6Al-4V at large strain rates. Dynamic load testing of titanium alloy Ti-6Al-4V are performed by the split Hopkinson pressure bar (SHPB) at different strain rates, which involve the SHPB compression test and the SHPB shear test. The material behaviour during the tests are measured and recorded. The strain rates for the compression and shear tests range from 5.0 ×102s−1 to 9.0 ×103s−1 and 1.0 ×104s−1 to 3.0 ×105s−1, respectively. The effect of competing mechanisms—strain rate hardening and thermal softening—on the adiabatic shear band is analysed. A size effect on shear band width is also found. According to the results, a modified Johnson–Cook (J–C) constitutive model is applied to tests at an ultrahigh strain rate. Furthermore, a finite element method (FEM) simulation is conducted to validate different aspects of the methodology. The SHPB shear test is confirmed as a process of pure shear. A comparison of the shear stress-strain curves from the mechanical tests and simulation show good agreement based on the modified J-C constitutive model.

Impact of cooling on shear strength of high salinity soils

Engineering activities have increased in northwestern China where high salinity soils exist extensively. This paper investigates the volumetric behavior and shear strength parameters of high salinity soils during cooling. Fine-grained saline soils with salt content varying from 36% to 2.6% were collected along a highway on the Qinghai-Tibet plateau to conduct laboratory cooling and direct shear tests. Cooling curves of soil specimens were obtained to assess the freezing point depression caused by salinity. Volumetric change data during cooling was presented. Direct shear tests were conducted at temperatures ranging from 20°C to −20°C at an interval of 10°C to obtain the shear stress-strain behavior and evaluate shear strength parameters including the cohesion and friction angle. Additional tests were carried out to investigate the effect of increased moisture content on shear strength parameters. Results showed that saline soils with >0.5% sulfate salt will exhibit large volumetric expansion due to salt crystallization and formation of mirabilite. It was found that, as the temperature was lowered from 20°C to −20°C, the shear stress-strain curves of high salinity soils demonstrated stronger dilative and strain-softening behavior, the friction angle remained constant or showed small but consistent gain, and the cohesion increased. It was interesting to find that the freezing of pore water in high salinity soils did not have nearly as large impact on soil strength as it would have for non-saline soils. In addition, a 3% increase in moisture content decreased the cohesion by 60–90% due to reduced matric suction resulted from increased degree of saturation and decreased tension at the water-soil interface. The results are of significance for highway engineering in cold regions with extensive saline soil distribution.

Simplified phenomenological model of the nonlinear behavior of FRPs under combined stress states

Nonlinear material behavior of FRPs under shear loading is widely observed and investigated. In case of combined stress states under tension and shear, an interaction between the macroscopic shear stress–strain curve evolution and the applied tension has been observed and described by several publications in the past. In the present work, the available experimental data with combined stress states are evaluated and a specific threshold shear stress is found, above which nonlinear material behavior occurs for all stress states. Further, a new simplified phenomenological model is derived to model the nonlinear behavior of FRPs when the threshold shear stress is exceeded. This simplified model only needs the threshold shear stress and one evolution parameter, both derived from a pure shear test, to model nonlinear behavior for all combined stress states. A comparison with the available experimental results and with the predictions of the WWFE-III participants for WWFE-III test case 1 shows a very good agreement.

Aspect ratio effect on shear modulus and ultimate shear strength of graphene nanoribbons

This paper focuses on shear modulus and shear deformation behavior of Graphene Nano Ribbons (GNR) post-wrinkling taking into account size effect. Atomistic modeling of armchair and zigzag GNR were performed at 300°K for GNR with a constant 10nm width and lengths ranging from 2.5nm to 25nm. Results show that ridge formation is oriented at 45 degrees for GNR with an aspect ratio less than one and that the number of ridges is equal to the reciprocal of the aspect ratio, while for aspect ratios higher than one, the ridge formation direction coincides with the diagonal direction of the GNR and only one ridge is formed. Once the diagonal tension reached its ultimate elastic level, three major stress-relaxing phenomena are reported. Results show that the average slope of the stress-strain curve beyond the ultimate elastic stress decreases with increasing GNR length. Moreover, the slope of the shear stress-strain curve in that region is always greater in armchair GNR than in Zigzag GNR. GNR can sustain very high plastic shear strains beyond 400% before failure for wide GNR. It is observed that the shear modulus is inversely proportional to the aspect ratio of the GNR.

A micro-macro description for pseudoelasticity of NiTi SMAs subjected to nonproportional deformations

A micro-macro constitutive model is developed and applied to the prediction of the pseudoelasticity (PE) of NiTi shape memory alloys (SMAs) subjected to nonproportional loadings. It is based on the work by Gall et al. and takes into account different elastic properties of the austenite and martensite. In the constitutive model for a single crystal, the activation of forward and inverse martensitic transformations and the volume fraction of each of the 24 martensite variants (MVs), and the interaction between the MVs are considered. The constitutive behavior of polycrystalline NiTi SMAs is obtained by assembling that of single crystals of different orientations with finite element method (FEM). The corresponding numerical algorithm and FEM model are developed, in which an additional step is adopted to get rid of the MVs that may irrationally be activated during transformation calculation, which directly reduces the dimension of the Jacobian and enables the convergence and stability of the numerical implement of the model, especially in the cases of complex multiaxial nonproportional deformation. A thin-walled cylindrical model is suggested for finite element analysis, in which the texture microstructure in the materials formed during the cold-drawn processes can be considered. It is shown that the MVs activated under tension are different from those under compression, and when subjected to shear deformation the MVs activated contain those appearing during tension, and more MVs activated may account for the larger slope in the shear stress-strain curve. The PE of NiTi SMAs subjected to uniaxial strain and nonproportional strain by some paths in ε−γ/3 plane is simulated, and the satisfactory agreement between the simulated and experimental results demonstrates the validity of the approach developed.

Application of the virtual fields method to the identification of the homogeneous anisotropic hardening parameters for advanced high strength steels

In the present paper, an inverse problem solution so called the virtual fields method (VFM) is implemented to identify the parameters of the homogeneous anisotropic hardening (HAH) model, a distortional plasticity-based model that describes the material plastic behavior when subjected to strain path changes. The framework of the identification method that combines the formulation of the yield condition, the constitutive stress–strain relation and the principle of virtual work is presented. For validation purpose, the proposed identification method was first attempted on finite element (FE) generated data for a forward-reverse simple shear test to investigate its capability in retrieving the input constitutive parameters. The influence of noise was also evaluated. Then, the identification method was applied to a selection of advanced high strength steel (AHSS), namely DP600, TRIP780 and TWIP980, sheet specimens, subjected to a small number of forward-reverse simple shear cycles. The material constitutive parameters were identified using the VFM based on which shear stress–strain curves were calculated and compared with their experimental counterparts. Good agreement was found between the calculated and the experimental curves despite the larger discrepancies observed in the reverse loading paths. To adjust these discrepancies, the original HAH model was modified with respect to the permanent softening related state variables. After modification, the model was simplified with only one state variable related to permanent softening. It was found that the discrepancies observed in the reverse loading paths were reduced with the modified HAH model.

Shear behavior of recycled aggregate concrete after exposure to high temperatures

This paper studied the shear behavior of concrete with different levels of recycled coarse aggregate (i.e., 0%, 50% and 100%) after being subjected to different temperatures (i.e., 20°C, 200°C, 300°C and 400°C). Thirty-six beam specimens with uniform depth and varying width were designed to test their mechanical parameters including shear strength, peak shear strain, stress–strain curves and shear modulus. We analyze how these parameters are influenced by recycled coarse aggregate (RCA) content and by high temperature. We establish the shear stress–strain equations for RCA-embedded concrete after exposure to different temperatures. It is found that the aforementioned mechanical parameters are minimally influenced by the RCA content at ambient temperature (about 20°C). After exposure to high temperatures, the RCA content affects the shear strength insignificantly but increases the peak strain slightly. As the temperature elevates, the residual shear strength and shear modulus decline rapidly whereas the peak strain increases linearly. Furthermore, the normalized shear stress–strain curves become more disperse with the increment of temperature.

Fabrication of lattice truss structures by novel super-plastic forming and diffusion bonding process in a titanium alloy

A novel superplastic forming/diffusion bonding method has been developed to produce lattice truss structure from Ti6Al4V titanium alloy. A three-layer lattice sandwich structure was fabricated. The compression and shear processes of as-made structures were simulated by finite element method and measured by tests. The results showed that the relationship between shear stress and strain for the present structure was different from that of structures made through traditional brazing or welding process. Several stress fluctuations occurred in the compressive stress–strain curve and there was no conventional yield platform in shear stress–strain curve. The compressive finite element simulation pattern was consistent with test result, while there was relatively large deviation between the shear simulation and test results. The face sheet-core interface had adequate bond strength and no node failure was observed in both tests. The node robustness was mainly attributed to the homogeneity of the fine microstructure at node positions.

Thermal behaviour of unsaturated silt at high suction magnitudes

A triaxial cell was developed to investigate the shear strength of unsaturated silt under elevated temperatures and high suction magnitudes. The results from a series of drained triaxial compression tests on compacted silt specimens are presented in this paper. After anisotropic compression, some specimens were heated before suction was applied, while others were heated after the application of suction. The shear stress–strain curves of the soils under high suction magnitudes showed a brittle failure mechanism, with a clear increase in peak shear strength with net confining stress. Heating after suction application led to a greater peak shear strength than reference tests at ambient temperature, whereas heating before suction application led to a lower peak shear strength. Despite the observed path effects, a single peak failure envelope was defined when evaluating the data in terms of effective stress. The suction stress concept was used to define the effective stress, and the values of suction stress were found to be linked with a non-isothermal definition of the soil-water retention curve.

Investigation of rock material under combined compression and shear dynamic loading: An experimental technique

Based on the Split Hopkinson Pressure Bar (SHPB) device, a new combined compression and shear loading technique is developed by adding cushions with designed oblique surfaces. Employing steel as standard material, the technique is calibrated by a series of quasi-static and dynamic experiments. A reliable data processing method of the technique is proposed to decompose the normal stress (σ) and the shear stress (τ) on the oblique surface. The results show that the coupled compression and shear responses of steel exhibit obvious strain rate effect. Validation of the technique is confirmed by using Von Mises criterion in σ-τ plane to describe the coupled strength of steel. Thus, series of experiments are conducted to investigate the compression and shear behaviors of a granite under quasi-static loading (strain rates ∼ 3 × 10−5 s−1) and impact loading with strain rates 50 s−1 and 100 s−1. Five oblique angles, e.g. zero, 15, 30, 45, and 60 degrees, are involved in the experiments. Slopes of the decoupled normal and shear stress-strain curves exhibit obvious load-path dependency, which is known as the coupled compression and shear effect, and strain rate effect. These two effects become more important with oblique angle increasing. Failure criterion of granite specimen at different strain rates can be preliminarily described by the Drucker–Prager (D-P) model, and the strengths of granite exhibit obvious strain rate sensitivity and load-path dependency. The technique is helpful for the investigation of the dynamic properties of rock materials under complex stress states.

Decomposition method based on a modified Arcan fixture and its application in an in situ combined load tester

A miniature in situ tester integrated with a modified Arcan fixture was developed, providing simultaneous tensile and shear loading functions, to investigate the mechanical behaviors of bulk materials under combined loads or unidirectional load. Using the tester, a decomposition method was proposed to obtain the true tensile stress–strain and shear stress–strain relationships. Then, the feasibility of the decomposition method was verified via tensile loading, combined loading and shear loading tests on an extruded AZ31B magnesium alloy with initial gripping angles of 0°, 45° and 90°, respectively. The tensile stress–strain curve and shear stress–strain curve were extracted from the combined stress–strain curve and compared with the results obtained from the unidirectional load tests. Finally, metallographic microscope images of the magnesium alloy under combined load conditions were captured as an illustration of the in situ function, and the fracture morphologies of the magnesium alloy under various loading conditions were also analyzed via a scanning electron microscope.

Shear strengths and volume changes of sand–attapulgite clay mixtures

Compacted sand–expansive clay mixture with low hydraulic conductivity and appropriate shear strength is employed as liner systems for waste containment systems to prevent groundwater contamination by leachate from the waste. The aim of this study was to assess the shear strength behavior and swelling potentials of sand–attapulgite clay mixtures. The attapulgite clay used in this study was obtained from the eastern province of Saudi Arabia and was characterized as highly expansive. A detailed experimental program was devised to evaluate the effects of clay content (ranging between 0 and 60 %), initial molding conditions (optimum and wet-of-optimum), normal stress, and wetting conditions (as-compacted and inundated) on shear strength behavior. Also, the effects of clay content and initial molding conditions on the swelling potential of the mixture were evaluated. Test results revealed different trends for the shear stress–strain curves, signifying that different structural arrangements resulted from the use of different clay contents and molding conditions. Furthermore, test results identified an optimum clay content of 30 % which yielded the maximum shear strength; beyond this, a significant reduction in the shear strength of the sand–attapulgite clay mixture was observed. Finally, the shear strengths of sand–attapulgite clay mixtures were compared to those of sand–bentonite mixtures.

In quest of methods for measuring 3D mechanical properties of composites

Abstract Accurate and efficient full three-dimensional characterization of mechanical properties of composite materials, including stress–strain curves and strength characteristics, is essential for understanding complex deformation and failure mechanisms of composites and optimizing material qualification efforts. This work summarizes the ongoing effort by the authors in pursuit of methods for measuring multiple mechanical properties of composite materials from a single experiment; and presents a new method enabling simultaneous assessment of the shear stress–strain curves in all three principal material planes. The method uses a small rectangular plate torsion specimen. The method is relying on digital image correlation to capture deformation including the out-of-plane strain components; and on finite element-based stress calculation. Nonlinear interlaminar shear stress–strain constitutive properties, generated in the 1–3 principal material plane, are compared with existing data for a practical carbon/epoxy tape material system. In addition, a stress–strain curve characterizing the nonlinear interlaminar shear properties in the 2–3 principal material plane at all strain levels including large shear strain, is captured in this work for the first time.

Anisotropies of elasticity and thermal conductivity in some novel superhard materials

Abstract The first principles calculations based on density functional theory are performed to investigate the anisotropies of four superhard materials (w-BN, w-BC2N, r3m-BC2N, and r3m-B2CN). By calculating Poisson’s ratio, we found that the atomic binding forces of the first three materials are non-central forces, whereas that of r3m-B2CN is a central force. According to the elastic percentage anisotropy (AB, AG, and AE) and the calculated values of shear anisotropic factor A, the four materials are proven to have elastic anisotropy. Moreover, the different shapes in the three-dimensional stereograms of Young’s modulus on all surfaces, as well as the tensile and shear stress–strain curves in different crystal orientations can further account for the anisotropies of these materials. In addition, the anisotropic factors of acoustic wave and thermal conductivities in the propagation directions of [0 0 0 1] and (0 0 0 1) are also calculated. w-BN, w-BC2N, and r3m-BC2N have similar calculated values, which explain why they have similar properties. By contrast, r3m-B2CN has a large degree of anisotropy, and the three-dimensional diagram of its Young’s modulus has an “8” shape.

Analysis of nonlinear shear stress–strain response of unidirectional GF/EP composite

Reasons for nonlinear stress–strain curves in shear of unidirectional glass fibre composite are analysed. Laminate with stacking sequence [45/−45]s is used in tensile quasi-static as well as in tensile creep and strain recovery tests to study the development of viscoelastic and viscoplastic shear strains in local coordinates of the ply. It is shown that Zapa’s integral representation of viscoplasticity is applicable for this material and methodology for parameter determination is given. Schapery’s nonlinear viscoelastic material model was used for shear response characterisation and the nonlinearity parameters’ dependence on the shear stress was determined and described by fitting functions. Microdamage development is quantified by measuring axial modulus and Poisson’s ratio of the laminate. The obtained nonlinear viscoelastic, viscoplastic model with included effect of microdamage was successfully used to predict the nonlinear shear stress–strain curve in strain controlled tensile loading.

In vitro micromechanical characterization of porcine periodontal ligament

Purpose: To evaluate some aspects of the experimental determination of the mechanical behavior of the periodontal ligament on porcine samples. The focus was on the mechanical properties of the periodontal ligament related to the presence/absence of fluid, and to the different position of the sample along the tooth root length. The application of these results could be used to develop computerized virtual models of the tooth-periodontium system. Methods and materials: Porcine mandibles were obtained from pigs (8–12 months old). From each one four blocks were cut, containing one complete inferior incisor and surrounding bone, then six sections were cut (each 2mm thick). Twelve samples were obtained from animals just suppressed and once sliced, put into a plastic container and immersed in physiologic solution. A testing chamber was built to apply tensile/compressive/shear displacements to samples in pressurized liquid. Inside the chamber a ±100N load cell was placed and a 100 cm long vertical tube allowing the application of a pressure when filled with liquid. The displacements were obtained through an endless screw activated by a servo-controlled motor. Preliminary tests were performed to determine the correct clamping method and the minimum non-slipping force of the grips. Tests were done at a constant displacement of 1mm/min. Experiments were done at room temperature (23 ◦C). Monotonic tension, compression, and shear tests, up to failure, have been performed and standard one-way ANOVA analyses was used (a=0.05). Results: Typical tension/compression and shear stress–strain curves were shown. Results in tension were substantially undisturbed by the presence/absence of liquid in the testing chamber. On the contrary, compression tests revealed a quite notable stiffness increase associated to the presence of pressurized liquid. It appears that only the shear mechanical parameters were correlated to the position of the sample along the tooth root. Conclusion: It is important to perform tests keeping the samples immersed in pressurized fluid. The most coronal sections seem to provide slightly higher strength values, as could be expected considering their proximity to the cementenamel junction.

A comparison of material characterizations in frequently used constitutive models of ligaments

Longitudinal tensile and simple shear stress-strain curves of human medial collateral ligaments (MCL) were fitted by six frequently used constitutive relations of ligaments using two different fitting methods for determining which was the best fitting method and the most preferable constitutive model for describing the ligament properties. According to the results of fitting goodness, two typical constitutive models were further analyzed by FEM to investigate the effect of the variation in MCL constitutive models under some physiological loads (i.e., 4.5 Nm external tibial and 10 Nm valgus tibial torques). It was found that different fitting methods induced great variations in describing the simple shear behavior whereas no obvious difference in the longitudinal tensile behavior. The most accurate description of both the longitudinal tensile and simple shear behaviors was obtained from the constitutive model with ground substance defined by an exponential function when the parameters were fitted by the two test data, respectively. Although the distributions of maximal principal stress were almost the same, the variation in MCL constitutive models affected the highest value of the stress greatly when MCL was under the complex physiological loads.