Stress-strain Curve Of Material Research Articles

Effect of Reinforcing Steel Area Loss on Flexural Behavior of Reinforced Concrete Beams

Reinforcing steel area may be reduced due to corrosion or mechnical damage. Moment-curvature relationships are obtained for reinforced concrete beams using the developed algorithm. The analysis is based on stress-strain curves for materials (steel and concrete). The developed iterative numerical procedure is demonstrated on a typical concrete bridge T-beam. Moment-curvature relationships are obtained for various degrees of reinforcing steel area loss.

Influence of strain hardening and initial imperfections on the collapse behaviour of plates

The paper presents the analysis of the post-buckling state in the elasto-plastic range of square plates subjected to uniform compression. Four boundary conditions along the unloaded edges are considered. The method is a combination of analytical and numerical solutions in which the Prandtl-Reuss equations are used. Different material stress-strain curves and initial imperfections such as: out-of-flatness and residual stresses are taken into account. The load-shortening curves for plates of different geometrical parameters and material properties are shown in diagrams.

Determination of Instability in Sheet-Metal Based on the Anisotropic Yield Ellipse

The paper presents expressions for the subtangents at the onset of diffuse, respectively local instability in sheet metal. The subtangents have been determined using definitions of the effective stress and the effective strain, which in case of uniaxial tension reduce to the true stress and true elongation strain. Using this approach, the material's stress-strain curve obtained in a uniaxial tension test, is directly applicable in the determination of the curves for diffuse and local instability.

Fracture failure prediction using a moving finite element mesh refinement scheme

A two-dimensional fracture mechanics finite element computer program using an automated mesh refinement scheme in regions of high stress concentration is presented. Constant stress-strain triangular elements are used to discretize the structural system so as to predict the initiation and propagation of fracture, yield patterns, load-displacement history and failure load under monotonically increasing loads. The material stress-strain curve is idealized by selecting yield points on the nonlinear portion of the curve and joining them by linear segments. For each yield point taken, a minimum element area is specified which is gradually decreased as one moves from a lower yield point stress (or strain) to a higher yield point stress (or strain). As loads are incremented, regions of high stress/strain concentration in an input coarse finite element mesh are detected by using either the von Mises or the St. Venant yield criterion. Then the elements in these regions are repeatedly refined until their areas reach the prescribed minimum area requirements. A five-noded triangular element is used to confine the mesh refinement locally. To redistribute the energy of the fractured element into the unfractured media the zero modulus unload-reload method is used. The method is demonstrated for a center-cracked rectangular panel under tensile load.

On the use of full stress-strain characteristics in structural analysis

This note discusses the implications for structural analysis in the use of full stress-strain curves for materials such as concrete. Attention is drawn to the underlying relationship between the load-deformation characteristics for concrete elements and the mechanics which controls their forms.

A fracture behaviour investigation of lower carbon seamless tube with longitudinal crack

The transverse true stress-strain curve of DIN 1629 BI.3 St45 seamless tube has been determined by cylinder expansion tests. The J value for internally pressurised open ended tubes with external axial crack has been determined by compliance tests. The results have been compared with the EPRI solutions for an externally axially cracked cylinder and used to improve a J- estimation procedure. The comparisons suggest that the EPRI solutions could be conditionally used to estimate J for material stress-strain curves of straight-line-and-parabola type and that the improved J estimation procedure could be used to make good estimates of J from the relations of internal pressures and changes in external volume of a unit length cylinder of a single specimen. Finally, the externally axially cracked cylinder (EACC) is treated as one kind of fracture specimen which has an advantage of service simulation. The J resistance curve has been got from the EACC specimen for St45 seamless tube.

The treatment of thermal and residual stresses in fracture assessments

The behaviour of a crack under combined mechanical and thermal/residual loads is described in terms of a reference stress or equivalent mechanical loading. The reference stress can be readily established from a knowledge of the stress intensity factor for the thermal/residual load, the magnitude of the mechanical load, and the material stress-strain curve. The result enables the J-integral to be evaluated and is also used to define a procedure for the inclusion of thermal/residual stresses in the CEGB defect assessment method (R6). In particular, a detailed procedure is given for treating thermal/residual stresses in recent revisions of R6 which cater for structures made of materials which strongly work-harden.

Energy density approach to calculation of inelastic strain-stress near notches and cracks

An energy-based method of calculating elastic-plastic strains and stresses near notches and cracks is presented. It was assumed that the strain energy density in the plastic zone ahead of a notch can be calculated on the basis of the elastic stress-strain solution. Good agreement between the calculated and measured notch strains was obtained for several notches, materials and loading conditions. It was shown that the assumption holds up to general plastic yielding. This method can also be applied in uniaxial and multiaxial stress states. A numerical procedure suitable for any material stress-strain curve is presented. Some possibilities concerning elastic-plastic stress-strain calculation near cracks are also discussed.

A finite element method for stress analysis or elastoplastic body with polygonal line strain-hardening

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.

The assessment of defects in structures of strain hardening material

J-estimation procedures based on finite-element solutions are expressed in terms of the material stress-strain curve by using reference stress techniques common in creep analysis. The result is an exact representation of the estimation procedures for materials which strain harden according to the simple power law used in the finite-element caclulations. For other materials, it is shown that an appropriate definition of the reference stress reduces the dependence of the results on the accuracy to which the strain hardening can be described by a simple power law. The resulting reference stress based estimation procedure is used to derive a failure assessment curve for use with the CEGB failure assessment route. Comparison is made with the modified failure assessment curve recently suggested by Milne and the implications of the results for defect assessments are discussed.

Elastic-plastic fracture mechanics analysis of an SENB specimen

This paper describes the elastic-plastic analysis of a Single Edge Notched Bend (SENB) specimen, a specimen commonly used for the determination of the fracture toughness of a material. First, a two-dimensional convergence study is described to investigate the influence of mesh size on the global response of the specimen and the fracture mechanics parameters J and COD. Then a three-dimensional analysis is compared with experimental results. The three-dimensional computational results show a good agreement with the experiments, except for the load region where the global deformations were dominated by the Lueders zone in the material stress-strain curve.

Collapse behaviour of aluminium plates

Theoretical predictions of the collapse behaviour of thin rectangular aluminium plates are presented and discussed. The plates are simply supported around all four edges, and are subjected to uniaxial in-plane compression. The method of analysis developed by the author is described elsewhere. The material behaviour of aluminium is characterised by the Ramberg-Osgood stress-strain formula. Two methods of using this formula are discussed—one based on the usual percentage proof stress, and the other on the stress at which the plastic strain is a stated proportion of the elastic strain. It is shown why the latter method is more suited to the normalisation of results for collapse analyses. The results presented here give an indication of the effects on plate strength of plate slenderness, initial out-of-flatness, and n, the “knee” factor of the material stress-strain curve.

Determination of the flow stress-strain curves for metals from axisymmetric upsetting

A new test method has been developed for determining flow stress-strain curves of materials used in bulk deformation processes such as extrusion, forging and croping. These curves are of vital importance in the industry. The test piece is made of a 14 mm diameter, 21 mm height cylinder which is deformed between two flat dies. The maximum height reduction is chosen to reproduce the maximum strain and strain rate required for the process. The stress-strain curve is plotted by using the values of forging load, height reduction and maximuu diameter-minimum diameter ratio of the deformed cylinder. This so-called shape ratio is found to correspond perfectly to the friction shear stress between the cylinder and the dies. Experiments have been performed on 1% carbide steel samples at room temperature, where the results have demonstrated the accuracy of the test for determining the stress-strain relationship under the friction conditions generally observed between the cylinder and the dies. The proposed test can be carried out on any simple press using a pair of flat dies. This very simple tooling may be accomodated in production equipment in order to obtain accurate results concerning stress-strain relationship at the relevant strain rate and temperature.

There is no hookean region in the stress-strain curve of keratin (Or other viscoelastic polymers)

Abstract Viscoelastic polymers exhibit stress relaxation, and it is therefore predicted that their stress-strain curves will be nonlinear at all strains. It is shown in this report that this behavior is observed only with straight and properly clamped specimens; when a specimen is crimped or badly clamped, the initial part of the curve exhibits “toe-in” (caused by straightening of the specimen), which obscures the viscoelastic curvature. In this case, a pseudo-linear region, strictly an inflection region, is observed at low strains, which arises from opposing viscoelastic and toe-in curvatures. There is thus no Hookean region in the stress-strain curve of (straight or crimped) viscoelastic polymers, and the concept of a Young's modulus is inapplicable; however, the inflection modulus, derived from the slope of the inflection region has limited applicability, particularly when the toe-in is not excessive. Instead of a Young's modulus, a unique stiffness parameter is proposed, termed the initial secant modulus, which is based on the secant near the origin of the “material stress-strain curve,” i. e., the curve in the absence of toe-in. It is proposed that in the case of keratin the term “Hookean region” be replaced by the term “pre-yield region.”

Properties of the Matrix in Keratins

It has been shown that the initial, so-called Hookean region (0-1.5% strain) in the stress strain curve of keratin is nonlinear, as predicted theoretically for a viscoelastic material such as keratin. Deviations from linearity are confirmed at strains as low as 0.03%. It is speculated that the concept of a Hookean (i.e. linear) region arose as a result of extension tests with wool fibers. In the decrimping phase of extension the stress-strain curve of wool is convex towards the strain axis (a feature referred to as "toe-in"), while the viscoelastic curvature of the material stress-strain curve is concave towards this axis. The combination of these two opposing curvatures results in a point of inflexion, and it is suggested that the apparent linearity of the inflexion region has been accepted uncritically as indicating the presence of a Hookean region. Instead of a Young's modulus, the concept of an inflexion modulus is proposed for stress-strain curves exhibiting toe-in. In compressional stress-strain experiments toe-in is unavoidable at present, but it is estimated, on the basis of extension tests, that the value of the compressional modulus near the origin of the material stress-strain curve may be double that of the observed inflexion modulus. It is proposed that the part of the curve up to ∼2% strain be termed the "pre-yield region" instead of the "Hookean region."

Elastic-plastic creep response of structures under composite time history of loading

High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. Starting with the principle of virtual work, exact equilibrium equations are derived for a stepwise Lagrangian formulation. The resulting equilibrium equations are then specialized to the incremental Piola-Kirchhoff stress computation and to small incremental strain formulation. Classical plasticity theory is used to develop a novel method based on the concept of ‘plastic stress’ for consideration of inelastic behavior. It is shown that the material's stress-strain curves can be followed to any desired degree of accuracy both for isotropic and kinematic hardening. It is further shown that for kinematic hardening it is necessary to base the incremental change on the state corresponding to the mean of the initial and the final states to satisfy the yield condition at the final state. The equation of state and strain hardening is used to describe the creep behavior. A novel numerical technique to describe a complex load history is developed by using time as a parameter, history breakpoint determination by scanning of various load vectors, and by linear interpolation between any two breakpoints in the load history. Efficient criteria for load incrementation in the form of a fraction of the total ‘plastic stress’ for any sequence of two load history break points are developed and made an internal function of the program. This saves the user significant hardship when faced with guessing the load increment for an unknown state of the solution at any of the load history breakpoints. The ‘plastic stress’ load vector concept is utilized with interation and extrapolation to converge to the equilibrium states with simultaneous satisfaction of the stress-strain relations for each of the iterated states. The essential features of the computer program DYPLAS-FSH, based on the theory and techniques described above, and a postprocessor program POR-FSH, based on RDT F9-5T for ratcheting and fatigue evaluation, are identified and discussed. In summary, the new results of this work are the efficient handling of an arbitrary load history, introduction of the ‘plastic stress’ concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the ‘plastic stress’ concept, and development of a computer code capable of solving practical three-dimensional problems.

Stress-strain relationship during transformation enhanced plasticity

The effects of a deformation induced reaction kinetics upon the stress-strain curve of materials which transform during deformation is theoretically discussed. It is shown that the observed work hardening rate, dσ*/de*p depends on both the occurrence of a transformation and on the instantaneous rate of the reaction.

Influence of structure on the abrasion resistance of a 1040 steel

The resistance to sliding abrasion was determined for a 1040 steel. Specimens were either hardened and tempered or cooled to produce various ferrite-pearlite structures. For the hardened and tempered condition the abrasion resistance follows a Hall-Petch relation with the cementite particle spacing. For the ferrite-pearlite structures the abrasion resistance is proportional to the volume fraction of pearlite present. It is shown that the bulk hardness, the microhardness of the abraded surface and the abrasion resistance all are interrelated via the material's stress-strain curve. The strain corresponding to abrasion was found to be 4.8 and the portion of the cutting work which is directly involved in the chip formation to be 18.5%.

The Bending of Some Common Beam Sections into the Plastic Range

SummaryThere is already in existence a fair volume of work on the subject of bending beyond the limit of proportionality, most of which requires the use of actual material stress-strain curves. This note aims to examine the problem in a more general way by using an accurate mathematical form for the stress-strain curve, strain and bending moments being expressed as functions of the ratios of various properties of the material.The value of maximum permissible fibre stress is considered in relation to current requirements for military aircraft stressing and a guide is presented for the maximum permissible bending moment in some of the more familiar beam cross sections bending about an axis of symmetry.