Showing papers on "Stress–strain curve published in 1998"

Plastic deformation and fracture behaviour of Ti–6Al–4V alloy loaded with high strain rate under various temperatures

Abstract: This study investigates the plastic deformation and fracture behaviour of titanium alloy (Ti–6Al–4V) under high strain rates and various temperature conditions. Mechanical tests are performed at constant strain rates ranging from 5×102 to 3×103 s−1 at temperatures ranging from room temperature to 1100°C by means of the compressive split-Hopkinson bar technique. The material's dynamic stress–strain response, strain rate, temperature effects and possible deformation mechanisms are discussed. Furthermore, the plastic flow response of this material is described by a deformation constitutive equation incorporating the effects of temperature, strain rate, strain and work hardening rate. The simulated results based on this constitutive equation are verified. The fracture behaviour and variations of adiabatic shear band produced by deformation at each test condition are investigated with optical microscopy and scanning electron microscopy. The results show that the flow stress of Ti–6Al–4V alloy is sensitive to both temperature and strain rate. Nevertheless, the effect on flow stress of temperature is greater than that of strain rate. Fracture observations reveal that adiabatic shear banding turns out to be the major fracture mode when the material is deformed to large plastic strain at high temperature and high strain rate.

Engineering Mechanics of Solids

Abstract: 1. Stress. 2. Strain. 3. Axial Deformation of Bars: Statically Determinate Systems. 4. Axial Deformation of Bars: Statically Indeterminate Systems. 5. Generalized Hooke's Law: Pressure Vessels. 6. Torsion. 7. Beam Statics. 8. Symmetric Beam Bending. 9. Unsymmetric (Skew) Beam Bending. 10. Shear Stresses in Beams. 11. Stress and Strain Transformation. 12. Yield and Fracture Criteria. 13. Elastic Stress Analysis. 14. Beam Deflections by Direct Integration. 15. Beam Deflections by the Moment-area Method. 16. Columns. 17. Energy and Virtual Work. 18. Classical Energy Methods. 19. Elastic Analysis of Systems. 20. Plastic Limit Analysis. Tables. Answers to Odd-numbered Problems. Index. Conversion Factors between U.S. Customary and SI Units.

Material characterization of human medial collateral ligament

Abstract: The objectives of this study were to determine the longitudinal and transverse material properties of the human medial collateral ligament (MCL) and to evaluate the ability of three existing constitutive models to describe the material behavior of MCL. Uniaxial test specimens were punched from ten human cadaveric MCLs and tensile tested along and transverse to the collagen fiber direction. Using load and optical strain analysis information, the tangent modulus, tensile strength and ultimate strain were determined. The material coefficients for each constitutive model were determined using nonlinear regression. All specimens failed within the substance of the tissue. Specimens tested along the collagen fiber direction exhibited the typical nonlinear behavior reported for ligaments. This behavior was absent from the stress-strain curves of the transverse specimens. The average tensile strength, ultimate strain, and tangent modulus for the longitudinal specimens was 38.6 +/- 4.8 MPa, 17.1 +/- 1.5 percent, and 332.2 +/- 58.3 MPa, respectively. The average tensile strength, ultimate strain, and tangent modulus for the transverse specimens was 1.7 +/- 0.5 MPa, 11.7 +/- 0.9 percent, and 11.0 +/- 3.6 MPa, respectively. All three constitutive models described the longitudinal behavior of the ligament equally well. However, the ability of the models to describe the transverse behavior of the ligament varied.

Strain rate behavior of composite materials

Abstract: The effect of strain rate on the compressive and shear behavior of carbon/epoxy composite materials was investigated. Strain rate behavior of composites with fiber waviness was also studied. Falling weight impact system and servohydraulic testing machine were used for dynamic characterisation of composite materials in compression at strain rates up to several hundred per second. Strain rates below 10 s −1 were generated using a hydraulic testing machine. Strain rates above 10 s −1 were generated using the drop tower apparatus developed. Seventy-two-ply unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions and [(0 8 /90 8 ) 2 /0 8 ] s crossply laminates were characterised. Off-axis (30 and 45°) compression tests of the same unidirectional material were also conducted to obtain the in-plane shear stress–strain behavior. The 90° properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The shear stress–strain behavior, which is also matrix-dominated, shows high nonlinearity with a plateau region at a stress level that increases significantly with increasing strain rate. The 0° and crossply laminates show higher strength and strain values as the strain rate increases, whereas the modulus increases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases the dynamic stress–strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal case and highest in the transverse and shear cases. Unidirectional and crossply specimens with fiber waviness were fabricated and tested. It is shown that, with severe fiber waviness, strong nonlinearity occurs in the stress–strain curves due to fiber waviness with significant stiffening as the strain rate increases.

High - strength concrete subjected to triaxial compression

Abstract: The behavior of high-strength concrete subjected to multiaxial states of stress was studied. An experimental program was undertaken to quantitatively determine the failure surface for high-strength concrete. Results from this study provide the means to predict the failure condition for high-strength concrete under combined stresses. The experimental program was comprised of testing high-strength concretes at three different compressive strength levels. The three strength levels included concretes with compressive strengths of 6 ksi (42 MPa), 10 ksi (69 MPa), and 15 ksi (103 MPa). The triaxial tests were performed on 4-by-8 in (100-by-200 mm) cylindrical specimens. The confining pressures employed in the experiments ranged from 1,200 psi (8.3 MPa) to 12,000 psi (82 MPa). A series of uniaxial tension and compression tests were also performed to develop the necessary data for establishment of the failure criterion. Empirical relationships were developed for prediction of axial strength as a function of confining pressure. In general, the axial strength of high-strength concrete increases with increased confining pressure. However, in comparison with the normal-strength concrete, the effect of confining pressure on the failure strength of high-strength concrete is less pronounced.

Stress-Strain Behavior of Concrete under Cyclic Loading

Abstract: A rational analysis of reinforced concrete (RC) structures requires satisfactory modeling of the behavior of concrete under general loading patterns. The behavioral characteristics of concrete dominantly depends upon its load history. For the study of concrete behavior, parametric study and experimental investigation into the behavior of concrete under load history of random cycles are performed. Through parametric study, the applicability of the previous concrete models is examined and a physically motivated modeling for the cyclic stress-strain relationships is proposed. The present modeling of concrete under general cyclic loading is initiated to provide substantial applicability, flexibility of mathematical expressions, and furthermore, to describe the behavior of random cycles. For the experimental study of concrete subjected to cyclic axial compressions, tests of 3 in (76 mm) by 6 in (152 mm) concrete cylinders are conducted under four different loading regimes to determine the major experimental parameters for the proposed analytical expressions. The model developed is based on the results of parametric study and experimental data obtained for the present study. The validity of the proposed general cyclic model is confirmed through a comparison of the experimental results and simulated behavior of the model.

Normal Wedge Indentation in Rocks with Lateral Confinement

Abstract: The paper reports results of a numerical analysis of the wedge indentation problem. The main objective of this research is to investigate the influence of the lateral confining stress on the development of the plastic zone under the indenter and on the initiation of tensile fractures. Numerical analysis indicates that the location of maximum tensile stress (interpreted as the point of crack initiation) moves away from the indentation axis as the lateral confinement increases. It is found that a small increase in the confining stress from zero induces a large increase in the inclination of this point on the indentation axis. However, the confinement does not reduce significantly the maximum tensile stress and it hardly influences the indentation pressure. These numerical results shed some light on the mechanism of formation of lateral or sub-horizontal tensile cracks observed in the indentation experiments.

Modified Slump Test to Measure Rheological Parameters of Fresh Concrete

Abstract: The ease of placement of concrete depends upon at least two physical properties, the yield stress and plastic viscosity. Currently the most common field test is the slump test, and it is related only to the yield stress. Therefore, a simple field test method intended to provide an evaluation of the two Bingham rheological parameters, yield stress and plastic viscosity, was developed. To determine the plastic viscosity the time necessary for the upper surface of the concrete in the standard slump cone to slump 100 mm was measured. The apparatus and test procedure are described. Semi-empirical models are proposed for the yield stress and for the plastic viscosity as function of the final slump and slumping time. The application of the modified slump test for the evaluation of the viscosity is limited to concretes with a slump of 120 to 260 mm. If the validity of this test is confirmed in the future, it could be used as a field quality control test.

Mechanical Behaviour of Cyclically Heated Fine Grained Rock

Abstract: The most vital difference between rock and rock mass are fractures and fissures. They affect the behaviour and strength of rock masses. According to their origin, size, and shape, rock mass contains several types of weakness planes varying from microfissure to faults. Other parameters such as underground water, temperature, time and stress state affect the rock's behaviour in its natural environment. The frequency of discontinuities in fractured rock is one of the basic parameters for reducing its strength. However it is generally difficult to test undisturbed fractured rock in a laboratory environment. In this study it was tried to open and loosen the grain boundaries of fine-grained rock specimens by cyclical heating and cooling. This should serve as a physical simulation of fractures in the rock mass and enables a discussion of the changes in mechanical behaviour of fractured rock. For this reason, laboratory test specimens of Carrara marble and Buchberger sandstone were used. The heating cycles were varied from 0 to 16. From the results of uniaxial compression, Brazilian and “Continuous Failure State” triaxial tests, it was pointed out that all of the mechanical parameters decreased gradually with an increasing number of heating cycles. Uniaxial compressive strength was reduced to about 50%, while the tensile strength decreased to about 60% for both types of rock. It was also observed that the variations of strength parameters were higher after the first heating cycles. As a result of cyclical heating, the slopes of pre-failure and post-failure curves in the stress-strain plane changed similarly, but the variations of modulus of elasticity were higher than the slopes of the post-failure curves for sandstone. The ratio between compressive and indirect tensile strength rose to a value of 98 after the last heating cycle. For unheated specimens of Carrara marble this ratio is 20. The axial strain at the failure point increased suddenly after the first heating cycle and the failure developed entirely intergranular in cyclically heated specimens.

Microscopic fracture processes in a granite

Abstract: The deformation of a competent, brittle, granitic rock is thought to have two main components: elastic and brittle deformation, the latter caused by axial microcracking. Dynamic fatigue testing of Lac du Bonnet granite would, however, suggest the presence of a third mechanism, compaction. Compaction is not the same as elastic crack closure; compaction entails permanent damage along grain boundaries that are under high compression. During compaction, the axial stiffness (elastic modulus) of the rock increases and the permanent crack volume becomes negative (compression). Compaction is active at all stress levels, but it is most noticeable at low stress where its presence is not masked by dilation caused by axial microcracking.

The strain rate and temperature dependence of the dynamic impact response of tungsten composite

Abstract: Liquid sintered tungsten (W) heavy alloy with a 92.5W–5.25Ni–2.25Fe composition was examined using a compression split-Hopkinson bar to realize the effects of strain rate and temperature on dynamic impact deformation behaviour. Both stress and strain were measured for specimens tested at temperatures ranging from 25 to 1100°C and strain rates ranging from 8×10 2 to 4×10 3 s −1 . The relationship between flow stress, strain rate and temperature was determined and the results have been successfully modeled by a proposed constitutive equation incorporating the effect of strain, strain rate and temperature. Our results show that flow stress increases with increasing strain rate. Alternatively, high temperature reduces flow stress significantly and improves the degree of thermal softening. During impact, initial cracking occurs preferentially either at tungsten–tungsten grain boundaries or at the tungsten–matrix interface, and failure is dominated principally by a mixture fracture model. Metallographic examinations show a dramatic increase in microcrack density and deformation of tungsten grains as strain rate and temperature are increased. Additionally, changes in microhardness are also found to correlate with changes in strain rate and temperature.

An analytical study of the influence of thermal residual stresses on the elastic and yield behaviors of short fiber-reinforced metal matrix composites

Abstract: An analytical model was developed to study the influence of thermal residual stresses on the elastic and yield behaviors of aligned short fiber-reinforced metal matrix composites. Three-dimensional solutions of elastic stress field in the matrix of a circular cylindrical unit cell were first obtained based on the theory of elasticity. On this basis, an alternative analysis of the stress transfers between the matrix and the fiber was given by using the shear lag analysis, which provides the expressions for the stress distributions in the matrix and the fiber. The thermal residual stresses and the distributions of the stresses under tensile and compressive loadings as a function of the material parameters, such as fiber volume fraction, fiber aspect ratio and matrix yield stress, were calculated. Furthermore, simple expressions for the composite elastic modulus and yield strength under tensile and compressive loadings were derived. These expressions were used to study the influence of the thermal residual stresses and the material parameters on the elastic moduli and yield strengths under tensile and compressive loadings. Finally, the model predictions were compared with the experimental results on the SiCw/Al–Li T6 composite and several SiCw/Al T6 composites in literature and also with the other theoretical models.

Micromechanics of rubber-toughened polymers

Abstract: A new micromechanical model is provided to account for the full interaction between rubber particles in toughened polymers. Three-dimensional large deformation elastic–plastic finite element analysis is carried out to obtain the local stress and strain fields and then a homogenization method is adopted to obtain the effective stress–strain relation. The dependence of the local stress and strain distributions and effective stress–strain relation on phase morphology and mechanical properties of rubber particles is examined under various transverse constraints. The profile for the effective yield surface is obtained at four different particle volume fractions. It is shown that stress triaxiality affects significantly the effective yield stress and the local stress concentrations. Rubber cavitation and matrix shear yielding are two coupled toughening mechanisms; which one occurs first depends on the properties of rubber particles and matrix and the imposed triaxiality. Rubber cavitation plays an important role in the toughening process under high tensile triaxial stresses. Axisymmetric modelling may underestimate, and two-dimensional plane-strain modelling may overestimate, the inter-particle interaction compared with three-dimensional modelling.

The change in conductivity of a rubber-carbon black composite subjected to different modes of pre-strain

Abstract: Conductivity of conductive rubber composites changes significantly when subjected to mechanical stress and strain. Electrical properties of different pre-strained samples derived from EPDM, 50 50 NBR/EPDM blend and NBR rubbers, were measured. It was found that electrical resistivity of strained samples depends on strain amplitude (% elongation), frequency of stress-strain cycle, and also number of stress-strain cycles. Samples were strained in three different instruments: an Instron UTM; a Monsanto fatigue to failure tester; and a Goodrich flexometer. Under different conditions, electrical properties of strained and unstrained (original) samples were measured. It was found that there is similarity in the change of modulus and electrical resistivity against degree of strain and frequency of strain for different samples. The results of different experiments have been discussed in light of breakdown and formation of the carbon black-rubber structure.