Departamento Ciencia y Tecnica de Materiales (Department of · Departamento Ciencia y Tecnica de Materiales (Department of ... for the determination of the stresses was the LUSAS

A failed mechanical part - its analysis

and design

E.S. Ayllon

Departamento Ciencia y Tecnica de Materiales (Department of

Materials Science and Technique) - CITEFA- Zufriategui 4380 -

(1603) V. Martelli - Argentina

Abstract

The purpose of this paper was to determine the stress conditions within amechanical part that failed catastrophically while being tested. The method usedfor the determination of the stresses was the LUSAS 12.1 finite elementcalculation approach (FEA). The part in question was a hydraulic brake cylinder,which, due to a failure in the test regulating valves, was subjected to an internalpressure at least three times its normal operating stress, with consequent ruptureof the cylinder wall. The explosion produced a crack which originated at thepressure inlet orifice in the cylinder wall. A design was proposed based onLUSAS analysis.

Introduction

The crack begins at the hole made for the pressure inlet running, in bothdirections, practically tangential to the said hole, Fig. 1.

The resulting expansion caused the detachment of the external threaded endcover. The cylinder was very long but the position of the piston when theaccident occurred was such that it was possible to examine a sector only about300 mm in length. The remaining part of the no longer pressurized cylinderworked as a restrictor to the expansion of the examined section in every radialdirection.

Transactions on the Built Environment vol 37 © 1999 WIT Press, www.witpress.com, ISSN 1743-3509

386 Computer Aided Optimum Design of Structures

Fig. 1: View of the exploded cylinder

Theory

The material used was hot rolled SAE 4140 steel without heat treatment. Theexternal diameter was 196 mm and the inner diameter 171 mm resulting,consequently, in a wall thickness of 12.5 mm.

According to information from Boyer (1990) a yield stress Sy of 600 MPa andan ultimated stress §„ of 750 MPa are to be expected.

The last recorded pressure when the explosion took place was of 25 MPa.

The rate of application of the pressure was unknown, the rise of the ratiocould have been between 0.8 and 1.0.

According to the well-known Lame formula, the stress in the cylinder wall wasSi = 184 MPa for the inner diameter and Si = 159 MPa for the external surfacegiving an average of 171.7 MPa.

The formula for thin wall cylinders shows a value of 171 MPa.


Computer Aided Optimum Design of Structures 38

As it can be seen, this value, increased by the coefficient of the stressconcentration of 3.7, suggested by Peterson for cylindrical holes, shows amaximum of 633 MPa for the wall of the cylinder, lower than the Su consideredfor the material.

In Fig. 2a we can see the pressure inlet plug and its attachment arrangement.

FEA LUSAS Aalysis

The modeling was made as shown in Fig. 3. The mesh used for the completemodel with a hole of 30 mm diameter with the threaded pressure inlet plugwelded inside it is presented.

Fig. 2: Pressure inlet plug



Fig.3: Mesh of the cylinder and plug

The results of the analysis show good concordance between the FEA approachand the mathematical theory of Lame and Peterson for an elastic stresscondition, in linear state for a 30 mm diameter hole. See the stress contours ofSi in Fig 4.

Fig. 4: Hole detail



We will now consider that for the adaptation of hose to measure internalpressure, a threaded plug 0.2 mm lower in diameter than the hole made in thecylinder wall was designed. The outer edge was welded to the external wall ofthe cylinder by means of the TIG method in order to fix it in place and to avoidhydraulic oil leaks. This arrangement modified the stress condition in the zoneof influence of the hole.

In Fig. 5 we presented the LUSAS results. The maximum value for stressesremained below the values required to crack the material of the cylinderbecause the max. values were concentrated in the plug.

A new hypothesis was formulated considering that the material of the tubewhich was directly affected by heat, HAZ, failed under stresses such as thosecalculated in the previous step, due to the poor penetration of the suppliedmaterial and the fissuring of the root of the weld collar. Detachment of thethreaded plug took place notably modifying the theoretical stress condition inthe cylinder wall, Fig 6.

In order to complete this paper, a non-linear analysis of the material based onthe plastic and hardening attributes were applied. See Table 1 and Fig. 7.

Slope98505386344717411144

Effective Plastic Strain0.00350.00830.01330.02811.0000

Table 1: Hardening Curve

A modified design of the weld was analyzed and a new internal threaded plugwelded by brazing process was proposed. Two options were analyzed byLUSAS, Fig 2 c, d and Fig. 8 and 9. The brass wire proposed was (Cu = 59%,Zn = 40%) with E = 100,000 MPa.

The results show that the redesign was unsuitable. Another modified techniquewas introduced, which consisted in welding the plug by electric resistancefusion and them welding by TIG, Fig. 2 e and Fig. 10. The FEA results show areduction of the risk under the same internal pressure.

Conclusions

The LUSAS 12.1 application explains the beginning of cracks in the hole areaof the cylinder wall where, in fact, said cracks appeared. The presence of awelded plug to prevent the shrinking in the Z direction changed the stress state,and the lack of metal penetration produced an increase of the stress in the areawhere the crack began. The last redesign was successfully introduced intoproduction.



Fig. 5: Von Mises (SE) and stress SI contour plost



Fig. 6: a]Von Mises (SE) contour plot, b] Stress SI contour plot



K«*A* N***?, #At N***

*»f "^ % 9f .1$4?4 \%- ^

< ;- \A .

Fig. 7: Von Mises (SE) and stress SI contour plots



Fig. 8: Von Mises (SE) and stress SI contour plots.



Fig. 9: a] Von Mises (SE) contour plot, b] Stress SI contour plot.



t

/ _ ^

Fig. 10: Von Mises (SE) and stress SI contour plots,

Acknowledgements

The author wants to thank Lie. Maria del C. LEIRO for her cooperation in thiswork and for the suggestions in the presentation of results, and to Tec. A.REYNOSO for the making of the figures.

References

- E. Boyer (1990). "Atlas of Stress - Strain Curves", pag. 203-206.- R.E. Peterson (1974). "Stress Concentration Factors", pag. 154.


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Departamento Ciencia y Tecnica de Materiales (Department of · Departamento Ciencia y Tecnica de Materiales (Department of ... for the determination of the stresses was the LUSAS