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Research Papers: Materials and Fabrication

Modeling and Measuring Residual Stress in Autofrettaged Hollow Cylinders Through the Initial Strain Distribution Method

[+] Author and Article Information
Matteo Loffredo

Mechanical Engineer,
Baker Huges, a GE company,
Via F. Matteucci 2,
Florence 50127, Italy
e-mail: matteo.loffredo@bhge.com

Andrea Bagattini

Senior Mechanical Engineer,
Baker Huges, a GE company,
Via F. Matteucci 2,
Florence 50127, Italy
e-mail: andrea.bagattini@bhge.com

Bernardo D. Monelli

DICI,
Università di Pisa Largo,
Lucio Lazzarino 2,
Pisa 56126, Italy
e-mail: bernardo.disma.monelli@unipi.it

Marco Beghini

Professor
DICI,
Università di Pisa Largo Lucio,
Lazzarino 2,
Pisa 56126, Italy
e-mail: marco.beghini@unipi.it

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 11, 2017; final manuscript received October 9, 2017; published online December 1, 2017. Assoc. Editor: Yun-Jae Kim.

J. Pressure Vessel Technol 140(1), 011402 (Dec 01, 2017) (9 pages) Paper No: PVT-17-1149; doi: 10.1115/1.4038227 History: Received August 11, 2017; Revised October 09, 2017

The paper presents a method for modeling and measuring the residual stress (RS) field in axisymmetric autofrettaged elements. The method is based on the assumption that an Initial Strain Distribution (ISD), originated by the plastic strain previously induced during the autofrettage process, is the source of RSs. The ISD is the quantity to be evaluated and, after being determined, it can be used, by means of a dedicated finite element (FE) model, to evaluate the RS field in the component or in any part extracted from it. The ISD is obtained by elaborating the relaxed strains produced by cutting the autofrettaged component in incremental steps. The elaboration is based on solving a set of Fredholm's integral equations in which the unknown function is the ISD and the kernel is an Influence Function (IF) correlating the measured relaxed strain to the ISD. After a general discussion of the RS induced by the autofrettage and the effect of the plastic properties of the material under process, the methods for obtaining the relaxed strains by a rational experimental setup and the procedures for obtaining the IFs are presented and discussed. The whole methodology is applied to evaluate the RS field in a hollow cylinder for which the autofrettage was modeled by a FE simulation. The consistency of the method is verified and useful indications for the experimental activities were obtained.

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Figures

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Fig. 1

Outline of the autofrettaged cylinder and of the slice of material extracted from its midsection for the slitting method

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Fig. 2

Loading–unloading σ − ε uniaxial curves of the constitutive models implemented in the FE analysis of the autofrettaged cylinder

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Fig. 3

Comparison of the RS hoop components σθθ(r) obtained in the FE model of the autofrettaged cylinder by assuming the two constitutive models

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Fig. 4

Plastic strain components εrr(p)(r), εθθ(p)(r), εzz(p)(r) obtained in the FE model of the autofrettaged cylinder by assuming the two constitutive models

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Fig. 5

General scheme for the deformation measurement during the slitting process

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Fig. 6

Cutting process in the circular slice after having placed the strain gauges

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Fig. 7

FE model built to evaluate the kth strain gauge response ekΔ(sh,r′i) for a triangular ISD

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Fig. 8

Portion of FE model mesh and arrangement of cut strain gauge reading

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Fig. 9

Three-dimensional plot (b) and Contour plot (c) of the IF W¯k(r,s) worked out for the strain gauge shown in (a) (dimensions in mm)

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Fig. 10

Ring dimensions and strain gauges arrangement for the simulated measurement process (dimensions in mm)

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Fig. 11

ISD (a) and residual hoop stress (b) worked out from the simulated measurement process

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