Numerical Analysis and Experimental Research of Autofrettaged

Shrink-fitted Three-layer Extrusion Cylinder

Gexia Yuan

, Juanping Wang

, Feizhou Li

and Baoyan Zhang

School of Mechanical Engineering, Baoji University of Arts and Sciences, No.44, Baoguang Road, Shaanxi Baoji, China

Keywords: Three-layer extrusion cylinder, Shrink-fit, Autofrettage, Residual stress, Strength, ANSYS

Abstract: Multilayer cylinder is a commonly used structure of ultra-high extrusion cylinder. In order to increase the

load carrying capacity and durability of a shrink-fit three-layer extrusion cylinder, the paper proposed the

multiple autofrettage process based on analysis of simulation. Firstly, A 3-D finite element contact model of

the extrusion cylinder has been constructed in the ANSYS environment; The element used here is 3D

SOLID 186, and using a bilinear isotropic hardening model approximating the real material behaviour.

Then, we have used the model to simulate processes of fitting, autofrettage and boring of extrusion cylinder

by multi-step load and birth and death element techniques, then comes to the residual stresses of different

times autofrettaged cylinder. The results show multiple-autofrettage can increase hoop compressive residual

stress. The extrusion cylinder was made three times autofrettage processes and boring machining, its actual

elastic operating pressure is consistent with finite element analysis results and it’s strength is improved

significantly.

1 INTRODUCTION

Hydrostatic extrusion technology is a new type of

material processing method, and it can extrude the

materials, which are difficult to use conventional

deformation process to machining, such as

hydrostatic extruding tungsten alloy materials, etc,

their strong toughness can be greatly improved[1-4].

Hydrostatic extrusion pressure of high strength

material as high as 1000 MPa to 1500 MPa, so the

design of extrusion cylinder strength is particularly

important [2, 3]. If the design is careless, the bore

area will cause plastic deformation even burst. For

example, in a research institute, the pressure of a

three-layer shrink-fit extrusion cylinder(TSEC) was

designed to be 1500MPa, according to the theory of

maximum tensile stress theory, however, when

extrusion pressure had not reached 1500MPa, the

bore area of the cylinder appeared plastic

deformation, which leading to squeeze rod difficult

to move and hard to be sealed, until it didn’t work.

Ultra-high pressure extrusion cylinder mostly is

adopted multi-layer cylinder structure, and strength

design used elastic failure criterion. AA Miraje, SA

Patil[5, 6] and Shildip D Urade [7] had researched

the residual stress distribution through the cylinder

thickness of multi-layer shrink-fit cylinder(MSC)

based on the theory of maximum tensile stress

theory; Yuan Gexia et al.[8] had researched

optimization design of MSC based on the theory of

the maximum shear stress theory using analytical

method and finite element method. Yuan Gexia and

Liu hongzhao[9,10] had researched residual stress of

shrink-fitted and autofrettaged double cylinder.

Cylinder is usually made of plastic material, and it is

in the three direction stress state, so designing

strength according to the maximum shear stress

theory is more close to actual value.

In this paper, according to the actual tensile

compressive stress-strain curve of material, using a

bilinear isotropic hardening model approximating

the real material behaviour, and applying 3D SOLID

186 element, We have constructed a 3-D finite

element contact model for the extrusion cylinder in

the ANSYS environment to simulate processes of

shrink-fitting, autofrettage and boring of the

extrusion cylinder. The simulation results show that

Multiple-autofrettage processes can effectively

generate favorable compressive residual stresses to

increase strength of shrink-fitted cylinder. Then,

three times autofrettage process and boring

machining to the extrusion cylinder were carried out,

and test its strength. The tested results are consistent

with the finite element simulation results.

2MODELING OF THE EXTRUSION

CYLINDER

2.1 Cylinder Material Model

The stress-strain curve of the material is shown in

Figure 1. It clearly demonstrates the Bauschinger-

effect. Analysis procedure for autofrettage process

involves overstrain which is typically based on

Tresca or Von. Mises failure criteria. Here, using a

bilinear isotropic hardening model approximating

the real material behaviour is shown in Figure 1; has

been used in which E1 is the slope of the linear line

in the tensile elastic region (modulus of elasticity),

H1 is the slope of the linear line in the tensile plastic

region, E2 is the slope of the linear line in the

compression elastic region (modulus of elasticity),

and H2 is the slope of the linear line in the

compression plastic region. This material’s constants

are as follows: E1=206GPa; H1=2GPa; E2=207GPa;

H2=57GPa; σy1 =1103 MPa, σy2

=1100 MPa, where, v, σy1, and σy2 are the

Poisson's ratio , tensile yield stress, compression

yield stress, respectively.

300

600

900

1.20.6

1.8

2.4

3.0

-0.6

-300

-1200

Strain / %

-600

-900

uniaxial tension-compression

Fitting model

Calculating model

Figure 1: Material strain-stress curve.

2.2 Finite Element Model

The finite element model of TSEC has been

constructed in ANSYS APDL 15.0. The geometric

model is 1/4 of circumference of the cylinder, and

the element used here is 3D SOLID 186, and

mapped mesh method be used for easy simulation of

boring bore.

The cylinder body is mainly subjected to radial

force. During shrinking and autofrettage, the contact

surfaces are all one-way contact behaviors between

the surfaces, and the material of the three-layer

cylinder is also the same, so the contact can be

regarded as the “surface to surface” contact model of

the “Flexible-Flexible”. The target surface is the

inner surface of the middle layer and the outer layer;

The element type used is Target170. The contact

surface is the outer surface and middle surface, the

element type is Contact174. The geometric

dimensions of every cylinders was the actual

dimensions, including the initial mutual penetration,

and penetration tolerance was 0.0001 mm, and the

contact algorithm was chosen to be the Augmented

Lagrangian Method.

2.3 Boundary Conditions

Analytical model was the 1/4 of the extrusion

cylinder, so it is necessary to apply symmetry B. C.

on the corresponding surface. For easy solution,

assuming that the extrusion cylinder was in the plane

strain state, then axial displacement constraints has

been applied the both ends of cylinder.

3 SIMULATION AND RESULT

ANALYSIS

In the ANSYS environment, a number of

simulations have been performed on the shrink-fit,

autofrettage, boring and loading processes of

cylinder to calculate the residual stress distribution

in the shrink-fitted and multiple autofrettaged

compound cylinder and the maximum elastic

pressure capacity. Here the autofrettage pressure was

1800 MPa (pressurized system up to maximum

pressure).

First, having simulated the shrink-fit process of

the three-layer cylinder, residual hoop stress(RHS) is

shown in Figure 2(a). It reveals that the inner layer is

subjected to compressive stress with a large

value,and stress at the inner bore area (working area)

is 1150.94MPa, and the inner part of middle cylinder

is subjected to tension, and the outer part is

subjected to compression, and the stress value is

small, and the outer layer is subjected tension. Mises

stress is shown in Figure 2(b), and the maximum

stress is 1028.67MPa, and it is lower than

compressive yield limit of material, on this

condition, the entire cylinder is in elastic state.

After the autofrettage process, the RHS of the

cylinder is shown in Figure 3(a), compared with the

stress after the shrink-fit, the residual compressive

stress of the inner cylinder is significantly increased,

and at the inner bore area is as high as 1638.07MPa.

The Mises stress is shown in Figure 3(b), and the

inner wall is up to 1409.59MPa, the inner part of the

inner cylinder has undergone reverse yield. after the

boring, the RHS of the cylinder wall is shown in

Figure 4, compared with the stress after once

autofrettage, the residual compressive stress is

reduced and it is reduced to 1594.32MPa. After

calculation [11], the elastic pressure of the cylinder

is 1553MPa.

（a）Hoop stress

（b）Mises stress

Figure 2: Residual stress of the shrink-fitted cylinder.

（a）Hoop stress

（b）Mises stress

Figure 3: Residual stress of once autofrettaged cylinder.

Figure 4: Residual hoop stress of once autofrettaged

and boring cylinder.

Figure 5: Residual hoop stress of double autofrettaged

cylinder .

In order to further enhance pressure capacity of

the cylinder, we investigated double and triple

autofrettage processes for the cylinder. The HRS of

double autofrettaged cylinder is shown in Figure 5,

compared with the stress of once autofrettaged

cylinder, the residual compressive stress of the bore

area increases significantly, with an increase of

340.74MPa. After the secondary autofrettage

simulation, the boring machining has been simulated

， the hoop compressive stress is 1870.75MPa ，

with an increase of 276MPa, as shown in Figure 6.

Figure 6: Residual stress of double autofrettaged

and boring cylinder.

The elastic pressure capacity(EPC) of the

different times autofrettaged cylinder is shown in

Table 1. EPC of the two times autofrettaged and

hole boring cylinder is 1710 MPa, EPC of three

times autofrettaged and hole boring cylinder is up

to1853 MPa. Since the strength is calculated by the

linear elasticity, the calculated value is slightly

lower than the actual value. It can be seen from

Table 1 that as the number of autofrettage increases,

the cylinder strength increases, but increment is

reduced.

Table 1: The RHS and EPC of different times

autofrettaged cylinder.

process

RHS

/MPa

EPC /MPa

Shrink-fit 1150 1300

Once autofrettage 1638 1578

Once autofrettage

and boring

1594 1553

Double autofrettage

and boring

1870 1710

Triple autofrettage

and boring

2120 1853

4 EXPERIMENTAL

VERIFICATION

The shrink fit process had been accomplished. The

cylinder was triple autofrettaged under pressure

1800MPa; Finally the inner hole was bored by 2mm.

when the operating pressure is 1800MPa, after the

pressure is released, the internal wall of the cylinder

can be fully recovered. It means that extrusion

cylinder elastic operating pressure can be up to

1800MPa, compared with the simulation value, and

the error is about 3%; Taking all differences of every

simulation value , the maximum error is about 5%,

which proves that the method and model in the paper

is correct.

5 CONCLUSIONS

Performing the autofrettage process to the shrink-fit

cylinder can increase hoop compressive residual

stress.

Multiple-autofrettage can further increase hoop

compressive residual stress, but as the number of

autofrettage increases, its increment is reduced.

Using the finite element model in the ANSYS

environment may better predict the residual stresses

of shrink-fit and autofrettage compound cylinder.

ACKNOWLEDGEMENTS

This project is supported by Shaanxi science and

technology research and development projects,

China (Grant No. 2013K08-14).

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