ABSTRACT - WIT Press€¦ · Surface Treatment Effects EXPERIMENTAL TESTS 15 In fig.l are shown the...

Experimental investigations and numerical

analyses on deep rolling residual stresses

G. Donzella," M. Guagliano,* L. Vergani*

" Universitd degli Studi di Brescia, Dipartimento di

Ingegneria Meccanica, Via Branze, 38, 25123

Brescia, Italy

^Dipartimento di Meccanica, Poltecnico di Milano,

f .zzo I. do Fmcz', 32, 2(%<%? Mz/aTio, 7W%/

ABSTRACT

The deep rolling is a mechanical surface treatment widely used to improvethe fatigue strength of the notched components. In order to optimize therolling parameters the surface residual stresses have been calculated bymeans of a numerical model of a roll compressing a prismatic bar.Experimental measurements of the residual stresses have been carried outon the same numerically modelled bar, by using the hole drilling methodand a new method. The results were compared.

INTRODUCTION

Mechanical and thermal treatments are today widely used to improvethe fatigue mechanical characteristics of the materials. In particular, if weconsider mechanical surface treatments (shot peening and deep rolling),the compressive residual stress state induced by these technologicalprocedures is directly responsible for the improvement in the fatiguebehaviour.

In literature the state of knowledge about residual stresses is extensive(e.g. Niku Lari [1], Kloos et al. [2], Fujiwara et al.[3]). In spite of this, withparticular reference to deep rolling, it is difficult to find information aboutthe values and the patterns of the residual stress field induced by

Transactions on Engineering Sciences vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-3533

14 Surface Treatment Effects

mechanical surface treatments. In fact unknown residual stresses are, stilltoday, qualitatively considered. Due to this it is difficult to optimize theresults of the treatment and the definition of the deep rolling parametersis based on empirical arguments.

In this paper the deep rolling procedure was considered. Two problemsin particular were studied: the numerical calculation of the residualstresses induced by the rolling, and the experimental determination of theresidual stresses in rolled elements. In fact the aim of the whole researchis the construction of a numerical model, validated by the comparison withthe experimental results, in order to optimize the rolling parameters (theroll diameter, the rolling load and the number of load applications).

The calculation of the residual stresses is very complicated because itinvolves two types of non-linear problems: the contact between two bodiesand the elastic-plastic behaviour of the material. A finite element modelwas then constructed to simulate a roll compressing and moving over aprismatic bar. The numeric results were compared with the experimentalresults, obtained by means of the same numerically modelled prismaticbar.

The residual stresses were experimentally measured by utilising thehole-drilling method. This technique is extensively treated in literature(Rendler et al. [4], Schajer [5] and [6], Bathgate [7], Niku Lari et al. [8],Flaman et al. [9]) and it is widely employed; nevertheless its use oftencauses large errors in the measurement evaluation. In fact, if there is agradient in residual stresses through the thickness of the sample thespecimen must be drilled step by step and the accuracy of themeasurements will be influenced by the depth of the first step: bydecreasing the depth of the hole the values obtained become nearer to thesurface value, but the instrument errors are percentually larger.

This paper proposes a new experimental method to measure theresidual stresses. This technique is semidistructive and considers theapplication of a bending moment, with fixed loading axis, on the rolledmechanical elements (Terranova et al. [10]) until the material yields bothin the in traction and in the compressed zones. The determination of theresidual stresses is based on the dissymmetry of the total stress patternsdue to the compressive surface residual stresses induced by the rolling.The experimental results, obtained by the different methods, aresubsequently compared with the numerical results.


Surface Treatment Effects

EXPERIMENTAL TESTS

15

In fig.l are shown the dimensions of the plane specimens and the strain

gauge positions.The samples have been previously subjected to a deep rolling procedure,with a load P=100 kN and a number of load applications n = 30. Thediameter of the roll was 160mm and the rotating speed 220rpm.The material of the bars is 35CrMo4 UNI 7874; the mechanicalcharacteristics are shown in table I.

Tab. I Mechanical characteristics of 35CrMo4 UNI 7874.

CI [MPa]572 764

E[MPa]205000

v0.28

Elongation9.4

Since the experimental evaluation of the residual stresses induced by therolling procedure is very difficult, two different methods have beenfollowed: the first is the hole drilling method and the second is the newmethod, which considers a bending load added to the compressive residualstress state.

/ ' ' /;-— ^3-4

105

/v

Ik

Fig.l Specimen dimensions, strain gages and rosettes location.

Hole drilling methodThe hole drilling technique permits the evaluation of the residual stress

state in a mechanical element by making a small hole. Removal of thestressed material causes localized stress and strain relaxations around thehole location, that are measured by using specially designed strain gaugerosettes, whose signals permit to obtain the residual stress statecomponents by using particular formulas indicated in the ASTM E837-92standard[ll].



The procedure proposed in the previously mentioned standard testmethod is only valid if the residual stresses do not vary significantly withdepth and do not exceed one half of the yield stress. In the rolled barsthere is a steep gradient in the thickness of the specimens; therefore thedata obtained from the measurements should be processed with otherprocedures, such as the Integral Method (Schajer [5], [6]), or theIncremental Strain Method (Bathgate [7]), which require preparation ofan accurate finite element model. However, in order to obtain a firstapproximation of the values of the residual stress state in the sample, theASTM normalised procedure was adopted; the final depth of the holeswas used to calculate the value of the constants A and B, necessary for the

processing of the results.

The previously rolled plane specimens were instrumented with HBMRY61 three element strain gage rosettes, designed for this particular

application (see fig.l).In order to avoid change in the residual stress state due to machining, thehole was made with an Air-Abrasive system (CEGB System). This systemalso permits a better control of the dimensions and of the shape of the

hole.

Two specimens were drilled at the location shown in fig.l: thus giving usindications on the residual stress state at the centre, at the border andalong the longitudinal axis of the specimens. The diameter D of the holesD, the final depth H and the ratio c between D and the H are shown in

tab.II for every hole.

Tab.II Values of D, H and c = H/D for the different holes.

Rosette D [mm] H [mm] c = H/DRl 1.77 3.60 2.03R2 1.79 2.92 1.63R3 1.80 3.02 1.67R4 1.80 3.30 1.83

The values obtained from these tests are shown in tab.III. By looking atthe values of /?, which is the angle between the longitudinal specimen axisand the first principal direction, it is also clear that a^ and a^ are almostprincipal stresses. The values of 0,1 seem to be fairly uniform for the two

specimens tested.The values of a^ are large even near the border of the sample.


Surface Treatment Effects 17

Bending load method

The qualitative pattern of the residual stress field in the 1-direction,

induced by the rolling, is shown in fig.2. The surface residual stresses in thefirst direction are of the compressive type, the internal stresses on thecontrary are traction ones.

Tab.III Residual stresses evaluated by means of the hole drilling method.

Strain gaugerosettesRlR2R3R4

[MPa]

-191-232-206-178

-213-296-255-329

#°]

15.0-8.6-0.8-10.6

If a bending load, with a fixed loading axis, is added to the rolled bar, the

stress pattern will be the same as in fig.2 as long as the stress behaviour islinear elastic.

Residual stresses + Bending stresses = Total stresses

Fig.2 Qualitative pattern of the residual stresses induced by the deeprolling in the first direction.

A dissymmetry in the total stress patterns can be noted; in fact, thebending stresses are algebraically added to the residual stresses and theresulting stresses are greater in the zone compressed by the bending load.If we then apply a bending load to an element with a residual stress fieldthe compressed zone will yield before the one in the traction zone.The value of this difference is correlated to the value of the residualcompressive stresses. The residual stress state is three-dimensional, withthe components cr , o^ and ^3 which can be considered principal. Sincethe free surface is being considered the residual stress state is plane(^2 = 0), and during the bending load application only Aa^O, the vonMises equivalent stress, becomes:



(1)

In fig.3 the diagram of the von Mises yielding locus is shown, considering,for simplification, that the yielding limit of the material does not changeduring the rolling procedure. In fact, the hardening of the material isneglected (due to the lack of experimental data).

-572

Fig.3 Von Mises yielding locus and experimental evaluation of theresidual stresses induced by the rolling.

If A(7; and Ao^, respectively the loading values necessary to reach yieldingin traction and in the compressed zone, are obtained from theexperimental tests it is possible to determine both the initial points and thevalues 0 3 and a .

Electrical strain gages were attached to the faces of the plane specimens(see fig.l) and four point bending tests were executed (see fig.4). The load-strain experimental diagrams have an initial linear shape according to thelinear-elastic behaviour: when the strain patterns leave the linear-elasticbehaviour both in the traction and in compression zones the test iscompleted. It is possible to find values Acr<, and Ao\, (fig.3) and, by usingthe von Mises ellipse, it is also possible to evaluate the a^ and a^ valuesassuming that the residual stresses are both compressive. The deviationfrom the linear shape of the load-strain diagrams has been determined onthe basis of the ANOVA on the residual of the experimental points fromthe line fitted on the initial elastic behaviour.Dissymmetry is shown by the measurements of a pair of strain gauges



positioned symmetrically on the opposite faces of the sample. Fig.5 showsthe behaviour of the strains in the middle of the specimens.

I P

Q

Fig.4 Scheme of the bending tests executed.

Fig.5 Load-strain trend in the bended sample: (a) compressed zone, (b) intraction zone.

Strain gauges were even positioned to verify the alignment in the thirddirection. It is readily noted the dissymetry of the traction and compressedzones; Ao\ and A^ values were determined for middle of the specimens,for the edge of the specimens and along the longitudinal axis of thesample. The residual stress values are therefore evaluated and arereported in tab.IV.



NUMERICAL ANALYSES

The numerical calculations were carried out by means of the Abaqusfinite element code in elastic-plastic field, assuming a linear-perfectlyplastic behaviour of the rolled material.

Tab.IV Residual stresses evaluated by means of the bendingmethod.

Strain gage pairsEl-2E3-4E5-6

-320-330-260

r,3 [MPa]-270-430-270

To begin with a plane strain model of the test sample was developed.Just half thickness of the sample was considered which, for symmetry, is7.5mm. The displacements in the 2 direction (the rolling load direction)were thus constrained along the symmetry line.

Four nodes plane strain linear elements distributed in a regular meshwere used to model the sample. Three different meshes were considered,with increasing number of elements, to study the convergence of thesolution. The first mesh was composed of 6 (thickness direction)x 32(longitudinal direction) elements, the second of 6x64 elements, the third of9x64 elements (fig.6).

Fig.6 The plane strain finite element model of the roll and of the specimen(9x64 mesh).



The bottom half side of the roll was also modelled imposing the diameterline to remain a straight, orizontal line. To improve the contact solution afine mesh was created near the roll surface. The material behaviour of the

roll was considerd to be linear elastic with a Young modulus equal to210000 MPa. The contact surface of the sample was defined by means ofslide line elements ([12], Hibbitt [13]), which allow for a finite slidecontact between two deformable bodies.

A verification of the model was carried out in the linear elastic field,with the roll located in the middle of the sample under the action of theimposed zones. The contact pressure calculated in this way was comparedwith the Hertz solution: the difference was about 5%.

The simulation of the rolling process was subdivided into three steps. Inthe first step the rolling load is applied to the roll, which is initially locatedin correspondence to one end of the sample. Thus it compresses thesample around the contact zone plastically. In the second step the sampletranslates under the roll (with the rolling load applied) up to its secondend. No friction is assumed during this step.In the third step the rolling load is removed from the roll and a residualstress state due to the plastic deformation is left in the sample. Thelongitudinal (a ) and the trasversal (0.3) residual stresses distribution onthe top surface of the sample (the contact surface) is shown in fig.7a forthe 9x64 mesh. The border effects in correspondance of the sample endscan be noted together with an almost costant distribution in the centralzone. In the same figure the a^ distribution through the thickness (withthe axis origin placed on the contact surface) in the central zone of thespecimen (fig.Tb) is shown. The results obtained from the other twomeshes are qualitatively the same. In tab V the values of a^ and a^stresses on the top surface in the central zone are shown for comparison.

Tab.V Residual stresses on the top surface in the central zone of thespecimen (plane strain model).

Mesh *ri[MPa] ( [MPa](medium) (medium)

6x32 slide line -150 -1406x64 slide line -245 -2809x64 slide line -250 -300



The convergence of the solution can be noted: a slight difference is shownbetween the results of the second and the third mesh.Another model was tested, by modelling the roll as a rigid surface [12]with circular shape and using the 6x64 element mesh to model the sample.Two node interface elements were employed to model the contact surfaceof the sample. A similar stress distribution was found in this case.

100.0 -0.00

0.0

-100.0 —

-200.0 ~

-300.0 -

-400.0 —

i i i i i i i i50.00l I i I I I I I

100.00I I I I

-300.0 -3 MPa

MPa(a) (b)

Fig.7 Numerical residual stress distribution on the top surface of thespecimen (plane strain, 9x64 mesh, slide lines):(a)on the contactsurface, (b) through the thickness of the sample.

The following a^ and o& values on the top surface in the central zone were

obtained (tab.VI).

Tab.VI Residual stresses on the top surface in the central zoneof the specimen (plane strain model, roll as rigid surface).

Mesh

6x64

?ri [MPa](medium)

-260

a,3 [MPa](medium)

-320

This last model gives results similar to the convergence solution of theslide line models, with the great advantage of a much lower number ofelements, and consequently shorter calculation time. Thus it was used to

study the three dimensional case.The influence of the rolling passes was also analysed on the same model,giving the results reported in tab. VII.It can be noted that the residual stresses do not change further after the

second pass.



Tab.VII Residual stresses on the top surface in the central zone of thespecimen (plane strain model, 6x64 mesh, roll as rigid surface).

Roll passes

123

a,JMPa](medium)

-260-270-270

(medium)-320-335-335

The three dimensional model is composed of 6 (thickness direction) x 64(longitudinal direction) x 12 (trasversal direction) eight nodes brickelements for the sample and a cylindrical rigid surface for the roll (fig.8).

Fig.8 Three dimensional finite element model of the sample.

For reasons of symmetry just one quarter of the sample was considered,constraining the correspondent displacements on the symmetry planes.The calculation was carried out following the three steps previouslydefined and gave the results showed in tab.VIII along the symmetry line ofthe top surface. The deformed mesh is shown is fig.9.

Tab.VIII Residual stresses on the top surface in the central zone of thespecimen (three dimensional model).

Mesh

6x64x12(3D rigid surface)

<M [MPa](medium)

-230

<r,3 [MPa](medium)

-310

The <r,.i and a^ distribution on the top surface along the middlelongitudinal line of the sample (lying on the 1-2 symmetry plane) can beseen in fig.lOa. In the same figure the a^ distribution through the thickness



on the 1-2 middle plane in the central zone of the specimen (fig.lOb) andthe G;I and a^ distribution on the top surface along the trasversal direction(third direction) (with the axes origin on the symmetry plane) are shown(fig.lOc). A comparison between these results and those of the plane case,confirms the valitidy of the plane strain model.

Fig.9 Deformed shape of the three dimensional finite element of the

sample. mo.o -=

0.00I I I I I I I I I I I I I I I I I I 0.0

-100.0 —

-20D.O —

-300.0 —' MPa

(b)

bending load method

hole drilling method-400.0 —'

Fig. 10 Numerical three dimensional residual stress distribution on the freesurface of the specimen: (a) on the contact surface along the firstdirection, (b) through the thickness in the middle, (c) along thetrasversal direction (third direction) of the sample.



DISCUSSION OF THE RESULTS

In fig. 10 the residual stress values experimentally evaluated by the holedrilling technique are compared with the ones obtained by means of thebending load method. The agreement is rather good and could be furtherimproved by taking into account the stress gradient through the thicknessof the specimens during the hole drilling data processing. Actually thevalues shown are the medium residual stress on the length of the hole.Due to the stress gradient, confirmed by the numerical analyses, throughthe thickness the surface residual stresses are of course larger and nearerto the values obtained by means of the bending method.In fig. 10 the numerical and the experimental values are also compared. Inthe same figure the residual stresses in the first direction along thelongitudinal axis are shown: the experimental and the numerical values areyet compared.

The measurements of the residual stresses in the lateral part of thespecimens were conducted at a distance from the border equal to 6mm(for the case of the hole drilling technique) and at a distance equal to 2.1and 2.4 mm (for the bending tests).

The experimental values, compared with the numerical results, confirmalso the suitability of the finite element model which permits us to analysethe global behaviour of the rolled specimens. These results show that theresidual stress state does not change meaningfully after two loadapplications. The diagram of the residual stress a^ along the thirddirection in the middle of the specimen shows a decreasing trend from themiddle to the lateral part of the specimen even if there is a border effectwith a large increase of the longitudinal residual stresses near the end ofthe section of the sample.

CONCLUSIONS

Two important problems were considered:

-the measurements of the residual stress state;-the numerical calculation of the residual stress state induced by therolling.

The measurement of the residual stresses is very difficult. The holedrilling method was considered and the results obtained were satisfing.Nevertheless it is possible to use this method if we have a plane specimen,



like the prismatic bar, on the contrary if we must measure the residualstresses in a mechanical element with curved geometry it is not possible toelaborate the strain relaxations in order to obtain the residual stresspattern. Therefore we propose a new method, considering thesuperposition of a bending load on the residual stress state.

The comparison between the results of the two methods is encouraging,even if it is surely necessary to increase the experimental data and toconsider the hardening of the material to have a substantial validation ofthe method. The advantage of the method proposed is that its applicationon mechanical complex elements does not present particular difficulties.

The numerical procedure developed permits the calculation of theresidual stresses, showing a very good agreement with experimentalresults. Therefore it can be used to analyse much complex cases. In thisway it is possible to evaluate the effects of the variations of the deeprolling parameters, such as the roll diameter, load and number of load

applications.

ACKNOWLEDGEMENTS

This work was supported by a MURST grant.

REFERENCES

1. Niku-Lari, A. (Ed). Advances in Surface Treatments, Vol. 4, PergamonBooks Ltd., 1987.

2. Kloos, K.H., Fuchsbauer, B., Adelmann, J., "Fatigue Properties ofspecimens Similar to Components Deep Rolled under OptimizedConditions" International Journal of Fatigue, Vol.9, No.l, pp.35-42,1987.

3. Fujiwara, H., Abe, T., Tanaka, K. (Ed). Residual Stresses III, Proc.Illrd Int. Conf. on Residual Stresses, Tokushima, Elsevier SciencePublishers, London, 1992.

4. Rendler, N.J., Vigness, I., "Hole Drilling Strain Gage Method ofMeasuring Residual Stresses" Experimental Mechanics, Vol. 6, No. 12,pp.577-586, 1966.

5. Schajer, G.S.,"Measurement of Non-Uniform Residual Stresses Using



the Hole-Drilling Method. Part I-Stress Calculation Procedures"Journal of Engineering Materials and Technology, Vol.110, No.4,pp.338-343, 1988.

6. Schajer, G.S.,"Measurement of Non-Uniform Residual Stresses Usingthe Hole-Drilling Method. Part II-Pratical Applications of the IntegralMethod" Journal of Engineering Materials and Technology, Vol.110,No.4, pp.344-349, 1988.

7. Bathgate, R.G., "Measurements of Non-Uniform Bi-Axial ResidualStresses by the Hole Drilling Method" Strain, Vol.IV, No.2, pp.20-29,1968.

8. Niku Lari, A., Lu, J., Flavenot, J.F., "Measurement of Residual StressDistribution by the Incremental Hole Drilling Method" ExperimentalMechanics, Vol. 25, No.6, pp. 175-185, 1985.

9. Flaman, M.T., Manning, B.H., "Determination of Residual StressVariation with depth by the Hole Drilling Method" ExperimentalMechanics, Vol.25, No.9, pp.205-207,1985.

10. Terranova, A., Vergani, L., "Strength of Components in Low CycleFatigue with Different Surface Treatments", pp. 1679-1684,FATIGUE'90, Proceedings of the IVth International Conference onFatigue and FatigueThresholds,Honolulu, Hawaii, 1990, MCEP Ltd,Birmingham, 1990.

11. "Determining Residual Stresses by the Hole Drilling Strain GageMethod", ASTM Standard E837-92.

12. ABAQUS Theory Manual, Ver.4.9, Hibbitt, Karlsson and Sorensen,Inc., Providence, Rhode Island, 1990.

13. Hibbitt, H.D., "Contact and Friction analysis with Abaqus" ,Proceedings of the III National Congress of Abaqus User Group, Milan,Italy, September 21-22, 1992.


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