The Stress and Deformation in Mild Steel During Axisymmetric Necking

1973 ◽  
Vol 40 (1) ◽  
pp. 271-276 ◽  
Author(s):  
M. A. Kaplan
Keyword(s):  
Mild Steel ◽  
Work Hardening ◽  
Flow Region ◽  
Material Behavior ◽  
Experimental Result ◽  
Radius Of Curvature ◽  
Specific Work ◽  
Flow Equations ◽  
Closed Form Solutions ◽  
Stress And Deformation

Closed-form solutions for the stress and deformation fields near the minimum section of the neck are obtained for a mild steel rod subject to axial extension by tensile loads. The procedure involves the use of an experimental result together with the incompressibility and symmetry conditions to find the deformations independently of the stresses. The stresses are then determined with the Levy-Mises flow equations without the use of a specific work-hardening rule. The solution, because of a simplifying assumption, is not valid throughout the entire plastic flow region. Experimental evidence indicates, however, that the region of validity extends well beyond the fracture region. The results enable the tensile test to be used to provide a complete description of material behavior until fracture. To accomplish this, it is necessary to measure the axial load and the radius and radius of curvature at the minimum section. As an example, the work-hardening characteristics of mild steel are determined under the usual work or strain-hardening hypothesis. The application of the results to ductile metals, other than mild steel, is briefly discussed.

Material Behavior of 2D Steel Lattices with Different Unit-Cell Patterns

2021 ◽  
Vol 1046 ◽  
pp. 15-21
Author(s):  
Paiboon Limpitipanich ◽  
Pana Suttakul ◽  
Yuttana Mona ◽  
Thongchai Fongsamootr
Keyword(s):  
Elastic Modulus ◽  
Experimental Studies ◽  
Base Material ◽  
Unit Cell ◽  
Material Behavior ◽  
Closed Form Solutions ◽  
The Past ◽  
Weight Density ◽  
Unit Cells ◽  
Cell Patterns

Over the past years, two-dimensional lattices have attracted the attention of several researchers because they are lightweight compared with their full-solid counterparts, which can be used in various engineering applications. Nevertheless, since lattices are manufactured by reducing the base material, their stiffnesses then become lower. This study presents the weight efficiency of the lattices defined by relations between the elastic modulus and the weight density of the lattices. In this study, the mechanical behavior of 2D lattices is described by the in-plane elastic modulus. Experimental studies on the elastic modulus of the 2D lattices made of steel are performed. Three lattices having different unit cells, including square, body-centered, and triangular unit cells, are considered. The elastic modulus of each lattice is investigated by tensile testing. All specimens of the lattices are made of steel and manufactured by waterjet cutting. The experimental results of the elastic modulus of the lattices with the considered unit-cell patterns are validated with those obtained from finite element simulations. The results obtained in this study are also compared with the closed-form solutions founded in the literature. Moreover, the unit-cell pattern yielding the best elastic modulus for the lattice is discussed through weight efficiency.

A Law of Work-Hardening

1948 ◽  
Vol 15 (3) ◽  
pp. 265-273
Author(s):  
A. M. Freudenthal ◽  
M. Reiner
Keyword(s):  
Mild Steel ◽  
Work Hardening ◽  
Wire Drawing ◽  
Total Work ◽  
Exponential Functions ◽  
Recoverable Strain ◽  
Annealed State ◽  
Logarithmic Measure ◽  
Work Of Deformation ◽  
Crystalline Metal

Abstract Based on the “blocking” theory of the strength of a poly-crystalline metal, a law of work-hardening is derived and checked experimentally on mild steel deformed by wire-drawing up to a deformation of 4.6 in the logarithmic measure. The law correlates the recoverable strain work with the total work of deformation in a series of exponential functions, the number of which corresponds to the number of sizes of crystal grains present in the annealed state.

Microtexture Development and Flow Stress Saturation during Triaxial Forging of an Al-3Mg-Sc(Zr) Alloy

2007 ◽  
Vol 546-549 ◽  
pp. 793-800
Author(s):  
S. Ringeval ◽  
David Piot ◽  
Julian H. Driver
Keyword(s):  
Flow Stress ◽  
Work Hardening ◽  
Room Temperature ◽  
Specific Work ◽  
Textural Evolution ◽  
Spatially Resolved ◽  
Grain Fragmentation ◽  
New Type ◽  
Grain Coalescence ◽  
Zr Alloy

An Al-3%Mg-0.25%Sc-0.12%Zr alloy was deformed by triaxial forging at 20-400°C up to strains of about 3. A study of its textural evolution reveals the tendency towards three symmetrical variants of a <110><1 10 ><001> component. This experimental observation is supported by a 3D spatially resolved crystal plasticity analysis. Samples strained at room temperature undergo grain fragmentation in the form of fine substructures and relatively weak textures. Conversely, at 300°C and above, more homogeneous intergranular deformation and rotations give rise to stronger textures. This eventually encourages grain coalescence and thus the development of interpenetrating “orientation chains”, creating a new type of microstructure. The influence of this texture development on the specific work hardening behaviour is discussed.

Internal wave propagation in an inhomogeneous fluid of non-uniform depth

1969 ◽  
Vol 38 (2) ◽  
pp. 365-374 ◽  
Author(s):  
Joseph B. Keller ◽  
Van C. Mow
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Experimental Result ◽  
Bottom Surface ◽  
Radius Of Curvature ◽  
Constant Density ◽  
Trapped Waves ◽  
Inhomogeneous Fluid ◽  
Sloping Beach ◽  
Scale Length

An asymptotic solution is obtained to the problem of internal wave propagation in a horizontally stratified inhomogeneous fluid of non-uniform depth. It also applies to fluids which are not stratified, but in which the constant density surfaces have small slopes. The solution is valid when the wavelength is small compared to all horizontal scale lengths, such as the radius of curvature of a wavefront, the scale length of the bottom surface variations and the scale length of the horizontal density variations. The theory underlying the solution involves rays, a phase function satisfying the eiconal equation, and amplitude functions satisfying transport equations. All these equations are solved in terms of the rays and of the solution of the internal wave problem for a horizontally stratified fluid of constant depth. The theory is thus very similar to geometrical optics and its extensions. It can be used to treat problems of propagation, reflexion from vertical cliffs or from shorelines, refraction, determination of the frequencies and wave patterns of trapped waves, etc. For fluid of constant density, it reduces to the theory of Keller (1958). The theory is applied to waves in a fluid with an exponential density distribution on a uniformly sloping beach. The predicted wavelength is shown to agree well with the experimental result of Wunsch (1969). It is also applied to determine edge waves near a shoreline and trapped waves in a channel.

A work-hardening model of the lower yield strength of discontinuously yielding alloys: Ni3Al and mild steel

1989 ◽  
Vol 4 (3) ◽  
pp. 470-472 ◽  
Author(s):  
E. M. Schulson
Keyword(s):  
Grain Size ◽  
Yield Strength ◽  
Mild Steel ◽  
Work Hardening ◽  
Lower Yield ◽  
Hardening Model ◽  
Lower Yield Strength ◽  
Work Hardening Model ◽  
Lüders Bands

The lower yield strengths of Ni3Al and mild steel and their respective relationships to (grain size)−0.8 and (grain size)−0.5 are explained in terms of work hardening within Lüders bands.

Experimental Analysis of Self-Folding SMA-Based Sheet Design for Simulation Validation

2014 ◽  
Author(s):  
Aaron C. Powledge ◽  
Darren J. Hartl ◽  
Richard J. Malak
Keyword(s):  
Performance Metrics ◽  
Permanent Deformation ◽  
Material Behavior ◽  
Image Correlation ◽  
Design Parameters ◽  
Radius Of Curvature ◽  
Element Analysis ◽  
Performance Metric ◽  
3D Digital Image Correlation ◽  
Thermally Actuated

The goal of this research is to experimentally characterize the capabilities of a concept for a self-folding reconfigurable sheet for use in origami-inspired engineering design and to use this characterization to validate simulations of physics-based models of the sheet. The sheet consists of an active, self-morphing laminate that contains two shape memory alloy (SMA) mesh layers and a passive compliant medium between these layers. The SMA layers are thermally actuated, allowing bending to occur in both positive and negative directions to create soft hill and valley folds. These folds are completely reversible, allowing the structure to fold and unfold without permanent deformation. Unlike past work on self-folding structures, these sheets can have folds along any line, be subsequently unfolded, and then be folded again in a new way. To explore the effect of changing design parameters on the performance metrics of the sheet, it is desirable to use Finite Element Analysis (FEA) simulations instead of relying on time consuming experiments. Such models have been created incorporating user material subroutines (UMATs) in an FEA solver such as Abaqus to capture material behavior, but these must now be validated against experimental data to establish how well they match experimental performance. The primary performance metric of the sheet was chosen to be the radius of curvature measured perpendicularly to the line of heating. Both experiment and simulation focus on the radius of curvature achieved by the sheet for a given set of design parameters and actuation path. The goal of validation is to achieve a desirable level of agreement and repeatability in these results. To measure the deformation and curvature in the sheet as it actuates, a 3D Digital Image Correlation (3D DIC) system is employed to track the movement of points along the surface of the sample as it is heated to a temperature above the transformation temperature of the SMA and allowed to fully actuate. These tools are utilized for a number of samples so that validation of the sheet encompasses multiple values for each of the primary design parameters.

scholarly journals A simple theory of static and dynamic hardness

1948 ◽  
Vol 192 (1029) ◽  
pp. 247-274 ◽  
Keyword(s):  
Work Hardening ◽  
Close Agreement ◽  
Elastic Recovery ◽  
General Relation ◽  
Theoretical Work ◽  
Empirical Method ◽  
Simple Theory ◽  
Radius Of Curvature ◽  
Strain Characteristic ◽  
Dynamic Hardness

When a hard spherical indenter is pressed into the surface of a softer metal, plastic flow of the metal specimen occurs and an indentation is formed. When the indenter is removed it is found that the permanent indentation is spherical in shape, but that its radius of curvature is greater than that of the indenter. It is generally held that this ‘shallowing’ effect is due to the release of elastic stresses in the material around the indentation. It is clear that if the recovery is truly elastic it should be reversible and that a second application and removal of the indenter under the original load should not change the size or shape of the indentation. Experiments show that this is the case. This means that when the original load is reapplied, the deformation of the indenter and the recovered indentation is elastic and should conform with Hertz’s equations for the elastic deformation of spherical surfaces. Measurements show that there is, in fact, close agreement between the observed deformation and that calculated from Hertz’s equations. These results have been applied to the case of indentations formed in a metal surface by an impacting indenter. The energy involved in the elastic recovery of the impacting surfaces is found to account for the energy of rebound of the indenter. This analysis explains a number of empirical relations observed in dynamic hardness measurements, and, in particular, reproduces the calibration characteristics of the rebound scleroscope. The results also show that for very soft metals the dynamic hardness is very much higher than the static hardness, and it is suggested that in rapid deformation of soft metals, forces of a quasi-viscous nature are involved. In the third part of the paper a simple theory of hardness is given, based on the theoretical work of Hencky and Ishlinsky. It is shown experimentally that for a material incapable of appreciable work-hardening, the mean pressure P m required to produce plastic yielding is related to the elastic limit Y of the material by a relation P m = cY , where c is a constant having a value between 2·6 and 3. An empirical method is described which takes into account the work-hardening produced in metals by the indentation process itself. This results in a general relation between hardness measurements and the stress-strain characteristic of the metal, and there is close agreement between the theory and the observed results. In addition, the theory explains the empirical laws of Meyer.

scholarly journals Experimental and Numerical Investigation on the Bearing Behavior of Curved Continuous Twin I-Girder Composite Bridge with Precast Concrete Slab

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Chuandong Shen ◽  
Yifan Song ◽  
Lei Yan ◽  
Yuan Li ◽  
Xiaowei Ma ◽  
...  
Keyword(s):  
Yield Strength ◽  
Bearing Capacity ◽  
Ultimate Load ◽  
Ultimate Bearing Capacity ◽  
Experimental Result ◽  
Small Radius ◽  
Radius Of Curvature ◽  
Construction Scheme ◽  
Composite Bridge ◽  
Bearing Behavior

Curved twin I-girder composite bridge (TGCB) is becoming popular in Chinese highway bridge building. To study its ultimate bearing behavior, in this paper, one 1 : 5 scale intact model of a two-span curved continuous TGCB was tested to failure to evaluate its safety reserve and ductility. Afterwards, based on the experimental result, 3D FE models were developed and validated. At last, using the validated 3D FE models, the effect of construction scheme, radius of curvature, yield strength of steel, concrete compressive strength, crossbeams, and bottom lateral bracings on the ultimate bearing capacity were examined. The experimental results showed that the ultimate load (Pu) is approximate 13.6 times the service equivalent load. The cracking load and yielding load are approximately 0.12 and 0.47 Pu, respectively. The ductility coefficients are 4.06∼4.40. These above may indicate that the TGCB designed according to Chinese codes has good safety reserve and ductility. From parameter analysis results, it was concluded that the TGCB with full-support construction scheme has larger yield load and ultimate load compared with the one with erecting machine construction scheme. On the other hand, the ultimate bearing capacity reduces nonlinearly with the increase of curvature. Besides, the yield strength of steel, crossbeams, and bottom lateral bracings has a significant effect on the ultimate bearing capacity of curved TGCB. And the smaller the radius of curvature, the more obvious the effect of the latter two factors is. Unfortunately, it is unwise to continuous to improve the ultimate load by increasing the grade of steel for the TGCB when steel grade exceeds Q390. Moreover, in consideration of the big difference in bearing capacity between the inner girder and outer girder of the TGCB with small radius of curvature as well as the economy, it is suggested that the inner and outer steel girders of that TGCB should be designed differently.

Net Mass Flow Components in a Three-Dimensional Unsteady Rotor Inflow Model

2003 ◽  
Author(s):  
Ke Yu ◽  
David A. Peters
Keyword(s):  
Mass Flow ◽  
Three Dimensional ◽  
Legendre Functions ◽  
Skew Angle ◽  
Pressure Potential ◽  
Associated Legendre Functions ◽  
Galerkin Approach ◽  
Flow Equations ◽  
Closed Form Solutions ◽  
Flow Components

Potential flow equations are converted to ordinary differential equations by the Galerkin approach in which velocity and pressure potential functions are expanded in terms of closed-form solutions to Laplace’s Equation. The reduced number of generalized coordinates in a Galerkin approach gives advantages in real-time simulations, preliminary design, and dynamic eigenvalue analysis for aeroelasticity. Net mass injection from rotor sources is expected to occur in some situations, but cannot be treated by previous models. It is included in the present formulation. In this paper, frequency response due to pressure distributions corresponding to net mass flow in both axial and skew-angle flight are given. These results are compared with exact solutions obtained by the approach of a convolution integral. A brief analysis is also included with respect to numerical simulations of the Associated Legendre Functions, in which it demonstrates that net mass flow components are extremely sensitive to the recursive process of seeking Associated Legendre Functions.

Stress and Buckling of Internally Pressurized, Elastic-Plastic Torispherical Vessel Heads—Comparisons of Test and Theory

1977 ◽  
Vol 99 (1) ◽  
pp. 39-53 ◽  
Author(s):  
D. Bushnell ◽  
G. D. Galletly
Keyword(s):  
Mild Steel ◽  
Large Deflection ◽  
Plastic Material ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Test Results ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Elastic Plastic Material ◽  
Good Agreement

Several aluminum and mild steel torispherical heads were tested by Galletly and by Kirk and Gill and subsequently analyzed by Bushnell with use of the BOSOR5 computer program. The thinnest specimens buckled at pressures for which part of the toroidal knuckle was stressed well beyond the yield point. The analysis includes large deflection effects, nonlinear material behavior, and meridional variation of the thickness. The calculated strains in the thicker specimens agree reasonably well with the test results, but the calculated prebuckling strains in the thinnest specimens are generally greater than the values measured in the torodial knuckle after the onset of plastic flow. Reasonably good agreement between test and theory is obtained for the buckling pressures of aluminum specimens, but the calculated buckling pressures for mild steel specimens are much lower than the observed values, a discrepancy that is attributed to circumferentially varying thickness and possible inability of the analytical model of the elastic-plastic material to predict accurately the state of stress in the toroidal knuckle where loading is nonproportional once yielding has occurred.

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