Showing papers on "Strain hardening exponent published in 1983"

Metal Forming: Mechanics and Metallurgy

Abstract: 1. Stress and strain 2. Plasticity 3. Strain hardening 4. Plastic instability 5. Temperature and strain-rate dependence 6. Work balance 7. Slab analysis and friction 8. Friction and lubrication 9. Upper-bound analysis 10. Slip-line field analysis 11. Deformation zone geometry 12. Formability 13. Bending 14. Plastic anisotropy 15. Cupping, redrawing and ironing 16. Forming limit diagrams 17. Stamping 18. Hydroforming 19. Other sheet forming operations 20. Formability tests 21. Sheet metal properties.

On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept

Abstract: Mise au point d'un modele mathematique de l'ecoulement plastique ou viscoplastique. Application a un alliage refractaire IN 100

Nonlinear Finite Element Analysis of Steel Frames

Abstract: A general formulation for the elastic and inelastic nonlinear analyses of multistory frames is presented The inelastic analysis includes the effects of residual stresses, strain hardening, gradual penetration of yield through the cross section and the spread of inelastic zones along the member lengths The technique is illustrated by solving a variety of problems for which alternative results are available

Application of the plane simple shear test for determination of the plastic behaviour of solid polymers at large strains

Abstract: A simple shear test apparatus was designed and used in experiments for determining the plastic behaviour of various amorphous and semicrystalline polymers at large shear strains. The geometry and dimensions of the specimens were determined after a critical evaluation of the test conditions, so as to avoid plastic buckling of the specimens, and to minimize undesirable stresses at the specimen ends. Using the present technique, it was possible to conduct tests at room temperature up to strains of 200% for polymethyl methacrylate (PMMA) and 1000% for polyethylene, without extensive crazing. Optimum precision and homogeneity of strains within the samples could be achieved because of firm guiding of the gripped specimen heads during the tests. A systematic study of the influence of shear strain rate and temperature on the plastic behaviour was made particularly for the polyethylene samples. The kinematics of large deformation simple shear is discussed and relations between the stress and the finite-strain tensors is presented, with particular attention being paid to the development of normal stresses. The problem of end effects is also investigated. Finally, it is shown that the strain hardening of polyethylene under simple shear is much smaller than under uniaxial tension. A possible interpretation of this behaviour is proposed in terms of the uniqueness versus multiplicity of slip systems.

Response of Various Metals to Large Torsional Strains Over a Large Range of Strain Rates—Part 1: Ductile Metals

Abstract: This paper presents torsional test results for six metals subjected to large shear strains and high strain rates. Included are 2024-T351 aluminum, 7039 aluminum, low alloy steel, S-7 tool steel, tungsten alloy and DU-.75Ti (Depleted Uranium). The specimens are strained to fracture at strain rates from quasi-static to over 100 s−1 . All of the materials exhibit strain hardening and strain rate hardening. At the higher strain rates some of the materials develop shear instabilities and localizations. Constitutive relationships are derived from the test data and finite element computations of the tests are performed.

Anisotropic elasto-plastic finite element analysis of thick and thin plates and shells

Abstract: An elasto-plastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered, which is based on a degenerate three-dimensional continuum element. The accommodation of variable material properties, not only along the surface of the structure but also through the thickness, is made possible by a discrete layered approach. Although isoparametric elements of the Serendipity family give satisfactory solutions for thick and moderately thin shells the results exhibit ‘locking’ for an increasing ratio of span to thickness. To develop a numerical model which is applicable to thick or thin plates and shells, the nine-node Lagrangian element and the Heterosis element are also introduced into the present model. Plastic yielding is based on the Huber-Mises yield surface extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed.

Effect of stress triaxiality on neck propagation during the tensile stretching of solid polymers

Abstract: Cylindrical samples of high density polyethylene were tested in tension at 21° C and a nominal strain rate of 8.5 × 10−4 sec−1. The occurrence of necking in the centre of the specimens was provoked by the introduction of area defects of various sizes. The stabilization of this constriction and its propagation towards the ends of the specimens was studied photographically. An analytical method for the description of neck development is outlined, based on the use of strain and strain rate gradients. The times corresponding to neck initiation and stabilization are shown to be associated with critical values of the local strain hardening coefficient of the material. The role of area, strength and temperature inhomogeneities in the kinetics of strain localization is discussed. A further inhomogeneity term based on the axial variation of the Bridgman triaxiality factor FT is introduced. It is shown that the transverse compressive stresses associated with the shoulders of the neck can play a significant role in neck propagation in otherwise homogeneous materials.

On work hardening and springback in plane strain draw forming

Abstract: Based on a simple forcebalance method, an approximate analysis of the plane strain, deep drawing of sheet metal is carried out under the assumptions of Coulomb friction and the membrane theory of shells. Using this analysis with an estimate of the ratio of ultimate to yield load in plane strain enables us to predict the maximum work hardening of the part. This hardening is shown to depend upon the draw bead settings, the frictional conditions on the die and punch, the wall angle of the draw die, and certain uniaxial material properties, chiefly, the ratio of ultimate to yield stress, but also including the rate sensitivity and the anisotropy parameter. The limitations of this theory (mainly, the neglect of bending effects) are discussed. Comparison is made between predicted work hardening and measured yield strengths in a bumper facebar of dual phase steel. Springback of a gently curved part is calculated for preloads and postloads. It is shown that postloads are more effective, and that they can, in principle, reduce springback to low levels in any typical automotive sheet metal. In practice, it is difficult to transmit forces of sufficient magnitude to the region under the punch for certain materials.

Elasto-plastic analysis of anisotropic plates and shells by the Semiloof element

Abstract: An elasto-plastic analysis of thin plates and shells by means of the finite element displacement method is considered for anisotropic materials, using the Semiloof curved shell element. The elasto-plastic analysis is based on the Huber-Mises yield criterion extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed. The practical problem of an aerofoil blade is also considered and some results presented.

Shear band bifurcations in ductile single crystals

Abstract: A shear band bifurcation analysis for a multiply slipping ductile single crystal is presented. The crystal is rate independent, and crystallographic slip is governed by Schmid's law. Attention is focused on double slip in a tensile deformation, so that comparison with previous studies is feasible. The results, which consider the rigid-plastic and elastic-plastic cases separately, show several qualitative features in agreement with experiment and with earlier analytical work based on a plane strain model. The shear band orientations exhibit the expected tendency, but the critical strain hardening values obtained here, while positive, are quite low. The present results also indicate the ready availability of non-uniform slip patterns, or ‘patchy slip’, a phenomenology consistent both with experimental observations and recent numerical studies.

Plastic flow phenomenology of 304L stainless steel

Abstract: The isothermal plastic flow behavior of annealed 304L austenitic stainless steel in uniaxial compression and torsional modes of deformation has been established over a wide range of temperatures and strain rates. In uniaxial compression, it was found that high rates of strain hardening, which persist to large strains (≽.7) at cold-working temperatures, are found only at small values of strain (⪯0.2) at hot-working temperatures because of the influence of dynamic softening processes. The effect of deformation heating on flow behavior, which occurs primarily at high strain rates, was most significant at cold-working temperatures. Deformation heating was observed to result in flow stress maxima and flow softening. A method of estimating high-strain rate, isothermal-flow curves in such instances was derived. Shear stress-shear strain curves derived from torsion tests exhibited dependences on temperature and strain rate similar to those observed in compression data. In contrast to the compression curves, however, the shear stress-shear strain curves showed lower rates of strain-hardening at room temperature, 400 °C, 800 °C, and (for high strain rates) 1000 °C. It was shown that the choice of definition for calculating effective stress-strain from the torsion data could not be modified to bring the two types of data into coincidence. Only a structure-sensitive explanation could be invoked to explain the difference.

Large strain plastic deformation of commercially pure nickel

Abstract: Commercially pure nickel was deformed to very large strains by cold rolling. Tensile tests on prestrained sheet were used to establish strain hardening behaviour and residual ductility. The hardening of nickel was found to be peculiar: initial rapid hardening was followed by an apparent plateau, which, in turn, was followed by another stage of rapid hardening at strains larger than 4. The residual elongation dropped precipitously with initial prestrain, levelled off, and then increased again during the final stage of hardening. Nickel rolled to a strain of 6·1 exhibited a remarkable tensile strength of 1400 MN m−2 with 4% total elongation. Extensive in-plane and limited edge-on transmission electron microscopy was used to examine the evolution of substructure. Dislocation cells formed at strains <0·10 and continued to refine in size with increasing strain. Definite evidence of dynamic recovery was found. The formation of elongated, well defined subgrains appears to coincide with a saturation of ha...

Plastic flow collapse vs. separation collapse in elastic-plastic strain-hardening structures

Abstract: In the present paper the possibility is discussed that the fracture collapse (separation) could precede the plastic flow collapse, in ductile materials. For this purpose two different constitutive laws of the material are considered: 1) elastic-linear hardening material; 2) power-law hardening material.

A third-invariant plasticity theory for frictional materials

Abstract: A nonassociated plasticity theory is given for frictional materials in terms of the first and third invariants of stress and inelastic strain. Features such as strain hardening, strain softening, dilatation, and compactionareexhibited. Limit states and the Ar0-condition are interpreted in a natural manner with the theory. Comparisons of predictions with experimental data for limit states and deformation paths are given for several materials.

A Rheological Model of Nonlinear Viscoplastic Solids

Abstract: A general rheological model of a nonlinear viscoplastic solid is developed, affording better quantitative prediction of behavior of viscoplastic materials. Rheological properties are quantified in terms of three types of curves obtained by tests, commonly used for description of mechanical material properties: constant rate, force deformation, creep, and relaxation curves. The mathematical model is based on a characteristic nonlinear differential equation describing the mechanical properties of a material. This equation defines the force F acting on a test specimen as composed of a cubic elasticity force K0x+rx3, viscous damping force Cẋ, and internal friction force Ff (sgn ẋ). The elastic parameter K0 quantifies linear elasticity while the strain hardening (or softening when negative) parameter r affords prediction of nonlinear behavior of the material. The viscous and Coulomb damping forces properly account for both rate‐dependent and rate‐independent energy dissipative properties of the material. Local...

Analysis of the puncture of a bisphenol-a polycarbonate disc

Abstract: The finite element technique is applied to analytically predict the response of a disc made of BPA-polycarbonate during a displacement-controlled puncture test with a hemispherical indenter. The analysis includes effects of contact load, large displacements and rotations, and large strains and material yielding. Two general topics are addressed with this analysis. First, it is shown that the load-displacement behavior of impacted, BPA-polycarbonate plates can be accurately predicted over a wide range of engineering interest (strains up to 30 percent) using a bilinear representation of the stress-strain curve and flow theory of plasticity. For this purpose, the von Mises criterion is applied to define yielding in a generalized biaxial stress state, and strain rate effects are incorporated through the use of a yield stress consistent with the initial strain rate during the test. Second, in order to broaden the understanding of results associated with this widely used test, a number of mechanical and material effects are discussed, including large displacements, friction at the clamped support and indenter head, and clamping pressure at the support. Lack of agreement between the present analysis and experimental results with regard to ultimate load at puncture suggests that strain hardening and strain rate hardening of the material during the high-strain portion of the test (30 percent-60 percent) must be more accurately modeled for improved predictive capability.

The effect of hydrogen on the multiaxial stress-strain behavior of titanium tubing

Abstract: The influence of internal hydrogen on the multiaxial stress-strain behavior of commercially pure titanium has been studied. Thin-walled tubing specimens containing either 20 or 1070 ppm hydrogen have been tested at constant stress ratios in combined tension and internal pressure. The addition of hydrogen lowers the yield strength for all loading paths but has no significant effect on the strain hardening behavior at strains e ≥ 0.02. Thus, the hydrogen embrittlement of titanium under plain strain or equibiaxial loading is not a consequence of changes of flow behavior. The yielding behavior of this anisotropic material is described well by Hill’s quadratic yield criterion. As measured mechanically and by pole figure analysis, the plastic anisotropy changes with deformation in a manner which depends on stress state. Hill’s criterion and the associated flow rule do not describe the multiaxial flow behavior well because of their inability to account for changes of texture which depend on multiaxial stress path. Hence, a strain dependent, texture-induced strengthening effect in equibiaxial tension is observed, this effect having the form of an enhanced strain hardening rate.

The effect of strain softening in the matrix material during void growth

Abstract: A Finite element analysis has been employed to investigate the growth of an initially spherical void embedded in a cylinder of elastic-plastic material. The boundary displacement of this cylindrical cell is regulated by the value of a parameter α which controls the radial shrinkage of the cell as it elongates. A large strain analysis was used and results for both strain hardening and strain softening (after an appropriate amount of hardening has taken place) have been obtained. The effects of different mean tensile stresses, equivalent strains and initial void volume fractions have also been included. The numerical work shows relationships between the mechanical and geometrical variables that may favour ductile fracture by void coalescence or by shear decohesion.

Strain modulation measurements of stiffening effects in carbon fibers

Abstract: An experimental technique for directly measuring strain‐induced stiffening effects in individual carbon fibers has been developed. The technique involves the superposition of a small amplitude oscillating strain (Δe∼10−4) on a slow linearly increasing strain (∼1.1×10−3 s−1). Synchronous detection of the resultant ac component of the measured stress yields a signal proportional to the slope of the stress versus strain curve provided the modulation amplitude is small compared to the ultimate strain at failure (∼0.005). The experimental arrangement has been designed for use in conjunction with an Instron tensile test apparatus. A novel design for a fiber gripping apparatus which permits direct measurement of the strain is also described. The technique has been applied to carbon fibers produced from two different precursor materials: polyacrylonitrile and mesophase pitch. Fibers from both precursors exhibited strain‐induced stiffening. The modulus of the pitch‐based fibers increased in proportion to the squar...