Shear Stress-strain Curves Research Articles

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.

Effect of the Strain Rate on the Twisting of Trabecular Bone from Women with Hip Fracture

As one of the major functions of bone is to provide structural support for the musculoskeletal system, it is important to evaluate its mechanical strength. Bones may be subjected to multiaxial stresses due to bone pathologies, accidental loads which may lead to hip, wrist fracture, or to a prosthetic joint replacement. Twist loading may lead to fractures, especially involving long bones from lower limbs. The aim of this work was to study the effect of the strain rate on the shear properties of trabecular bone samples from women with hip fracture (from 65 to 100 years). Cylindrical samples were core drilled from human femoral heads along the primary trabecular direction. The cylinder's ends were polished and embedded in blocks of polymeric material which fit the grips of the testing device. Deformation rates of 0.005, 0.01, 0.015, and 0.05 s⁻¹ were applied. Twisting tests were conducted with or without an applied axial load of 500 N. From the torque-angular displacement curves, the shear stress-strain curves were obtained. The maximum shear strength and the shear modulus (i.e. the slope of the linear region) were determined. A large scatter of the results of the shear strength and the shear modulus was found, which is probably related to the heterogeneity of nonhealthy human bone samples. There is no significant effect of the strain rate on the maximum shear stress and the shear modulus, either in tests undertaken with or without the application of an axial load. The effect of strain rate on nonhealthy bone trabecular twisting properties did not follow the trend observed on the effect of strain rate in healthy bone, where an increase is detected.

단순전단 시험법 구축 및 바우싱거효과를 고려한 경화거동 예측

In this study we establish a process to predict hardening behavior considering the Bauschinger effect for zircaloy-4 sheets. When a metal is compressed after tension in forming, the yield strength decreases. For this reason, the Bauschinger effect should be considered in FE simulations of spring-back. We suggested a suitable specimen size and a method for determining the optimum tightening torque for simple shear tests. Shear stress-strain curves are obtained for five materials. We developed a method to convert the shear load-displacement curve to the effective stress-strain curve with FEA. We simulated the simple shear forward/reverse test using the combined isotropic/kinematic hardening model. We also investigated the change of the load-displacement curve by varying the hardening coefficients. We determined the hardening coefficients so that they follow the hardening behavior of zircaloy-4 in experiments.

Short‐beam Shear Method for Assessment of Stress–Strain Curves for Fibre‐reinforced Polymer Matrix Composite Materials

ABSTRACTThis work presents a thorough description of a short‐beam shear (SBS) test method coupled with digital image correlation (DIC) for the measurement of shear stress–strain curves of polymer matrix composites. The method provides a time‐ and cost‐effective alternative to established methods, and the authors hope this work can serve as a starting point for discussions on the developments of new standards for the characterisation of shear stress–strain curves for composites. The experimental set‐up, including several modifications to the American Society of Testing and Materials current standard configuration, is described. Implementation of the DIC technique to obtain accurate surface strain in the SBS specimens is also presented. Accuracy of beam theory‐based shear stress calculation is assessed using a non‐linear finite element model (FEM). A simple means to improve the accuracy of the closed‐form shear stress approximation is provided. Glass/epoxy and carbon/epoxy composite material systems are used to demonstrate the developed method. Strain surveys are conducted to compare the experimentally generated and FEM‐computed strain fields and verify the accuracy of the shear stress–strain curves. Shear stress–strain response generated from SBS tests is also compared with V‐notched beam test results for further verification.

Evaluation of in-plane ply shear properties from unidirectional plate torsion tests

Torsion tests were conducted on unidirectional carbon/epoxy laminated plates. Preliminary finite element analyses showed that the specimen geometry selected avoided pronounced geometric non-linearity and ensured that a significant volume of material would be under a high fraction of the maximum shear stress. Furthermore, the clear prevalence of in-plane shear stresses allowed the development of a simplified data analysis model. Calculated shear-stress strain curves were consistent with the results of tensile tests on angle-ply coupons, despite lower failure stresses that may have been caused by surface defects or by spurious transverse tensile stresses. Nevertheless, the unidirectional plate torsion test is worthy of further research, given the structural relevance of torsional loads and the problems of in-plane shear tests methods.

Assessing strength and local plastic behaviour of welds by shear testing

In order to assess the strength and plastic properties across different weld zones, a shear testing procedure specially conceived for sampling and testing narrow weld portions, is presented in current paper. The local constitutive behaviour of the welds is assessed from local shear stress–strain curves, plotted up to large values of plastic deformation. The shear testing tool, developed in order to enable running the shear tests in a universal tensile testing machine, is described, as well as the shear sample geometry and the procedures used for strain data acquisition via Digital Image Correlation (DIC). Results of the mechanical characterisation of the nugget of AA5083 friction stir welds, produced under different welding conditions, are used to demonstrate the quality and variety of the results obtained applying the proposed mechanical characterisation technique.

Study on Particle Breakage and Strength Characteristic of Different Coarse-Grain Contents

The significant particle size grading and the particle breakage of deep soils are two major characteristics of super-high dumping-site. Based on the refitted large-scale direct shear experiments, this paper studied the particle breakage and shear strength of different coarse-grained soil. The experimental results indicates a conclusion: particle breakage index is very small when upright stress is less than 400kPa .The breakage rate increases obviously with the increase of upright stress. The particle breakage index is very little when coarse-grained contents are less than 46.0% .It increases significantly when coarse-grained contents are larger than 46.0%. Hyperbolic curves can express the relationship between particle breakage index and upright stress. The experiments studied on shear strength shows that the shear stress-strain curves are micro-softening model or micro-hardening model under low upright stress. The curves are slight-softening model at higher upright stress when the coarse-grained contents are equal to 24.0%. At coarse-grained contents equal 78.0%, the shear stress-strain curves are softening model under low upright stress. The shear strength envelope expressed nonlinear under higher upright stress.

Nonlinear stress-strain relations for crystalline solids in initially deformed state

We show a general nonlinear stress-strain response for crystalline materials subject to an initial deformation. The scheme is implemented using 3rd, 4th, and higher order elastic constants. We apply the formulation to a face-centered cubic crystalline Au under shear while in an initially hydrostatically deformed state. We then compare the nonlinear shear stress-strain relations from our derived formulation with Hellmann-Feynman shear stress-strain curves obtained directly from ab initio calculations. The results show that the general analytical expression for the nonlinear stress-strain relation is satisfactory and thus expected to have many applications where ab initio calculations are limited, including cases at finite temperature.

High-rate bulk and shear responses of bovine brain tissue

This experimental study systematically investigates the dynamic response of bovine brain tissue under uniaxial strain and pure shear loading conditions. The combination of such stress states and strain rates are representative in the brain under blast loading in which both bulk and shear deformation may be involved. The dynamic uniaxial strain experiments (bulk response) were conducted on a modified Kolsky compression bar with an aluminum confinement collar. Bovine brain samples were sealed in the collar and loaded by the Kolsky bars so that the specimen only deformed in the axial direction. The resultant stress-strain curves reflected the pressure–volume relations from which the bulk modulus were obtained. The dynamic shear response was determined by using a recently developed Kolsky torsion bar technique for tissue materials characterization. Quasi-static torsion experiments were also conducted on an MTS system to construct a full set of shear stress-strain curves over a wide range of shear strain rates (0.01–700 s−1). The experimental results show that the dynamic bulk modulus of brain is in the range of 1.68–2.33 GPa which is close to the low rate values reported in the literature, while the shear responses show significant rate sensitivity over the tested strain rate range.

Characterization of nonlinear shear properties for composite materials using digital image correlation and finite element analysis

Abstract A method for accurate assessment of nonlinear shear stress–strain relations of composite materials is developed in this work using short-beam shear (SBS) tests. The method is based on a combination of a finite element model (FEM) for stress calculation and a digital image correlation (DIC) technique for full-field measurement of deformation. An inverse problem of generating shear stress–strain curves is solved using an iterative procedure which starts with a beam theory-based closed-form approximation of shear stresses, and updates the stresses through a number of finite element simulations. The method is demonstrated on unidirectional carbon/epoxy SBS specimens. Experimentally-generated strain fields are compared with FEM-computed strain fields to verify accuracy of the developed method. Shear stress–strain data are compared with V-notched beam test results for further verification.

A novel high-speed shear test for lead-free flip chip packages

Despite the importance of lead-free solders in modern environmentally friendly packaging, few studies have been conducted on their mechanical reliability at the wafer level. In the present study, high-speed die shear tests were conducted to investigate the effects of strain rate on the shearing resistance and fracture mode of Sn-3wt%Ag-0.5wt%Cu solder joints on electroless Ni-P/immersion Au surface finish pads. The results indicated that the solder joints underwent ductile and mixed ductile-brittle fracture at low ( 25,385 s−1) strain rates, respectively. Thus, the overall shear stress-strain curve can be divided into three areas according to Hollomon’s law, starting from low strain rates: area I, 100% ductile fracture of the solder itself; area II, mixed ductile-brittle fracture resulting in a ductile-brittle transition region; and area III, 100% brittle fracture at the interface between the intermetallic compound and the Ni-P layer.

Shear behavior on monel alloy porous sheet materials

As one of the important metallic filter materials, sintered porous monel alloy has been widely used in chemical, nuclear and petrochemical industries because of its extremely high temperature corrosion resistance, high resistance to impact and good weldabilty. In the present paper, porous monel samples were prepared by power metallurgy and the shear test was carried out. The experiment results indicated that the sample has two stages of deformation and failure during the shear test, corresponding to two peak points at the shear stress-strain curve. Before the first peak point appears the porous metal sheet is compressed and extruded. The porous metal sheet is stretched after the first peak point appears. The shear strength of the porous plate decreased with the porosity increases.

Study on Mathematical Stress-strain Model of Frozen-thawed Soil Based on Structure Mechanism

The stress-strain behavior of frozen-thawed soil is a main issue of the frozen soil mechanics. In this paper, the change rules of soft soil shear strength, friction angle, cohesive force and other mechanical parameters were studied. After frozen-thawed cycles, the friction angle of soft soil increases with lower cohesive force, the constitutive property gradually weakened with the nature of transformation from cohesive soil to cohesionless soil. Mathematical characteristics for shear stress-strain curve of frozen-thawed soil are analyzed. Structure mechanism index is presented to indicate the relation between stress-strain curve and soil structure mechanism. The result of this paper is helpful to the numerical analysis and practical engineering design of frozen-thawed soil foundations.

Crystal Plasticity Predictions of Forward-Reverse Simple Shear Flow Stress

The flow stress behavior of a bake-hardenable steel during a few simple shear cycles is investigated using a crystal plasticity model. The simple shear test provides a stable way to reverse the loading direction. Stress reversals were accompanied with a lower yield stress, i.e., the Bauschinger effect, followed by a transient hardening stage with a plateau region and, permanent softening. The origins of these three distinct stages are discussed using a crystal plasticity model. To this end, the representative discrete grain set is tuned to capture such behavior by coupling slip system hardening appropriately. The simulated results are compared with experimental forward-reverse simple shear stress-strain curves. It is shown that the characteristic flow stress stages are linked to texture evolution and to the Bauschinger effect acting on the different slip systems.

Effect of Spew Fillets on Strength of Single-Lap Adhesive Composites Joints

Tension tests on T700/EXOPY unidirectional laminates single-lap joints of spew fillets at overlap ends under uniaxial tensile loading are performed in the presented paper. Two different types of joints are designed and analyzed in order to study effect of spew fillets and no spew fillets at overlap ends on strength and failure mode of single-lap adhesive joints. According to the results, failure mode of two joints are characterized and analyzed. Shear stress—strain curves are analyzed and compared. At the same time, a finite element simulation is carried out to analyze the peel/shear stress fields inside the joint interface. It is found that joint strength was much affected by spew fillets in overlap ends. Nerveless, joints strength is decreased with the increasing thickness of spew fillets in overlap ends. The computational results are in good agreement with the experimental values.

Determination of Hardening Coefficient of Large Strain Constitutive Model Based on Torsion Tests

Uni-tension test and torsion test with specimens of A3 steel are completed, and deformation rate, the spin of Euler configuration to Lagrange configuration and generalized Jaumann rate of Kirchhoff stress in torsion problem are given. Large strain constitutive relationship with generalized Jaumann stress rate is studied based on torsion test. The simple shear problem is discussed by using the constitutive model given in this paper. The result indicates that the hardening coefficient of constitutive model with generalized Jaumann rate may be given by the same expression as that of constitutive model with Jaumann objective rate when determining by using torsion tests and the shear stress response curve in simple shear problem obtained by using the constitutive model in this paper is similar to the shear stress-strain curve given in solid circular shaft torsion tests.

Hyperelastic Constitutive Modeling of Hexagonal Honeycombs Subjected to In-Plane Shear Loading

The in-plane flexible shear property of hexagonal honeycombs may be useful for the compliant structural applications. In this paper, hyperelastic strain energy functions are developed for a finite in-plane shear deformation of hexagonal honeycombs over a constituent material’s elastic range. Effective shear stress-strain curves of hexagonal structures and local cell wall deformation are investigated using the finite element based homogenization method. The hyperelastic models, which are only related to the effective properties of a honeycomb, may not be good enough to capture the nonlinear behavior at a high macroscopic shear strain level. The primary microscopic cell wall deformation mode under macroscopic in-plane shear loading was identified to be the bending of the vertical cell wall h, which is perpendicular to the macroscopic loading direction. The re-entrant hexagonal structures having a negative Poisson’s ratio shows a high macroscopic shear flexible property associated with the high h when the honeycombs are designed to have the same macroscopic shear modulus.

Novel Methods for Assessment of Three-Dimensional Constitutive Properties for Composites

Accurate three-dimensional stress-strain constitutive properties are essential for understanding of complex deformation and failure mechanisms for glass-fiber and carbon-fiber reinforced polymer-matrix composites. A large number of different methods and specimen types, which are currently required to generate three-dimensional allowables for structural design, slow down material characterization. Also, some of the material constitutive properties are never measured due to prohibitive cost of the specimens needed. This work shows that simple short-beam shear specimens are well-suited for measurement of 3D constitutive properties for composite systems. In particular, a methodology to measure tensile and compressive material properties, generate shear stress-strain curves and measure the shear strength in a simple short beam shear test will be presented. The methodology is based on the Digital Image Correlation (DIC) full-field deformation measurement. Short-beam and curved-beam tests are accomplished to generate 3D stress-strain response for glass/epoxy and carbon/epoxy tape composite material systems. Accuracy of constitutive properties is also verified using standard methods and data available in the public domain.

A Simple Relationship Between Axial and Torsional Cyclic Parameters

The ultimate purpose of the present article is to theoretically estimate the cyclic shear strength coefficient and the cyclic shear strain hardening exponent. For this purpose, the relationship between axial and torsional cyclic parameters is addressed in light of the von-Mises criterion. Material data for 15 kinds of material have been taken from the technical literature to check the accuracy and reliability of the developed correlations. Maximum differences of 18.6 and 27.7% were observed for theoretical versus experimental results for the cyclic shear strength coefficient and the cyclic shear strain hardening exponent, respectively. Experimental verifications show that the devised relationship can describe the cyclic shear stress-strain curves well. The characteristic of the theoretical approach is simple and easy to use. In addition, the theoretical results can be further applied to examine the correctness of the test data.

Effect of potato starch modification on mechanical parameters and granules morphology

Research was conducted to recognise the interrelations between morphology and mechanical properties of powders used in the food industry (dried potato protein, granulated starch, gelatinising starch, potato starch, pudding flour, starch thickener, and six kinds of dextrins: 40% white dextrin, 60% white dextrin, yellow dextrins: S, N, W, WB). Microscopic examination, determination of particle size distribution, particle shape index, as well as direct shear tests were performed. Single particles of dextrins were found to have similar shapes and dimensions. Classification of materials based on the results of mechanical testing was found to be in close agreement with classification based on morphology. The values of unconfined yield strength of dextrins and other materials investigated were found to be close, and characteristic of easy flowing and cohesive materials. Oscillations in the shear stress–strain curves were observed for two experimental materials: potato starch and white dextrin 60%, while those for other experimental materials run smooth. The highest values of unconfined yield strength σ c were found in a range from 4.5 to 8 kPa for dried potato protein, at major consolidation stress values of 4 and 10 kPa, respectively. The lowest values of σ c, characteristic for easy flowing and free flowing materials, were found for potato starch and granulated potato starch. The results of this study confirmed the relevance of morphology to the mechanical properties of powders.