On expanding a hole from zero radius in a thin infinite plate

1954 ◽  
Vol 226 (1167) ◽  
pp. 543-561 ◽  
Keyword(s):  
Residual Stresses ◽  
Yield Stress ◽  
Axial Stress ◽  
Plastic Region ◽  
Infinite Plate ◽  
Middle Surface ◽  
Constant Thickness ◽  
Maximum Pressure ◽  
Boiler Steel ◽  
Zero Radius

As a criterion of the maximum pressure attainable on the interface between tube and plate when tubes are expanded into boiler drums, a theory is required which will allow for work-hardening and thickening of the plate, and it is also necessary to take into account the elastic as well as the plastic strains. Such a theory is set out in this paper, assuming a uniform hydrostatic pressure, the hole being expanded from zero radius in an infinite plate. The plate varies in thickness proportionately with the radius, and it is shown that the system remains geometrically similar irrespective of the degree of expanding, i.e. of the extent of the plastic region. The axial stress perpendicular to the middle surface of the plate is assumed to be zero for this problem, so that the tube and plate can be considered as a continuous medium. The problem is then one of plane stress in Which all variables become functions of a single parameter r / c , where r is any radius and c is the radius of the current plastic-elastic interface. The equilibrium equation, the compressibility relation and the strain relations (through the Reuss equations) are expressed in terms of this parameter and of the velocity v of any element, using c as the time scale. The resulting four equations are solved by taking finite increments of the variables, the appropriate value of the yield stress being inserted for each step using the yield stress curve for a typical boiler steel. The stress and displacement patterns are compared with those for a plate of constant thickness (Taylor 1948; Hill 1950). The residual stresses on release of the expanding pressure are determined assuming no secondary yielding occurs. In addition, the earlier theory due to Nadai is extended to allow an estimate to be made of the effect of secondary yielding owing to the residual stresses reaching the yield stress.

scholarly journals Description of Residual Stress and Strain Fields in FGM Hollow Disc Subject to External Pressure

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Stanislav Strashnov ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Elastic Modulus ◽  
Plastic Strain ◽  
Yield Stress ◽  
Plastic Region ◽  
External Pressure ◽  
Plastic Strain Rate ◽  
Constant Thickness ◽  
Stress And Strain ◽  
Strain Fields ◽  
Tensile Yield Stress

Elastic/plastic stress and strain fields are obtained in a functionally graded annular disc of constant thickness subject to external pressure, followed by unloading. The elastic modulus and tensile yield stress of the disc are assumed to vary along the radius whereas the Poisson’s ratio is kept constant. The flow theory of plasticity is employed. However, it is shown that the equations of the associated flow rule, which are originally written in terms of plastic strain rate, can be integrated with respect to the time giving the corresponding equations in terms of plastic strain. This feature of the solution significantly facilitates the solution. The general solution is given for arbitrary variations of the elastic modulus and tensile yield stress along the radial coordinate. However, it is assumed that plastic yielding is initiated at the inner radius of the disc and that no other plastic region appears in the course of deformation. The solution in the plastic region at loading reduces to two ordinary differential equations. These equations are solved one by one. Unloading is assumed to be purely elastic. This assumption should be verified a posteriori. An illustrative example demonstrates the effect of the variation of the elastic modulus and tensile yield stress along the radius on the distribution of stresses and strains at the end of loading and after unloading. In this case, it is assumed that the material properties vary according to power-law functions.

Residual Stresses in Transition Zones of Heat Exchanger Tubes

1992 ◽  
Vol 114 (2) ◽  
pp. 149-156 ◽  
Author(s):  
D. P. Updike ◽  
A. Kalnins ◽  
S. M. Caldwell
Keyword(s):  
Mathematical Model ◽  
Heat Exchanger ◽  
Theoretical Model ◽  
Residual Stresses ◽  
Stress Corrosion ◽  
Yield Stress ◽  
Axial Stress ◽  
Parameter Study ◽  
Transition Zones ◽  
Material Parameters

A theoretical model of an expanded tube-to-tubesheet joint is developed and examined with the objective to determine the residual stresses in the transition zone, which lies between the expanded and unexpanded regions of the tube. Owing to their effect on the development of stress corrosion cracks, the residual tensile stresses on the surfaces of the tube are of particular interest. A mathematical model that can predict these residual stresses is developed. Results of the model show that the maximum tensile residual stresses are axial and occur on the inside diameter of the expanded tube. It is shown in a parameter study that, for expansions that ensure a leak-tight joint, the maximum residual tensile axial stress on the inside surface of the tube reaches 80–95 percent of the yield stress of the tube, regardless of the geometrical and material parameters of the tube and tubesheet.

scholarly journals Parametric Optimization of Isotropic and Composite Axially Symmetric Shells Subjected to External Pressure and Twisting

2021 ◽  
Vol 5 (5) ◽  
pp. 128
Author(s):  
Marek Barski ◽  
Paweł J. Romanowicz ◽  
Małgorzata Chwał ◽  
Adam Stawiarski
Keyword(s):  
Isotropic Material ◽  
Orientation Angle ◽  
Optimization Procedure ◽  
Middle Surface ◽  
External Pressure ◽  
Optimal Structure ◽  
Constant Thickness ◽  
Geometrical Shape ◽  
Axially Symmetric ◽  
Fiber Orientation Angle

The present paper is devoted to the problem of the optimal design of thin-walled composite axially symmetric shells with respect to buckling resistance. The optimization problem is formulated with the following constraints: namely, all analyzed shells have identical capacity and volume of material. The optimization procedure consists of four steps. In the first step, the initial calculations are made for cylindrical shells with non-optimal orientation of layers and these results are used as the reference for optimization. Next, the optimal orientations of layers for cylindrical shapes are determined. In the third step, the optimal geometrical shape of a middle surface with a constant thickness is determined for isotropic material. Finally, for the assumed shape of the middle surface, the optimal fiber orientation angle θ of the composite shell is appointed. Such studies were carried for three cases: pure external pressure, pure twisting, and combined external pressure with twisting. In the case of shells made of isotropic material the obtained results are compared with the optimal structure of uniform stability, where the analytical Shirshov’s local stability condition is utilized. In the case of structures made of composite materials, the computations are carried out for two different materials, where the ratio of E1/E2 is equal to 17.573 and 3.415. The obtained benefit from optimization, measured as the ratio of critical load multiplier computed for reference shell and optimal structure, is significant. Finally, the optimal geometrical shapes and orientations of the layers for the assumed loadings is proposed.

X-ray residual stress analysis of cylindrically curved surfaces—estimation of circumferential distributions of residual stresses

2003 ◽  
Vol 38 (5) ◽  
pp. 459-468 ◽  
Author(s):  
T Oguri ◽  
K Murata ◽  
Y Sato
Keyword(s):  
Residual Stresses ◽  
Least Squares Method ◽  
Stress Measurement ◽  
Incident Angle ◽  
Axial Stress ◽  
Circumferential Stress ◽  
Distribution Functions ◽  
Scanning Method ◽  
X Ray ◽  
Reference Axis

A new measuring technique utilizing X-ray diffraction is proposed in order to estimate the circumferential distributions of residual stresses on convex/concave cylindrical surfaces. This technique requires neither tilting X-ray beams in the circumferential direction in which the X-ray incident angle tends to be limited nor adjusting the normal of the irradiation area to the reference axis of the ψ angle. The circumferential distributions of the circumferential stress and of the axial stress are estimated from the diffraction angles at ψ = 0° and the axial stresses obtained by the stress measurement on multiple inclined areas on the cylindrical surfaces under the configuration of the axial stress measurement using the iso-inclination scanning method. This estimate technique was applied to two round bars of steel, one with circumferential distributions of the residual stresses and the other with almost uniform stresses. The distribution functions of the residual stresses were expanded to a couple of Fourier series, and the coefficients of them were determined by the least-squares method. The estimated distributions of the residual stresses were in good agreement with the actual ones.

Determining Stresses in Composites

1991 ◽  
Vol 35 (A) ◽  
pp. 439-447
Author(s):  
J. B. Cohen
Keyword(s):  
Thin Films ◽  
Residual Stresses ◽  
Stress Tensor ◽  
Yield Stress ◽  
Load Sharing ◽  
Lattice Parameter

AbstractThe basic diffraction techniques for examining the stress tensor are reviewed, with particular emphasis on what can be done without knowing the unstressed lattice parameter(s). Examples are given of the residual stresses in thin films, how to measure the bonding and yield stress in composites and separating the micro and macrostresses to examine load sharing between phases.

Investigation of Residual Stress Development During Swage Autofrettage, Using Finite Element Analysis

2009 ◽  
Author(s):  
Michael C. Gibson ◽  
Amer Hameed ◽  
John G. Hetherington
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Axial Stress ◽  
Slope Angle ◽  
Subsequent Development ◽  
Element Model ◽  
Pressure Vessels ◽  
Element Analysis ◽  
Reverse Yielding

Swaging is one method of autofrettage, a means of pre-stressing high-pressure vessels to increase their fatigue lives and load bearing capacity. Swaging achieves the required deformation through physical interference between an oversized mandrel and the bore diameter of the tube, as it is pushed through the tube. A Finite Element model of the swaging process was developed, in ANSYS, and systematically refined, to investigate the mechanism of deformation and subsequent development of residual stresses. A parametric study was undertaken, of various properties such as mandrel slope angle, parallel section length and friction coefficient. It is observed that the axial stress plays a crucial role in the determination of the residual hoop stress and reverse yielding. The model, and results obtained from it, provides a means of understanding the swaging process and how it responds to different parameters. This understanding, coupled with future improvements to the model, potentially allows the swaging process to be refined, in terms of residual stresses development and mandrel driving force.

scholarly journals Effect of Residual Stresses on the Fatigue Behaviour of Torsion Bars

Metals ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 1056 ◽  
Author(s):  
Vinko Močilnik ◽  
Nenad Gubeljak ◽  
Jožef Predan
Keyword(s):  
Fatigue Crack ◽  
Residual Stresses ◽  
Stress Amplitude ◽  
Plastic Region ◽  
Fatigue Crack Initiation ◽  
Fatigue Behaviour ◽  
Technological Processes ◽  
Compressive Stresses ◽  
Stress Zone ◽  
Loading Ratio

This article deals with the effect of residual stresses on the fatigue behaviour of torsion bars exposed to cyclic torsional loading with different effective loading ratios, R. The residual compressive stresses on the surface were induced during technological processes by cold surface rolling and torsional overloading (presetting) into the plastic region due to the increase in the elastic linear range for torque. In the paper, we consider two different technological processes for introducing compressive residual stress on the surface of same material. We analysed the stress states affected by different residual and applied stress using the Drucker-Prager criterion in order to determine the actual stress state. Results show that the fatigue limit can be achieved if the maximum principal stresses (combined from residual and applied stresses) do not overcome the safe stress zone. As soon as the maximum principal stress reaches the edge of the safe zone, the number of cycles to failure rapidly reduces. Experimental results show that the effective loading ratio Reff, and consequently the stress amplitude, varies through the cross section of the bar. This initiates the fatigue crack under the surface, in the highest amplitude stress zone, independent of the effective loading ratio Reff. Consequently, increasing the compressive residual stresses on the surface by a second technological process has no significant effect on fatigue crack initiation in situ far from the surface. Increasing the plastic torsional prestress can shift the maximum stress amplitude far from the surface, but a significant volume of material should remain elastically loaded in order to ensure balance with compressive stresses from the surface of the solid bar section.

Effects of Pipe Dimensions and Outer Surface-Buttering Weld Conditions on Residual Stress Distributions

2008 ◽  
Author(s):  
Nobuyoshi Yanagida
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Outer Surface ◽  
Hoop Stress ◽  
Axial Stress ◽  
Butt Joint ◽  
Stress Distributions ◽  
The Finite Element Method ◽  
Butt Joints ◽  
Inner Surface

Effects of pipe dimensions and outer surface-buttering weld conditions on residual stress distributions were evaluated using the finite element method. Residual stresses were analyzed for 508–mm-diameter (500A) pipe 38.1 mm thick, 508–mm-diameter (500A) pipe 15.1 mm thick, and 267–mm-diameter (250A) pipe 15.1 mm thick. After the residual stresses at pipe butt joints were analyzed, residual stresses at these joints subjected to the outer surface-buttering welds were analyzed. Residual stresses were determined for various weld widths, thicknesses, and heat inputs. These analyses indicate that tensile axial stress occurred at inner surface of the pipe butt joint and that it decreased with increasing the outer surface buttering-weld width or heat input. They also indicate that compressive hoop stress occurred at inner surface of the joint and that outer surface-buttering weld increased it. The outer surface-buttering weld conditions that generate compressive residual stress at the inner surface of the pipe butt joints were determined.

Wheel Rim Axial Residual Stress and a Proposed Mechanism for Vertical Split Rim Formation

2011 ◽  
Author(s):  
Cameron Lonsdale ◽  
John Oliver
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Stress Measurement ◽  
Axial Stress ◽  
X Ray Diffraction ◽  
X Ray ◽  
Axial Residual Stress ◽  
Railroad Wheels ◽  
Hoop Stresses ◽  
Future Work

Railroad wheels are manufactured with beneficial residual compressive hoop stresses, which are imparted by rim quenching and tempering. Hoop and radial residual stresses for wheels have been studied in detail by various organizations over the years and are relatively well characterized. However axial residual stresses, in the orientation across the rim width from back rim face to front rim face, have not been extensively investigated. This paper describes a failure mode known as a vertical split rim (VSR) and describes efforts to measure the axial residual stresses in, 1) new wheels, 2) service worn wheels and 3) wheels that have failed from VSRs. Initial axial residual stress measurement efforts, using core drilling and x-ray diffraction from the tread surface, are briefly reviewed. Further more extensive work using x-ray diffraction to measure axial residual stress on radial wheel slices is described and data are presented, focusing on differences between the three wheel types. The concept of Axial Stress Amplification (ASA) is outlined, and the relationship of axial residual stress to VSRs is discussed. A proposed mechanism for VSR formation is described. Future work, with a goal of reducing or eliminating VSRs in service, is considered.

Hole-Drilling Method for Residual Stress Measurement - Consideration of Elastic-Plastic Material Properties

2013 ◽  
Vol 768-769 ◽  
pp. 174-181 ◽  
Author(s):  
David von Mirbach
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Yield Stress ◽  
Material Properties ◽  
Plastic Material ◽  
Hole Drilling ◽  
Hole Drilling Method ◽  
Drilling Method ◽  
Elastic Plastic Material ◽  
Ring Core

Two commonly used mechanical methods for the determination of residual stresses are the hole-drilling method and the ring-core method, which can be regarded as semi-destructive. The most restricting limitation for the general applicability of both methods, according to the current state of science and technology, is the fact that the scope for relatively low residual stress under 60% of the yield stress is limited.This is a result of the notch effect of the hole or ring core, which leads to a plastification around and on the bottom of the hole and ring shaped groove already at stresses well below the yield stress of the material. The elastic evaluation of the resulting plastic strains leads consequently to an overestimation of the delineated residual stresses. In this paper the influence of elastic-plastic material properties no the specific calibration function for the hole-drilling method using the differential method is studied, and the method of adaptive calibration functions is presented.

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